Equal torques are applied to thin-walled tubes of the same length L same thickness t, and same r

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Equal torques are applied to thin-walled tubes of the same...

Key Concepts

Torsional Rigidity and Torsional Constant

Torsional rigidity, defined as the product of the shear modulus and the torsional constant (GJ), measures a member’s resistance to twisting. For thin-walled members, the torsional constant is derived from the geometry of the cross-section and is distinctly different for closed sections (which involve an additional contribution from the enclosed area) compared to open sections. This concept directly influences both the maximum shear stress and the angle of twist for a given torque.

Shearing Stress in Torsion

Shearing stress under torsion is the internal resistance to twisting, arising from the applied torque and the geometry of the cross-section. In thin-walled tubes, the maximum shear stress can be evaluated using approximations based on the wall thickness, enclosed area, and distribution of the shear flow, with closed and open sections exhibiting different stress concentrations due to their distinct boundary conditions.

Angle of Twist

The angle of twist is the rotational displacement of a member along its length due to applied torque, and it is calculated by dividing the torque by the torsional rigidity and multiplying by the member’s length. Differences in cross-sectional geometry, such as having a slit (open section) versus a closed tube, result in variations of the torsional constant and thus lead to different twist angles under the same loading conditions.

Torsion of Structural Members

Torsion refers to the twisting of a structural element due to an applied torque, resulting in shear stresses distributed across the cross?section. Analysis of torsion involves understanding how a given moment produces rotational deformation, and it forms the fundamental basis for determining both shear stress distribution and angular deflection in shafts and tubes.

Thin-Walled Tube Theory

In thin-walled structures, the wall thickness is small relative to other dimensions, which allows for simplifications in analysis. This theory assumes that the shear stress is uniformly distributed across the wall thickness and that stress concentrations can be ignored. It permits the use of mean geometric properties and closed versus open section distinctions to calculate torsional responses accurately.

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