Structural Engineering & Statics
where the load goes
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Which failure arrives first — page 4

Essays 73 to 78 of 78 on this thread, in the same order.
centre of masscentre of rigidity1000 kNwest wall500 kN direct+ 39 torsional= 539 kNeast wall500 kN direct+ 39 torsional= 539 kNsouth wall0 kN direct− 19 torsional= 19 kNnorth wall0 kN direct+ 19 torsional= 19 kNcentre of rigidity at x = 15.00 m, y = 9.00 mtorsional radius r = 17.02 m against a plan radius of 10.10 mtorsionally stiff by the usual criterion Structural form

The corner that moves most

A lateral force is shared out in proportion to stiffness only if it passes through the centre of rigidity, which is not the centre of the plan and not the centre of mass. The distance between the two is a torque, and the wall that pays for it is the one furthest away and carrying least.

 s_s = 100l_y = 559flangewebspread 5.6 times the bearingyield resistance 1586 kN · elastic critical 510 kNresistance 450 kN at a slenderness of 1.76 Stability

The load that chooses its own length

Every other load in this collection arrives over a length somebody decided. A wheel on a crane girder does not — the flange bends under it and spreads it along the web, and how far it spreads is an output of the flange's own stiffness against the web's own strength. The effective length is 5.6 times the bearing that produced it.

 bending, as a solid column doesP_E = 1341 kNracking, which a solid column cannotS_v = 31500 kN1/P꜀ᵣ = 1/P_E + 1/S_v → 1287 kNthe smaller of the two governs, and here it is the bending Stability

The column made of two columns

A solid column buckles when its bending stiffness runs out. A laced one has a second way to go — the lattice shears, the chords stay straight — and the two flexibilities add rather than the two stiffnesses. A battened column reaches 23% of its own Euler load and behaves as though its slenderness were twice what it is.

 02040608000.20.40.60.811.21.41.6brace stiffness (units of EI/L³)effective length factor k23.2 EI/L³ = 1.41 N꜀ᵣ/L0.77 — held1.32 — freepast the threshold the frame buckles in a mode the brace does not hold Stability

The most dangerous day is before it is finished

A structure is analysed once, complete, with every restraint present. It spends weeks in states nobody drew — a beam landed with no deck on it holds 17% of the moment its section is worth, a frame not yet braced buckles at a third of the load it will, and a bolt not yet tightened is a pin where the analysis assumed a fixity.

 4020080030002000000.20.40.60.81stiffness of each supportfraction of the deflection that is bendingrigid supportsare over here1%the beam drawn Deflection

The deflection that belongs to the support

A beam calculation answers a question about a beam sitting on things that do not move. Real ones sit on bearings, on other beams and on columns that shorten, and every one of those is a spring in series with the member — so a deflection is the sum of two things and only one of them is a property of the beam.

 water table39.2 kN/m² upward, everywhereweight 18.7 MN6 muplift 23.54 MN · weight 18.72 MNfactor against flotation 0.80no strength appears anywhere in that ratio Equilibrium

A basement is a boat

Every load in this collection presses down and is resisted by strength. Hydrostatic uplift presses up, is resisted by weight, and does not care what is built on it — so the check contains no material property at all. It is a ratio of two weights, and one of them is water.

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