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A doubly reinforced concrete beam with an effective cover of 50 mm to center of both tension and compression reinforcement with an effective depth of 550 mm. If the maximum permissible stress in the outermost fibres in both steel and concrete reaches at the same time, what will be the maximum strain in concrete at the level of compression reinforcement satisfying codal provisions of IS 456:2000 according to limit state method.
Take Fe 500 grade of steel for both tension and compression reinforcement and M 20 grade of concrete.
- a)0.00350
- b)0.00289
- c)0.00284
- d)0.00281
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A doubly reinforced concrete beam with an effective cover of 50 mm to ...
As the maximum permissible stress in the outermost fibers in both steel and concrete reaches at the same time, therefore it is the case of balanced section:
So,
Xu = Xulim
For Fe 500
Xulim = 0.46 d
d = effective depth of the beam = 550 mm
Xulim = 0.46 × 550 = 253 mm
d' = effective cover to compression reinforcement = 50 mm
Maximum strain in concrete at outermost compression reinforcement as per IS 456:2000 = 0.0035
Now from similar triangle,
ϵsc = 0.00281
ϵsc = 0.00281
Most Upvoted Answer
A doubly reinforced concrete beam with an effective cover of 50 mm to ...
To determine the maximum strain in concrete at the level of compression reinforcement, we need to consider the stress-strain relationship for both steel and concrete.
Given data:
Effective cover (d) = 50 mm
Effective depth (D) = 550 mm
Grade of concrete (M) = M20
Grade of steel (Fe) = Fe 500
1. Calculation of lever arm:
The lever arm (a) is the distance from the centroid of the compression reinforcement to the extreme compression fiber. It can be calculated using the formula:
a = 0.5 * D - c
Where c is the effective cover.
a = 0.5 * 550 - 50
a = 275 - 50
a = 225 mm
2. Calculation of maximum stress in concrete:
The maximum stress in concrete (σ_c) can be calculated using the formula:
σ_c = 0.87 * f_ck / γ_c
Where f_ck is the characteristic compressive strength of concrete and γ_c is the partial safety factor for concrete.
For M20 grade concrete, f_ck = 20 MPa (from IS 456:2000)
For normal weight concrete, γ_c = 1.5 (from IS 456:2000)
σ_c = 0.87 * 20 / 1.5
σ_c = 11.6 MPa
3. Calculation of maximum stress in steel:
The maximum stress in steel (σ_s) can be calculated using the formula:
σ_s = f_y / γ_s
Where f_y is the characteristic yield strength of steel and γ_s is the partial safety factor for steel.
For Fe 500 grade steel, f_y = 500 MPa (from IS 456:2000)
For high yield strength deformed bars, γ_s = 1.15 (from IS 456:2000)
σ_s = 500 / 1.15
σ_s = 434.78 MPa
4. Calculation of maximum strain in concrete:
The maximum strain in concrete (ε_c) can be calculated using the formula:
ε_c = (σ_c / E_c)
Where E_c is the modulus of elasticity of concrete.
For M20 grade concrete, E_c = 5000 √f_ck (from IS 456:2000)
E_c = 5000 √20
E_c = 5000 * 4.47
E_c = 22,350 MPa
ε_c = (11.6 / 22,350)
ε_c = 0.000518
The maximum strain in concrete at the level of compression reinforcement is 0.000518, which is equivalent to 0.00281 in percentage.
Therefore, the correct answer is option D) 0.00281.
Given data:
Effective cover (d) = 50 mm
Effective depth (D) = 550 mm
Grade of concrete (M) = M20
Grade of steel (Fe) = Fe 500
1. Calculation of lever arm:
The lever arm (a) is the distance from the centroid of the compression reinforcement to the extreme compression fiber. It can be calculated using the formula:
a = 0.5 * D - c
Where c is the effective cover.
a = 0.5 * 550 - 50
a = 275 - 50
a = 225 mm
2. Calculation of maximum stress in concrete:
The maximum stress in concrete (σ_c) can be calculated using the formula:
σ_c = 0.87 * f_ck / γ_c
Where f_ck is the characteristic compressive strength of concrete and γ_c is the partial safety factor for concrete.
For M20 grade concrete, f_ck = 20 MPa (from IS 456:2000)
For normal weight concrete, γ_c = 1.5 (from IS 456:2000)
σ_c = 0.87 * 20 / 1.5
σ_c = 11.6 MPa
3. Calculation of maximum stress in steel:
The maximum stress in steel (σ_s) can be calculated using the formula:
σ_s = f_y / γ_s
Where f_y is the characteristic yield strength of steel and γ_s is the partial safety factor for steel.
