Explanation Given information: The mass of the rod is m . The length of the rod is L . Calculation: Calculate the mass moment of inertia ( I ) as shown below. I = 1 12 m L 2 Sketch the Free Body Diagram as shown in Figure 1. Refer to Figure 1. Calculate the acceleration ( a ) as shown below. a = L 2 α Apply the Equilibrium of moment about A as shown below. ∑ M A = I G α + m a d W × L 2 = I α + m a L 2 Substitute m g for W , m L 2 12 for I , and L 2 α for a . m g L 2 = m L 2 12 α + m L 2 α × L 2 g 2 = L 12 α + L 4 α g 2 L = 4 α 12 α = 3 2 g L Calculate the acceleration at end B ( a B ) as shown below. a B = a n + a B / A = 0 + L α = L α Substitute 3 2 g L for α . a B = L × 3 2 g L = 3 2 g Apply the Equilibrium of forces along y direction as shown below. ∑ F y = m a y A − m g = − m a Substitute L 2 α for a . A − m g = − m × L 2 α Substitute 3 2 g L for α . A − m g = − m × L 2 × 3 2 g L A = m g − 3 4 m g A = 1 4 m g Sketch the Free Body Diagram with portion AJ as shown in Figure 2. Refer to Figure 2. The external forces acting on the portion AJ of the rod are, reaction at A , uniformly distributed load, shear V J , and bending moment M J . Calculate the acceleration ( a J ) as shown below. a J = x α Substitute 3 g 2 L for α . a J = 3 g x 2 L Calculate the inertial terms of the mass center ( m L a J ) as shown below. m L a J = m L × 3 g x 2 L = 3 m g x 2 L 2 Sketch the Free Body Diagram of the portion AJ as shown in Figure 3. Refer to Figure 3. Apply the Equilibrium of forces along y direction as shown below. ∑ F y = m a y m g L x − m g 4 + V J = 1 2 × 3 m g 2 L 2 x × x V J = m g 4 − m g L x + 3 m g 4 L 2 x 2 (1) Apply the Equilibrium of moment about J as shown below. ∑ M J = I G α + m a d ( m g L x ) × x 2 − m g 4 x + M J = 1 2 × 3 m g 2 L 2 x × x × x 3 M J = m g 4 x − m g 2 L x 2 + m g 4 L 2 x 3

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 16.2, Problem 16.152P

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Draw the shear and bending moment diagram of the beam.

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Chapter 16.2, Problem 16.151P

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Chapter 16 Solutions

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

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Draw the shear and bending moment diagram of the beam.

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