GATE CE 2015 Set 2 — Question 43
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Structural Engineering → Indeterminate Analysis & Influence Lines → Flexural Stresses
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Question
A simply supported beam of span, is subjected to two wheel loads acting at a distance, apart as shown in the figure below. Each wheel transmits a load, and may occupy any position along the beam. If the beam is an -section having section modulus, , the maximum bending stress (in GPa) due to the wheel loads is ___________.
Correct answer
1.78 to 1.79
Solution
1.Find the maximum bending moment ():
For two equal point loads at a distance apart on a simply supported beam of span , the maximum bending moment occurs when the center of the span is midway between one of the loads and the center of gravity of the load system. The center of gravity of the two loads is at from each load.
The maximum bending moment occurs under one of the loads when that load is at a distance of from the center of the span.
Position of load from support : .
Position of load from support : .
Reaction at ():
.
Maximum bending moment under : .
2.Calculate maximum bending stress ():
Given .
.Rounding to two decimal places, we get 1.78 to 1.79 GPa.
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