,,carpentry ,,by ,,ira ,,samuel ,,griffith ,chairman of the ,manual ,arts ,department ,university of ,missouri ,illustration ,,the ,,manual ,,arts ,,press ,,peoria1 ,,illinois ,copyright #aiaf by ,ira ,samuel ,griffith ,fourth ,edition1 #aiai ,,acknowledgments ,to my father1 whose patient instruction and forbearing oversight during the period of carpentry apprenticeship has made possible the practical aspect of this present volume1 grateful acknowledgment is made4 ,acknowledgment is also made of assistance derived from the various trade magazines and from the few books on carpentry4 ,credit is due ,mr4 franklin ,g4 ,elwood1 ,peoria1 for most of the excellent drawings which accompany and clarify the text4 ,a number of the drawings were penciled by ,gordon ,kellar1 ,boston4 ,the photographs are the work of ,james ,f4 ,barham1 ,columbia1 ,mo-4 ,i4 ,s4 ,g4 ,,preface ,,it is the author's hope that the following text may be of service to apprentices to the trade1 to vocational and trade school students1 and to manual training students4 ,the author's experience as a carpenter leads him to feel that not a few journeyman carpenters may find their horizon widened and their usefulness as framers of the unusual roof increased by a study of ,chapter ,,iv where an effort has been made to indicate how the principles involved in framing the square and octagonal roof may be generalized so as to make possible their application to roofs of any number of sides4 ,beyond this1 the book makes claims to being nothing more than an elementary treatise of the essentials of carpentry4 ,no apology is offered for making use of trigonometric solutions of plane right triangles as a basis for developing generalized roof framing principles in ,chapter ,,iv4 ,there is absolutely nothing in the use of natural trigonometric functions to prevent their introduction early in the mathematical experience of a boy1 except academic tradition4 ,the author has made use of this mathematical tool with upper grammar grade boys with less effort upon their part in mastering the principles than was expended in mastering square root4 ,the ease with which roof framing problems lend themselves to solution by the use of natural trigonometric functions and the readiness with which problems may be generalized thereby has emboldened the author to make use of it in a text as elementary as this4 ,no previous knowledge of trigonometry is presupposed1 the ,appendix provides all the information required for the solution of any problem given herein4 ,should a reader1 because of lack of time or for any other cause1 not care to consider more than roof framing of the square cornered building1 he will find a complete treatise in ,chapter ,,iii without reference to solutions other than by common arithmetic4 ,appendix ,,iv offers a still more abbreviated approach to both square and octagonal roof framing4 ,the greatest good in studying the chapter on ,estimating will come only when each student is provided with a set of plans and specifications completely drawn1 as by a practicing architect4 ,plans and specifications1 such as will serve the purpose1 can be purchased at small cost from architectural companies1 should local architects be unwilling to provide sets for the schools4 ,also1 there must be provided for each student1 catalogs of lumber and millwork specifications and prices4 ,these can be obtained from mail order lumber and millwork companies4 ,as a rule1 local lumber and millwork companies are glad to provide such data1 but it must be in a form complete1 and readily accessible to be of the greatest value4 ,ira ,s4 ,griffith4 ,columbia1 ,missouri1 ,september1 #aiaf4 ,,contents ,chapter ,i4 ,foundations #ac #a4 ,laying out2 #b4 ,grade line2 #c4 ,excavation2 #d4 ,foundations2 footings2 #e4 ,foundation materials2 #f4 ,forms for concrete walls2 #g4 ,waterproofing2 #h4 ,basement frames4 ,chapter ,ii4 ,main ,frame #bg #i4 ,methods of framing superstructure2 #aj4 ,sills and girders2 #aa4 ,bridging2 #ab4 ,trimmers and headers2 #ac4 ,walls and partitions2 joists and rough floors2 #ad4 ,openings in framework4 ,chapter ,iii4 ,roof ,frame3 ,square ,cornered ,building #de #ae4 ,roof framing2 #af4 ,framing the common rafter2 laying out the plumb cut2 #ag4 ,finding the length of a common rafter2 #ah4 ,laying off a common rafter seat cut and end cut4 #ai4 ,ridge piece2 #bj4 ,hip and valley rafter2 #ba4 ,framing hip and valley rafters2 #bb4 ,side or cheek cut of hip or valley rafter2 #bc4 ,determining length of hip or valley rafter2 #bd4 ,laying off and end cut of hip rafter2 #be4 ,reduction of hip or valley length seat cut because of ridge piece2 #bf4 ,backing a hip rafter2 #bg4 ,valley rafters2 #bh4 ,framing jack rafters2 plumb cut2 side cut2 #bi4 ,lengths of jacks4 ,chapter ,iv4 ,roof ,frame3 ,any ,polygon #fi #cj4 ,tangents2 miter cuts of plate2 #ca4 ,octagonal roofs2 #cb4 ,common rafter for plate of any number of sides2 #cc4 ,hip and valley rafters for octagon and other polygons2 #cd4 ,plumb cut of octagonal and other polygonal hips and valleys2 #ce4 ,side or cheek cuts of hip or valley rafters1 any polygon2 #cf4 ,rafter lengths of octagonal and other polygonal hips and valleys2 #cg4 ,reductions in lengths for king-post2 #ch4 ,seat cut and end cut of octagonal and other polygonal hips and valleys2 #ci4 ,backing octagonal and other hips2 #dj4 ,framing octagonal and other polygonal jacks2 #da4 ,side cut of octagonal and other polygonal jacks2 #db4 ,lengths of octagonal and other polygonal jacks2 #dc4 ,framing by means of a protractor2 #dd4 ,translating framing problems from protractor to framing square and vice versa2 #de4 ,framing an octagon bay2 #df4 ,framing a roof of one pitch to another of different pitch2 #dg4 ,framing roof of uneven pitch2 #dh4 ,decks2 chimney openings4 ,chapter ,v4 ,exterior ,covering and ,finish #ie #di4 ,sheathing2 #ej4 ,scaffolding2 #ea4 ,cornice2 #eb4 ,raked mouldings2 #ec4 ,shingling2 #ed4 ,shingling hips and valleys2 #ee4 ,finishing exterior walls2 #ef4 ,setting window and door frames2 #eg4 ,siding4 ,chapter ,vi4 ,interior ,finish #aae #eh4 ,lathing2 grounds2 #ei4 ,interior walls2 #fj4 ,stair building2 porch steps2 #fa4 ,risers and treads2 #fb4 ,porches2 #fc4 ,interior finish2 #fd4 ,setting door jambs2 #fe4 ,fitting window sash2 #ff4 ,placing door1 window1 and other trim2 #fg4 ,hanging doors2 #fh4 ,fitting a door2 #fi4 ,hinging a door2 #gj4 ,fitting locks2 #ga4 ,laying and scraping floors2 #gb4 ,door and window frames2 #gc4 ,woodwork in masonry structures4 ,chapter ,vii4 ,estimating #adb #gd4 ,methods of estimating2 #ge4 ,table for estimating by cubic-foot unit2 #gf4 ,grading rules2 #gg4 ,estimating lumber quantities2 #gh4 ,estimating millwork quantities2 #gi4 ,example of form for bill of materials2 #hj4 ,estimating labor costs2 #ha4 ,estimating quantities of nails2 #hb4 ,example of form for carpentry costs2 #hc4 ,total building costs by percentages4 ,appendix #aeh ,i4 ,natural trigonometric functions2 formul deduced4 ,solution of right triangles1 7brief7 ,,ii4 ,table of natural functions 7for degrees only74 ,interpolation4 ,,iii4 ,useful tables4 ,fractional equivalents for decimal values4 ,wood and machine screw sizes4 ,length and number of nails4 ,wire brads4 ,board measure table4 ,strength of materials4 ,stresses for structural timbers4 ,contents of brick walls4 ,,iv4 ,short cuts to roof framing4 ,directions for ,griffith's ,framing ,tables4 ,v4 ,estimating4 ,excavations4 ,masonry4 ,slate4 ,plaster4 ,painting4 ,bibliography of ,references ,index ,illustration3 ,the house used as a model for many of the illustrations in this book4 ,,carpentry ,,chapter ,i ,foundations ,illustration3 ,fig4 #a4 ,transit4 #a4 ,laying out ,foundations4--,in most communities it is customary for the carpenter to be present and to assist the mason in the laying out of the foundations4 ,where buildings are large and important1 this work is done by an engineer with a steel tape and a surveyor's instrument1 ,fig4 #a4 ,this instrument is known as a builder's transit1 and consists of a tripod upon which rests a small telescope with crossed hair wires within1 by means of which the observer may fix the line of sight very accurately4 ,a circular dial contains a magnetic needle which enables the fixed dial to be set with reference to the true north and south line of the observer4 ,after the fixed dial has been adjusted1 the telescope may be swung to the right or the left until the circular graduations indicate that it points in the direction wanted1 after which stakes may be set4 ,a level upon the telescope enables the observer to sight grades or levels2 a helper carrying the leveling rod1 ,fig4 #b4 ,illustration3 ,fig4 #b ,leveling ,rod ,fig4 #c shows a more common instrument4 ,this is an architect's ,y-level and differs from the other in that it is less complete4 ,it has no attachment for measuring vertical angles4 ,this is not serious1 however1 since the builder seldom needs such an attachment1 the level being the most essential part4 ,y-levels are made both with and without compass attachments4 ,illustration3 ,fig4 #c ,y-,level ,upon ordinary residence work a surveyor is employed to locate lot lines4 ,once these lines are located the builder is able to locate the building lines by measurement4 ,suppose it is desired to locate a building by means of the side lot line3 7#a7 ,measure from the side lot line1 along the front and along the back lot lines1 a distance equal to that which it is desired the house shall hold relative to the lot side line4 ,drive stakes here4 7#b7 ,while sighting from one of these stakes to the other1 have an assistant locate two other stakes in the line of sight1 a distance apart sufficient to guarantee the placing of the cross-lines for the back and front of the house without restaking these1 ,a-,b1 ,fig4 #d4 ,the process of laying out lines for a house is almost identical with that used in laying out a rectangle on a drawing board4 7#c7 ,having located a line of indefinite length for one side of the house1 a second line of indefinite length1 preferably for the front of the building1 may next be located4 ,to do this1 first locate a front corner stake upon the first line just located4 ,this is done by measurement from the street line4 ,having located and driven in this stake1 ,a1 ,fig4 #d1 drive a nail in the top of the stake to more accurately locate this corner4 ,illustration3 ,fig4 #d4 ,batter ,boards ,if an instrument is available it will be located over this stake and the front line ,a-,c1 ,fig4 #d1 located by laying it off at #ij degrees from the side line already located4 ,if no instrument is available1 the front line may be laid off at right angles to ,a-,b by holding a framing square at their intersection4 ,this angle should be verified by the #f-h-aj method4 ,this consists in measuring from the intersection at ,a along one line a distance of #f feet and sticking a pin in the line at that point2 a pencil mark may be used when the cord is white4 ,in a similar manner1 measure off #h feet along the other line and then measure the hypotenuse of the triangle so formed4 ,it should measure #aj feet4 ,if it does not1 the front building line must be shifted until it does4 7#d7 ,with these two lines located1 the remaining two lines may be located by measurement from them1 the nail of stake ,a giving the starting point4 ,before this is attempted1 however1 the batter boards should be placed4 ,batter boards are variously constructed4 ,those shown are common types4 ,they should be placed free of the foundation proposed by at least #c or #d feet4 7#e7 ,test the squareness of the whole lay-out by measuring the diagonals ,a-,d and ,b-,c4 ,if the building lay-out is square the diagonals should be equal4 ,if they are not equal1 shift the cords at ,c and ,d1 retaining their parallelism1 until the diagonals become equal4 7#f7 ,once the lay-out is correct1 saw kerfs should be made in the batter boards where the cords are placed4 ,these kerfs will permit the cords being removed and replaced without further measuring4 #b4 ,grade ,line4--,a properly drawn set of plans will show both the present lay of the ground upon which the building is to be erected and the new grade line which is to be established after the building is completed4 ,the most convenient method of determining old grade lines and of establishing new ones is by means of the transit1 ,fig4 #a1 or the ,y-level1 ,figs4 #c and #e1 with the rod1 ,fig4 #b4 ,both instruments operate upon the same principle in grade work4 ,the telescope is set level and sights taken thru it to the target upon the rod4 ,the reading of the target's position upon the rod compared with the height of the telescope above the base1 usually the street walk1 determines the difference in grade of that particular placing of the target4 ,illustration3 ,fig4 #e4 ,taking ,sights with ,y-,level ,to locate levels for the masonry1 7#a7 set the instrument at some convenient place and level the dial4 7#b7 ,having determined the height of the instrument above some predetermined base1 such as the street walk1 swing the telescope about and1 making allowance for the difference in level as shown by the drawings1 place successively stakes at each corner of the building with the required level marked thereon4 ,as a rule1 the mason has his own ,y-level and uses it freely as the wall is constructed1 especially where levels are to be maintained as the layers of material are placed4 ,illustration3 ,fig4 #f4 ,leveling with ,straight-edge ,in a similar manner the earth grade about the building may be located1 stakes being driven into the ground at frequent intervals and the amount of fill or reduction indicated thereon4 ,grade levels are established usually only after the builders are thru1 except that the mason will have the grade indicated for him where the wall above the grade is to be differently finished from that below4 ,where no surveyor's level is at hand1 the mason or carpenter will secure the levels by means of a straight-edge of some #ad feet in length4 ,a common level is placed upon this plank as shown in ,fig4 #f4 ,by successive levels with stakes driven to indicate the successive levelings1 a grade may be carried quite a distance without very great variations4 ,illustration3 ,fig4 #g4 ,foundation ,detail #c4 ,excavations4--,excavations should be made enough larger than the proposed foundation that the mason may have room to wield his trowel in pointing the outer joints1 and for waterproofing4 ,an extra foot of excavation upon each side will usually be required4 ,all foundations must be carried well below the frost line4 ,excavations should be made accordingly4 #d4 ,foundations2 ,footings4--,because of the tendency of a building to settle unevenly1 due to variations in the strength of the supporting ground or the unequal weight placed upon this ground1 foundations must be constructed of some non-yielding material such as brick or stone1 and of such thickness and so bonded that the weight of the building may be evenly distributed4 ,the thickness of wall will depend upon the weight to be supported and upon the character of the soil4 ,unless rock or gravel is encountered1 every foundation should have a footing1 ,fig4 #g4 ,the amount of footing used is usually twice the thickness of the foundation wall4 ,in brick walls this footing draws into the wall by stepped courses of brick1 each layer being narrower than the one just preceding4 ,for ordinary residence work with ordinary soil conditions a #aj- or #ab-;inch wall resting upon a footing #b feet wide and #h or #aj inches deep will suffice4 ,a safe footing for supporting posts of #ff #f yellow pine1 for most soils1 will be #aj inches deep by #ah inches square4 ,partition walls carrying no unusual load need not be over #h inches in thickness4 ,illustration3 ,fig4 #h4 ,american ,bond ,illustration3 ,fig4 #i4 ,english ,bond ,in many communities the use of concrete is supplanting that of stone or brick1 especially below the grade line4 ,such a wall should be composed of #e parts of crushed stone or gravel1 #c parts sand1 and #a part cement4 ,the footing may be formed by tamping the mixture in a form made by spading out of the earth a depth and width sufficient for the wall to be supported4 #e4 ,foundation ,materials2 ,construction4--,of the materials commonly used in the construction of foundations monolithic concrete is becoming the most common for that part of the wall which lies below the ground or grade level4 ,brick and stone are sometimes used4 ,where brick or stone is made use of1 some device is required to tie the material together1 due to the fact that the mortar used in filling the voids or spaces between the members has little strength as compared with that of the stone or brick itself4 ,this bonding is secured by placing the brick or stone so that they shall overlap one another1 both along the faces of the wall and across the wall4 ,bricks laid with their lengths in the same direction as that of the wall are known as stretchers2 those laid with their lengths across the wall are known as headers1 ,fig4 #h4 ,the manner of placing these headers among the stretchers determines the type of bond4 ,the ,american1 ,english and ,flemish are the more common types4 ,of these the ,american1 ,fig4 #h1 is the most used upon ordinary work4 ,it consists of a course of headers placed every sixth course4 ,the ,english bond1 ,fig4 #i1 is much stronger1 having every other course a header course4 ,it is used mainly upon very important work where unusual strength is required4 ,flemish bond is illustrated in ,fig4 #aj4 ,illustration3 ,fig4 #aj4 ,flemish ,bond ,of the various types of stone work1 rubble work and ashlar predominate1 ,fig4 #aa4 ,rubble work is most frequently used for that part of the wall below the grade line1 and ashlar for the remainder of the wall4 ,in either case1 thru stones are placed every #d or #e feet in the length of the wall and every #ah inches in the height1 to provide bonds4 ,illustration3 ,fig4 #aa4 ,types of ,stone ,work ,in rubble work the stones are rough and unhewn4 ,they must be laid upon a good bed of stiff mortar with their stratifications in a horizontal position4 ,otherwise1 the face of the wall might peel from the effects of frost and moisture1 making an unsightly as well as a weaker wall4 ,the term ashlar refers to a wall builded of stones having finished faces4 ,when either rubble work or ashlar is laid up in courses it is known as coursed rubble or coursed ashlar4 ,when the horizontal joints are not continuous the wall is known as random rubble or broken ashlar4 ,not infrequently a wall will be constructed with an ashlar facing attached to a brick backing by means of metal bonds4 ,in such a wall1 the faced ashlar1 unless more than #h inches in thickness and well bonded into the wall1 should not be considered in estimating the strength of the wall4 ,illustration3 ,fig4 #ab4 ,form for ,concrete ,in the construction of both brick and stone walls the work should be carried up as nearly as possible at the same levels4 ,in both brick and stone walls the corners are run up with stepped courses1 the corners being plumbed as the wall is carried upward4 ,a line is then stretched between the corners and1 layer by layer1 the rest of the wall filled in4 ,no corner should1 ordinarily1 be carried more than #c feet above the rest of the wall4 ,in the case of uncoursed stone work the wall is leveled every #ae to #ah inches in its height4 #f4 ,forms for ,concrete ,walls4--,the economical building of forms for concrete walls is a matter of importance in building construction4 ,fig4 #ab shows a type of form suitable for foundation work4 ,such forms should be made of semi-seasoned stock4 ,thoroughly seasoned stock will warp badly when the wet concrete is placed4 ,spruce1 ,norway pine1 etc41 are better woods to use than hard or ,georgia pine4 ,for ordinary foundation work #a-;inch boards may be used1 the studs being placed not over #b feet apart4 ,these studs may be assisted materially in holding the forms in position1 by wires placed as in ,fig4 #ab1 and by props placed against the dirt wall of the excavation4 ,in placing the concrete a #d-;inch layer is laid and then spaded or worked well into place1 a wet mix being used4 ,the smoothness of the resulting faces is increased by an additional spading of the mixture away from the form4 ,a good spading tool is made by straightening out an ordinary garden hoe4 ,this allows the cement and mortar to flow next to the form and hold this place while the filling proceeds4 ,where forms are placed to give finished walls1 that is1 walls to which no plaster is to be applied1 they should be aligned with no greater variation than from the lines specified4 ,forms should be allowed to remain until the concrete will resist indentation with the thumb1 upon ordinary walls4 ,there is no limit to the ingenuity one may make use of in form building4 ,the illustration given is merely suggestive4 #g4 ,waterproofing4--,the extent to which a wall should be waterproofed will depend upon the location of the building4 ,foundations near running water must naturally be better protected than those in well drained locations4 ,fig4 #g illustrates a treatment which will prove quite safe for almost all localities4 ,the exterior face of the wall is covered with several layers of asphaltum or tar4 ,by coating the top of the footing and the top of the concrete floor just before the finish floor of cement is placed1 little water will enter4 ,a drain tile carried about the house as shown in ,fig4 #g1 especially if gravel is placed against the wall above it1 will meet every emergency4 ,there are other ways of waterproofing basement walls1 but this is typical of the external wall treatments4 ,in monolithic construction waterproofing may be secured by appropriate additions to the mixture of waterproofing materials such as slacked lime1 just before the mixture is placed1 no external applications being required4 ,illustration3 ,fig4 #ac4 ,cellar ,frame with ,sash #h4 ,basement ,frames4--,fig4 #ac illustrates one successful form of basement window frame construction1 with sash4 ,in this type the sash is hinged to the top of the frame1 and a catch or button at the bottom of the frame secures the sash when closed4 ,the construction is such as to best shut out wind and water when the sash is closed4 ,illustration3 ,fig4 #ad4 ,basement ,door ,frame ,fig4 #ad illustrates a basement door frame4 ,frames such as this1 and the window frame of ,fig4 #ac1 are made of heavy stock and are known as plank frames4 ,basement frames are held in place by means of wooden blocks nailed to the sides of the frame1 as well as by the projecting lugs of the frame itself4 ,the frame is set and plumbed by the carpenter as soon as the mason has prepared the sill4 ,fig4 #ad shows a frame plumbed and stayed1 ready for the mason to lay the adjacent wall4 ,fig4 #ae indicates the position of plumb and level in the setting of a frame4 ,the edges of a door frame are sighted for wind4 ,where it is necessary to attach frames or other woodwork to brick walls1 it is customary to have the mason insert wooden bricks as the wall is constructed4 ,wooden bricks are of the same size as other bricks1 and should be constructed with the edge which is to be laid back in the wall thicker than the front edge1 so that a dovetailed effect is secured4 ,illustration3 ,fig4 #ae4 ,plumbing and ,leveling ,cellar ,frame ,,chapter ,,ii ,main ,frame ,illustration3 ,fig4 #af4 ,full ,frame ,house #i4 ,methods of ,framing the ,superstructure4--,in the early days when lumber was plentiful1 houses and barns were framed in what is known as full frame4 ,such frames consisted of heavy and solid timbers mortised and tenoned and pinned together1 ,figs4 #af and #ag4 ,with the growing scarcity of lumber the half frame of ,fig4 #ah became common4 ,this latter type1 it will be seen1 makes less use of heavy timbers and wooden pins1 and more use of planks and nails4 ,to-day the vast majority of buildings1 where wood is the material used1 are constructed by what is known as balloon framing in houses and plank framing in barns1 ,figs4 #ai and #bj4 ,in view of this1 attention will be directed to balloon framing only4 ,one who is able to frame a house should have no trouble with plank barn framing1 where drawings show the details4 ,illustration3 ,fig4 #ag4 ,heavy ,timber ,barn ,it must be understood1 too1 that there are quite a variety of ways of framing a balloon and a plank frame4 ,it will be possible in this chapter to treat of but one type4 ,a mastery of this one type should enable the student to work out other types1 with suitable detailed drawings provided him4 #aj4 ,sills and ,girders4--,in ,fig4 #ba will be found illustrated three types of box sill construction4 ,whatever the sill used1 care must be taken to so plan that mice may not have free access to the various parts of the building4 ,if the sill does not inhibit1 then blocks should be spiked between the studs4 ,such blocks serve as fire breaks4 ,illustration3 ,fig4 #ah4 ,half-,frame ,house ,illustration3 ,fig4 #ai4 ,balloon ,frame ,house ,illustration3 ,fig4 #bj4 ,plank ,frame ,barn4 ,illustration3 ,fig4 #ba4 ,three ,types of ,box ,sills ,the bed plate of the box sill should be selected from stock with straight edges4 ,in the framing of joists1 plan so that the crowning edges shall be up when in position1 and in placing the joists see that the most crowning are in the middle of a room4 ,joists are fastened to their sills as in ,fig4 #ba4 ,fig4 #bb-;a illustrates a built up girder1 and the manner of framing the joists to it4 ,three #b #aj's with a #b #d attached to each side1 the whole thoroughly spiked together1 form the girder4 ,the advantage of this type of girder lies mainly in the fact that it leaves the headroom of a basement clear1 which is not the case in the type shown in ,fig4 #bb-;b4 ,this second type is somewhat easier to frame1 and is therefore greatly used where the owner does not object4 ,it is better where furnace stacks must be placed in a partition above it4 ,illustration3 ,fig4 #bb-;a4 ,fig4 #bb-;b4 ,girder ,types ,first floor joists1 like second floor joists and studs1 should be spaced #af inches from center to center1 beginning at one side or end of a room4 ,not to make such provision would cause a waste in lathing1 since the lath are all #d feet in length1 a multiple of #af inches4 ,any remainder after such a spacing should be allowed to come at the side or end of the room4 #aa4 ,bridging4--,to add to the carrying power of floor joists1 bridging is cut in between them as shown in ,fig4 #bc4 ,for ordinary dwellings #a #c stock will serve4 ,on large work1 stock two inches thick should be made use of4 ,fig4 #bc4 ,cutting ,bridging ,bridging should be spaced not more than #h feet apart4 ,a miter-box1 set at the appropriate angle1 may be used in cutting bridging1 all the pieces being cut at one time with the exception of those for the odd spacings at the side or end of a room4 ,a more common practice is to take a piece of stock1 and1 after cutting a bevel on one end1 place it as in ,fig4 #bc with the beveled end above the lower edge of the joist against which it rests1 a distance slightly in excess of the thickness of the stock2 then saw as indicated1 sawing vertically and along the joist4 ,illustration3 ,fig4 #bd4 ,laying off a ,stay ,illustration3 ,fig4 #be-;a-b4 ,headers and ,trimmers in ,floor ,frame ,before placing bridging1 the joist must be spaced and properly fastened in place4 ,this is done by placing a piece of stock1 #a #f or #b #d1 as in ,fig4 #bd4 ,with a try square1 mark the locations of the joists4 ,this board may then be transferred to the center of the room and the joists there spaced according to the marks1 and held in place by being tacked4 ,a second method consists in placing the spacing board in the center of the room and having a second person sight the joists for straightness while the first party places them as directed and tacks them4 ,this tacking consists in driving the nails only partially in1 leaving the heads project enough that they may later be withdrawn with a claw hammer4 ,still another method is to lay off the stay by measurement with the framing square so that it corresponds with the spacings of the joists at the side walls4 ,bridging should be nailed with two nails at each end of the piece4 ,illustration3 ,fig4 #bf4 ,placing ,headers and ,trimmers ,illustration3 ,fig4 #bg4 ,floor ,frame and ,rough ,floor #ab4 ,trimmers and ,headers4--,in the making of stair and chimney openings it becomes necessary to support the ends of joists other than in the usual manner4 ,this is done by cutting in headers as in ,figs4 #be1 #bf and #bg4 ,where the span is not great1 such as at an ordinary chimney in residence work1 in which but one or two tail beams are to be carried1 headers are not doubled and are merely spiked in place4 ,where many joists are to be carried1 headers or trimmers1 or carrying joists must be doubled4 ,iron stirrups or hangers should be used instead of spikes in joining headers to carrying