Explanation Given information: The outer and inner diameters of the shaft are 4.5 in. and 3 in. Calculation: The value of torque T A B is 5 , 000 lb ⋅ ft and T B C is 8 , 000 lb ⋅ ft . Determine the angle of twist ( ϕ ) of the shaft using the relation: ϕ = T L J G Here, applied torque is T , the length of the shaft is L , the polar moment of inertia is J , and the shear modulus of elasticity of the material is G . Rearrange the Equation for of the shaft at A relative to C ( ϕ A / C ) . ϕ A / C = ∑ T L J G = ( T A B L A B + T B C L B C ) J G (1) Here, length of segment AB is L A B and length of segment BC is L B C . Refer the properties of A -36 steel: The value of shear modulus of elasticity of A -36 steel is 11 × 10 6 psi . The polar moment of inertia for outer radius ( r 0 ) and inner radius ( r i ) of the shaft is π 2 ( r 0 4 − r i 4 ) . The value of outer radius ( r 0 ) and inner radius ( r i ) of the shaft is 2.25 in. and 1.5 in. Substitute π 2 ( r 0 4 − r i 4 ) for J in Equation (1). ϕ A C = ( T A B L A B + T B C L B C ) ( π 2 ( r 0 4 − r i 4 ) ) G = 2 ( T A B L A B + T B C L B C ) ( π ( r 0 4 − r i 4 ) ) G Substitute 5 , 000 lb ⋅ ft for T A B , 15 ft for L A B , 8 , 000 lb ⋅ ft for T B C , 20 ft for L B C , 2

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ISBN: 8220102955295

Author: HIBBELER

Publisher: PEARSON

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Chapter 10.4, Problem 51P

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Find the angle of twist of the shaft at A relative to C.

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Find the angle of twist of the shaft at A relative to C .

Solution Summary: The author calculates the angle of twist of the shaft at A relative to C using the relation: varphi =TLJG.

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Find the angle of twist of the shaft at A relative to C.

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