Structural Engineering & Statics
where the load goes
Generator

The warping-torsion generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
Two mechanisms, and they add up to the torque at every sectionSaint-Venant torque and warping torque along a 305 by 165 mm I-section of 6 m, twisted by 0.5 kN·m with the ends fixed-free. J is 1.31×10⁵ mm⁴ and I_w 1.63×10¹¹ mm⁶, so k = √(GJ/EI_w) gives kL = 3.34 and a decay length of 1.80 m — 30% of the member. At the built-in end the shearing mechanism is exactly zero and all 0.5 kN·m is carried by the flanges bending in opposite directions; a decay length along, that share has fallen to 37%, and at the far end it is 7.1%. The two curves sum to the flat line at 0.5 kN·m at every one of the 161 stations, to the last bit of the arithmetic, which is the equilibrium of a slice of the member and is the only reason the split may be believed.012345600.10.20.30.40.5distance along the member (m)torque (kN·m)1/k = 1.80 msum = 0.5 kN·mSaint-Venantcirculating shearwarpingthe flanges bending

Two mechanisms, and they add up to the torque at every section. Saint-Venant torque and warping torque along a 305 by 165 mm I-section of 6 m, twisted by 0.5 kN·m with the ends fixed-free. J is 1.31×10⁵ mm⁴ and I_w 1.63×10¹¹ mm⁶, so k = √(GJ/EI_w) gives kL = 3.34 and a decay length of 1.80 m — 30% of the member. At the built-in end the shearing mechanism is exactly zero and all 0.5 kN·m is carried by the flanges bending in opposite directions; a decay length along, that share has fallen to 37%, and at the far end it is 7.1%. The two curves sum to the flat line at 0.5 kN·m at every one of the 161 stations, to the last bit of the arithmetic, which is the equilibrium of a slice of the member and is the only reason the split may be believed.

2 essays call warping-torsion. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

+67.0 N/mm²−67.0 N/mm²+67.0 N/mm²−67.0 N/mm²I-section, ω = ±12169 mm² at a tiptop flangebottom flangeh = 295V_f = 1.69 kN each way · V_f × h = 0.500 kN·m = the torque at the built-in endM_f = 3.04 kN·m each way · M_f × h = 0.897 kN·m² = the bimomentflange plan, sideways movement ×20 against the length Sections and stress

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.

 200030004000500060007000800090000200400600800length of the column (mm)critical load (kN)torsionalflexural about yflexural about zthe mode changes at 3442 mmthe lowest root — what the column actually does Stability

The column that twists instead of bending

Euler's column has one mode. A real column has three, and which of them governs is settled by where the shear centre sits. A cruciform strut buckles by rotating about its own length at a load that does not change no matter how short it is made.

The library, page 5 of 5 — where warping-torsion sits