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A certain steel has proportionality limit of 3000kg/cm^2 simple tension.it is subjected to principal stress of 1200kg/cm^2(tensile),600kg/cm^2(tension) and 300kg/cm^2(compression).find the factor of safety according to maximum shear stress theory.?
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A certain steel has proportionality limit of 3000kg/cm^2 simple tensio...
Factor of Safety Calculation using Maximum Shear Stress Theory
Given Data:
- Proportionality limit of steel: 3000 kg/cm^2
- Principal stress (tensile): 1200 kg/cm^2
- Principal stress (tension): 600 kg/cm^2
- Principal stress (compression): 300 kg/cm^2
Step 1: Calculate the Maximum Shear Stress
The formula to calculate maximum shear stress (τ) using the principal stresses (σ1, σ2, σ3) is:
τ = (σ1 - σ3) / 2
Given values:
σ1 = 1200 kg/cm^2
σ3 = 300 kg/cm^2
Substitute the values:
τ = (1200 - 300) / 2
τ = 450 kg/cm^2
Step 2: Calculate the Factor of Safety
The factor of safety using the maximum shear stress theory is calculated as:
Factor of Safety = Proportionality Limit / Maximum Shear Stress
Given values:
Proportionality Limit = 3000 kg/cm^2
Maximum Shear Stress = 450 kg/cm^2
Substitute the values:
Factor of Safety = 3000 / 450
Factor of Safety = 6.67
Conclusion:
The factor of safety according to the maximum shear stress theory is 6.67. This means that the material can withstand 6.67 times the maximum shear stress before failure, providing a safe design margin.
Given Data:
- Proportionality limit of steel: 3000 kg/cm^2
- Principal stress (tensile): 1200 kg/cm^2
- Principal stress (tension): 600 kg/cm^2
- Principal stress (compression): 300 kg/cm^2
Step 1: Calculate the Maximum Shear Stress
The formula to calculate maximum shear stress (τ) using the principal stresses (σ1, σ2, σ3) is:
τ = (σ1 - σ3) / 2
Given values:
σ1 = 1200 kg/cm^2
σ3 = 300 kg/cm^2
Substitute the values:
τ = (1200 - 300) / 2
τ = 450 kg/cm^2
Step 2: Calculate the Factor of Safety
The factor of safety using the maximum shear stress theory is calculated as:
Factor of Safety = Proportionality Limit / Maximum Shear Stress
Given values:
Proportionality Limit = 3000 kg/cm^2
Maximum Shear Stress = 450 kg/cm^2
Substitute the values:
Factor of Safety = 3000 / 450
Factor of Safety = 6.67
Conclusion:
The factor of safety according to the maximum shear stress theory is 6.67. This means that the material can withstand 6.67 times the maximum shear stress before failure, providing a safe design margin.
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A certain steel has proportionality limit of 3000kg/cm^2 simple tension.it is subjected to principal stress of 1200kg/cm^2(tensile),600kg/cm^2(tension) and 300kg/cm^2(compression).find the factor of safety according to maximum shear stress theory.?
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A certain steel has proportionality limit of 3000kg/cm^2 simple tension.it is subjected to principal stress of 1200kg/cm^2(tensile),600kg/cm^2(tension) and 300kg/cm^2(compression).find the factor of safety according to maximum shear stress theory.? 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 certain steel has proportionality limit of 3000kg/cm^2 simple tension.it is subjected to principal stress of 1200kg/cm^2(tensile),600kg/cm^2(tension) and 300kg/cm^2(compression).find the factor of safety according to maximum shear stress theory.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain steel has proportionality limit of 3000kg/cm^2 simple tension.it is subjected to principal stress of 1200kg/cm^2(tensile),600kg/cm^2(tension) and 300kg/cm^2(compression).find the factor of safety according to maximum shear stress theory.?.
A certain steel has proportionality limit of 3000kg/cm^2 simple tension.it is subjected to principal stress of 1200kg/cm^2(tensile),600kg/cm^2(tension) and 300kg/cm^2(compression).find the factor of safety according to maximum shear stress theory.? 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 certain steel has proportionality limit of 3000kg/cm^2 simple tension.it is subjected to principal stress of 1200kg/cm^2(tensile),600kg/cm^2(tension) and 300kg/cm^2(compression).find the factor of safety according to maximum shear stress theory.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain steel has proportionality limit of 3000kg/cm^2 simple tension.it is subjected to principal stress of 1200kg/cm^2(tensile),600kg/cm^2(tension) and 300kg/cm^2(compression).find the factor of safety according to maximum shear stress theory.?.
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