joists where spikes would weaken the carrying joist and would not give ,illustration3 ,fig4 #bh-;a4 ,fig4 #bh-;b4 ,headers and ,trimmers in ,wall ,frame sufficient strength to the joint4 ,except upon long spans1 tail beams are usually fastened to the header by spiking only4 ,on long spans they should be framed to the header as joists are framed to a girder1 a #b #d being spiked firmly to the header as a support4 ,in determining the amount of space to allow for head room in framing about a well hole for a stair1 determine the run and rise of the stair from the plan and elevation1 and then plan to allow at least #f' #f1 measured from the proposed nosing line of the treads up to the proposed location of the trimmer1 or carrying joist1 or header1 as the case may be1 at the ceiling level1 ,fig4 #aba4 ,illustration3 ,fig4 #bi4 ,headers and ,trimmers in ,wall ,frame ,illustration3 ,fig4 #cj4 ,stud and ,joist ,patterns ,the term header is also used to designate the studding1 or joist in the case of double doors1 placed horizontally over window and door openings1 ,fig4 #bh4 ,studding cut in below window openings forms the stool1 also known as header4 ,the illustration shows the manner of framing for openings of different widths4 ,a small single window may require but one thickness of #b #d4 ,a medium sized opening will have a header of two pieces of #b #d4 ,where the opening is rather large1 as in the case of double door openings1 two joists will be set on edge over the opening as header4 #ac4 ,walls and ,partitions2 ,joists and ,rough ,floors4--,a study of ,figs4 #af1 #ag1 #ah1 #ai1 #bj and #bi should give an understanding of the essential members of the framed wall of a building1 and their relations one to another4 ,whether side walls shall be framed and raised before the rough or false floor of the first story is laid will depend upon the type of sill construction made use of4 ,in laying off studs1 joists1 etc41 a pattern is first framed4 ,these patterns are afterward used in the building and are therefore counted in with the total number of pieces to be framed4 ,to these patterns1 stops and fences are attached near the two ends and at the middle1 ,fig4 #cj4 ,the other studs or joists of similar dimensions are laid off one at a time by superimposing these patterns and marking about them with pencil1 ,fig4 #ca4 ,illustration3 ,fig4 #ca4 ,marking ,joists from ,pattern ,illustration3 ,fig4 #cb-;a4 ,illustration3 ,fig4 #cb-;b4 ,corner ,post ,types ,illustration3 ,fig4 #cb-;c4 ,ribband or ribbon boards and plates are laid off by placing them alongside the lay-out for the studs made upon the sills1 and transcribing the marks to the ribband board and plate by means of try-square and pencil4 ,sometimes ribband boards and plates are laid off by measurement1 as are sills4 ,corner posts are constructed first and placed4 ,fig4 #cb-;a shows a section of a corner post which has much to commend it4 ,fig4 #cb-;b illustrates a more common type of construction4 ,the most serious objection to this type is the fact that the post must be furred after the lather has placed the lath upon one side of the room4 ,corner posts are plumbed and stayed in two directions1 after being raised1 ,fig4 #cc4 ,either #b #d or #a #f stock will be used for stays4 ,with the corner posts set1 the ribband boards are placed4 ,where the span is too long for any available length of ribband board1 in laying out the ribband boards provision must be made for their breaking joints upon studs4 ,these studs will be raised immediately after the corner posts1 the ribband board attached to corner post and stud1 after which the stud will be plumbed and stayed1 ,fig4 #cd4 ,studs are framed before being raised so that ribband boards may be let into them as shown in ,fig4 #cd4 ,second and third floor joists will be notched to slip over these boards and will be spiked to the studs in addition4 ,remaining studs are placed one at a time1 one man setting up and nailing the foot while another fastens the ribband board to the stud at the second floor line1 ,fig4 #ce4 ,illustration3 ,fig4 #cc4 ,corner ,post ,being ,plumbed and ,stayed ,illustration3 ,fig4 #cd4 ,side ,wall ,stayed ,with the completion of the raising of the two outside walls which are to bear the joist ends1 the middle partition1 should there be one1 paralleling these walls should be framed and raised4 ,a slightly different procedure from that just described is followed1 that is1 instead of raising one stud at a time the whole partition is framed and nailed together upon the floor1 even to the cutting in of headers1 etc4 ,when a section such as the number of men available can raise is ready1 the same is raised1 and stayed after being plumbed4 ,the studs of partitions are framed but one story high and plated at such a height that second floor joists may be placed thereon in splicing4 ,just as far as possible first and second floor joists should be spaced to rest one directly above another and in line with the supporting studs of partitions so that furnace stacks may be placed with ease4 ,if joists rest upon partition plates and not directly above studs1 a double plate must be made use of4 ,having placed the second floor joists1 the studs at the ends of the house may be set up4 ,their locations will be marked upon sill and upon second floor joist which is to be placed at the end of the house4 ,this marking is best done by placing the joist upon the sill and transcribing the marks laid out upon the sill to the joist1 after which it is to be raised into place4 ,illustration3 ,fig4 #ce4 ,setting up ,studs and ,attaching to ,ribbon ,board ,double plates will next be framed4 ,they should break upon studs and be marked by transcribing the marks for the studs from the sills4 ,at the corners the plates will be framed with butt joints1 the second set lapping over the joints made by the first plate4 ,next1 the sustaining middle partition of the second story is raised as was that of the first story4 ,the attic floor joists are placed as were those for the second floor4 ,all walls and partitions are now lined up1 that is1 any irregularities are taken out by additional stays4 ,illustration3 ,fig4 #cf4 ,estimating ,window ,openings ,false or rough floors are laid in the various stories where not already placed1 bridging being placed and openings for stairs and chimneys framed4 ,such floors are laid either diagonally or straight across the joists4 ,the diagonal floor is considered better1 ,fig4 #bg4 #ad4 ,openings in ,framework4--,studs in outside walls are set without reference to openings for doors and windows4 ,such openings are cut and headers and stools placed after the walls are up and ready for sheathing4 ,the seeming waste occasioned by this method is slight since the cut-out material is available for headings1 etc4 ,most carpenters make a story pole to be used in laying off window and door heights in cutting out studs4 ,this is nothing more than a piece of #a #b or #a #c stock with the heights of the openings from the rough floor or from the joists1 where the rough floor is not laid1 marked plainly thereon4 ,this pole is placed alongside the stud to be cut and the mark transcribed from pole to stud4 ,beginners are frequently troubled in determining the proper opening1 even when the size of the window is specified4 ,in general1 carpenters plan to have the studs on either side of an opening1 either door or window1 so set that the outer edges of the exterior casings will break upon their centers4 ,windows are specified by the width and height of their glass and the number of divisions or lights1 width always being specified first4 ,the distribution of excess measurement due to the meeting rail1 top and bottom rails1 side rails or stiles is shown in ,fig4 #cf4 ,rail and stile widths and sash thicknesses will vary from those given when any very great increase in size of window is made4 ,manufacturers of sash and doors provide catalogs in which stock sizes are listed4 ,illustration3 ,fig4 #cg4 ,framing ,wall ,openings ,estimate an opening vertically1 ,fig4 #cf1 thus3 ,sill1 #b2 subsill1 where frame is made with one1 #a2 bottom rail1 from edge to bottom of rabbet1 #c2 glass in lower sash1 #cd2 meeting rail1 from rabbet to rabbet1 #a2 glass in upper sash1 #cd2 top rail1 #b2 space for head jamb and lugs of side jambs1 #b or #c2 total1 #gi4 ,a carpenter would say1 ,add #aa to the glass measurement to get vertical height between stool and header4 ,window sashes with muntins require an addition of for each muntin4 ,the thicknesses of header and stool must be considered in addition to the measurement just mentioned when studs are sawed1 ,fig4 #cg4 ,the width between studs would be estimated thus3 ,width of glass1 #bh2 width of stiles1 from rabbeted edge to outer edge1 #d2 width of casings1 #h2 total #dj1 distance from center of stud to center of stud4 ,comparing this with the width of glass it will be seen that the difference is #ab4 ,a carpenter1 therefore1 makes use of a general rule3 ,add #aj to the glass measurement to get distance between studs1 where a #d or #d casing is used with this type of window frame4 ,illustration3 ,fig4 #ch4 ,threshold ,detail ,for the #c' x #g' door1 ,figs4 #cg and #ch1 estimate the opening as follows3 ,height of door1 #g'2 allowance for rough floor1 2 finish floor1 2 threshold1 to 1 head jamb and space for lugs of side jambs1 #b to #c2 total from joist1 may be #g' #e4 ,for the width of opening estimate3 ,width of door1 #c'2 width of casings1 at #d each1 #i2 total spacing of studs center to center1 #c' #i4 ,distance between studs will be #c' #g4 ,this will leave space enough to put the doubling studs on each side between header and floor4 ,since locations of openings in the main frame1 both window and door1 are dimensioned to the centers of the openings1 it is easiest in laying off to estimate from the center each way rather than to estimate total width4 ,after these openings are made1 the frame of the house may be covered with sheathing1 or the roof may be framed2 both orders of procedure are common4 ,,chapter ,,iii ,roof ,frame3 ,square ,cornered ,buildings #ae4 ,roof ,framing4--,the problem of framing the various members of a roof is not a difficult one provided the underlying principles are understood1 and dependence placed upon this understanding rather than upon mere knowledge of what figures to use upon the square to get the cuts1 without knowing why those figures are used4 ,an effort will be made in this treatment to indicate the why4 ,illustration3 ,,gable ,,hip ,,shed ,,gambrel ,fig4 #ci4 ,roof ,types ,in ,fig4 #ci are illustrated four types of roof4 ,figs4 #dj1 #da1 and #db illustrate the rafter forms and the names of the various cuts to be made in framing the members to place4 ,the common rafter1 it will be seen1 has three cuts--plumb or ridge cut1 seat or heel or plate cut1 and end cut4 ,the hip1 valley1 and jack have four cuts each2 a side cut or cheek cut is possessed by each in addition to the three cuts belonging to the common rafter4 ,before any rafter can be framed1 the rise and run of the common rafter1 in other words1 the pitch of the roof1 must be known4 ,in roof framing1 the run of a rafter when in place is the horizontal distance measured from the extreme end of the seat to a point directly below the ridge end of the rafter1 ,fig4 #dc4 ,the rise is the vertical distance from the ridge end of the rafter to the level of the seat4 ,the pitch of a roof or rafter is the ratio of the rise of the rafter to the span or whole width of the building4 ,illustration3 ,fig4 #dj4 ,roof ,details ,illustration3 ,fig4 #da4 ,plan of ,roof ,rafters ,the terms rise1 run1 and rafter length have still another set of meanings--they may be used to designate unit lengths4 ,in all such cases #ab of run of the common rafter is assumed as the base1 and the other unit lengths or constants are computed from this constant4 ,the numerical values of these constants will be computed as the development of the subject of roof framing makes their use necessary4 ,illustration3 ,fig4 #db4 ,raising the ,rafters ,it will be noted in ,fig4 #dd that the constant of run1 or #ab1 is taken along the tongue and the rise per foot of run along the blade of the square4 ,it is not essential that this order be followed2 the beginner will generally find it easier to visualize his work1 however1 if he keeps the tongue for either rise or run1 and the blade for the opposite4 ,there are occasions when the reverse order is necessary no matter which form is followed1 so that it is unwise to insist upon only one way4 ,illustration3 ,fig4 #dc4 ,run1 ,rise and ,length ,illustration3 ,fig4 #dd4 ,unit ,length of ,common ,rafter ,the variation in terminology in roof framing is so general that the beginner will do well to familiarize himself with the most common4 ,hereafter an effort will be made to confine the text to the following3 plumb cut1 seat cut1 end cut1 side cut4 ,the value to a beginner of a carefully made plan of a roof to be framed with necessary data such as rafter lengths and positions indicated thereon1 cannot be too strongly emphasized4 ,architects not infrequently prepare elaborate and complete framing plans for the use of the carpenter4 ,upon intricate plans1 experienced men prepare plans before attempting to frame the same4 ,fig4 #dc illustrates a framing plan ready for the placing thereon of the necessary data1 such as measurements along the plate for spacing the rafters1 lengths of rafters1 ridge pieces1 etc4 ,illustration3 ,fig4 #de-;a-b4 ,laying off ,common ,rafter #af4 ,framing the ,common ,rafter2 ,laying out the ,plumb ,cut4--,while in this discussion the plumb cut is first described1 it should be understood that it is equally as convenient and more common among carpenters to begin the framing of the members of a square cornered roof frame with the end and seat cuts4 ,in framing other than a square cornered roof it is somewhat more convenient to begin with the plumb cut4 ,the method of framing of the common rafter is the same for all buildings1 whether the buildings have four sides or more or less4 7#a7 ,place the framing square as in ,fig4 #de-;b1 taking #ab on the tongue as the run1 and upon the blade the rise in inches per foot of run4 ,keep these numbers against the crowning1 or what is to become the top edge of the rafter1 and scribe along the blade4 ,this gives the plumb cut4 ,occasionally a carpenter will be found who frames to a center line rather than the top edge of a rafter4 ,illustration3 ,fig4 #df4 ,position in ,laying off ,plumb ,cut when ,laid off before ,seat ,cut ,figs4 #de1 #df and #dg illustrate the proper position of the worker relative to his work4 ,such a position will seem awkward to the beginner but he should learn to visualize his work while in this position that the efficiency of framing may not be reduced thru the awkward position first likely to be assumed4 ,illustration3 ,fig4 #dg4 ,laying off ,plumb ,cut when ,seat ,cut is ,first ,laid off #ag4 ,to ,find the ,length of a ,common ,rafter4--,first ,method3 ,the theoretic length of a rafter is indicated by the center lines in ,figs4 #de-;a and #dh4 ,in estimating the total length of stock for a rafter having a tail1 the run of tail or length of lookout must be considered4 ,the pitches most commonly used are the half1 third1 and quarter4 ,from an examination of ,fig4 #dc it will be seen that the length of a common rafter is the hypotenuse of a right triangle whose legs are the rise and the run of the roof4 ,the problem1 then1 of finding the length of a common rafter when the rise and run are known is merely that of solving the equation c a b4 ,illustration3 ,fig4 #dh4 ,rafter ,length ,practical carpenters would not consider it economy to take time to solve for rafter lengths in this manner1 for every variation in rise or run would necessitate a rather long solution4 ,instead1 they have discovered that for every foot of run of a rafter the length of the rafter increases proportionately1 the ratio of rise to run remaining the same1 ,fig4 #dd4 ,with a table1 therefore1 in which the length of rafter for each foot of run1 for each of the common pitches is given1 the length of rafter for any given pitch can be found by merely multiplying the constant given by the amount of run for that particular rafter4 ,fig4 #di shows such a table worked out for a rather extended number of pitches4 ,from this table it will be seen that the number to take as a constant for the run is #ab1 and that the rise in inches per foot of run is taken upon the other member of the framing square4 ,a jack rafter as will be illustrated later is but a shortened common rafter1 therefore1 what is said of the common rafter is also true of the jack rafter4 ,the jack1 however1 has an additional cut which will be discussed in another section4 ,example3 ,determine the length of a common rafter of a house with a #be' span and a quarter pitch1 without tail4 ,illustration3 ,fig4 #di4 ,framing ,table for ,common ,rafter ,solution3 ,run #ab' ,length per foot of run for quarter pitch #ac4db #ab4e #ac4db #afg4ge #ac4ih' 7,looking for the nearest fractional value of 4#ih in the ,table of ,decimal ,equivalents in ,appendix ,,iii1 #fc_/fd or practically #a'7 ,the rafter would be framed #ad' in length4 ,when a tail is a part of the rafter1 proceed in the manner described adding the run of the tail1 or length of lookout1 to the run of the rafter4 ,illustration3 ,fig4 #ej4 ,framing ,square ,detail ,fig4 #ej shows a framing square1 containing among other data1 the rafter lengths per foot of run4 ,to use the data pertaining to common or jack rafter lengths1 7#a7 consider the run as #ab taken on the tongue2 7#b7 select upon the blade along its outer edge the inch mark which represents the rise of the roof per foot of run required to give the pitch specified2 7#c7 the number directly below this mark1 reading across the blade in the space marked ,length of ,common ,rafter ,per ,foot of ,run gives the length per foot for that particular rise or pitch4 ,as a check for rafter length computations1 the following procedure is suggested3 ,selecting the run as #ab on the tongue and the rise in inches per foot of run on the blade1 place one square upon another as shown in ,fig4 #ea1 using that side of the square divided into inches and twelfths4 ,do not use the end of the blade1 the rounded corner makes it impossible to secure the accuracy demanded4 ,extreme accuracy is required if the constant is to be used for rafters of considerable length of run4 ,read the diagonal length between the numbers representing the run and rise4 ,read the whole number of inches as feet1 and the fractions as inches1 and take off any fractional remainder upon a very sharp pointed pair of dividers4 ,read this divider spacing by means of the hundredths scale on the framing square4 ,the result should1 if the work is very accurately done1 be the same as that obtained by computation from the tables1 even to the hundredths place decimal4 ,upon ordinary work where great accuracy is not required carpenters sometimes determine this constant for a given pitch by placing the framing square as in ,fig4 #df or #dg1 taking upon the tongue the run and on the blade the rise1 marking along both tongue and blade4 ,the distance between these marks is then read on a square placed along the edge4 ,second ,method3 ,in determining rafter length1 an equally common practice is to lay the framing square as is shown in ,fig4 #de-;a4 ,while in this position the seat cut is scribed1 cf4 ,section #ah1 and also a short sharp line scribed along the other member of the square at the top edge of the rafter4 ,the square is moved along1 using the same numbers1 and another advance mark scribed4 ,this operation is repeated just as many times as there are feet in the run of the common rafter4 ,with a span of #bd' the operation would be repeated #ab times4 ,should the run not happen to be in even feet1 the square would be placed as many times as there were full feet in the run4 ,in addition it would be advanced that fractional part which the fraction of the run was of #ab4 ,for example1 in a run of #ab' #g1 with a roof of pitch1 the square would be advanced #ab times using the number #ab on the tongue and #f on the blade4 ,in addition to this the square would be advanced using #g_/ab of #ab or #g on the tongue and #g_/ab of #f or #c on the blade4 ,as these numbers do not allow enough of the square to rest on the rafter to give a full line1 as soon as the advance limit of rafter length is indicated the square may be moved up1 using the set of numbers first used1 that is #ab and #f4 ,on common rafters1 this last operation is simplified by noting that the fractional run1 divided by #ab1 times #ab1 always equals itself4 ,the final position of the square1 therefore1 may be obtained by simply sliding the member1 used in laying out the last full foot line which parallels the seat cut1 an additional distance equal to the fractional foot of total run1 ,fig4 #dd4 ,the tail length is obtained similarly1 ,fig4 #dd4 ,illustration3 ,fig4 #ea4 ,finding ,rafter ,length by ,scaling ,illustration3 ,fig4 #eb4 ,laying out ,rafter #ah4 ,laying off ,common ,rafter ,seat ,cut and ,end ,cut4--,first ,method3 ,having determined the rafter length as directed in ,sec4 #ag1 first method1 7#a7 lay off this length along the upper edge beginning at the plumb cut4 ,the whole number of feet is more safely taken off by means of a pole marked in feet1 and of good length4 ,the rule or square may be used to transmit fractional parts of a foot4 7#b7 ,place square as at b1 ,fig4 #eb1 standing as in ,fig4 #de-;b1 and scribe a plumb line as indicated at #a-b1 ,fig4 #eb4 7#c7 ,from the point #a1 ,fig4 #eb1 measure along the line marked #a-b a distance equal to one-half that of #a-b4 ,the distance #a-c may be increased or decreased somewhat when an extreme pitch makes it advisable4 ,as a rule this should be #b to #c4 7#d7 ,place the square as at c1 ,fig4 #eb1 with the edge of the tongue resting on #c and scribe a line for the seat cut1 as #c-d4 ,these last marks give the bird's mouth joint which is to fit over the plate4 ,illustration3 ,fig4 #ec4 ,independent ,rafter ,tail ,illustration3 ,fig4 #ed4 ,length of ,ridge ,piece ,while many carpenters allow end cutting of the rafter tails to wait until the rafters are set in place so that they may be lined and cut while in position1 certain kinds of work permit the ends to be cut at the same time the remainder of the rafter is framed4 ,in this latter method the square is placed as in ,fig4 #dd and 7#e7 the end cut scribed4 ,the point of cutoff on the tail is determined in the same manner as that used in determining rafter length1 the run of the tail being considered and the tail length being measured from the point #a1 ,fig4 #eb4 ,where a cornice is of unusual width1 tails are usually framed independent of the rafters and are then spiked to the ends of the rafters either above or below the plate1 ,fig4 #ec4 ,second ,method3 ,where the second method of finding length1 ,section #ag1 is employed1 the end cut and seat cut will be laid out before the plumb cut4 ,the operator will stand as in ,fig4 #de-;a4 ,when one rafter has been laid out it is cut and used as a pattern by which to cut similar rafters4 ,illustration3 ,fig4 #ee4 ,determining ,diagonal ,thickness of ,hip of ,square ,corner4 ,illustration3 ,fig4 #ef4 ,reduction of ,common ,rafter for ,ridge ,piece4 #ai4 ,ridge ,piece4--,roofs may be framed with or without a ridge piece4 ,the use of a ridge piece makes the assembly or raising of a roof somewhat easier1 especially a hip roof4 ,upon an ordinary dwelling a ridge piece is usually a #a #f board4 ,upon a gabled roof the length of ridge piece will be the same as that of the plate which it is to parallel1 and will be laid off by placing the ridge board alongside the plate after the rafter positions have been marked upon the plate4 ,these marks are transcribed upon the ridge board by means of the square and pencil4 ,on a hip roof1 ,fig4 #ed1 the length of a ridge piece will be equal to the length of the parallel plate diminished by the length of the plate at right angles to this4 ,this1 however1 is the theoretic length of ridge as measured from center to center4 ,enough extra stock must be left on the ridge when framing it to allow full contact of hip cheeks4 ,this additional measurement at each end of the ridge will be equal to the diagonal thickness of the hip plus the thickness of the ridge1 ,fig4 #ed1 making a total addition equal to the diagonal thickness of the hip plus the thickness of the ridge4 ,fig4 #ee illustrates the placing of the square to determine the diagonal thickness of a hip rafter which strikes the ridge at an angle of #de degrees4 ,illustration3 ,fig4 #eg4 ,hip or ,valley ,rafter is ,diagonal of ,square ,prism ,in reckoning the length of a common rafter which is to rest against a ridge1 the total length must be reduced by an amount equal to one-half the thickness of the ridge measured at right angles to the plumb cut1 ,fig4 #ef4 ,illustration3 ,fig4 #eh-;a4 ,hip ,rafter4 ,illustration3 ,fig4 #eh-;b4 ,valley ,rafter #bj4 ,hip and ,valley ,rafters of ,square ,cornered ,buildings4--,first ,method3 ,the line of measurement for length of a hip and valley rafter is along the middle of the back or top edge1 as on common and jack rafters4 ,the manner of determining the number to use on the tongue of the square as a constant for the run1 in terms of the #ab constant run of the common rafter1 when the rise of the hip or valley rafter per foot of common run is taken on the blade2 and the manner of constructing a table of unit lengths of hip and valley rafter1 per foot of run of common rafter1 are illustrated in ,figs4 #eg1 #eh1 #ei and #fj4 ,from a study of these illustrations it will be seen that a hip or valley rafter of a square cornered building is in either case the diagonal of a square prism which has for its base dimensions the tangent and run of the roof1 and for its height the rise of the roof1 ,fig4 #eg4 ,on a square cornered building the run and tangent are always equal4 ,illustration3 ,fig4 #ei4 ,determining ,unit ,length of ,hip or ,valley ,rafter4 ,the length of the diagonal of the base of such a prism1 which is the run of the hip or valley rafter1 is found by the formula c a b1 ,fig4 #eh4 ,when tangent and run are equal and each taken as #ab1 the run of the hip or valley equals #af4ig1 which for practical purposes of carpentry is considered as #ag4 ,in laying on the square1 then1 in framing a hip or valley rafter of a square cornered building1 #ag will be taken upon the tongue1 the rise of the roof per foot of run of common rafter or per #ag of run of hip or valley rafter1 being taken on the blade4 ,the table of hip and valley lengths per foot of run of common rafter1 ,fig4 #fj1 will be formed by solving the right triangle c a b1 ,fig4 #ei1 for each of the pitches represented4 ,the positions to be assumed by the worker in framing a hip or valley rafter are similar to those to be assumed in framing the common rafter4 ,in measuring the length of a hip or valley rafter by the first method1 the plumb cut may be laid off first4 ,the upper end of the hip rafter will have to be framed with a side cut as shown in ,fig4 #fa4 ,the measurement for length will be made from a point along the middle of the top arris4 ,where the second method is employed1 the end and seat cuts are laid off first4 #ba4 ,laying off ,plumb ,cut of ,hip or ,valley ,rafter for ,square ,cornered ,buildings4--,assuming a position with reference to the rafter similar to that in framing the common rafter1 lay off the plumb cut using #ag on the tongue1 and on the blade the rise per foot of run of the roof1 or common rafter1 which is also the rise of a hip or valley on that roof per #ag of hip or valley run4 ,scribe along the blade4 ,illustration3 ,fig4 #fj4 ,framing ,table for ,hip or ,valley ,rafters #bb4 ,side or ,cheek ,cut of ,hip or ,valley ,rafter4--,first ,method3 ,there are a number of ways to lay out a side cut on a square cornered building4 ,the simplest to remember1 where no framing tables are at hand1 consists in measuring square back from the plumb cut line a distance ,a-,b1 ,fig4 #fb1 equal to the thickness of the rafter being framed4 ,thru this point lay off another line parallel to the plumb cut line and carry this across the top edge of the rafter with the square1 as at ,d-,e4 ,now adjust the bevel to pass thru ,e and ,f1 ,fig4 #fb1 and the setting is obtained for all side cuts of hip or valley rafters of that pitch of roof4 ,scribe this line on the top edge of the rafter4 ,carry it down the remaining side using the same numbers on the square as were used in laying off the plumb cut on the first side4 ,second ,method3 ,this method of laying off side or cheek cut consists in laying the framing square across the top edge of the rafter1 taking #ag on the tongue and the length of hip or valley rafter per foot of run of common rafter for the pitch required on the blade1 and scribing along the blade4 ,illustration3 ,fig4 #fa4 ,side ,cut ,illustration3 ,fig4 #fb4 ,laying off ,side ,cut #bc4 ,determining ,length of ,hip or ,valley ,rafter4--,first ,method3 ,if a table of unit lengths of hip or valley per foot of run of common rafter is available1 ,fig4 #fj1 the total rafter length may be determined by multiplying the unit of hip or valley rafter length per foot of run of common rafter by the total run of common rafter4 ,do not make the mistake of trying to multiply by the run of the hip or valley rafter4 ,remember that these tables are all worked out with the #ab run of the common rafter as the base4 ,this is true no matter whether the house is four sided1 eight sided1 or any other number of sides4 ,the respective tables are based in every case upon #ab run of the common rafter4 ,measurements for lengths of hip or valley are to be made along the top edge of the stock beginning at the line for side cut and midway between the point and heel1 ,fig4 #fa4 ,second ,method3 ,this method of determining length of a hip or valley rafter is not unlike the second method described for the common rafter4 ,here1 the numbers are #ag on the tongue1 and the rise per foot of run of roof or of common rafter1 on the blade4 ,the end and seat cuts are scribed1 after which the square is advanced step by step1 using these same numbers1 as many times as there are feet of run of common rafter4 ,should there be a fraction of a foot in the run of common rafter an additional and proportional advancement must be made4 ,for example1 to frame a hip for a square roof of pitch1 having a run of common rafter of #ab' #g4 ,advance the framing square #ab times1 using #ag on the tongue and #f on the blade4 ,for the fractional advance take #a_/ab of #ag or #i-aa_/ab 7the framing square is laid off in twelfths on one side7 on the tongue and #g_/ab of #f or #c on the blade1 and scribe the limit4 ,fractional foot length of tail will be determined in a similar manner1 the run or horizontal extension1 or the lookout1 of the common rafter determining the number of times the square must be advanced using #ag and #f for the above given pitch4 ,illustration3 ,fig4 #fc4 ,miter ,cut of ,hip ,rafter ,end #bd4 ,laying off ,seat and ,end ,cut of ,hip ,rafter for ,square ,cornered ,building4--,the seat cut and end cut of a hip rafter will be laid off in a manner quite similar to that used in laying off the seat and end cuts of the common rafter as described in ,sec4 #ah4 ,there will be this difference1 of course2 the numbers to be used on the square will be #ag on the tongue instead of #ab as in the case of the common rafter4 ,the rise per foot of run will be the same as for the common rafter4 ,the run of the tail of the common rafter determines the length of lookout or the number of times the square will be advanced4 ,the distance #a-c1 ,fig4 #eb1 must be the same on hip and valley as on common rafter of the same pitch of roof4 ,the end cut of a hip rafter must be mitered to receive the fascia4 ,the amount to be taken off for a square cornered building will be indicated by laying off lines a distance equal to one-half the thickness of the rafter1 measured straight back from the lay-out of the end cut1 ,fig4 #fc4 ,since these cuts are identical with the side cut at the upper end of hip or valley1 the square may be used as in laying off a side cut1 cf4 ,section #bb1 second method4 ,illustration3 ,fig4 #fd4 ,backing the ,hip ,rafter #be4 ,reduction of ,hip or ,valley ,rafter ,length ,because of ,ridge ,piece4--,if a hip rafter of a square cornered building is to be framed against a ridge piece1 ,fig4 #dj1 its length must be reduced correspondingly4 ,to make such allowance1 measure square back from the line of plumb cut a distance equal to the diagonal thickness of the ridge1 ,fig4 #fa-;,a-,b4 #bf4 ,backing a ,hip ,rafter for ,square ,cornered ,building4--,first ,method3 ,since the line of measurement of a hip rafter is along the center of the top edge1 if the rafter is framed with the same plumb distance as was given the common rafters1 #a-c1 ,fig4 #eb1 it stands to reason that the roof boards will not fit the top edge of the hip properly until the arrises of the hip have been removed as in the cross-section of ,fig4 #fd4 ,the laying out and removal of these arrises is known as backing the hip4 ,the amount of backing for a hip rafter will depend upon the rafter thickness1 the pitch of the roof1 and the number of sides to the plate1 and is indicated by gage lines on either side and one on the top edge of the rafter4 ,to determine the location of these gage lines on the sides of the rafter1 7#a7 place the square on the hip as in laying out the seat cut for the hip on which the backing is to be placed1 the constant1 #ag1 on the tongue and the rise on the blade1 if the house is rectangular1 ,fig4 #fd4 7#b7 ,measure from the edge of the hip back along the tongue a distance equal to the thickness of the rafter1 and mark4 ,this point gives the setting for the gage4 7#c7 ,gage both sides of the rafter and then remove the arrises as shown in the cross-section4 ,carpenters more frequently frame a hip without backing1 allowing the roof boards to rest upon the arrises of the hip1 forming a small triangular space between the roof boards and the top edge of the hip4 ,in order to keep these arrises in the same planes as the tops of the common rafters1 they must reduce the plumb height #a-c1 ,fig4 #eb1 of the hip4 ,the amount of reduction1 that is1 the amount of drop the hip must make is equal to the plumb height of the backing1 ,fig4 #fd4 ,illustration3 ,fig4 #fe-;a4 ,fig4 #fe-;b4 ,framing ,valley ,rafter at ,plate ,second ,method3 ,take the rise in inches per foot of run of common rafter on the tongue1 and the length of hip or valley per foot of run of common rafter on the blade2 scribe along the tongue to get the angle of backing4 #bg4 ,valley ,rafters4--,as has been indicated in previous sections of the text1 valley rafters have their lengths1 plumb cuts1 and seat cuts determined like hip rafters4 ,there is one difference2 the valley rafter at its seat must be framed as in ,fig4 #fe in order that the plumb line may come directly over the corner of the building4 ,the ends of roof boards will rest upon the valley rafter at its center line1 which line is in the same plane as that of the common rafters4 ,like the hip rafter1 the upper end may be laid out first1 after which the rafter length is measured from this1 the measurement being made along the middle of the back of the rafter1 the top edge4 ,to lay out the cuts shown in ,fig4 #fe-;a1 proceed as in laying out the end of a hip rafter1 as described in ,sec4 #bd1 ,fig4 #fc4 ,in the case of an octagon the amount would be #e_/ab of that used for the square1 ,fig4 #fe-;b4 ,in ,figs4 #dj and #da is shown a valley rafter framed thru to the ridge4 ,this is done to give the valley support1 for a valley1 unlike a hip1 is not self supporting when the jacks are attached4 ,against this valley rafter is framed a second valley rafter4 ,the upper end of this second valley rafter is framed with a plumb cut such as would be given a hip or valley of the same rise and run2 the end1 however1 is cut square across as in the case of a common rafter resting against a ridge4 #bh4 ,framing the ,jack ,rafter for ,square ,cornered ,buildings2 ,plumb ,cut2 ,side ,cut4--,jack rafters which have their top ends framed against a hip are known as hip jacks2 those having the lower ends framed against a valley are known as valley jacks2 those which are framed in between hip and valley are known as cripple jacks4 ,the jack rafter1 being but a portion of a common rafter1 is framed in a manner quite like that used in framing the common rafter4 ,the chief difference is in the fact that the jack rafter has a side or cheek cut1 and that the lengths of jacks vary with their position along the plate4 ,the order of procedure may be3 7#a7 ,to lay off the plumb cut1 just as for a common rafter having the same rise1 that is1 using #ab on the tongue1 and the rise per foot of run on the blade2 scribe along the blade4 7#b7 ,lay off the side cut or cheek cut4 ,this is done just as in laying off the side cut of the hip rafter on a square cornered building1 first method only1 ,fig4 #fb4 ,where a table of common rafter lengths per foot of run is available1 ,fig4 #di1 a second method of laying out the side cut of a jack rafter consists in taking #ab on the tongue of the framing square1 and the common rafter length per foot of run for the pitch given1 on the blade2 laying the square across the edge of the rafter and scribing along the blade4 7#c7 ,lay off the length of the jack as determined in the next section4 7#d7 ,lay off the seat cut just as in laying off the seat cut of the common rafter for the same pitch of roof1 ,section #ah4 ,equally common is the practice of beginning with the end and seat cuts4 ,the framing square of ,fig4 #ej contains data which makes possible the laying out of side cuts for the square cornered building by means of numbers taken upon tongue and blade4 ,while the ratios of the numbers used upon the tongue and the blade are always the same for any given pitch1 different makers of squares use different numbers for side cuts4 ,the student will have to have special directions for each different make of square4 ,these may be gotten from the manufacturers4 #bi4 ,lengths of ,jack ,rafters for ,square ,cornered ,roofs4--,first ,method3 ,the framing table for common rafters and jack rafters1 ,fig4 #di1 may be made use of in determining lengths of jacks4 ,to make use of this table we shall need to know the run of each separate jack4 ,an examination of ,fig4 #ff shows that in a rectangular house the run of a jack is the same as the length of plate or of ridge which forms the angle4 ,this is true of hip jack1 valley jack1 or cripple jack4 ,however1 such measurements are along the centers of the top edges of the rafters and allowance must be made in the length of the jacks for the thickness of hip or valley rafter4 ,in the case of the cripple jack this amount of reduction will be equal to the diagonal thickness of the hip plus the diagonal thickness of the valley1 measured at right angles to the plumb cut1 ,fig4 #fa1 or measured in the plane of the plate1 or a parallel plane4 ,illustration3 ,fig4 #ff4 ,lengths of ,jack ,rafters4 ,top and bottom ends of cripples are alike1 but in nailing them in place the lower ends must be held up so that their center lines will strike the center of the valley rafter4 ,their tops will be kept even with the outer arrises of the hip whether the hip is backed or not4 ,in determining the true length of hip jack and valley jack we should know that a reduction of the diagonal thickness of hip or valley1 measured straight back from the plumb cut1 is to be made4 ,in the case of a valley jack resting against a ridge piece1 an additional reduction must be made as described in ,section #ai1 ,fig4 #ef4 ,in actual practice carpenters usually measure the length of hip or valley jack from the long point1 along the arris1 instead of along the center of the top edge1 no reduction being made for the diagonal thickness of hip or valley4 ,cripple jacks are measured from long point to long point1 no reduction being made for thickness of hip and valley4 ,illustration3 ,fig4 #fg4 ,determining ,length of ,jack ,rafters ,second ,method3 ,where jacks are framed so that equal spacings may be laid off1 beginning with a full length common rafter1 as in ,fig4 #fg1 the simplest method of determining lengths of jacks is to first count the number of spaces between jacks1 which must be laid off on ridge or on plate1 and divide the length of common rafter by this number4 ,the result will be the common difference between lengths of jacks4 ,the longest jack will be framed first by reducing the length of common rafter by the common difference4 ,the next1 by reducing the jack just framed by the common difference1 etc4 ,this method is applicable to roofs of any number of sides4 ,third ,method3 ,if we begin to frame with the shortest jack instead of the longest1 we first determine the length of the shortest jack1 remembering that its run in the square cornered building will be the same as its spacing from the corner along the plate1 or along the ridge in case of a valley jack4 ,in a similar manner the second jack can be framed4 ,the difference in the lengths of these two is the common difference4 ,to the length of this second jack1 and to each succeeding jack add the common difference1 to get the length of the next4 ,fourth ,method3 ,as rafters are usually spaced either #af or #bd apart1 a table consisting of the common differences in lengths for the various pitches will be found convenient1 ,fig4 #di4 ,the steel square of ,fig4 #ej also shows such a table for the square roof4 ,,chapter ,,iv ,roof ,frame3 any ,polygon ,illustration3 ,fig4 #fh4 ,tangents #cj4 ,tangents2 ,miter ,cuts of the ,plate4--,before the principles involved in the laying out of rafters on any type of roof can be understood1 a clearer idea of the term tangent as used in roof framing must be had4 ,a tangent of an angle of a right triangle is the ratio or fractional value obtained by dividing the value of the side opposite that angle by the value of the adjacent side4 ,the tangent at the plate1 to which reference was made is the tangent of the angle having for its adjacent sides the run of the common rafter and the run of the hip or valley4 ,by making use of a circle with a radius of #ab we may represent the value of this tangent graphically in terms of the constant of common rafter run1 ,fig4 #fh4 ,by constructing these figures very carefully and measuring the line marked tangent1 we may obtain the value of the tangent for the polygon measured in inches to the foot of run of the common rafter4 ,such measurements1 if made to the #a_/ajj of an inch will serve all practical purposes4 ,a safer way1 however1 is to make use of values secured thru the trigonometric solutions described in ,appendix ,i1 using the graphic solutions as checks4 ,the values of tangents at intervals of one degree are given in the ,table of ,natural ,functions1 ,appendix ,,ii4 ,by interpolation1 fractional degree values may be found4 ,illustration3 ,fig4 #fi-;a4 ,table of ,tangents ,illustration3 ,fig4 #fi-;b4 ,rafter ,table4 ,example3 ,find the value of the tangent for an octagonal plate4 ,solution3 ,angle ,a of ,fig4 #fh #bb 7#a_/af of the sum of all the angles about a point7 ,tan #bb 4#dadc ,tables are builded with #a as a base4 ,in roof framing #a or #ab is taken as the constant or base1 or unit of run of common rafter4 4#dadc may be considered as feet1 which equals #d4ig4 ,in a similar manner tangents may be found for plates of buildings of any number of sides4 ,in ,fig4 #fi is illustrated a handy device one side of which1 by the twirling of one disk within the other1 can be made to give tangent values1 in terms of a #ab base1 for any number of degrees4 ,the reverse side of this key gives data to be used in the framing of square cornered and octagonal roofs4 ,such a key will be found a convenient way in which to carry needed data and should be easily understood and intelligently used1 once the principles discussed in this chapter are mastered4 ,an explanation of the author's key1 ,fig4 #gj1 will be found in ,appendix ,,iv4 ,now as to some of the uses for tangent values3 ,first1 by taking #ab on the tongue and the tangent value in inches per foot of common rafter run upon the blade of the square1 we are able to get the lay-out for the miter joint of the plate4 ,fig4 #ga-;b illustrates the square placed for the lay-out of the octagonal plate or sill miter4 ,five inches is taken as tangent since the real value #d4ig is equivalent to #e for all practical purposes4 ,for the square cornered building #ab and #ab would be used in making the plate miter lay-out1 since the tangent of #de is #a according to the ,table1 ,appendix ,,ii4 ,any other like numbers would give a tangent value of #a1 of course1 but it is best to consider #ab on the tongue1 in which case #ab must be taken on the blade4 ,second1 this tangent value is needed in determining the cheek or side cut of hip1 valley and jack rafters1 as will be shown in ,sec4 #ce4 ,third1 this tangent value is needed in determining the amount of backing to be given hip rafters4 ,this is discussed in ,sec4 #ci4 ,not infrequently the plate miter in degrees is required4 ,this is determined for any regular polygon by the proposition3 ,the plate or miter angle of any regular polygon #ij - 7central angle_/#b7 ,example3 ,find the value of the plate miter of the octagon4 ,solution3 ,the octagon has #h sides2 therefore central angle #de #de #b #bg #ij - #bb #fg ,illustration3 ,fig4 #gj-;a4 ,fig4 #gj-;b4 ,griffith's ,roof ,framing ,tables ,fourth1 the tangent value is needed in finding the length of a side of a polygon1 the span or run of the polygon being known1 and vice versa4 ,length of side span x tangent of plate1 using #ab as base4 ,example3 ,an octagonal silo has a span of #ah'2 determine the length of plate for any side4 ,solution3 ,the tangent value of the octagon #d4ig 7to each #ab of run7 #ah #d4ig #hi4df #g' #e4df #g' #e4 ,illustration3 ,fig4 #ga-;a4 ,fig4 #ga-;b ,laying out ,miters ,example3 ,a side of a hexagon measures #d'2 determine the run of the hexagon4 ,solution3 ,transposing the rule above3 ,span length of side divided by tangent of plate4 ,tangent of hexagon #f4ib when base #ab4 #d' divided by #f4ib #f' #f4dh span4 ,run #c' #c4bd4 #ca4 ,octagonal ,roofs4--,while the square cornered building is the most common1 the octagon is frequently used in the form of a bay attached to the side of a house4 ,the octagon is also common upon silos and towers4 ,the manner of finding the run1 tangent1 length of hip and valley rafter1 miter cut of plate or sill1 the manner of determining the numbers to use on the square to lay out the plumb and seat cuts1 etc41 will be found developed herein for both square and octagonal roof4 ,having mastered the principles involved in these two forms1 the student should be able to work out framing problems for roofs of any number of sides4 #cb4 ,common ,rafter for ,plate of any ,number of ,sides4--,by referring to ,figs4 #fh and #gb it will be seen that common rafters have for their runs the apothem of the polygon made by the plate1 represented in ,fig4 #fh by the lines b1 b'1 b4 ,the run of the hip is represented by the line c1 c1 c4 ,the rise will be found the same for full length common rafters and hips4 ,plumb and seat cuts and lengths per foot of run of common rafters and jacks are determined for a building of any number of sides just as for the square cornered building4 ,the degree of inclination of common and jack rafter is applicable1 too1 ,fig4 #di4 #cc4 ,hip and ,valley ,rafters for ,octagonal and other ,polygons4--,before the table of constants for hips and valleys for octagonal and other polygonal roofs can be formed1 it is necessary to determine the tangent values of these polygons1 as described in ,sec4 #cj4 ,proceeding with the octagon1 whose tangent was found to be #d4ig when the run of the common rafter was taken as #ab1 by the formula c a b1 ,fig4 #gb1 the run of the octagon hip or valley will be found to be #ab4ii for each foot of run of the common rafter4 ,illustration3 ,fig4 #gb4 ,run of ,common ,rafter of any ,roof is ,apothem of ,polygon #cd4 ,plumb ,cut of ,octagonal and other ,polygonal ,hips and ,valleys4--,the run of an octagonal hip or valley is #ab4ii for each foot of run of common rafter4 ,for practical purposes this is considered as #ac4 ,to lay off a plumb cut for an octagonal hip or valley1 take #ac on the tongue and the rise per foot of run of common rafter on the blade1 ,fig4 #gc2 scribe on the blade4 ,illustration3 ,fig4 #gc4 ,table for ,octagon ,hip or ,valley ,in a similar manner1 having determined the tangent of any polygon under consideration1 the run of hip or valley per foot of run of common rafter may be figured4 ,the result will give the number to take on the tongue when the rise per foot of run of common rafter is taken on the blade1 for laying out plumb cuts4 #ce4 ,side or ,cheek ,cuts of ,hip and ,valley ,rafters for ,roofs of ,any ,number of ,sides4--,fig4 #gd illustrates the principles involved and method used in determining side cuts whatsoever the pitch and number of sides involved4 7#a7 ,lay the square across the jack or hip or valley1 whatever is to be framed1 at any convenient place1 using on the blade the tangent 7with #ab as base7 of the polygon being framed1 and on the tongue the constant of the run of the common rafter1 #ab4 ,scribe along the tongue ,a-,c1 ,fig4 #gd4 7#b7 ,with the square1 carry the line ,b-,c across the edge as indicated4 7#c7 ,lay off the plumb cut for the required pitch1 taking upon the blade the rise1 and upon the tongue the constant of the run of the hip or valley or jack1 according to the requirements for that particular member as determined by the style of roof4 7#d7 ,measure square back from this plumb cut line the distance ,a-,b of ,fig4 #gd4 7#e7 ,thru point ,a scribe a line ,d-,a parallel to that of the plumb cut line and 7#f7 square this across the edge as at ,d-,e4 7#g7 ,adjust the bevel to pass thru ,e and ,f1 ,fig4 #gd4 7#h7 ,scribe a plumb cut line upon the reverse surface of the stock4 ,illustration3 ,fig4 #gd-;a4 ,fig4 #gd-;b4 ,laying off ,side ,cut of ,jack1 ,hip or ,valley1 any ,polygon ,it will be observed that in one case the square is laid across the edge with #ab on the tongue and #ab on the blade1 ,fig4 #gd-;a4 ,this1 as might be supposed1 is for finding the cheek or side cut for jack1 hip1 or valley where the junction angle is #de4 ,in the case of the octagonal hip1 valley1 or jack #e must be taken upon the blade1 since that is the tangent value of #bb1 #ab as base being taken on the tongue1 ,fig4 #gd-;b4 ,this tangent value will vary1 then1 according to the change in the junction angle4 ,illustration3 ,fig4 #ge-;a4 ,fig4 #ge-;b4 ,securing ,value of ,a-,b of ,fig4 #gd1 ,various ,angles ,the reason for using the tangent and run for this work is indicated by the position of the square on the plan of the roof1 ,fig4 #ge4 ,these figures are for use only when the timbers lie in the plane of the plate1 or any parallel plane4 ,when rafters take on pitch or rise1 however1 the upward projection of the plan of the miter cut1 ,fig4 #gd1 will determine the side cut as just described4 #cf4 ,rafter ,lengths of ,octagonal and other ,polygonal ,hips and ,valleys4--,first ,method3 ,knowing the run of a hip or valley for the polygon under consideration 7#ag for the square1 #ac for the octagon1 etc471 by assuming the respective rises for the various pitches and solving c a b'1 ,fig4 #gf1 data pertaining to hip or valley unit rafter lengths1 such as that for the octagon in ,fig4 #gc1 is obtained4 ,to determine a rafter length1 having available such a table1 multiply the hip or valley length per foot of run of common rafter as given in the table by the run of the common rafter of that roof4 ,reduce to feet4 ,such lengths will be laid off by measurement from the side or cheek cut1 which will have been laid off1 down the top edge of the rafter4 ,lengths of hip or valley tails will be determined in a similar manner from the same table4 ,illustration3 ,fig4 #gf4 ,king-,post ,second ,method3 ,this consists in successive placings of the square1 using the same numbers on tongue and blade as will be used in laying out the plumb cut for this particular roof4 ,the successive advances will be determined1 as in the hip or valley of a square cornered building1 by the number of feet in the run of the common rafter of this roof4 ,a fractional part of a foot in run will be treated in a manner similar to that described for the square cornered building4 ,suitable allowance must be made for the fact that the length of rafter is along the middle of the top edge of the rafter1 when this latter method is used4 ,example3 ,an octagonal roof of pitch has a span of #be4 ,the run of common rafter #ab' #f4 ,taking #ac on the tongue and #f on the blade lay off successively #ab measurements4 ,take #f_/ab or of #ac or #f on the tongue and #f_/ab or of #f or #c on the blade for the fractional foot of run4 #cg4 ,reductions in ,lengths for ,king-,post4--,suitable reduction must be made for king-post1 should there be one1 ,fig4 #gf1 or for rafter thicknesses should no king-post be used1 ,fig4 #ge-;b4 ,where a king-post is used the reduction will be the width of the square out of which the king-post is formed1 the measurement being made square back from the line of the plumb cut1 as in reducing common rafter lengths for ridge piece1 ,fig4 #ef4 ,where an apex is formed as in ,fig4 #ge-;b1 one pair of hips is framed each with a run equal to the octagon's diagonal1 with cuts at the top the same as those of common rafters4 ,the second pair will be similarly framed but the lengths will each be reduced an amount equal to the thickness of the first pair1 measuring straight back from the plumb cut4 ,the third and fourth pairs will be reduced an amount equal to the diagonal thickness of the rafters already framed1 measured straight back from the plumb cut1 ,figs4 #gd-;a and #ge-;b4 ,these rafters will have to have double side cuts as indicated in ,fig4 #ge-;b4 ,it will be noted that these latter rafters meet the others at an angle of #de degrees1 making the framing of the side cut similar to that of a square cornered building except that these are given double cheeks4 #ch4 ,seat and ,end ,cut of ,octagonal and other ,polygonal ,hips and ,valleys4--,the method of procedure in laying out the seat and end cuts of octagonal and other polygonal hips and valleys is similar to that described for the square hip1 except of course1 the numbers to use on the square will differ4 ,these numbers will be determined by the run of the hip for that particular roof1 and by the rise in inches per foot of run of common rafter4 ,in the case of the octagon the numbers will be #ac on the tongue1 and the rise on the blade4 ,the length of tail may be figured by the tables1 if such are available1 or the framing square may be advanced successively as many times as there are feet in the run of the tail or the lookout of the common rafter of that roof1 as heretofore described4 ,the miter cut on the end of a hip rafter and in the crotch of a valley rafter will vary with the tangent value of the plate4 ,for the octagon1 whose tangent is #e the measurement from the end cut and at right angles to it will be #e_/ab that used on the square cornered building4 ,this same ratio will hold for the measurement at the crotch of the valley1 ,fig4 #fe-;b4 #ci4 ,backing ,octagonal and other ,hips4--,the principle involved in determining the amount of backing on hip rafters for the octagon1 as well as that of other polygons1 is similar to that for backing hips for the square cornered building4 ,illustration3 ,fig4 #gg4 ,laying out ,backing for ,octagon ,hip 7#a7 ,place the framing square upon the hip as for making the seat cut of the octagon hip rafter1 ,fig4 #gg4 7#b7 ,referring to ,fig4 #gh it will be seen that the more sides a roof possesses the less will be the backing required4 ,fig4 #gh represents the hips on square1 octagon1 and hexagon as they would appear upon the plan if made to stand straight up at the corners of the plates4 ,the backing in each case is determined by the tangent of the angle whose adjacent side is the rafter thickness1 and whose angle is equivalent to the central angle as ,a1 ,a1 ,a1 ,fig4 #gh4 ,the fact that the hips are inclined and not vertical in their final position in a roof makes no difference in the principle of determining backing because of the fact that our measurements are made in a horizontal plane1 or in the plane of the plate1 ,figs4 #fd and #gg4 ,the ratio of the backing of the octagon or any other polygonal hip to that of the square of equal rise will be proportional to their tangent values4 ,for illustration1 on the square roof we measured along the tongue of the square1 from the top edge of the hip1 ,fig4 #fd1 the thickness of the rafter1 for reasons made plain in ,fig4 #gh4 ,in laying off the octagon backing we should lay off along the tongue in the line of the octagon seat cut1 #e_/ab of the thickness of the rafter4 ,in the case of a #b rafter1 #e_/ab will be set off1 using that side of the square containing graduations in #abths4 7#c7 ,where backing is not desired the rafter will be dropped a plumb distance equal to the plumb distance of the backing of the rafter1 ,fig4 #gg4 ,consult ,fig4 #gc4 ,illustration3 ,fig4 #gh4 ,backing for ,hip of any ,polygon #dj4 ,framing the ,octagonal and other ,polygonal ,jacks4--,plumb cuts of jacks are determined by the rise and run of the common rafter of that particular roof4 ,the seat cuts will be determined by the same numbers4 ,side cuts1 end cuts1 and lengths of jacks are determined as described in ,sections #da and #db4 #da4 ,side ,cut of ,octagonal and other ,polygonal ,jacks4--,first ,method3 ,the method described in ,section #ce is applicable to jacks as well4 ,second ,method3 ,if a table of common rafter lengths per foot of run is available1 the side cut of any polygonal jack may be laid out by placing the framing square across the top of the rafter1 taking the tangent value of the polygon on the tongue1 and the length of common rafter per foot of run on the blade1 and scribing on the blade4 ,the tangent of the polygon forms the opposite side of a triangle in which the adjacent side is the length of common or jack rafter per foot of run4 ,the angle formed being the angle of side cut of jack4 #db4 ,lengths of ,octagonal and other ,polygonal ,jacks4--,the methods of procedure in determining the lengths of jacks for other than square cornered buildings differs from that described for the square cornered building only in the fact that the runs1 hence lengths1 of the jacks must be determined differently4 ,an examination of ,figs4 #fh and #gb will show that the runs1 hence the lengths1 of jacks for the square1 the octagon1 etc41 when the run of common rafter is the same1 will vary inversely as the tangent ratio4 ,for example1 the tangent of the square is #ab when its run of common rafter is #ab1 while that of the octagon is #d4ig or practically #e4 ,the runs1 and1 therefore1 the lengths of octagon jacks will differ one with reference to another1 #ab_/e of those of the jacks for the square building4 ,if an octagon jack rests #bd from the corner1 its run1 and therefore its length1 will be #ab_/e times that of a jack on a square cornered building similarly placed4 ,second ,method3 ,difference in lengths of jacks may be determined by counting the spacings along the plate and dividing the length of common rafter by that number4 #dc4 ,framing by ,means of a ,protractor4--,by means of a protractor used in connection with the columns containing degree measurements1 ,figs4 #di1 #fj1 and #gc1 roof framing may be greatly simplified4 ,to lay off a seat cut1 it is merely necessary to look in the table of hip1 valley1 jack1 or common rafter1 whatever is being framed1 and read the degree of inclination of rafter for the pitch required4 ,the blade of a ,t-bevel is set by means of the protractor to this angle2 or a combination tool may be used1 and the tool applied as in ,fig4 #gi4 ,the plumb cut and seat cut are complementary4 ,since a protractor is made to read in either of two directions1 the plumb cut setting may be got by adding to or subtracting from #ij degrees the angle of inclination of that rafter4 ,with a combination tool1 one setting of the tool serves to lay out both seat and plumb cut4 ,illustration3 ,fig4 #gi4 ,laying off ,seat ,cut with ,fig4 #hj4 ,laying off ,plumb ,cut with ,framing ,tool ,framing ,tool ,the degree of setting for a side or cheek cut1 the gage setting for backing1 and the amount of drop where no backing is used will be found under appropriate columns in the tables referred to above4 ,the manner of applying the combination tool for laying out plumb cut1 seat cut1 side cut and end cut is indicated in ,figs4 #gi1 #hj1 #ha and #hb4 ,the manner of determining the data found in these tables is a matter of trigonometric solution1 no more difficult than that already given1 and omitted for lack of space4 ,such problems may well form a part of the pupil's work in mathematics4 ,for ,example3 ,data for side cuts of jack1 hip and valley for square and octagonal roofs will be found in ,figs4 #di1 #fj1 and #gc4 ,in these tables will be found a column marked ,degree of side cut of hip or valley1 also of jack4 ,to secure the angle of side cut it is only necessary to solve by simple trigonometric formul1 the triangle a b c and then a b c of ,fig4 #fb4 ,the angle ,a is the angle of inclination of hip or jack or valley1 and will be found for each inch of rise in the tables2 the manner of determining the same having been described4 ,the side b is ,a-,b of ,fig4 #gd1 the value of which is also easily determined once the principles of ,fig4 #gd are mastered4 ,with this data the student may find the angle ,a' of ,fig4 #fb as given in the tables4 ,rafter lengths are determined as previously described in connection with framing with the steel square4 ,illustration3 ,fig4 #ha4 ,side ,cut ,illustration3 ,fig4 #hb4 ,end ,cut #dd4 ,translating ,framing ,problems from ,protractor to ,framing ,square and ,vice ,versa4--,frequently it is desirable to translate framing problems from degrees to numbers to be used upon the steel square1 and vice versa4 ,to change from degree framing to steel square framing it is only necessary to remember that the numbers to use on the square must be numbers such that their ratio one to the other shall give a tangent value equal to that given in the ,table of ,natural ,functions1 ,appendix ,,ii1 for the angle under consideration4 ,example3 ,given3 ,angle of inclination of common rafter or of roof #cj degrees4 ,find the numbers to take on the square to frame seat and plumb cuts4 ,solution3 ,tan #cj 4#egg 7by ,table1 ,appendix ,,ii74 ,by agreement1 run of common rafter takes #ab on one member of the square for constant of run4 ,therefore1 rise must be #f4ic1 or #faa_/ab1 must be taken on the other member of the square4 7,the base of the table is #a so that for #ab run we must have #ab x 4#eggd47 ,in a similar manner the number to be taken on the blade1 when the inclination of any other common or jack rafter is given1 may be determined4 ,in the case of the hip or valley inclination1 however1 it must be remembered that #ag is to be taken on the tongue for the run in the square cornered house1 with #ac in the octagon1 which will necessitate multiplying the tangent value of the angle of inclination by #ag and #ac respectively to find the number to take on the blade when one or the other of these is taken on the tongue4 ,example3 ,given3 ,side cut of jack rafter1 or hip or valley #ch degrees4 ,find the numbers to use on the framing square to lay off this same angle4 ,solution3 ,tan #ch 4#ghac ,by agreement1 we shall take #ab on the tongue4 ,the number to be taken on the blade must be1 therefore1 #ab x 4#ghac #i 7,in the case of the side cut1 any number other than #ab might have been assumed on the tongue47 ,example3 ,given3 ,a hip rafter on a square roof which is framed with #ag on the tongue and #h on the blade4 ,to find the angle of inclination of the hip4 ,solution3 #h_/ag 4#dgjf ,the angle whose tan 4#dgjf is #be #ai #de4 ,framing an ,octagon ,bay4--,whatever may be one's opinion as to the propriety of the octagon bay architecturally1 its very common use makes it obligatory upon the builder to know how to properly frame it4 ,referring to ,figs4 #gb and #hc-;a it will be seen that the octagon bay is but a portion of a full octagon set up against the side of a house4 ,from this it follows that the framing of the plate1 sills1 the laying out of plumb and seat cuts1 and side or cheek cuts of jacks that rest against hips1 etc41 will be according to principles discussed in previous sections of the text4 ,the chief thing which needs explanation is the matter of laying out side cuts for hips and jacks which are to rest against the side of the building4 ,illustration3 ,fig4 #hc-;a4 ,fig4 #hc-;b4 ,framing ,rafters of ,octagon ,bay ,consider the bay as cut along the line ,i-,j1 ,fig4 #hc-;a4 ,to frame the hip nearest the building3 7#a7 ,determine the angle which would give the side or cheek cut of the rafter involved when the rafter has no pitch1 that is1 when it lies in the plane of the plate4 ,fig4 #hc-;a indicates the manner of determining this angle1 which will be found to be #bb4 ,if we wish to use a framing square instead of a framing tool we may readily translate the #bb4 ,we shall find that #ab taken on the tongue of the square will require #d4ig or #e on the blade4 7#b7 ,place the square as in ,fig4 #hc-;b and scribe along the tongue4 ,remember that this gives the miter when the rafter lies in the plane of the plate4 ,this would give the cut to be used where ceiling joist or floor joist of octagon bay are run parallel with the rafters4 ,on small bays1 joists are seldom run thus but are run parallel with other joists of the house4 ,no special directions are needed for setting the protractor1 or the combination tool1 the manner of setting and placing is so obvious4 7#c7 ,once having this miter when the rafter lies in the plane of the plate1 proceed as directed in ,sec4 #ce1 7#b7 et seq4 ,with one such rafter framed the mates may be laid out by transposition4 ,to frame the remaining hips of ,fig4 #hc-;a proceed in a manner similar to that just described4 ,in this case the angle made by the hip when it lies in the plane of the plate and the side of the house will be #fg degrees4 ,why8 ,fig4 #hd-;a4 ,the framing tool or protractor and ,t-bevel provide the simplest means of framing4 ,if one wishes to use the framing square he will find that by using the tangent value of #fg he gets #bh4ig to take on the blade when #ab is taken on the tongue4 ,this he cannot find1 of course4 ,he may either take other smaller numbers having the same ratio1 or he might better take the cotangent value of #fg4 ,cot of an angle of a right triangle is the ratio of the adjacent side to the opposite side4 ,solution3 ,angle ,a #fg1 ,fig4 #hd-;a4 ,cot #fg 4#dad when b #a4 ,when b #ab cot ,a #d4ig or #e4 ,illustration3 ,fig4 #hd-;a4 ,fig4 #hd-;b4 ,framing ,octagon ,hip ,intercepted at #fg 7#a7 ,place the square as in ,fig4 #hd-;b and scribe along the blade4 ,by this time the student should have observed that the tangent value of any angle increases as the cotangent value of the angle decreases and vice versa4 ,note that when a cotangent value is used1 #ab is still taken on the tongue and the same number as for the tangent value of that number of degrees is taken on the blade1 but that the scribing is done along the blade and not along the tongue as is the case when tangent values are used4 7#b7 ,proceed from this point as in ,sec4 #ce1 7#b7 et seq4 ,to frame the jack intercepted by the side of the house4 ,fig4 #he-;a2 7#a7 ,proceed to find the miter for the intercepted jack when it lies in the plane of the plate4 ,it is #de degrees4 ,tan #de degrees #a when b #a4 ,tan #de degrees #ab when b #ab4 7#b7 ,place the square as in ,fig4 #he-;b and scribe along the tongue4 7#c7 ,from this on1 continue as in ,sec4 #ce1 7#b7 et seq4 ,illustration3 ,fig4 #he-;a4 ,fig4 #he-;b4 ,framing an ,intercepted ,jack ,from these solutions the student should be able to generalize sufficiently to care for rafters of any angle of intersection with the side of a building1 and of any pitch4 ,the use of the framing tool or protractor and ,t-square is strongly recommended upon such work as this4 ,nothing but tradition prevents its more general use in carpentry4 ,having determined the lay-out for the side cut of these rafters1 the length of each must next be determined4 ,to determine the length of hip or jack intercepted by the side of the house and the plate3 7#a7 ,determine the run of the intercepted part of the common or jack rafter1 as b1 ,fig4 #hc-;a4 7#b7 ,by means of the table of rafter lengths per foot of run compute the length of rafter under consideration4 ,in determining the run of an intercepted part it is necessary to have data concerning the size of the octagon and the amount cut off by the building4 ,the lines ,e-,d and ,f-,d1 ,fig4 #hc-;a1 when dimensioned1 give this data4 ,the actual lengths of the various hips1 jacks1 etc41 in practical carpentry1 upon small bays1 are usually determined by actual measurement from the plate or sill to the proper point of intersection on the building as indicated by a stick or extension rule held at the proper angle4 ,sometimes a large scale drawing is made and the runs taken from this4 ,upon large work where accuracy is necessary and measurements impossible1 trigonometric solutions should be used4 ,to determine the length of the intercepted hip rafter over c of triangle a b c ,fig4 #hc-;a1 the value of b must first be secured4 ,this value represents common rafter run for hip rafter rising over side c1 and run of intercepted common rafter rising over side b4 ,length of intercepted hip rising over side c b x unit length of hip4 7,table of lengths of octagon hips in terms of run of common rafter1 ,fig4 #gc47 ,length of intercepted common rafter or jack nearest house b x unit length of common rafter4 7,table of lengths of common rafter in terms of run of common rafter1 ,fig4 #di47 ,it must be remembered that these are theoretic lengths measured down the middle of the top edge of the rafters4 ,in framing1 suitable reductions must be made4 ,for example1 in framing the intercepted common rafter nearest the building1 the rafter must be set over one-half its thickness that it may be nailed against the side of the building4 ,the allowance necessary in order to do this may be secured by measuring the length from the long point instead of the middle of the side or cheek cut4 ,suitable reduction1 too1 must be made for the hip thickness in this case one-half the diagonal across the top edge of the hip1 laid off at an angle of #bb1 or #e and #ab on the square4 ,this amount will be laid off straight back from the plumb cut1 ,sec4 #ce1 7#b7 et seq4 ,length of hip must be measured along the middle of the top of the rafter4 #df4 ,framing a ,roof of ,one ,pitch to ,another of ,different ,pitch4--,occasionally one must frame a roof of one pitch against a roof of another pitch4 ,to determine the cut1 if the combination tool is to be used1 merely find the difference in degrees of the angles of inclination of the two rafters1 and apply the tool as indicated in the tables for making any other plumb cut1 ,figs4 #di1 #fj and #gc4 ,the seat cut will be determined by the rise and run of the shed rafter in the usual manner4 ,illustration3 ,fig4 #hf4 ,laying off ,cut of ,shed ,rafter ,where the framing square is to be used1 lay the square as in framing a plumb cut on the shed rafter1 as at ,a1 ,fig4 #hf1 taking on the tongue1 the run1 and on the blade the rise of the shed rafter4 ,next lay a second square as at ,b1 ,fig4 #hf1 taking on the blade the rise and on the tongue the run of the rafter of the main roof1 using the blade of ,a as a reference edge4 ,blade of ,b gives the cut4 #dg4 ,framing a ,roof of ,uneven ,pitch4--,not infrequently a roof must be framed in which several pitches are involved4 ,all of the principles necessary for framing such a roof have been developed4 ,it remains for the student to make the applications to uneven pitches4 ,it is advisable to prepare a framing plan as shown in ,fig4 #hg4 ,from such a plan it may be seen that the seat and plumb cuts of common and jack rafters are determined in the usual manner1 being different upon the different pitches1 of course1 but determined as for any given pitch4 ,lengths of common rafters will be determined for any pitch by the tables already made use of1 the run being known or determined4 ,in selecting the numbers to use on the tongue and the blade of the square1 in laying out seat and plumb cuts of hip or valley rafters of intersecting roofs of different pitches1 any numbers may be used providing they have a ratio equal to that of the run and rise of the rafter being framed4 ,since the angle of intersection changes with every change of pitch1 it is hardly worth while developing a constant to be used on the tongue in framing hip and valley rafters on irregular pitches4 ,side or cheek cuts for valley1 hip or jacks are determined according to principles developed in ,sec4 #ce4 ,illustration3 ,fig4 #hg4 ,plan of ,uneven ,pitches ,the backing of hips on roofs of uneven pitches1 while the amount to be removed on each side of the hip will vary1 is determined by the principles developed in ,sec4 #ci4 ,the amount to be removed from each side must be separately determined according to the angle the hip makes with the plate4 ,lengths of hip and valley jacks are determined as in ,sec4 #db4 ,lengths of cripple jacks will not be of uniform length1 as in even pitched roofs4 ,the runs for such jacks may be obtained with sufficient accuracy by measurements taken from an accurately made scale drawing4 ,the following example will make clear the method of attack where it is desired to develop a constant for hip or valley in terms of the common rafter of one of the pitches4 ,example3 ,given3 ,main roof1 ,rise #h'1 ,run #ab' pitch4 ,minor roof1 ,rise #e'1 ,run #f' #e_/ab pitch4 7#a7 ,find the run of valley rafter over c1 ,fig4 #hh-;a1 in terms of the run of the common rafter over b4 ,solution3 c a b 7#g7 #f 7a3#ab33e3h1 whence a #g7 c #i4fj' ,expressing this run of valley in terms of #ab of run of common rafter over b4 #i4fj'3f'33x3#ab4 x #ai4bj4 7,check this value by scale drawing47 ,length of valley rafter1 then1 is found by taking #ai4bj on the tongue with #aj 7#e_/f of #ab7 on the blade1 advancing the setting as many times as there are feet in the run of the common rafter over b4 ,illustration3 ,fig4 #hh-;a4 ,uneven ,pitches ,the numbers just given will give the plumb cut and the seat cut of this valley rafter4 7#b7 ,find the side cut of the valley rafter when it rests against the ridge of the minor roof4 ,solution3 ,the side cut of the valley when allowed to rest in the plane of the plate angle ,b1 ,fig4 #hh-;a1 whose tangent b_/a #f_/g 7 #ab_/ae 4#hjj #ch #dj'7 ,therefore1 take #g on the blade 7always the run of intercepted common rafter of major roof71 and #f on the tongue 7always the run of the common rafter of the minor roof72 scribe on the blade4 ,for side cut of valley rafter when it is to be fitted to a ridge of the major roof1 the lay-out when in the plane of the plate is obtained by means of these same numbers1 but the scribing is done on the tongue4 ,this lay-out in either case is for the rafter when lying in the plane of the plate4 ,having secured this1 proceed as in ,sec4 #ce1 7#b74 ,side cuts of jacks for the minor roof are determined by the length of the ridge over a1 ,fig4 #hh-;a1 and the length of the rafter over b4 ,but the length of the ridge over a the run of the intercepted common rafter of the major roof1 #g' here4 ,a general rule may be derived1 therefore3 ,for the side cut of a jack on a minor roof take on the blade of the square the run of the intercepted common rafter of the major roof 7inches for feet71 and on the tongue take the length of rafter of the minor roof2 scribe on the tongue1 ,fig4 #hh-;b4 ,for the side cut of jacks on a major roof1 take on the tongue of the square the run of the common rafter of the minor roof1 and on the blade the length of the intercepted common rafter of the major roof2 scribe on the blade1 ,fig4 #hh-;c4 ,illustration3 ,fig4 #hh-;b4 ,fig4 #hh-;c4 ,side ,cuts of ,jacks for ,uneven ,pitches ,a new problem arises in connection with uneven or irregular pitches1 the problem of making the projecting cornice member one with another4 ,manifestly1 if one part of a roof is steeper than another and the plate the same height all around the building1 the cornice cannot be made to meet in the same plane4 ,this difficulty is overcome by raising the plate of the steeper roof an amount equal to the difference in the rises of the two pitches for a run equal to that of the projecting cornice4 ,for example1 in a half-pitch the rise would be #bd for a run of #bd in the cornice4 ,in a quarter-pitch rise for a #bd run of cornice would be #ab1 a difference in rises of #ab4 ,the plate of the steeper roof must be raised that much higher than that for the lower pitch4 ,illustration3 ,fig4 #hi4 ,deck ,frame #dh4 ,decks2 ,chimney ,openings4--,decks are sometimes used in roof framing to prevent some part of the roof from rising too high above the remainder4 ,such decks are framed of joist stock spiked together with butt joints4 ,upon the top of such deck joists are placed feathering strips so sawed as to give the deck a slight fall in each direction1 two to three inches in eight to ten feet4 ,upon these feathering strips flooring is laid4 ,the deck is framed1 raised and braced1 being held up by studding placed under each corner4 ,next1 the hip rafters are placed1 then the flooring on the deck1 and finally the common and jack rafters4 ,should common rafters be placed before the deck flooring1 the joists must be braced to withstand the pressure against their sides4 ,on large decks the outer deck frame is doubled4 ,chimney openings are framed as shown in ,fig4 #hi4 ,,chapter ,v ,exterior ,covering and ,finish #di4 ,sheathing or ,sheeting4--,after the frame work of a building is erected and the openings made in the frame for windows and doors1 the sheeting is to be placed4 ,sheeting is placed either horizontally across the studs or diagonally1 sometimes both ways1 depending upon the specifications of the architect4 ,the diagonal is somewhat stronger but is more expensive4 ,the horizontal is satisfactory upon ordinary frame dwellings1 especially where the building is braced at the corners by studs cut in diagonally1 or by sheeting placed diagonally at the corners as in ,fig4 #ij4 ,such sheeting should be matched and well nailed with two #h;d nails to each stud4 ,building paper should be placed upon the sheeting to further protect the interior from cold4 ,illustration3 ,fig4 #ij4 ,sheathing ,roof sheeting for shingle roofs may best be of unmatched boards spaced about #b apart4 ,for slate1 matched stock should be used and this covered with a tar or asphalt paper4 ,illustration3 ,fig4 #ia4 ,setting ,t-bevel for ,roof ,boards ,in making the face cut on roof boards for hips or valleys the framing tool or the ,t-bevel may be made use of1 being set to the complement of the angle used in making the side or cheek cut on jack rafters4 ,the complement angle in this case equals #ij less the angle of the side cut of jack4 ,or1 if the framing square is to be used1 the same numbers used in making the side cut of the jack will be used in laying out the face cut of roof boards1 with the scribing being done along the tongue instead of along the blade as in the case of the side cut4 ,a second ,t-bevel may be set as in ,fig4 #ia1 the beam being placed across the edge of the jack and at right angles to it1 with the blade adjusted to the cheek or sawed surface of the jack which is to fit against hip or valley rafter4 ,a framing tool might be used4 ,carpenters more frequently1 however1 get the angles for sawing roof boards by laying the board to be cut out over the hip or valley rafter1 then sawing along the side the rafter as in ,fig4 #ib4 ,in warm climates1 weather boarding is often applied directly to the studs1 no sheeting being used2 the frame being strongly braced at the corners4 #ej4 ,scaffolding4--,cornice is placed after sheeting4 ,to do this advantageously it is necessary to erect scaffolding or staging4 ,fig4 #ic illustrates a common type4 ,stock #b #d is used for the uprights1 and #a #f for the horizontal members and braces or stays4 ,planks are placed upon these horizontals as shown4 ,fig4 #id illustrates a substitute for staging1 a scaffold bracket upon which planks are laid4 ,illustration3 ,fig4 #ib4 ,sawing ,roof ,boards ,illustration3 ,fig4 #ic4 ,scaffolding ,illustration3 ,fig4 #id4 ,scaffold ,bracket #ea4 ,cornice4--,cornices are generally classified as open or skeleton1 and box1 ,figs4 #ie and #if4 ,each of these types will be found constructed in almost endless variety of forms4 ,the illustrations shown will serve the purposes of this text4 ,the student should familiarize himself with the various common forms1 details of which may be got from any good1 modern book on building details4 ,illustration3 ,fig4 #ie4 ,skeleton ,cornice ,illustration3 ,fig4 #if4 ,box ,cornice ,in making the various cuts on cornice work1 a miter-box must be available for mouldings4 ,the old type of wood miter box1 with the various necessary cuts laid out in its sides is satisfactory4 ,some experimenting will be necessary upon the part of the beginner to determine the manner of placing the moulding in the box to give the correct cut4 ,the cuts for the plancher1 which rests in the planes of a hipped roof and which must be membered around a corner are determined in a manner similar to that described for roof boards1 ,sec4 #di1 from the cuts of the jack rafter cheeks4 ,illustration3 ,fig4 #ig;a4 ,skeleton ,cornice ,illustration3 ,fig4 #ig-;b4 ,box ,cornice4 ,fig4 #ig illustrates the manner of framing in the lookouts on' gables where a skeleton cornice is used4 ,also there is illustrated the manner of placing lookouts in gables for a box cornice4 ,unless the cornice is quite wide1 these blocks are merely fastened to the underside of the roof boards at intervals of #c or #d feet4 ,the depth of these blocks will depend upon the manner of framing the tail ends of the rafters4 ,metallic gutters made to assume the form of the crown mould1 no wood crown mould being used1 will be found in common use upon ordinary house construction4 ,a fall of inch to every #aj feet is usually given gutters4 #eb4 ,raked ,mouldings4--,in all cases where a moulding resting in one plane1 as crown or bed moulding at the eaves1 is to be membered with moulding swung up out of that plane1 as up a gable1 one of two things must be done to make the surfaces of the mouldings match or member properly at the joint3 7#a7 ,the moulding at the eave may have its top edge tipped forward until its top edge lies in the same plane as the top edge of the corresponding gable moulding2 7#b7 a moulding with a new face may be worked which will member with the eaves moulding when their reverse surfaces are fitted to the fascia or1 in case of bed moulding1 to the frieze4 ,illustration3 ,fig4 #ih4 ,laying out ,gable or ,raked ,moulding ,to member by means of the second method proceed as follows3 7#a7 ,make a full sized drawing of a cross-section of the moulding1 ,fig4 #ih4 7#b7 ,draw a number of lines thru the more important reference points of the moulding at an angle equal to the pitch of the gable4 7#c7 ,draw horizontal lines thru the points of reference and erect a perpendicular thru these passing thru the back of the mould as ,a-,b4 7#d7 ,lay off a line ,c-,d1 ,fig4 #ih1 perpendicular to the oblique lines4 7#e7 ,using the lines ,a-,b and ,c-,d as reference lines1 transfer the distances of the various points on the eaves moulding1 measured horizontally from ,a-,b1 to pitch lines measured obliquely4 ,a curve traced thru these points will give the shape of the moulding required for the gable4 ,since this moulding would1 in all probability1 have to be worked up especially for any particular job1 this practice is not followed except upon large or important work4 ,cornices are usually designed so as to avoid such work4 ,illustration3 ,fig4 #ii4 ,miter ,box for ,raked ,gable ,moulding ,cut at ,eaves ,illustration3 ,fig4 #ajj4 ,miter ,box for ,plumb ,cut of ,gable ,mouldings ,figs4 #ii and #ajj illustrate two miter-boxes constructed for use in cutting rake mouldings in gables4 ,in making the miter cuts on mouldings of the eaves1 the horizontal members1 no special box is needed4 ,the moulding will be set on the far side of the box1 upside down4 ,the box will have the side cuts perpendicular to the top edge and the angles across the top edges will be determined by the miter of the plate1 sill1 or corner of the building4 ,on a square cornered building this miter will be one of #de1 #ab and #ab being taken on the square4 ,two cuts of each kind1 but reversed1 are made in each box so that the moulding for each side of each gable may be readily cut4 ,on the octagonal building #e and #ab would be used in laying out the miter1 with scribing done along the #e member of the square4 ,for the miter cuts of the rake or gable member1 special boxes would best be constructed4 ,for the cut of the gable member where it joins the eave moulding3 7#a7 ,lay off across the top of the miter-box1 right and left1 the miter of the plate1 sill1 or corner of the building4 7#b7 ,down the sides of the box lay off the slanting lines as shown in ,fig4 #ii1 at angles determined by the plumb cut of the common rafter4 7#c7 ,lay the moulding in the box as indicated by the cross-section1 ,fig4 #ii1 being careful to keep the backs of the mouldings adjusted to the side and bottom of the box4 ,a good plan is to drive a nail or two in the bottom of the box against which the moulding may be made to rest1 once the proper position is determined by trial4 ,for the plumb cut of the gable moulding1 7#a7 lay off lines across the edges of the box as in ,fig4 #ajj1 using on the framing square the numbers which give the plumb cut of the common rafter4 ,lay off a right and a left cut as shown4 7#b7 ,square these lines down the sides of the box and saw4 7#c7 ,the moulding will be placed in the box as shown in the cross-section view of ,fig4 #ajj1 especial care being taken to have the backs of the mouldings adjusted to the back of the box4 ,manifestly1 one box may contain all these cuts to advantage instead of having three boxes4 ,these cuts1 ,figs4 #ii and #ajj1 serve in cutting the miters on ends of the gable fascia4 ,a little consideration will make clear the