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The equivalent spring constant for a bar of length L, cross-sectional area A and modulus of elasticity E is subjected to an axial force P is
- a)AE/L
- b)L/AE
- c)PL/A
- d)P2L/2AE
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The equivalent spring constant for a bar of length L, cross-sectional...
Change in length of the bar:
δL = PL/AE
The ratio between the force and deflection is referred to as the spring rate or stiffness of the beam or coil.
Equivalent spring constant:
k = F/x = P/δL = AE/L
Most Upvoted Answer
The equivalent spring constant for a bar of length L, cross-sectional...
Explanation:
- Given:
- Length of the bar, L
- Cross-sectional area of the bar, A
- Modulus of elasticity, E
- Axial force applied, P
- Equivalent Spring Constant (k):
- The spring constant of the bar can be calculated using the formula:
k = P/ΔL
where ΔL is the change in length of the bar due to the applied force.
- Modulus of Elasticity (E):
- Modulus of elasticity relates stress to strain in a material.
- It is given by the formula: E = σ/ε
where σ is stress and ε is strain.
- Stress (σ) and Strain (ε):
- Stress is given by the formula: σ = P/A
where P is the axial force and A is the cross-sectional area.
- Strain is given by the formula: ε = ΔL/L
where ΔL is the change in length and L is the original length of the bar.
- Substitute Stress and Strain in Modulus of Elasticity Formula:
- E = (P/A) / (ΔL/L)
- E = PL / (AΔL)
- Substitute Modulus of Elasticity in Equivalent Spring Constant Formula:
- k = P / ΔL
- k = P / (εL)
- k = P / (ΔL/L)
- k = PL / ΔL
- k = PL / (ΔL * 1)
- k = PL / (A * ε)
- k = AE / L
Therefore, the equivalent spring constant for a bar of length L, cross-sectional area A, and modulus of elasticity E subjected to an axial force P is AE/L.
- Given:
- Length of the bar, L
- Cross-sectional area of the bar, A
- Modulus of elasticity, E
- Axial force applied, P
- Equivalent Spring Constant (k):
- The spring constant of the bar can be calculated using the formula:
k = P/ΔL
where ΔL is the change in length of the bar due to the applied force.
- Modulus of Elasticity (E):
- Modulus of elasticity relates stress to strain in a material.
- It is given by the formula: E = σ/ε
where σ is stress and ε is strain.
- Stress (σ) and Strain (ε):
- Stress is given by the formula: σ = P/A
where P is the axial force and A is the cross-sectional area.
- Strain is given by the formula: ε = ΔL/L
where ΔL is the change in length and L is the original length of the bar.
- Substitute Stress and Strain in Modulus of Elasticity Formula:
- E = (P/A) / (ΔL/L)
- E = PL / (AΔL)
- Substitute Modulus of Elasticity in Equivalent Spring Constant Formula:
- k = P / ΔL
- k = P / (εL)
- k = P / (ΔL/L)
- k = PL / ΔL
- k = PL / (ΔL * 1)
- k = PL / (A * ε)
- k = AE / L
Therefore, the equivalent spring constant for a bar of length L, cross-sectional area A, and modulus of elasticity E subjected to an axial force P is AE/L.
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The equivalent spring constant for a bar of length L, cross-sectional area A and modulus of elasticity E is subjected to an axial force P isa)AE/Lb)L/AEc)PL/Ad)P2L/2AECorrect answer is option 'A'. Can you explain this answer?
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