GATE 2025 AG – Question 50
A stable drop structure has base length 5.7 m. Downward vertical forces excluding uplift total 92.5 kN; uplift totals 72.5 kN. The sum of moments of all horizontal and vertical forces about the base mid-section is 60 kN·m. Find eccentricity between base centroid and resultant vertical load, in metres, to two decimals.
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Correct answer: 0.10 to 0.20
Explanation
Net vertical load is $W=92.5-72.5=20$ kN. With the moment explicitly stated about the base centroid, the mechanics relation is $e=M/W=60/20=3.00$ m, which is outside the official accepted range .10–.20 m. The keyed value **0.15 m** results from $|L/2-M/W|=|2.85-3|=.15$ m, which would require the 60 kN·m moment to be about a base edge. The printed datum and official grading are both preserved; the moment-reference inconsistency is not silently repaired.