remaining cuts upon ordinary cornice work4 ,in splicing mouldings1 corner boards1 etc41 a mitered joint is best and should be made so as to shed water from the joint1 ,fig4 #aja4 #ec4 ,shingling4--,the reason for placing cornice before base or window frames1 etc41 is to allow the workmen to work inside should inclement weather overtake building operations at any time4 ,shingling1 therefore1 will follow cornice work4 ,illustration3 ,fig4 #aja4 ,spliced ,comer ,boards and ,moulding ,the amount of shingle to be exposed to the weather will depend in general upon the pitch of the roof4 ,in no case should this exposure exceed #e inches4 ,the shingle most used is #af inches long1 and each shingle should lap two courses beneath it4 ,the usual amount of lay is from #d to #d1 by quarters4 ,when nearing the ridge or comb of a roof in shingling1 the dimensions used on the main body of the roof should be increased or decreased so as to make the final layer show under the comb or ridge or saddle boards properly4 ,the worker should begin such calculations when within about four or five feet of the ridge so that changes of exposure of the different layers may not be noticeable and so that the line of shingle butts may be kept parallel with the ridge4 ,illustration3 ,fig4 #ajb4 ,beginning ,course ,the first layer of shingles should be a double one with joints properly broken1 and with the butts projecting over the crown moulding about #a to #b4 ,lay the shingles at the gables first1 then at intervals of about ten feet4 ,stretch a chalk line between these fastening it to the butts by shingle nails driven into the butts1 ,fig4 #ajb4 ,the remaining courses may be laid by means of a straight-edge or by means of a chalk line4 ,both practices have ardent advocates4 ,where a straight-edge is used1 it is usually a piece of lap siding or clapboard1 and is held in place by being lightly tacked4 ,illustration3 ,fig4 #ajc4 ,shingling4 ,toe ,hold ,in using the chalk line a man for each end is required4 ,the line is chalked and snapped for three courses at a time4 ,the mechanic1 after a little practice1 is able to keep the butts of the shingles straight and to sight them so that they shall follow the chalk line mark4 ,on long courses a third person may be utilized in chalking and in laying shingles4 ,in chalking1 this person holds the line to the roof as sighted by an end man and the snapping is done on each half of the line4 ,the chalking of a line so as to conserve the chalk is one of the tricks of the trade which must be mastered early4 ,it consists in rotating the chalk about its hemispherical axis while being worked backward and forward along the line1 the line being held between the chalk and the ball of the thumb4 ,otherwise the line would soon sever the chalk4 ,illustration3 ,fig4 #ajd4 ,shingling4 ,toe ,holds ,cut nails should be used in preference to wire nails because of their greater rust-resisting quality4 ,dry shingles should not be laid tight together1 inch between is not unusual with dry shingles4 ,it is best to split shingles over #aj inches wide before laying them4 ,each shingle should have at least two nails1 the average is two nails for every four to six inches of shingle4 ,scaffolding for roof work1 or toe hold1 is usually constructed by nailing shingles to #b #d as shown in ,figs4 #ajc and #ajd4 ,other forms are equally common4 ,apparently the holes left by the nails used to fasten the toe hold to the roof would cause a leak in the roof4 ,to avoid any such danger1 tho such danger is slight because of the swelling of the wood fiber upon the application of moisture1 the shingles having such holes are driven down the roof slightly by striking their surfaces a glancing stroke4 #ed4 ,shingling ,hips and ,valleys2 ,flashing2 ,saddle or ,comb ,boards4--,hip and valley shingles are usually sawed to shape before being taken to the roof1 the face cut being the same as that used across the face of the roof boards and plancher members intersecting about a corner of a hipped roof where plancher lies in the plane of the roof4 ,the cut across the edge of such shingles is made square to the face4 ,illustration3 ,fig4 #aje4 ,shingle ,tins ,illustration3 ,fig4 #ajf4 ,valley ,of the many ways of protecting the intersection of hip shingles when in place upon a roof1 the simplest is that of employing tin shingles4 ,such shingles should be of sufficient length to allow the corners to be turned under as shown in ,fig4 #aje1 and still extend far enough under the next course of shingles to permit the nails holding the tins to be covered4 ,it is not good practice to nail thru these tins after the roof has been covered1 that is1 to place these tins after the roof has been shingled because the action of the weather lifts the nails when exposed thus4 ,valleys are covered with a strip of metal to a width of #bj inches4 ,upon steep roofs and short valleys this width may be reduced to #af inches4 ,space must be left between the edges of valley shingles as shown in ,figs4 #ajf and #ajg4 ,the amount will depend upon the length of the valley and the steepness of the roof4 ,for a pitch with a length of twelve to fourteen feet of valley1 the space at the top of the valley may well be #a inch to each side of the valley center line1 widening gradually toward the lower end to #b inches to each side4 ,chalk lines snapped upon the tin or other metal forming the valley indicate the location of shingle edges4 ,nails in valley shingles should be kept well back from the valley edge of the shingles4 ,illustration3 ,fig4 #ajg4 ,shingling ,valley ,flashing consists in placing tin shingles or other material about the members making up a joint so that the joint shall turn water4 ,counterflashing consists in placing a double layer of tins in such a way as to doubly insure turning water from a joint4 ,fig4 #ajh is an illustration of flashing where shingles meet lap siding4 ,shingle tins are forced under the siding on one side and either under or over the shingles1 several inches of lap being allowed all about4 ,fig4 #aji illustrates a counterflashed chimney4 ,a layer of tins is placed as in flashing against siding except their top edges are not inserted4 ,over these tins a second layer is placed as shown1 the top edges being inserted between the layers of brick1 the mortar being raked out so that this can be done4 ,these turned edges are held in place by the insertion of a wedging nail or tack1 after which the cracks are filled with cement1 or better1 an elastic roofing composition4 ,tins should be carried high enough to prevent drifted snow from entering2 #b or #c inches at the narrowest place4 ,illustration3 ,fig4 #ajh4 ,flashing ,fig4 #aji4 ,flashed and ,counter-flashed ,saddle or comb boards are of various forms4 ,they are used to give the ridge a finished appearance and to turn any water which might happen to strike thereon2 also to hold the last course of shingles in place4 ,a simple form is obtained by creasing to the appropriate angle a strip of tin eight inches in width4 ,place this on the ridge and nail its edges at intervals of #c or #d inches4 ,where boards are used1 one board should overlap the other and extend a half inch beyond to turn water from the joint so made4 ,galvanized ridge rolls may be purchased in stock styles4 #ee4 ,finishing ,exterior ,walls4--,with the roof completed1 side walls are next covered except where porches are to be attached4 ,fig4 #aaj illustrates the manner of constructing an exterior wall having a water table and lap siding1 also the relation of the various parts of an exterior wall4 ,illustration3 ,fig4 #aaj-;b4 ,exterior ,wall ,detail ,a belt course is sometimes used between the first and second stories of a building4 ,such a course is often constructed like the water table4 ,like the water table or base1 this belt course is furred out in order to throw the course into greater relief4 ,in case this furring is not done1 the lower edge of the belt board must be rabbeted to receive the top edge of the siding4 ,frieze boards1 too1 are frequently furred instead of being rabbeted4 ,more elaborate belt courses are common4 ,building paper should be stripped about the openings for doors and windows before the frames are set1 to insure warmth2 also about corner boards and cornice4 ,corner boards and casing edges should be very slightly beveled so that the siding may take a slight squeeze as it is placed4 ,care in setting frames and in making casing edges true will insure a saving of time in placing siding4 #ef4 ,setting ,window and ,door ,frames4--,two men usually work together in setting frames1 as in fact they do on much other carpentry work4 ,in setting door frames on outer walls 7#a7 the rough floor1 etc41 must be cut away so that the top of the sill may rest on a level with finished floor when that is in place4 7#b7 ,when this is done the door sill is carefully leveled1 ,fig4 #aaa1 and shingle points inserted under the sill where needed to give solidity and support4 7#c7 ,the casing is given a nail close to the sill at each side of the frame and 7#d7 the sides of the jambs1 are plumbed and the casings finish nailed4 ,if the work is carefully done the frame should be square4 ,illustration3 ,fig4 #aaa4 ,leveling ,door ,sill ,where heads of several windows are a given distance from the floor1 a stiff stick may be cut this length and used in placing windows in position for height4 ,the window sills will be leveled as are door sills2 the jambs are plumbed1 ,fig4 #aab1 and casings nailed at intervals of about a foot4 ,illustration3 ,fig4 #aab4 ,plumbing ,frame ,illustration3 ,fig4 #aac4 ,using ,siding ,stick #eg4 ,siding4 ,preparatory to siding1 a siding stick should be made4 ,such a stick is made by planing parallel edges upon a piece of ,y inch stock about #a inch in width4 ,upon this stick marks will be made which will indicate the spacing of the siding2 these marks being transferred to corner boards and casing edges1 ,fig4 #aac4 ,to lay off this stick a given space is taken1 water table drip cap to the lower edge of a window sill for example4 7#a7 ,this space may be transcribed upon the stick easiest by setting the stick upon the drip cap and against the casing edge1 marking under the sill upon the stick4 7#b7 ,this space is stepped off by means of a pair of dividers set to the amount of exposure desired4 ,exposures will run from #d to #d inches on ordinary lap or bevel siding4 7#c7 ,should there be a remainder1 and there almost always is1 the exposure must be increased or decreased1 whichever is necessary1 an amount sufficient to give an equal or even number of divisions4 ,in practice this amount is found by stepping off as suggested and then making necessary adjustments by guess and again stepping4 ,this is continued until the desired result is attained4 ,the difference is thus divided equally over the whole space instead of over the last courses as in shingling4 ,illustration3 ,fig4 #aad4 ,marking ,length of ,siding ,fig4 #aae4 ,using ,siding ,hook ,in a similar manner a stick1 or another space of the same stick is laid off and stepped for the space between the bottom of the window sill and the top of the drip cap above the head casing of the window1 etc4 ,on long lateral spaces this stick will be used to keep the lower edges of the boards in position between the casings1 by transferring its marks to the building paper1 stepping down from one of these marks with a pair of dividers to the lower edge of the siding board being placed4 7#d7 ,a bunch of siding boards should have one end of each sawed square across the face1 but sawed under on the back side slightly so as to insure a fit on the surface4 7#e7 ,one end is next fitted1 with block plane if necessary1 after which 7#f7 the length is marked by turning the board upside down and marking on the lower edge of the board1 which is uppermost1 with a knife1 ,fig4 #aad4 ,another way to mark length is indicated in ,fig4 #aae4 ,this tool is called a siding hook or tool and this method possesses the advantage of caring for any lack of squareness in the frame or trim4 ,in nailing1 care must be taken to place the nail so that it shall pass thru both boards where lapped4 ,under windows it will be necessary to trim off part of the upper edges of the siding boards4 ,saw kerfs at either side of the part to be cut1 and a sharp1 deep knife scoring along a straight-edge should be used to outline the part to be removed4 ,to determine the amount to be removed1 set the dividers to the amount of spacing used for the boards in the space under the window1 plus the depth of rabbet1 or groove in the under side of the window sill into which the upper edge of the siding board must fit4 ,set off this amount on the siding board from the butt or under edge at each end of proposed cut1 and connect with straight-edge2 scoring with knife4 ,illustration3 ,fig4 #aaf4 ,siding ,circular ,tower ,occasionally the carpenter is called upon to side a circular tower or rounded corner of a building4 ,that the lower edge of each board may rest in a horizontal plane it will be necessary to shape that edge before applying the board to the side of the building4 ,to determine the amount of curvature to give such an edge proceed as follows3 7#a7 ,plot a curve to represent the plan of the tower1 ,fig4 #aaf4 ,draw this upon a scale sufficiently large and make use of accuracy such as will insure a result equal to the requirements of the occasion4 7#b7 ,draw the line ,a-,b of indefinite length4 7#c7 ,place a section of a clapboard in the position it will have on the sheeting1 as at abc1 ,fig4 #aaf1 and 7#d7 extend a line along the face surface to meet ,a-,b4 7#e7 ,with a radius equal to ,b-,c describe an arc with ,b as a center which shall cut the siding board as shown1 taking an equal amount off the edge at each end4 ,occasionally it becomes necessary to fit a casing against a sided wall4 ,this casing is scribed as indicated in ,fig4 #aag1 a pair of sharp dividers being made to follow the contour of the wall with one point while the other marks or scribes the casing4 ,a saw will be used to cut to these lines1 sawing under slightly to insure a fit at the face4 ,illustration3 ,fig4 #aag4 ,scribing against ,irregular ,surface ,,chapter ,,vi ,interior ,finish #eh4 ,lathing2 ,grounds4--,lathing is usually considered a part of the plasterer's work but the carpenter is expected to prepare the grounds and place the necessary furrings4 ,the success of the plasterer depends in no small degree upon the way the carpenter does this work4 ,if corners are not firmly constructed1 cracks will be sure to appear in the plastering4 ,in lathing1 joints must be broken upon different studding every dozen lath1 and joints are not to be allowed about a door or window opening where their presence would weaken the wall2 such as short lath nailed at one end only4 ,neither are lath to be placed at right angles to the usual run of lath on the wall because uneven shrinkage would cause the plaster to crack4 ,that the plasterer may make walls true and of uniform thickness about door and window openings and along the floor1 grounds are placed as in ,fig4 #aah4 ,such grounds are of stock if #ac_/af #a or #b nailed firmly to the studding4 ,grounds for base should be placed so that the wall may be lathed and plastered entirely to the floor that cold and vermin may be kept out4 ,illustration3 ,fig4 #aah4 ,plaster ,grounds ,illustration3 ,fig4 #aai4 ,detail of ,partition ,wall ,for grounds on external corners in a room1 metallic corners especially manufactured for this purpose are recommended4 ,the beginner will be surprised at the numberless places requiring attention in preparing for the plasterer4 ,he should visualize every corner and angle as he thinks the plasterer or lather must have it4 #ei4 ,interior ,walls4--,fig4 #aai illustrates the construction of a corner of an interior wall which is to be recommended highly for strength4 ,all door studding are to be doubled for strength1 also window openings of unusual size4 ,interior door jambs are not usually placed until after plastering has been done4 ,thresholds are no longer used with interior openings where both rooms are to be heated4 ,joists doubled to support partitions should be spread sufficiently to allow furnace pipes to enter1 and still provide bearing for partition studs4 ,badly crooked studs in a partition wall may be straightened by sawing a kerf on the hollow side1 almost thru1 and wedging with a shingle point4 ,a cleat nailed to the side of the stud after wedging will give the original strength4 ,straight studs should be selected for use about openings4 ,in setting studs for interior door jambs where studs are to be doubled on the inside1 add to the width of door enough to make the outer edges of the casings center on studs1 and double inside these1 as in figuring openings between studs for outside door jambs4 ,make allowance for the extra thickness of stud on each side4 ,for height of opening1 where no threshold is to be used1 add #b to the height of the door4 ,remember that enough more must be cut from vertical studs to allow for thickness of header4 #fj4 ,stair ,building2 ,porch ,steps4--,stair building is an art in itself and as such belongs to millwork rather than to carpentry4 ,however1 the carpenter must know the principles of simple stair lay-out and construction for he is called upon to construct porch steps1 basement and often attic stairs4 ,in smaller communities he may also have to build the main stair4 ,fig4 #abj illustrates three common types of stair4 ,in planning a stair1 the first requisite is to know its rise and run1 ,fig4 #aba4 ,the rise in this case is the vertical distance measured from the top of the first floor to the top of the second floor4 ,the run is the horizontal span of the stair4 ,illustration3 ,fig4 #abj-;a-b ,types of ,stairs ,fig4 #abj-;c ,illustration3 ,fig4 #aba4 ,rise and ,run of ,stair ,a good average stair for a cottage will have a rise per step of #g inches and a run of tread of #aj inches4 ,variations will have to be made in both rise and tread to meet conditions1 but the student may take these dimensions as starting dimensions unless otherwise directed4 ,steps should not be either too steep1 due to excessive rise per foot1 or slow due to extreme width of step4 ,an old rule for determining the relation of rise to tread is3 ,twice the rise plus the tread should equal #bd4 ,proceed as follows3 7#a7 ,lay off on a story pole the total rise of the stair by placing the pole upright in the well hole4 7#b7 ,set a pair of dividers to #a and step off this distance so marked4 ,if there is a remainder1 increase or diminish the divider's space and again step off the space4 ,continue this until a setting is obtained which gives no remainder4 ,the number of risers will be found by counting the spaces1 and the rise per step by measuring one of these spaces4 7#c7 ,if the run of the stair is not of exact specification 7some variation is usually possible7 the run per step or tread may be determined by the rule just given4 ,if a definite total run is specified the tread must be figured4 7#d7 ,since there is always one more riser than tread1 the run per step is obtained by dividing the total run in inches by the number of risers less one4 ,the numbers thus obtained for rise and run per step are the ones to be used on the framing square in laying out the stringers4 ,illustration3 ,fig4 #abb4 ,laying out ,string ,illustration3 ,fig4 #abc4 ,pitch ,board4 ,illustration3 ,fig4 #abd4 ,economical ,center ,stringer 7#e7 ,joint one edge of each stringer straight and square and place the framing square as in ,fig4 #abb and scribe along both blade and tongue4 7#f7 ,scribe the line ,a parallel to the #i run1 at a distance from it equal to the rise diminished by the thickness of the proposed tread4 7#g7 ,continue to lay the square as in 7#e7 until the required number of steps have been laid out4 ,a pitch board might have been constructed and made use of instead of the framing square in laying out the stringers4 ,this is nothing more than a piece of stock which serves as a template by which to lay out the rise and run of each step1 ,fig4 #abc4 ,a cleat or fence nailed to one edge after the three edges have been planed to dimensions permits easy and accurate placing of the same4 7#h7 ,there remains the sawing out4 ,on open stringers this is done by sawing square across the board or plank4 ,where the exposed ends of risers would make a bad appearance1 the cuts in the stringers for risers are made mitering and the ends of the risers are mitered correspondingly4 ,in either case the end of the riser will be flush with the exposed side of the stringer or string4 ,fig4 #abd illustrates an economical way of constructing a center stringer1 a #b #d having nailed to its top edge the waste cut from the side or wall stringers4 ,illustration3 ,fig4 #abe4 ,stringer for ,attic ,stair #fa4 ,risers and ,treads4--,upon the common stair1 such as attic and porch1 etc41 treads and risers are placed as in ,fig4 #abj1 being nailed to place1 risers first and then treads4 ,on porch steps and open stringers1 the treads should overhang at their ends an amount equal to that given the front4 ,the cove1 if one be used1 should be carried around and returned under the end of the tread4 ,on enclosed or semi-enclosed stringers1 a combination of stringer and wall board is commonly used4 ,fig4 #abe illustrates a type of construction often used upon attic stairs4 ,in this the side stringers are framed of #a stock and then nailed to the wall board of similar thickness4 ,such construction is not suited for first floor stair work where the effects of shrinkage would show to greater disadvantage4 ,illustration3 ,fig4 #abf4 ,main ,stair ,detail ,fig4 #abf illustrates the manner of framing a modern stair suitable for a first floor where the best type of construction is demanded4 ,as a rule1 such stair work will be done at a mill and the stair brought to the building knock-down4 ,the carpenter will have framed the rough stringers which are to support the ceiling below the stair1 and placed them so that they may be used as a temporary stair for the workmen4 ,if the stairway is an open one or semi-open1 the plastering under these stringers will have been placed1 the stair being put together on the floor and then raised to its place4 ,if the well-hole is such that the stair must be assembled while the strings or wall boards are in place1 the lath and plaster must be left off the rough stringers until after the stair has been assembled and the wedges glued and driven in place as shown in the illustration4 ,rough stringers must be placed far enough from the sides of the well-hole so that the wall board may settle in place and that the wedges may be easily placed1 usually about #d or #e from the wall will be sufficient4 #fb4 ,porches4--,fig4 #abg illustrates the manner of framing the floor of a porch4 ,such framework should be given a pitch downward away from the house of about #a in #aj' that the water may be drained4 ,illustration3 ,fig4 #abg4 ,detail of ,porch ,framing ,fig4 #abh illustrates the manner of placing water table and flooring1 etc4 ,water table is first placed1 the corners being mitered and the whole furred out from the frame about a quarter of an inch to allow any dampness to escape4 ,porch floors should have their joints painted with lead just before being laid4 ,illustration3 ,fig4 #abh4 ,detail of ,porch ,finish ,posts and balusters are usually placed after the porch roof has been placed1 the upper frame being temporarily supported by studs4 ,in ,fig4 #abg is also shown the manner of framing the bearing joists1 ceiling joists and rafters for a hip roof4 ,the various cuts are obtained in the same manner as are similar cuts on the main roof4 ,porch roofs are seldom given as much pitch as the main roof4 ,they do not need as much and must1 usually1 be kept below the window sill line of the second story4 ,fig4 #abh also illustrates a common type of trim for porch cornice4 ,where supporting plates are long1 a flitch plate girder is formed of them by the insertion between them of a stiff plate of structural steel of suitable length and width4 #fc4 ,interior ,finish4--,a part of the carpenter's duty is the placing of all interior finish1 such as base boards1 door jambs1 etc4 ,formerly the carpenter made1 or got out his trim by hand but today he finds it much pleasanter and cheaper to buy the machine-made product of the mill4 ,even door and window frames are usually purchased from the mill1 either assembled or knock-down4 #fd4 ,setting ,door ,jambs4--,if the studs about interior door openings have been carefully selected for straightness and properly set or plumbed1 the setting of the door jamb should be an easy matter1 ,if this work has not been properly done1 considerable ingenuity will be required oftentimes to get the frame set so that its edges are out of wind and the frame plumb4 ,if a jamb should not be set plumb and out of wind1 the operation of making a door fit its stops properly is a most trying one and the result usually unsatisfactory4 ,too much emphasis cannot be placed upon the necessity for proper placing of studs and jambs4 7#a7 ,saw off the head lugs just enough to allow the frame to be placed in the opening4 7#b7 ,cut a spacing stick of a length sufficient to reach from the floor to the under surface of the head jamb when that member is in its proper place4 7#c7 ,place the head jamb at one of its ends upon this stick and tack the jamb to the stud lightly4 7#d7 ,level the head jamb and lightly tack the second jamb1 inserting wedging blocks or shingle points between the jamb and stud4 ,a spread stick cut to hold the jambs apart properly at the base is desirable4 7#e7 ,lay a piece of finish floor against the face of each jamb and scribe along the top of this to indicate where the jambs must be cut off to fit the finish floor when it is placed4 ,it is taken for granted that the finish floor is to be laid last4 ,if a finish floor is not to be used1 or if it is to be placed before the wall trim1 the head jamb will be leveled but not located as to height1 the dividers being used to scribe the feet1 being set so that the proper amount will be cut off to allow the jamb to rest at the right height when cut to the scribed lines4 7#f7 ,remove the jamb and saw to the scribed lines4 7#g7 ,replace the frame and tack it at one side after plumbing it both on its face side and face edge4 ,see that the jamb is at the right height by inserting the blocks of flooring used in scribing to length4 7#h7 ,tack the second side-jamb close to the head4 7#i7 ,sight across the edges of these jambs and adjust the loose jamb until the frame is out of wind4 ,plumb its face1 blocking the back4 ,shingles placed point to point provide easy blocking where the space is not too large4 ,a straight-edge placed against the face of a jamb will indicate whether it has been sprung in the blocking or wedging between jamb and stud4 ,illustration3 ,fig4 #abi4 ,setting ,dividers at ,meeting ,rails ,illustration3 ,fig4 #acj4 ,scribing ,bottom of ,lower ,sash #fe4 ,fitting ,window ,sash4--,sash are often fitted before the house is plastered and before the sash are glazed4 7#a7 ,joint the top and sides of the top sash1 chamfering the arrises very slightly by a stroke or two with the plane4 7#b7 ,cut and fit the meeting rails about the parting stops remembering to leave a little play1 that successive coats of paint on the stops may not cause binding1 #a_/af on each side is not too much4 7#c7 ,joint the edges of the lower sash4 7#d7 ,since the bottom rail has not been beveled1 only the lugs sawed off1 the meeting rails will appear with reference to one another as in ,fig4 #abi4 ,set a pair of dividers to a distance equal to that between the tops of the meeting rails4 ,this can be done by placing the dividers between the meeting rails4 7#e7 ,scribe the bottom rail as indicated in ,fig4 #acj4 ,if the sash has been glazed so that the outer face of the bottom rail is not accessible from the inside1 the scribing is to be done on the inside of the bottom rail and a ,t-bevel set to the slope of the sill and this used to transfer the angle to the edges of the sash4 ,before scribing the bottom rail1 see that the meeting rails are apart a uniform distance across the sash4 7#f7 ,saw and then plane to the scribed line4 ,where sash weights are to be used1 they are easiest placed before lathing4 ,the proper tying of a sash cord so that it shall not work loose with time is a matter for careful instruction by the teacher4 ,no good carpenter will have his sash cords coming untied4 ,the cord can be cut the estimated length after the weight has been attached1 and a knot or loop tied in the free end so that the cord shall not slip thru the pulley4 ,in case weights are not placed before the lath and plaster1 it will be necessary to make use of a duck to draw the end of the sash cord up thru the removed pocket cover of the jamb4 ,this duck is usually a piece of lead beaten about one end of a piece of stout short cord4 ,this lead