Consider the following model steel bridge. What would the real bridge weigh and would the real bridge sag?

Question

Consider a model steel bridge that is 1/100 the exact scale of the real bridge that is to be built. If the model bridge weighs 50 N, what will the real bridge weigh? If the model bridge does not appear to sag under its own weight, is this evidence the real bridge, built exactly to scale, will not appear to sag either?

Leo Abeyta · Accepted Answer

Because of the 'square-cube rule', the bridge will be 10,000 times as strong as the model but weigh 1 million times more. The fact that the model does not appear to sag does not guarantee that the bridge will not appear to sag.

This demonstrates the'square-cube rule' in action: when objects change in size, their cross-sectional area (and surface area) changes as the length squares, while their volume (and, if the materials' densities are the same, their mass) changes as the length cubes. So if the real bridge is 100 times as large as the model, its mass will be #100^3# = #1,000,000# times the mass, = #50,000,000# or #5.0 imes 10^7# #N#. The strength of the beams holding up the bridge will be related to their cross-sectional thickness, which will increase as the square of the length, so they will be #100^2# = #10,000# times as strong. The fact that the model does not appear to sag does not guarantee that the bridge will not appear to sag because it is 10,000 times stronger than the model but 1 million times heavier.

Charles Aeschliman · Answer

undefined The weight of the real bridge would depend on various factors, including the dimensions, materials used, and design specifications. Whether the real bridge sags depends on the bridge's structural integrity, load-bearing capacity, and the materials employed in its construction. Detailed engineering analysis is required to determine the specific weight and structural behavior of the actual bridge.