To determine The largest angle ( θ ) measured from the vertical. Explanation Given information: The diameter of the circular cross section is 30 mm. The length of the bar is 2 m. The mass of the bar is 5 kg m . Calculation: Calculate the weight acting at the mid of the bar using the formula: w = m g l (1) Here, m is the mass, g is the acceleration due to gravity and l is the length of the bar. Substitute 5 kg m for m , 9.81 m s 2 for g , and 2 m for l in Equation (1). w = ( 5 kg/m ) ( 9.81 m/s 2 ) ( 2 m ) = 98.1 N Let V be the shear force, M be the moment, and N be the normal reaction acting on the bar. Sketch the free body diagram of the bar as shown in Figure 1. Refer to Figure 1. The normal force is N = − 98.1 cos θ . The moment is M = 98.1 sin θ . The radius of the bar is 15 mm. Determine the cross sectional area of the circular bar ( A ) using the relation: A = π 4 d 2 (2) Here, d is the diameter of the circular cross section. Substitute 30 mm for d in Equation (2). A = π 4 ( 30 mm ) 2 = π 4 ( 30 mm × 10 − 3 m 1 mm ) 2 = 7.0686 × 10 − 4 m 2 Determine the moment of inertia of the bar ( I ) using the relation: I = π 64 d 4 (3) Substitute 30 mm for d in Equation (3). I = π 64 ( 30 mm ) 4 = π 64 ( 30 mm × 10 − 3 m 1 mm ) 4 = 3

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 8, Problem 8.78RP

To determine

The largest angle (θ) measured from the vertical.

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Chapter 8, Problem 8.77RP

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