For Fe 500 grade steel, f_y = 500 MPa (from IS 456:2000)
For high yield strength deformed bars, γ_s = 1.15 (from IS 456:2000)
σ_s = 500 / 1.15
σ_s = 434.78 MPa
4. Calculation of maximum strain in concrete:
The maximum strain in concrete (ε_c) can be calculated using the formula:
ε_c = (σ_c / E_c)
Where E_c is the modulus of elasticity of concrete.
For M20 grade concrete, E_c = 5000 √f_ck (from IS 456:2000)
E_c = 5000 √20
E_c = 5000 * 4.47
E_c = 22,350 MPa
ε_c = (11.6 / 22,350)
ε_c = 0.000518
The maximum strain in concrete at the level of compression reinforcement is 0.000518, which is equivalent to 0.00281 in percentage.
Therefore, the correct answer is option D) 0.00281.
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A doubly reinforced concrete beam with an effective cover of 50 mm to center of both tension and compression reinforcement with an effective depth of 550 mm. If the maximum permissible stress in the outermost fibres in both steel and concrete reaches at the same time, what will be the maximum strain in concrete at the level of compression reinforcement satisfying codal provisions of IS 456:2000 according to limit state method.Take Fe 500 grade of steel for both tension and compression reinforcement and M 20 grade of concrete.a)0.00350b)0.00289c)0.00284d)0.00281Correct answer is option 'D'. Can you explain this answer?
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A doubly reinforced concrete beam with an effective cover of 50 mm to center of both tension and compression reinforcement with an effective depth of 550 mm. If the maximum permissible stress in the outermost fibres in both steel and concrete reaches at the same time, what will be the maximum strain in concrete at the level of compression reinforcement satisfying codal provisions of IS 456:2000 according to limit state method.Take Fe 500 grade of steel for both tension and compression reinforcement and M 20 grade of concrete.a)0.00350b)0.00289c)0.00284d)0.00281Correct answer is option 'D'. 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 concrete beam with an effective cover of 50 mm to center of both tension and compression reinforcement with an effective depth of 550 mm. If the maximum permissible stress in the outermost fibres in both steel and concrete reaches at the same time, what will be the maximum strain in concrete at the level of compression reinforcement satisfying codal provisions of IS 456:2000 according to limit state method.Take Fe 500 grade of steel for both tension and compression reinforcement and M 20 grade of concrete.a)0.00350b)0.00289c)0.00284d)0.00281Correct answer is option 'D'. 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 concrete beam with an effective cover of 50 mm to center of both tension and compression reinforcement with an effective depth of 550 mm. If the maximum permissible stress in the outermost fibres in both steel and concrete reaches at the same time, what will be the maximum strain in concrete at the level of compression reinforcement satisfying codal provisions of IS 456:2000 according to limit state method.Take Fe 500 grade of steel for both tension and compression reinforcement and M 20 grade of concrete.a)0.00350b)0.00289c)0.00284d)0.00281Correct answer is option 'D'. Can you explain this answer?.
A doubly reinforced concrete beam with an effective cover of 50 mm to center of both tension and compression reinforcement with an effective depth of 550 mm. If the maximum permissible stress in the outermost fibres in both steel and concrete reaches at the same time, what will be the maximum strain in concrete at the level of compression reinforcement satisfying codal provisions of IS 456:2000 according to limit state method.Take Fe 500 grade of steel for both tension and compression reinforcement and M 20 grade of concrete.a)0.00350b)0.00289c)0.00284d)0.00281Correct answer is option 'D'. 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 concrete beam with an effective cover of 50 mm to center of both tension and compression reinforcement with an effective depth of 550 mm. If the maximum permissible stress in the outermost fibres in both steel and concrete reaches at the same time, what will be the maximum strain in concrete at the level of compression reinforcement satisfying codal provisions of IS 456:2000 according to limit state method.Take Fe 500 grade of steel for both tension and compression reinforcement and M 20 grade of concrete.a)0.00350b)0.00289c)0.00284d)0.00281Correct answer is option 'D'. 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 concrete beam with an effective cover of 50 mm to center of both tension and compression reinforcement with an effective depth of 550 mm. If the maximum permissible stress in the outermost fibres in both steel and concrete reaches at the same time, what will be the maximum strain in concrete at the level of compression reinforcement satisfying codal provisions of IS 456:2000 according to limit state method.Take Fe 500 grade of steel for both tension and compression reinforcement and M 20 grade of concrete.a)0.00350b)0.00289c)0.00284d)0.00281Correct answer is option 'D'. Can you explain this answer?.
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