GATE CE 2025 Set 1 — Question 52
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Structural Engineering → RC Fundamentals & Beams → Working Stress Method
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Question
Consider a reinforced concrete beam section of 300 mm width and 700 mm depth. The beam is reinforced with the tension steel of 2000 mm area at an effective cover of 50 mm. Concrete in the tension zone is assumed to be cracked. Assume the modular ratio of 12 and Young’s modulus of 200 GPa for steel. When the extreme fibre in the compression zone undergoes the strain of 0.0004 due to the applied bending moment, the stress in the steel (in MPa) is ______________ (rounded off to the nearest integer).
Correct answer
125 to 127
Solution
1.Given Data:
- Width () = 300 mm
- Overall depth () = 700 mm
- Effective cover = 50 mm
- Effective depth () = mm
- Area of tension steel () = 2000 mm
- Modular ratio () = 12
- Young's modulus of steel () = 200 GPa = MPa
- Strain in extreme compression fiber () = 0.0004
For a cracked section, the moment of area of the compression zone about the neutral axis equals the modular ratio times the moment of area of the tension steel about the neutral axis:
Solving the quadratic equation:
3.Determine the strain in steel ():
Using the linear strain distribution across the section:4.Calculate the stress in steel ():
Rounding to the nearest integer, the stress in the steel is 126 MPa.Continue learning with Success Tracker
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