A rectangular bar of width b and height h is being used as a cantilever. The loading is in a plane parallel to the side b. The section modulus is

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This question was previously asked in

BPSC AE Paper 5 (Civil) 14 Oct 2022 Official Paper

Answer 1

Concept:

Section Modulus(z):

Section modulus is defined as the ratio of moment of inertia of a beam about its C.G to the maximum distance of extreme section of the beam (Ymax).
The section modulus (Z) of the cross-sectional shape is significant in designing beams.
It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.
The unit of the Section modulus is mm3

Section modulus, \(Z = \frac{I}{y_{max}}\)

For rectangular section:

Moment of inertia and the maximum distance of neutral axis from top fiber for a rectangular beam is given by,

I = \(\frac{bh^3}{12}\) and ymax = h/2

Hence, Z = \(\frac{\frac{bh^3}{12}}{\frac{h}{2}}\) = \(\frac{bh^2}{6}\)