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   Evolution of Trusses
  </title><link href=../homstyl.css rel=STYLESHEET><body><h2>Early Evolution of Trusses</h2><p id=Foreword><hr><p><p>The application of wood and iron to bridge-building stimulated the design of trusses, which were suitable to the new materials. Unlike stone, wood and iron can resist tension as well as compression, which offers many new possibilities. Bridges could be built more cheaply and rapidly from the new materials, which was the most important factor in their use. In this paper, the development of wood and iron truss bridges in the United States is followed until about 1877, when steel bridges were coming in, and truss design had approached a modern rational form.<p>Before 1800, nearly all major bridges were stone arches, a thoroughly satisfactory but very expensive form of bridge. Arches can be made from wood or iron as well as from stone, and many examples can be found, from the wooden arch bridges of early America to the giant steel arches of Hell Gate in New York City to the Sydney Harbour Bridge. Early America had much wood, but little money, so wooden bridges were the rule, with few exceptions. The wooden arch is examined in <a href=burr.htm> The Burr Truss </a> elsewhere on this site. In this paper, we will first go back to the ancient bridge type that long antedated the arch, the beam, and show how it developed into the truss bridge.<p><img align=RIGHT hspace=10 src=truss.gif><p>At A in the Figure on the right is a simple beam, with a concentrated load F acting on it. The beam is supported at its ends, where <i> reactions </i> R <sub> 1 </sub> and R <sub> 2 </sub> are exerted. The beam is in equilibrium under these forces, which means that there is no net force causing it to move, and no net torques causing it to rotate. These conditions allow the determination of the reactions, using the equations on the right. Ideally, the beam is free to rotate about the supports, and free to move horizontally. The top of the beam is in compression, shown by the blue color, and the bottom is in tension, shown by the red color. Of course, the compression or tension is distributed over the cross-section of the beam, and is shown on the surface only for simplicity. The <i> span </i> of the bridge is the distance between supports, here the distance a + b. The loads on the bridge may be concentrated, as shown, or distributed in any way along the span. The weight of the bridge itself is a load, the <i> dead load </i> . The weight of traffic on the bridge, or occasional snow and wind, make up the <i> live load </i> .<p>Now suppose the beam is too long, or the load too great, so that the beam tends to sag excessively, or even break. At B is one solution, a prop underneath the beam. It is shown directly under the load, so that it carries all the load, and the reactions disappear. In other cases, it will carry a share of the load, and the beam the rest. This prop is under compression, and must be designed so that it will not <i> buckle </i> under the load, that is, deflect sideways. The beam has now become a <i> continuous beam </i> extending over three supports. If supports can go anywhere under the bridge, it is usual to make the span no longer than the beam can safely cross, and the result is a <i> trestle </i> , a very simple and economical form of bridge. A continuous beam over the trestle supports, or <i> bents </i> , is more economical than a series of simple beams.<p>If this cannot be done, some way must be found to strengthen the beam without using a prop. One way is shown at C. The members are all timber, except for the vertical tension rod that is shown supporting the load at its lower end. If the vertical member were also of wood, this would be a <i> king-post </i> truss, a very old and useful kind of bridge. However, wrought iron rods were the first iron bridge members, and are very good at resisting tension. The beam is no longer a beam, but a tension member countering the outwards thrust of the two inclined members. The compression is still on top, and the tension on the bottom, of the structure, something we will see is quite general. This is very much like a <i> tied arch </i> , but executed in wood. The horizontal member is called the <i> lower chord </i> , and eventually would have also been iron. The greatest difficulty with this kind of bridge is the execution of the connections, especially the joining of the inclined and horizontal members at the ends of the span.<p>The force triangle at D shows how the load F is balanced by the compressive force C in the inclined members and the tensile force T. If F is known, C and T can easily be found by scaling from this triangle. Most early bridge designers who worried about such forces preferred such graphical calculations, which could be carried out on a diagram of the bridge itself, where the members were represented by simple lines, called a <i> skeleton diagram </i> . The duty of the bridge is to transfer the load F to the supports at the end of the span. We observe that a necessary accompaniment is the creation of horizontal components of force, which must always be properly accommodated.