Time to read: 6 min
Introduction to Torsional Stress
Torsional stress is a specific type of shear stress that a body experiences when subjected to a twisting force. Unlike other loading mechanisms, torsional stress involves a torque load applied transversely rather than longitudinally. A practical example of torsional stress can be observed in a car’s axle, where the engine/gearbox applies a turning force, and the wheels resist this turning, inducing torsional stress around the axle's center point.
Understanding the physics of torsional stress is crucial for predicting the performance of load-bearing shafts or bodies. Torsional stresses can lead to either elastic or plastic deformation in a shaft, which is why shafts must be designed to effectively resist such stresses.
How Torsional Stress Operates
Torsional stress operates similarly to a bending moment by applying a force at a distance along a lever arm. The key difference is that while a bending moment applies force parallel to the axis, torsional stress applies force perpendicular to the axis of rotation, resulting in a twisting force.
Torsional stress is often caused by a force couple acting around the center point of a shaft. A force couple consists of two forces that act at the same distance from the point of rotation in opposite and equal manners. Examples of torsional stress caused by a force couple can be found in rotating elements such as car axles, gear shafts, drills, mandrels, and wind turbine generators. In all these cases, torsional stress affects the object along its entire axis.
It's important to note that torsion does cause shear stress because the force applied is not uniform between the point of force application and the point of rotation. Instead, the force starts at zero at the point of rotation and increases gradually along the radius to the point of force application.
Torsional Stress vs. Normal Stress
Normal stress, such as compression or tension, acts perpendicular to the cross-section of an object. In contrast, torsional stress works perpendicular to the cross-section about a center point. For compression and tension to occur, forces must act concentrically. If the forces are not concentric, a shear force is induced, whereas torsional forces only need to be parallel, opposite, and an equal distance from the midpoint.
The Torsional Stress Formula
The magnitude of torsional stress depends on several factors, including the distance of the applied force from the center of rotation, the twisting moment, and the polar moment of inertia. These factors are all considered in the equation for torsional stress:
t=T?rJt=JT?r
Where:
- tt represents torsional stress,
- TT is the transmitted torque,
- rr is the distance from the center of rotation,
- JJ is the polar moment of inertia area.
The radius is measured in meters, and torsional stress is given in newton meters or pascals (Pa). To calculate torsional stress, the formula must be used after identifying the values for the variables: the distance between the applied load and the center of rotation, the torque being transmitted, and the polar moment of inertia area. These values are then substituted into the torsional stress equation to yield a value in pascals.
Several assumptions must be true for the torsion equation to effectively analyze the torsional stress of an object:
- The material must be uniform throughout the body.
- The load should be uniformly distributed along the shaft axis.
- The torque must not exceed the material's elastic deformation.
- The shaft cross-section must be circular.
- The length of the shaft must remain unchanged during loading.
Torsional Stress vs. Bending Stress
Both bending and torsional loads are moments, where a force is applied at a distance along an arm. However, torsional stress is caused by a force that acts transversely about an axis of rotation, causing the body to rotate. In contrast, bending stress acts longitudinally to an axis, causing the body to bend along its axis.
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