A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). Obtain a formula for the maximum bending stress max due to the falling weight in terms of h,...

A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure).

Obtain a formula for the maximum bending stress

_max
due to the falling weight in terms of h,

 _st, and d , where
_st
is the maximum bending stress and

_st
is the deflection at the midpoint when the weight W acts on the beam as a statically applied load.

Plot a graph of the ratio

_max
/
_st
(that is, the ratio of the dynamic stress to the static stress) versus the ratio h/
_st. (Let h/
_st
vary from 0 to 10.)