Module 9 · Course notes
Three dimensions: twist, axes and load sharing
A flat drawing or a rendered model can hide what a structure really does in three dimensions. Loads that miss a line of resistance produce twist; a floor can rotate in plan as well as translate; and a member's behaviour depends on axes the picture may not show. This module trains you to look for the spatial response a two-dimensional view leaves out.
An eccentric load — one that misses the line, plane or centre that resists it — produces a twist or a rotation as well as a direct action. This single idea runs through three-dimensional behaviour: a wheel near one edge of a deck, a wind load offset from a building's stiffness centre, a load that misses a beam's shear centre — each adds torsion to the direct load.
A rigid floor diaphragm ties the vertical frames of a building together, forcing them to move as one. If the lateral load (wind or earthquake) passes through the centre of stiffness, the floor simply translates and every frame shares in proportion to its stiffness. If the load is offset, the floor *translates and rotates in plan* — plan torsion — and the frames take unequal shares, the far ones working harder.
Two more traps come from axes. A member's bending and torsion must be read in its own local axes, not inferred from how it looks on screen: a rendered member's deep-looking direction is not automatically its strong analytical axis. And an open section (a channel, an angle) has a shear centre that is not at its centroid — a load applied through the centroid still twists the member, because it misses the shear centre.
Worked example
Worked example — a load that misses the shear centre
An open channel section carries a transverse load. Whether it twists depends on where the load acts.
Step 1 — load off the shear centre
Apply the load through the web (near the centroid). For a channel the shear centre lies outside the section, away from the web. The load therefore misses the shear centre, so the member bends AND twists.
Step 2 — load through the shear centre
Now move the load out to the shear centre. The twisting is removed: the member bends only. The shear centre is exactly the point through which a transverse load causes no twist.
In the exercises, look for the twist, the plan rotation and the axis trap that a two-dimensional view leaves out.
How to read these problems
The three-step method
- 1Points of certainty. The deflected curve must pass through every support and deflect downward under the load. Mark what each support prevents before drawing anything.
- 2Deflected shape and reaction directions. Sketch the compatible deflected shape. To find a reaction's direction, imagine removing that support: the direction that pushes the structure back to its place is the reaction's sense (it may be a hold-down).
- 3Bending moment and contraflexure. Draw the bending-moment diagram on the tension side and check it against the shape: hogging where the curve is convex-up, sagging where convex-down, zero at pins and at every contraflexure.
Rules that must always hold
- 1.The bending moment is zero at a simple support and at an internal pin or hinge.
- 2.A bending-moment diagram crosses the baseline exactly at a point of contraflexure.
- 3.Under a distributed load the bending-moment diagram is curved; under point loads alone it is straight lines.
- 4.At a fully fixed support the deflected shape leaves the support with zero rotation (tangent along the member).
- 5.If a part of the structure stays straight after loading, it carries no bending moment there.
- 6.The moment is drawn on the tension side: sagging below the member, hogging above it.
Now predict for yourself
Three-dimensional behaviour exercises
13 exercises on grid load sharing, plan torsion of a diaphragm, the shear centre and local axes. Predict, then reveal an explanation.
Start the exercises →This lesson is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions.