GATE CE 2018 Set 2 — Question 48
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Structural Engineering → Stress, Strain & Beams → Flexural Stresses
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Question
An 8 m long simply-supported elastic beam of rectangular cross-section (100 mm 200 mm) is subjected to a uniformly distributed load of 10 kN/m over its entire span. The maximum principal stress (in MPa, up to two decimal places) at a point located at the extreme compression edge of a cross-section and at 2 m from the support is ______
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Solution
1.Calculate Bending Moment at 2 m from support:
For a simply supported beam with UDL kN/m and span m, the reaction at each support is kN.Bending moment at m: kNm.
2.Calculate Bending Stress at extreme compression edge:
Cross-section: mm, mm.Moment of Inertia mm.
Distance to extreme edge mm.
Bending stress MPa.
Since it's the compression edge, MPa.
3.Calculate Principal Stresses:
At the extreme edge, shear stress .The principal stresses are .
With MPa, , and , the principal stresses are and MPa.
The maximum principal stress (algebraically) is MPa.
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