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Can anyone tell me what equation I need to use to determine the torsional shear stress using the thin cylinder theory to a copper cylinder which is under pressure and a twisting force (torque).
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Thin Cylinder Theory is a method used in engineering and physics to calculate the stresses and strains in a cylindrical object subjected to torsion, or twisting. It assumes that the cylinder is thin-walled and the thickness is much smaller than the radius of the cylinder. This theory is used to determine the distribution of torsional shear stress along the length of the cylinder.
Thin Cylinder Theory takes into account the material properties of the cylinder, such as its elasticity and shear modulus, as well as the geometry of the cylinder, including its radius and length. It also considers the applied torque and the resulting shear stress on the cylinder.
In addition to assuming that the cylinder is thin-walled, Thin Cylinder Theory also assumes that the material is homogeneous, isotropic, and in a state of pure torsion. It also assumes that the cylinder is subjected to a constant and uniformly distributed torque.
According to Thin Cylinder Theory, the torsional shear stress is assumed to be distributed in a linear manner along the length of the cylinder. This means that the shear stress is directly proportional to the distance from the axis of the cylinder, with the highest stress occurring at the outer surface of the cylinder.
Thin Cylinder Theory is commonly used in the design and analysis of structures and components that are subjected to torsional loads, such as drive shafts, propeller shafts, and turbine blades. It is also useful in predicting the failure of thin-walled pressure vessels and pipes due to torsional stresses.