Structural systems

Following the load: what loads act on it, where each enters, which members carry it, and how it reaches the ground. Describing its appearance is not analysis.

In bending the stress is highest at the outer surfaces and nearly zero on the neutral axis, so material in the middle would add mass and carry almost nothing — the same reason an I-beam has thick flanges and a thin web.

Pure tension: no member is ever pushed, so nothing can buckle and every strand can be extremely thin. The same principle as a suspension bridge or a bicycle spoke.

A member carrying nothing is mass, cost and an extra joint that can fail, for no return — usually the fastest improvement available in an existing product.

The allowable load is exactly the load at which the structure fails, so any variation at all — material, manufacture, use or age — causes failure.

Nothing is made exactly to drawing, no material is exactly as published, no load is exactly as calculated, and nothing stays as strong as it started.

Up: a severe consequence, uncertain or dynamic loads, an inconsistent material, a part that cannot be inspected. Down: certainty, consistency, inspection, and a margin that costs a lot of mass.

Loads are known precisely, material is tested batch by batch, every part is inspected on a schedule, and every kilogram costs fuel for the life of the aircraft.

What carries the load. A frame carries it along slender members meeting at joints; a shell through a thin curved surface; a solid through its bulk, mostly in compression.

Ask what a hole would do. A frame loses one member, which bracing may cover. A shell loses most of its stiffness, because the surface was the structure.

A four-bar rectangle folds into a parallelogram with no member changing length. A diagonal makes two triangles, and a triangle cannot change shape unless a member stretches or shortens.

It carries load in bending, which is the weak way. Curvature, a fold or a rib converts bending into in-plane forces, which is what makes a shell stiff.

The supports: a pin lets the beam rotate there, a fixed end does not, a cantilever has one support only, a continuous beam has three or more.

A simply supported beam in the middle; a cantilever at its root; a fixed beam at the ends as well as the centre; a column sideways, by buckling.

A bracket is a cantilever and the bending moment is largest at its root and zero at its tip, so material is placed where the bending is.

It becomes unstable sideways at a load far below its crushing strength. Doubling its length makes it about four times easier to buckle, so shortening or bracing it helps far more than a stronger material.

Compression squashes, tension stretches, shear slides one part across another along a plane, torsion twists about the long axis, and bending stretches one face while squashing the other.

A loaded beam is in tension along one face and compression along the other, with a neutral axis between where the stress is zero — which is why an I-beam has thick flanges and a thin web.

Static forces are steady — self weight, a shelf of books, a parked car. Dynamic forces change — a person walking, wind gusting, a door slammed — and they cause fatigue at a fraction of the static load.

A closed section carries the twist as a continuous shear flow all the way round. Slotting it lengthways breaks that loop, so torsional stiffness collapses while bending stiffness barely changes.

Stress is the force divided by the cross-sectional area carrying it. Strain is the extension divided by the original length, so it has no units.

The elastic region, whose gradient is Young's modulus; the yield point where deformation becomes permanent; the ultimate strength at the peak; and fracture at the end.

Past yield the deformation is permanent. A part loaded to its ultimate strength has not broken, but it has deformed for ever — which for almost every product is already a failure.

Stiffness, which is the gradient of the elastic line. A stronger material with the same modulus deflects just as much; section depth is what changes deflection.

The gradient of the elastic line on a stress-strain graph — stress divided by strain. It measures stiffness: how little a material deflects under load.

A door seal that fills a varying gap and recovers; a snap-fit catch that bends to click and springs back; a suspension bush or grip that absorbs vibration.

Steel is about three times stiffer than aluminium, while doubling a beam's depth is worth roughly eight times — so changing the section is almost always cheaper and lighter.

Load follows stiffness, so the stiff part carries almost all of it — which is how a metal insert ends up taking the entire load in a plastic housing.

The forces sum to zero in every direction, and the moments sum to zero. Balanced forces alone still allow a structure to rotate.

A force multiplied by its perpendicular distance from a pivot. Doubling the distance doubles the turning effect for the same force.

Tipping, when the weight's line of action falls outside the support base; sliding, when a horizontal force beats friction or the fixings; and material failure, when a member yields, fractures, shears or buckles.

Two of the three failure modes — tipping and sliding — have nothing to do with strength, and no stronger material prevents either. Both are fixed by geometry, friction or a fixing.

Struts and ties, shape, lamination, and composite materials. Three of the four add almost no material.

It uses the same material formed differently, and bending stiffness rises with the cube of depth — so a fold, a rib or a tube buys enormous stiffness for no extra material.

Thin layers are bonded with alternating grain, so the weak direction of one layer is the strong direction of the next. It also resists splitting and warping and allows curved forms.

From the bottom hinge corner up to the top latch corner, so it works in compression. The other way it is in tension and a timber joint pulls apart.

The ratio of a structure's absolute strength — the load at which it actually fails — to the allowable load it is designed to carry. Allowable load = absolute strength ÷ SF.

Material variation, manufacturing defects, users overloading or misloading the product, degradation over time from corrosion and fatigue, and the assumptions made in the calculation.

The consequence of a failure, the certainty of the loads, and whether the part can be inspected. A rope carries a far larger factor than a shelf bracket.

It means more material, mass, cost and embodied impact, and sometimes a product that is worse to use. An over-specified part is a design failure, not a cautious success.