Explanation Given information: The modulus of elasticity of the aluminum rod E = 10.6 × 10 6 psi . The allowable normal stress σ all = 22 ksi . Calculation: Calculate the area of the rod ( A ) as shown below. A = π d 2 4 Calculate the minimum area of the rod ( A min ) as shown below. Substitute 1.5 in . for d . A min = π × 1.5 2 4 = 1.7671 in . 2 Calculate the load ( P ) as shown below. P = σ all A min Substitute 22 ksi for σ all and 1.7671 in . 2 for A min . P = 22 × 1.7671 = 38.8762 kips × 1 , 000 lb 1 kips = 38 , 876.2 lb Calculate the strain energy ( U ) of the tapered rod AB as shown below. U = ∫ P 2 2 E A d x Substitute π d 2 4 for A . U = P 2 2 E ∫ 1 π d 2 4 d x = 4 P 2 2 π E ∫ 1 d 2 d x = 2 P 2 π E ∫ 1 d 2 d x (1) Apply Simpson’s rule for ∫ 1 d 2 d x for the interval of h = 1.5 in . as shown below. ∫ 1 d 2 d x = h 3 ∑ m 1 d 2 (2) Here, m is the multiplier in Simpson’s rule and h is the interval. For the first interval. Substitute 1.5 in . for d and 1 for m

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Chapter 11.3, Problem 17P

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Find the maximum strain energy of acquired by the aluminum rod.

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Chapter 11 Solutions

EBK MECHANICS OF MATERIALS

Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - Prob. 7P Ch. 11.3 - Prob. 8P Ch. 11.3 - Using E = 29 106 psi, determine (a) the strain...Ch. 11.3 - Using E = 200 GPa, determine (a) the strain energy...

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Find the maximum strain energy of acquired by the aluminum rod.

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Find the maximum strain energy of acquired by the aluminum rod.

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