,,instructions ,,on ,,modern ,,american ,,bridge ,,building4 ,,with ,,practical ,,applications ,,and ,,examples1 ,,estimates ,,of ,,quantities1 ,,and ,,valuable ,,tables4 ,illustrated by four ,plates and ,thirty ,figures4 ,,by ,g4,b4,n4 ,,tower1 ,,civil ,,and ,,mechanical ,,engineer1 ,formerly ,chief ,engineer ,u4,s4 ,navy1 and late ,chandler ,instructor in ,civil ,engineering at ,dartmouth ,college4 ,,boston3 ,a4 ,,williams ,,company1 #ace ,,washington ,,street4 #ahgd4 ,entered according to act of ,congress1 in the year #ahgd1 by ,a4 ,,williams ,,co41 in the office of the ,librarian of ,congress1 at ,washington1 ,d4,c4 ,,preface4 ,this little treatise was written for the purpose of supplying a want felt by the author while giving instruction upon the subject4 ,it was intended for an aid to the young ,engineer1 and is not to be considered as a complete substitute for the more elaborate works on the subject4 ,the first portion of this work mentions the various strains to which beams are subjected1 and gives the formul used in determining the amount of those strains1 together with a few examples to illustrate their application1 and also the method of calculating a simple truss4 ,the second portion names and explains the various members of a ,bridge ,truss1 and1 by means of examples1 shows the method of calculating the strains upon the various timbers1 bolts1 etc41 as well as their proper dimensions2 and gives1 in addition1 several useful tables4 ,the explanatory plates1 which are referred to freely throughout the work1 are believed to be amply sufficient for the purpose intended4 ,so much has been written on this subject that it is next to impossible to be wholly original1 and no claim of that nature is preferred4 ,it is simply an arrangement of ideas1 gleaned from the various works of standard authorities1 and modified by the author's practice1 embodied in book form4 ,to give a correct list of all the books consulted would be simply impossible2--but it is well to state that the ,hand-book of ,railroad ,construction1 by ,prof4 ,g4,l4 ,vose1 under whom the author served as an ,engineer1 has been used as authority in many cases where there has been a difference of opinions among other authors4 ,some parts have been quoted entirely2 but due credit has been given1 it is believed1 wherever such is the case4 ,it is not claimed that this little work covers the whole ground1 but it is intended to describe1 and explain thoroughly1 three or four of the more prominent styles of ,truss1 leaving the other forms of ,wooden ,bridges to a subsequent volume4 ,abutments and ,piers1 as well as ,box and ,arch ,culverts1 belonging more properly to masonry1 will be treated of hereafter under that head4 ,iron ,bridges form a distinct class1 and may be mentioned separately at some future period4 ,if this small volume should lead the student of ,engineering to examine carefully the best ,bridges of modern practice1 and study the larger scientific works on this art1 the author will feel satisfied that his efforts have not been entirely in vain4 ,cambridge1 ,february #bc1 #ahgd4 ,,tower',s ,modern ,american ,bridge ,building4 ,,bridge ,,building ,the simplest bridge that can be built1 is a single beam1 or stick of timber1 spanning the opening between the abutments--but this is only of very limited application--7only for spans of #bj feet and less7 owing to the rapid increase in sectional dimensions which is required as the span becomes greater4 ,next comes the single beam supported by an inclined piece from each abutment meeting each other at the middle point of the under side of the beam--or1 another arrangement1 of two braces footing securely on the beam and meeting at a point above the middle point of the beam1 which is suspended from the apex of the triangle formed by them1 by means of an iron rod--,these arrangements may be used up to #ej feet4 ,for any span beyond #ej feet1 modifications of this arrangement are used which will be described hereafter4 ,now let us investigate shortly the different strains that the various parts of a bridge have to bear--and the strength of the materials used4 ,the theory of strains in bridge trusses is merely that of the ,composition and ,resolution of ,forces4 ,the various strains1 to which the materials of a bridge are subjected--are compression1 extension and detrusion4 ,wood and ,iron are the materials more generally employed in bridge construction--and in this pamphlet we shall take the following as the working strength of the materials--per square inch of section4 ,tension4 ,compression4 ,detrusion4 ,wood1 #bjjj #ajjj #aej ,wro't ,iron1 #aejjj #aajjj ,cast ,iron1 #dejj #bejjj ,tension4 ,if a weight of #bjjj lbs4 were hung to the lowest end of a vertical beam1 so that the line of action of the weight and axis of the beam formed one and the same straight line--the tension on the beam would be #bjjj lbs4 ,but1 if the beam were inclined1 and the force acted in a vertical direction1 then the strain would be increased in the ratio of the increase of the diagonal of inclination over the vertical2--suppose the beam is #bj ft4 long and inclined at an angle of #de--;and let #bjjj lbs41 as before1 be suspended from its lower end4 ,now the diagonal being #bj1--the vertical will be #ad4jad ft4--and the strain will be found as follows1-- #ad4jad 3 #bj 33 #bjjj 3 #bhed--lbs4 ,the greater the angle of inclination from the horizontal1 the less the strain from a given load--and when the beam is vertical the weight causes the least strain4 ,compression4 ,if we load a vertical post with a weight of #bjjj lbs41 the strain of compression exerted upon the post will be #bjjj lbs4 ,now1 if we incline the post--the strain will be increased1 as we have shown above under the head of tension1 and in like manner1 dependent upon the inclination4 ,but when wood1 iron1 or any other material is used for a pillar or strut1 it has not only to resist a crushing force1 but also a force tending to bend or bulge it laterally4 ,a post of circular section with a length of #g or #h diameters will not bulge with any force applied longitudinally1 but will split4 ,but if the length exceeds this limit--it will be destroyed by an action similar to that of a transverse strain4 ,a cast iron column of thirty diameters in length1 is fractured by bending2 when the length is less than this ratio--by bending and splitting off of wedge shaped pieces4 ,but by casting the column hollow1 and swelling it in the middle1 its strength is greatly increased4 ,barlow's formula for finding the weight that can be sustained by any beam1 acting as a pillar or strut1 before bending1 is3-- ,,wl bd x #hj ,e ---- bd1 whence ,w ----------- #hj ,e ,l ,te,x3 frac,,wl#bhj ,e bd#c1 whence ,w fracbd#c x #hj ,e,l#b now1 having the weight given1 and assuming the dimensions of the cross-section--we shall have ----- _/ ,,wl ,,wl d _/ -----1 and b ------ _/ #hj ,eb #hj ,ed ,te,x3 d sqrt#c;frac,,wl#bhj ,,eb1 and b frac,,wl#bhj ,,ed#c in the above formul1 ,w weight in pounds4 ,l length in feet4 ,e a constant4 b breadth in inches4 d depth in inches4 ,transverse ,strains4 ,the strain caused by any weight1 applied transversely1 to a beam supported at both ends1 is directly as the breadth1 and square of the depth1 and inversely as the length4 ,it causes the beam to be depressed towards the middle of its length1 forming a curve1 concave to the horizontal and below it4 ,in assuming this form--the fibres of the upper part of the beam are compressed1 and those of the lower part are extended--consequently there must be some line situated between the upper and lower surfaces of the beam where the fibers are subjected to neither of these two forces1 this line is called the neutral axis4 ,these two strains of compression and extension must be equal in amount--and upon the relative strength of the material to resist these strains1 as well as its form and position1 the situation of this axis depends4 ,if wood resists a compression of #ajjj lbs4 per square inch of section1 and a tension of #bjjj lbs4 the axis