Structural Engineering & Statics
where the load goes
The route a load takes

Fields

Seven areas, in the order a load travels through a structure — and one that is not a step on that route at all, but the assumption the other six are resting on.
A beam, its loads and its reactions. A free body: the beam cut away from everything it touches, with the forces that were doing the touching drawn on it. The reactions are computed from the loads, so their arrows are to scale relative to each other.

Equilibrium

Nothing moves, so everything adds to nothing — and the free body decides what everything means.

54 essays A Pratt truss of 6 panels. A Pratt truss under equal panel-point loads. The joint equilibrium equations were assembled and solved; 10 members came out in tension, 9 in compression and 2 carrying nothing.

Structural form

Trusses, cables and arches: the shapes that carry load by geometry rather than by bulk.

55 essays The same beam, cut at x = 5. A beam separated at one station. On the exposed face a shear force and a bending moment appear, equal and opposite on the two pieces, with values obtained by summing the forces on whichever piece is easier.

Internal forces

What a cut reveals — shear, moment and axial force, and the diagrams that track them along a member.

56 essays Every strip counts by the square of its distance. A rectangular section divided into equal strips, with each strip's contribution to the second moment of area drawn beside it. The strips are identical in size; only their distance from the neutral axis differs.

Sections and stress

How a cross-section resists a moment, and why where the material sits matters more than how much there is.

54 essays The column curve. Failure load against slenderness, as a fraction of the squash load. A stocky column crushes; a slender one buckles at the Euler load; the crossover is where the two curves meet, and real columns fall below both near it.

Stability

Strong enough and still falling over: buckling, slenderness, and loads that make themselves worse.

54 essays Which limit arrives first. Utilisation of the strength limit and of the deflection limit, against span. Strength grows as the square of the span and deflection as the fourth power, so the two cross — and past the crossing a beam is sized by how far it moves rather than by what it can carry.

Deflection

Stiffness is not strength. What moves, how far, and why the answer goes as the fourth power of the span.

54 essays Three materials pulled until they stop. Three stress-strain curves — mild steel, high-strength steel, aluminium alloy — plotted to a strain of 2.0%. One of them has a plateau, so the stress at which yielding starts is something the specimen does rather than something anyone chooses. The 0.2% offset construction is drawn on the high-strength steel: a line of slope E from a strain of 0.002, cutting the curve at 460 N/mm².

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.

54 essays A bolt group under an eccentric load. A 3 by 2 bolt group carrying 100 kN at 150 mm from its centroid, with the resultant force on each bolt drawn to scale, by the elastic vector method. The load is shared equally and the torque is not, so the worst bolt carries 50.37 kN against 16.67 kN of direct shear alone — 3.02 times as much.

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.

54 essays 20 kN applied at once and held, on a structure of 0.500 s period. Displacement against time for a single-degree-of-freedom structure of natural period 0.500 s and 2.0% damping, under 20 kN applied at once and held. The static deflection under the same peak force is 12.67 mm and the peak response is 24.56 mm — a factor of 1.94.

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.

54 essays

A field says what an essay is about, and the order above is the order a load travels: it is applied, it is resisted by a form, it becomes an internal force, it meets a section, and then two things can go wrong — the member buckles, or it moves too far. The last three sit after that route rather than along it, and each removes an assumption the other six rest on: that stress is the modulus times the strain, that a joint is a point, and that the load arrives slowly and stays. Threads say what an essay rhymes with, ladders say how deep one idea goes, and the concept index says which essays name the same objects.