Explanation Given information: The Weight of the block is 100-lb. The Falling height of block is h = 3 ft = 36 in . . The Downward velocity of the block is v = 4 ft/sec = 48 in ./sec . The Young’s modulus or modulus of elasticity is E W = 1.9 ( 10 3 ) ksi = 1.9 ( 10 6 ) psi . The allowable bending stress in the beam is σ Y = 8 ksi . The Acceleration due to gravity is g = 32.2 ft/sec 2 = 32.2 × 12 in ./sec 2 . Refer to Appendix C , ‘Slopes and Deflections of beams’ in the textbook. Find the deflection for the cantilever beam with point load as follows: Δ s t = P L 3 3 E I Here, P is load applied on the beam, L is length of the beam, E is Young’s Modulus, and I is moment of inertia. Moment of inertia: Determine the moment of inertia of the rectangular beam using the formula. I = b d 3 12 (1) Here, b is width of the beam and d is depth of the beam. Substitute 12 in. for b and 18 in. for d in Equation (1). I = 12 × 18 3 12 = 5 , 832 in . 4 Stiffness constant of the beam ( k b e a m ) : Determine the stiffness constant of the beam using the relation: k = P Δ b e a m (2) Substitute P L 3 3 E I for Δ b e a m in Equation (2). k = P P L 3 3 E I k = 3 E I L 3 (3) Substitute 1.9 × 10 3 ksi for E , 5 , 832 in . 4 for I , and 5 ft for L in Equation (3). k = 3 × 1.9 × 10 3 × 5 , 832 ( 5 ft × 12 in . 1 ft ) 3 = 153.9 kip/in . Mass of the block: Determine the mass of the block using the relation. m = W g (4) Here, W is weight of block and g is acceleration due to gravity. Substitute 100 lb for W and 32.2 × 12 in ./sec 2 for g in Equation (4). m = 100 32.2 × 12 = 0.2588 slug Conservation of energy: Express the equation for conservation of energy as follows: U e = U i 1 2 m v 2 + W ( h + Δ max ) = 1 2 k ( Δ max ) 2 (5) Here, v is falling rate of the block, W is weight of block, h is falling height of the block, and Δ max is maximum displacement

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 14.4, Problem 14.63P

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The maximum stress in the beam due to impact and the maximum deflection of point B.

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The maximum stress in the beam due to impact and the maximum deflection of point B .

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The maximum stress in the beam due to impact and the maximum deflection of point B.

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