will be twice as far from the top as from the bottom in a rectangular beam4 ,the following table by ,mr4 ,g4,l4 ,vose gives1 with sufficient accuracy for practice1 the relative resisting powers of wood1 wrought1 and cast iron1 with the corresponding positions of the axis4 ,dist4 of axis ,resistance ,resistance from top in to to frac's of ,material4 ,extension4 ,compression4 ,ratio4 the depth4 ,wrought ,iron1 #ij #ff #ij_/ff #ij_/aef1 or #j4eh4 ,cast ,iron1 #bj #aaa #bj_/aaa #bj_/aca1 or #j4ae4 ,wood1 #b #a #b_/a #b_/c1 or #j4ff4 ,thus we see that the resistance of a beam to a cross strain1 as well as to tension and compression1 is affected by the incompressibility and inextensibility of the material4 ,the formula for the dimensions of any beam to support a strain transversely is #d bd ,s ---- l ,te,x3 ,s frac#d bd#bl ,s the ultimate strength in lbs4 b the breadth in inches4 d the depth in inches4 l the length in inches4 ,detrusion4 ,detrusion is the crushing against some fixed point1 such as obtains where a brace abuts against a chord1 or where a bridge rests on a bolster2 and the shearing of pins1 bolts and rivets1 also comes under this head4 ,general ,abstract4 ,the resistance to the above mentioned strains varies as the area of the cross section2 so that by doubling the area we double the strength4 ,any material will bear a much greater strain for a short time than for a long one4 ,the working strength of materials1 or the weight which does not injure them enough1 to render them unsafe1 is a mooted point1 and varies1 according to the authority1 from #a-c to #a-aj of the ultimate strength4 ,the ratio of the ultimate strength to the working strength is called the factor of safety4 ,the following is a table of ultimate and working strengths of materials1 and factors of safety3 ,weight ,ult4 ,ult4 ,working ,strengths ,factor ,safety4 in lbs4 ,materials4 ,ext4 ,comp4 ,exten4 ,comp4 ,tension ,comp4 #cj ,wood4 #ad1jjj #g1jjj #b1jjj #a1jjj #g #g #dhj ,wrou't ,iron4 #fj1jjj #fd1jjj #ae1jjj #ab1jjj #d #e4cc #dej ,cast ,iron4 #ah1jjj #ajj1jjj #d1ejj #be1jjj #d #d ,lateral ,adhesion4 ,lateral adhesion is the resistance offered by the fibres to sliding past each other in the direction of the grain1 as when a brace is notched into a chord1 or tie beam1 at its foot1 it is prevented by the lateral adhesion of the fibres from crowding off the piece1 to the depth of the notch1 against which it toes4 ,barlow's experiments give the lateral adhesion of fir as #fjj lbs4 per square inch1 and the factor of safety employed varies in practice from #d to #f1 giving a working strength of from #aej to #ajj lbs4 per square inch4 ,,table ,,of ,,compressive ,,resistance ,,of ,,timber4 ,length ,safety ,length ,safety ,length ,safety given in ,weig't in given in ,wt4 in given in ,wt4 in ,diameters4 ,pounds4 ,diameters4 ,pounds4 ,diameters4 ,pounds4 #f #ajjj #bd #ddj #db #bjc #h #ifj #bf #cid #dd #ahe #aj #iaj #bh #ceh #df #afi #ab #hfj #cj #cbh #dh #aee #ad #haj #cb #bii #ej #adc #af #gfj #cd #bgf #eb #acb #ah #gaj #cf #beh #ed #abb #bj #ffj #ch #bci #ef #aad #bb #egj #dj #bbd #eh #ajf #fj #ii ,in tensional strains1 the length of the beam does not affect the strength2 but in the beams submitted to compression1 the length is a most important element1 and in the table given above1 the safety strains to which beams may be subjected1 without crushing or bending1 has been given for lengths1 varying from #f to #fj diameters4 ,,practical ,,rules4 ,tensional ,strain4 ,let ,t whole tensional strain4 ,s strength per square inch4 a sectional area in inches4 ,then we have ,t ,sa4 ,now to find the necessary sectional area for resisting any strain1 we have the following general formula3 ,t a --- ,s ,te,x3 a frac,t,s or1 by substituting the working strengths for the various materials in the formula1 we have for wood1 a ,t_/#bjjj ,wrought ,iron1 a ,t_/#aejj ,cast ,iron1 a ,t_/#dejj ,but1 in practice1 cast iron is seldom used except to resist compression4 ,strains of ,compression4 ,allowing the same letters to denote the same things as above1 we have for ,wood1 a ,t_/#ajjj ,wrought ,iron1 a ,t_/#abjjj ,cast ,iron1 a ,t_/#bejjj ,as this pamphlet has to do with wooden bridges only1 nothing will be said of the proper relative dimensions of cast-iron columns to sustain the strains to which they may be subjected1 but a table of the strength of columns will be found further on4 ,transverse ,strains4 ,let ,w breaking weight in lbs4 s constant in table4 b breadth in inches4 d depth in inches4 ,l length in inches4 ,then1 for the power of a beam to resist a transverse strain1 we shall have1 #d sbd ,w ------ ,l ,te,x3 ,w frac#d sbd#b,l ,this formula has been derived from experiments made by the most reliable authorities4 ,the constant1 #abej1 adopted for wood in the following formula1 is an average constant1 derived from the table1 of those woods more commonly used4 ,now to reduce the formula to the most convenient shape for use1 we substitute the value of s1 and we have #d x #abej bd ,w ------------1 ,l ,te,x3 ,w frac#d times #abej bd#b,l or #ejjj bd ,w --------4 ,l ,te,x3 ,w frac#ejjj bd#b,l ,but1 to reduce the load to the proper working strain1 we must divide this equivalent by #d1 the factor of safety1 and we shall have #ejjj bd ,w --------4 #d,l ,te,x3 ,w frac#ejjj bd#bd ,l ,let us apply the formula-- ,case ,i4 ,given a span of #ad feet1 a breadth of #h inches1 a depth of #ad inches4 ,required the safe load4 #ejjj bd ,the formula ,w -------- #d,l ,te,x3 ,w frac#ejjj bd#bd ,l becomes1 by substitution1 #ejjj x #h x #aif ,w -------------- #aa4fff lbs4 #d x #h ,te,x3 ,w frac#ejjj times #h times #aifd times #afh #aa1fff lbs4 ,case ,,ii4 ,given the safety load #ahjjj lbs4 the breadth #i inches1 the length #ad feet4 ,required the depth4 ,from the above formula we have ------- _/ ,w ,x #d,l d _/ ------ _/ #ejjj b ,te,x3 d sqrtfracw times #d,l#ejjj b substituting ---------------- _/ #ahjjj x #afh x #d ------ d _/ --------------- _/ #bfh4h #af1 inches nearly4 _/ #ejjj x #i _/ ,te,x3 d sqrtfrac#ahjj times #afh times #dejjj times #i sqrt#bfh4h #af ,case ,,iii4 ,given the safety load #bb1djj lbs4 the depth #ah inches4 the length #ad feet4 ,required the breadth4 ,deriving b from the foregoing1 we have1 ,w x #d,l b ---------- #ejjj x d ,te,x3 b frac,w times #d,l#ejjj times d#b substituting #bbdjj x #d x #afh b --------------- #i4c inches nearly4 #ejjj x #cbd ,te,x3 b frac#bbdjj times #d times #afhejjj times #cbd #i4c ,for a cast iron beam or girder--,mr4 ,hodgkinson found from numerous carefully conducted experiments that1 by arranging the material in the form of an inverted ,t--thus creating a small top flange as well as the larger bottom one1 the resistance was increased1 per unit of section1 over that of a rectangular beam1 in the ratio of #dj to #bc4 ,in this beam the areas of the top and bottom flanges are inversely proportional to the power of the iron to resist compression and extension4 ,mr4 ,hodgkinson's formula for the dimensions of his girder1 is #bf ad ,w ------ ,l ,te,x3 ,w frac#bf ad,l ,the factor of safety being #f for cast iron beams--the formula for the working load will be1 #bf ad ,w ------ #f ,l ,te,x3 ,w frac#bf ad#f ,l and1 to find area of lower flange1 we shall have #f ,,wl a ---- #bf d ,te,x3 a frac#f ,,wl#bf d ,the general proportions of his girders are as follows3 ,length1 #af ,height1 #a ,area ,top ,flange1 #a4j ,area ,bottom ,flange1 #f4a ,in the above formula for cast iron beams1 ,w weight in tons4 a area in square inches of bottom flange4 d depth in inches4 h length in inches4 ,the web uniting the two flanges must be made solid--as any opening1 by causing irregularity in cooling1 would seriously affect the strength of the beam4 ,example4--,required the dimensions of a ,hodgkinson girder--for a span of #fj feet--with a load of #aj tons in the centre4 #f x #aj x #fj x #ab a ---------------- #cg inches nearly4 #fj x #ab #bf x ------- #af ,te,x3 a frac#f times #aj times #fj times #abbf times frac#fj times #abaf #cg and the area of the top flange will be1 #cg -- #f4af