Q.Three kinds of stress can act on a body: tensile (or compressive) stress, shearing stress, and hydraulic (volume) stress. Explain, with one everyday or laboratory example of each, how the deforming force is applied differently in each case and what kind of deformation (change in length, change in shape, or change in volume) each one produces.

Tensile (or compressive) stress is produced when a force is applied along the length of a body, either pulling its two ends apart (tensile) or pushing them together (compressive). Example: hanging a weight from the lower end of a vertical wire stretches the wire -- the wire gets longer, but its overall cross-sectional shape stays essentially unchanged. The corresponding strain is the fractional change in length, $\Delta L/L$.

Shearing (or tangential) stress is produced when a force is applied parallel to a surface of the body, typically to one face while the opposite face is held fixed. Example: pushing sideways on the top cover of a closed book resting on a table, while the bottom cover stays fixed by friction against the table -- the book's pages shift relative to each other, and the whole stack leans over into a slanted, parallelogram-like shape, with no change at all in the total volume of pages. The corresponding strain is the shear angle, $\theta \approx \Delta x/L$.

Hydraulic (or volume) stress is produced when a uniform pressure acts on every point of a body's surface at once, as happens to any object submerged in a fluid. Example: a submarine hull deep underwater experiences a uniform inward pressure from every direction, squeezing it into a very slightly smaller version of exactly the same shape -- there is a change in volume, but (ideally) no change in shape at all. The corresponding strain is the fractional change in volume, $\Delta V/V$.

For each stress type, identify (i) how the force is applied relative to the body's surface, and (ii) which single geometric property of the body -- length, shape, or volume -- changes as a result, holding the other two effectively fixed.

• Confusing shearing stress with compressive stress, since both can involve forces applied "sideways" to some part of the body in a loose everyday sense -- the defining test is whether the force is tangential (parallel) to the surface (shear) or normal (perpendicular) to it (tensile/compressive).
• Thinking hydraulic stress requires a liquid specifically -- it applies equally to a gas exerting uniform pressure on a body's surface.