<p>At E a skeleton diagram is shown with the previous bridge inverted, and the load F applied at the center of the horizontal member, which is now the <i> upper chord </i> . The stresses in each member have been reversed; what was in tension is now in compression. The forces, however, are the same in magnitude, so this bridge is equivalent to the first one. Either bridge can be called a <i> trussed arch </i> . In E, the compression members could be wood and the tension members iron, in fact a continuous iron rod from one end of the horizontal member to the other, passing through a saddle on the verical member, or <i> post </i> . Small iron castings could be used for the saddle, and for the connections at the ends of the rods. A similar trussed beam could have two posts instead of one. Such structures should be very familiar.<p>This idea was used by Albert Fink for major bridges, as shown at F. If the unsupported horizontal spans are too large for a single post and truss, they are each divided in two by a post and truss, and this process is continued as far as necessary. Each division is called a <i> panel </i> . The vertical posts at the ends of each panel need not be the same height, so in some cases they can be made just long enough to reach the diagonal members. This economy is seen in the roof truss at G, where we have inverted the truss. As usual, tension members become compression members, and vice-versa, so the upper chord is still in compression and the lower in tension. The loads are shown applied to the tops of the posts, as is natural for a roof truss. Note that the dotted members have become superfluous with the loads in the new position. If the lower chord were a compression member, they would be quite necessary to prevent buckling, but here are of little use except to support the dead load of the horizontal tie. Although the Fink bridge truss has long fallen out of use, the Fink roof truss is still alive and well.<p>Instead of the tension members only reaching the next subdivision point, they may be carried all the way to the ends, as shown in H. This results in the <a href=bolltrus.htm> Bollman Truss </a> , treated in detail in the link. This truss was all-iron, using wrought iron for the ties, and cast iron for the posts and horizontal compression member. Each panel point is supported independently of the others. The Fink and Bollman trusses are examples of <i> suspension trusses </i> , a type of bridge that is now rare. These bridges have no functional lower chords, which distinguishes them from the more familiar kinds of truss bridges.<p>Instead of trussing a beam, a second method of approach was to strengthen the beam itself by making it deeper. With solid beams, there is a definite limit to this process. However, the material can be rearranged to put more of it where needed, and to eliminate underutilized material. In a beam, the maximum stress occurs at top and bottom, with the material in between under less stress. Therefore, the material could be concentrated in upper and lower chords as far apart as necessary. This cannot be done literally, since a beam must also support vertical <i> shear </i> forces. In the case of the simple beam, there is a vertical force R/2 between the supports and the concentrated force F. Even if there were no shear force, the compressive upper chord would still have to be prevented from buckling.<p>The first answer to this in iron was the box and plate girder. Cast iron was found to be too brittle for such use, so most of these bridges were constructed of wrought iron plates, riveted together. The plate girder, consisting of upper and lower flanges, connected by a thin web, is very practical for short-span bridges.<p>In wood, one answer was the lattice truss. The Town lattice truss, made entirely of wood planks 2-3" thick and 9-12" wide was commonly used in America for common road bridges. Connections were made by trenails, wooden dowels driven into holes. They tended to warp badly, especially when made of green wood. The bridge was sheathed with shingles to protect it from the weather, forming the traditional "covered bridge." They were very unsatisfactory as a railway bridge, because they could not be rationally proportioned for the new heavy loads, connections worked loose, and other reasons. In iron, however, lattice trusses have proved successful, though not widely used in the United States.<p><img align=LEFT hspace=10 src=truss2.gif> Another plan was to frame a beam-like structure as a series of rectangular <i> panels </i> , ideally squares but usually taller than long for increased strength without members of inconvenient size. A square frame such as A in the Figure depends on the rigidity of its corners. When subjected to a shearing stress, it tends to distort as in B, one diagonal becoming longer, and the other shorter. This can be resisted by diagonal braces, which will be in tension (red) in one direction, in compression (blue) in the other. Wooden diagonals are better used in compression, avoiding troublesome tension connections, while iron rods are useful only in tension, since they buckle under compression.