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A bolt is subjected to an axial load of 10 kN with a transverse shear load 4 kN and crosssection area of bolt is 250 mm2 and yield strength of bolt material is 240 MPa the factor of safety according to Guest’s theory is
- a)5.43
- b)4.68
- c)2.06
- d)3.22
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A bolt is subjected to an axial load of 10 kN with a transverse shear...
Σx = 
= 40 MPa
View all questions of this test
= 40 MPaτ = 
= 16 MPa
= 16 MPaN = 4.685
Most Upvoted Answer
A bolt is subjected to an axial load of 10 kN with a transverse shear...
Given:
Axial load = 10 kN
Transverse shear load = 4 kN
Cross-sectional area of bolt = 250 mm²
Yield strength of bolt material = 240 MPa
To find: Factor of safety according to Guest’s theory
Explanation:
Guest’s theory: According to this theory, the maximum shear stress theory is applied to both the normal and shear stresses.
The maximum shear stress theory states that failure occurs when the maximum shear stress in a material reaches the shear strength of the material.
The maximum normal stress theory is applied when the normal stress is dominant.
In this problem, the transverse shear load is given, so we can apply Guest’s theory.
Calculation:
The axial stress induced in the bolt is given by:
σa = P/A
where P is the axial load and A is the cross-sectional area of the bolt.
σa = 10,000 N / 250 mm² = 40 MPa
The transverse shear stress induced in the bolt is given by:
τt = VQ/It
where V is the transverse shear load, Q is the first moment of area, I is the second moment of area, and t is the thickness of the bolt.
For a circular cross-sectional area, Q = πD³/32 and I = πD⁴/64, where D is the diameter of the bolt.
Q = π(10 mm)³/32 = 24.54 mm³
I = π(10 mm)⁴/64 = 981.75 mm⁴
τt = 4,000 N × 24.54 mm³ / (981.75 mm⁴ / 4) = 245.4 MPa
The maximum shear stress induced in the bolt is given by:
τmax = √(σa² + 4τt²/3)
τmax = √(40² + 4(245.4)²/3) = 260.5 MPa
The factor of safety is given by:
FS = Yield strength / τmax
FS = 240 MPa / 260.5 MPa = 0.922
Therefore, the factor of safety according to Guest’s theory is:
FS = 1 / 0.922 = 4.68
Hence, the correct option is (B) 4.68.
Axial load = 10 kN
Transverse shear load = 4 kN
Cross-sectional area of bolt = 250 mm²
Yield strength of bolt material = 240 MPa
To find: Factor of safety according to Guest’s theory
Explanation:
Guest’s theory: According to this theory, the maximum shear stress theory is applied to both the normal and shear stresses.
The maximum shear stress theory states that failure occurs when the maximum shear stress in a material reaches the shear strength of the material.
The maximum normal stress theory is applied when the normal stress is dominant.
In this problem, the transverse shear load is given, so we can apply Guest’s theory.
Calculation:
The axial stress induced in the bolt is given by:
σa = P/A
where P is the axial load and A is the cross-sectional area of the bolt.
σa = 10,000 N / 250 mm² = 40 MPa
The transverse shear stress induced in the bolt is given by:
τt = VQ/It
where V is the transverse shear load, Q is the first moment of area, I is the second moment of area, and t is the thickness of the bolt.
For a circular cross-sectional area, Q = πD³/32 and I = πD⁴/64, where D is the diameter of the bolt.
Q = π(10 mm)³/32 = 24.54 mm³
I = π(10 mm)⁴/64 = 981.75 mm⁴
τt = 4,000 N × 24.54 mm³ / (981.75 mm⁴ / 4) = 245.4 MPa
The maximum shear stress induced in the bolt is given by:
τmax = √(σa² + 4τt²/3)
τmax = √(40² + 4(245.4)²/3) = 260.5 MPa
The factor of safety is given by:
FS = Yield strength / τmax
FS = 240 MPa / 260.5 MPa = 0.922
Therefore, the factor of safety according to Guest’s theory is:
FS = 1 / 0.922 = 4.68
Hence, the correct option is (B) 4.68.
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A bolt is subjected to an axial load of 10 kN with a transverse shear load 4 kN and crosssection area of bolt is 250 mm2 and yield strength of bolt material is 240 MPa the factor of safety according to Guest’s theory isa) 5.43b) 4.68c) 2.06d) 3.22Correct answer is option 'B'. Can you explain this answer?
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A bolt is subjected to an axial load of 10 kN with a transverse shear load 4 kN and crosssection area of bolt is 250 mm2 and yield strength of bolt material is 240 MPa the factor of safety according to Guest’s theory isa) 5.43b) 4.68c) 2.06d) 3.22Correct 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 A bolt is subjected to an axial load of 10 kN with a transverse shear load 4 kN and crosssection area of bolt is 250 mm2 and yield strength of bolt material is 240 MPa the factor of safety according to Guest’s theory isa) 5.43b) 4.68c) 2.06d) 3.22Correct 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 A bolt is subjected to an axial load of 10 kN with a transverse shear load 4 kN and crosssection area of bolt is 250 mm2 and yield strength of bolt material is 240 MPa the factor of safety according to Guest’s theory isa) 5.43b) 4.68c) 2.06d) 3.22Correct answer is option 'B'. Can you explain this answer?.
A bolt is subjected to an axial load of 10 kN with a transverse shear load 4 kN and crosssection area of bolt is 250 mm2 and yield strength of bolt material is 240 MPa the factor of safety according to Guest’s theory isa) 5.43b) 4.68c) 2.06d) 3.22Correct 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 A bolt is subjected to an axial load of 10 kN with a transverse shear load 4 kN and crosssection area of bolt is 250 mm2 and yield strength of bolt material is 240 MPa the factor of safety according to Guest’s theory isa) 5.43b) 4.68c) 2.06d) 3.22Correct 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 A bolt is subjected to an axial load of 10 kN with a transverse shear load 4 kN and crosssection area of bolt is 250 mm2 and yield strength of bolt material is 240 MPa the factor of safety according to Guest’s theory isa) 5.43b) 4.68c) 2.06d) 3.22Correct answer is option 'B'. Can you explain this answer?.
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