Explanation Given information: The W 12 × 45 simply supported beam is made of A-36 steel. The modulus of elasticity of the beam ( E ) is 29 × 10 3 ksi . The moment of inertia of the beam ( I ) is 350 in . 4 . The point load act at center of the beam ( P ) is 12 kip . The moment act at left end of the beam ( M ) is 50 kip ⋅ ft . The length of the beam ( L ) is 24 ft . The distance of segment ( x ) is 12 ft . Calculation: Show the free body and elastic curves for the partial uniform distributed load and couple moment of the beam as in Figure 1. Refer to Figure 1. Calculate the deflection at C ( Δ C ) 1 for point load ( P ) using the formula: ( Δ C ) 1 = P L 3 48 E I (1) Substitute 12 kip for P and 24 ft for L in Equation (1). ( Δ C ) 1 = 12 × 24 3 48 E I = 3 , 456 E I kip ⋅ ft 3 ↓ Calculate the deflection at C ( Δ C ) 2 for moment ( M ) using the formula: ( Δ C ) 2 = M x 6 E I L ( L 2 − x 2 ) (2) Substitute 50 kip ⋅ ft for M , 12 ft for x , and 24 ft for L in Equation (2). ( Δ C ) 2 = 50 × 12 6 E I × 24 ( 24 2 − 12 2 ) = 4

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and af…

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Chapter 12.5, Problem 12.87P

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The deflection at center C of the simply supported beam (ΔC) .

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Chapter 12.5, Problem 12.86P

Chapter 12.5, Problem 12.88P

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The deflection at center C of the simply supported beam ( Δ C ) .

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The deflection at center C of the simply supported beam (ΔC) .

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