GATE 2022 CE (CE1) – Question 65
For the dual-wheel carrying assembly shown in the figure, P is the load on each wheel, a is the radius of the contact area of the wheel, s is the spacing between the wheels, and d is the clear distance between the wheels. Assuming that the ground is an elastic, homogeneous, and isotropic half space, the ratio of Equivalent Single Wheel Load (ESWL) at depth z = d/2 to the ESWL at depth z = 2s is ___________. (round off to one decimal place) (Consider the influence angle to be 45° for the linear dispersion of stress with depth)
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Correct answer: 0.49 to 0.51
Explanation
In the stipulated linear-dispersion model, at depth d/2 the two stress bulbs just start to overlap, so the equivalent single-wheel load is P. At depth 2s their effects merge fully and ESWL becomes 2P.
The ratio is therefore $P/(2P)=\mathbf{0.5}$. This uses the specified approximate stress-dispersion model, not an exact elastic integration.