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Determine ultimate moment of resistance of a beam section of size (250×500)mm take effective cover of 50mm grade of concrete M20 and that of steel is fe 415 use LSM?
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Determine ultimate moment of resistance of a beam section of size (250...
Beam Section Details
- Beam Size: 250 mm x 500 mm
- Effective Cover: 50 mm
- Concrete Grade: M20 (fck = 20 MPa)
- Steel Grade: Fe 415 (fy = 415 MPa)
Effective Depth Calculation
- Overall Depth (D): 500 mm
- Effective Depth (d) = D - Effective Cover - (Diameter of Steel Bar / 2)
- Assuming 20 mm diameter bars, d = 500 mm - 50 mm - 10 mm = 440 mm
Area of Steel Required (Ast)
- Design Moment (Mu) can be computed using the formula: Mu = 0.138 fck b d²
- Where:
- fck = 20 MPa
- b = 250 mm
- d = 440 mm
Substituting values:
- Mu = 0.138 x 20 x 250 x 440² = 1.907 x 10^6 Nmm or 1.907 kNm
Calculate Area of Steel (Ast)
- Using the formula: Ast = Mu / (0.87 fy d)
- Ast = 1.907 x 10^6 / (0.87 x 415 x 440)
- Ast = 1,036.53 mm²
Number of Bars Required
- If using 20 mm diameter bars:
- Area of one 20 mm bar = π/4 x (20)² = 314 mm²
- Number of bars = Ast / Area of one bar = 1036.53 / 314 ≈ 3.30, round up to 4 bars.
Ultimate Moment of Resistance
- Moment of Resistance (Mu) = 0.138 fck b d²
- With the calculated Ast, the ultimate moment of resistance for the beam section is approximately 1.907 kNm.
This approach ensures the beam section is adequately reinforced according to the Limit State Method (LSM), providing safety and serviceability for the structure.
- Beam Size: 250 mm x 500 mm
- Effective Cover: 50 mm
- Concrete Grade: M20 (fck = 20 MPa)
- Steel Grade: Fe 415 (fy = 415 MPa)
Effective Depth Calculation
- Overall Depth (D): 500 mm
- Effective Depth (d) = D - Effective Cover - (Diameter of Steel Bar / 2)
- Assuming 20 mm diameter bars, d = 500 mm - 50 mm - 10 mm = 440 mm
Area of Steel Required (Ast)
- Design Moment (Mu) can be computed using the formula: Mu = 0.138 fck b d²
- Where:
- fck = 20 MPa
- b = 250 mm
- d = 440 mm
Substituting values:
- Mu = 0.138 x 20 x 250 x 440² = 1.907 x 10^6 Nmm or 1.907 kNm
Calculate Area of Steel (Ast)
- Using the formula: Ast = Mu / (0.87 fy d)
- Ast = 1.907 x 10^6 / (0.87 x 415 x 440)
- Ast = 1,036.53 mm²
Number of Bars Required
- If using 20 mm diameter bars:
- Area of one 20 mm bar = π/4 x (20)² = 314 mm²
- Number of bars = Ast / Area of one bar = 1036.53 / 314 ≈ 3.30, round up to 4 bars.
Ultimate Moment of Resistance
- Moment of Resistance (Mu) = 0.138 fck b d²
- With the calculated Ast, the ultimate moment of resistance for the beam section is approximately 1.907 kNm.
This approach ensures the beam section is adequately reinforced according to the Limit State Method (LSM), providing safety and serviceability for the structure.
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Determine ultimate moment of resistance of a beam section of size (250×500)mm take effective cover of 50mm grade of concrete M20 and that of steel is fe 415 use LSM?
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Determine ultimate moment of resistance of a beam section of size (250×500)mm take effective cover of 50mm grade of concrete M20 and that of steel is fe 415 use LSM? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Determine ultimate moment of resistance of a beam section of size (250×500)mm take effective cover of 50mm grade of concrete M20 and that of steel is fe 415 use LSM? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine ultimate moment of resistance of a beam section of size (250×500)mm take effective cover of 50mm grade of concrete M20 and that of steel is fe 415 use LSM?.
Determine ultimate moment of resistance of a beam section of size (250×500)mm take effective cover of 50mm grade of concrete M20 and that of steel is fe 415 use LSM? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Determine ultimate moment of resistance of a beam section of size (250×500)mm take effective cover of 50mm grade of concrete M20 and that of steel is fe 415 use LSM? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine ultimate moment of resistance of a beam section of size (250×500)mm take effective cover of 50mm grade of concrete M20 and that of steel is fe 415 use LSM?.
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