A steel shaft is to be manufactured either as a solid circular or as circular tube. The shaft is required to transmit a torque of 1200 Nm without exceeding an allowable shear stress of 40 MPa, nor an allowable rate of twist of 0.75º/m. For G = 78GPa, determine: The required diameter do of the solid shaft. The required outer diameter d2 of the hollow shaft if the thickness t of the shaft is specified as one-tenth of the outer diameter.

A steel shaft is to be manufactured either as a solid circular or as circular tube. The shaft is required to transmit a torque of 1200 Nm without exceeding an allowable shear stress of 40 MPa, nor an allowable rate of twist of 0.75º/m. For G = 78GPa, determine: The required diameter do of the solid shaft. The required outer diameter d2 of the hollow shaft if the thickness t of the shaft is specified as one-tenth of the outer diameter.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.7.3P: A motor driving a solid circular steel shaft with diameter d = 1.5 in, transmits 50 hp to a gear at...

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Concept explainers

Torsion

In mechanical engineering, torque, torsion, and twisting moment are three of the most important concepts which have different meanings. Torque is the consequence of a moment of a force that produces an angular acceleration in a body or induces rotational kinetic energy in a body. For instance, in an automobile, the power transmission shaft is a body that is always under rotation due to the external torque acting on it, this torque is created by the engine.

Question

A steel shaft is to be manufactured either as a solid circular or as circular tube. The shaft is required to transmit a torque of 1200 Nm without exceeding an allowable shear stress of 40 MPa, nor an allowable rate of twist of 0.75º/m. For G = 78GPa, determine:

The required diameter d_o of the solid shaft.
The required outer diameter d₂ of the hollow shaft if the thickness t of the shaft is specified as one-tenth of the outer diameter.

The ratio of diameters (that is, the ratio d₂/d_o and the ratio of the weights of the hollow and solid shafts.

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