Tension, compression, bending, torsion, and shear

In brief

Pull a rope taut and it stretches; stand a brick column under a roof and it squashes; bend a diving board and its top surface stretches while its bottom compresses; twist a screwdriver and the shaft resists turning; slide one playing card sideways against the one beneath it and the deck shears. These look like five different experiences, and mechanically they are, but every one of them is force acting on the internal structure of a material, and every real part in every real machine is doing some combination of these five things at once. Learning to separate them, tension, compression, bending, torsion, and shear, is what lets an engineer look at a part and say not just "this will fail" but "this will fail here, in this way, because of this specific kind of internal force," which is the difference between guessing at a fix and designing one.

The full treatment

First look: five things happening to one paperclip

Take an ordinary paperclip and do five things to it. Pull its two ends apart: that is tension, the material stretching along its length. Push the ends together instead, and if it does not simply bow sideways, that is compression, the material squeezing along its length. Hold one end and push down on the other so the clip flexes into a curve: that is bending, and notice the outside of the curve stretches while the inside squeezes, tension and compression happening simultaneously on opposite sides of the same piece. Grip both ends and twist them in opposite directions around the clip's own length: that is torsion. Finally, imagine slicing straight across the wire with scissors: the two faces of the cut slide past each other before separating, which is shear. All five loadings can be applied to the exact same piece of material, and each one stresses the wire in a mechanically distinct way, which is why the wire can survive one kind of loading comfortably and fail almost immediately under another.

Defining stress: force spread over the area that carries it

None of these five loadings can be compared fairly by force alone, because a thick rod and a thin wire pulled by the same force do not feel the same internal strain. What matters is stress, defined as force divided by the area over which that force acts (stress equals force divided by area). A ten-pound pull spread across a fat cable barely strains it; the same ten pounds concentrated on a wire a tenth as thick produces ten times the stress. Tension and compression produce normal stress, acting perpendicular to the cross-section being pulled or pushed. Shear produces shear stress, acting parallel to the surface being slid. Bending and torsion do not fit neatly into either category alone; they produce a stress that varies across the cross-section, which is the next idea to build.

Bending: why the surface works hardest and the middle barely works at all

When a beam bends, one surface stretches and the opposite surface compresses, and somewhere in between there is a line, called the neutral axis, where the material is neither stretched nor squeezed at all. The farther a layer of material sits from that neutral axis, the more it is stretched or compressed, so the outer surfaces of a bent beam carry by far the highest stress while the material near the center does very little work. This single fact is why structural beams are commonly shaped like an I, with most of the material pushed out to the top and bottom flanges, far from the neutral axis where it is most effective, and comparatively little material left in the thin web near the center where stress is low anyway.

Torsion: the twisting cousin of bending

Torsion behaves like bending's rotational sibling. Twist a shaft and the outer surface, farthest from the central axis, experiences the highest shear stress, while the very center of a solid shaft, on its own axis of twist, experiences almost none. This is why a torsion-loaded shaft is often made hollow, a tube instead of a solid rod: the material removed from the center was doing very little work anyway, so a tube of the same outer diameter as a solid rod loses little twisting strength while shedding significant weight, the same logic that shapes an I-beam applied to a rotating rather than a bending problem.

Shear: the sliding failure that hides inside the other four

Shear rarely shows up alone in ordinary parts, but it is present, often unnoticed, inside bending and torsion both, and it dominates certain connections outright: a bolt loaded so that two plates try to slide past each other is being sheared directly across its shank, not stretched along its length. Shear stress tends to concentrate at surfaces and joints rather than through the bulk of a member, which is exactly why fasteners, welds, and glued joints are so often the location where a structure actually gives way, even when the members they connect are comfortably strong in tension or bending.

Lineage

Galileo's 1638 analysis of a cantilevered beam is usually cited as the first serious attempt to reason about bending stress in a structural member, though his specific answer for where a beam breaks was later shown to be wrong by Edme Mariotte and others who correctly located the neutral axis. Robert Hooke's proportional relationship between force and stretch, published in 1678 as an anagram he later revealed to mean "as the extension, so the force," underlies the treatment of tension and compression used ever since. Charles-Augustin de Coulomb's eighteenth-century work on torsion in twisted wires and rods gave the subject its formal mathematical footing, and the nineteenth-century development of mechanics of materials as a discipline, driven by the need to design iron bridges and machinery with confidence, consolidated all five loading types into the unified framework taught today.

The strongest case for it

Sorting internal force into five categories works because the categories are not arbitrary labels, they correspond to genuinely different stress distributions inside a material, and each distribution has its own well-characterized failure behavior. A designer who identifies that a part is dominated by bending immediately knows to worry about the outer surface and can predict that adding material there, rather than at the center, gives the most strength per unit of added weight. The framework applies without modification from a paperclip to a bridge girder to a turbine shaft, because it describes the mechanics of the material itself rather than any particular object built from it, which is why it has remained the shared vocabulary of structural and mechanical engineering for two centuries.

The strongest case against it

Almost no real part experiences a single pure loading type in isolation; a bolt in a bracket is typically stretched, sheared, and bent all at once, and the categories are a simplification that must eventually be recombined to judge a real failure. The neutral-axis picture for bending assumes the material behaves the same in tension as in compression, which fails for materials like cast iron or concrete that are strong in compression but weak in tension, and for those materials the neutral axis itself shifts and the simple picture must be replaced. A common misconception is treating "the material is strong" as a single number; a material can be strong in tension and weak in shear, or the reverse, so the relevant strength depends entirely on which of the five loading types actually governs the part in question, not on strength in general.

Where it stands now

The five-way classification of internal loading, and the stress formulas built on it for simple shapes, remain the settled, load-bearing foundation of mechanics of materials, taught essentially unchanged since the nineteenth century because the underlying physics has not changed. What has advanced is the ability to handle combined loading in complex geometries, through numerical methods that superimpose the effects of tension, bending, torsion, and shear acting together on an irregularly shaped part, a computation the hand formulas were never meant to do alone but whose results are still checked against the same five basic categories.

Test yourself

A wrench is used to turn a stuck bolt: you push down on the handle while the bolt resists turning at the jaw. Identify which of the five loading types acts on the wrench's handle near where your hand grips it, which acts through the shaft connecting handle to jaw, and explain why the two locations are not carrying the same kind of stress even though it is a single, rigid tool. Then say where on the wrench's cross-section, near which surface, you would expect the highest stress to occur at each of those two locations, and why.