Torsion (mechanics)

In the field of solid mechanics, torsion is the twisting of an object caused by an applied torque. Torque is a force that causes rotation. When an object undergoes torsion, it experiences strain, which is a type of angular deformation. This deformation is measured by the angle of twist, or how much a specific section rotates from its original equilibrium position.

Engineers must understand these forces to prevent machines from breaking. The internal resistance to this twisting is called torsional shear stress. This stress is measured in pascals (Pa) or pounds per square inch (psi). The torque itself is measured in newton metres (N·m) or foot-pound force (ft·lbf).

The way an object twists depends heavily on its shape and material. In circular rods or tubes with constant wall thickness, the torsion constant is equal to the polar moment of inertia. However, for other shapes, this constant can be much lower. If a cross-section is not circular, the twisting often causes a distortion known as warping. Warping occurs when the transverse sections of the object do not remain flat or plane.

To calculate these complex effects accurately, engineers often use finite element analysis (FEA). Other methods include the membrane analogy or shear flow approximation. The physical properties of the object are often expressed through torsional rigidity, which is the product of the torsion constant, the length, and the shear modulus. The shear modulus, also called the modulus of rigidity, is usually measured in gigapascals (GPa).

Understanding where stress occurs is vital for safety. The highest shear stress always happens on the outer surface of a shaft. This is because the radius is at its maximum at the surface. High stresses can be made even worse by stress concentrations, such as rough spots on the material. To increase the service life of a part, engineers often polish shafts to a fine surface finish. This reduces the maximum stress and helps prevent early failure.

The amount of twist can be calculated by looking at the torque, the length of the object, the shear modulus, and the torsion constant.

When a shaft is loaded only by torsion, the stresses can be broken down into principal stresses. Using a method called Mohr's circle, we can see that one principal stress will be in tension and the other will be in compression. These stresses sit at a 45-degree helical angle around the shaft. This leads to specific ways that materials fail. If a shaft is made of a brittle material, a crack will start at the surface and move toward the core. This crack travels in a 45-degree helical shape, much like twisting a piece of blackboard chalk.

For thin, hollow shafts, excessive load can cause a different failure called twisting buckling. This results in wrinkles forming at a 45-degree angle to the shaft axis.

Engineers use these mathematical principles to design massive industrial components. For example, consider the shaft of a modern steam turbine in a nuclear power plant.

These shafts may carry 1000 MW of power. In Europe, the electricity frequency is 50 Hz, while in North America, it is 60 Hz. This frequency helps determine the angular frequency of the rotation. For a large plant, the torque might reach 3.1831 million N·m. If the steel has a yield stress of 250 million N/m2, engineers must apply a factor of safety. By using a safety factor of 5, a shaft that might only need a 40 cm diameter could actually require a diameter of 69 cm to remain safe.

Specialized tools like the torsional resonator allow scientists to study the deeper properties of materials. A torsional resonator is an analytical system used to study the elastic or viscoelastic behavior of fibers. The setup typically involves a fiber fixed at one end and a rigid rod attached to the other. As the rod rotates, it introduces torsional deformation to the fiber. The fiber acts like a spring, and its motion can be described by its torsional stiffness and the moment of inertia of the system. This allows researchers to see how much energy a material dissipates during motion.

Most research focuses on viscoelastic materials, which show both elastic and viscous behaviors. An elastic material is one that restores its original shape after deformation because its energy is conserved. However, a viscous material loses some of its energy through dissipation and does not return to its original shape. Scientists use complex terms, like the complex modulus, to account for both of these behaviors. The real part describes the elastic behavior, while the imaginary term describes the viscous damping.

This helps researchers understand how energy moves through different substances.

This method of study has important applications in biology. For instance, researchers Valtorta and Mazza used a torsional resonator to study the properties of soft tissue. By observing how a fiber responds to biological materials, they could characterize the complex shear modulus of the tissue. This allows scientists to assess how much energy is dissipated within living things. Understanding these mechanics helps connect the physics of twisting to the fundamental way biological systems function under stress.