# Conceptual Question about Suspension Bridge Forces

Two walkways are suspended from vertical rods. In the first scenario, one long rod supports both walkways and is attached to the ceiling. In the second scenario, two shorter rods are attached to each bridge independently. I do not understand how the pin A, feels different force magnitude in each scenario. It says that pin A supports the weight of both bridges in the second scenario, but shouldn't it be the same for scenario 1? It explains pin A in the first scenario only supports the weight of the upper walkway. Shouldn't pin A support both walkways? Pin A is in equilibrium.

## 4 Answers

Consider what would happen to the bottom walkway if you would remove pin A. In the first scenario the bottom walkway remains hanging, in the second scenario it would fall down.

Also consider if you would start pulling the beam down with more and more force: In the first scenario it would break from the ceiling as the top walkway would just be pulled down together with the beam and no extra stress on pin A. In the second scenario you would be applying more pressure on pin A and the one below it.

In first scenario the continueing rod supports the load of first deck and experiences stress concentration around the drilled opening for pin A, and pin A is only loaded with the weight of one deck. However the rod above pin A supports both decks' load.

But in the second case the rod is discontinued and pin A is loaded with both decks' loads , because the second deck is already loaded with the weight of first deck as well.

• This problem is based on the "Hyatt Regency walkway collapse" of 1981. There is a Wikipedia article about the incident with the phrase in quotes as its title. The subtle $mg\to 2mg$ error caused the deaths of 114 people. – mike stone Jun 13 '19 at 17:17

Look at it from the side, and make some free body diagrams:

In the first case (left), the load paths for each walkway meet at the rod after the pins. Each pin only supports one walkway (blue and red) and the rod supports both (purple).

In the second case (right), the entire weight of the bottom walkway goes through the top walkway support resulting in the top pin to have to support both. Each rod has to be in static equilibrium and since the top rod is a two force member, the $$2mg$$ reaction on the top has to come from the pin. Here I have marked with purple the forces of both walkways.

Actually, I'm not sure about magnitude of forces acting on pins. But, what I AM sure of, is that in case (b) walkways has more degrees of freedom, because of several contact points involved with gap, and thus (b) configuration is highly unstable. In theory walkways moves independently of each other in case (b) inducing random stresses to either of pins and on some conditions it may even summon stress resonance on either of pins, thus resulting in avalanche of events.

Illustration of more degrees of freedom in case (b) :

So, conclusion is that (b) design is flawed for sure.