GATE 2021 CE (CE2) – Question 54
A 2.8 m ×3.5 m footing at depth 1.5 m in clay carries vertical load at eccentricity 0.8 m along its width. γ=18.2 kN/m³,c=40 kPa,φ=0°. Given Nc=5.14,Nq=1,Nγ=0,sc=1.16,dc=1.1, and all other factors 1, find Meyerhof allowable load for FS=2.5 in kN to two decimals.
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Correct answer: 439 to 442
Explanation
Meyerhof effective width is B′=2.8−2(0.8)=1.2 m and effective area is1.2×3.5=4.2 m². The net ultimate bearing pressure is cNcscdc=40(5.14)(1.16)(1.1)=262.3456 kPa. The surcharge γDf cancels when gross capacity is converted to net capacity because Nq=1. Apply safety factor2.5 to net capacity:Qnet=262.3456(4.2)/2.5=**440.74 kN**,matching the official range. This is the net allowable applied load.