Explanation Given information: The steel beam AB acts to stop the oncoming railroad car, which has a mass of 10 Mg and is coasting towards it at v = 0.5 m/sec . The beam is simply supported and only horizontal forces occur at A and B . Assume that the railroad car and the supporting framework for the beam remain rigid. The modulus of elasticity of steel E s t is 200 GPa. The yield stress is 250 MPa. The acceleration due to gravity is g = 9.81 m/sec 2 . Deflection of the beam: Determine the deflection of the simply supported beam using the equation. Δ s t = P L 3 48 E s t I (1) Here, P is load on the beam, L is length of the beam, E is Young’s modulus of the steel, and I is moment of inertia of the section. Load on the beam: Determine the load on the beam using the relation. P = m g (2) Here, m is mass of the beam and g is acceleration due to gravity. Substitute 10 Mg for m and 9.81 m/sec 2 for g in Equation (2). P = 10 Mg × 1,000 kg 1 Mg × 9.81 m/sec 2 = 98 , 100 N Moment of inertia: Determine the moment of inertia of the beam using the formula. I = b d 3 12 (3) Here, b is width of the beam and d is depth of the beam. Substitute 200 mm for b and 200 mm for d in Equation (3). I = ( 200 mm × 1 m 1,000 mm ) × ( 200 mm × 1 m 1,000 mm ) 3 12 = 1.333 × 10 − 4 m 4 Substitute 98,100 N for P , 2 m for L , 200 GPa for E s t , and 1.333 × 10 − 4 m 4 for I in Equation (3). Δ s t = 98 , 100 × 2 3 48 × 200 GPa × 10 9 N/m 2 1 GPa × 1.333 × 10 − 4 = 0.613125 × 10 − 3 m Determine the stiffness using the equation. k = W Δ s t (4) Substitute 98,100 N for W and 0.613125 × 10 − 3 m for Δ s t in Equation (4). k = 98 , 100 0.613125 × 10 − 3 = 160 × 10 6 N/m Maximum deflection of the beam: Determine the maximum deflection of the beam using the formula. Δ max = Δ s t v 2 g (5) Here, v is speed of the car

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 14.4, Problem 14.49P

To determine

The maximum stress developed in the beam if it is struck at its center by the car

the maximum deflection of the beam.

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Chapter 14.4, Problem 14.48P

Chapter 14.4, Problem 14.50P

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The maximum stress developed in the beam if it is struck at its center by the car the maximum deflection of the beam.

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Chapter 14 Solutions

The maximum stress developed in the beam if it is struck at its center by the car

the maximum deflection of the beam.