Explanation Given information: Mass of the bolt is 2 kg. Height of the fall is h = 30 mm = 0.030 m . Diameter of the bolt is d = 4 mm = 0.004 m Permissible stress in the bolt is σ max = 150 MPa = 150 × 10 6 N/m 2 . Assumptions: Young’s modulus or modulus of elasticity of the A-36 steel is E s t = 200 GPa = 200 ( 10 9 ) N/m 2 . The acceleration due to gravity is g = 9.81 m/sec 2 . Explanation: Area of the bolt: Determine the area of the bolt ( A ) using the formula. A = π d 2 4 (1) Here, d is diameter of the bolt. Determination of Weight: Determine the weight using the relation. W = m g (2) Here, m is mass and g is acceleration due to gravity. Conservation of energy: Express the equation for conservation of energy as follows: U e = U i 1 2 W Δ s t = W 2 L 2 A E (3) Here, W is the weight, Δ s t is the displacement of the bolt, L is length of the bolt, and E is Young’s modulus of theA-36 steel bolt. Stress in the steel: Determine the stress in the steel bolt using the formula: σ s t = W A (4) Maximum stress in the bolt ( σ max ) : Determine the maximum stress developed in the cable using the formula. σ max = n σ s t (5) Here, n is impact factor. Determination of impact factor: Determine the impact factor using the formula. n = 1 + 1 + 2 ( h Δ s t ) (6) Here, h is height of fall. Show the calculation of values as follows: Conclusion: Substitute 0.004 m. for d in Equation (1). A = π × 0.004 2 4 = 1.2566 × 10 − 5 m 2 Substitute 2 kg for m and 9.81 m/sec 2 for g in Equation (2). W = 2 × 9.81 = 19.62 N Substitute 19.62 N for W , 1.2566 × 10 − 5 m 2 for A , and 200 ( 10 9 ) N/m 2 for E in Equation (3)

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 14.4, Problem 14.49P

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Chapter 14 Solutions

Mechanics of Materials (10th Edition)

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