An illustrated collection of essays about how structures carry load — equilibrium, trusses, bending, buckling and deflection, with every figure solved rather than sketched. https://www.structural-engineering-statics.com/ 2026-08-03T14:34:21.912Z https://www.structural-engineering-statics.com/essays/everything-adds-to-nothing/ 2026-08-03T14:34:21.912Z

A structure that stays put obeys two statements — the forces on it sum to zero, and so do the moments. Every number in the subject comes out of those two sentences.

https://www.structural-engineering-statics.com/essays/the-free-body-is-a-choice/ 2026-08-03T14:34:21.912Z

Cutting a structure open is not a step in the method. It is the method — and where the cut is made decides whether the answer takes one line or twenty.

https://www.structural-engineering-statics.com/essays/three-forces-must-meet/ 2026-08-03T14:34:21.912Z

A body held by exactly three forces has their lines of action concurrent. That is a theorem, it is enough to solve for direction and magnitude, and for a century it was done with a straightedge.

https://www.structural-engineering-statics.com/essays/counting-the-unknowns/ 2026-08-03T14:34:21.912Z

Two equations per joint, one unknown per member, one per restraint. Subtract, and the sign of the answer says whether the structure is a mechanism, solvable, or beyond what equilibrium alone can settle.

https://www.structural-engineering-statics.com/essays/the-triangle-that-cannot-fold/ 2026-08-03T14:34:21.912Z

A square of pinned bars is a mechanism. A triangle is not, and that single fact is the reason trusses exist and the reason they look the way they do.

https://www.structural-engineering-statics.com/essays/the-shape-that-carries-itself/ 2026-08-03T14:34:21.912Z

Hang a chain and it takes the one shape that carries its load in pure tension. Turn the shape upside down and it carries the same load in pure compression. That is what an arch is.

https://www.structural-engineering-statics.com/essays/depth-is-the-cheapest-strength/ 2026-08-03T14:34:21.912Z

Doubling the depth of a truss halves its chord forces without adding a gram of material to the chords. Nothing else in structural design is that cheap, and almost every structure has already spent it.

https://www.structural-engineering-statics.com/essays/what-a-cut-reveals/ 2026-08-03T14:34:21.912Z

Cut a beam anywhere and two quantities appear on the face — a shear force and a bending moment. Nothing was applied there. They are what the material was already doing.

https://www.structural-engineering-statics.com/essays/the-diagram-is-an-integral/ 2026-08-03T14:34:21.912Z

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.

https://www.structural-engineering-statics.com/essays/where-to-put-the-supports/ 2026-08-03T14:34:21.912Z

Moving the supports of a uniformly loaded beam inward by about a fifth of its length halves the worst bending moment. The load has not changed and nor has the beam.

https://www.structural-engineering-statics.com/essays/the-material-far-from-the-middle/ 2026-08-03T14:34:21.912Z

A strip of steel contributes to bending stiffness in proportion to the square of its distance from the centre. Move the same steel outward and the section gets stiffer for nothing.

https://www.structural-engineering-statics.com/essays/bending-is-a-pair-of-forces/ 2026-08-03T14:34:21.912Z

A bending moment is not a mysterious twisting. It is a push near the top of a section and a pull near the bottom, separated by a lever arm — a couple, made out of stress.

https://www.structural-engineering-statics.com/essays/the-same-steel-in-a-different-shape/ 2026-08-03T14:34:21.912Z

Four sections of identical area, identical weight and identical cost. The stiffest is dozens of times the stiffest of the flattest, and the only thing that changed was the arrangement.

https://www.structural-engineering-statics.com/essays/strong-enough-and-still-falls-over/ 2026-08-03T14:34:21.912Z

A column can fail at a fraction of the load its material could carry, by going sideways. Buckling is a failure of stability rather than of strength, and it is decided by geometry.

https://www.structural-engineering-statics.com/essays/the-ends-decide-the-length/ 2026-08-03T14:34:21.912Z

Four columns of identical height and section, buckling at loads sixteen times apart. Nothing differs but what is holding the two ends.

https://www.structural-engineering-statics.com/essays/the-load-that-makes-itself-worse/ 2026-08-03T14:34:21.912Z

A structure that has leaned carries its weight off the axis, which makes it lean further. The amplification is one over one minus the load ratio, and it runs away long before the buckling load.

https://www.structural-engineering-statics.com/essays/stiffness-is-not-strength/ 2026-08-03T14:34:21.912Z

A beam can be nowhere near failure and still be unusable, because it has moved too far. For most long-span members that limit arrives first, and stronger steel does not help at all.

https://www.structural-engineering-statics.com/essays/span-to-the-fourth/ 2026-08-03T14:34:21.912Z

Doubling a span multiplies its deflection by sixteen. No other relationship in ordinary structural work is that steep, and it is the reason long spans are always a different kind of structure.

https://www.structural-engineering-statics.com/essays/one-support-too-many/ 2026-08-03T14:34:21.912Z

Add a redundant restraint and the load has two routes to the ground. Equilibrium cannot say how it splits, and the answer turns out to depend on stiffness — which is a different kind of question.