inches-- #f ,te,x3 frac#cgf #f4af so that our dimensions will be as follows3 ,length1 #cj feet4 ,depth1 #de inches4 ,area ,top ,flange1 #f4af inches4 ,area ,bottom ,flange1 #cg inches4 ,illustration3 ,pl4 #a4 ,the thickness of web is usually a little greater at the bottom than at the top1 and varies from #a_/ad to #a_/bd of the depth of the girder4 ,the bottom rib is usually made from six to eight times as wide as it is thick1 and the top rib from three to six times as wide as thick1 so that1 in the example above given1 we could have as dimensions for the parts ,top ,flange1 #d #a_/d x #a #a_/b inches nearly4 ,bottom ,flange1 #f x #b #a_/b inches nearly4 ,web1 #a #a_/b inches thick4 ,the simplest bridge1 consisting of a single stick1 to span openings of #bj feet and under1 is calculated according to the formula ------ _/ #d,,wl d _/ ------ -- _/ #ejjj b ,te,x3 d sqrtfrac#d ,,wl#ejjj b ,example4--,the depth of a beam1 of #ab feet span and #ab feet wide1 to support a load of #bbdjj lbs4 will be ------ -------------------- _/ #d,,wl _/ #d ,x #bbdjj x #ab x #ab ------- d _/ ------ _/ ------------------- _/ #bae4jd #ae in4 nearly _/ #ejjj b _/ #ejjj x #ab _/ ,te,x3 d sqrtfrac#d ,,wl#ejjj b sqrtfrac#d times #bbdjj times #ab times #abejjj times #ab sqrt#bae4jd #ae ,the following ,table was calculated by the above rule--and the dimensions altered according to the actual practice of the writer4 ,span4 ,breadth4 ,depth4 #d #aj #ab #f #aj #ab #h #ab #ab #aj #ab #ac #ab #ab #ae #af #ab #ah #ah #ab #bj #bj #ab #bb ,these dimensions will give ample strength and stiffness4 ,fig4 #a1 ,plate ,i4 gives an illustration of this kind of bridge--in which a1 a1 are the bolsters or wall plates1 shown in section1 to which the bridge beams are notched and bolted4 ,fig4 #a1 ,a1 ,plate ,i1 shows the method of diagonally bracing these beams by planks1 dimensions of which in general use are #f to #h by #b to #c inches4 ,the track should rest on ties1 about #f inches by #h or #aj inches--the same bolt confining the ends of the ties and diagonal braces when practicable4 ,these ties should be notched on the string pieces #b or #c inches--without cutting the stringers4 ,below is a table giving general dimensions1 in inches1 of the several parts of a bridge of this description4 ,span4 ,bolsters4 ,stringers4 ,ties4 ,braces4 ,diameter of ,bolts4 #d #ab x #ab #aj x #ab #f x #h #b x #h #a inch4 #aj #ab x #ab #ab x #ac #f x #h #b x #h #a #af #ad x #ad #ab x #ah #f x #h #b x #h #a #bj #ad x #ad #ab x #bb #f x #h #b x #h #a ,each bolt must have a washer under the head1 and also under the nut4 ,for a span of from #ae to #cj feet1 we can use the combination shown in ,plate ,,ii1 ,fig4 #c4 ,the piece ,a ,f must have the same dimensions as a simple string piece of a length ,a ,b--so that it may not yield between ,b and either of the points ,a or ,d4 ,the two braces ,d ,f and ,e ,f must be stiff enough to support the load coming upon them4 ,suppose the weight on a pair of drivers of a ,locomotive to be #aj tons1 then each side must bear #e tons1 and each brace #b-a_/b tons #b-a_/b x #bbdj #efjj lbs4 ,now1 to allow for sudden or extra strains1 call #hjjj lbs4 the strain to be supported by each brace1 and1 accordingly1 #h square inches of sectional area would be sufficient for compression only2 but1 as the brace is inclined1 the strain is increased4 ,let the vertical distance from ,a to ,d be #aj ft41 and1 calling the span #cj ft4--,a ,b will be #ae ft4--from whence ,d ,f must be #ah ft41 then we shall have the proportion #aj 3 #ah 33 #hjjj 3 #addjj lbs4 which would require an area of about #ae square inches of section to resist compression1 or a piece #cx#e inches4 ,now1 as this stick is more than #f or #h diameters in length1 it will yield by bending--and consequently its area must be increased4 ,the load1 which a piece of wood acting as a post or strut will safely sustain1 is found by the formula already given4 #bbdj bd ,w -------- ,l ,te,x3 ,w frac#bbdj bd#c,l#b ,now substituting #c for b1 and #e for d1 we have #bbdj x #c x #abe #hdjjjj ,w -------------- ------ #beib lbs4 #cbd #cbd ,te,x3 ,wfrac#bbdj times #c times #abecbd;frac#hdjjjjcbdbeib which is not enough4 ,using #f for b and #h for d1 we have #bbdj x #f x #eab ,w -------------- #babch lbs4 #cbd ,te,x3 ,w frac#bbdj times #f times #eabcbd #babch which is something larger than is actually required1 but it is no harm to have an excess of strength4 ,now in many cases this arrangement would be objectionable1 as not affording sufficient head room on account of the braces--and we can as well use the form of structure given in ,pl4 ,i4 ,fig4 #c1 since it is evidently immaterial whether the point ,b be supported on ,f or suspended from it1 provided we can prevent motion in the feet of the braces1 which is done by notching them into the stringer at that point4 ,this of course creates a tensional strain along the stringer1 which is found as follows3--,representing the applied weight by ,f ,b1 ,pl4 ,,ii1 ,fig4 #b1 draw ,b ,d parallel to ,f ,c1 also ,d ,h parallel to ,a ,c--,d ,h is the tension4 ,this is the graphical construction1 and is near enough for practice4 ,geometrically we have the two similar triangles ,a ,f ,b and ,d ,f ,h1 whence ,a ,f 3 ,d ,f 33 ,a ,b 3 ,d ,h ,d ,f x ,a ,b and ,d ,h --------- ,a ,f ,te,x3 ,,dh frac,,df times ,,ab,,af ,this style of structure may be used up to #ej feet1 but it is not employed for spans exceeding #cj feet in length4 ,it is very customary to make the braces in pairs so as to use smaller scantling1 and gain in lateral stiffness--the two pieces forming one brace by being properly blocked and bolted together4 ,below is given a table of dimensions for the various parts of this style of structure3 ,span4 ,rise4 ,bolster4 ,stringer4 ,braces4 ,rod4 ,no4 ,size4 #ae #f #ab x #ab #ab x #ab #b--e x #f #a-a_/h #bj #g #ad x #ad #ab x #ac #b--e x #h #a-c_/h #be #h #ad x #ad #ab x #ae #b--f x #h #a-a_/b #cj #aj #ad x #ad #ab x #ah #b--f x #i #a-e_/h ,single ,beams under each rail firmly braced laterally1 and trussed by an iron rod1 7or preferably by two iron rods17 and a post on the under side of the beam4 ,the deflection of the rod is usually taken at #ah of the span4 ,pl4 ,,ii41 ,fig4 #a1 represents this style of trussing a beam--which is generally used for spans of from #ae to #cj ft4 ,below is a table of dimensions for this truss with single and double rods2 if double rods are used only half the given section will be necessary for each one of the pair4 ,span4 ,rise4 ,stringer4 ,post4 ,rod4 ,rods4 ,feet4 ,in ,feet4 7single47 7double47 #ae #a-g_/h #ab x #ab #f x #h #b-a_/h diam4 or #a-a_/b diam4 #bj #b-a_/b #ab x #ad #g x #h #b-a_/b #a-c_/d #be #c-a_/h #ab x #af #h x #h #b-c_/d #b #cj #c-c_/d #ac x #ah #i x #i #c #b-a_/h ,it is as well to tenon the post into the beam1 and also strap it firmly with iron plates--and the end should be shod with iron to form a saddle for the rods to bear upon4 ,now if we should make a bridge1 on the plan of ,fig4 #c1 ,pl4 ,i41 #ge or #ajj feet1 or perhaps more1 in length1 the braces ,a ,f and ,f ,c1 would not only be very long but very large and heavy1 and one chief requisite in a good bridge is1 to have all the beams so proportioned that they will resist all the strains acting upon them1 without being unnecessarily large4 ,it now becomes necessary to have a different arrangement of the parts of the truss in order to obtain increased length of span4 ,suppose we have a span1 of #dj feet1 as represented in ,fig #b1 ,pl4 ,i4 ,now instead of running the braces from ,a ,c until they meet in a point1 as before we stop them at a1 and c1 and place the straining beam1 a c1 between them to prevent those points from approaching1 suspend the points ,b and ,d from them1 and start the braces ,b b and ,d b--and1 if the truss were longer1 would continue on in the same manner as far as needful4 ,to prevent the4 truss from altering its form1 as shown by the dotted lines ,a' b ,c'1 and ,a ,e ,c1 by any passing load1 we insert the counter braces marked ,r4 ,the braces ,a a and ,c c1 must