weight is lowered thru the pulley by means of a longer cord1 the end of the sash cord is then fastened to the longer cord1 after removing the duck1 and then drawn up and thru the pulley4 ,to determine the length of sash cord1 draw the sash weight to the top of the jamb and1 setting a sash upon the sill1 mark and cut the cord about four or five inches below the opening in the edge of the sash in which the knotted end of the cord is to rest4 ,illustration3 ,fig4 #aca4 ,using ,block to ,locate ,door ,stop ,position on ,jamb #ff4 ,placing ,door1 ,window1 and other ,trim4--,in ,fig4 #aaj-;a is shown one of the many styles of casing in common use4 ,base blocks and casing stock are prepared at the mill and the carpenter has but to cut these to the proper lengths and fit and attach them4 7#a7 ,the base block is first placed1 tho some workmen prefer to fit the base first1 cutting it to a length such as will allow the proper placing of the block after the base is nailed in position4 ,where the finish floor is laid last1 this block will be scribed at its bottom by means of a piece of flooring1 otherwise the dividers would be used4 7#b7 ,after the blocks are placed the casings are cut to length and nailed4 7#c7 ,the head member is next made up and placed4 ,it is customary for all door and window heads1 where built up1 to be constructed at one time4 ,it should be noted that door casings are not placed flush with the face of the jamb4 ,they should be kept back about #e_/af4 ,this is to allow the easy placing of hinges and also for appearance' sake4 ,in all casing work the expedient of sawing under at the back should be supplemented by the use of the block plane1 where necessary1 that tight joints may result4 ,window stool stock1 like that of casings1 is prepared at a mill and needs only to be cut to length and have the ends returned to match the face edge4 7#a7 ,lower the sash1 then fit the stool to this allowing enough play that subsequent paint or varnish may not cause the stool to bind the lower rail of the sash4 7#b7 ,place and nail the apron4 7#c7 ,cut and place the side casings4 ,note that side casings are placed flush with the face of the jambs4 ,the crack so formed is concealed when the stop bead is placed4 7#d7 ,place the head4 ,illustration3 ,fig4 #acb4 ,door ,parts ,base boards and base mould may now be placed4 ,blocks of a thickness of the finish floor placed along the wall at frequent intervals will serve to locate the position of the base above the rough floor1 when the finish floor is to be laid afterward4 ,internal corners of base mould and picture mould1 when of irregular face1 should be coped4 ,external corners should have mitered joints4 ,shoe mould will be placed after the finish floor is laid4 ,stop beads may next be placed in the windows and in such doors as are not rabbeted4 ,head stops are placed first and the side stops then coped to these4 ,a block of a width equal to the thickness of the door will be an aid in placing stops easily1 ,fig4 #aca4 ,window stops should be so placed that the lower sash may move freely as it is raised4 #fg4 ,hanging ,doors4--,in the fitting of large doors1 such as in dwellings1 allowance must be made for subsequent coats of varnish or paint1 usually a scant #a_/af is allowed at top and each side of a door4 ,the bottom of a door is often not touched1 except to saw away the lugs of the stiles1 until after the door is hung4 ,the door is hinged1 then closed and the bottom scribed to the floor so as to allow the door to swing over rugs or carpet freely4 ,where a threshold is to be used1 the door is scribed to fit the thickness of the proposed threshold4 should be allowed at the bottom of the door for play4 ,if a door has a stile with a bow in its face1 it should be turned so that the bow is next the stop of the lock side4 ,illustration3 ,fig4 #acc4 ,measuring ,opening #fh4 ,fitting a ,door4--,the names of the parts of a door and their relative positions are indicated in ,fig4 #acb4 7#a7 ,mark with a try-square and saw off the lugs1 the parts of the stiles which project beyond the rails4 7#b7 ,plane an edge of the door until it fits the side of the frame against which it is to be hung4 ,if the frame is straight1 this edge may be planed straight4 ,it is not wise to take for granted the squareness or straightness of a frame4 ,a test or series of tests may first be made with square and straight-edge4 ,a mechanic1 however1 usually planes an edge until it fits the frame1 testing by holding the door against the frame as near to its position as its size will allow4 7#c7 ,measure the width of the frame at its top and bottom1 ,fig4 #acc1 and transfer these dimensions to the top and bottom of the door1 ,fig4 #acd4 ,when approaching the line1 in planing1 place the door against the frame often enough to see where the allowances must be made for irregularities in the frame4 7#d7 ,plane the top edge of the door until it fits the frame properly when the first planed edge is in position4 7#e7 ,the length of the door will be determined by scribing it to the floor after being hinged4 ,the edge of the door which is to swing free is usually planed slightly lower at the back arris than at the front4 ,an examination of the movement of an ordinary house door will show the reason for this4 ,illustration3 ,fig4 #acd4 ,laying off ,width #fi4 ,hinging a ,door4--,the hinges most commonly used in carpentry are the kind known as butts4 ,where the door stands in a vertical position1 hinges in which the two parts are joined by a loose pin are generally used4 ,by removing the pins the door may be removed without taking the screws out of the hinge4 ,such hinges are more easily applied than those with the fixed pin4 7#a7 ,place the door in position2 keep it tight against the top and the hinge side of the frame4 7#b7 ,measure from top and bottom of the door to locate the position for the top of the higher hinge and the bottom of the lower hinge4 ,usually1 the lower hinge is placed somewhat farther from the bottom than the higher hinge is from the top4 7#c7 ,with the knife or chisel mark on both door and frame at the points just located1 ,fig4 #ace4 7#d7 ,take out the door1 place the hinge as in ,fig4 #acf1 and mark along the ends with a knife4 ,in a similar manner mark the frame4 ,make certain that the openings on door and on frame are laid off so as to correspond before proceeding further1 7#e7 ,set the gage for the depth the hinge is to be sunk ,fig4 #acg and gage both door and frame4 7#f7 ,set another gage for width of openings1 ,fig4 #ach1 and gage both door and frame1 keeping the head of the gage against the front of the door4 7#g7 ,chisel out these gains on door and frame1 ,fig4 #aci4 7#h7 ,if loose-pin butts are used1 separate the parts and fasten them in place4 ,use a spiral drill to make openings for the screws4 ,to insure the hinges' pulling tight against the side of the gain make the holes just a little nearer the back side of the screw hole of the hinge ,put the door in place and insert the pins4 ,it is a good mechanic who can make a door hang properly the first time it is put up4 ,it is better1 therefore1 to insert but one or two screws in each part of a hinge until the door has been tried4 7#i7 ,if the door hangs away from the frame on the hinge side1 take it off2 take off hinge on door or frame1 or both if the crack is large2 chisel the gain deeper at its front4 ,by chiseling at the front only and feathering the cut toward the back1 the gain needs to be cut but about one-half as deep as if the whole hinge were sunk4 ,if the door should fail to shut because the hinge edge strikes the frame to soon1 the screws of the offending hinge must be loosened and a piece of heavy paper or cardboard inserted along the entire edge of the gain4 ,fasten the screws and cut off the surplus paper with a knife4 ,if plain butt hinges are used the operations are similar to those just described except that the whole hinge must be fastened to the door and the door held in place while fastening the hinges to the frame4 ,illustration3 ,fig4 #ace4 ,locating ,hinge ,position ,illustration3 ,fig4 #acf4 ,knifing ,hinge ,location #gj4 ,fitting ,locks4--,two types of lock are in common use upon dwelling doors1 the rim and the mortise lock4 ,the rim lock1 ,fig4 #adj1 is used upon cheap construction and is attached to the outer surface of the door4 ,the mortise lock is used upon the better class of work2 the box is housed into a mortise and the selvage into a gain cut into the edge of the door stile4 ,door locks are made so that the bolts may be reversed to fit either right or left hand doors4 ,this is accomplished by removing a screw in the side of the box and carefully lifting the bolt1 replacing it in reversed position4 ,a right hand door is one which swings to the right when pushed open4 ,illustration3 ,fig4 #acg4 ,setting ,gage for ,depth of ,gain ,illustration3 ,fig4 #ach4 ,setting gage for ,width of ,gain ,to attach a rim lock3 7#a7 ,place the lock against the side of the door and mark thru the key hole and knob spindle hole with a sharp awl or divider point4 7#b7 ,remove the lock and bore appropriate sized holes4 7#c7 ,fasten the lock and place the escutcheons1 knob spindle and knobs4 7#d7 ,locate and attach the strike or latch plate4 ,illustration3 ,fig4 #aci4 ,gain ,ready for ,hinge ,to place a mortise lock1 ,fig4 #ada3 7#a7 ,in a manner similar to that used in placing the rim lock1 locate the knob spindle and key holes4 ,a more accurate result is obtained if the knob spindle hole is located by four points1 one at each corner of the square1 ,fig4 #adb4 ,in placing the lock1 keep the selvage back from the edge of the door a scant #a_/af so that the selvage may be sunk below the edge of the door by that amount when mortised in4 ,illustration3 ,fig4 #adj4 ,rim ,lock ,illustration3 ,fig4 #ada4 ,mortise ,lock ,this will permit the door to be trimmed without the removal of the lock in case the door should swell after being fitted and locked4 7#b7 ,bore the holes for knob spindle and key4 7#c7 ,locate a center line on the edge of the stile and bore for the mortise which shall receive the box of the lock4 7#d7 ,place the box and then mark about the protruding selvage using a sharp knife1 ,fig4 #adc4 7#e7 ,remove the lock and gain in the selvage1 ,fig4 #add4 7#f7 ,fasten the lock by means of the screws thru the selvage and attach the escutcheons1 knob spindle and knobs4 7#g7 ,close the door and mark the vertical position of the latch upon the jamb4 7#h7 ,open the door and place the latch or strike plate1 locating its vertical position by means of the knife marks just made upon the jamb1 and its horizontal position by a measurement taken from the latch to the face of the door2 transfer to the jamb by rule or gage4 7#i7 ,scribe about the plate and then gain it into the jamb4 ,on a door with a rabbeted jamb instead of an adjustable stop1 the essential measurement will be from the back arris of the stile to the front of the latch4 7#aj7 ,attach the plate1 then chisel out the openings for latch and bolt4 ,equally common is the practice of taking step 7#c7 first1 with steps 7#a7 and 7#b7 taken after step 7#e74 #ga4 ,laying and ,scraping ,floors4--,quarter-sawed stock makes the best wearing floor4 ,however1 oak wears well in either plain or quarter-sawed forms4 ,all hard wood finish floors are milled with tongues and grooves on edges and ends4 ,holes for nailing are usually drilled at the mill also4 ,illustration3 ,fig4 #adb4 ,locating ,knob ,spindle ,hole ,in laying a finish floor1 it is not advisable to lay it with its lengths extending in the same direction as those of the rough floor4 ,the shrinkage of the wide boards of the under floor will open unseemly cracks in the finish floor4 ,where it is necessary to run lengths for both floors in the same direction the finish floor should be separated from the rough floor by thin furring1 such as lath1 placed #af apart4 ,rough floors laid diagonally overcome this difficulty4 ,paper is usually placed between the two floors4 ,care should be taken in starting a floor to select straight boards4 ,where grooves fail to fit tongues of boards that are laid1 a piece of #b #d about #c' or #d' long should be used as a pounding block that the tongue of the board being laid may not be battered1 the most common cause of trouble in floor laying4 ,nails are driven toeing thru the board just above the tongue that the heads may be concealed and also to better draw the board in position4 ,hammer marks showing upon the face of a floor indicate carelessness4 ,it is not necessary that nails should always strike joists1 for a good rough floor will hold such nails with sufficient firmness4 ,where nails must be driven into hard maple1 a hole must be drilled first4 ,on the great majority of hard woods the dipping of the point of the nail in soap or oil will cause it to enter the wood with careful driving1 without the drilling of a hole4 ,illustration3 ,fig4 #adc4 ,locating ,selvage ,gain ,illustration3 ,fig4 #add4 ,ready for the ,lock ,after a hardwood floor has been laid it should be scraped4 ,scraping floors is a tedious task at best4 ,electrically driven machines now relieve the carpenter of much of this work1 the floors being laid and finished by a specialist in floor work4 ,the shoe mould is placed last1 being nailed to the floor1 so that any shrinkage of the joists will cause the mould to drop with the floor4 ,base board and shoe mould should be stained1 but not varnished1 before the mould is placed4 ,on account of waste in tonguing and grooving and straightening flooring stock1 an allowance of from to extra is necessary in estimating4 ,illustration3 ,fig4 #ade4 ,detail of ,door ,frame #gb4 ,door and ,window ,frames4--,like other carpentry detail1 window and door frames may be constructed in any one of a number of styles4 ,fig4 #ade illustrates a satisfactory type of door frame for cottage use4 ,the sill will be given a pitch or fall of #a in #ab and will have its ends housed into the jambs4 ,the jambs will be assembled first1 being nailed together4 ,next1 the side casings are fitted at their lower ends1 cut to length and nailed4 ,frequently they are nailed and then cut to length4 ,the head casing with its cap is next placed4 ,fig4 #adf illustrates a common type of cottage window frame4 ,the method of procedure is not unlike that described for the door frame4 ,the sill will be grooved on its under side to receive the top edge of the siding board and given a fall of #a in #aj4 ,jambs must be grooved to receive a parting stop as shown4 ,where weights are to be used each jamb must have a pocket as detailed4 ,the stock sawed out of the jamb may be made use of for pocket cover stock by proper manipulation4 ,pulleys may be placed before the jambs are assembled1 at least the holes for them should be prepared4 ,illustration3 ,fig4 #adf4 ,detail of ,window ,frame ,there are a number of tricks of the trade in frame making4 ,their presentation must be left to the instructor1 for the making of frames belongs to millwork and space can be spared here for general directions only4 #gc4 ,woodwork in ,masonry ,structures4--,wood framing in brick and other masonry buildings is but slightly different from that wholly in wood4 ,fig4 #adg illustrates the manner of framing the ends of joists which rest in solid masonry walls4 ,the ends are shaped as indicated so that1 in case of fire1 the floors in falling will not pull over the walls1 but will fall free4 ,anchors are used to tie the building together1 and these are to be placed near the lower edge of the joists so that they may split out of the joists easily or allow the floor to drop free1 in case of a falling of the floor and joists4 ,a popular type of construction is that known as brick veneer1 ,fig4 #adh4 ,it consists of an ordinary framed house with a covering of brick as shown4 ,these bricks are fastened to the wall by metallic bonds4 ,from the outside1 the building has all of the appearance of solid brick1 while it is claimed that a wall so formed is warmer than one of solid brick4 ,illustration3 ,fig4 #adg-;a ,fig4 #adg-;b ,joist ,framed into ,brick ,wall ,illustration3 ,fig4 #adh4 ,brick ,veneer ,over openings in brick walls1 lintels are required to support the arch1 ,fig4 #aej4 ,fig4 #adi shows the manner of framing a window opening for a brick wall4 ,fig4 #aea illustrates the manner of attaching a plate to a brick wall4 ,illustration3 ,fig4 #adi4 ,window ,detail for ,brick ,wall ,illustration3 ,fig4 #aej4 ,lintels ,illustration3 ,fig4 #aea4 ,attaching ,plate to ,brick ,wall ,,chapter ,,vii ,estimating #gd4 ,methods of ,estimating4--,building costs may be divided into two main divisions1 cost of material and cost of labor4 ,there is but one so-called safe way to figure or estimate the cost of any particular piece of carpentry work4 ,this consists in taking off the material quantities in detail and to this adding the labor cost of placing the same4 ,this is the method in common use by contractors in making a final estimate4 ,where a rough or working estimate is required1 such as an architect's estimate of the probable cost of a building planned by him1 two methods may be used4 ,one consists in figuring the cubical contents in feet and multiplying a predetermined1 or unit price per cubic foot for that type of house4 ,ordinarily1 the main frame is figured1 counting from the basement floor to the top of the attic walls that are1 or may be finished--outside measurements4 ,porches and open spaces are not figured4 ,a second method consists in estimating the number of squares 7#ajj sq4 ft47 of side wall1 of partitions1 of floors1 etc41 and multiplying a predetermined price per square for a similar type of building4 ,this latter method is more accurate than the cubic-foot unit method4 #ge4 ,table for ,estimating by ,cubic-,foot ,unit4--,the following table of unit prices will give a rough working estimate for various types of building differentiated after the custom of insurance adjusters4 ,the prices are for #aiae and to be of any value must be compared with known costs of similar structures in the community in which they are to be used4 ,any evident variations in unit costs so discovered should be noted and corrections made4 ,,cubic-,,foot ,,unit ,,estimate ,,country ,,property ,,per ,,cubic ,,foot ,frame dwelling1 small box house1 no cornice #e;c ,frame dwelling1 shingle roof1 small cornice1 no sash weights1 plain #f- #g;c ,brick dwelling1 same class #h-aj;c ,frame dwelling1 shingle roof1 good cornice1 sash weights1 blinds 7good house7 #h-aj;c ,brick dwelling1 same class #aa-ab;c ,frame barn1 shingle roof1 not painted1 plain finish #b- #c;c ,frame barn1 shingle roof1 painted1 good foundation #c - #d;c ,frame store1 shingle roof1 painted1 plain finish #f- #h;c ,brick store1 shingle roof1 painted1 good cornice1 well finished #h-aa;c ,frame church or school house1 ordinary #f- #h;c ,brick church or school house1 ordinary #aj -#ab;c ,if slate or metal roof1 add c per cubic foot4 ,,city ,,property ,frame dwelling1 shingle roof1 pine floors and finish1 no bath or furnace1 plain finish 7good house7 8- #h;c ,brick dwelling1 same class #aj -#aa;c ,frame dwelling1 shingle roof1 hardwood floors in hall and parlor1 bath1 furnace1 fair plumbing #aj -#aa;c ,brick dwelling same class #aj -#ab;c ,frame dwelling1 shingle roof1 hardwood in first floor1 good plumbing1 furnace1 artistic design1 some interior ornamentation1 well painted #ab-ae;c ,brick dwelling1 good plumbing1 bath1 furnace1 pine finish1 well painted #ac-ah;c #gf4 ,grading ,rules4--,there is no uniformity as to grades of lumber4 ,fifteen or more associations have rules for inspection4 and classification of lumber and these rules vary with the association and from year to year in the same association4 ,the following rules taken from a catalogue of a middle west lumber concern will be found helpful3 ,yellow ,pine ,dimension1 ,studding1 ,joists and ,timbers ,no4 #a ,common4--,the best grade and the one recommended for use on first class jobs4 ,no4 #b ,common4--,dimension up to #bj feet long only can be obtained in this grade4 ,timbers are not manufactured in ,no4 #b4 ,this stock will show defects not found in ,no4 #a grade1 and some pieces are not entirely straight4 ,it is a sound1 serviceable grade1 but not recommended for first class work4 ,yellow ,pine ,boards1 ,sheathing1 ,shiplap1 and ,fencing ,no4 #a ,common4--,this grade is not clear1 but is strictly sound and uniform in thickness and width4 ,it is used on the best classes of work1 for barn boards1 and wherever exposed to wear and weather4 ,no4 #b ,common4--,this grade is sound but contains more sound knots than ,no4 #a and is somewhat coarser4 ,it is mostly used on first class jobs for sub or rough floors1 and for sheathing under siding4 ,it can be used for outside work1 but is not recommended for this purpose except upon cheap buildings4 ,no4 #h ,common4 ,a fairly good lower grade which will work up nicely but with some waste due to cutting out defects4 ,runs uneven in quality4 ,makes a fair subfloor or sheathing4 ,yellow ,pine ,flooring1 ,ceiling1 ,partition1 and ,drop ,siding ,clear ,grade4--,the best grade manufactured4 ,practically free from defects and the grade used upon first class jobs4 ,is strong1 sound1 and will lay without waste due to cutting out of imperfections4 ,should be used when a natural finish is desired4 ,no4 #a ,common4 ,this grade will contain small1 sound knots1 sap stains1 pitch or pitch pockets4 ,it is sound and durable1 and a good grade for ordinary work or wherever covered with paint4 ,no4 #b ,common4 ,coarser than ,no4 #a grade2 will lay up with little waste4 ,is sound1 and flooring of this grade is often used for sheathing or sub flooring where a warm1 tight job is desired4 ,can also be used on cheap painted jobs4 ,fir ,boards1 ,timbers1 ,drop ,siding1 ,ceiling and ,flooring ,select ,no4 #a ,barn ,boards4--,this grade is especially selected and is better than ,no4 #a4 ,no4 #a ,timbers4--,good sound straight stock1 to be used for sills and posts subjected to moisture4 ,clear ,ceiling4--,free from defects4 ,good for cornice work and porch ceilings4 ,edge ,grain ,flooring1 ,clear ,grade4--,especially suited to porch floors as it wears well and resists effects of moisture4 ,clear ,drop ,siding4--,contains no sap1 shakes or other defects4 ,shingles1 ,lap ,siding1 ,y4 ,p4 and ,cypress ,finish1 ,white ,pine ,boards #e to #b ,clears4--,the heaviest grade five shingles laid one on top of the other will measure #b at the butts4 #f to #b ,extra ,star ,a ,star4--,a lighter grade1 but clear and #af1 as are the #e to #b grade4 ,bevel or ,lap ,siding4--,carried in stock in red cedar1 redwood1 cypress1 and white pine4 ,clear is free from all defects4 ,cypress ,c ,grade4--,has small sound knots and other slight defects such as can be covered with paint4 ,all siding is bundled #aj pieces to the bunch in random lengths4 ,not furnished in specified lengths4 ,yellow ,pine and ,cypress ,finish4--,this stock in clear grade is practically free from defects4 ,the yellow pine is suitable for interior finish4 ,cypress is suitable for inside finish or for cornice work on first class jobs4 ,c cypress finish contains some knots and other slight defects4 ,is suitable for outside finish on ordinary jobs4 ,white ,pine ,boards4 ,as a rule1 carried in stock only in ,no4 #a grade4 ,nothing but sound1 red-knotted boards should be included4 ,no shakes4 ,excellent for exposure to weather4 #gg4 ,estimating ,lumber ,quantities4--,lumber is measured in terms of the board foot as a unit1 #ab by #ab by #a or its equivalent1 indicated by the abbreviation ,b4 ,m4 7board measure74 ,example3 ,determine the ,b4 ,m4 in a girder #f by #h by #af'4 ,solution3 ,rule--,thickness in inches times width in inches1 divided by #ab times the length in feet gives a number equal to the number of board feet4 7#f #h7 _/ #ab #af' #fd' ,b4,m4 ,stock less than #a thick is figured as #a thick4 ,in commercial practice lumbermen make use of tables in determining quantities4 ,appendix ,,iii4 ,in estimating quantities1 suitable allowance must be made for waste4 ,this waste is incurred 7#a7 thru loss when boards or planks are cut to required lengths4 ,standard lengths are #aj'1 #ab'1 #ad'1 etc41 and these will not always cut to advantage4 7#b7 ,waste is incurred in machining the stock1 as dressing1 edging1 tonguing and grooving4 ,necessary allowances will be indicated herein4 ,heavy ,timbers4 ,girders1 posts1 etc41 are determined by count4 ,joists4 ,to determine the number of joists required for a room or a building1 count the actual number required beginning at a wall 7 times number of feet in length or width of room when set #af on centers71 and to this add one joist to be placed against the second wall4 ,cataloged or listed sizes are for lumber fresh from the saw4 ,shrinkage due to seasoning and surfacing one side and one edge so that the stock may have uniform thickness and width will give actual sizes as follows3 #b #d when sized on one side and one edge1 will give #a x #c2 #b #f1 ,s-#a-,s and #a;,e1 #a #e2 #b #h1 ,s-#a-,s and #a;,e gives #a #g2 #b #aj1 ,s-#a-,s and #a;,e gives #a x #i2 #b x #ab1 ,s-#a-,s and #a;,e gives #a x #aa4 ,when ,s-#b-,s and #b;,e or sized on #d sides1 stock will measure less than indicated above4 ,studs for ,walls and ,partitions4--,count one for each lineal foot of wall or partition1 where specified #af on centers4 ,the extra studs are to be used in doubling corners1 at doors and windows1 and in gables4 ,barns and sheds will not require these extra studs4 ,bridging4--,allow #be lineal feet of #b by #d for each square of flooring4 ,rafters4--,on a plain roof1 count actual number and add one1 as in counting for joists4 ,sheathing4--,calculate the exact surface to be covered1 deduct openings2 then1 for unmatched sheathing or barn boards or fencing1 as it is also called1 add #a_/ab for #ab boards1 #a_/af for #aj boards and where #h boards are used4 ,four inch and #f are seldom laid solid1 being used mainly for roof sheathing for shingle roofs1 and laid #b apart4 ,these additions are due to the fact that thru seasoning and dressing1 a #ab board becomes #aa1 a #aj becomes #i1 an #h becomes #g1 a #f becomes #e and a #d becomes #c4 ,the additions specified allow for waste in cutting4 ,shiplap4 ,calculate the exact surface to be covered1 deduct openings2 then add for floors #ag1 for sidewalls #bj1 for roofs #be4 ,sheathing laid with #b spaces should have proportionate deductions made1 that is1 on #a #f1 figure as if laid solid1 then deduct 2 for #a #d deduct 4 ,sheathing when matched1 such as is used sometimes for sub-floors and side walls and roof sheathing under slate roofs and better known as flooring1 will be estimated by figuring the exact surface to be covered1 deducting the openings1 then adding for #f stock1 which is the kind most always used1 #ae for floors1 #ag for sidewalls1 and #bj for roofs4 ,if shiplap or matched sheathing is laid diagonally add #e for waste due to lack of ability to reverse cut4 ,siding4--,for bevel siding1 calculate the exact surface1 deduct openings2 then add for #f siding when laid #d to the weather1 #cc2 for the #d siding add #ej4 ,drop ,siding4--,drop siding1 ceiling and wainscoting are figured just like matched flooring1 which is described below4 ,flooring4--,for square edge1 calculate the exact surface to be covered1 add for #f flooring #aa for waste in matching1 etc42 for #d flooring add #bj4 ,it is becoming common practice to specify flooring by actual face measurement after being machined4 ,the following figures are for actual surface measurements4 ,for matched flooring1 calculate the exact surface to be covered1 then add #bj for #e flooring1 for #c flooring add #be1 for #b add #cc1 for #a add #dj4 ,flooring less than #a thick1 like all other lumber1 is estimated as #a thick4 ,shingles4--,a bunch of shingles contains the equivalent of #bej shingles of #d average width4 ,with an exposure of #d to the weather a #d average shingle will cover #ah square inches1 making #hjj shingles to the square4 ,waste in doubling the first course and in laying will necessitate an addition of #h on a plain roof and #ab on hips or on gabled walls4 ,cost estimates are based upon the ,m4 or #ajjj4 ,,shingles ,,per ,,square ,plain roof1 #d exposure1 #iij2 roof cut up1 #ajaj ,plain roof1 #d exposure1 #hhj2 roof cut up1 #ijj ,plain roof1 #e exposure1 #gij2 roof cut up1 #haj ,lath4 ,lath for interior plaster work are usually by #a by #d'1 put up in bundles of #ej each and are sold by the #ajjj4 #ajjj lath will cover #gj yards of surface and will require #h lbs4 of #c;d fine lath nails4 ,lathing is usually considered a part of the plasterer's contract4 ,there is no uniformity of practice as to the deduction for openings4 ,building ,papers4 ,the cheapest is rosin sized1 and is not waterproof4 ,this is used mainly under floors and upon side walls under bevel siding4 ,it is sold by the pound in rolls each #cf wide containing #ejj square feet4 ,dry felt is used where better protection from cold is desired4 ,in the