GATE 2023 MN – Question 48
Pillar strength is $S_p=S_1(0.64+0.54w/h-0.18w^2/(lh))$, with l≥w. A 30 m square pillar of height 3 m is split by a 5 m roadway into two equal pillars. The figure shows the tributary boundaries, 2.5 m outside the original edges. Find the safety-factor ratio of one half-pillar to the original pillar, to two decimals.
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Correct answer: 0.49 to 0.52
Explanation
Original strength factor is 0.64+0.54×10−0.18×10=4.24. A half-pillar has w=12.5, l=30 and h=3 m, giving strength factor 2.5775. Original stress multiplier is 35²/30²=1.36111. For one half, tributary area is 35×17.5 and pillar area is 30×12.5, giving stress multiplier 1.63333. Safety-factor ratio is (2.5775/4.24)×(1.36111/1.63333)=0.50658, or 0.51. Use one half-pillar’s tributary load and area consistently.