Structural Engineering & Statics
where the load goes
Concept

Continuous beam — where it appears

A beam running over its supports rather than stopping at each one, so that the spans share their bending with each other. Continuity cuts the mid-span moment and creates a hogging moment over each support, and it makes the beam redundant so that stiffness decides the split.

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

00.20.40.60.810%20%40%60%80%100%shear, as a fraction of the web's capacitymoment capacity leftthe sectionthe web alone√(1 − v²)96.5%85.3%web 26.1% of the plastic modulus · M_pl 744 kNm · V_pl 959 kN

Both at once, and neither matters until it does

A section carrying shear has less moment capacity, and the reduction is the web's share of the plastic modulus times one minus the root of one minus the shear ratio squared. On a rolled beam that share is a quarter, so half the shear capacity costs three and a half per cent — and then the last tenth costs more than the first eight.

sections · shear moment interaction 0510152025-100-5050position along the beam (m)bending moment (kNm)-98.6-98.6hinges releasedsupports released

Choose what to take away

The other machine for a redundant structure works by removing restraints until what is left can be solved by statics, then putting back exactly enough force to close the gaps that opened. Which restraints are removed does not change the answer at all, and changes the arithmetic completely — one choice gives a tridiagonal matrix a person can solve on paper, and another gives a full one.

deflection · force method

Named alongside it

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

Bending momentBending stressCompatibilityEquilibriumFlangeFlexibilityForce methodIndeterminacyInteractionMatrixMoment distributionPlastic hinge

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