BASSWOOD BRIDGE TESTING Andrew Pace, Nick Villagra, Roby Velez, Ryo Akasaka Engineering Department, Swarthmore College Submitted May 3, 2006 Abstract

Using a Multiframe™ analysis, we designed a basswood bridge prototype and a final design with the following properties:

Weight: 33.3g Overall dimensions Length: 331mm Height: 84.7mm Width: 54.0mm Ultimate Load Borne: 150 lbs Load to Weight ratio: 4.50

Our design was formed by adding members such that stresses were

evenly distributed over the bridge and moments were minimized. The prototype was loaded and failed at 195 lbs. Failure occurred from shearing at the joint at the top of the portal frame. In our subsequent design, we added gusset plates at the top of the portal frame and we made the portal frame consist of continuous members to fit the specifications for the bridge design. Our final design failed at 150lbs when the bottom member buckled, mainly due to insufficient glue application; however, the overall truss remained intact. Further design improvements would include more application of glue at the junctions in the bottom members and greater consideration for better load distribution. by adding gusset plates at the bottom members of the bridge.

Designing the Bridge

The design of the bridge was largely done by the use of Multiframe™, which allowed us to visually analyze the stresses and the deflections applied on a structure of our choice using material that was comparable in size.

We first began by choosing a bridge structure we thought would be viable for construction by selecting among several standard structures that are in use today, such as the Howe, Pratt and the Warren trusses. The designs we found were intended for steel bridges, so we had to change some configurations to best suit a wood design by taking into account the fact that wood is weak under shear stress. Having then chosen the curved chord Pratt truss design as ideal, largely due to sources that indicated that the overall displacement of the bridge would be minimal with respect to loads applied at the center of the bottom deck of the bridge1, we set out to redesign the bridge with the intention to keep the stresses on the bridge evenly distributed throughout the whole members, rather than having portions of the bridge suffer greater compressive or tensile strengths. We figured that by doing so we could cut back on multiple bridge members glued together, and thus cutting back on the weight.

Another consideration was the general ‘flow’ of the stresses throughout the bridge – instead of having compressive and tensile members located at the top and bottom sections of the bridge respectively, we thought to construct the bridge such that once again they would evenly space out throughout the bridge. Thus the construction seen below has compressive members extending towards the middle of the bridge where they intersect with members that are in tension.

We were, however, unable to accurately gauge the deflections on the bridge because our members were designed significantly smaller with regards to the applied loads. We were able to get a very rough (and by no means accurate) idea of what the deflections would be using members that were made using sections of metal and of considerable larger size. The applied load in our model was a relatively large 2kN (450lbf) distributed evenly on four joints – two on either side of the middle with 0.5kN each – which is not an accurate reflection of the real testing situation, since more of the blocks are loaded on the joints closer to the middle. A solution to this is explained in the construction of the bottom deck.

1 “Truss Bridge Types”, Pinecoast Software, http://www.pinecoast.com/v_example4.htm

A slight consideration that must be mentioned is the fact that Multiframe™ distinguishes between a single member spanning the bottom deck and several shorter members (see Figure 6.1) – a result perhaps due to it not considering that the joints are connected at the bottom.

We emphasize the fact that our design was not made such that the bridge

completely resisted deflection. By providing for a design that spread the applied load as evenly as possible throughout the bridge, we were striving for deflection to take place, but such that the entire bridge would still be able to support the deflections (up to a maximum point). Many architectural structures are designed to give way even slightly rather than resist movement completely, and we had this in mind while designing the bridge. This is also why our bottom deck is composed of two parallel strands of basswood oriented laterally rather than vertically (into the bridge’s interior, rather than above or below) – the applied load would allow for more deflection to take place, but also less stress to be applied unevenly on compression members (in particular the portal frame area).

Figure 1 - Loading diagram of prototype

Figure 2 - Bending moment of prototype

Figure 3 - Shear stress of prototype

We printed our bridge design to scale and fitted the basswood members over the blueprint, notching the ends of the members so they fit smoothly with each other. After the members were in place, we put glue in the intersections of the members. This same procedure was repeated for the other side of the bridge. We then linked the two ends of the bridge with horizontal cross members of 50mm length attached at the base of each pair of vertical members. Our analysis was that a shorter width of the bridge would prevent a bending moment to develop as the load is applied. Also, to remedy the fact that more of the load would be applied at the bottom cross-member closer to the middle (the middle joint would experience no load because it would be between the two blocks), we made notched diagonal members joining the cross member closest to the middle with the one spanning the middle.

Horizontal cross members were also attached at the top of the each pair

of vertical members, and a similar configuration for diagonal members was added. A single cross member was placed at 50mm height from the bottom, connecting both sides of the truss panel in order to prevent the bridge from collapsing inward on itself. Finally, gusset plates were attached at the intersections of members at the sides of the bridge. Designing the Bridge, part 2.

Upon testing the first prototype constructed exactly as the diagram shown, we realized, among other construction faults, the following:

1) The bridge could not qualify under the rules – the portal frame had to be constructed using one diagonal member extending from the bottom of the bridge to a point where the vertical height exceeded at least 70mm, whereas our first bridge’s portal frame consisted of two.

2) Our bridge width could be shortened – the width of the bottom deck where the testing blocks were resting was 50mm, which led to an overall bridge width of 56mm without gusset plates.

3) Our bridge failed because both sides were not exactly symmetric (see Figure 5.1). This was due to the fact that our initial plans created on Multiframe™ had been scaled to real size, but in doing so we failed to realize that one half of the bridge was not entirely symmetric to the other, and therefore changing the orientation of the truss panel meant that both sides were no longer the same. Some consequences of this were the woods shear strength failed earlier than we hoped, revealed by looking at the glue and noticing wood fibers on it. Moreover, we realized that our portal frame was most likely the culprit for the notched cross members pulling outwards as it did—removing the gambreled portal frame would prevent a similar thing from happening.

