The Bridge That Sags
A Year 11 group is building model bridges from 6 mm square balsa for a competition. Each bridge must span 400 mm and carry a 5 kg load at mid-span. One team's first attempt is a simple flat Warren truss: two horizontal chords with zig-zag diagonals, all joints glued with PVA. It carries 2 kg before the bottom chord snaps near mid-span. The team notices the failure is a clean break across the grain of the balsa, and that the top chord shows no damage. They have enough balsa for one more attempt and one week before the competition.
1. Analyse why the bottom chord failed while the top chord survived, and explain what this tells you about the truss design.
Read the worked answer
When a simply supported beam or truss is loaded at mid-span, it bends into a curve that is concave upward. The top chord is in compression and the bottom chord is in tension.
Balsa is much weaker in tension across the grain than in compression along it, and a clean break across the grain is a classic tension failure. The bottom chord was doing the hardest job in the structure with the least suitable material orientation.
The top chord survived because compression along the grain suits balsa well, and because the diagonals were bracing it. The design is not fundamentally wrong, but it is unbalanced: the tension member needs more material, better grain orientation, or both. The diagonals also transfer load to the bottom chord at discrete points, creating stress concentrations at the glued joints.
2. Recommend changes for the second attempt, explaining how each change addresses the failure you identified.
Read the worked answer
1. Strengthen the bottom chord in tension. Double the bottom chord (two 6 mm pieces laminated side by side) or add a second bottom chord with a small gap and connect them with verticals. Tension members should have continuous grain running the full span; avoid joints at mid-span.
2. Deepen the truss. Increasing the depth of the truss reduces the forces in both chords for the same load, because the chords are further from the neutral axis. A deeper truss with the same amount of balsa will carry more load than a shallow one.
3. Improve the joints. PVA is weak in shear and creeps under load. Use a stronger adhesive appropriate to the material, and add gusset plates at the joints to spread the load over more area rather than concentrating it at a point.
4. Pre-load test. Build a test rig and load the bridge gradually, recording the load at first cracking. This gives evidence for the final design rather than relying on guesswork.
The reasoning is to put material where the forces are highest (the tension chord) and to reduce those forces by geometry (greater depth) before adding more material.