Structural Engineering & Statics
where the load goes
Concept

Overstrength — where it appears

The margin between a structure's actual strength and the strength its design assumed, arising from rounded sections, minimum requirements and redistribution. It is a reserve for the element that yields and a demand on every element intended to stay elastic, which is why capacity design treats it as a load rather than as a bonus.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

The two braces balance until one of them buckles. An inverted-V brace after the compression member has gone. While both braces are elastic they carry equal and opposite forces and their vertical components cancel on the beam above, which is why the beam in a chevron bay is usually sized for gravity alone. The compression brace buckles at 445 kN and then sheds most of what it was carrying — 30% is left here — while the tension brace goes on to yield at 1065. The difference between the two vertical components is 659 kN, applied at the middle of the span with no help from either brace, and it asks the beam for 1317 kNm against the 200 kNm the gravity load asks for — 6.6 times as much. The beam drawn does not: 1517 kNm against a capacity of 731. The force is not a load case anybody applies; it is what the frame leaves behind on its way to the state it will actually be in.

The force the brace leaves behind

Two braces meeting under a beam carry the storey shear as a tension and a compression whose vertical components cancel, so the beam above sees nothing. They cancel only while both braces are elastic. Once the compression brace buckles it sheds most of its force, the tension brace goes on to yield, and the difference is a point load at midspan that nobody applied.

structures · Chevron brace Where the demand crosses the capacity. Base shear against roof displacement for a eight-storey frame pushed with a triangular load pattern. It is elastic to 1994 kN, where the first storey reaches its shear capacity, and flattens as each of the others follows — 7 yield events in the order 3, 4, 2, 1, 5, 6, 7. The demand is a displacement rather than a force: the elastic spectrum at the building's own period of 0.93 s gives 173 mm, and the participation factor of 1.26 makes that 219 mm at roof level. Against an idealised yield of 70 mm that is a ductility demand of 3.10.

Pushed over until it will not stand

A structure in an earthquake is asked for a displacement rather than a force. A pushover answers a different question cheaply — how much base shear the frame has against how far its roof moves — and the whole art is in what happens when the two are laid over each other.

dynamics · Pushover The loop a brace has when it cannot buckle. Force against axial deformation for two braces with the same core area, cycled six times at a storey drift of 2 per cent. An ordinary brace yields at 900 kN in tension and buckles at 482 in compression — 54 per cent of it — and the buckled shape leaves a plastic hinge that does not straighten, so the compression side loses capacity every cycle and is at 12 per cent of its first value by the last. A restrained brace has a casing that carries no axial force at all and only holds the core straight, which decouples axial capacity from flexural stiffness — the coupling that makes a strut weaker than a tie — so it yields at the same force both ways and hardens instead. The energy dissipated is 2.07 times as much over the six cycles, and the casing has to satisfy one inequality: π²EI/L² above the fully hardened core force, 2.56 here, which is a buckling check on a member carrying nothing.

The brace that yields both ways

An ordinary diagonal yields in tension at its full strength and buckles in compression at half of it, and the buckle leaves a hinge that does not straighten. Stop it buckling with a sleeve that carries no load at all and the loop becomes symmetric.

dynamics · Buckling-restrained A bigger top column attracts more moment, and only the joint stops it. The top storey of the edge column of a braced six-storey frame — 4 m storeys, a 254 UC 89 below the splice and a 203 UC 60 above — carrying a 9 m beam at every floor on partial-strength joints of 261 kN·m, with each of seven columns that might be chosen for it: the moment its floor's edge joint delivers at the design load of 60 kN/m (dark) and at the beams' collapse load (light), against what the column can carry at its top end, its plastic moment reduced for the axial force (line). 203×203 UC 46: 148 and 195 against 167; 203×203 UC 60: 171 and 225 against 230; 203×203 UC 71: 189 and 247 against 283; 203×203 UC 86: 205 and 261 against 347; 254×254 UC 73: 218 and 261 against 352; 254×254 UC 89: 232 and 261 against 435; 254×254 UC 107: 243 and 261 against 527. A stiffer column attracts more of the joint's moment until the joint's 261 kN·m caps it; the lightest column that carries what it attracts at collapse is the 203 × 203 UC 60.

The column on the other side of the joint

A partial-strength joint is sold as a fuse: it caps the moment a beam can put into its support at the joint's own resistance. At an interior column that is true. At the edge of a frame the column is not a support that stays still; it is a spring in series with the joint, so the joint delivers less than its resistance in service and almost exactly what a rigid joint would. The column then carries three times the moment the simple-construction rule gave it, and at the top storey, where it stands alone and is lightest, it is weaker than the joint it was meant to be protected by.

connections · Joint classification

Named alongside it

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

DuctilityBucklingCapacity designHysteresisBraceBracingCapacity curveChevron braceContinuityDesign momentDriftEnergy dissipation

All concepts