Structural Engineering & Statics
where the load goes
Concept

Tee-section — where it appears

A beam section with a wide flange on one face and a narrow web below it, the shape a floor unit or a beam acting with its slab takes. Its centroid sits near the flange, so its two section moduli differ widely and it is much stronger for one fibre than the other.

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

The four corners of an opening, on the tee's own interaction diagram. The plastic interaction of the tee left above and below a 400 × 300 mm opening — every point on it computed by sweeping the plastic neutral axis through the section rather than from an interaction formula. Its squash load is 1519 kN and its plastic moment 32.2 kNm. At the working load the global moment puts 301 kN into each tee — compression above the hole, tension below — and the shear puts the same Vierendeel moment of 6.3 kNm into all four corners. The line is the path the demand takes as the load rises, and it reaches the surface at a load factor of 3.89 against 1.49 for first yield at one corner: the elastic check is finding one corner and the mechanism needs all four.

Four corners and a mechanism

The check on a hole in a web adds an axial stress to a local bending stress and compares the sum with the yield stress at one corner. What ends the opening is four hinges arriving together — and the gap between the two is a factor that varies along the span from two and a half to exactly one.

sections · Web opening Each fibre has to earn its own prestress. For each section on a 12 m span carrying its own weight and 20 kN/m more: bars, the top and bottom moduli it has; ticks, the moduli its two pairs of limits need — the top fibre holding the service compression and the transfer tension, the bottom holding the service tension and the transfer compression, both from the same prestress. The symmetric I: top 28.9 against 17.4 needed, bottom 28.9 against 23.5 (× 10⁶ mm³) — a prestress exists; the tee: top 48.5 against 17.8 needed, bottom 22.7 against 24.0 (× 10⁶ mm³) — no prestress exists; the bulb-tee: top 46.0 against 17.7 needed, bottom 37.4 against 23.8 (× 10⁶ mm³) — a prestress exists.

The flange the prestress cannot use

The four stress limits on a prestressed section pair up by fibre: the bottom fibre has to hold the service tension and the transfer compression from the same force, and the top fibre the service compression and the transfer tension. Each pair is possible only if that fibre's own section modulus is large enough, whatever the eccentricity. On a symmetric section the two pairs are close to balanced. On a tee they are not: its wide flange multiplies the top fibre's modulus and hardly touches the bottom's, so a tee with half as much concrete again as a symmetric I cannot be prestressed for a load the I carries.

sections · Prestress limits

Named alongside it

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

Asymmetric sectionCellular beamInteraction diagramKernLoad factorMagnel diagramMechanismPlastic hingePlastic momentPlastic neutral axisPrestressPrestress losses

All concepts