GATE CE 2022 Set 1 — Question 52
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Structural Engineering → Indeterminate Analysis & Influence Lines → Influence Lines
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Question
Consider a simply supported beam PQ as shown in the figure. A truck having 100 kN on the front axle and 200 kN on the rear axle, moves from left to right. The spacing between the axles is 3 m. The maximum bending moment at point R is _________ kNm. (in integer)
Correct answer
180 to 180
Solution
To find the maximum bending moment at point R, we use the Influence Line Diagram (ILD) for bending moment at R.
Thus, the maximum bending moment is 180 kNm.
1.The length of the beam m. Point R is at m from P and m from Q.
2.The peak ordinate of the ILD at R is .
3.The truck has two axle loads: kN (front) and kN (rear), with a spacing of 3 m. It moves from left to right.
4.Maximum bending moment at R occurs when the heavier load (200 kN) is placed at R.
- Case: 200 kN at R, 100 kN is 3 m ahead (at m from P).
- The ordinate at 4 m from P is .
- Total Bending Moment kNm.
Thus, the maximum bending moment is 180 kNm.
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