GATE CE 2015 Set 2 — Question 41
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Structural Engineering → RC Fundamentals & Beams → Limit States (Collapse & Service)
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Question
A simply supported reinforced concrete beam of length 10 m sags while undergoing shrinkage. Assuming a uniform curvature of along the span, the maximum deflection (in m) of the beam at mid-span is _______________.
Correct answer
0.05 to 0.05
Solution
Given:
Length of the beam,
Uniform curvature, For a simply supported beam with a uniform curvature , the deflection curve can be found by integrating the curvature equation:Integrating once with respect to :At mid-span (), the slope is zero due to symmetry:So, Integrating again:At the supports (), the deflection is zero ():Thus, the deflection equation is:The maximum deflection occurs at mid-span ():Substituting the given values:Therefore, the maximum deflection at mid-span is .
Length of the beam,
Uniform curvature, For a simply supported beam with a uniform curvature , the deflection curve can be found by integrating the curvature equation:Integrating once with respect to :At mid-span (), the slope is zero due to symmetry:So, Integrating again:At the supports (), the deflection is zero ():Thus, the deflection equation is:The maximum deflection occurs at mid-span ():Substituting the given values:Therefore, the maximum deflection at mid-span is .
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