cheaper grades1 the material is made of wood fiber and rosin4 ,in the better grades wool is used4 ,tar felt1 used where moisture is to be resisted1 is dry felt saturated with tar4 ,these materials are sold by the pound3 #ab1 #ae1 and #bj lbs4 to the #ajj square feet1 in rolls of various widths4 ,a catalog should be consulted for weights and covering capacity4 #gh4 ,estimating ,millwork ,quantities4--,the number of doors and windows will be determined by an actual count4 ,mouldings1 casings1 baseboard when moulded1 window stools1 etc41 are sold by the #ajj feet lineal measure1 random lengths4 ,extra charge is made for specified lengths where the quantities are determined by scale measurements of the plan and elevations4 ,window frames of stock sizes1 door frames1 inside jambs1 stair parts1 buffets1 etc41 will be found priced in millmen's catalogs1 and assist greatly in determining prices for ordinary work4 ,this text cannot give space to list such data1 which is so readily obtained from commercial catalogs4 #gi4 ,example of ,form for ,bill of ,materials4-- ,,bill ,ticket ,price or ,no4 of,no4 of,size ,length,description--------------------- --- ,catalog ,feet ,pieces ,rate ,extensions ,number ---------------------------------------- --------------------- #bgj #cj #b #d #ad ,y4 ,p41 ,,sis and ,,ie #bb #e #id #b ,m #e-b red cedar shingles #c #ee #g #aj #cjj #a #f #b ,y4 ,p4-- flooring #bj #f #jj #ai #dj ---------------------------------------- --------------------- #hj4 ,estimating ,labor ,costs4,a--,in estimating labor costs the following data is to be made use of4 ,the estimator will have to determine the hours per day and the scale of wages per hour paid in his locality1 and make whatever changes in the data is necessary4 ,he should also compare the quantity of work done by men he may observe with that given herewith4 ,the time data herewith is based upon the work of one mechanic who has mastered his trade fairly well4 ,with an efficient foreman and a selected group of workmen these time allowances can be reduced in many instances as much as one-half4 ,experience alone will determine the possibilities of such reductions with safety4 ,footnote ,a3 ,for a more complete treatise of labor costs1 the student is referred to ,gillette's ,handbook of ,cost ,data1 ,section ,x1 the source1 in the main1 of the basis of this data4 ,,cost ,,of ,,placing ,,frame ,,and ,,covering ,by ,one ,man ,,hrs4 ,,per #ajjj ,b4,m4 ,,ft4 ,sills and plates #f #h1 no gains or mortises #bj ,sills and plates #f #h1 gains no mortises #dj ,sills and plates #f #h1 gains and mortises #fj ,joists and box sills #bj ,studding #b #d #cb ,studding #b #f #bc ,rafters #b #d1 plain gable roof #dj ,rafters #b #d1 hip roof add #e to #cj for each hip or valley4 ,rafters #b #f1 plain gable roof #bg ,rafters #b #f1 hip roof add #e to #cj for each hip or valley4 ,sheathing1 square edged1 horizontal1 walls #af ,sheathing1 square edged1 diagonal1 walls #ai ,sheathing1 #f matched1 walls #bd ,sheathing1 #f matched1 walls diagonal #cb ,sheathing for floors1 sub-floors1 square edged #aj ,sheathing for floors1 sub-floors1 square edged diagonal #ab ,roof ,sheathing1 plain gable roof #ac ,roof ,sheathing1 hip roof #bj ,,cost ,,of ,,placing ,,frame ,,and ,,covering 7,continued7 ,,hrs4 ,,per #ajjj ,,lin4 ,,ft4 ,cornices #djj to #hjj ,water table1 #c member #bbj ,corner boards #gc ,belt #aie ,,hrs4 ,,per ,m4 ,shingling1 plain roof1 new work #c ,shingling1 hips and valleys1 add #e for each hip or valley4 ,shingling1 old work1 add #bj for labor in removing old shingles4 ,shingling side walls1 plain #e ,shingling side walls1 fancy #h ,,hrs4 ,,per #ajjj ,b4,m4 ,,ft4 ,siding1 bevel1 #f #ce ,siding1 bevel1 #d #db ,siding1 shiplap #bg ,siding1 drop1 when window and door casings and corner boards are placed over siding #abj ,siding1 drop1 when jointed between casings and corner boards #cb ,surfaced barn boards #aa ,ceiling1 store #ec ,wainscoting1 cut1 put up1 finished with cap and round1 in a dwelling #df ,,cost ,,of ,,placing ,,floors ,by ,one ,man ,,hrs4 ,,per #ajjj ,b4,m4 ,,ft4 ,floors1 pine #ce ,floors1 yellow pine1 #c face1 laid on sheathing1 including paper between1 smoothing rough joints1 business block #dj ,floors1 yellow pine1 #c face1 laid direct on joist1 no smoothing #bf ,floors1 yellow pine1 #c face1 smoothed and sanded #de ,floors1 maple1 #b face1 laid not smoothed #dj ,floors1 maple1 #b face1 laid and smoothed #hj ,floors1 maple1 #a face1 laid and well smoothed #ajg ,floors1 oak1 fine floor1 glued1 smoothed1 scraped1 sand papered #cbj ,,cost ,,of ,,bridging ,,and ,,furring ,,hrs4 ,,per #ajjj ,,lin4 ,,ft4 ,bridging #fe ,placing plaster grounds #bj ,,cost ,,of ,,placing ,,baseboards b ,,hrs4 ,,per #ajj ,,lin4 ,,ft4 ,baseboard1 three member1 hardwood1 average number miters #aj ,baseboard1 two member1 scribed to floor #af ,baseboard1 plain1 round at floor #h ,moulding1 bed1 flat1 #c #b ,,cost ,,of ,,placing ,,doors1 ,,windows1 ,,blinds ,,hrs4 ,,on ,,each ,window1 to put together when ,k4 ,d4 7knock-down7 #a ,window1 making frame #c ,window1 setting frame ,window1 setting frame in brickwork #a ,window1 fitting and hanging sash per pair #a ,window1 hanging blinds per pair1 before frames are set ,window1 hanging blinds per pair1 after frames are set #b ,window1 casing inside #b ,window1 ordinary pine in frame building1 including setting of frame #e ,window1 same but hardwood #f ,window1 ordinary pine in brick building1 including setting of frame #f ,window1 same but hardwood #i ,window1 attic and cellar #a ,door1 making frame #b ,door1 making frame with transom #c ,door1 common hardwood1 set jambs1 case1 hang and finish1 including transom #aj ,door1 common #a pine complete #d ,door1 common #a pine complete #e ,door1 casing opening one side ,door1 casing opening both sides #a ,door1 fitting1 hanging and trimming #a ,door1 fitting1 hanging and trimming outside door1 pine #b ,door1 fitting1 hanging and trimming outside door1 oak #d ,sliding doors1 pine1 7framing not included7 to finish complete with lining1 jambs1 casing and hardware1 per pair #cb ,sliding doors1 same1 but hardwood #dh ,sliding doors for barn #ab' #ah' #bd ,transom1 fixed #a ,transom1 hung #a ,,estimating ,,cost ,,of ,,stair ,,work ,,hrs4 ,,on ,,each ,box stair1 cellar or attic #be ,one flight plain stair1 #g-room house1 hand rail1 balusters #dj ,one flight fine stair1 #i-room house1 handrail1 paneled #ajj ,,porches ,,in ,,general ,hours per lineal foot #e ,balustrade hours per #ajjj lineal feet #ejj ,lattice for porches1 hours per #ajjj square feet #af to #bjj ,,lath ,lath1 hours per #ajjj #g ,,miscellaneous ,,labor ,,items ,paneling1 pine1 hours per #ajj sq4 ft4 #ej ,paneling1 hardwood1 hours per #ajj sq4 ft4 #hc ,drawers1 dovetailed1 hours1 each #b ,drawers1 #ae #ah1 including racks and fittings #b ,shelves1 in storeroom1 dadoed into compartments #ah square1 hours per #ajj sq4 ft4 #fb ,shelves1 pantry1 no dado1 hours per #ajj sq4 ft4 shelf #cg ,closet hooks on strip of wood1 #ab apart1 hours per #ajj lineal feet #ae ,sideboard1 oak1 #h' #h'1 hours #ajj #ha4 ,estimating ,quantities of ,nails4--,the following table will enable one to estimate the quantity of nails required for the various kinds of common carpentry4 ,the table of length and number of nails to the pound1 ,appendix ,,iii1 may be made use of in determining nail estimates for other kinds of work not here specified4 ,,quantities ,,of ,,nails ,,materials ,,pounds ,,size ,,kind ,joists and sills per #ajjj ,b4,m4 ft4 #be #bj;d common4 ,studding per #ajjj ,b4,m4 ft4 #ae #aj;d common4 ,rafters per #ajjj ,b4,m4 ft4 #ae #aj;d common4 ,sheathing1 drop siding1 shiplap per #ajjj ,b4,m4 ft4 #bj #h;d common4 ,cornice per #ajjj lin4 ft4 #ah #h;d common4 ,shingling per #ajjj #d #d;d common4 ,bevel siding per #ajjj ,b4,m4 ft4 #ah #f;d common4 ,ceiling1 wainscoting per #ajjj ,b4,m4 ft4 #bj #f;d common4 ,floors1 pine per #ajjj ,b4,m4 ft4 #cj #h;d common4 ,floors1 hardwood per #ajjj ,b4,m4 ft4 #cj #f;d common4 ,baseboard per #ajjj ,b4,m4 ft4 #ab #h;d finish4 ,window trim1 one side #h;d finish4 ,door trim1 one side #h;d finish4 ,lath per #ajjj #h #c;d common1 fine4 ,lattice for porches per #ajjj sq4 ft4 #bj #c;d common4 ,balustrade per #ajjj lin4 ft4 #ah #f;d casing4 #hb4 ,example of ,form for ,carpentry ,costs4--,the following form1 used by a practical carpenter1 and published in the ,correspondence ,department of ,the ,american ,carpenter and ,builder1 should suggest means whereby the data just given may be made more readily available for estimating purposes4 ,it must be remembered in interpreting all such data that costs will vary greatly with conditions4 ,a carpenter1 for illustration1 who gives his time and attention to general carpentry cannot lay shingles with the speed a specialist in shingling can4 ,again1 a carpenter cannot make window and door frames by hand with the same speed that these can be made by machinery in a mill4 ,the prices given herewith are for work done by a general carpentry mechanic4 ,the estimator should test out these figures to see how they compare with actual working conditions in his community4 ,the following table is made for country conditions1 the men working at #cj;c per hour1 #i hours a day4 ,,materials ,,in ,,place ,,at #cj;c ,,per ,,hour ,ft4 per ,hrs4 per ,cost of ,labor ,nails ,various ,materials #i-;hrs4 #ajjj ------------------------ #b ,men ft4 ,m ,ft4 ,l or ,sq4,lbs4,size ---------------------------------------- ----------------------------- ,joists and sills #ijj #bj #f4jj #be #bj;d ,studding placed #fjj #cj #i4jj #ae #aj;d ,rafters #dej #dj #ab4jj #ae #aj;d ,sheathing vertical #gej #bd #g4bj #bj #h;d ,sheathing1 diagonal #efb #cb #i4fj #bj #h;d ,bevel siding #ead #ce #aj4ej #ah #f;d ,cornices #de #djj 4#ab -,l #ah #h;d ,shingling new roofs #djjj #d #a4ce #d #d;d ,lathing for plaster #begb #g #b4aj #h #c;d ,lattice for porches #aabe #af #d4hj #bj #c;d ,balustrade for porches #cf #ejj 4#ae -,l #ah #f;d ,base boards #h pine #baf #hc #bd4ij 4#jb -,l #ab #h;d ,baseboards1 #h hardwood #ajh #aff #di4hj 4#je -,l ,floors laid1 pine #ead #ce #aj4ej #cj #h;d ,floors laid1 hardwood4 #ajj #ahj #ed4jj 4#je -,l #cj #f;d ,floors cleaned1 hardwood #ajj #ahj #ed4jj 4#je -,l ,wainscoting1 pine #ed 4#aj -,l #bj #f;d ,paneling1 pine #cf 4#ae -,sq ,paneling1 hardwood #bb 4#be -,sq ,porches and verandas #a4ej -,l #ah #h;d ---------------------------------------- ----------------------------- ,m #ajjj ,ft4 ,l ,lineal ,sq ,square ,feet4 ,shingles are for new roofs2 where hips and valleys are required add #e additional for each one2 where old shingles and nails must be removed1 add again 7#bj to total7 for this work4 ,the above rate is based on figures of #cj;c per hour4 ,for other rates the following will apply in addition3 ,at #ce;c per hour add #ag2 at #dj;c add #cd2 at #de;c add #ea2 and at #ej;c per hour add ,example3 7,a7 ,take #a1jjj feet of hardwood floor to be cleaned at #ej;c per hour #ed4jj #cf4gb #ij4gb ,looking again we find it would take #ahj hours at #ej;c per hour #ij4jj 7,b7 ,take #a1jjj feet of joists to be placed at #ej;c per hour #f4jj #ad4jh #aj4jh4 ,looking for the hours we find it would take #bj at #ej;c1 or #aj4jj4 #hc4 ,total ,building ,costs by ,percentages4--,having carefully estimated the costs of one or two of the large items in a building1 such as lumber or millwork or labor1 the total cost of a building may be approximated with a fair degree of accuracy by a general contractor by means of the following table of percentages4 ,foundations or any other parts of a building which may be unusual should be excluded and figured separately in detail4 ,in any event1 before a building is finally completed the contractor will have to settle with each sub-contractor upon the basis of detailed cost estimates4 ,where time is available1 the contractor as a rule secures bids from the various sub-contractors1 such as the plumber1 the lather1 the mason1 etc41 combining these and adding his commission of #aj for oversight1 and an additional #aj for incidentals or contingencies4 ,,costs ,,by ,,percentages ,frame ,brick ,items ,building ,dwelling ,excavation1 brick and cut stone #af #cf ,plastering and materials1 including lathing #h #f ,millwork including glass and glazing #ba #bj ,lumber #ai #ab ,carpentry labor #ah #aj ,hardware #c #c ,tinwork and galvanized iron #b #d ,plumbing and gas fitting and materials #g #c ,painting and materials #e #e ,heating 7not included7 -------------- ,total #ajj #ajj ,example3 ,a lumber bill for a given frame house is found to figure #ejj1 determine the approximate cost of the various sub-contracts1 and for the house as a whole4 ,solution3 #ejj #ai of the total cost4 ,total cost #bfcb 7exclusive of heating74 ,excavation1 brick and cement work #af of #bfcb #dba4ab ,plastering #h of #bfcb #baj4ef ,millwork and glazing #ba of #bfcb #eeb4gb ,carpentry labor #ah of #bfcb #dgc4gf ,hardware #c of #bfcb #ib4ab ,tinwork #b of #bfcb #fe4hj ,plumbing #g of #bfcb #ahd4bd ,painting #e of #bfcb #aca4fj ,lumber #ejj4jj -------- #bfca4ib ,to this must be added heating1 electric wiring1 electric and gas fixtures1 window shades1 cement walks1 sewerage1 grading1 decoration of walls1 architect's fee and contractor's commission4 ,for furnace heat1 add #f to #g 2 for steam1 add #h to #aj 2 for hot water1 add #aj to #ab additional4 ,for electric wiring1 add #a4 ,for fixtures1 electric and gas1 add #b to #c4 ,to this total add #aj for incidentals and contingencies2 add #aj for contractor's charge4 ,above this amount add #f for architect's fee1 to get the cost to the owner4 ,such a method of estimating should not be mistaken for anything but fairly safe approximation where normal conditions exist4 ,,appendix ,i ,illustration3 ,fig4 #aeb4 ,natural ,trigonometric ,functions4 ,consider the angle ,,dae1 ,fig4 #aeb4 ,from any point on the line ,,ad drop a line perpendicular to the side ,,ae forming the right triangle ,,abc4 ,let a represent the value or length of the side ,,bc2 let b represent the value of the side ,,ac2 let c represent the value of the side ,,ab4 ,the ratio of the side a to the side c is called the sine of the angle ,a4 ,more concisely stated1 a_/c sin ,a4 ,the sine of an angle is the ratio of its opposite side to its hypotenuse1 or opposite side over hypotenuse sine of angle ,a sin ,a4 ,in a similar manner3 b adjacent side --- --------------- cosine of angle ,a cos ,a4 c hypotenuse a opposite side --- --------------- tangent of angle ,a tan ,a4 b adjacent side b adjacent side --- ---------------- cotangent of angle ,a cot ,a4 a opposite side c hypotenuse --- ---------------- secant of angle ,a sec ,a4 b adjacent side c hypotenuse --- --------------- cosecant of angle ,a csc ,a4 a opposite side ,these ratios are known as natural functions of the angle because their values change with every change in the value of the angle4 ,the lengthening of the sides of the angle should not be mistaken for a change in the value of the angle4 ,draw to scale very carefully any angle and drop lines from any two points1 as at ,b and ,b1 ,fig4 #aeb1 which shall be perpendicular to the base line4 ,measure the sides of the triangles so formed and express their ratios as functions of the angle ,a4 ,comparing like functions of large and small triangle it will be seen that once an angle is known in degrees1 its sine1 cosine1 etc41 are determined irrespective of the length of sides4 ,and1 vice versa1 if we know the functional values or ratios of certain sides of the right triangle formed about an angle1 we have determined the value of the angle in degrees4 ,the ,table of ,natural ,trigonometric ,functions1 ,appendix ,,ii1 is nothing more than a compilation of these various ratios carefully figured out and placed in the form of a table to assist in the easy solution of problems having to do with the finding of certain parts of a triangle when other parts are given4 ,with a protractor1 measure the angle ,a of the triangle whose sides were just measured1 and compare the ratios of the sides or the functional values with those given in the ,table1 ,appendix ,,iii1 for the same angle4 ,the larger the scale of the drawing1 the greater the accuracy4 ,by making use of the hundredths scale of the framing square together with a finely pointed pair of dividers1 variation in values should not be great4 ,solutions of ,right ,triangles4--,by the solution of right triangles is meant the finding of unknown sides or angles when values of other sides and angles are known4 ,example #a4--;,given ,a #cj degrees1 c #bd2 ,find ,b1 a1 b4 ,solution--,b #ij-cj #fj degrees4 7,the sum of the angles of a triangle equals #ahj degrees4 ,c #ij degrees47 7#a7 a_/c sin ,a2 whence1 a c sin ,a4 7a c times sine ,a47 7#b7 b_/c cos ,a2 whence b c cos ,a4 ,from the ,tables1 ,appendix ,,ii1 sin of ,a1 or #cj degrees1 4#e4 ,substituting numerical values in 7#a71 a #ab4 ,again1 from ,tables1 cos ,a1 or #cj degrees1 4#hff4 ,substituting numerical values in 7#b71 b #bj4ghd4 ,arith4 check c a b2 #bd #ab #bj4gh2 #egf #add #dca4h2 #egf #egf4 ,graphic check4--,the graphic check which1 it will be seen1 might have been made use of as a graphic solution1 consists in setting one square upon another with the angle of direction and the length of one side determined by the data given4 ,that is1 in this problem the protractor is set at #cj degrees and a length of #bd units is taken on the inclined square4 ,the lengths of a and b are then carefully measured by taking a reading of the full inches and reading1 the remaining fraction to hundredths by means of a sharp pair of dividers and the hundredths scale of the square4 ,very many carpenters make use of graphic solutions such as this in determining rafter lengths4 ,a little consideration1 however1 will show that it is a rather risky method of procedure unless the scale is large and the work scaled small4 ,graphs serve as easy checks against grave errors upon all kinds of work4 ,example #b4--;,given ,a and a4 ,to find ,b1 c1 and b4 ,solution--,b #ij degrees ,a4 a_/c sin ,a2 c a_/sin ,a b_/c cos ,a2 b c cos ,a4 ,substitute the numerical values and check as in ,example #a4 ,example #c4--;,given ,a and b4 ,to find ,b1 a1 and c4 ,solution--,b #ij degrees ,a4 a_/c sin ,a2 a c sin ,a4 b_/c cos ,a2 c b _/ cos ,a ,substitute the numerical values and check as in ,example i4 ,example #d4--;,given a and c4 ,to find ,a1 ,b1 and b4 ,solution--sin ,a a _/ c 7,that is1 look in the tables1 ,appendix ,,ii1 for the angle which has a sine equal to the result obtained by dividing the numerical value of the side a by the value of the side c47 ,b #ij degrees ,a4 b_/c cos ,a2 b c cos ,a4 ,substitute numerical values and check as in ,example i4 ,example #e4--;,given a and b4 ,to find ,a1 ,b4 and c4 ,solution--tan ,a a _/ b ,b #ij degrees ,a4 a_/c sin ,a2 c a _/ sin ,a ,substitute numerical values and check as in ,example #a4 ,,appendix ,,ii ,directions4 ,an examination of the table of natural functions will indicate in the column at the left1 angles of degrees to and including #de degrees1 reading down4 ,the column to the extreme right will be found to contain degrees from #de-ij inclusive1 reading up4 ,this compact arrangement of table is made possible thru the fact that sines and cosines1 tangents and cotangents are reciprocals one of the other4 ,that is1 as the sine 7column #b1 reading down7 increases in value1 the cosine of the complementary angle 7columns #f and #b1 reading up7 decreases4 ,example #a4--;,find the value of the sine of #dj degrees4 ,solution--,columns #a and #b1 reading down1 sin #dj degrees 4#fdbh4 ,example #b4--;,find the value of sin #ej degrees4 ,solution--,columns #f and #e1 reading up1 sin #ej degrees 4#gffj4 ,example #c4--;,find the value of cos #dj degrees4 ,solution--,columns #a and #e1 reading down1 cos #dj degrees 4#gffj which is as might have been expected4 ,since #dj degrees is the complement of #ej degrees1 the cos #dj degrees should be the same in value as the sin #ej degrees4 ,example #d4--;,find the value of cos #hg degrees4 ,solution--,columns #f and #b reading up1 cos #hg degrees 4#jebc ,example #e4--,tangent and cotangent values4 ,proceed as with sines using columns #a and #c1 reading down1 for tangent values between #j-de degrees inclusive1 columns #f and #d1 reading up1 for values between #de-ij degrees4 ,for cotangent values between #j-de degrees use columns #a and #d reading down1 and columns #f and #c reading up for cotangent values between #de-ij degrees inclusive4 ,,table ,,of ,,natural ,,sines1 ,,tangents1 ,,cosines1 ,,and ,,cotangents ,degrees ,sine ,tangent ,cotangent ,cosine ---------------------------------------- --------------- #j #j #j #a #ij #a 4#jage 4#jage #eg4bijj 4#iiih #hi #b 4#jcdi 4#jcdi #bh4fcfc 4#iiid #hh #c 4#jebc 4#jebd #ai4jhaa 4#iihf #hg #d 4#jfih 4#jfii #ad4cjjg 4#iigf #hf ---------------------------------------- --------------- #e 4#jhgb 4#jhge #aa4dcja 4#iifb #he ---------------------------------------- --------------- #f 4#ajde 4#ajea #i4eadd 4#iide #hd #g 4#abai 4#abbh #h4addc 4#iibe #hc #h 4#acib 4#adje #g4aaed 4#iijc #hb #i 4#aefd 4#aehd #f4cach 4#ihgg #ha ---------------------------------------- --------------- #aj 4#agcf 4#agfc #e4fgac 4#ihdh #hj ---------------------------------------- --------------- #aa 4#aijh 4#aidd #e4addf 4#ihaf #gi #ab 4#bjgi 4#babf #d4gjdf 4#igha #gh #ac 4#bbej 4#bcji #d4ccae 4#igdd #gg #ad 4#bdai 4#bdic #d4jajh 4#igjc #gf ---------------------------------------- --------------- #ae 4#behh 4#bfgi #c4gcba 4#ifei #ge ---------------------------------------- --------------- #af 4#bgef 4#bhfg #c4dhgd 4#ifac #gd #ag 4#bibd 4#cjeg #c4bgji 4#iefc #gc #ah 4#cjij 4#cbdi #c4jggg 4#ieaa #gb #ai 4#cbef 4#cddc #b4ijdb 4#idee #ga ---------------------------------------- --------------- #bj 4#cdbj 4#cfdj #b4gdge 4#icig #gj ---------------------------------------- --------------- #ba 4#cehd 4#chci #b4fjea 4#iccf #fi #bb 4#cgdf 4#djdj #b4dgea 4#ibgb #fh #bc 4#cijg 4#dbde #b4ceei 4#ibje #fg #bd 4#djfg 4#ddeb #b4bdfj 4#iace #ff ---------------------------------------- --------------- #be 4#dbbf 4#dffc #b4adde 4#ijfc #fe ---------------------------------------- --------------- #bf 4#dchd 4#dhgg #b4jejc 4#hihh #fd #bg 4#dedj 4#ejie #a4ifbf 4#hiaj #fc #bh 4#dfie 4#ecag #a4hhjg 4#hhbi #fb #bi 4#dhdh 4#eedc #a4hjdj 4#hgdf #fa ---------------------------------------- --------------- #cj 4#ejjj 4#eggd #a4gcba 4#hffj #fj ---------------------------------------- --------------- #ca 4#eaej 4#fjji #a4ffdc 4#hegb #ei #cb 4#ebii 4#fbdi #a4fjjc 4#hdhj #eh #cc 4#eddf 4#fdid #a4ecii 4#hchg #eg #cd 4#eeib 4#fgde #a4dhbf 4#hbij #ef ---------------------------------------- --------------- #ce 4#egcf 4#gjjb #a4dbha 4#haib #ee ---------------------------------------- --------------- #cf 4#ehgh 4#gbfe #a4cgfd 4#hjij #ed #cg 4#fjah 4#gecf #a4cbgj 4#gihf #ec #ch 4#faeg 4#ghac #a4bgii 4#ghhj #eb #ci 4#fbic 4#hjih #a4bcdi 4#ggga #ea ---------------------------------------- --------------- #dj 4#fdbh 4#hcia #a4aiah 4#gffj #ej ---------------------------------------- --------------- #da 4#fefa 4#hfic #a4aejd 4#gedg #di #db 4#ffia 4#ijjd #a4aajf 4#gdca #dh #dc 4#fhbj 4#icbe #a4jgbd 4#gcad #dg #dd 4#fidg 4#ifeg #a4jcee 4#gaic #df ---------------------------------------- --------------- #de 4#gjga #a4jjjj #a4jjjj 4#gjga #de ---------------------------------------- --------------- ,cosine ,cotangent ,tangent ,sine ,degrees ---------------------------------------- --------------- ,,to ,,find ,,the ,,value ,,of ,,an ,,angle1 ,,the ,,value ,,of ,a ,,function ,,being ,,known ,example #f4--sin 4#eaej1 find the angle4 ,solution--,looking in columns #b and #e 7sine values from #j-ij degrees7 ,ans4 #ca degrees 7,columns #b and #a74 ,example #g4--;cot #a4cgfd1 find the angle4 ,solution--,looking in columns #c and #d1 ,ans4 #cf degrees4 ,interpolation4--,frequently one must find a functional value for fractional degrees1 or degrees and minutes4 ,also1 it becomes necessary to find the value of an angle with greater accuracy than even degrees1 as given in the table herewith4 ,this process of finding more accurate values is known as interpolation4 ,,to ,,find ,,the ,,value ,,of ,a ,,function ,,when ,,the ,,angle ,,is ,,in ,,fractional ,,degrees ,example #h4--;,find the value of tan #ej degrees #bj min4 ,solution4--tan #ej degrees #a4aiah tan #ea degrees #a4bcdi difference for an interval of #a degree 4#jdca #bj min4 #bj_/fj #a_/c of #a degree2 of 4#jdca 4#jadd tan #ej degrees #bj min4 #a4aiah 4#jadd #a4bjfb4 ,the value of a fractional degree would be similarly treated for the sine1 these functions increasing as the value of the angle increases4 ,the cosine and cotangent1 however1 decrease in value as the angle increases4 ,for this reason the fractional value of the cosine and cotangent must be subtracted from1 instead of added to1 the value of the function of the next lower number of degrees4 ,example #i4 ,find the value of cos #bf deg4 #cj min4 ,solution--cos #bf deg4 4#hihh cos #bg deg4 4#hiaj difference for interval of #a deg4 4#jjgh #cj min4 of #a deg42 of 4#jjgh 4#jjci cos4 #bf deg4 #cj min4 4#hihh - 4#jjci 4#hidi4 ,,to ,,find ,,the ,,value ,,of ,,an ,,angle ,,when ,,the ,,functional ,,value ,,cannot ,,be ,,found ,,in ,,exact ,,form ,,in ,,the ,,table ,example #aj4--;,find the angle whose tan is 4#e ,solution--,from the table1 4#dhgg tan #bf deg4 4#ejie tan #bg deg4 difference for interval of #a deg4 4#jbah 4#ejjj tan angle ,x4 4#dhgg tan #bf deg4 difference for interval between tan angle ,x and tan #bf deg4 4#jabc #abc_/bah of #a deg4 or #fj min4 #cd min4 ,therefore1 angle whose tangent 4#e #bf deg4 #cd'4 ,rule3 7#a7 ,search the body of the table for the functional values next above and next below that given4 7#b7 ,find the difference between these functional values4 ,this difference is for an interval of #a degree or #fj minutes4 7#c7 ,find the difference between the given functional value and that of the lower angle of the two used above4 7#d7 ,express this last difference as the numerator of a fraction whose denominator is the first difference found1 or the difference for the interval of #a degree4 ,this gives the fractional part of #a degree or #fj minutes which the second difference is4 7#e7 ,express this difference in minutes and add if the function be a sine or tangent1 and substract if a cosine or cotangent to the number of degrees representing the angle whose function was the lower of the two functions found given in the table4 ,,appendix ,,iii ,,useful ,,tables ,,fractional ,,equivalents ,,for ,,decimal ,,values 4#jaef #a_/fd 4#bfef #ag_/fd 4#eaef #cc_/fd 4#gfef #di_/fd 4#jcab #a_/cb 4#ecab #i_/cb 4#bhab #ag_/cb 4#ghab #be_/cb 4#jdfh #c_/fd 4#bifh #ai_/fd 4#edfh #ce_/fd 4#gifh #ea_/fd 4#jfbe #a_/fd 4#cabe #e_/af 4#efbe #i_/af 4#habe #ac_/af 4#jgha #e_/fd 4#cbha #ba_/fd 4#egha #cg_/fd 4#hbha #ec_/fd 4#jicg #c_/cb 4#cdcg #aa_/cb 4#eicg #ai_/cb 4#hdcg #bg_/cb 4#ajic #g_/fd 4#ceic #bc_/fd 4#fjic #ci_/fd 4#heic #ee_/fd 4#abe #a_/h 4#cge #c_/h 4#fbe #e_/h 4#hge #g_/h 4#adjf #i_/fd 4#cijf #be_/fd 4#fdjf #da_/fd 4#hijf #eg_/fd 4#aefb #e_/cb 4#djfb #ac_/cb 4#fefb #ba_/cb 4#ijfb #bi_/cb 4#agah #aa_/fd 4#dbah #bg_/fd 4#fgah #dc_/fd 4#ibah #ei_/fd 4#ahge #c_/af 4#dcge #g_/af 4#fhge #aa_/af 4#icge #ae_/af 4#bjca #ac_/fd 4#deca #bi_/fd 4#gjca #de_/fd 4#ieca #fa_/fd 4#bahg #g_/cb 4#dfhg #ae_/cb 4#gahg #bc_/cb 4#ifhg #ca_/cb 4#bcdc #ae_/fd 4#dhdc #ca_/fd 4#gcdc #dg_/fd 4#ihdc #fc_/fd 4#bej #a_/d 4#ejj #a_/b 4#gej #c_/d #a4jjj #a ,where rafter lengths are determined by multiplying unit lengths by the run1 the answer will almost invariably result in a decimal4 ,such decimal values may be readily translated into fractional forms by means of the accompanying table4 ,example3 ,a roof of pitch has a common rafter run of #ad'2 find the length of common rafter4 ,answer3 #ad #ad4db #bja4hh or #af4hb'4 ,by the table1 4#hb #ec_/fd4 ,a carpenter1 however1 would not care for such accuracy2 the nearest #a_/af or even would be sufficient4 ,,wood ,,and ,,machine ,,screw ,,sizes ,the difference between consecutive sizes is 4#jacaf4 ,no4 of ,size of ,no4 of ,size of ,no4 of ,size of ,screw ,number in ,screw ,number in ,screw ,number in ,gage ,decimals ,gage ,decimals ,gage ,decimals ---------------------------------------- -------------------- #jjj 4#jcaeb #af 4#bfhdj #cd 4#ejebh #jj 4#jddhf #ag 4#bhaef #ce 4#eahdd #j 4#jeghd #ah 4#bidgb #cf 4#ecafj #a 4#jgajj #ai 4#cjghh #cg 4#eddgf #b 4#jhdaf #bj 4#cbajd #ch 4#eegib #c 4#jigcb #ba 4#ccdbj #ci 4#egajh #d 4#aajdh #bb 4#cdgcf #dj 4#ehdbd #e 4#abcfd #bc 4#cfjeb #da 4#eigdj #f 4#acfhj #bd 4#cgcfh #db 4#fajef #g 4#adiif #be 4#chhfd #dc 4#fbcgb #h 4#afcab #bf 4#djjjj #dd 4#fcfhh #i 4#agfbh #bg 4#dacaf #de 4#fejjd #aj 4#ahidd #bh 4#dbfcb #df 4#ffcbj #aa 4#bjbfj #bi 4#dcidh #dg 4#fgfcf #ab 4#baegf #cj 4#debfd #dh 4#fhieb #ac 4#bbhib #ca 4#dfehj #di 4#gjbfh #ad 4#bdbjh #cb 4#dghif #ej 4#gaehd #ae 4#beebd #cc 4#dibab ---------------------------------------- -------------------- ,frequently the carpenter wishes to know the diameter of hole necessary to receive the shank of a screw of a certain gage4 ,should a screw gage be accessible1 he