support all of the weight of the bridge and its load within the parallelogram ,b a c ,d--and the next set of braces1 ,b b and ,d b1 sustain that part of the load which comes over the centre of the bridge4 ,consequently the braces must increase in size from the centre towards the abutments4 ,the rods resist the same pressure in amount as their braces--but being vertical1 do not need the increase1 given to the braces on account of their inclination--but increase simply with the strain upon them1 from the centre to the ends of the truss4 ,there are many forms of small bridges differing from those enumerated1 in various minor details1 but sufficient has been said to give the reader a fair idea of the strains upon the different parts1 and how to arrange and proportion the materials to resist them4 ,,practical ,,rules ,,and ,,examples ,,in ,,wooden ,,bridge ,,building4 ,in any case that may arise1 we must determine approximately the gross weight of the bridge and its load--as a basis1 and then we can proceed as follows--in case of a ,howe1 ,pratt1 or ,arch ,brace ,truss4 ,to find the dimensions of the ,lower ,chord4 ,the tension at the centre of the ,lower ,chord is found by dividing the product of the weight of the whole bridge and load by the span1 by sight times the height--or letting ,ttension in lbs41 ,wweight of bridge and load in lbs41 ,sspan in feet1 and hrise or height--we have ,w x ,s ,t ----- --4 #h h ,te,x3 ,t frac,w times ,s#h h ,in this case we have taken the rise at #a_/h of the span1 which is evidently the best ratio between those dimensions1 as it equalizes the vertical and horizontal forces4 ,as to the proportions of the bays or panels1 7or that portion of the truss bounded by two adjacent verticals1 as struts or ties1 and the chords17 the ratio of the rise 7or the vertical distance between the centre lines of the two chords17 and the length on the chord should be such1 that the diagonal truss members may make an angle of about #ej with the chords2 as the size of the timbers is increased by decreasing the angle1 and1 if the angle is increased1 there are more timbers required4 ,mr4 ,g4,l4 ,vose1 in his admirable work on ,r4,r4 ,construction1 observes very truly that ,the braces1 at the end of a long span1 may be nearer the vertical than those near the centre1 as they have more work to do4 ,if the end panel be made twice as high as long1 and the centre panel square1 the intermediates varying as their distance from the end1 a good architectural effect is produced4 ,now it is necessary for us to have some data from which to determine the approximate weight of the bridge1 and also its load4 ,these can be found by comparing weights of bridges in common use1 as obtained from reports4 ,in a small bridge of short span1 the weight of the structure itself may be entirely neglected1 because of4 the very small proportion the strains caused by it bear to those due to the load2--but1 in long spans1 the weight becomes a very important element in the calculations for strength and safety--inasmuch as it may exceed the weight of the load4 ,in all ,bridges of #abj ft4 span1 about #a_/c of a ton1 per foot run1 will be the weight of each truss for a single track1 including floor timbers--transverse bracing1 c4 ,if the bridge were loaded with ,locomotives only1 the greatest load would be1 on the whole bridge--#afj tons #a4cc tons per ft4 run of the bridge or 4#fff tons per ft4 run of each truss4 ,now if we make the rise of the bridge #ae ft41 and divide the span into #ab panels of #aj ft4 each1 we shall have for total weight of bridge and load #bdj tons1 or for a single truss #aj tons to each panel4 ,lower ,chords4 ,now to find the tension on the ,lower ,chords1 ,w x ,s ,t ----- and supplying values1 we have #h h ,te,x3 ,t frac,w times ,s#h h #bdj x #abj ,t --------- #bdj tons1 or #ecgfjj lbs41 #h x #ae ,te,x3 ,t frac#bdj times #abjh times #ae #bdj for the two ,lower ,chords1 and #a_/b of this1 or #bfhhjj lbs4 for one chord4 ,the ,tensional ,strength of timber for safety may be taken at #bjjj lbs4 per square inch of section1 and hence the area of timber required to sustain the above strain will be #bfhhjj ------ #acd4d sq4 inches4 #bjjj ,te,x3 frac#bfhhjjbjjj #acd4d ,but this chord has also to sustain the transverse strains arising from the weights passing over it1 and1 as in the case of a ,locomotive1 the weight of #bj tons on #b pair of drivers1 7or #aj tons for one truss17 may be concentrated on the middle point of a panel--the chord must be so proportioned as to safely bear1 as a horizontal beam1 this weight4 ,suppose we take three sticks of #h x #ab1 to form the chord 7the greater dimension being the depth17 we shall have #c x #h x l#b #bhh square inches area of section1 and allowing for splicing #gb square inches1 foot blocks1 #bd bolts1 #bd washers1 #h we shall have after deducting allowances 7#bhh-abh7 #afj square inches area1 giving an excess over #acd4d1 the area demanded1 sufficient to cover allowances for any accidental strain4 ,upper ,chords4 ,the upper chords are compressed as forcibly as the lower ones suffer tension--owing to the action and reaction of the diagonals4 ,in this case the compression is #bfhhjj lbs41 and as #a square inch of section will safely bear #ajjj lbs41 we have for the #bfhhjj area required1 ------ #bfh4h #ajjj ,te,x3 frac#bfhhjjajjj #bfh4h square inches1--three pieces #h x #aa will give #bfd square inches and this area will require no reduction1 as the whole chord presses together when properly framed and is not weakened by splicing4 ,so far1 the calculations made would apply to either of the three ,bridges mentioned1 as well as to a ,warren ,truss4 ,but now1 to obtain the dimensions of the web members1 so called1 of the ,truss1 it is necessary to decide upon the specific variety4 ,the form of ,bridge in more general use in the ,united ,states is called the ,howe ,truss1 from its inventor1 and in spans of #aej feet1 and under1 is very reliable2 for spans exceeding #aej ft4 it should be strengthened either by ,arch ,braces or by the addition of ,arches1 as the heavy strains from the weight of bridge and load bearing on the feet of the braces near the abutments1 tend to cripple and distort the truss by sagging1 although the ,baltimore ,bridge ,co4 have built a ,wooden ,howe ,bridge of two ,trusses of #cjj ft4 span1 #cj ft4 rise1 and #bf ft4 wide1 without any arch1 but it has a wrought iron lower chord1 and is only proportioned for a moving load of #ajjj lbs4 per ft4 run4 ,vide ,vose on ,r4,r4 construction4 ,in order to ensure uniformity in strength in the chords--but one joint should be allowed in a panel--and that should come at the centre of the panel length--but in long spans this cannot always be done4 ,web ,members4 ,we will now proceed to calculate the web members of a ,howe ,truss of the foregoing dimensions1 when subjected to the strains above mentioned4 ,braces4 ,the end braces must evidently support the whole weight of the bridge and load1 which for one end of one truss will be #acddjj lbs41 and as these braces are in pairs1--#fgbjj lbs4 will be the strain vertically on the stick--but as this stick is a diagonal--whose vertical is #ae ft41 and horizontal #aj ft41 we shall have for its length #ah ft4 in round numbers1 whence the strain along the diagonal will be found from the proportion #ae 3 #ah 33 #fgbjj 3 #hjfdj lbs41 whence we have an area of #hj inches required for compression1 or a stick of #h x #aj4 ,now1 to ascertain if this is stiff enough for flexure1 we will substitute these values in the equation #bbdj bd ,w --------1 and we have ,l ,te,x3 ,w frac#bbdj times bd#c,l#b #bbdj x #h x #ajjj ,w ---------------1 or reducing1 ,w#eecjh lbs4 #cbd ,te,x3 ,w frac#bbdj times #h times #ajjjcbd #eecjh ,now1 these proportions will give ample strength for both flexure and compression1 for if we block the two sticks composing the end brace together1 and firmly connect them by bolts1 we shall have a built beam #bbdj x #bd x #ajjj of #bd x #aj--whence ,w ---------------- #afeibe lbs41 #cbd ,te,x3 ,w