Explanation Assumption: Consider the force indicating right side as positive and left side as negative in horizontal components of forces. Consider the force indicating upward is taken as positive and downward as negative in vertical components of forces. Consider clockwise moment as negative and anti-clock wise moment as positive wherever applicable. Apply the Equation of equilibrium wherever applicable. Calculation; Show the free-body diagram of the entire beam as in Figure 1. Determine the vertical reaction at point A by taking moment about point B . ∑ M B = 0 − A y ( 2 L 3 ) + 1 2 × w 0 × L × 1 3 × L = 0 A y ( 2 L 3 ) = w 0 L 2 6 A y = w 0 L 4 Determine the vertical reaction at point B by resolving the vertical component of forces. ∑ F y = 0 A y + B y − 1 2 × w 0 × L = 0 w 0 L 4 + B y − w 0 L 2 = 0 B y = w 0 L 4 Determine the horizontal direction at point B by resolving the horizontal component of forces. ∑ F x = 0 B x = 0 Region 0 ≤ x < L / 3 from left end: Show the free-body diagram of the region 0 ≤ x < L / 3 as in Figure 2. Determine the shear force at the section by resolving the vertical component of forces. ∑ F y = 0 − 1 2 × w 0 L × x × x − V = 0 V = − w 0 x 2 2 L Determine the moment at the section by taking moment about the section. ∑ M x = 0 M + 1 2 × w 0 L × x × x × 1 3 × x = 0 M = − w 0 x 3 6 L Region L / 3 < x ≤ L from left end: Show the free-body diagram of the region L / 3 < x ≤ L as in Figure 3. Determine the shear force at the section by resolving the vertical component of forces. ∑ F y = 0 A y − V − 1 2 × w 0 L × x × x = 0 w 0 L 4 − V − w 0 x 2 2 L = 0 V = w 0 L 4 − w 0 x 2 2 L (1) Determine the moment at the section by taking moment about the section

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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In general, we can define the bending moment as the reaction induced when a certain amount of load or force is applied to an element which makes it bend.

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Chapter 11.2, Problem 27P

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Plot the shear and moment diagrams for the beam.

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Chapter 11.2, Problem 26P

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Chapter 11 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 11.2 - In each case, the beam is subjected to the...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - Prob. 5FP Ch. 11.2 - Prob. 6FP Ch. 11.2 - In each ease, draw the shear and moment diagrams...Ch. 11.2 - Prob. 8FP Ch. 11.2 - Prob. 1P

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Plot the shear and moment diagrams for the beam.

Solution Summary: The author illustrates the shear and moment diagrams for the beam. The vertical reaction at point A is determined by taking moment about point B.

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Plot the shear and moment diagrams for the beam.

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Chapter 11 Solutions