Explanation Given information: The load P causes the open coils of the spring to make an angle θ with the horizontal when the spring is stretched. Cross section: Show the free-body diagram of the cross-section as in Figure 1. Moment about the section: Determine the moment at the section by taking moment about the section. ∑ M x = 0 M − P R sin θ = 0 M = P R sin θ Torque about the section: Determine the torque at the section by taking torque about the section. ∑ T = 0 T − P R cos θ = 0 T = P R cos θ Here, P is the external load acting on the spring and R is the distance of the wire from center to outer edge. Moment of inertia: Determine the moment of inertia of the spring using the formula. I = π d 4 64 Here, d is diameter of the curved rod. Polar moment of inertia: Determine the polar moment of inertia of the spring using the formula. J = π d 4 32 Bending stress: Determine the bending stress in the spring using the bending equation. σ x = M c I (1) Here, c is the distance between the centroidal axis and the outermost fibre of the spring wire. c = d 2 Substitute P R sin θ for M , d 2 for c , and π d 4 64 for I in Equation (1). σ x = P R sin θ × d 2 × π d 4 64 = 32 P R sin θ π d 3 Shear stress: Determine the shear stress in the spring using the torsion equation. τ x y = T c J (2) Substitute P R cos θ for T , d 2 for c , and π d 4 32 for I in Equation (2). τ x y = P R cos θ × d 2 × π d 4 32 = 16 P R cos θ π d 3 Maximum normal stress: Determine the maximum normal stress due to bending moment and torque using the formula

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 14.3, Problem 14.37P

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To show: that for the given position of the spring causes a torque T=PRcosθ and a bending moment M=PRsinθ at the cross section.

the maximum normal stress in the material.

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Chapter 14.3, Problem 14.36P

Chapter 14.3, Problem 14.38P

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that for the given position of the spring causes a torque T = P R cos θ and a bending moment M = P R sin θ at the cross section. the maximum normal stress in the material.

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To show: that for the given position of the spring causes a torque T=PRcosθ and a bending moment M=PRsinθ at the cross section. the maximum normal stress in the material.

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Chapter 14 Solutions

To show: that for the given position of the spring causes a torque T=PRcosθ and a bending moment M=PRsinθ at the cross section.

the maximum normal stress in the material.