Two beams of equal cross-sectional area are subjected to equal bending moment. If one beam has a square cross-section and the other has a circular cross-section, then ______.

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This question was previously asked in

SSC JE CE Previous Year Paper 19 (Held On: 1st March 2017 Evening)

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Answer 1

Concept:

SSC JE CE 16 SOM images Q10

Both are of equal area \(\Rightarrow {b^2} = \frac{{\pi {d^1}}}{4}\)

\(\Rightarrow b = \frac{d}{2}\sqrt \pi \)

For circular section modulus,

\({Z_c} = \frac{{\pi {d^3}}}{{32}}\)

For square section,

\(\begin{array}{l} {Z_{square}} = \frac{{{b^3}}}{6} = \frac{{\pi \sqrt \pi {d^3}}}{{48}}\\ \therefore {Z_{square}} = 1.18{Z_{circular}} \end{array}\)

So for the same cross-section area, a square section is better than the circular section in bending.

Note:-

For the same cross-sectional area, the order of sections in increasing the bending strength

SSC JE CE 16 SOM images Q10a