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25. A circular arc of radius 6 m is made up from a steel plate by bending. The steel plate has width of 150 mm and a thickness of 20 mm. Determine the maximum stress induced and the bending moment. Consider Young’s modulus E = 205 GPa.?
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25. A circular arc of radius 6 m is made up from a steel plate by bend...
Introduction:
In this problem, we are given a circular arc made from a steel plate through bending. We need to determine the maximum stress induced and the bending moment in the arc. The dimensions of the steel plate are also provided, including its width and thickness, as well as the Young's modulus of the steel material.
Given data:
- Radius of the circular arc (r) = 6 m
- Width of the steel plate (b) = 150 mm = 0.15 m
- Thickness of the steel plate (h) = 20 mm = 0.02 m
- Young's modulus of steel (E) = 205 GPa = 205 x 10^9 Pa
Calculating the bending moment:
The bending moment (M) can be calculated using the formula:
M = σ × S
Where:
- σ is the maximum stress induced in the steel plate
- S is the section modulus of the steel plate
Calculating the section modulus:
The section modulus (S) can be calculated using the formula:
S = (b × h^2) / 6
Calculating the maximum stress induced:
The maximum stress induced (σ) can be calculated using the formula:
σ = (M × c) / S
Where:
- c is the distance from the neutral axis to the outermost fiber of the steel plate
Calculating the distance from the neutral axis:
The distance from the neutral axis (c) can be calculated using the formula:
c = r - (h/2)
Substituting the values and calculating the results:
- Substituting the values of b and h, we get S = (0.15 × 0.02^2) / 6 = 0.0002 m^3
- Substituting the values of r and h, we get c = 6 - (0.02/2) = 5.99 m
- Substituting the values of M, c, and S, we get σ = (M × 5.99) / 0.0002
Results:
The maximum stress induced (σ) and the bending moment (M) in the steel arc are calculated using the given formulas and the provided values. The values of σ and M can be obtained by substituting the values of S, c, and M in the respective formulas.
In this problem, we are given a circular arc made from a steel plate through bending. We need to determine the maximum stress induced and the bending moment in the arc. The dimensions of the steel plate are also provided, including its width and thickness, as well as the Young's modulus of the steel material.
Given data:
- Radius of the circular arc (r) = 6 m
- Width of the steel plate (b) = 150 mm = 0.15 m
- Thickness of the steel plate (h) = 20 mm = 0.02 m
- Young's modulus of steel (E) = 205 GPa = 205 x 10^9 Pa
Calculating the bending moment:
The bending moment (M) can be calculated using the formula:
M = σ × S
Where:
- σ is the maximum stress induced in the steel plate
- S is the section modulus of the steel plate
Calculating the section modulus:
The section modulus (S) can be calculated using the formula:
S = (b × h^2) / 6
Calculating the maximum stress induced:
The maximum stress induced (σ) can be calculated using the formula:
σ = (M × c) / S
Where:
- c is the distance from the neutral axis to the outermost fiber of the steel plate
Calculating the distance from the neutral axis:
The distance from the neutral axis (c) can be calculated using the formula:
c = r - (h/2)
Substituting the values and calculating the results:
- Substituting the values of b and h, we get S = (0.15 × 0.02^2) / 6 = 0.0002 m^3
- Substituting the values of r and h, we get c = 6 - (0.02/2) = 5.99 m
- Substituting the values of M, c, and S, we get σ = (M × 5.99) / 0.0002
Results:
The maximum stress induced (σ) and the bending moment (M) in the steel arc are calculated using the given formulas and the provided values. The values of σ and M can be obtained by substituting the values of S, c, and M in the respective formulas.
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25. A circular arc of radius 6 m is made up from a steel plate by bending. The steel plate has width of 150 mm and a thickness of 20 mm. Determine the maximum stress induced and the bending moment. Consider Young’s modulus E = 205 GPa.?
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25. A circular arc of radius 6 m is made up from a steel plate by bending. The steel plate has width of 150 mm and a thickness of 20 mm. Determine the maximum stress induced and the bending moment. Consider Young’s modulus E = 205 GPa.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 25. A circular arc of radius 6 m is made up from a steel plate by bending. The steel plate has width of 150 mm and a thickness of 20 mm. Determine the maximum stress induced and the bending moment. Consider Young’s modulus E = 205 GPa.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 25. A circular arc of radius 6 m is made up from a steel plate by bending. The steel plate has width of 150 mm and a thickness of 20 mm. Determine the maximum stress induced and the bending moment. Consider Young’s modulus E = 205 GPa.?.
25. A circular arc of radius 6 m is made up from a steel plate by bending. The steel plate has width of 150 mm and a thickness of 20 mm. Determine the maximum stress induced and the bending moment. Consider Young’s modulus E = 205 GPa.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 25. A circular arc of radius 6 m is made up from a steel plate by bending. The steel plate has width of 150 mm and a thickness of 20 mm. Determine the maximum stress induced and the bending moment. Consider Young’s modulus E = 205 GPa.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 25. A circular arc of radius 6 m is made up from a steel plate by bending. The steel plate has width of 150 mm and a thickness of 20 mm. Determine the maximum stress induced and the bending moment. Consider Young’s modulus E = 205 GPa.?.
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