Structural Engineering & Statics
where the load goes
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Ladders — page 4

A field says what an essay is about. A ladder says what else there is to say about it — the distinct arguments that stand against one idea, from the one that introduces it to the one that assumes all the others.
real Mpeak 32.0a unit load, here and nowhere elseunit mM × marea ÷ EI = 213.33the unit load is the only place the question 'deflection where?' is asked

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.

1 rung · deflection 100 kNpeak 0.88Two points at maximum radiusthe radius rule finds the peak hereequal radius, stresses differ ×1

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.

1 rung · connections 0102030405060708090020406080100120140160angle between the weld and the load, degreescapacity, kN0° · 116.83 kN45° · 127.98 kN90° · 143.09 kN×1.22along

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.

1 rung · connections

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