Explanation Given information: The uniformly distributed load act at a distance from left end of the beam is w . The point load act at right end of the beam is P . The flexural rigidity of the beam is E I . The length of the beam ( L ) is 2 a . Calculation: Show the free bodydiagram of the beam 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 − ( w × a ) − P = 0 R A − w a − P = 0 R A = w a + P 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 M A − ( w × a × a 2 ) − ( P × 2 a ) = 0 M A − w a 2 2 − 2 P a = 0 M A = w a 2 2 + 2 P a Show the moment area diagramsfor the point load and uniformly distributed load of the beam as in Figure 2. Refer to Figure 2. Show the bending monument calculation follows: Calculate the bending moment at A ( M A ) u for uniformly distributed load: ( M A ) u = − ( w × a × a 2 ) = − w a 2 2 Calculate the bending moment at A ( M A ) p for point load: ( M A ) p = − ( P × 2 a ) = − 2 P a Calculate the bending moment at B ( M B ) u for uniformly distributed load: ( M B ) u = − ( w × 0 × 0 2 ) = 0 Calculate the bending moment at B ( M B ) p for point load: ( M B ) p = − ( P × a ) = − P a Calculate the bending moment at C : M C = ( P × 0 ) = 0 Show the deflected shape of the shaft as in Figure 3. Refer to Figure 3. The support at A is fixed. Therefore, the slope at A ( θ A ) is 0

10th Edition

ISBN: 8220102744110

Author: 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 12.4, Problem 12.79P

To determine

The slope at C(θC).

The deflection at C(υC).

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Chapter 12.4, Problem 12.78P

Chapter 12.4, Problem 12.80P

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