Axial stresses

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An analysis of the state of stresses generated by torsion in twisted non-circular bars


One of the main problems that must be solved in the design of the machine components stressed in torsion is to establish their optimum shapes and dimensions in order to resist for a given twisting load. Also, in the case of some parts (crankshafts, ornamental bars, blades of screw propeller for torpedoes) manufactured by using plastic torsion as technologic operation the designer must determine the needed deformation energy. An important factor that has a direct implication on the designing methodology and on the resistance to torsion of these components is the state of stress generated by the twisting load application. Usually, the components that transmit or must support twisting moments are circular or tubular in cross-section, but in certain cases components with other than circular sections can be used. The present paper reviews the main aspects concerning the state of stress generated by elastic and plastic torsion in non-circular bars.


Torsion; State of stress; Shearing stresses; Axial stresses; Non-circular bars

1. Introduction

By considering a non-circular bar stressed in torsion, the following effects generated by the twisting load application are emphasized by the Theory of Elasticity in the twisted bar:

• the helical orientation of the initially straight fibres, especially, for large angles of twist;

• the warping of the plane cross-sections;

• the change in length of the material fibres and differences in length from a deformed fibre to another;

• the modification of the initially right angle between the deformed fibre and the section normal to it.

One of the main factors that generates or influences these effects is the state of stress, which occurs in bars during torsion.

Relating to this state of stress generated by torsion, the Theory of Elasticity and Plasticity discusses, generally, about the shearing stresses that act on the cross-sections of the twisted bars.

1.1. Remark

The solutions for the problems concerning the shearing stresses magnitude and distribution on the cross-sections of elastic, elastic-plastic and plastic twisted bars, circular or non-circular in cross-section, can be found in Refs.[1],[2],[5],[6],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17]and[18].

Some authors analyzed the possibility that axial stresses to be developed in certain conditions in the twisted bars. Thus, an experimental analysis concerning the development of axial stresses during hot torsion tests, for the case of round samples twisted for different ranges of temperature, is presented in Ref.[7]. According to the obtained results it has been concluded that hot torsion develop in twisted bars axial stresses whose distribution and magnitude depend on temperature range. Some aspects relating to the generation of axial stresses in the twisted non-circular bars are also discussed in Ref.[3].

The knowledge of the values and distribution of the stresses in a twisted bar is of a great importance for the designing and manufacturing processes of different machine components.

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