Structural Engineering & Statics
where the load goes
Concept

Cantilever — where it appears

A member supported at one end and free at the other, whose root moment is the whole of the load times its distance from the support. It is the arrangement with the largest moment for a given span and load, which is why it appears as a construction condition far more often than as a finished one.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The corner columns take what the middle ones did not. Axial stress in the columns across one flange face of a 30 by 40 m framed tube, at the base. Plane sections says the flat line: every column on the face at the same distance from the neutral axis, therefore at the same stress. The solved distribution is the curve — 69.4 N/mm² at the corner against 18.2 in the middle, a ratio of 3.81. The middle columns lag because the only route the axial force has into them is the in-plane shear of the spandrel frame, bay by bay from the corner. The face is carrying its resultant on an effective width of 51 per cent, and the tube deflects as though its second moment were 72 per cent of the gross.

The corner columns take more than their share

A framed tube is a hollow cantilever, and a hollow cantilever's flange ought to be uniformly stressed. It is not, and the reason is that the only route the axial force has into a column in the middle of a face is the in-plane shear of the frame — one bay at a time, from the corner inwards.

structures · Framed tube Every section is hogged and sagged before the bridge exists. The bending moment envelope of a launched deck, section by section along its own length, taken over every position of the launch. In service each section has one sign; during the launch 100 per cent of them see both, because each passes over every pier and through every span on its way out. The worst launch moment is 42568 kNm against 40500 in service, and with no launching nose at all it would be 185977. That is why a launched bridge is a constant-depth box with symmetric flanges: the design case is not a load, it is a history.

Every section was somewhere else

A bridge pushed out over its piers subjects each of its cross-sections to a history rather than to a load case. Every one passes over every support and through every span, so the design envelope is the envelope of envelopes — and no in-service condition produces it.

structures · Launched bridge

Named alongside it

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

BracingConstruction sequenceContinuityCorner columnDriftEffective widthFramed tubeHoggingLateral systemLaunching noseLoad arrangementMoment envelope

All concepts