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Question

If a beam of rectangular cross-section is subjected to a vertical shear force V, the shear force carried by the upper one-third of the cross section is

A
Zero
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B
7V27
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C
8V27
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D
V3
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Solution

The correct option is B 7V27

Upper one third means y varies from d/6 to d/2

Shear stress at distance y from NA,

τ=VA¯¯¯yIb

shear force = shear stress × Area

=d/2d/6VA¯¯¯yIb.b.dy

=Vd/2d/6(d2y).b.12(d2+y)dybd312

=6Vd3d/2d/6(d24y2)dy

=6Vd3[d24yy33]d/2d/6

=6Vd3×7d3162=727V

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