The following columns have same material, height and weight, whic
A. I-section
B. Solid circular section
C. Solid square section
D. Thin hollow circular section
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Explanation:
The critical load for a column is given by,
\({P_{cr}} = \frac{{{\pi ^2}EI}}{{L_{eff}^2}} \)
where E is the modulus of elasticity, I is the moment of inertia, Leff is the effective length.
for the same material, height, and weight the value of E, L or Leff, and weight W be the same for all columns.
Thus, \( {P_{cr}} \propto I\)i.e Pcr will depend on the moment of inertial of the column.
The lower the Pcr the lower will be the tensile load or weight supported, and higher Pcr means higher tensile load or weight supported.
from the I - section, solid circular section, solid square section, and thin hollow circular section
the moment of inertia in decreasing order is,
I - section > Solid square section > thin hollow circular section > solid circular section.
also, the moment of inertia is maximum for the shape in which the mass of the material is located away from the centre or the rotating axis.
thus the maximum weight will be supported by I- section.