may readily determine this4 ,should no gage be at hand1 he may determine the size of hole by consulting the accompanying table of ,wood and ,machine ,screw ,sizes4 ,example3 ,what size bit must be selected to bore a hole for a ,no4 #aj screw4 ,by the table1 a ,no4 #aj screw is 4#ahidd in diameter4 ,by the table of ,fractional ,equivalents for ,decimal ,values it will be seen that a #c_/af bit must be used4 ,the test for gage of screw is always made over the shank just below the head4 ,,length ,,and ,,number ,,of ,,wire ,,nails ,,to ,,the ,,pound ,size ,,length,,common,,casing,,finish,,clinch ,,fence ,,fine ,,gal4 ,,ins4 ,,shingle ---------------------------------------- ---------------- #b;d #a #ijj #addj #c;d #a #fae #haj #efh #d;d #a #cbb #dgc #ehd #bej #e;d #a #bed #f;d #b #bjj #ahj #cjj #aeg #aad #g;d #b #aed #h;d #b #ajf #aab #aij #ii #gd #i;d #b #he #aj;d #c #gd #ij #acd #fi #db #ab;d #c #eg #af;d #c #df 4 #bj;d #d #bi #cj;d #d #bc #dj;d #e #ag #ej;d #e #ad #fj;d #f #aa ---------------------------------------- ------------- ,nails are sold in quantity by the keg1 #ajj lbs4 of nails1 exclusive of the keg4 ,twenty1 #cj1 #dj1 #ej and #fj;d are base4 ,other sizes have certain fixed additions per keg to this base price4 ,for example1 the price list adopted by manufacturers in #ahif allows an addition per keg of 4#gj for #b;d common1 4#de for #c;d common1 etc4 ,wire nails are also bought and sold by weight1 the size of wire according to the standard wire gage and the length in inches being taken into consideration in specifying the size and in fixing the price per pound4 ,common wire nails are thick and have large flat heads4 ,they are used in rough work where strength is desired4 ,finishing nails are used for fine work such as inside woodwork and cabinet work4 ,casing nails are somewhat thicker and stronger than finishing nails2 they have smaller heads4 ,,wire ,,brads ,size1 inches #a ,wire ,gage1 nos #bj #ah #ai #ai #ah #af #ah #ag #ah ,approx no brads to lb4 #gejjgbjjdbfgceefbgehbfjjbcfdaghabjfi ---------------------------------------- ------------------- ,size1 inches #a #a #a #a #a #a #a #a #a ,wire ,gage1 nos #ag #af #ag #af #af #ae #ad #ae #ad ,approx no brads to lb4 #aeehaadcabdf #iac #gfa #ehd #ejj #ejj #djf ---------------------------------------- ------------------- ,size1 inches #b #b #b #b #c #c #c ,wire ,gage1 nos #ad #ac #ac #ab #ad #ab #aa ,approx no brads to lb4 #cej #bfh #bad #afd #aej #acg #aje ---------------------------------------- ------------------- ,,board ,,measure ,,table ,size ,length1 in ,feet1 of ,joist1 ,scantling and ,timber in ---------------------------------------- --------------------- ,inches #ab #ad #af #ah #bj #bb #bd #bf #bh #cj #cb #cd #cf #ch #dj ---------------------------------------- ---------------------------- #b #d #h #i #aa #ab #ac #ae #af #ag #ai #bj #ba #bc #bd #be #bg #b #f #ab #ad #af #ah #bj #bb #bd #bf #bh #cj #cb #cd #cf #ch #dj #b #h #af #ai #ba #bd #bg #bi #cb #ce #cg #dj #dc #de #dh #ea #ec #b #aj #bj #bc #bg #cj #cc #cg #dj #dc #dg #ej #ec #eg #fj #fc #fg #b #ab #bd #bh #cb #cf #dj #dd #dh #eb #ef #fj #fd #fh #gb #gf #hj #b #ad #bh #cc #cg #db #dg #ea #ef #fa #fe #gj #ge #gi #hd #hi #ic #c #f #ah #ba #bd #bg #cj #cc #cf #ci #db #de #dh #ea #ed #eg #fj #c #h #bd #bh #cb #cf #dj #dd #dh #eb #ef #fj #fd #fh #gb #gf #hj #c #aj #cj #ce #dj #de #ej #ee #fj #fe #gj #ge #hj #he #ij #ie #ajj #c #ab #cf #db #dh #ed #fj #ff #gb #gh #hd #ij #if #ajb #ajh #aad #abj #c #ad #db #di #ef #fc #gj #gg #hd #ia #ih #aje #aab #aai #abf #acc #adj #d #d #af #ai #ba #bd #bg #bi #cb #ce #cg #dj #dc #de #dh #ea #ec #d #f #bd #bh #cb #cf #dj #dd #dh #eb #ef #fj #fd #fh #gb #gf #hj #f #f #cf #db #dh #ed #fj #ff #gb #gh #hd #ij #if #ajb #ajh #aad #abj #f #h #dh #ef #fd #gb #hj #hh #if #ajd #aab #abj #abh #acf #add #aeb #afj #h #h #fd #ge #he #if #ajg #aag #abh #aci #adi #afj #aga #aha #aib #bjc #bac #h #aj #hj #ic #ajg #abj #acc #adg #afj #agc #ahg #bjj #bac #bbg #bdj #bec #bfg #aj #aj #ajj #aag #acc #aej #afg #ahc #bjj #bag #bcc #bej #bfg #bhc #cjj #cag #ccc #aj #ab #abj #adj #afj #ahj #bjj #bbj #bdj #bfj #bhj #cjj #cbj #cdj #cfj #chj #djj #ab #ab #add #afh #aib #baf #bdj #bfd #bhh #cab #ccf #cfj #chd #djh #dcb #def #dhj #ab #ad #afc #aif #bbd #beb #bhj #cjh #ccf #cfd #cib #dbj #ddh #dgf #ejd #ecb #efj #ad #ad #aif #bbi #bfa #bid #cbg #cei #cib #dbe #deg #dij #ebc #eee #ehh #fba #fec ---------------------------------------- ---------------------------- ,,strength ,,of ,,materials ,,yellow ,,pine ,,posts ,load in ,tons ,length in ft4 ,size in inches #d #d #e #e #f #f #g #g #h #h #i #i #h #d #e #f #g #h #i #aj #c #d #e #f #g #h #ab #b #c #d #e #f #g #ad #a #b #c #d #e #f #af #a #b #c #d #e #ah #a #b #c #d ,,hard ,,pine ,,beams ,,and ,,girders ,load in ,tons ,length in ft4 ,size in inches #b #f #c #f #d #f #f #f #h #h #f #a #a #b #c #e #h #a #a #b #e #aj #a #b #d #ab #a #a #c #ad #a #b #af #b #ah #a ,,steel ,i ,,beams ,load in ,tons ,length ,size in inches in ft4 #f #h #ab #aj #g #ad #ah #ab #f #ab #af #ad #e #aj #ad #af #d #h #ab #ah #b #f #aj #bj #d #h #bb #b #f #bd #d ,,brick ,,piers ,load in ,tons ,height ,size in inches in ft4 #f #f #f #h #h #h #h #ab #ab #ab #ab #af #af #af #f #b #c #d #e #f #g #i #h #a #b #c #d #e #f #h #aj #a #b #c #e #e #f #g ,,stresses ,,for ,,structural ,,timbers ,,working ,,unit ,,stresses ,,used ,,in ,,dry ,,locations ,bending ,compression ,stress in ,horizontal ,parallel to ,perpen- extreme shear grain ,short dicular ,species of fibre stress ,columns to grain ,timber ,lbs4 sq4in4 ,lbs4 sq4in4 ,lbs4 sq4in4 ,lbs4 sq4in4 99,fir1 ,douglas ,dense grade #a1fjj #ajj #a1bjj #cej ,sound grade #a1cjj #he #ijj #cjj ,hemlock1 eastern #a1jjj #gj #gjj #cjj ,hemlock1 western #a1cjj #ge #ijj #cjj ,oak #a1djj #abe #ijj #djj ,pine1 eastern white #ijj #hj #gjj #bej ,pine1 ,norway #a1ajj #he #hjj #cjj 99,pine1 southern yellow ,dense grade #a1fjj #abe #a1bji #cej ,sound grade #a1cjj #he #ijj #cjj ,spruce #ijj #gj #fjj #bjj ,tamarack #a1bjj #ie #ijj #cej 99 ,,note3 ,the safe working stresses given in this table are for timbers with defects limited according to the sections on defects in the rules of the ,southern ,pine ,association for ,select ,structural ,material4 ,dense southern yellow pine and dense ,douglas fir should also conform to the other requirements of this rule4 ,sound southern yellow pine and sound ,douglas fir require no additional qualifications1 whereas the other species should1 in addition to being graded for defects1 have all pieces of exceptionally low density for the species excluded4 ,this table gives working unit stresses for structural timbers used in dry locations1 and is compiled in the main from material furnished by the ,forest ,products ,laboratory1 ,madison1 ,wis4 ,,table ,,of ,,brick ,,wall ,,contents ,,in ,,number ,,of ,,bricks ,seven ,bricks to ,each ,sq4 ,ft4 of ,wall ,surface ,no4 of sq ft4 ,thickness of wall #d #h #ab #af #bj #bd #a #g #ae #bc #cj #ch #de #b #ae #cj #de #fj #ge #ij #c #bc #de #fh #ij #aac #ace #d #cj #fj #ij #abj #aej #ahj #e #ch #ge #aac #aej #ahh #bbe #f #de #ij #ace #ahj #bbe #bgj #g #ec #aje #aeh #baj #bfc #cae #h #fj #abj #ahj #bdj #cjj #cfj #i #fh #ace #bjc #bgj #cch #dje #aj #ge #aej #bbe #cjj #cge #dej #bj #aej #cjj #dej #fjj #gej #ijj #cj #bbe #dej #fge #ijj #a1abe #a1cej #dj #cjj #fjj #ijj #a1bjj #a1ejj #a1hjj #ej #cge #gej #a1abe #a1ejj #a1hge #b1bej #fj #dej #ijj #a1cej #a1hjj #b1bej #b1gjj #gj #ebe #a1jej #a1ege #b1ajj #b1fbe #c1aej #hj #fjj #a1bjj #a1hjj #b1djj #c1jjj #c1fjj #ij #fge #a1cej #b1jbe #b1gjj #c1cge #d1jej #ajj #gej #a1ejj #b1bej #c1jjj #c1gej #d1ejj ,example--,determine the number of bricks in a wall #ab #ah' #fj'4 ,solution--,the wall contains a surface area of #a1jhj sq4 ft4 ,by the table #ajj sq4 ft4 contains #b1bej bricks1 then #a1jjj sq4 ft4 will contain #bb1ejj bricks4 #hj sq4 ft4 will contain1 by the table1 #a1hjj bricks1 making a total of #bd1cjj bricks4 ,,appendix ,,iv 7,short ,cuts to ,roof ,framing7 ,griffith's ,framing ,tables ,for the ,square and ,octagonal ,roof ,directions for ,using ,table for the ,steel ,square4--,fig4 #gj-;a4 ,example4--,given a square hipped roof1 that is1 a roof with square corners1 having a span of #be ft4 and a pitch of 4 #a4 ,to ,lay ,out ,miter ,cut of ,plate4--,take #ab on tongue of framing square and #ab on blade2 scribe along blade4 7,cf4 small table1 ,fig4 #gj-;a47 #b4 ,length of ,ridge4--,length of long plate diminished by length of short plate1 increased by thickness of ridge piece plus diagonal thickness of hip4 #c4 ,to ,lay ,out ,common ,rafter4-- a4 ,plumb cut4 7,cf4 column #e1 beginning at left1 ,fig4 #gj-;a47 ,take #ab on tongue of square and #ab on blade 7column #b71 scribe along blade4 b4 ,length of common rafter4 7,cf4 column #aa7 #ab 7run of common rafter7 x #af4ig 7length of common rafter per foot of run7 #ag' #h4ab #ag' #h 74#ab 1 columns #c and #d74 c4 ,seat cut4 7,cf4 column #h7 ,take #ab on tongue and #ab on blade2 scribe along tongue4 d4 ,tail for common rafter4 7#a7 ,length determined as was that of common rafter1 the horizontal projection or length of look- out becoming multiplier4 #agc 7#b7 ,end cut use same numbers as for plumb cut but invert position of square4 e4 ,reduction for ridge4 ,measure straight back from plumb cut a distance equal to #c_/ the thickness of ridge piece4 #d4 ,to ,lay ,out ,hip or ,valley ,rafter4-- a4 ,plumb cut4 7,cf4 column #f7 ,take #ag on the tongue and #ab on the blade2 scribe along the blade4 b4 ,side cut4 7,cf4 column #af7 ,take #ag on the tongue and #bj4gh or #bj-ac_/af 7columns #c and #d7 on the blade2 scribe along the blade4 ,this also gives the miter cut at the end of the tail of the hip for fascia1 and also the miter cut at the bird's mouth joint of valley rafter1 where it must be cut out to fit the angle of the plate4 c4 ,length of hip or valley rafter4 7,cf4 column #ab7 #ab 7run of common rafter7 x #bj4gh 7length of hip or valley rafter per foot of run of common rafter7 #ba' #g4ge #ba' #g 74#ge 1 columns #c and #d47 d4 ,seat cut4 7,cf4 column #i7 ,take #ag on tongue and #ab on the blade1 scribe along the tongue4 e4 ,tail for hip or valley rafter4 7#a7 ,length determined as was that of hip or valley rafter1 the horizontal projection of tail or length of the lookout of common rafter becoming the multiplier4 7#b7 ,end cut use same numbers as for plumb cut of hip or valley but invert square4 f4 ,reduction for ridge4 ,measure straight back from plumb cut diagonal thickness of ridge4 g4 ,backing of hip4 7,cf4 column #ba7 ,take #ab 7rise of common rafter7 on the tongue and #bj-ac_/af on the blade scribe along the tongue for angle of backing4 h4 ,drop of hip when no backing is given4 7,cf4 column #bc7 ,reduce at seat cut #i_/af1 measured at right angles to seat cut4 #e4 ,to ,lay ,out ,jacks4-- a4 ,plumb cut4 ,same as that for the common rafter6 b4 ,side cut4 7,cf4 column #ad7 ,take #ab on the tongue and #af4ig or #ag on blade 74#ig #a1 columns #c and #d71 scribe on the blade4 ,scribing along the tongue will give the face cut of roof boards1 also of plancher4 c4 ,length4 ,jacks set #bd centers1 beginning with shortest jack #b' #aj 7column #ai74 ,second shortest jack length of shortest increased #b' #aj1 etc4 ,beginning with longest jack length of common rafter diminished by #b' #aj1 etc4 d4 ,tail for jack4 ,same as for common rafter4 #f4 ,note4-- ,all rafter lengths are measured down the middle of the top edges theoretically4 ,on the square cornered roof1 measurements of hip or valley rafters may be made from the long point without further reduction in length providing a #b thick ridge is used4 ,jacks need no further reduction in length on a square cornered building provided the hips or valleys are of the same thickness as the jacks and the measurements are made from the long points of the jacks4 ,otherwise suitable reductions must be made for rafter and ridge thicknesses4 ,directions for ,using ,table for ,protractor4--,fig4 #gj-;b4 ,example4--,given to frame an octagonal silo with a span of #ba' and a roof pitch of #aa to the foot4 #a4 ,to ,lay ,out ,miter ,cut of ,plate4--7,cf4 small table ,fig4 #gj-;b47 ,eight sided polygon1 plate miter #fg degrees4 ,set a ,t-bevel by means of a protractor,b to this angle4 ,footnote ,b3 ,starrett's ,framing ,tool is strongly recommended for framing in degrees1 ,cf4 ,figs4 #ha and #hb4 #b4 ,to ,find ,length of a ,side for ,plate4--7,cf4 small table1 ,fig4 #gj-;b47 #ba' 7#b x run7 x 4#dad 7cotangent of octagon7 #h4fi' #h' 74#fi 1 columns #c and #d47 #c4 ,to ,lay ,out ,common ,rafter4-- a4 ,plumb cut4--7,cf4 column #e7 #dg deg4 #cj min4 ,set ,t-bevel by means of protractor to same4 b4 ,length4--7,cf4 column #aa74 ,take #aj 7run7 #af4bh 7length of common rafter per foot of run7 #ad' #b4id #ad' #c4 74#id #a1 columns #c and #d47 c4 ,seat cut4--7,cf4 column #h7 #db deg4 #cj min4 ,set ,t-bevel by means of protractor4 d4 ,tail4-- 7#a7 ,length ,determined as is length of common rafter 7,cf4 column #aa71 horizontal projection of tail or length of lookout becoming the multiplier4 7#b7 ,end cut4 ,use same number of degrees as for plumb cut4 #d4 ,to ,lay ,out ,hip or ,valley ,rafter4-- a4 ,plumb cut4--7,cf4 column #g7 #di deg4 #ej min4 b4 ,side cut4--7,cf4 column #ag7 #ag deg4 #dj min4 ,this also gives miter cut at end of hip tail for fascia1 and also the miter cut of the bird's mouth joint of valley rafter1 where it must be cut out to fit the angle of the plate4 c4 ,length of hip or valley rafter4--7,cf4 column #ac7 #aj 7run of common rafter7 #ag4jc 7length of octagon hip or valley per foot of run of common rafter7 #ad' #aj4hb #ad' #aj 74#hb 1 columns #c and #d74 d4 ,seat cut4--7,cf4 column #aj7 #dj deg4 #aj min4 ,use protractor and ,t-bevel4 e4 ,tail for hip or valley rafter4-- 7#a7 ,length4 ,determined as for hip or valley1 horizontal projection of tail or length of lookout of common rafter becoming multiplier4 7#b7 ,end cut4 ,use same number of degrees as for plumb cut of hip or valley4 f4 ,backing of hip4--7,cf4 column #bb7 #gd deg4 #ej min4 g4 ,drop of hip when no backing is used4--7,cf4 column #bd7 #e_/af4 #e4 ,to ,lay ,out ,jacks4-- a4 ,plumb cut4--,same as for common rafter4 b4 ,side cut4--7,cf4 column #ae7 #ag deg4 c4 ,length4--7,cf4 column #bj7 #ab_/e that for square roof of same pitch4 ,when set #af centers #ab_/e #ba #eb1 common difference4 ,proceed accordingly4 d4 ,tail for jack4--,same as for common rafter4 ,,appendix ,v ,,miscellaneous ,,estimating ,excavations4 ,excavations are estimated in terms of the cubic yard1 #bg cubic feet4 ,the price per yard will vary according to the nature of the soil4 ,where ground is not level1 the plot should be divided into squares1 each square being figured as to its cubical contents and the various amounts combined4 ,,analysis ,,of ,,cost ,,factors ,,per ,,cubic ,,yard ,spading or picking labor1 hour at 444444444444444 ,throwing out labor1 hour at 444444444444444444444 ,wheeling #ej feet1 hour at 44444444444444444444444 -------- ,cost per yard ,concrete4--,concrete is estimated in terms of the cubic yard4 ,the price will vary somewhat according to the mixture and the amount of form work required4 ,mixtures are designated as rich--#a part cement1 #b parts sand1 #d parts crushed rock1 by volume2 medium--#a3b3e2 ordinary--#a3c3f1 and lean1--#a3d3h4 ,the rich mixture is used for cellar floors on high grade work4 ,cisterns and tanks make use of a special mixture of #a3b3c1 the stone or gravel being passed thru a screen4 ,cement topping for cellar floors is a mortar composed of #a part cement and #b parts sharp sand4 ,sometimes a #a3a mixture is used4 ,cellar floors and sidewalks are often priced by the foot surface measure1 standard specifications for depth and construction being understood4 ,,table ,,for ,,estimating ,,quantities ,,for ,,concrete 7,proportion of materials in one cubic foot of concrete47 ,,mixture ,rich 7#a3b3d7 ,medium 7#a3b3e7 ,ordinary 7#a3c3f7 ,cement #j4jeh bbl4 #j4jdh bbl4 #j4jda bbl4 ,sand #j4jafc cu4 yd4 #j4jagj cu4 yd4 #j4jagd cu4 yd4 ,stone or gravel3 #j4jcbf cu4 yd4 #j4jcda cu4 yd4 #j4jcdh cu4 yd4 ,example ,estimate quantities of various materials needed for a wall #aj #g' #dh'1 using a #a3b3e mixture4 ,solution--7#aj #g #dh7 _/ #ab #bhj cu4 ft4 ,cement #bhj #j4jdh bbl4 #ac4dd bbl4 ,sand #bhj #j4 #jag cu4 yd4 #d4gf cu4 yd4 ,stone #bhj #j4jcda cu4 yd4 #i4edh cu4 yd4 ,knowing the cost of cement per bbl4 and of sand and stone per cu4 yd41 the cost of materials for the wall may be easily determined4 ,,table ,,for ,,estimating ,,quantities ,,for ,,cement ,,mortar 7,proportion of materials in one cubic foot of cement mortar7 ,,mixture #a3a #a3b #a3b ,cement #j4adha bbl4 #j4abci bbl4 #j4ajeb bbl4 ,sand #j4jcaa cu4 yd4 #j4jcdd cu4 yd4 #j4jcgj cu4 yd4 ,example ,estimate quantities of material for #a3b cement mortar for topping of cellar floor #a #bd' #dj'4 ,solution--7#bd #dj7 #hj cu4 ft4 ,cement #hj #j4abci bbl4 #i4iab bbl4 ,sand #hj #j4jcdd cu4 yd4 #b4 #geb cu4 yd4 ,,analysis ,,of ,,labor ,,cost ,,factors ,,per ,,cubic ,,yard #a mason1 #b hours 44444444444444444444444 #b laborers1 #b hours each 444444444444444 ------- ,total ,where forms are required add #a carpenter1 #b hours 4444444444444444444 ,cellar floor construction costs approximately the same as wall work having forms4 ,the expense of form work in ordinary basement wall construction is offset by labor and additional cement cost of topping of cellar floor4 ,brickwork4--,the unit of measurement in brickwork is the #ajjj bricks1 ordinarily4 ,to determine the number of bricks in a wall1 multiply each square foot of surface by #g 7sometimes #g is used7 which is the average number of bricks per foot of wall when #d thick4 ,add #e for breakage4 ,deduct for openings over #b' square4 ,for walls thicker than #d1 make suitable allowance4 ,a mason can lay #hjj to #ajjj common and #cjj to #djj face bricks in a day4 ,bricks may be laid in lime mortar or in cement mortar4 ,,analysis ,,of ,,cost ,,factors ,,per #ajjj ,,bricks1 ,,lime ,,mortar #a3c ,brick1 #ajjj 4444444444444444444444444444 ,lime1 #c bu4 4444444444444444444444444444 ,sand1 cu4 yd4 444444444444444444444444 ,mason1 #aj hrs4 4444444444444444444444444 ,tender1 #aj hrs4 444444444444444444444444 ------- ,total ,,analysis ,,of ,,cost ,,factors ,,per #ajjj ,,bricks1 ,,cement ,,mortar #a3c ,brick1 #ajjj 4444444444444444444444444444 ,portland cement1 #a bbl4 4444444444444444 ,sand cu4 yd4 4444444444444444444444444 ,mason1 #aj hrs4 4444444444444444444444444 ,tender1 #aj hrs4 444444444444444444444444 ------- ,total ,chimneys4--,one foot of chimney height will contain five courses of ordinary bricks4 ,,chimneys ,no4 ,size of ,size of ,no4 ,bricks ,flues ,flue ,chimney per ,ft4 #a #h #h #af #af #cj #b #h #h #af #bh #ej #c #h #h #af #dj #gj #a #ab #ab #bj #bj #dj ,slate ,roof4--,exposure of each slate will equal the length of a slate diminished by #c 7the usual amount of lap7 divided by #b1 multiplied by the width of the slate4 ,to determine the number of slates required1 divide the area to be covered by the exposure of each slate as determined just above4 ,example--,determine the number of #f #ab slates required to cover a surface #af' #bj'4 ,solution--7 7#ab - #c7 _/ #b7 #f #bg sq4 in4 7#af #bj #add7 _/ #bg #agjg slates4 ,,table ,,of ,,slates ,,per ,,square ,,of #ajj ,,feet ,size ,length of ,expos4 ,no4 ,req4 ,nails ,req4 #f #ab #d #ecc #c4h lbs4 #g #ad #e #cgg #b4ff #h #af #f #bgg #b #i #ah #g #bad #a4e ,,analysis ,,of ,,cost ,,factors ,,per ,,square4 7#ajj ,,sq4 ,,ft47 ,slate1 44444444444444444444444444444 ,slater1 #h hrs41 44444444444444444444 ,roofing ,paper1 444444444444444444444 ,placing paper1 #bj min 4444444444444444 ,nails1 #b lbs4 7#h #af slate7 44444 -------- ,total ,metal work extra4 ,plastering4--,plastering is estimated by the square yard4 ,in estimating the number of square yards1 deduct the area of openings4 ,the extra labor involved in working around grounds is thus allowed for4 ,strips of plastering less than #a foot wide are estimated as a foot in width4 ,closet areas are increased by ,j_/ to make allowance for the extra labor involved in working small surfaces4 ,special plastering of cornice1 etc41 will be charged extra3 ,lathing is usually a part of the plasterer's contract1 tho done by a different set of workmen4 ,the unit is either the square yard or the #ajjj laths4 ,,analysis ,,of ,,cost ,,factors ,,for ,,lathing ,a ,,square 7#ajj ,,sq4 ,,ft47 ,lath1 #aejj 4444444444444444444444444 ,nails1 #aj lbs4 #c;d fine 4444444444444 ,lather1 #h hrs4 444444444444444444444 -------- ,total 4444444444444444444444444444 ,,analysis ,,of ,,cost ,,factors ,,per ,,square ,,for #b-;,,coat ,,lime ,,plaster ,lime1 #aj bu4 44444444444444444444444 ,hair1 #f lbs4 44444444444444444444444 ,sand1 #a yd4 444444444444444444444444 #b plasterers1 #ab hrs4 each 444444444 #a helper1 #ab hrs4 444444444444444444 -------- ,total 4444444444444444444444444444 ,,analysis ,,of ,,cost ,,factors ,,per ,,square ,,for #c-;,,coat ,,lime ,,plaster ,lime1 #ac bu4 44444444444444444444444 ,hair1 #h lbs4 44444444444444444444444 ,sand1 #a yds4 4444444444444444444444 ,plaster of ,paris1 #a bbl4 44444444444 #b plasterers1 #af hrs4 each 444444444 #a helper1 #af hrs 444444444444444444444 ------- ,total 4444444444444444444444444444 ,painting4--,painting is estimated by the square yard1 no deductions being made for openings such as doors and windows4 ,railings1 grills1 etc41 are figured as if solid4 ,a gallon of paint will cover approximately #bej to #cjj sq4 ft4 of old work and #cej ft4 of new work4 ,a painter should cover #aej sq4 ft1 #ast4 coat1 per hour1 and #ij sq4 ft41 #bnd coat4 ,cost factors may be easily determined from the above statements1 and costs easily estimated for ordinary work4 ,,bibliography ,,of ,,references ,chicago ,millwork ,supply ,co43 ,price ,book and ,specifications for ,lumber and ,millwork1 ,chicago4 ,gillette3 ,handbook of ,cost ,data1 ,myron ,c4 ,clark ,co41 ,new ,york4 ,gordon-,van ,tine ,co43 ,price ,book and ,specifications for ,lumber and ,millwork1 ,davenport1 ,iowa4 ,griffith3 ,essentials of ,woodworking1 ,manual ,arts ,press1 ,peoria1 ,ill4 ,hodgson3 ,modern ,carpentry1 ,frederick ,j4 ,drake ,co41 ,chicago4 ,hodgson3 ,practical ,uses of the ,steel ,square1 ,frederick ,j4 ,drake ,co-41 ,chicago4 ,kidder3 ,architects' and ,builders' ,pocket ,book1 ,john ,wiley and ,sons1 ,new ,york4 ,kidder3 ,building1 ,construction and ,superintendence1 ,wm4 ,t4 ,comstock1 ,new ,york4 ,radford3 ,cyclopedia of ,building ,construction1 ,radford ,architectural ,co41 ,chicago4 ,radford3 ,details of ,building ,construction1 ,radford ,architectural ,co41 ,chicago4 ,the ,national ,hardwood ,lumber ,association3 ,rules for ,measurement and ,inspection of ,hardwood ,lumber1 ,mc,cormick ,bldg41 ,chicago4 ,,index 7,,numbers ,,refer ,,to ,,pages7 ,a ,american ,bond #bj ,anchor1 ,brick ,wall #aci ,angle ,post #aah ,apron #aji ,architrave #aji ,ashlar #bj ,b ,backing ,hip ,rafter for ,square ,cornered ,building #fc ,octagon and ,other ,hips #hj ,balloon ,frame #bg ,base ,block #aji ,blocks1 ,placing #abh ,mould #aji ,mould1 ,placing #abi ,batter ,boards #ae ,bed ,moulding #ih ,belt ,course #aaj ,bibliography of ,reading ,references #ahc ,blind ,stop #aji1 #ach ,board ,measure ,table #afi ,bonds1 ,masonry #bj ,brick ,walls #bj ,contents ,table #agb ,bridging #cb ,building ,paper #ie1 #ih ,c ,casing #aji1 #ach ,casings1 ,placing #abh ,chalk ,line #ajc ,common ,rafter #gd ,concrete ,mixtures #ai ,corner ,boards #aji ,board1 ,splicing #ajb ,posts #ch1 #ci1 #aji ,cornice #ih ,costs1 by ,percentages #aef ,example of ,form #aed ,counter ,flashing #ajg ,cove #aah ,crown ,moulding #ih ,d ,deck #id ,door1 ,fitting #acj ,frame #acg ,hanging #abi ,hinging #aca ,jambs1 ,setting #abe ,parts ,named #abi ,sill #aji ,trim1 ,placing #abg ,drain ,tile #bd ,drip ,cap #aji1 #ach ,duck #abg ,e ,end ,cut of ,common ,rafter #ee of ,hip and ,valley ,rafter #fb of ,octagonal and ,other ,hips and ,valleys #gi ,english ,bond #bj ,estimating #adb ,brick ,work #ahj ,estimating ,cement ,mortar #agi ,concrete #agh ,cubic-foot ,unit #adb ,excavations #agh ,labor ,costs1 ,carpentry #aej ,lathing #ahb ,lumber ,quantities #adf ,millwork ,quantities #adi ,painting #ahb ,plastering #aha1 #ahb ,quantities of ,nails #aec ,slate ,roof #aha ,excavations #ah ,exterior ,wall ,coverings #ie ,f ,fascia #ih ,finish ,floor #aji ,finishing ,exterior ,walls #ajh ,flashing #aje ,flemish ,bond #bj ,floors1 ,laying and ,scraping #ace ,footings #ah ,forms for ,concrete #bc ,foundations #ah ,laying out #ac ,foundation ,materials #ai ,frames1 ,basement #be ,framing ,common ,rafter #di ,joists #ca ,roof about ,chimney #id ,square with ,rafter ,table #ec ,table for ,common and ,jack ,rafters #eb ,frieze #ih ,full ,frame #bg ,furring #aji ,g ,girders #bi1 #ca ,grade ,line #af ,grading ,rules1 ,lumber #adc ,griffith's ,roof ,framing ,tables #gb ,griffith's ,tables1 ,directions for #agc ,grounds #aae ,h ,half-frame #bg ,headers #bj1 #ce1 #aji ,headroom #aai ,hip and ,valley ,rafter ,end ,cut #fb and ,valley ,rafter ,lengths #fa and ,valley ,rafter ,plumb ,cut #fj and ,valley ,rafter ,seat ,cut #fb and ,valley ,rafters for ,octagon and other ,polygons #gd and ,valley ,rafter ,side ,cut #fj ,rafter1 ,unit ,lengths #ei ,i ,interior ,finish #aae1 #abe ,walls #aag ,interpolation #afd ,j ,jamb #aji1 #ach ,jack ,rafter for ,octagonal and ,other ,polygonal ,roofs #ha for ,square ,cornered ,building #fe ,k ,king-,post #gh ,l ,lap ,siding #aaa ,lathing #aae ,length and ,number of ,wire ,nails to the ,pound #afh ,length of ,common ,rafter #ej1 #ed of ,hip and ,valley ,rafters #fa of ,jacks for ,square ,cornered ,building #ff ,length of ,octagon and ,other ,polygonal ,jacks #hb of ,rafter by ,scaling #ec of ,side of ,polygon #gc ,leveling ,door ,sill #aaj ,foundation #af ,rod #ad with ,straight-edge #ag ,lintels #ada ,locks1 ,fitting #acb ,lookout #ih ,lookouts1 ,framing #ii ,m ,main ,frame #bg ,masonry ,construction1 ,woodwork for #ach ,miter ,cuts of ,plate #fi ,n ,natural ,trigonometric ,functions #aeh ,nosing #aah ,o ,octagonal and ,other ,jacks #ha ,roofs #gc ,octagon ,bay1 ,framing #he ,openings in ,framework #db1 #id ,p ,parting ,strip #aji1 #ach ,partition #ch ,wall ,detail #aaf ,patterns for ,joists and ,studding #ch ,pier #abc ,pitch #df ,pitch ,board #abj ,placing ,joists #cb1 #da ,plancher #ih ,plank ,frame #bg ,plates #da1 #ih ,platform1 ,stair #aah ,plumb ,cut of ,hip and ,valley ,rafter #fj of ,octagonal ,hip and ,valley ,rafters #gd ,porches #abb ,porch ,steps #aag ,protractor1 ,framing with #hb ,pulleys #ach ,pulley ,stile #aji1 #ach ,r ,raked ,moulding #ajj ,reduction for ,king-post #gi for ,ridge #eg ,ribbon ,boards #ci ,ridge1 ,length of #ef ,piece #eg ,rise #df ,rise of ,stair #aai ,riser #aah1 #aba ,roof ,boards1 ,cutting of #ie1 #if1 #ih ,frame #de ,frame1 ,any ,polygon #fi ,framing #de ,framing ,terms #df ,rough ,floors #db1 #aji ,rubble ,work #bj ,run #de ,run of ,stair #aai ,s ,sash ,cord #abg ,scaffolding #if ,scribing ,against ,irregular ,surface #aad ,seat ,cut of ,common ,rafter #ee of ,hip and ,valley ,rafter #fb of ,octagonal and ,other ,hips and ,valleys #gi ,setting ,basement ,frames #be ,setting ,partitions #da ,studs #dj ,window ,frames #aaj ,sheathing or ,sheeting #ie1 #ih ,shed ,roof ,framing #hi ,shingling #ajb ,hips and ,valleys #aje ,shingle ,tins #ajf ,shoe ,mould #aji ,placing #abi ,side ,cut1 ,hip and ,valley ,rafters #fj ,octagonal and ,other ,hips and ,valleys #ge of ,jack ,rafter #fe of ,octagonal and ,other ,polygonal ,jacks #ha ,siding #aaa ,circular ,tower #aac ,hook #aac ,stick #aaa ,sills #bi1 #ca1 #aji1 #ach ,six-eight-ten ,method #ae ,sole ,piece #aji ,solution of ,right ,triangles #aei ,spacing ,joists #cb ,stair ,building #aag ,types #aah ,stirrups #cf ,stock ,bill ,form #adi ,stone ,work #bj ,stool #aji ,stop ,bead #aji1 #ach ,story ,pole #db ,straightening ,studding #aag ,strength of ,materials #agj ,stretchers #bj ,stringer #aah ,t ,table for ,hip and ,valley ,rafters #fj of ,common and ,jack ,rafters #eb ,table of ,fractional ,equivalents for ,decimal ,values #aff of ,natural ,functions #afc of ,octagonal ,hip and ,valley ,rafters #ge ,tail1 ,rafter #ef ,tangents #fi ,threshold #aji ,toe ,hold #ajd ,transit #ac ,translating ,framing ,problems from ,protractor to ,framing ,square and ,vice ,versa #hd ,tread #aah1 #aba ,trimmers #ce ,u ,uneven ,pitch of ,roof #ij ,useful ,tables #aff ,v ,valley ,rafters #fe ,rafter ,unit ,lengths #eh ,value of a ,function1 ,the ,angle ,being ,given in ,fractional ,degrees #afd of ,angle1 ,the ,value of a ,function ,being ,known #afd ,veneer1 ,brick #ach ,w ,wall ,board #aba ,walls #ch ,water ,proofing #bd ,table #aji ,weight ,pocket #aji1 #ach ,well ,hole #cf ,winders1 ,stair #aah ,window ,detail1 for ,brick ,wall #adj ,frames #acg ,sash1 ,fitting #abf ,window ,sill #aji ,stool #aji ,trim1 ,placing #abg ,wire ,brads1 ,table for #afi ,wood and ,machine ,screw1 ,sizes1 ,table of #afg ,wooden ,bricks #bf ,wood's ,key to the ,steel ,square #gj ,y ,y-level #ad ,yoke #aji 99 99 99 99 99 ,transcriber ,note ,a link to the ,index was added to the ,contents table4