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The circumferential joint of a boiler of diameter 1 m is made of lap joint with rivet diameter of 20 mm. If the allowable shear stress for the material of the rivet is 50 MPa and the boiler has to withstand an internal pressure of 2.5 MPa, then the minimum number of rivets required to prevent the failure of the joint is
- a)150
- b)125
- c)100
- d)75
Correct answer is option 'B'. Can you explain this answer?
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Given data:
- Diameter of the boiler (D) = 1 m
- Diameter of the rivet (d) = 20 mm
- Allowable shear stress for the rivet material (τ) = 50 MPa
- Internal pressure of the boiler (P) = 2.5 MPa
To prevent the failure of the joint, we need to ensure that the shear stress on each rivet does not exceed the allowable shear stress.
- The circumferential length of the joint (C) can be calculated using the formula: C = πD
- The number of rivets required (N) can be calculated using the formula: N = C / (πd)
Let's calculate the values step by step:
1. Calculate the circumferential length of the joint:
- C = πD
- C = π * 1 m
- C = 3.14 m
2. Calculate the number of rivets required:
- N = C / (πd)
- N = 3.14 m / (π * 0.02 m)
- N = 157
The calculated number of rivets required is 157, which is not a whole number. Since we cannot have a fraction of a rivet, we need to round up to the nearest whole number.
Therefore, the minimum number of rivets required to prevent the failure of the joint is 157, which is closest to option 'B' (125).
Note: It's important to note that the calculation above assumes that each rivet shares an equal amount of the load. In practice, additional factors such as the distribution of load, safety factors, and the strength of the joint itself should be considered to determine the exact number of rivets required.
- Diameter of the boiler (D) = 1 m
- Diameter of the rivet (d) = 20 mm
- Allowable shear stress for the rivet material (τ) = 50 MPa
- Internal pressure of the boiler (P) = 2.5 MPa
To prevent the failure of the joint, we need to ensure that the shear stress on each rivet does not exceed the allowable shear stress.
- The circumferential length of the joint (C) can be calculated using the formula: C = πD
- The number of rivets required (N) can be calculated using the formula: N = C / (πd)
Let's calculate the values step by step:
1. Calculate the circumferential length of the joint:
- C = πD
- C = π * 1 m
- C = 3.14 m
2. Calculate the number of rivets required:
- N = C / (πd)
- N = 3.14 m / (π * 0.02 m)
- N = 157
The calculated number of rivets required is 157, which is not a whole number. Since we cannot have a fraction of a rivet, we need to round up to the nearest whole number.
Therefore, the minimum number of rivets required to prevent the failure of the joint is 157, which is closest to option 'B' (125).
Note: It's important to note that the calculation above assumes that each rivet shares an equal amount of the load. In practice, additional factors such as the distribution of load, safety factors, and the strength of the joint itself should be considered to determine the exact number of rivets required.
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The circumferential joint of a boiler of diameter 1 m is made of lap joint with rivet diameter of 20 mm. If the allowable shear stress for the material of the rivet is 50 MPa and the boiler has to withstand an internal pressure of 2.5 MPa, then the minimum number of rivets required to prevent the failure of the joint isa) 150b) 125c) 100d) 75Correct answer is option 'B'. Can you explain this answer?
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The circumferential joint of a boiler of diameter 1 m is made of lap joint with rivet diameter of 20 mm. If the allowable shear stress for the material of the rivet is 50 MPa and the boiler has to withstand an internal pressure of 2.5 MPa, then the minimum number of rivets required to prevent the failure of the joint isa) 150b) 125c) 100d) 75Correct answer is option 'B'. Can you explain this answer? 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 The circumferential joint of a boiler of diameter 1 m is made of lap joint with rivet diameter of 20 mm. If the allowable shear stress for the material of the rivet is 50 MPa and the boiler has to withstand an internal pressure of 2.5 MPa, then the minimum number of rivets required to prevent the failure of the joint isa) 150b) 125c) 100d) 75Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The circumferential joint of a boiler of diameter 1 m is made of lap joint with rivet diameter of 20 mm. If the allowable shear stress for the material of the rivet is 50 MPa and the boiler has to withstand an internal pressure of 2.5 MPa, then the minimum number of rivets required to prevent the failure of the joint isa) 150b) 125c) 100d) 75Correct answer is option 'B'. Can you explain this answer?.
The circumferential joint of a boiler of diameter 1 m is made of lap joint with rivet diameter of 20 mm. If the allowable shear stress for the material of the rivet is 50 MPa and the boiler has to withstand an internal pressure of 2.5 MPa, then the minimum number of rivets required to prevent the failure of the joint isa) 150b) 125c) 100d) 75Correct answer is option 'B'. Can you explain this answer? 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 The circumferential joint of a boiler of diameter 1 m is made of lap joint with rivet diameter of 20 mm. If the allowable shear stress for the material of the rivet is 50 MPa and the boiler has to withstand an internal pressure of 2.5 MPa, then the minimum number of rivets required to prevent the failure of the joint isa) 150b) 125c) 100d) 75Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The circumferential joint of a boiler of diameter 1 m is made of lap joint with rivet diameter of 20 mm. If the allowable shear stress for the material of the rivet is 50 MPa and the boiler has to withstand an internal pressure of 2.5 MPa, then the minimum number of rivets required to prevent the failure of the joint isa) 150b) 125c) 100d) 75Correct answer is option 'B'. Can you explain this answer?.
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