Structural Engineering & Statics
where the load goes
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The load must go somewhere — page 5

Essays 97 to 106 of 106 on this thread, in the same order.
40 N/mmas appliedbendingpure torsiondistortion=++torque 60 kNm per metre · the distortional half is 30the third and fourth cases add to the second: same torque, and one of them has none of it Sections and stress

The section that will not keep its shape

A box girder is closed, so torsion costs it almost nothing. What an eccentric load actually does to it is something a torsion calculation contains no term for — the rectangle becomes a parallelogram, in its own plane, along the whole length of the span.

 as builtthe same fold under axial pull, exaggeratedE along the girder = 222 N/mm², against 210 GPa for the plate itselfso the web takes 0.106% of the bending stress and all of the shear Sections and stress

The web that carries no bending

A corrugated web needs no stiffeners, because the folds give it in one direction a depth it does not have in its thickness. In the other direction the same folds make it an accordion — and a web that cannot be stretched cannot carry a bending stress at all.

 -15-10-551015020406080across the face (m from the centre)column stress (N/mm²)11 columns at 3.0 mcorner 69.418.2 in the middleplane sectionseffective width 51% · stiffness 72% of gross Structural form

The corner columns take more than their share

A framed tube is a hollow cantilever, and a hollow cantilever's flange ought to be uniformly stressed. It is not, and the reason is that the only route the axial force has into a column in the middle of a face is the in-plane shear of the frame — one bay at a time, from the corner inwards.

 0.10×0.32×3×10×00.20.40.60.81tie stiffness, relative to the one drawnthrust ÷ its rigid-tie value, and bending ÷ its worstthrustbending, to 7422 kNmas built: 2168 kN, tie stretches 68 mmfunicular wL²/8f = 2250 kN · rigid tie 2229 · the difference is the rib's own shortening Structural form

The thrust that never reaches the ground

Every arch on this site has ended at the same sentence — the foundation is where an arch is really decided. A tie changes the sentence without changing the arithmetic: the horizontal force is still there, still the same size, and it now closes on itself through a bar at deck level.

 259 kN95299 kN83221 kN112wind 3 N/mmtop moves 100 mmleewardwindwardaxial load from the guys 801 kN · deflection exaggerated 0.5× Structural form

Held by something that goes soft

A guy is a cable, so it has no stiffness of its own — what resists a mast's movement is the guy's geometry changing, and how much of that there is depends on the tension already in it. Wind pushes the mast towards the leeward guy, which is the one losing tension.

 00.511.5200.20.40.60.81distance from the loaded end (depths)self-equilibrating remainder ÷ mean stressa point loadspread over h/5split in twoone depthsame resultant, same moment · one per cent left by 1.18 depths Internal forces

How far a wrong load reaches

Every figure in this collection applies a load as a point, a line or a uniform pressure, and no real load is any of those. The licence is Saint-Venant's, it is usually quoted as a principle, and it is really a statement about a wavelength.

 load on the top chordthe same load, hung from the soffit600 kN in the hangernothing in the same memberchord forces identical to machine precision · hanger steel 1200 mm², shear steel 96 mm² over the same length Internal forces

The load that has to be lifted

Every shear calculation on this site assumes the load arrives on the top of the beam and walks down a diagonal to the support. Hang the same load from the soffit and the diagonal cannot start — the load has to be carried up to the compression zone first, by a tie no sectional calculation contains.

 00.20.40.60.8100.20.40.60.81along the memberdensity ÷ its peak, and running sharewhere it comes fromrunning totalhalf nearest the root: 87.5% of it · worth 7.0× stiffening the other half Deflection

Where a deflection comes from

The unit-load method gives a deflection as an integral, and this collection has treated that integral as a number to evaluate. It is not a number. It is a density, and it says which millimetres of the member produced the answer — which is not the same map as where the moment is largest.

 02040608005101520angle to the grain (degrees)strength (N/mm²)Hankinsona straight linetension4.47 at 45°, not 11.821 per cent of the strength along the grain, at half a right angle Materials

The material that has a direction

Every material in this collection so far has had one modulus and one strength. Timber has three of each, differing by more than an order of magnitude, and the consequence is not a correction to steel design — it is a different set of checks with a different one governing.

 -150-100-505010015000.20.40.60.811.21.4the redundant — horizontal reaction at the right base (kN)load factorbeam 1.00sway 1.25combined 0.71best lower bound 0.714every mechanism is at or above the answer; every admissible field is at or below it Equilibrium

Two ways of being wrong

Plastic analysis has two theorems and they point in opposite directions. Any equilibrium field that nowhere exceeds the plastic moment gives a load at or below the collapse load; any mechanism gives one at or above it. Only one of those errors is safe.

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