(a) Explanation Given information: The magnitude of load P 1 is 1 , 080 lb . The magnitude of load P 2 is 810 lb . Refer to problem P8.19 in the textbook. The diameter ( d ) of the shaft is 1.75 in . Calculation: Refer to problem P8.19 in the textbook. Find the value of c using the relation: c = 1 2 d (1) Here, d is the diameter of the shaft. Substitute 1.75 in . for d in Equation (1). c = 1 2 × 1.75 = 0.875 in . Find the polar moment of inertia ( J ) using the relation: J = π 2 c 4 (2) Here, c is the half of the diameter. Substitute 0.875 in for c in Equation (2). J = π 2 ( 0.875 ) 4 = 0.92077 in 4 Sketch the free body diagram of horizontal plane as shown in Figure 1. Calculate the reaction for the given structure. Taking a moment about B , ∑ M B = 0 D y × 20 − ( 810 × 10 ) = 0 20 D y − 8 , 100 = 0 D y = 405 lb ∑ F y = 0 A y + D y = 810 (3) Substitute 405 lb for D y in Equation (3). B y + 405 = 810 B y = 405 lb Calculate the bending moment in horizontal plane at point C . B M D = 405 × 10 = 4 , 050 lb ⋅ in Sketch the bending moment diagram in horizontal plane as shown in Figure 2. Calculate the shear force in vertical plane just to the left of point B as follows: Refer to Figure 3, S F A = 1 , 080 lb Calculate the bending moment in vertical plane just to the left of point B as follows: Refer to Figure 3, B M C = 1 , 080 × 13 − ( 1 , 242 × 10 ) = 14 , 040 − 12 , 420 = 1 , 620 lb ⋅ in B M B = 1 , 080 × 3 = 3 , 240 lb ⋅ in Find the value of Torque over portion ABC . T = 6 × 1 , 080 = 6 , 480 lb ⋅ in Sketch the bending moment diagram in vertical plane as shown in Figure 3. Sketch the cross section left of point B as shown in Figure 4 (b) To determine The values of τ H and τ K in a section just to the left C .

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 8.2, Problem 22P

(a)

To determine

The values of τH and τK in a section just to the left B.

(b)

To determine

The values of τH and τK in a section just to the left C.

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Chapter 8.2, Problem 21P

Chapter 8.2, Problem 23P

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The values of τ H and τ K in a section just to the left B .

Solution Summary: The author calculates the polar moment of inertia (J) using the relation: cj=pi 2

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The values of τH and τK in a section just to the left B.

The values of τH and τK in a section just to the left C.

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