A Bridge of Sticks: A Physics Project

Yes, my school has much, much work. That goes without saying, some are pretty repetitive and boring and all the usual stuff you'll say about homework.

But that also goes without saying, some jobs were pretty cool. The last two weeks, one of our physics teachers (we have two for each year) tasked us to make a bridge of ice cream sticks, when studying rigid body rotations.

Seems unrelated. But we'll test supporting forces, those that keep the bridge from shearing off. Then, the bridge's maximum load will be tested to the point of breaking. The following is my report's analysis and conclusion. This could be a good starter's guide to design a super-strong bridge of ice cream sticks, perhaps when bored.

Special thanks to all my team members who worked together to finish this task: Gabriella, Anfield, Bobby, and Arthur.

Analysis

The finished bridge.

Original design of the bridge.

Testing the supporting forces of the bridge.

Testing the maximum load of the bridge.

The bridge after load testing.

Our finished product has a mass of 345.8 g. It did not break even with a load of about 76.41 kg. This means it has a load-to-mass proportion of at least 1 : 220.97.

Finally, its supporting forces, the forces that hold the bridge from buckling in the center, on either side are as follows, when different loads were used:

Load, N	Supporting Force, left (F1), N	Supporting Force, right (F2) N
0	1.701	1.699
0.981	2.187	2.187
1.978	2.678	2.678
2.963	3.189	3.189

From that table, we could see that the supporting forces are actually almost always perfectly balanced between the two sides of the bridge. There were no differences in supporting forces on both sides of the bridge but for when the load was zero, which was a very small difference, thus they both overlap in the graph. However, we did use two beam balances because the bridge was too heavy for an electronic balance, so human error was a possibility. We still could say that the bridge was properly built, though: able to spread load equally, and was made neatly enough so that the initial weight distribution was equal. This will contribute to the bridge’s strength.

The thickness of the bridge we used was three sticks thick at the center, three sticks for the horizontal-running trusses, two sticks for the vertical and diagonal trusses on the side, and four sticks for the diagonal trusses. There are seven pairs of vertical columns on side, each pair connected with a horizontal column above, then each corner are connected with diagonal struts. The amount and thickness of the trusses made the bridge able to withstand a higher amount of weight, as expected, because it could spread the weight throughout the whole bridge.

The forces acting on the bridge. Green is tension and red is compression.
                The web application at http://ivanmarkov.com/truss-simulator.html was used.

The amount and positioning of trusses contributed primarily to the bridge’s strength. We used a truss bridge design, where crisscrossing bars are made to spread the load equally throughout the bridge, so that it would not break. The trusses that formed the diagonal shapes could made the tension and compression from the weight in the center spread outwards, then along the span of the bridge to the ends, where it could be channeled to the ground.

During construction, there might have been some errors that might have made the results different than our hopes during design. First of all, due to a shortage of ice cream sticks, we used a different type of sticks for half of the upper part of the bridge’s base. This ice cream stick is denser and harder to break, which could have moved the equilibrium and the supporting forces. However, it turned out that the sticks might have the same weight distribution so that the supporting forces remained balanced.

Another factor that contributed to our bridge’s strength is the glue that we used. The strength of the glue is crucial in keeping the base of the bridge connected with the trusses that support it. We used PVA glue, which seem to be able to be used optimally for wood. With a strong bond, the forces would be transmitted better and thus will be spread more equally.

Finally, how accurately the bridge was made also became a factor. To spread weight maximally, the trusses must be accurately and tidily placed, evenly spaced, so that no part of the bridge receive more stress than others. Actually, we did not measured exactly where the horizontal columns were placed, nor did we precisely measure the length of each stick, leading to the need for sandpaper to make sure all parts glue together precisely. However, we did make the trusses of both sides as symmetrical as possible, so that the tension and compression travel equally on both sides.

Conclusion

The bridge that we made managed to withstand a load of about 76.41 kg without breaking. As the mass of the structure is 345.8 g, the bridge has a mass-to-load ratio of at least 1 : 220.97. This is caused by the truss design of the bridge, where the amount of vertical columns and crisscrossing trusses spread the tension and compression forces on the bridge equally.

The supporting forces on the two ends of the bridge are balanced, with only a very small difference. This is also caused by the truss bridge being able to spread a load equally, and also the equal weight distribution of the bridge itself.

Thus, to make a bridge as strong as possible, supporting elements must be added to spread the tension and compression, in this case the truss. The truss could be thickened or more trusses could be added, and a strong binder must be used, in this case, PVA glue. Finally, the precision and tidiness during construction, especially in making the bridge symmetrical, makes sure that the load is spread equally.