frac#bbdj times #bd times #ajjjcbd #afeibe and as #acddjj lbs4 was all that the conditions demand1 we really have an excess of strength4 ,the next set of braces supports the weight of the rectangle included between the upper ends of the braces and the two chords1 and the dimensions of the sticks are calculated in the same manner4 ,we find1 as we approach the centre of the bridge1 that the strains on the braces become less1 and consequently their scantling should be reduced1 but in ordinary practice this is seldom done4 ,rods4 ,the next thing is to ascertain the dimensions of the various tie rods4 ,it is evident that the same weight comes upon the first set of rods1 as on the first set of braces--which will give for the rods at one end of one truss1 #acddjj lbs42 and as there are two of these rods1 each will sustain a strain of #fgbjj lbs4--and1 at #ae1jjj lbs4 per square inch1 will have an area of #d4dh sq4 inches1 and1 by ,vose's ,tables1 must have a diameter of #b-a_/b inches4 ,the sizes of the rods in each set will decrease towards the centre of the bridge as the weight becomes less4 ,illustration3 ,pl4 ,,ii4 with ,fig4 #a41 ,fig4 #b41 ,fig4 #c41 ,fig4 #d4 ,counterbraces4 ,now1 as to the necessity of ,counterbracing1 there are various opinions4 ,the object of it is to stiffen the truss and check vibrations4 ,if a load be placed over any panel point1 it causes that portion of the truss to sink1 and produces an elevation of the corresponding panel point at the other end of the truss--thus producing a distortion1 which change of form is resisted by proper counterbraces4 ,the strain to which this timber is subjected is caused by the moving load on one panel only--and requires only scantling of the size of the middle braces4 ,these counterbraces should not be pinned or bolted to the braces where the cross--as their action is thereby entirely altered--but it is well to so confine them as to prevent vertical or lateral motion4 ,shoes4 ,formerly it was the custom to foot the braces and counters on hard wood blocks on one side of the chord1 the vertical rods passing through and screwing against a block on the other side--thus the whole strain tended to crush the chord across its fibres4 ,this is now remedied by the use of cast iron blocks1 bearing on one side of the chord1 but having tubes extending through to the other side1 where the washer plate for the bolts fits firmly on their ends1 forming a complete protection1 as all the crushing strain is received on the block itself4 ,width4 ,it now becomes necessary to determine upon the width between the two trusses4 ,for a single track bridge for a railroad1 #ad ft4 is the usual width adopted1 and for a highway bridge1 from #ab to #af ft4 ,when a double track is required1 three trusses are usually employed1 with a width for each roadway of #ad ft4 for railroads4 ,bolsters4 ,large timbers #ab x #ab1 or thereabouts1 are laid on the bridge seats of the abutments to support the ends of the trusses1 one of these should be directly under each of the extreme panel points4 ,a panel point is the intersection of the centre line of a brace produced1 with the centre line of a chord4 ,the rise of a truss is the vertical distance between the centre lines of the upper and lower chords4 ,camber4 ,were a bridge to be framed with its chords perfectly horizontal1 it would be found to fall below the horizontal line on being placed in its proper position1 owing to the closing up of the joints in the upper parts of the structure1 and opening of joints in the lower parts1 as well as to the compression of the parts4 ,to obviate this defect1 it is usual to curve the chords slightly in a vertical direction1 by elongating the upper chord1 so that the bays or panels are no longer rectangular but of a trapezoidal form--and1 as a consequence1 the inclined web members are slightly lengthened1 and the verticals become radii of the curve4 ,the amount of deviation from a horizontal line is called the ,camber4 ,a table of ,cambers for different spans will be found further on1 as also a table of multipliers1 by which to multiply the camber in order to find the elongation of the upper chord4 ,part of the ,camber table is taken from ,trautwine's ,engineer's ,pocket-,book1 7which should be the inseparable companion of every engineer17 and part was calculated for this pamphlet1 according to ,trautwine's rules4 ,the table of multipliers is ,trautwine's4 ,diagonal ,bracing4 ,in order to stiffen a bridge1 it should have the two ,trusses braced together at the ,lower ,chords always1 at the ,upper ,chords when practicable--and in case of a deck bridge1 where the roadway is supported on the upper chords1 it is as well to have rods for vertical diagonal braces1 their planes being perpendicular to the axis of the bridge4 ,the more usual form is similar to the web members of the ,howe ,truss--the rods from #c_/d to #a in diameter1 and the braces of #f x #g scantling1 footed on wooden blocks1 usually4 ,it is more usual to have the tie rods of the horizontal diagonal bracing1 and the braces themselves1 meet in a point about midway of a ,truss panel on the centre line1 nearly1 of the chord4 ,this will generally give a half panel of diagonal bracing near each end of the truss--and it is very usual to have the diagonals foot at their intersection there against a cross timber interposed between the trusses1 while the tie rod prevents any spreading4 ,floor ,timbers4 ,the general dimensions of the transverse floor beams1 when about #c feet apart1 from centre te centre1 are #h x #ad1 the largest dimension being the depth4 ,the stringers should be notched to the floor beams about #a or #b1 and should be about #aj or #ab x #ad4 ,the cross ties should be #ah to #bd apart1 from centre to centre1 and be #c-a_/b x #f4 ,large1 heavy bridges require no fastening to connect them with their seats1 but light bridges should be fastened1 as the spring on the sudden removal of a load1 7as when the last car of a train has passed17 may move it from its proper position4 ,splices4 ,as the upper and lower chords have to be made in several lengths1 securely fastened to each other1 and1 in order to weaken the built beam as little as possible1 it is necessary to adopt some form of splicing whereby the greatest amount of tensional strength may be retained in the chord with the least amount of cutting1 and yet have a secure joint4 ,such a splice is shown in ,pl4 ,,ii1 ,fig4 #d1 and below is a table from ,vose's ,hand-book1 giving reliable dimensions4 ,span4 ,a ,c ,b ,b ,c ,d ,feet4 ,feet4 ,inches4 ,feet4 #ej #a4jj #a-a_/b #a4ej #ajj #a4be #b #b4jj #aej #a4ge #b-a_/b #b4be #bjj #b4jj #c #b4ge ,this manner of splicing requires the back of the splice block to be let into the chord stick1 against which it lies1 about #c_/d of an inch4 ,to show how the various ,engineers differ1 as to their estimates of the sizes of the several parts of bridges1 ,i subjoin two ,tables--one by ,prof4 ,g4,l4 ,vose1 a well known ,engineer1 and one by ,jno4 ,c4 ,trautwine1 an ,engineer of note also--and ,i would premise that a bridge built according to either would be amply strong4 ,,table ,,for ,,dimensioning ,a ,,howe ,,truss ,,bridge4 ,g4,l4 ,,vose4 ,end ,centre ,centre ,span4 ,rise4 ,panel4 ,chords4 ,braces4 ,braces4 ,end ,rods4 ,rods4 #ej #aj #g #b--h x #aj #g x #g #e x #e #a--a-a_/h #b--a #ge #ab #i #b--h x #aj #h x #h #e x #e #b--a-a_/b #b--a #ajj #ae #aa #b--h x #aj #h x #i #f x #f #b--a-c_/d #b--a #aej #bj #ac #d--h x #ab #aj x #aj #f x #g #c--b #c--a #bjj #be #ae #d--h x #af #ab x #ab #g x #g #e--b #e--a ,,table ,,for ,,dimensioning ,a ,,howe ,,truss ,,bridge4 ,,jno4 ,c4 ,,trautwine1 ,c4,e4 ,an ,upper ,a ,lower ,an ,end ,a ,centre ,end ,centre ,clear ,no4 ,chord4 ,chord4 ,brace4 ,brace4,counter4 ,rod4 ,rod4 ,span ,rise of ---------------------------------------- ------------------------- in in ,pan- ,no ,no ,no4 ,no ,no ,no4 ,no4 feet4feetels4,pcs,size4,pcs,size4,pcs4,s ize,pcs,size,pcs,size,rods,size4 ,rods,size4 ---------------------------------------- ------------------------------ #be #f #h #c #dx#e #c #dx#aj #b #dx#f #b #ex#e #a #dx#e #b #a-e_/af #b #g_/h #ej #i #i #c #fx#g #c #fx#aj #b #fx#g #b #ex#f #a #ex#f #b #a-e_/h #b #a-a_/af #ge #ab #aj #c #fx#i #c #fx#aa #b #fx#h #b #fx#f #a #fx#f #b #a-g_/h #b #a-c_/af #ajj #ae #aa #c #fx#aj #c #fx#ab #b #hx#i #b #fx#h #a #fx#h #b #b-c_/af #b #a-e_/af #abe #ah #ab #d #fx#aj #d #fx#ac #b #hx#aj #b #fx#i #a #fx#i #b #b-e_/h #b #a-c_/h #aej #ba #ac #d #hx#aj #d #hx#ad #c #ix#aj #c #fx#i #b #fx#i #c #b-c_/h #c #a-c_/af #age #bd #ad #d #ajx#ab #d #ajx#ae #c #ix#aa #c #hx#h #b #hx#h #c #b-e_/h #c #a-a_/d #bjj #bg #ae #d #abx#ab #d #abx#af #c #ix#ab #c #hx#aj #b #hx#aj #c #b-g_/h #c #a-c_/h ,both of these tables were calculated for a single ,railroad track1 and would answer equally well for a double ,highway ,bridge4 ,in the bridge according to ,trautwine's ,table1 each lower chord is supposed to have a piece of plank1 half as thick as one of the chord pieces1 and as long as three panels1 firmly bolted on each of its sides1 in the middle of its length4 99 99 99 99 99 ,,pratt',s ,,bridge4 ,this is opposite in arrangement of parts to a ,howe ,bridge1 as the diagonals are rods1 and sustain tension1 and the verticals are posts1 and suffer compression3 ,example4--,span #ajj feet4 ,rise #ab ,panel #aj ,weight per lineal ft4 #cjjj lbs4 ,the tension on the lower1 or compression on the upper chord1 will be #cjjjjj x #ajj ------------ #ccccccc lbs4 #if ,te,x3 frac#cjjjjj times #ajjif #ccccccc ,the dimensions of the chord and splicing would be found in the same manner as for a ,howe ,truss4 ,suspension ,rods4 ,fig4 #a1 ,pl4 ,,iii41 represents an elevation of a ,pratt ,bridge4 ,now1 it is evident that the first sets of rods must support the weight of the whole bridge and its load1 which we have found to be #cjjjjj lbs4 ,each truss will have to sustain #aej1jjj lbs41 and each end set of rods #ge1jjj lbs4 ,now1 if there are two rods in each set1--each rod will have to bear a strain of #cgejj lbs41 and this will have an increase due to its inclination1 so that the strain on it must be found by the following proportion3 ,height 3 diagonal 33 ,w 3 ,w' or #ab 3 #ae4h 33 #cgejj 3 #dicge lbs4 ,referring to the ,table for bolts1 we find that #b-a_/h gives a strength a little in excess1 and will be the proper size4 ,the next set of rods bear the weight of the whole load1 less that due to the two end panels1 and so on4 ,fig4 #b1 ,pl4 ,,iii1 shows the manner of applying the rods4 ,the bevel block should be so fitted to the chord that it will not have a crushing action4 ,counters4 ,top and bottom chords are always used in this bridge1 and consequently the counter rods have only to sustain the movable load on one panel4 ,the weight of the moving load cannot be more than #bjjj lbs4 per lineal foot which1 for a panel of #aj ft41 gives #bjjjj lbs41 or #aj1jjj lbs4 for each set1 and if we have two rods in a set1 the strain on each rod will be #ejjj lbs41 increasing this for inclination1 we shall have1 #ab 3 #ae4h 33 #ejjj 3 #fehe lbs41 requiring a rod of #c_/d of an inch diameter4 ,the posts in this bridge correspond to the braces of the ,howe ,truss1 but being vertical1 are not so large4 ,subjoined are two ,tables1 one by ,prof4 ,g4,l4 ,vose1 and one by ,mr4 ,trautwine1 giving principal dimensions for bridges of different spans of the ,pratt type of ,truss4 ,,table ,,of ,,dimensions ,,of ,a ,,pratt ,,truss4 ,,prof4 ,g4 ,l4 ,,vose4 ,end ,centre ,end ,centre ,counter ,span4 ,rise4 ,chords4 ,post4 ,post4 ,rod4 ,rod4 ,rod4 #ej #aj #b--hx#aj #e x #e #d x #d #b--a-c_/h #b--a #a--a-a_/b #ge #ab #b--hx#aj #f x #f #e x #e #b--a-e_/h #b--a #a--a-a_/b #ajj #ae #c--hx#aj #g x #g #f x #f #b--a-c_/d #b--a #b--a-a_/h #abe #ah #c--hx#aj #h x #h #f x #f #c--a-g_/h #c--a #b--a-a_/c #aej #ba #d--hx#ab #i x #i #f x #f #c--b-a_/h #c--a #h--a-a_/h #bjj #bd #d--hx#af #aj x #aj #f x #f #e--a-g_/h #e--a #c--a-a_/h ,,table ,,of ,,dimensions ,,of ,a ,,pratt',s ,,truss4 ,upper ,lower ,main ,brace ,rods4 ,counter ,clear ,no4 ,chord4 ,chord4 ,rods4 ,posts4 ,span ,rise of ---------------------------------------- --------- ---------- in in ,pan-,no4 ,no4 ,no4 ,size ,no4,size4,num ,no4 ,size,no4,size4 feet4feetels4,pcs,size4,pcs,size4,ctr,ce ntre,end ,end4ber ,size4 ,end ,end4,ctr,centre ---------------------------------------- --------------------------------- #be #f #h #c #dx#e #c #dx#aj #b #a #b #a-c_/h #a #a-g_/af #c #dx#e #c #dx#d #ej #i #i #c #fx#g #c #fx#aj #b #a-c_/af #b #a-a_/h #a #a-e_/h #c #fx#f #c #fx#e #ge #ab #aj #c #fx#i #c #fx#aa #b #a-e_/af #b #b-a_/b #a #a-g_/h #c #fx#g #c #fx#e #ajj #ae #aa #c #fx#aj #c #fx#ab #b #a-g_/af #b #b-g_/h #a #b #c #fx#i #c #fx#g #abe #ah #ab #d #fx#aj #d #fx#ac #b #a-a_/b #b #b-c_/h #a #b-a_/h #d #fx#i #d #fx#g #aej #ba #ac #d #hx#aj #d #hx#ad #c #a-e_/af #c #b-a_/b #b #a-e_/h #d #hx#h #d #hx#g #age #bd #ad #d #ajx#ab #d #ajx#ae #c #a-e_/h #c #b-c_/d #b #a-aa_/af #d #ajx#aj #d #ajx#h #bjj #bg #ae #d #abx#ab #d #abx#af #c #a-a_/b #c #c-a_/h #b #a-ac_/af #d #abx#aj #d #ajx#h ,this table is partly given in ,trautwine's ,engineer's ,pocket ,book1 and partly made up from directions therein given4 ,,table ,,of ,,dimensions ,,for ,,small ,,single ,,track ,,pratt ,,trusses4 ,at centre ,at end ,centre ,end ,clear ,chords ,centre ,end of truss1 of truss1 ,counter1 ,counter1 ,span1 each1 ,post1 ,posts1 ,diam4 of ,diam4 of ,diameter1 ,diameter1 ,ft4 ,ins4 ,ins4 ,ins4 ,rods4 ,rods4 ,ins4 ,ins4 #cj #i x #aa #d x #i #g x #i #a #a-e_/h #a-c_/h #a #dj #aj x #ab #d x #aj #h x #aj #a-a_/h #a-g_/h #a-e_/h #a #ej #aj x #ad #e x #aj #i x #aj #a-a_/d #b-a_/h #a-c_/d #a #fj #ab x #ae #e x #ab #i x #ab #a-c_/h #b-c_/h #b #a #gj #ab x #ag #f x #ab #aa x #ab #a-a_/b #b-a_/b #b-a_/h #a ,this bridge possesses an advantage over the ,howe ,truss1 for the panel diagonals can be tightened up by screws1 so that every part of the truss can be forced to perform its work4 ,in ,howe's bridge the adjustments must be made by wedging the braces and counters4 ,below are given the dimensions of a ,howe bridge on the ,vermont ,central ,r4,r41 at ,south ,royalton1 7single track1 deck47 ,no4 of ,upper ,lower ,span4 ,rise4 ,panels4 ,chord4 ,chord4 ,braces4 ,counters4 #aej #bj #ab #d--f-a_/b x #ac #d--f-a_/b x #ac #b--h x #i #a--h x #i ,rods4 ,transverse ,bracing4 ,braces4 ,rods4 #c--a-a_/d #f x #h #g_/h ,the bridge over the ,white ,river1 on the ,passumpsic ,r4,r41 is a ,howe ,truss1 strengthened by an arch4 ,the verticals are of wood1 and the diagonals foot on steps formed by enlarging the ends of the verticals4 ,the counters are in two lengths1 and are adjusted by wedges at the points where they intersect the braces4 ,the bridge is in two spans1 and has a double track1 and consequently three trusses4 ,there are two timber arches to each truss1 and the truss is supported on them by connecting them to the verticals by short cross pieces notched into the posts1 and resting on the upper surface of the arches4 ,it is a very stiff bridge1 and similar to the one at ,bellows ,falls1 both having their axis oblique to the channel of the stream they cross4 ,the timbers could hardly be procured now1 except at great expense4 ,no4 of ,upper ,lower ,span ,pan- ,rods ,chord ,chord ,braces ,counters ,uprights ,arches els #ahb #ad #ba #b--h x#af #b--h x#ag1 #a--ba x#h #a--h x#aj #ba x#aa #b--h x#i #a--e x#af #b--d x#ag1 #a--e x#ag1 ,diagonals #f x #h1 ,rods #g_/h4 ,floor timbers suspended both from arches and truss1 #i x #ac2 stringers #aj x #ad4 ,in the ,cheshire ,bridge1 the braces are only #bjx#h1 and the span is only #age feet1 the number of ,panels being #ad1 as in the ,w4,r4 ,bridge--the other dimensions are the same4 ,below are given the dimensions of a ,howe ,truss of #ajh ft4 span1 weight to be borne on upper chord4 ,no4 of ,upper ,lower ,e4 ,floor ,rise ,camber ,pan- ,chord ,chord ,braces ,counters ,rods ,timbers ,ft4 ,ins4 els ,ins4 ,ins4 ,ins4 ,ins4 ,ins4 ,ins4 #ac-a_/b #c #ab #h--c x#ab #h--c x#ab #b--h x#aj #a--g x#aj #b--b-a_/h #i x#af ,as plank is used for the chords1 the pieces must be bolted thoroughly with #e_/h bolts4 ,a