Structural Engineering & Statics
where the load goes
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The load must go somewhere — page 3

Essays 49 to 52 of 52 on this thread, in the same order.
webb = 3.00 mb_eff = 2.531 mfree edgedrawn flange 2 × 3.00 m = 120000 mm² at 20 mm thickworking flange 2 × 2.531 m = 101238 mm², on a span of 20 m18762 mm² is there, and paid for, and carrying almost nothing Sections and stress

The flange that is not all there

Stress can only get into a wide flange through shear along its junction with the web, and shear takes distance to do it. So the width that is working is set by the span, and a flange 3 m wide on a 20 m span has 18762 mm² of steel that is there, and paid for, and hardly carrying anything.

 00.20.40.60.811.2020406080100120140160midspan sag (m)total load on the cable (kN)the design load, 150 kNsolved 0.740 m1.125 mtangent here 341.2 kN/mk₀ = 8T₀/L = 133.3 kN/mthe flat-cable law Structural form

The stiffness that comes from the shape

A cable has no bending stiffness whatever, and it still holds up a roof. What resists the load is the change of its own geometry, so its stiffness is a function of the tension already in it — and prestress buys stiffness that no change of material could.

 0102030405060-60-40-20020angle from the crown (degrees)membrane force (kN/m)N_θ = 0 at 51.8273°meridional N_φ-60.0 kN/mhoop N_θ15.0 kN/mcompression abovetension below Structural form

The surface that carries by being curved

A flat plate spends its thickness on a lever arm of a few millimetres. Curve the same sheet and the load is carried in the surface itself, at a thirtieth of the thickness — and the entire bill is presented at the edges.

 P = 6000 kNfrom 10 storeys abovea = 3 mstrength wants 1.94 mstiffness wants 2.55 mslope 4500 kN1500 kN13500 kNm under the column12 m Structural form

The column that stops

A load path that runs straight to the ground costs almost nothing. Interrupting one costs depth in proportion to the square root of the load times the distance it is moved — and the interruption's own deflection becomes the settlement of everything standing on it.

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