To determine The deflection of the centroid at A due to the loading. Explanation Given information: The W 10 × 30 cantilevered beam is made of A-36 steel. The moment is M = 4.5 kip ⋅ ft . Calculation: Modulus of elasticity of A-36 steel is E = 29 , 000 ksi . The moment of inertia for the W 10 × 30 beam is I x = 170 in 4 and I y = 16.7 in 4 . Resolve the moment into components as shown below. Along x direction, x max = ( M sin θ ) L 2 2 E I y Here, M is the applied moment, θ is the angle, L is the length of the beam, E is the modulus of elasticity, and I y is the moment of inertia about y axis. Substitute 4.5 kip ⋅ ft for M , 30 ° for θ 15 ft for L , 29,000 ksi for E , and 16.7 in 4 for I y . x max = ( ( 4.5 kip ⋅ ft × 12 in . 1 ft ) sin 30 ° ) ( 15 ft × 12 in . 1 ft ) 2 2 × 29 , 000 ksi × 16.7 in 4 = 874 , 800 968 , 600 = 0.9032 in . Along y direction, y max = ( M cos θ ) L 2 2 E I x Here, I x is the moment of inertia about x axis

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 12.92P

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The deflection of the centroid at A due to the loading.

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Chapter 12.5, Problem 12.91P

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