Where the load goes.
Every load applied to a structure reaches the ground by some route, and choosing that route is most of what design is. This is a collection of essays about tracing it — one idea at a time, illustrated to the point where the argument becomes visible, with every figure solved rather than drawn to look convincing.
Start anywhere
738 essays across nine fields, built around 313 ideas with a ladder of their own and 1298 named objects threaded through them. Browse every essay, or by thread, or by the figure family that drew it, or by search. There is also a list of what this site refutes, which is the shortest route in for anybody who has been taught the subject already.
Stability
The bearing is not a smaller bearing
An isolated building's bearings work displaced, sheared sideways by a large share of their own width, and the top plate then sits over only a lens of the bottom one. Design reduces the buckling load in proportion to the lens's area, which sounds like treating the bearing as a smaller bearing. It is not. Reducing every part of the section to that lens gives half the design rule's load, because the lens's bending stiffness falls far faster than its area. The rule works out close to a different and stranger object: a bearing whose rubber still shears across its whole area, while only its bending has moved to the lens.
Deflection
The load goes to the cable furthest along
Applied to one stiffening member, Castigliano's theorem halves or thirds its deflection and leaves its force alone, since there is only one member to carry it. A net has many, each at its own place on its own curve, and when the wrong energy has to divide a load among them it hands it to whichever is furthest along. The peak cable force comes out a fifth too high on one net and a quarter too low on another, by the same mistake. Only a net with no pretension at all gets the force right, and even that one gets the deflection wrong by a factor of three.
Materials
The angle that forgets the liner
Every filament-wound pressure vessel is laid at about 55 degrees, because a closed tube pulls twice as hard round its hoop as along its axis, and a fibre at that angle carries the two in exactly that ratio. Wrap those fibres over a steel liner and the ratio has stopped being the fibres' business, because the steel is carrying a share of each. Wound slack, the best angle is nearly a hoop and 55 degrees is the second-worst sensible choice. Wind it tight enough to squeeze the bore to its floor, though, and the helix returns, for a reason the fibres had nothing to do with: it is the only winding that also presses the steel along its length.
Dynamics
The fuse that makes the span work harder
A rock-fall canopy's beams hang on connections weaker than themselves, so it seems natural to let those connections be fuses: let them take the blows, replace them after a bad winter, and keep the beam clean. A falling weight is an energy, though, and a mechanism fixes how far its hinges turn relative to each other. Weaken the ends and each drop's energy has less moment to spend itself against, so every hinge turns further, and the one under the weight turns furthest. Under a big rock the fuse is the part of the beam that does less of the work, and it takes the span a third sooner to its limit. It keeps its promise only for the rocks too small to bend the span at all.
Equilibrium
A slip measures the slope it fell from
A slipped cutting is a full-scale shear test, and a railway has hundreds of them, so a line through all those points ought to be the clay's strength, with the scatter averaged away. It is not. Each slip's point lies on a ray whose slope is its own cutting's angle, whatever the clay, so the line through them reads mostly the slopes that were built and the pore pressure the analyst assumed. More slips only make the same wrong answer more precise. The clay is in the cuttings that stood, and at the line between what fell and what did not.
Internal forces
Nine piles and a third of the pull
A group of piles in settling ground settles several times further than one pile, because each pile drags the soil around its neighbours down with it. Put the same group in heaving clay and the same interaction runs the other way, and in the pile's favour. Each pile holds the clay back from its neighbours, the clay between them rises with the piles rather than past them, and the pile at the middle of a nine-pile square, which might have been expected to be pulled hardest of all, is hardly pulled at all. The tension that remains goes to the corners, and it is about half of what a pile alone would carry.
The fields
Six of them follow the order a load travels — it is applied, resisted by a form, carried as an internal force, met by a section, and then two things can go wrong. The other three are not steps on that route at all: each removes an assumption the first six are resting on. All nine.
Equilibrium
Nothing moves, so everything adds to nothing — and the free body decides what everything means.
Structural form
Trusses, cables and arches: the shapes that carry load by geometry rather than by bulk.
Internal forces
What a cut reveals — shear, moment and axial force, and the diagrams that track them along a member.
Sections and stress
How a cross-section resists a moment, and why where the material sits matters more than how much there is.
Stability
Strong enough and still falling over: buckling, slenderness, and loads that make themselves worse.
Deflection
Stiffness is not strength. What moves, how far, and why the answer goes as the fourth power of the span.
Materials
The assumption every other field rests on: that stress is the modulus times the strain, without limit and in both directions. It is not, and here is what happens instead.
Connections
Structures do not fail in the middle of a member. They fail where two of them meet — which is the one place the theory behind every other field explicitly does not hold.
Dynamics
Every other field assumes the load arrives slowly and stays. When it does not, the same structure gives a different answer — twice as large for a load put down suddenly, twenty-five times for one applied at the rate the structure likes, and unbounded for one the structure's own motion creates.
Threads running through
themes, not chapters
The load must go somewhere
Every force applied to a structure reaches the ground by some route. Choosing that route is most of what design is, and tracing it is most of what analysis is.
Geometry beats material
Moving the same steel further from the neutral axis, or making the truss deeper, buys more than making the steel stronger. Shape is the cheap variable.
The statics of things that do not move
Every result here is obtained by imagining a motion that does not happen and insisting the sums cancel. Nothing in the subject is measured directly.
One support too many
Indeterminacy: more restraints than equations. It buys robustness, costs a stiffness calculation, and makes a structure sensitive to things statics cannot see.
Which failure arrives first
A member can yield, buckle, deflect too far or shear through. The governing limit state is rarely the one being thought about.
Drawing as calculation
Force polygons, funicular shapes and Cremona diagrams solved real structures for a century. The drawing was not an illustration of the answer — it was the answer.
The load that will not hold still
Statics assumes a load arrives slowly and stays. Almost none of them do, and the same structure answers differently when they do not — bounded, if at all, by a damping ratio nobody designed.
Scale changes everything
Weight grows as the cube and strength as the square. A large structure is not a small one enlarged, and the difference is why bridges and beetles are built differently.