Structures

Statics is the case {a}{=}{0} of Newton's second law, and the two conditions it gives are enough to find what the ground pushes back with, until suddenly they are not.

A framework of pin-jointed bars carries load by axial force alone, and the same two equilibrium conditions applied joint by joint find every member force in it.

Cut a beam open and the exposed face carries an axial force, a shear force and a bending moment, all varying along the span according to two simple derivatives.

Dividing the internal force by the area that carries it turns kilonewtons into a number that can be compared against a laboratory test on a sample the size of a pencil.

Letting the material deform supplies the equations equilibrium cannot, and one measured constant, Young's modulus, links how hard you push to how much it moves.

The stress-strain curve stops being straight long before it stops, and every design stress in this course is one of its measured landmarks divided by a margin.

Twisting a shaft is the first case where the stress is not the same everywhere on the section, so how the material is arranged starts to matter as much as how much of it there is.

Plane sections stay plane, so bending stress varies linearly across the depth, and the resistance of a section turns out to be its second moment of area.

Because the bending moment changes along a span, the fibres of a beam must slide against one another, and the horizontal shear that resists it is what glue lines, nails and webs carry.

Curvature is the bending moment divided by the flexural rigidity, so integrating twice gives the deflected shape, sizes floors that would otherwise bounce, and solves beams statics cannot.

A slender strut in compression goes sideways at a load the stress calculation says is safe, and the load at which it does depends on stiffness and length, not on the strength of the material.

Real members carry several actions at once, and a point inside one is in a state of stress that needs three numbers, a transformation, and a criterion before it can be compared with a tensile test.

Write down the mass of a component that just meets its constraint and the material properties always group into a single index, which is what a selection rule maximises.