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A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16mm dia in tension and 4 bars of 12mm in compression The effective cover to both tension and compression steel are 50mm each calculate moment of resistance using WSM Grade of concrete and steel are m20 and fe 415 respectively?
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A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16...
Beam Dimensions and Reinforcement
- Size: 250 mm (width) x 500 mm (depth)
- Effective cover: 50 mm for both tension and compression steel
- Tension reinforcement: 4 bars of 16 mm diameter
- Compression reinforcement: 4 bars of 12 mm diameter
Effective Depth Calculation
- Effective depth (d) = Total Depth - Effective Cover = 500 mm - 50 mm = 450 mm
Area of Steel Reinforcement
- Area of tension steel (Ast_tension) = 4 × (π/4) × (16 mm)^2 = 201.06 mm²
- Area of compression steel (Ast_compression) = 4 × (π/4) × (12 mm)^2 = 113.10 mm²
Moment of Resistance Calculation
- Design strength of concrete (fck) = 20 MPa
- Design strength of steel (fy) = 415 MPa
- Calculate the lever arm (z):
z = d - (Ast_tension × fy) / (0.87 × fck × b)
- Lever arm approximation:
z ≈ 0.95 × d = 0.95 × 450 mm = 427.5 mm
- Factored Moment of Resistance (Mu):
Mu = 0.138 × fck × b × d²
- Substitute values:
Mu = 0.138 × 20 × 250 × (450)²
Final Calculation
- Mu = 0.138 × 20 × 250 × 202500
- Mu = 0.138 × 20 × 250 × 202500 / 10^6 (to convert to kNm)
- Mu = 138 kNm approx.
Conclusion
The moment of resistance of the given rectangular beam is approximately 138 kNm. This calculation ensures that the beam is adequately designed to resist the applied moments using the Working Stress Method (WSM). Always verify with local codes and standards for precise designs.
- Size: 250 mm (width) x 500 mm (depth)
- Effective cover: 50 mm for both tension and compression steel
- Tension reinforcement: 4 bars of 16 mm diameter
- Compression reinforcement: 4 bars of 12 mm diameter
Effective Depth Calculation
- Effective depth (d) = Total Depth - Effective Cover = 500 mm - 50 mm = 450 mm
Area of Steel Reinforcement
- Area of tension steel (Ast_tension) = 4 × (π/4) × (16 mm)^2 = 201.06 mm²
- Area of compression steel (Ast_compression) = 4 × (π/4) × (12 mm)^2 = 113.10 mm²
Moment of Resistance Calculation
- Design strength of concrete (fck) = 20 MPa
- Design strength of steel (fy) = 415 MPa
- Calculate the lever arm (z):
z = d - (Ast_tension × fy) / (0.87 × fck × b)
- Lever arm approximation:
z ≈ 0.95 × d = 0.95 × 450 mm = 427.5 mm
- Factored Moment of Resistance (Mu):
Mu = 0.138 × fck × b × d²
- Substitute values:
Mu = 0.138 × 20 × 250 × (450)²
Final Calculation
- Mu = 0.138 × 20 × 250 × 202500
- Mu = 0.138 × 20 × 250 × 202500 / 10^6 (to convert to kNm)
- Mu = 138 kNm approx.
Conclusion
The moment of resistance of the given rectangular beam is approximately 138 kNm. This calculation ensures that the beam is adequately designed to resist the applied moments using the Working Stress Method (WSM). Always verify with local codes and standards for precise designs.
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A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16mm dia in tension and 4 bars of 12mm in compression The effective cover to both tension and compression steel are 50mm each calculate moment of resistance using WSM Grade of concrete and steel are m20 and fe 415 respectively?
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A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16mm dia in tension and 4 bars of 12mm in compression The effective cover to both tension and compression steel are 50mm each calculate moment of resistance using WSM Grade of concrete and steel are m20 and fe 415 respectively? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16mm dia in tension and 4 bars of 12mm in compression The effective cover to both tension and compression steel are 50mm each calculate moment of resistance using WSM Grade of concrete and steel are m20 and fe 415 respectively? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16mm dia in tension and 4 bars of 12mm in compression The effective cover to both tension and compression steel are 50mm each calculate moment of resistance using WSM Grade of concrete and steel are m20 and fe 415 respectively?.
A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16mm dia in tension and 4 bars of 12mm in compression The effective cover to both tension and compression steel are 50mm each calculate moment of resistance using WSM Grade of concrete and steel are m20 and fe 415 respectively? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16mm dia in tension and 4 bars of 12mm in compression The effective cover to both tension and compression steel are 50mm each calculate moment of resistance using WSM Grade of concrete and steel are m20 and fe 415 respectively? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular beam of size (250×500)mm is reinforced with 4 bars of 16mm dia in tension and 4 bars of 12mm in compression The effective cover to both tension and compression steel are 50mm each calculate moment of resistance using WSM Grade of concrete and steel are m20 and fe 415 respectively?.
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