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Question

A homogeneous prismatic simply supported beam is subjected to a point load F. The load can be places anywhere along the span of the beam. The very maximum flexural stress developed in the beam is

A
3FL2BD2
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B
3FL4BD2
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C
2FL3BD2
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D
4FL3BD2
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Solution

The correct option is A 3FL2BD2
Max. bending stress,

σmax=MmaxZ

Section modulus,

Z=Iymax=BD3/12D/2=BD26

BM will be maximum when load is mid-span,

Mmax=FL4

σmax=FL/4BD2/6=6FL4BD2=3FL2BD2

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