Explanation Concept Used: Write the equation for the slope and elastic curve for x . E I d 2 v d x 2 = M ( x ) (I) Here, modulus of elasticity is E and moment of inertia is I . Calculation: The free body diagram of the beam is shown below: Figure (1) Here, component of force in y-direction at point A is A y , component of force in y-direction at point B is B y . Calculate moment about point A. ∑ M A = 0 B y ( 20 ft ) = 8 k-ft − 8 k-ft B y = 0 k Calculate all forces in vertical direction. ∑ F y = 0 A y + B y = 0 A y = − B y A y = 0 k Calculate moment at a section x from point A. M ( x ) = 8 k-ft Calculate the equation for the slope and elastic curve for x . Substitute 8 k-ft for M ( x ) in Equation (I). E I d 2 v d x 2 = 8 k-ft (II) Calculate the slope equation. Integrate Equation (II) to get the slope equation. E I d v d x = ( 8 k-ft ) x + c 1 (III) Calculate the deflection equation. Integrate Equation (III) to get the deflection equation. E I v = ( 8 k-ft ) x 2 2 + c 1 x + c 2 (IV) Apply boundary conditions to calculate the constants Substitute 0 ft for x and 0 ft for v in Equation (IV). E I ( 0 ft ) = ( 8 k-ft ) ( 0 ft ) 2 2 + c 1 ( 0 ft ) + c 2 c 2 = 0 Substitute 20 ft for x , 0 ft for v and 0 for c 2 in Equation (IV). E I ( 0 ft ) = ( 8 k-ft ) ( 20 ft ) 2 2 + c 1 ( 20 ft ) + 0 c 1 = − 80 Substitute θ for d v d x and − 80 for c 1 in Equation (III)

The equation of elastic curve using coordinate x , the slope at A and the maximum displacement of the beam.

Structural Analysis (10th Edition)

10th Edition

ISBN: 9780134610672

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 7, Problem 7.6P

To determine

The equation of elastic curve using coordinate x, the slope at A and the maximum displacement of the beam.

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