<p>A bridge of this type is associated with the name of Stephen H. Long, early West Point graduate and officer of the U. S. Topographic Service. The bridge was used with success around Baltimore. It was a wooden frame with diagonal braces in both directions in each panel, and seems to have used iron rod ties. We can call such a truss a Long truss to classify it, but this does not imply either that Long was first to use that bridge skeleton, or that the later builder owed much to Long. A bridge type is generally named after the person who designed a complete bridge, not just the skeleton, and saw the bridge actually constructed and used successfully. One can always find examples of a particular bridge skeleton used previously, it seems.<p>The Howe Truss, at C, has the great advantage of simplicity with strength. Unlike other inventors of the time, who added superfluous elements to their designs on the basis of faulty understanding, Howe reduced the number of members to a minimum. If any member fails, the whole bridge collapses. This is by no means a disadvantage, since it also implies that the forces in each member can be uniquely determined, and the member can be proportioned to bear its load safely. Such a structure is called <i> statically determinate </i> , since the forces are found in the first approximation by the equations of statics alone, and do not depend on the details of construction. These forces are found when the load is known, and the bridge skeleton is determined. The nature of the force, whether tension or compression, is shown for each member with the static loading shown. In the original Howe Truss, all members were of wood except for the vertical ties, which were iron rods threaded at the ends and secured by nuts. Careful attention was paid to the connections, especially of the lower chord, and the bridge was very successful. The bridge skeleton, incidentally, appears in Palladio, and the diagonal compression braces were used in the Burr truss.<p><p>A very similar bridge is the Pratt Truss, at D. The only difference is the direction of the diagonals, but this turns them into tension members, and the vertical members into posts. Again, this truss was first made of wood, except for the iron rod diagonals. It used somewhat more iron than the Howe Truss, but was equally successful. A great improvement was made when the lower chord was formed from iron eye bars. These made a stronger and more reliable tension member than wood. Connections were made at the panel points by means of iron pins through the bars of the lower chord, the posts, and the diagonals. Such a <i> pin-connected </i> truss was truly statically determinate, and became the favorite with American railway civil engineers, who were very wary of bridge failures. The statically-determinate bridge, while not the most economical, was very safe.<p>The loads on a bridge truss are applied at the panel points, either on the upper chord or the lower chord. If applied at the upper chord, the bridge is called a <i> deck </i> bridge, and if applied at the lower chord, a <i> through </i> bridge. The loads here are represented as for a deck bridge. A complete bridge consists of at least two trusses connected by transverse bracing, the roadway, usually of simple beams, and the abutments or piers at the ends. A truss bridge, acting as a beam, exerts no horizontal forces on its supports<p>To find out whether the force in a diagonal is compression or tension, imagine the loaded bridge cut by a vertical plane in the middle of a panel. Now find the net upward force to the left of the cutting plane, which will be the abutment reaction less the loads on that side. This must be balanced by the forces exerted through the cut members. The upper and lower chords cannot contribute, since they are horizontal. The net vertical force, or shear, which is usually upwards, must be balanced by the force in the diagonal member. This means a compression in a Howe diagonal, and a tension in a Pratt diagonal.<p><img align=RIGHT hspace=10 src=truss3.gif> However, suppose that a heavy load, such as a locomotive, is approaching the center of the bridge, as in the Figure on the right. The bridge has been cut at plane AA', and all forces acting on the left-hand side are shown. The right-hand side of the bridge has been moved away a little. This is a <i> free-body </i> diagram, an extremely useful tool in structural analysis that students usually ignore out of inexperience. The live load is assumed to act at the first panel point, at the center of gravity of the locomotive shown. The reactions are 25 t and 75 t as shown. The net vertical force of the reaction and load is 25 t <i> downwards </i> , and is known as the <i> shear </i> at the cross-section AA'. Since the net force on the free body must be zero in any direction (or the bridge would fly away), we look for other vertical forces. The only one is that exerted by the cut diagonal, F <sub> 2 </sub> , and it must be a <i> compression </i> ! The vector diagram shows that the magnitude of the compression is 35.4 t. As for the forces in the chords, the upper chord is relieved by 25 t, and the lower chord has an extra 25 t, due to the force on the diagonal. Now, suppose the locomotive moves so that its center of gravity is at the center of the span. Now the shear at AA is 50 t <i> upwards </i> , and the tension in the diagonal is 71 t.