Explanation Given information: The beam is made of wood. The modulus of elasticity of the beam ( E ) is 1.5 × 10 3 ksi The moment of inertia of the beam is I The width of the beam ( b ) is 3 in . The height of the beam ( h ) is 6 in . The uniformly distributed load act entire span of the beam ( w ) is 100 lb/ft . The length of the beam ( L ) is 12 ft . Calculation: Calculate the support reactions A and B ( R A and R B ) : Calculate the moment about point A by applying the equation of equilibrium: Sum of moments about point A is equal to 0. ∑ M A = 0 ( R B × 12 ) − ( 100 × 12 × 12 2 ) = 0 12 R B − 7200 = 0 R B = 600 lb Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 R A + R B − ( 100 × 12 ) = 0 R A + 600 − 1200 = 0 R A = 600 lb Calculate the moment function with respect of the x distance M ( x ) : M ( x ) = ( 600 × x ) − ( 100 × x × x 2 2 ) = ( 600 x − 50 x 2 ) lb ⋅ ft Elastic Curve and slope is, E I d 2 υ d x 2 = M ( x ) Substitute ( 600 x − 50 x 2 ) lb ⋅ ft for M ( x ) , E I d 2 υ d x 2 = 600 x − 50 x 2 Differentiate both sides of the Equation. E I d υ d x = 600 x 2 2 − 50 x 3 3 + C 1 = 300 x 2 − 16.667 x 3 + C 1 (1) Differentiate both sides of the Equation (1). E I υ = 300 x 3 3 − 16.667 x 4 4 + C 1 x + C 2 = 100 x 3 − 4.16675 x 4 + C 1 x + C 2 (2) Apply boundary conditions. υ = 0 at x = 0 υ = 0 at x = 12 ft Apply the first boundary condition in Equation (2). E I ( 0 ) = 100 ( 0 ) 3 − 4.16675 ( 0 ) 4 + C 1 ( 0 ) + C 2 C 2 = 0 Substitute 0 for C 2 in Equation (5). E I υ = 100 x 3 − 4.16675 x 2 + C 1 x + 0 E I υ = 100 x 3 − 4

Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)

5th Edition

ISBN: 9780134301006

Author: Russell C. Hibbeler

Publisher: PEARSON

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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 16.2, Problem 4FP

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Find the maximum deflection of the simply supported beam (υmax).

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Chapter 16 Solutions

Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)

Ch. 16.2 - In each ease, determine the internal bending...Ch. 16.2 - Prob. 1FP Ch. 16.2 - Determine the slope and deflection of end A of the...Ch. 16.2 - Prob. 3FP Ch. 16.2 - Prob. 4FP Ch. 16.2 - Determine the maximum deflection of the simply...Ch. 16.2 - Prob. 6FP Ch. 16.2 - An L2 steel strap having a thickness of 0.125 in....Ch. 16.2 - The L2 steel blade of the band saw wraps around...Ch. 16.2 - A picture is taken of a man performing a pole...

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Find the maximum deflection of the simply supported beam ( υ max ) .

Solution Summary: The author calculates the maximum deflection of the simply supported beam (upsilon_mathrmmax) by applying the equation of equilibrium: Sum of moments about point

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