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The torsion constant or torsion coefficient is a geometrical property of a bar's cross-section. It is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous linear elastic bar. The torsion constant, together with material properties and length, describes a bar's torsional stiffness.
The shear stress at a point within a shaft is: = Note that the highest shear stress occurs on the surface of the shaft, where the radius is maximum. High stresses at the surface may be compounded by stress concentrations such as rough spots. Thus, shafts for use in high torsion are polished to a fine surface finish to reduce the maximum stress ...
Torsional stresses: = where is the torsional shear stress, is the applied torque, is the distance from the central axis, and is the polar second moment of area. Note: In a circular shaft, the shear stress is maximal at the surface of the shaft.
The formula to calculate average shear stress τ or force per unit area is: [1] =, where F is the force applied and A is the cross-sectional area.. The area involved corresponds to the material face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force.
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.
is the average shear stress, is the shear force applied to each section of the part, and is the area of the section. [1] Average shear stress can also be defined as the total force of as = This is only the average stress, actual stress distribution is not uniform.
The attempts to provide precise expressions were made by many scientists, including Stephen Timoshenko, [12] Raymond D. Mindlin, [13] G. R. Cowper, [14] G. R., 1966, "The Shear Coefficient in Timoshenko’s Beam Theory", J. Appl. Mech., Vol. 33, No.2, pp. 335–340.</ref> N. G. Stephen, [15] J. R. Hutchinson [16] etc. (see also the derivation ...
Assuming that the direction of the forces is known, the stress across M can be expressed simply by the single number , calculated simply with the magnitude of those forces, F and the cross sectional area, A. = Unlike normal stress, this simple shear stress is directed parallel to the cross-section considered, rather than perpendicular to it. [13]