## Chapter 14

## Q. 14.8.2

## Q. 14.8.2

Fig. 14.8-3(a) shows a propped cantilever supporting a uniformly distributed load w per unit length. If the collapse load factor is to be A, determine the required plastic moment of resistance M_{P}.

## Step-by-Step

## Verified Solution

Let the unknown location of the sagging plastic hinge be defined by ** x**, as in Fig. 14.8-3(b). The work equation is

or \qquad \qquad M_{P}=\lambda wL\frac{x(L-x)}{2L-x}

By the unsafe theorem, the value of M_{P} corresponding to an arbitrarily assigned value of ** x** is less than, or at best equal to, the plastic moment required to withstand the load

*λ***. Hence**

*w***M_{P} is maximised with respect to**

*,***:**

*x*COMMENTS

The above solution is based on the unsafe or upper bound theorem. An alternative solution, based on the safe or lower bound theorem is given in Example 14.8-3.