Collapse Mechanism

So for our previous beam, we know that we require two hinges for collapse (one more than its degree of redundancy), and we think that the hinges will occur under the points of peak moment, A and C. Therefore impose a unit virtual displacement at C and relate the corresponding virtual rotations of the hinges using,

 Other Collapse Mechanisms

For the collapse mechanism looked at previously, it seemed obvious that the plastic hinge in the span should be beneath the load. But why? Using virtual work we can examine any possible collapse mechanism. So let's consider the following collapse mechanism and see why the plastic hinge has to be located beneath the load.

Plastic Hinge between A and C:

Imposing a unit virtual deflection at B, we get the following collapse mechanism:

And so we see that the collapse load factor for this mechanism depends on the position of the plastic hinge in the span.