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Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0 Stress 167 f 14 14. 000200035 strain A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M20. The depth of the neutral axis from the compression fibre is (a) 76 mm (6) 81 mm (c) 87 mm (d) 100 mm?
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Assume straight line instead of parabola for stress-strain curve of co...
Introduction:
To calculate the depth of the neutral axis of a rectangular under-reinforced concrete section, we need to consider the stress-strain curve of concrete, the partial factor of safety, and the dimensions and reinforcement details of the section.
Given:
- Width of the section (b): 300 mm
- Effective depth of the section (d): 500 mm
- Grade of reinforcement bars: Fe-415
- Diameter of reinforcement bars (D): 16 mm
- Concrete mix: M20
- Partial factor of safety: 1.0
Calculating the area of steel reinforcement:
The area of steel reinforcement can be calculated using the formula:
A_s = (π/4) * D^2 * n
where A_s is the area of steel reinforcement, D is the diameter of the reinforcement bars, and n is the number of reinforcement bars.
In this case, the area of steel reinforcement is:
A_s = (π/4) * (16 mm)^2 * 3 = 603.19 mm^2
Calculating the area of concrete:
The area of concrete can be calculated using the formula:
A_c = b * d - A_s
where A_c is the area of concrete, b is the width of the section, d is the effective depth of the section, and A_s is the area of steel reinforcement.
In this case, the area of concrete is:
A_c = (300 mm) * (500 mm) - 603.19 mm^2 = 149396.81 mm^2
Calculating the stress in concrete:
The stress in concrete can be calculated using the formula:
σ_c = f_c / γ_m
where σ_c is the stress in concrete, f_c is the characteristic compressive strength of concrete, and γ_m is the partial factor of safety.
In this case, the stress in concrete is:
σ_c = 16.7 MPa / 1.0 = 16.7 MPa
Calculating the strain in concrete:
Since we are assuming a straight line stress-strain curve for concrete, the strain can be calculated using the formula:
ε_c = σ_c / E_c
where ε_c is the strain in concrete and E_c is the modulus of elasticity of concrete.
The strain in concrete for a straight line curve can be calculated using the formula:
ε_c = (σ_c / f_cm) * (2 + 3 * (σ_c / f_cm)) / 2
In this case, the strain in concrete is:
ε_c = (16.7 MPa / 20 MPa) * (2 + 3 * (16.7 MPa / 20 MPa)) / 2 = 0.8385
Calculating the depth of the neutral axis:
The depth of the neutral axis can be calculated using the formula:
d_n = d * (1 - (ε_c / ε_cu))
where d_n is the depth of the neutral axis, d is the effective depth of the section, ε_c is the strain in concrete, and ε_cu is the ultimate compressive strain of concrete.
In this case, the ultimate compressive strain of concrete can be taken as 0.0035.
Calculating the depth of the neutral axis:
To calculate the depth of the neutral axis of a rectangular under-reinforced concrete section, we need to consider the stress-strain curve of concrete, the partial factor of safety, and the dimensions and reinforcement details of the section.
Given:
- Width of the section (b): 300 mm
- Effective depth of the section (d): 500 mm
- Grade of reinforcement bars: Fe-415
- Diameter of reinforcement bars (D): 16 mm
- Concrete mix: M20
- Partial factor of safety: 1.0
Calculating the area of steel reinforcement:
The area of steel reinforcement can be calculated using the formula:
A_s = (π/4) * D^2 * n
where A_s is the area of steel reinforcement, D is the diameter of the reinforcement bars, and n is the number of reinforcement bars.
In this case, the area of steel reinforcement is:
A_s = (π/4) * (16 mm)^2 * 3 = 603.19 mm^2
Calculating the area of concrete:
The area of concrete can be calculated using the formula:
A_c = b * d - A_s
where A_c is the area of concrete, b is the width of the section, d is the effective depth of the section, and A_s is the area of steel reinforcement.
In this case, the area of concrete is:
A_c = (300 mm) * (500 mm) - 603.19 mm^2 = 149396.81 mm^2
Calculating the stress in concrete:
The stress in concrete can be calculated using the formula:
σ_c = f_c / γ_m
where σ_c is the stress in concrete, f_c is the characteristic compressive strength of concrete, and γ_m is the partial factor of safety.
In this case, the stress in concrete is:
σ_c = 16.7 MPa / 1.0 = 16.7 MPa
Calculating the strain in concrete:
Since we are assuming a straight line stress-strain curve for concrete, the strain can be calculated using the formula:
ε_c = σ_c / E_c
where ε_c is the strain in concrete and E_c is the modulus of elasticity of concrete.
The strain in concrete for a straight line curve can be calculated using the formula:
ε_c = (σ_c / f_cm) * (2 + 3 * (σ_c / f_cm)) / 2
In this case, the strain in concrete is:
ε_c = (16.7 MPa / 20 MPa) * (2 + 3 * (16.7 MPa / 20 MPa)) / 2 = 0.8385
Calculating the depth of the neutral axis:
The depth of the neutral axis can be calculated using the formula:
d_n = d * (1 - (ε_c / ε_cu))
where d_n is the depth of the neutral axis, d is the effective depth of the section, ε_c is the strain in concrete, and ε_cu is the ultimate compressive strain of concrete.
In this case, the ultimate compressive strain of concrete can be taken as 0.0035.
Calculating the depth of the neutral axis:
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Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0 Stress 167 f 14 14. 000200035 strain A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M20. The depth of the neutral axis from the compression fibre is (a) 76 mm (6) 81 mm (c) 87 mm (d) 100 mm?
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Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0 Stress 167 f 14 14. 000200035 strain A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M20. The depth of the neutral axis from the compression fibre is (a) 76 mm (6) 81 mm (c) 87 mm (d) 100 mm? 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 Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0 Stress 167 f 14 14. 000200035 strain A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M20. The depth of the neutral axis from the compression fibre is (a) 76 mm (6) 81 mm (c) 87 mm (d) 100 mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0 Stress 167 f 14 14. 000200035 strain A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M20. The depth of the neutral axis from the compression fibre is (a) 76 mm (6) 81 mm (c) 87 mm (d) 100 mm?.
Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0 Stress 167 f 14 14. 000200035 strain A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M20. The depth of the neutral axis from the compression fibre is (a) 76 mm (6) 81 mm (c) 87 mm (d) 100 mm? 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 Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0 Stress 167 f 14 14. 000200035 strain A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M20. The depth of the neutral axis from the compression fibre is (a) 76 mm (6) 81 mm (c) 87 mm (d) 100 mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0 Stress 167 f 14 14. 000200035 strain A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter. Concrete mix is M20. The depth of the neutral axis from the compression fibre is (a) 76 mm (6) 81 mm (c) 87 mm (d) 100 mm?.
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