Figure 4 - Image of completed prototype bridge. Note the gambreled portal frame, which would have disqualified us at the ultimate testing stage.

Figure 5 – Point of failure for prototype

Figure 5.1 – Side view of failed bridge. Note the very apparent inclination of the bridge to the left side

In order to remedy these design problems, we set out to alter our first

design, but to not such a large extent as to render ineffective whatever we were able to gain from the testing we had performed. Therefore we changed the portal frame such that it consisted of one member only, added cross members that significantly strengthened the upper part of the bridge, and shortened the width of the bridge such that the bottom deck only spanned 46mm, giving an ultimate bridge width of 52mm, just 2mm beyond what the rules allowed the width to be. In doing so, we ensured that the bottom deck would remain sturdy and not develop a bending moment in the members that spanned it.

We also added gusset plates to the top deck of the bridge in order to ensure that both truss panels would not separate. Diagonal, notched cross-members were added at two locations within the bridge between the panels with the same intention, as well as on the portal frame. Three supporting cross-members spanned the bridge at a height of 42mm because we realized that the bridge would be stronger laterally if a member spanning the bridge were located at the lowest possible location between the two panels.

Joints

All joints were notched, with the intent that the connection between them would be stronger than with glue alone, and so that the members would not pull apart. The notches were made so that they fit snugly so much so that much of the truss panel was self-standing even without glue. The joints of particular importance were located at the bottom deck, which would support the load, and the top section of the portal frame, where we had noticed failure in our prototype. The gusset plates were oriented such that the direction of the load applied was the same direction as the grain in order to maximize the efficiency of each gusset plate. Upon inspecting that the failure in the prototype occurred at the top of the portal frame, we added a pair of gusset plates along the top of the portal frame to prevent the joints from shearing outwards.

. Figure 6 – Loading diagram for final design

Figure 6.1 - Loading diagram of prototype. Note how the loads are different with the

bottom member built as a single member

Figure 7 – Bending moment diagram for final design

Figure 8 – Shear stress diagram for final design

Expected Point of Failure

While we did add additional gusset plates to the second bridge design, the portal frame was expected to remain the weakest part of the bridge since shearing stresses were highest at the ends of our bridge in the Multiframe™ analysis. We thought the gusset plates at the portal frame would shear apart, albeit at a higher load than the first bridge. Another noted

Chronicle of the Bridge Test

After our bridge passed all the requirements, needing only a quick sanding to allow the 40 x 40 x 330 mm block of wood through the entire structure, it was ready to be tested.

Figure 9 – Loading of our bridge

The load was steadily increased, with only a couple of snaps heard before the bridge was under 100 lbs of force.

As the load increased the snapping of the glue became more apparent, as

did the deflection of the bottom beam. At a load of just over 100lbs, one of the diagonal members was severed from its glued joint, but since it did not apparently impact the load-carrying capacity of the bridge, loading was continued. Suddenly, as the load hit 150 lbs., one of the joints near the middle was pulled out, ending the bridge’s chance of further loads.

Figure 10 – Point of failure for final bridge Final Specifications of the bridge:

Weight: 33.3g Overall dimensions Length: 331mm Height: 84.7mm Width: 54.0mm Ultimate Load Borne: 150 lbs Load to Weight ratio: 4.50

Failure Analysis The main causes of our bridge’s failure were due to insufficient transferring of the load from the deck to the trusses as well as weak end pieces. The bridge would have lasted longer if more glue had been applied on the gusset plates on the deck of the bridge. As the load was being applied to the deck, it was then transferred through the diagonal and vertical members of the

truss to the arch. As the load increased, the tension in the glue did as well, until the force overcame the strength of the glue and the deck tore away from the truss. The ends of the bridge had a notched configuration, causing less wood then desired to be in this important corner. With less wood, there was not as much strength in this joint, and shearing occurred here, not allowing as much load to be borne as it might have. A possibly remedy to this problem would have been to not notch this corner or add more gusset plates here. Some other factors came into contributed to our bridge’s failure. We also noticed by making a greater emphasis on keeping the two sides of the truss panel together, we weakened the structural integrity of the bottom half of the bridge; the insufficient glue application on the bottom section was testament to this fact, as well as the fact that the bottom deck began to deflect earlier than the top half of the truss. Indeed, were it not for the significant consideration made to prevent the bridge to fall apart in one direction by the adding of gusset plates, more load would have been applied elsewhere. As it was, the gusset plates at the top deck prevented it from deflecting more so than the bottom deck, putting significant strain on the members underneath the loading blocks. Overall, our truss remained intact. This was because other parts of the bridge failed earlier, not allowing the truss to undergo the full possible load. Conclusion Through this bridge project we were able to use our knowledge of truss design and analysis, as well as tools such as Multiframe™ in order to construct a working design for a basswood bridge that we then loaded and tested using a machine. Though through fault of lack of glue our bridge did not hold the load that was expected given the design and the care taken to notch members together and glue gusset plates in the right orientation, but it nonetheless allowed us to understand the fundamentals of proper bridge design. Moreover, by striving towards a better load-to-weight ration we also aimed towards economizing the use of material, a key component in successful engineering designs.

Roles Taken by Members Much of the bridge construction and assembly was performed as a group, although Roby Velez added his input in constructing the truss panels using the band saw at the wood shop. The design of the bridge was done over a significant amount of time over a weekend in discussion with the entire group, and a prototype was constructed within the following week. Much of the gluing was done by Rio Akasaka, and gusset plates as well as cross members were cut and applied by the group.