question_answer

Let us consider the case of a beam loaded at the centre and supported near its ends as shown in figure. A bar of length /, breadth b and depth d.

The total amount of load at the centre of a beam \[(\delta )\] is given by

A) \[w{{l}^{3}}/(4b{{d}^{3}}y)\]

B) \[w{{l}^{2}}/(4b{{d}^{2}}y)\]

C) \[w{{l}^{3}}/(4b{{d}^{2}}y)\]

D) \[w{{l}^{4}}/(4bd)\]

Correct Answer: A

Solution :

When loaded at the centre by a load w sags by an amount given by

From equation, we see that to reduce the bending for a given load, one should use a material with a large Young's modulus Y. For a given material, increasing the depth d father than the breadth b is more effective in reducing the bending since \[\delta \] is proportional to \[{{d}^{-3}}\]and only \[{{b}^{-1}}\](of course the length \[l\]of the span should be as small as possible).