(a) Explanation Given information: The diameter of the solid brass rod ( d ) is 1.2 in . . The maximum shearing stress of the rod ( τ max ) is 13.5 ksi . Calculation: Calculate the radius of the solid brass rod ( c ) using the relation: c = 1 2 d Here, d is the diameter of solid brass bar. Substitute 1.2 in. for d . c = 1 2 ( 1.2 ) = 0.600 in . Find the coordinate distance z : z = γ γ max (1). Here, γ is shearing strain and γ max is maximum shearing strain. Substitute ρ for γ and c for γ max in Equation (1). z = ρ c (2). Modify the Equation (2). ρ = z c Calculate the torque ( T ) using the relation: T = 2 π ∫ 0 c ρ 2 τ d ρ Here, ρ is radius of curvature, τ is shearing stress, and d is diameter. Substitute z c for ρ . T = 2 π ∫ 0 c ( z c ) 2 τ d z c = 2 π c 3 ∫ 0 c z 2 τ d z Set the limit for the above equation 0 to 1. T = 2 π c 3 ∫ 0 1 z 2 τ d z Take the integral I as ∫ 0 1 z 2 τ d z . T = 2 π c 3 I (3). Calculate the integral I using the Simpson’s rule: I = Δ z 3 [ ( z 1 + z 5 ) + 4 ( z 2 + z 4 ) + 2 ( z 3 ) ] (4). Here, z 1 , z 2 , z 3 , z 4 , and z 5 are the coordinates and Δ z is difference between the coordinates (b) To determine Find the angle of twist ( ϕ ) in a 24 in. length of the rod.

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 3.8, Problem 110P

(a)

To determine

Find the magnitude of the torque (T).

(b)

To determine

Find the angle of twist (ϕ) in a 24 in. length of the rod.

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Chapter 3.8, Problem 109P

Chapter 3.8, Problem 111P

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Mechanics of Materials, 7th Edition

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Find the magnitude of the torque ( T ) .

Solution Summary: The author calculates the radius of the solid brass rod (c) using the relation c=12d.