Hey it's a me again @drifter1! Today we continue with Physics and more specifically the branch "Classical Mechanics" to continue with the chapter of Equilibrium and Elasticity. In this article we will get into Cross-Sectional Stress and Strain. So, without further ado, let's dive straight into it!
Shear Stress
Shear stress arises from parallel forces that tend to cause deformation along a plane or planes parallel to imposed stress. What differentiates shear stress from "normal" stress is that "normal" stress arises from forces perpendicular to a cross-sectional area of the material, whilst shear stress is parallel to the cross-sectional area. Such forces cause the material to rotate about the application point.
Mathematically, the shear force per unit area on the face of a cross-section is defined as:
The most common symbol of shear stress is τ (tau). Shear stress is measured in force per unit area (N/m2) or pascals (Pa).
Shear Strain
The deflection of a point B per unit length, as a result of shear stress, is defined as shear strain. Its equal to the translation of point B, x, divided by the initial height of the material, L. Mathematically speaking:
Shear strain γ is positive when it causes the right angle of the 1st quadrant to decrease. In the same way, shear strain is negative if it causes that same angle to increase. The angle is measured in radians, which is a non-unit, making shear strain dimensionless.
Shear Modulus
In the same way as we defined Young's modulus for tensile stress and strain, and Bulk's modulus for volumetric stress and strain, we can also define a modulus for shear stress and strain. Shear Modulus is a value that can be used for measuring the ability of a material to withstand shear stress. Shear Modulus is also defined as the modulus of rigidity. Mathematically:
G, shear modulus
τ, shear stress
γ, shear strain
For the most metals we can approximate the Shear Modulus, G, using Young's Modulus, E, by using the formula:
