Structural Engineering & Statics
where the load goes
Concept

Moment diagram

5 essays name this object, across 4 fields. What follows is each of them, and the objects they name alongside it.
20H 10.0 M 22.2H 10.0 M 22.2the two base shears add to the applied 20 — the split came from stiffness, not staticsthe sway is exaggerated; a real frame at this load moves a fraction of a millimetre

The frame that leans, and what stops it

A rectangle of pinned bars folds flat. Make the corners rigid instead of adding a diagonal and it does not — which buys an unobstructed opening and costs bending in every member of it.

structures · portal frame 4 per unit lengthshear16.0moment32.0 at x = 4.00the moment peaks exactly where the shear passes through zero

The diagram is an integral, and that is why it can be drawn by eye

Load, shear and moment are one function and its two integrals. Once that is seen, the diagrams stop being things to calculate and become things to sketch.

internal-forces · diagram relations the station being watched, x = 3unit load, at its worst position2.100shaded: where a spread load must stand to make this quantity worstthe horizontal axis is where the load is, not where the beam is cut

The worst place to stand

A bridge is not designed for a load. It is designed for a load that moves, and for every station along it there is a different position of that load that does the most damage.

internal-forces · influence line 2000400060008000100001200002004006008001000distance between lateral restraintsthey cross at 3803the plastic capacity of the sectionelastic critical momentSt Venant torsion alone — what is left at long lengthswarping dominates here

The beam that fails sideways

A deep narrow beam bending in its strong plane can, at a moment well below its capacity, swing out of that plane and twist. The failure has nothing to do with how much it can carry and everything to do with what is holding it.

stability · lateral torsional real Mpeak 32.0a unit load, here and nowhere elseunit mM × marea ÷ EI = 213.33the unit load is the only place the question 'deflection where?' is asked

One deflection, without solving everything

To find how far one point of a structure moves, put an imaginary force of one unit there, multiply two moment diagrams together, and integrate. The answer arrives without ever solving for the deflected shape.

deflection · virtual work

Named alongside it

The objects these essays reach for when they reach for this one.

Area ruleAxle trainCompatibilityCompression flangeCritical momentDiscontinuityEffective lengthForce methodInfluence lineIntegrationJoint rigidityLateral restraint

All concepts