<p>All this came as a shock to bridge designers, who had been used to heavy bridges since antiquity, where the live load was small, and the most important load had been the weight of the bridge itself. With railways, the loads were now heavier than the bridges themselves. The solution for stress reversal is to add <i> counters </i> , or ties in the other diagonal, at least to the center panels where the danger of stress reversal is greatest. This is shown at E. When the shear reverses, the other diagonal takes over in tension, and the bridge is secure. Haupt continually mentions the need for counter bracing for railway bridges, and that the lack of it was responsible for failures.<p>Shear and bending moment diagrams, unknown in the early days, now make it much easier to visualize the stresses on a bridge as a heavy live load moves over it, and to determine the true maximum stresses in any member. This is specially easy and reliable for statically-determinate trusses. Computer programs are available to eliminate the arithmetic, and allow the design of a bridge without knowing much about it. This results in surprises that seem to be becoming more common.<p>Stress reversal was only one of the surprises for bridge engineers when railways arrived. Another was the effect of a sudden application of load. If a load is simply applied suddenly at a point, even without impact or violence of any kind, the instantaneous stresses are <i> double </i> the static stresses. Any impact, of course, just makes the conditions worse. Wood can actually absorb a reasonable amount of impulsive stress energy, but cast iron cannot (in tension), which was the principal reason cast iron was not used in railway bridges, except in arches and for small fittings, where this defect would not be dangerous. The failure of a cast-iron beam bridge over the River Dee in England, designed by Robert Stephenson in 1848, was significant. Severe speed restrictions were applied over early American railway bridges, and enginemen were instructed not to work steam if possible, to keep impact to a minimum.<p>Another surprise was stress concentration. The eye-bars used as lower chords were usually proportioned with the same cross-sectional area at the hole for the pin as in the body of the bar, since they carried the same tensile stress. However, the stress was not uniformly distributed around the pin, and was at least double in some places. This encouraged cracks to form, perhaps largely from fatigue as the bars were loaded and unloaded repeatedly, and the eyebars failed with catastrophic result. This led to very cautious and conservative design rules for eyebars, as well as an extensive testing program for these critical components.<p>The two trusses at F and G are large iron trusses of the 1870's for the replacement of earlier wooden bridges. The Pettit truss F claims to be a triangular truss, and indeed it is. However, we see that it is basically a Pratt truss with the upper chord stiffened by trussing, and have shown the stress states corresponding to this assumption. A moving load might give different results. A bridge of this type replaced the massive Wernwag timber arch at Trenton in 1875. By comparison with this giant, the new bridge looked light and spidery. Perhaps you can detect its weakness. Stress reversals would not be well handled with thin members designed only for tension under a static uniform load. Something like this may have been the case, for the bridge was soon replaced by a steel Pratt truss, perhaps as early as 1877.<p>The single-track wooden bridge over the broad Susquehanna at Rockville, Pennsylvania was the last wooden bridge between Philadelphia and Pittsburgh on the Main Line, and the Pennsylvania Railroad Company was as eager to replace it with iron as they had done with the Trenton bridge. However, a new truss was devised for the 1877 replacement, possibly as the result of experience. This was a double-track bridge with three parallel trusses, of the form shown at G. This truss can be derived from the Pettit truss by extending the short diagonals to cross the whole height of the truss, and eliminating the redundant verticals. The diagonal members were proportioned to resist reversed stresses, making a true triangular truss. In fact, it is two Warren trusses superimposed. Warren trusses, very popular roof trusses, have no verticals, just zigzag diagonals. This bridge was successful, lasting until replaced by a four-track stone arch in 1902.<h3>References</h3><ol><li>H. Haupt, <i> General Theory of Bridge Construction </i> (New York: D. Appleton & Co., 1851)<li>A good tutorial on bridges can be found at <a href=http://www.polymorf.net/> Polymorf </a></ol><p><hr> Return to <a href=techhom.htm#civil> Tech Index </a><p><p id=Postscript>Composed by J. B. Calvert <br> Created 26 October 2000 <br> Last revised 27 February 2004