12.9: Problem Solving on Stress and Strain
Stress is a quantity that describes the magnitude of a force that causes deformation, generally defined as internal force per unit area. When forces pull on an object and cause its elongation, like the stretching of an elastic band, it is called tensile stress. When forces cause the compression of an object, it is known as compressive stress. When an object is being squeezed uniformly from all sides, like a submarine in the depths of the ocean, we call this kind of stress bulk stress (or volume stress). In other situations, the acting forces may be neither tensile nor compressive and still produce a noticeable deformation. For example, suppose you are holding a book tightly between the palms of your hands. Then, with one hand, you pull the front cover away from you, while with the other hand, you pull the back cover toward you. In such a case, when deforming forces act tangentially to an object's surface, they are known as 'shear' forces, and the stress they cause is called shear stress.
The concepts of shear stress and strain are concerns in solid objects or materials. Buildings and tectonic plates are objects that may be subjected to shear stresses.
Shear deformation occurs when two antiparallel forces of equal magnitude are applied tangentially to opposite surfaces of a solid object, causing no deformation in the transverse direction to the line of force. Shear deformation is characterized by a gradual shift of layers with respect to one another in the direction tangential to the acting forces. This gradation occurs over some distance within the object.
Shear strain is defined by the ratio of the largest displacement to the transverse distance. The largest displacement occurs in the direction parallel to the applied forces. It is caused by shear stress, which occurs due to forces that act parallel to the surface. The shear modulus is defined by the ratio of stress to strain.
