Question

A massive pillar of height ‘h’ density ρ and having uniform cross–section ‘a’ rests on a rigid base and supports a maximum vertical load W newton at its upper end. The peak compressing strength of the pillar is S. Taking a safety factor of 10; the minimum area of cross–section of the pillar should be (g = 10 m/s² )

(1) 10 w/S-100h p

(2) 10 w/S- 10 h p

(3) 10 w/S

(4) 10S/W-10h p

Answer 1

(1) 10 w/S-100h p

The pillar supports the load W as well as its own weight at the bottom. Therefore

Total load = Weight of the pillar + W

This stress should not exceed S/10 as safety factor desired is 10. Therefore