A) Both beams will be equally strong
B) Circular section beam will be stronger
C) Square section beam will be stronger
D) The strength of the beam will depend on the nature of loading
Correct Answer: C
Solution :
\[{{A}_{s}}={{A}_{C}}=A\] Let a = side of square d = diameter of circle Then \[{{a}^{2}}=A\,\,\,or\,\,\,a=\sqrt{A}\] \[\frac{\pi }{4}{{d}^{2}}=A\,\,or\,\,d=\sqrt{\frac{4A}{\pi }}\] Moment of resistance, \[{{M}_{r}}=\sigma z\] For same \[\sigma ,{{M}_{r}}\propto Z\] \[{{z}_{s}}=\frac{{{a}^{3}}}{6}=\frac{1}{6}{{A}^{3/2}}\] \[{{z}_{C}}=\frac{\pi {{d}^{3}}}{32}=\frac{\pi }{32}{{\left( \frac{4A}{32} \right)}^{3/2}}=\frac{1}{7}{{A}^{3/2}}\] \[\therefore \] Square beam is stronger than circular beamYou need to login to perform this action.
You will be redirected in
3 sec