Structural Engineering & Statics
where the load goes
Concept

Biaxial bending — where it appears

Bending of a section about both its principal axes at once, produced by a load lying in the plane of neither. The two stresses add at the corner, and the neutral axis follows the moment ratio scaled by the ratio of the two second moments rather than the direction of the moment vector.

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

the axis the drawing suggestsneutral axis, -30.6°it moves this wayprincipal axes at 45.0° · I₁/I₂ = 3.90

Loaded straight down, and it moves sideways

Every section this collection has drawn had an axis of symmetry, and that symmetry has been doing silent work. Take it away and a vertical load produces a neutral axis that is not horizontal, a deflection that is not vertical, and on one ordinary section a sideways movement larger than the downward one.

sections · principal axes neutral axis, 70°moment, 5°489 N/mm²tan α = (M_z/M_y)(I_y/I_z), and I_y ÷ I_z = 30.8489 N/mm² at the corner against 258 for the same moment straight down

Two moments and a neutral axis that obeys neither

Tilt the load on a rolled beam by five degrees and the neutral axis swings by seventy. The section is doubly symmetric, its product of inertia is exactly zero, and none of that helps — because what decides the axis is the moment ratio multiplied by a stiffness ratio of thirty.

sections · biaxial bending

Named alongside it

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

Bending stressNeutral axisPrincipal axesInteraction diagramPlastic modulusProduct of inertiaPurlinRestraintSecond momentSecond moment of areaSection modulusServiceability

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