form of bridge that has been used to some extent on the ,baltimore and ,ohio ,railroad1 by ,mr4 ,latrobe1 is the ,arch ,brace ,truss4 ,in this form of ,truss the braces lead directly from the abutments to the head of each vertical2 thus the load is transferred at once to the abutments1 without passing through a series of web members4 ,the counterbracing is effected by means of a light lattice1--and is applied to both sides of the chords1 and the intersections of the diagonals are fastened while the bridge is strained by a load--thus preventing recoil--so that the effect of a moving load is to lighten the strain on the lattice--without otherwise affecting the ,truss4 ,illustration3 ,pl4 ,,iii4 with ,fig4 #a41 ,fig4 #b41 ,fig4 #c41 ,fig4 #d41 ,fig4 #e4 ,there are two models of this style of bridge1 to my knowledge2 one built by ,prof4 ,g4,l4 ,vose1 on a scale of #a_/b an inch to the foot1 and representing a span of #aej feet1 which supported #b1ejj lbs4 at the centre1 and a movable load of #aej lbs41 proving itself to be strong and rigid enough for any thing4 ,the other1 on a scale of #a inch to the foot1 and representing a span of #gf feet1 was built by the ,class of '#gc1 of the ,thayer ,engineering ,school1 under the writer's direction1 and though bearing very heavy weights1 has never been thoroughly tested--it has1 however1 been subjected to the sudden shock of #ajdj lbs4 falling #bj inches1 without injury1 several times4 ,subjoined are the dimensions of the models mentioned4 ,,dimensions ,,of ,a ,,model ,,of ,,an ,,arch ,,brace ,,truss4 ,g4,l4 ,,vose4 ,length1 #g feet4 ,height1 #a foot4 ,width1 #a foot4 ,chords1 #d--a_/d x #a_/b inch4 ,braces #d--a_/d x #a_/h ,lattice1 #a_/d x #a_/af ,this represented a span of #aej ft1 a rise of #bj feet1 and a panel of #ae ft4 ,weight1 per running foot of bridge and load1 was taken at #cjjj lbs4 ,the method of calculating the dimensions of this truss1 from the foregoing data1 is as follows4 ,the half number of panels is #e1 and the lengths of the corresponding diagonals 7neglecting fractions7 are --------- _/#bj #ae #be feet4 ,te,x3 root#bjb #aeb #be _/ --------- _/#bj #cj #cg ,te,x3 root#bjb #cjb #cg _/ --------- _/#bj #de #di ,te,x3 root#bjb #deb #di _/ --------- _/#bj #fj #fd ,te,x3 root#bjb #fjb #fd _/ --------- _/#bj #ge #gh ,te,x3 root#bjb #geb #gh _/ ,the weight upon each set of braces is that due to one panel1 or #cjjj x #ae #dejjj lbs41 half of this1 or #bbejj lbs41 is the weight for one truss only--and1 as there is a brace under each of the #d chord sticks1 we divide by #d1 and have #efbe lbs4 per stick of the brace2--now1 correcting for inclination1 we shall have #bj 3 #be 33 #efbe 3 #gjca lbs4 #bj 3 #cg 33 #efbe 3 #ajdjf lbs4 #bj 3 #di 33 #efbe 3 #acgha lbs4 #bj 3 #fd 33 #efbe 3 #ahjjj lbs4 #bj 3 #gh 33 #efbe 3 #baicg lbs4 ,the weights fouud show the compressional strains on the several braces2--and1 were the pieces to be proportioned for compression only1 their ,scantling would be quite small--but on account of their elasticity1 they require larger dimensions4 ,these braces should not be fastened to the verticals1--but should be confined both laterally and vertically1 where they pass them4 ,the length of beam1 for which we have to guard agains flexure1 is the length between verticals in any panel4 ,in panel ,no4 #a1 it will be #be feet1 #b1 #ah #c1 #ag #d1 #af #e1 #af ,now1 using the formula #bbdj b d --------- ,w1 ,l ,te,x3 frac#bbdj bd#c,l#b ,w we shall have1 in round numbers1 the following dimensions3 ,for the #ast panel1 #be feet long1 #h x #aj #b;d #cg #h x #aj #c;d #di #h x #aj #dth #fd #h x #aj #eth #gh #h x #aj ,for the lattice work1 a double course on each side of each truss1 in long spans2 and a single course1 in shorter spans1 of #c x #f1 or #b x #i plank1 bolted at intersections1 is sufficient4 ,,general ,,table ,,of ,,dimensions ,,for ,,arch ,,brace ,,truss4 ,g4,l4 ,,vose4 ,span4 ,rise4 ,chords4 ,ties4 ,braces4 ,lattice4 #ej #aj #b--h x #aj #a--h x #aj #b--f x #f #ge #ab #b--h x #aj #a--h x #aj #b--f x #f #b x #i #ajj #ae #c--h x #aj #b--h x #aj #c--f x #f or #aej #bj #d--h x l#b #c--h x #aj #d--f x #h #c x #f #bjj #be #d--h x #af #c--h x #aj #d--f x #i ,the arch braces must all foot on an iron thrust block1 of which a view is given in ,fig4 #d1 ,pl4 ,,iii2 and the centre of pressure of the braces must be directly over a bolster1 to prevent crippling4 ,the several sticks forming a brace must be blocked together at intervals1 and ,when they are spliced1--a butt joint ,should be used--and it should come in the centre of a panel4 ,below are given the dimensions of the ,thayer ,engineering ,school model4 ,height ,ins4 #ab ,no4 ,panels #h ,chords ,ins4 #b--a x #a_/b ,posts ,ins4 #a--b_/c x #e_/f ,braces ,ins4 #b--a_/b x #a_/b ,lattice ,ins4 #a_/d x #a_/b ,width ,ins4 #ac ,there are several other forms of ,bridge1 the most notable among which are the ,whipple1 ,mc,callum's1 ,post's1 ,towne's1 ,haupt's1 and ,burr's4 ,but enough has been said to give the student an idea of the general arrangement of the different parts of a ,truss1 and to enable him to determine the strains to which the various members are subjected4 ,nothing will be said in regard to ,wooden ,arches1 as our space is too limited4 ,pile ,bridging4 ,a bridge of this description is useful in crossing marshes1 or in shallow water4 ,fig4 #e1 ,pl4 ,,iii1 gives a good example of this kind of bridge1 under #bj feet in height4 ,if on a curve1 there must be extra bracing on the convex side4 ,trestle ,work4 ,this is a combination of posts1 caps1 and braces2 and is used for both temporary and permanent works4 ,plate ,,iv1 ,figs4 #a1 #b1 #c and #d1 give some of the best varieties in use4 ,figs4 #a and #b1 may be used up to #ae feet in height2 ,fig4 #d1 up to #bj feet2 and ,fig4 #c1 to #cj ft4 ,the distance apart of the various bents should not exceed #aj or #ab ft41 unless bracing is introduced between them1 and the bents should always be raised above the ground a few feet on a solid masonry foundation4 ,want of space forbids any mention of abutments and piers1 which really come more properly under the head of masonry4 ,iron ,bridging is gradually working its way into favor1 and ,will probably eventually supersede wooden trusses2--but in many cases wood is the only material at hand--and therefore some knowledge of ,wooden ,bridging is desirable4 ,it is intended to follow this pamphlet with a portfolio of sheets containing working drawings of several kinds of ,wooden ,bridges1 taken from actual measurements of some of the best specimens of the different styles of ,truss in use4 99 99 99 99 99 ,,practical ,,notes4 ,when putting a truss together in its proper position1 on the abutments1 'false works' must first be erected to support the parts until they are so joined together as to form a complete self-sustaining truss4 ,the bottom chords are first laid as level as possible on the false works1 then the top chords are raised on temporary supports1 sustained by those of the lower chord1 and are placed a few inches higher at first than their proper position1 in order that the web members may be slipped into place4 ,when this is done the top chords are gradually lowered into place4 ,the screws are then gradually tightened1 7beginning at the centre and working towards both ends17 to bring the surfaces of the joints into proper contact1 and by this method1 the camber forms itself1 and lifts the lower chords clear of the false works1 leaving the truss resting only upon its proper supports4 ,the subjoined ,table will be found useful in estimating the strains on a truss when proportioning a bridge for any moving load4 ,table of weights per running foot of a bridge1 7either of wood or iron17 including weights of floor1 lateral bracing1 c41 complete1 for a single track4 ,clear ,weight of ,span4 ,bridge4 ,tons4 lbs4 #be 4#bff #eif #cj 4#bha #fbi #dj 4#cac #gja #ej 4#cdc #gfh #fj 4#cgd #hch #gj 4#djd #ije #hj 4#dcd #igb #ij 4#dfd #ajci #ajj 4#did #aajf #abj 4#eed #abda #adj 4#fad #acge #aej 4#fdc #addj #afj 4#fgc #aejg #agj 4#gjc #aege #ahj 4#gcc #afdb #bjj 4#gib #aggd #bbe 4#hfg #aidb #bej 4#idj #baje #bge #a4jac #bbfi #cjj #a4jhg #bdce ,the weight of a single track railway bridge may be taken as equal to that of a double track highway bridge1--and the trusses that will be large enough for one will be large enough for the other4 ,the greatest load that a highway bridge can be subjected to is #abj lbs4 to the square foot of surface4 ,,table ,,of ,,cambers ,,for ,,bridge ,,trusses4 ,span4 ,camber4 ,span4 ,camber4 ,span4 ,camber4 ,span4 ,camber4 feet4 ,inches4 ,feet4 ,inches4 ,feet4 ,inches4 ,feet4 ,inches4 #be #j4h #ge #b4e #age #e4h #bge #i4b #cj #a4j #ajj #c4c #bjj #f4g #cjj #aj4j #ej #a4g #abj #d4j #bbe #g4e #cbe #aj4h #fj #b4j #aej #e4j #bej #h4c #cej #aa4g ,,trautwine',s ,,table ,,for ,,finding ,,increase ,,in ,,length ,,of ,,upper ,,chord ,,beyond ,,the ,,lower ,,chord ,,on ,,account ,,of ,,the ,,camber4 ,multiply ,multiply ,depth of ,camber ,depth of ,camber ,truss4 by ,truss4 by #a-d span #b4jj #a-ab span 4#fff #a-e #a4fj #a-ac 4#fad #a-f #a4cc #a-ad 4#ega #a-g #a4ae #a-ae 4#ecc #a-h #a4jj #a-af 4#ejj #a-i 4#hhh #a-ag 4#dgj #a-aj 4#hjj #a-ah 4#ddd #a-aa 4#gbg #a-bj 4#djj ,,table ,,of ,,american ,,woods4 ,weight per ,resistance in lbs4 per ,kind4 cubic foot square inch4 ,value of s4 in pounds4 ,extension ,compression4 ,white ,pine4 #bf #ab1jjj #fjjj #abbi ,yellow ,pine4 #ca #ab1jjj #fjjj #aahe ,pitch ,pine4 #df #ab1jjj #fjjj #agbg ,red ,pine4 #ce #ab1jjj #fjjj #aebg ,virginia ,pine4 #cg #ab1jjj #fjjj #adef ,spruce4 #dh #ab1jjj #fjjj #ajcf ,tamarack4 #bf #ab1jjj #fjjj #ijg ,canada ,balsam4 #cd #ab1jjj #fjjj #aabc ,white ,oak4 #dh #ae1jjj #gejj #agdc ,red ,oak4 #da #ae1jjj #gfjj #afhg ,birch4 #dd #ae1jjj #gjjj #aibh ,ash4 #ch #af1jjj #hajj #agie ,hickory4 #ea #ae1jjj #gbjj #babi ,elm4 #de #af1jjj #hjaa #aigj ,the above table is compiled from a much fuller one in ,vose's ,treatise on ,r4,r4 ,construction4 ,,table ,,of ,,bolts ,,and ,,nuts ,,calculated ,,for ,a ,,working ,,strain ,,of #ae1jjj ,,lbs4 ,,per ,,square ,,inch ,,of ,,section4 ,diameter4 ,area4 ,strength in ,weight per ,thick's ,no4 thr's ,inches4 ,sq4 inches4 ,pounds ,foot4 ,square nut4 of nut4 per inch4 #a_/b 4#aifce #bidj #j4ff #a-a_/d in #c_/d in #ab #e_/h 4#cjfhj #dfjb #a4jc #a-c_/h #c_/d #aj #c_/d 4#ddagi #ffcj #a4di #a-a_/b #g_/h #aj #g_/h 4#fjacb #ijai #b4jc #a-c_/d #a #i #a 4#ghedj #aagge #b4fe #b #a #h #a-a_/h 4#iidjb #adiaj #c4cf #b #a-a_/h #g #a-a_/d #a4bbgb #ahdje #d4ag #b-a_/d #a-a_/d #g #a-c_/h #a4dhdi #bbbfj #e4jb #b-a_/b #a-c_/h #f #a-a_/b #a4gfga #beeje #e4ig #b-c_/d #a-a_/b #f #a-e_/h #b4jgci #cajie #g4ja #b-g_/h #a-e_/h #e #a-c_/d #b4djec #cfjge #h4ac #c #a-c_/d #e #a-g_/h #b4gfab #dadae #i4cc #c-a_/d #a-g_/h #d-a_/b #b #c4adaf #dgacj #aj4fb #c-a_/b #b #d-a_/b #b-a_/h #c4eaff #ecaij #ab4jj #c-c_/d #b-a_/h #d #b-a_/d #c4igfa #eifdj #ac4dj #d #b-a_/d #d #b-c_/h #d4dcja #ffdej #ae4jj #d-a_/h #b-c_/h #d #b-a_/b #d4ijhg #gcfbj #af4gj #d-a_/d #b-a_/b #c-a_/b #b-e_/h #e4daai #haagh #ah4bj #d-a_/b #b-e_/h #c-a_/b #b-c_/d #e4icif #hijid #bj4jj #d-c_/d #b-c_/d #c-a_/b #b-g_/h #f4diah #igcgg #ba4ij #e #b-g_/h #c #c #g4jfhf #ajfjbi #bc4hj #e-a_/d #c #c #c-a_/d #h4bieh #abddcg #bg4ij #e-c_/d #c-a_/d #c #c-a_/b #i4fbaa #addcaf #cb4dj #f #c-a_/b #b-a_/b ,,table ,,of ,,safe ,,working ,,load ,,in ,,lbs41 ,,for ,,hollow ,,cast-,,iron ,,columns4 ,g4,l4 ,vose4 ,outside ,length or height in ,feet ,metal ,diameter ,thickness in inches4 #f #h #aj #ab #ae #ah #bj in inches4 #c #afjjj #adjjj #acjjj #aajjj #ijjj #gjjj #fjjj #c_/h #d #cjjjj #bijjj #bfjjj #bdjjj #bbjjj #ahjjj #afjjj #a_/b #e #ejjjj #cgjjj #dejjj #dbjjj #cijjj #cgjjj #cajjj #e_/h #f #eijjj #egjjj #eejjj #ebjjj #dijjj #ddjjj #dajjj #c_/d #g #ajajjj #iijjj #ifjjj #ibjjj #hhjjj #hajjj #gfjjj #ac_/af #h #acajjj #abijjj #abfjjj #abbjjj #aahjjj #ajijjj #ajejjj #g_/h #i #afijjj #afgjjj #afdjjj #afjjjj #aefjjj #adfjjj #adajjj #a #aj #bajjjj #bjjjjj #bjjjjj #bjjjjj #aijjjj #ahjjjj #ahjjjj #a-a_/h #aa #bejjjj #bejjjj #bdjjjj #bdjjjj #bdjjjj #bcjjjj #bbjjjj #a-a_/d #ab #cjjjjj #cjjjjj #bijjjj #bijjjj #bijjjj #bgjjjj #bgjjjj #a-a_/b #ad #dejjjj #dcjjjj #dajjjj #chjjjj #cgjjjj #cejjjj #ccjjjj #a-c_/d #af #ebjjjj #ejjjjj #dhjjjj #dfjjjj #ddjjjj #dbjjjj #djjjjj #b #ah #fejjjj #fcjjjj #fajjjj #eijjjj #efjjjj #ebjjjj #dgjjjj #b-a_/b #bj #hjjjjj #gfjjjj #gdjjjj #fijjji #fejjjj #eijjjj #edjjjj #c ,illustration3 ,pl4 ,,iv4 with ,fig4 #a41 ,fig4 #b41 ,fig4 #c41 ,fig4 #d4 ,transcriber's ,notes3 ,,disclaimer3 ,this document should ,,not be used to engineer any bridge projects6 ,many typesetting errors were found1 and it is possible that there are further errors in the information that were not caught4 ,formulas have been provided both as ,,ascii and ,te,x following in brackets4 ,bold headings are handled with equal signs before and after the bold text4 ,italicised text uses the standard underlines before and after the text4 ,fractions are expressed in the format3 #b-a_/d means two and one quarter4 ,the page numbers listed below are project page numbers4 7,the original book used ,roman numerals to number the pages47 ,note that the book uses the long ton equal to #b1bdj pounds4 ,,corrections ,,made3 #a4 ,page #h--the formula for d must use a cube root1 which is how it is shown here1 but the '#c' to indicate a cube root is not found in the original document4 #b4 ,page #h--typo in word 'sectien'--changed to 'section'4 #c4 ,page #aj--,value for working comp4 strength of cast iron in the table had a typo 7#be1v#jj74 ,since other values use round numbers1 it is assumed the value should be #be1jjj4 #d4 ,page #aj--,two other typos4 ,changed 'the the' to 'the'1 and in table heading1 original word was 'detrution'1 changed to correct spelling of 'detrusion'4 #e4 ,page #ab--;changed 'woooden' to 'wooden'4 #f4 ,page #ac--;,example ,,ii--,in the calculations1 the intermediate value in the book was printed as the square root of #fg4b4 ,the left part is correct1 but reduces to the square root of #bfh4h1 and that is #af4cie4 ,so ,i have corrected the intermediate value4 #g4 ,page #ac--;,because the original page scan cut off the text on the right edge1 ,i have made assumptions on what text was missing4 ,because the scans came from an outside source1 ,i could not get the missing information1 which was the words at the end of ,example ,,ii1 and words in the last paragraph of the page4 #h4 ,page #ad--,three typos found3 'dimensiens' for 'dimensions'1 'betng' for 'being'1 and 'ars' for 'are'4 #i4 ,page #ag--;a value in a formula was printed as #fjjj1 but in the context of the other information1 particularly the example immediately following1 the value was believed to be incorrect1 and was changed to #ejjj4 #aj4 ,page #bc--,the value of #chh sq4 inches at the top of the page in the book is incorrect2 #c x #h x #ab #bhh1 so has been corrected4 #aa4 ,page #bd--,rods section1 numerical value appeared to be #ae4jjj in the book1 but from context1 must be #ae1jjj instead4 #ab4 ,page #bh--,typos3 changed ',trautwine's ,edgineer's ,pocket-,bood' to ,trautwine's ,engineer's ,pocket-,book'2 corrected 'af' to 'as'1 'bracas' to 'braces'4 #ac4 ,page #cj--;,apparent typo in the table at the bottom of page4 ,value for ,center ,brace size for #bjj' span was shown as '#h x #a'1 believed from context of table to be '#h x #aj'4 #ad4 ,page #cc--table of dimensions of a ,pratt ,truss1 last column1 row starting with #aej1 the original says #h--a-a_/h1 this is believed to be1 and has been changed to1 #c--a-a_/h4 #ae4 ,page #cg--,the five formulas with square roots were incorrectly printed in the book1 multiplying the terms inside the square root instead of adding them1 which is obviously incorrect per the ,pythagorean theorem of right triangles4 #af4 ,page #ch3 ,the fifth ratio in the group of five near the top of the page must start with #bj1 not #aj as in the book #ag4 ,page #ch--,the equation for ,w as printed on this page is not consistent with that found on pages #ah to #bd1 so has been corrected from 'bd#b' to 'bd#c'4 #ah4 ,page #ci--;arch brace truss table heading typo-changed ',,foe' to ',,for'4