4. Suspension Bridges

As the practical limits of beam bridges and arch bridges were reached, engineers were forced to look for a new approach. Eventually, they combined the features of simple rope bridges with the remarkable strength of steel chains and cables. The result was the modern suspension bridge. To understand how a suspension bridge works, consider a hammock. Three main forces typically the weight of the person in the hammock, and two matching tension forces in the supporting ropes. For purposes of analysis, engineers often break forces into their components. Here, we break the force in the rope on the right, that is F2, into its horizontal and vertical components. To do so, we draw the rope force as a vector, making its angle match the direction of the rope and drawing its length proportional to the magnitude of the force it carries. The first step in graphically resolving F2 into its components is to construct a right angle triangle with horizontal and vertical edges and with F2 as its hypotenuse. One can show mathematically that the length of the horizontal edge of the resulting triangle is proportional to the horizontal component of the force F2. Similarly, the vertical edge of the triangle is proportional to the vertical force component. In this case, the horizontal component of the force is clearly much larger than the vertical one. We don't need to analyze the forces on the left side of the hammock in detail, because they mirror those on the right. We can verify our graphical findings by building a model hammock. We can support the right end of the hammock using a single angled spring scale and directly measure the force F2. Alternatively, we can use vertical and horizontal scales in combination, so as to mechanically resolve the force F2 into its horizontal and vertical components. It is then easy to see that the horizontal force is much larger than the vertical one, just as our graphical analysis predicted. Now, let's suspend the entire model hammock from one scale in order to measure its total weight, which turns out to be 40 newtons. How does the vertical force on the right rope compare with the total weight of the hammock? It turns out to be exactly half of that weight. The same is true for the vertical force on the left rope. Suppose we allow the hammock to sag more, so that its ends are more steeply sloped. Do you think the vertical force will change? If so, how? Do you think the horizontal force will change? To answer these questions, we again use our model hammock. As you can see from this experiment, when there is more sag, the vertical force does not change. It still equals half of the total hammock weight. However, the horizontal component decreases significantly. A graphical analysis would have told us the same thing. Notice that the forces in the rope also decrease significantly when there is more sag in the hammock. The main cables of a suspension bridge carry their load the same way as a hammock does. The forces in the bridge cables can be broken into vertical and horizontal components, just like the hammock forces. And, if the bridge cables have a steeper slope at their ends, the cable tensions will be reduced, allowing a less expensive cable to be used. However, steeper cable angles require taller support towers, and they cost more money to build. The heights of the towers in real bridges are calculated so as to minimize the total bridge cost. The large horizontal forces produced by bridge cables have important design implications. If they were to act on tall, thin bridge towers, they would produce a lot of bending in those towers, and that would not be good. Those forces could, however, be resisted by sturdy, wide towers, and that's exactly the strategy used in the London Tower Bridge. Another approach would be to mirror the ends of the main span. One could then use the mirrored sections as approaches from the adjacent land, and the horizontal forces from the mirrored spans would balance and cancel out the ones from the main span. When this strategy is followed, thin towers like those seen on modern suspension bridges can be used. The next challenge is how to transfer the vehicle and other loads to the main cables. This load transfer is usually done using deck panels, and they are carried by beams running across the width of the bridge. The ends of these transverse beams are in turn carried by vertical rods or wires called suspenders, and they are in turn connected to the main cables, which rest on the towers and their foundations. The complete load transfer path involves the deck panels, transverse beams, suspenders, main cables, towers, and foundations. By using a model, we can experiment with each of these components, including the foundations, main cables and suspenders, and the deck. The model lets you experience firsthand the consequences of poor construction sequences, and the benefits of good ones. Remember that a large fraction of structural failures occur during construction. The model also demonstrates some of the deflection issues that can arise if a deck is too flexible. Indeed, one of the most famous suspension bridges to collapse was the Tacoma Narrows Bridge, and that failure could have been prevented if a less flexible deck had been used. We can reduce the flexibility of the model deck by adding these panels, and doing so solves the excessive deflection problem. As this video has shown, suspension bridges can be both elegant and efficient. Many suspension bridges have become icons for the cities in which they were built. Suspension bridges, and the lessons they taught us, have made possible many clever and interesting kinds of cable-supported structures. We hope you enjoyed this video, and that you will watch some of our other Engineering Models videos.