Ladders — page 6
The slab that spans both ways
A panel supported on four sides sends its load in two directions at once, and the share is decided by a fourth power — so a panel a third longer than it is wide has already stopped being a two-way slab in any useful sense. What it does at collapse is a different calculation with a different answer.
What is left when the load comes off
Unload a section that has yielded and it does not return to nothing. It returns to a self-equilibrating stress field it did not have before, a permanent set, and an elastic range wider than the one it started with.
The machine that shakes the building
Put a machine on springs to keep its vibration out of the floor, and below a frequency ratio of root two the springs make things worse. Every transmissibility curve ever drawn passes through exactly one at that ratio, whatever the damping — so a soft mount either works well or fails badly, with nothing in between.
One deflection, without solving everything
To find how far one point of a structure moves, put an imaginary force of one unit there, multiply two moment diagrams together, and integrate. The answer arrives without ever solving for the deflected shape.
The wind that brings its own frequency
Every other load in this subject arrives at whatever rate it happens to arrive at. Vortex shedding arrives at a rate set by the wind speed — so for any chimney, mast or cable there is always a wind speed at which the shedding matches the structure exactly, and it is a breeze rather than a storm.
The section that cannot stay flat
Twist an I-section and its cross-section dishes out of its own plane. Stop that happening at one end and the member finds a second way to resist — the flanges bend in opposite directions — and the stress resultant that describes it has units nothing else in statics has.
The corner that is not the worst point
Check the point furthest from the centroid. It is the standard rule for a weld group under an eccentric load, it is exactly right for some shapes, and for others it misses the peak by sixteen per cent — or picks one of four points it cannot tell apart whose stresses differ by two thirds.
The weld that is stronger across than along
The same fillet weld, the same size, the same steel, carries twenty-two per cent more when the load runs across it than along it. The factor is exactly the square root of three over the square root of two, and it comes out of the yield criterion rather than out of a test.