Explanation Given information: Length of the shaft is 1 m. Diameter of the shaft is 40 mm. Yield stress is 100 MPa. The value of G is 80 GPa. Calculation: The expression to find the yield stress ( τ Y ) in the shaft is shown below: τ Y = T Y c J (1) Here, T Y is the maximum elastic torque, c is the outer radius of the shaft, and J is the polar moment of inertia of the shaft. The polar moment of inertia of a shaft with radius r is π 2 r 4 . Diameter of the shaft is 40 mm. So the radius value of the shaft is 20 mm. Substitute r for c and π 2 r 4 for J in Equation (1). τ Y = T Y r π 2 r 4 (2) Substitute 100 MPa for τ Y and 20 mm for r in Equation (2). 100 MPa = T Y ( 20 mm ) π 2 ( 20 mm ) 4 100 MPa ( 1 N mm 2 1 MPa ) = T Y ( 20 mm ) π 2 ( 20 mm ) 4 T Y = 1.26 × 10 6 N ⋅ mm T Y = 1.26 kN ⋅ m Therefore, the maximum elastic torque in the solid shaft is 1.26 kN ⋅ m _ . Find the value of shear strain ( γ Y ) using the relation: γ Y = τ Y G (3) Here, G is the shear modulus of elasticity of the material. Substitute 100 MPa for τ Y and 80 GPa for G in Equation (3). γ Y = 100 MPa 80 GPa = 100 MPa 80 GPa ( 10 3 MPa 1 GPa ) = 0.00125 rad Find the angle of twist ( ϕ ) of the shaft using the relation: ϕ = γ Y ρ Y L (4) Here, L is the length of the shaft and ρ Y is the radius of the elastic core. Substitute 0.00125 rad for γ Y , 20 mm for ρ Y and 1 m for L in Equation (4). ϕ = 0.00125 rad 20 mm ( 1 m ) = 0.00125 rad 20 mm ( 1 m × 10 3 mm 1 m ) = 0.0625 rad = 0.0625 rad ( 180 ° π rad ) = 3

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ISBN: 9780137605521

Author: HIBBELER

Publisher: RENT PEARS

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Chapter 5.10, Problem 125P

To determine

The maximum elastic torque in the solid shaft.

The angle of twist in the solid shaft.

The angle of twist for torque T=1.2TY.

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Chapter 5.10, Problem 124P

Chapter 5.10, Problem 126P

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MECHANICS OF MATERIALS

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The maximum elastic torque in the solid shaft. The angle of twist in the solid shaft. The angle of twist for torque T = 1.2 T Y .

Solution Summary: The author calculates the maximum elastic torque in the solid shaft, the angle of twist, and the polar moment of inertia of the shaft.

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The maximum elastic torque in the solid shaft.

The angle of twist in the solid shaft.

The angle of twist for torque T=1.2TY.

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Chapter 5 Solutions

The maximum elastic torque in the solid shaft. The angle of twist in the solid shaft. The angle of twist for torque T = 1.2 T Y .

Solution Summary: The author calculates the maximum elastic torque in the solid shaft, the angle of twist, and the polar moment of inertia of the shaft.

Concept explainers

Videos

The maximum elastic torque in the solid shaft. The angle of twist in the solid shaft. The angle of twist for torque T=1.2TY.

Want to see the full answer?

Chapter 5 Solutions

The maximum elastic torque in the solid shaft.

The angle of twist in the solid shaft.

The angle of twist for torque T=1.2TY.