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A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2 of steel in tension and 628 mm2 of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.
Q.The moment of resistance of the section is
- a)206 kNm
- b)209.20 kNm
- c)236.80 kNm
- d)251.90 kNm
Correct answer is option 'B'. Can you explain this answer?
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To calculate the moment of resistance of the doubly reinforced rectangular concrete beam, we need to consider the following steps:
1. Determine the stress in the tension steel:
The stress in the tension steel can be calculated using the formula:
Stress in tension steel = (Tension force in steel) / (Area of tension steel)
Given that the area of tension steel is 2200 mm2 and the steel used is Fe250, which has a yield strength of 250 MPa, we can calculate the tension force in steel as:
Tension force in steel = (Area of tension steel) x (Yield strength of steel)
Substituting the values, we get:
Tension force in steel = 2200 mm2 x 250 MPa = 550000 N
Therefore, the stress in the tension steel is:
Stress in tension steel = 550000 N / 2200 mm2 = 250 MPa
2. Determine the stress in the compression steel:
The stress in the compression steel can be calculated using the formula:
Stress in compression steel = (Compression force in steel) / (Area of compression steel)
Given that the area of compression steel is 628 mm2 and the steel used is Fe250, which has a yield strength of 250 MPa, we can calculate the compression force in steel as:
Compression force in steel = (Area of compression steel) x (Yield strength of steel)
Substituting the values, we get:
Compression force in steel = 628 mm2 x 250 MPa = 157000 N
Therefore, the stress in the compression steel is:
Stress in compression steel = 157000 N / 628 mm2 = 250 MPa
3. Determine the stress block parameters:
As per IS: 456-2000, the stress block parameters for M20 grade concrete are:
- Depth of the stress block (a) = 0.48 x effective depth = 0.48 x 500 mm = 240 mm
- Lever arm (z) = 0.87 x effective depth = 0.87 x 500 mm = 435 mm
4. Determine the moment of resistance:
The moment of resistance (MR) can be calculated using the formula:
MR = (Area of tension steel) x (Stress in tension steel) x (Lever arm for tension steel) + (Area of compression steel) x (Stress in compression steel) x (Lever arm for compression steel)
Given that the effective cover for compression steel is 50 mm, the lever arm for compression steel is:
Lever arm for compression steel = effective depth - cover - (0.5 x diameter of compression steel)
Substituting the values, we get:
Lever arm for compression steel = 500 mm - 50 mm - (0.5 x √628) mm = 452.80 mm
Substituting the values into the formula, we get:
MR = (2200 mm2) x (250 MPa) x (435 mm) + (628 mm2) x (250 MPa) x (452.80 mm)
MR = 209.20 kNm
Therefore, the moment of resistance of the doubly reinforced rectangular concrete beam is 209.20 kNm, which corresponds to option (b).
1. Determine the stress in the tension steel:
The stress in the tension steel can be calculated using the formula:
Stress in tension steel = (Tension force in steel) / (Area of tension steel)
Given that the area of tension steel is 2200 mm2 and the steel used is Fe250, which has a yield strength of 250 MPa, we can calculate the tension force in steel as:
Tension force in steel = (Area of tension steel) x (Yield strength of steel)
Substituting the values, we get:
Tension force in steel = 2200 mm2 x 250 MPa = 550000 N
Therefore, the stress in the tension steel is:
Stress in tension steel = 550000 N / 2200 mm2 = 250 MPa
2. Determine the stress in the compression steel:
The stress in the compression steel can be calculated using the formula:
Stress in compression steel = (Compression force in steel) / (Area of compression steel)
Given that the area of compression steel is 628 mm2 and the steel used is Fe250, which has a yield strength of 250 MPa, we can calculate the compression force in steel as:
Compression force in steel = (Area of compression steel) x (Yield strength of steel)
Substituting the values, we get:
Compression force in steel = 628 mm2 x 250 MPa = 157000 N
Therefore, the stress in the compression steel is:
Stress in compression steel = 157000 N / 628 mm2 = 250 MPa
3. Determine the stress block parameters:
As per IS: 456-2000, the stress block parameters for M20 grade concrete are:
- Depth of the stress block (a) = 0.48 x effective depth = 0.48 x 500 mm = 240 mm
- Lever arm (z) = 0.87 x effective depth = 0.87 x 500 mm = 435 mm
4. Determine the moment of resistance:
The moment of resistance (MR) can be calculated using the formula:
MR = (Area of tension steel) x (Stress in tension steel) x (Lever arm for tension steel) + (Area of compression steel) x (Stress in compression steel) x (Lever arm for compression steel)
Given that the effective cover for compression steel is 50 mm, the lever arm for compression steel is:
Lever arm for compression steel = effective depth - cover - (0.5 x diameter of compression steel)
Substituting the values, we get:
Lever arm for compression steel = 500 mm - 50 mm - (0.5 x √628) mm = 452.80 mm
Substituting the values into the formula, we get:
MR = (2200 mm2) x (250 MPa) x (435 mm) + (628 mm2) x (250 MPa) x (452.80 mm)
MR = 209.20 kNm
Therefore, the moment of resistance of the doubly reinforced rectangular concrete beam is 209.20 kNm, which corresponds to option (b).
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A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer?
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A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer?.
A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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ample number of questions to practice A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm2of steel in tension and 628 mm2of steel in compression. The effective cover for compression steel is 50 mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250, respectively. The stress lock parameters (rounded off to first two decimal places) for concrete should be as per IS: 456-2000.Q.The moment of resistance of the section isa)206 kNmb)209.20 kNmc)236.80 kNmd)251.90 kNmCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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