Question

Out of the two beams of the same material and same cross-section area, one is of circular cross-section and the other is of square cross-section. If each of these is subjected to bending moment of the same magnitude, then

• A. both sections would be equally strong
• B. both sections would be equally economical
• C. square section would be more economical than circular section
• D. square section would be less economical than circular section

Answer 1

The correct option is C square section would be more economical than circular section

The strength of a section will be proportional to its section modulus

as $M\propto Z$

$\therefore$ Let diameter of circular section = D, and Side of square section = a

$\therefore \frac{\pi D^2}{4}=a^2$

$\Rightarrow \frac{D^2}{a^2}=\frac{4}{\pi }$

$\therefore \frac{Z_{square}}{Z_{circular}}=\frac{I_{square}}{y_{square}}/\frac{I_{circular}}{y_{circular}}$

$=\frac{\frac{a_4}{12}}{a/2}/\frac{\frac{\pi D^4}{64}}{D/2}$

$=\frac{a^3}{6}/\frac{\pi D^3}{32}=\frac{32}{6\pi }\left(\frac{a^3}{D^3}\right)$

= 1.18

$\therefore Z_{square}>Z_{circular}$

Hence square section would be more economical.