Explanation Given information: The point load act at left end and center of the AB is P . The flexural rigidity of the rod is E I . The length of the rod is 4 a . Calculation: Show the free body diagram of the moment area and tangent of the rod as in Figure 1. Refer to Figure 1. 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 − P − P = 0 R A + R B − 2 P = 0 R A + R B = 2 P (1) 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 × 2 a ) − ( P × a ) + ( P × a ) = 0 2 a R A − P a + P a = 0 2 a R B = 0 R B = 0 2 a R B = 0 Substitute 0 for R B in Equation (1). R A + 0 = 2 P R A = 2 P − 0 R A = 2 P Calculate thevertical distance between the tangentat a point A and B ( t A / B ) : t A / B = 1 2 ( − P a 2 E I ) ×

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 12.4, Problem 12.54P

To determine

The slope at B(θB).

The deflection at C(υC).

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Chapter 12.4, Problem 12.53P

Chapter 12.4, Problem 12.55P

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