Shear stress

Shear stress is a specific type of force acting within a material. It occurs when a force is applied parallel to a material's cross-section. This is different from normal stress, which acts perpendicular to a surface.

Scientists often use the Greek letter tau to represent shear stress. Understanding this concept is vital for engineering and physics. It helps us predict how solids deform and how fluids flow.

To calculate the average shear stress, you must use a specific formula. You take the shear force and divide it by the cross-sectional area.

The force must be the component that is coplanar with the section. If you apply force to the top of a rectangular block while the bottom stays still, the shape tilts. This deformation turns the rectangle into a parallelogram. This process shows exactly how the internal layers of a material slide against one another.

There are several distinct types of shear stress used in different fields. Beam shear is the internal stress found inside a beam when a force is applied.

In semi-monocoque structures, engineers divide the cross-section into parts. They use stringers to carry axial loads and webs to carry shear flows. You can find the maximum shear stress by looking at the web with the minimum thickness. There is also pure shear stress, which relates to the shear modulus of an isotropic material. This involves Young's modulus and Poisson's ratio in its calculation.

History shows how our understanding of these forces has grown. In 1855, Dmitrii Ivanovich Zhuravskii derived a formula for beam shear. This is now known as the Zhuravskii shear stress formula. In the study of fluids, Isaac Newton provided a foundation with his constitutive law. For Newtonian fluids, the shear stress is proportional to the strain rate. This relationship relies on a constant called dynamic viscosity. In these specific fluids, the viscosity does not change even if the flow velocity changes.

Shear stress is highly significant in both natural and human-made environments. In biology, wall shear stress is a factor in arterial blood flow. It can affect the atherogenic process within our blood vessels. In civil engineering, the weight of an earth-filled dam can cause subsoil to fail. This failure can result in a collapse similar to a small landslide. Even in solid objects, like a round bar, impact can create maximum shear stress.

Fluid dynamics provides many examples of how shear stress operates. When a fluid moves along a solid boundary, it experiences wall shear stress. A rule called the no-slip condition states that fluid speed at the boundary is zero. However, the fluid moves faster as you move away from that boundary. The region between the stationary boundary and the faster flow is the boundary layer.

For non-Newtonian fluids, the viscosity is not constant, meaning the stress and velocity do not have a simple linear relationship.

Scientists use advanced technology to measure these invisible forces. One method uses diverging fringe shear stress sensors. These sensors use light beams and parallel slits to create an interference pattern. By observing how particles move through these fringes, researchers can calculate the velocity gradient. Another method uses micro-pillar sensors made of a polymer called polydimethylsiloxane. These tiny, flexible pillars bend when they feel the drag forces of a nearby fluid. There is also the electro-diffusional method, which uses microelectrodes to measure the shear rate in a liquid phase. All these tools help us map the complex movements of the physical world.