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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 depth of the neutral axis is
- a)205.30 mm
- b)184.56 mm
- c)160.91 mm
- d)145.30 mm
Correct answer is option 'C'. Can you explain this answer?
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Solution:
Given data:
Width of the rectangular beam (b) = 300 mm
Effective depth of the beam (d) = 500 mm
Area of tension steel (Ast) = 2200 mm²
Area of compression steel (Asc) = 628 mm²
Effective cover for compression steel (d’) = 50 mm
Grade of concrete (fck) = M20
Grade of steel (fy) = Fe250
Assume both tension and compression steel yield.
Let's calculate the depth of the neutral axis of the beam.
Step 1: Calculation of modular ratio (m)
m = (280/fck)^(1/2)
m = (280/20)^(1/2)
m = 5.2915
Step 2: Calculation of compression steel ratio (ρc)
ρc = (Asc/bd)
ρc = (628/(300 × 500))
ρc = 0.00419
Step 3: Calculation of maximum compression strain (εcbc)
εcbc = (0.0035 + 0.45(ρc))/m
εcbc = (0.0035 + 0.45(0.00419))/5.2915
εcbc = 0.00187
Step 4: Calculation of depth of neutral axis (x)
x = (0.87fyAst + 0.36fckbdεcbc)/(0.87fyAst +fckbdεcbc)
x = (0.87 × 250 × 2200 + 0.36 × 20 × 300 × 500 × 0.00187)/(0.87 × 250 × 2200 + 20 × 300 × 500 × 0.00187)
x = 160.91 mm
Therefore, the depth of the neutral axis of the beam is 160.91 mm.
Hence, option (C) is the correct answer.
Given data:
Width of the rectangular beam (b) = 300 mm
Effective depth of the beam (d) = 500 mm
Area of tension steel (Ast) = 2200 mm²
Area of compression steel (Asc) = 628 mm²
Effective cover for compression steel (d’) = 50 mm
Grade of concrete (fck) = M20
Grade of steel (fy) = Fe250
Assume both tension and compression steel yield.
Let's calculate the depth of the neutral axis of the beam.
Step 1: Calculation of modular ratio (m)
m = (280/fck)^(1/2)
m = (280/20)^(1/2)
m = 5.2915
Step 2: Calculation of compression steel ratio (ρc)
ρc = (Asc/bd)
ρc = (628/(300 × 500))
ρc = 0.00419
Step 3: Calculation of maximum compression strain (εcbc)
εcbc = (0.0035 + 0.45(ρc))/m
εcbc = (0.0035 + 0.45(0.00419))/5.2915
εcbc = 0.00187
Step 4: Calculation of depth of neutral axis (x)
x = (0.87fyAst + 0.36fckbdεcbc)/(0.87fyAst +fckbdεcbc)
x = (0.87 × 250 × 2200 + 0.36 × 20 × 300 × 500 × 0.00187)/(0.87 × 250 × 2200 + 20 × 300 × 500 × 0.00187)
x = 160.91 mm
Therefore, the depth of the neutral axis of the beam is 160.91 mm.
Hence, option (C) is the correct 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution 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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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 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 depth of the neutral axis isa)205.30 mmb)184.56 mmc)160.91 mmd)145.30 mmCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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