The GATE Grind

GATE 2021 CE (CE1) – Question 56

Geotechnical Engineering · Shallow foundations: bearing capacity, combined footing, raft, settlement · 2 marks · Numerical answer

A trapezoidal combined footing has end widths 5 m and 1.5 m and length L. Two 0.5 m square columns, 5 m centre-to-centre, carry 2000 and 1500 kN. The first column centre lies 0.25 m from the wider end. For uniform bearing stress, find L in m to two decimals.

see the reproduced source diagram and its labels.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 5.70 to 5.90

Explanation

The load resultant lies at $\bar x=0.25+1500(5)/3500=2.392857$ m from the wider end. The trapezoid centroid is $L(b_1+2b_2)/[3(b_1+b_2)]=8L/19.5$. Equating resultant and centroid gives $L=2.392857(19.5)/8=\mathbf{5.83}$ m.