Structural Engineering & Statics
where the load goes
Concept

Ageing coefficient — where it appears

A factor of about 0.8 that lets one effective modulus stand in for concrete whose stress changes while it creeps. It weights the creep coefficient applied to the stress change, and its value depends on the kind of problem: near 0.8 for a growing restraint, nearer 1.3 for a strain held constant.

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

The stress that leaks away. A restrained shrinkage strain of 300 microstrain in concrete of modulus 32000 N/mm². Ignoring creep it produces 9.60 N/mm², which is above the tensile strength of 3.5 and predicts that every restrained concrete member ever cast has cracked. Counting creep by the superposition integral leaves 2.32 N/mm² after 27 years, and the one-line age-adjusted shortcut at the usually quoted ageing coefficient of 0.8 leaves 3.31. The two disagree — this creep function implies an ageing coefficient of 1.32, not 0.8 — and both are below the tensile strength, so the conclusion turns on counting creep at all rather than on how it is counted.

The strain that was imposed, and the stress that leaked away

Multiply a restrained shrinkage strain by the modulus and the answer is three times the tensile strength — which predicts that every restrained concrete member ever cast has cracked. Most have not, and the reason is that the material creeps while it is being stressed.

materials · Relaxation Stressed bay by bay, the beam keeps half its secondary moment. The secondary moment along a 4-span beam of 16 + 16 + 16 + 16 m prestressed with 2,400 kN on a parabolic tendon, straight between supports: stressed in one operation, stressed one bay at a time, and bay by bay after creep with a coefficient of 2.0. At the first interior support it is 350 kN·m stressed at once, 164 bay by bay and 307 after creep; at the next, 234, 160 and 216.

The beam stressed one bay at a time

A long continuous beam is rarely stressed in one pull. It is cast and stressed a bay at a time, each new length of tendon coupled to the last, and at every stage the structure is a different beam. The secondary moments the finished beam carries are the sum of what each stage did to the beam that existed then — about half of what the one-stage analysis gives — and creep spends the following years taking most of the other half back.

internal-forces · Secondary prestress

Named alongside it

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

CreepPrestressSuperpositionCarry-overConstruction sequenceContinuityCrackingImposed deformationIndeterminacyRelaxationRestraintSecondary prestress

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