Choose your section, enter dimensions, and compute. Get J and Cw with clear intermediate values. Download CSV or PDF for reports and sharing easily.
| bf | tf | tw | d | J | Cw |
|---|---|---|---|---|---|
| 200 mm | 15 mm | 10 mm | 300 mm | 5.40e5 mm^4 | 4.07e11 mm^6 |
| 150 mm | 12 mm | 8 mm | 250 mm | 2.11e5 mm^4 | 9.57e10 mm^6 |
| 8 in | 0.5 in | 0.3 in | 12 in | 0.766 in^4 | 1.41e3 in^6 |
The calculator estimates the torsional constant J, the warping constant Cw, and the rigidities GJ and E·Cw. Add torque and length to get twist rate and stiffness for quick checks today.
Open sections can distort axially when they twist. That distortion is warping, and it can be restrained by end plates, continuity, or bracing. Restraint increases resistance and can introduce additional stresses, so Cw becomes a useful property in design models and stability checks.
For thin‑walled I‑sections, the approximation uses thickness cubed. If t_f doubles, the flange contribution to J increases eightfold. Width b_f affects J linearly but can strongly raise Cw via I_y, especially when flanges are wide and thin.
The I‑section warping constant uses Cw = I_y h_o² / 4. Increasing depth raises h_o, and Cw grows with its square. This is why deeper, slender beams often show large warping constants even when J stays modest. If warping is free, the member may still twist easily under service torque.
Thin‑walled rectangular tubes resist torsion efficiently because shear flow circulates around the perimeter. The estimate depends on median dimensions and the enclosed area term squared. Small size increases can boost J quickly, but very thin walls remain tolerance‑sensitive and can buckle locally. Use realistic thickness values and avoid mixing inside and outside dimensions.
Circular sections have simple formulas and stable behavior. Since J scales with diameter to the fourth power, modest diameter changes can greatly reduce twist. Hollow shafts often deliver strong torsional rigidity with less material, but extremely thin walls may require detailed checks.
With torque T and length L, twist is computed as θ = T·L/(GJ). Doubling L doubles θ; doubling G halves it. The stiffness k = GJ/L helps compare alternative sections quickly and supports early sizing decisions.
These are fast engineering estimates. The I‑section and tube options assume thin walls, and the solid rectangle uses a standard approximation for J. For fillets, cutouts, or non‑prismatic members, compare against section tables or a section‑property program before final design. When results drive safety‑critical decisions, confirm with a verified reference or finite‑element section analysis.
J is a geometric property that links torque to twist in elastic torsion. Larger J means smaller twist for the same torque, length, and shear modulus.
Cw quantifies how much an open section can warp during torsion. It becomes important when warping is restrained by end plates, bracing, or continuity.
Closed thin‑walled tubes and circular shafts mainly resist torsion through shear flow around the perimeter. Warping is minimal in typical design assumptions, so Cw is often taken as approximately zero.
The thin‑walled I‑section and tube formulas are best when thickness is small compared with widths. For thick shapes, verify with tabulated section properties or numerical methods.
When you enter torque T and length L, twist is calculated as θ = T·L/(GJ). This is Saint‑Venant torsion without additional warping restraint effects.
Thickness dominates because it appears cubed in the thin‑walled approximation. Small changes in tf or tw can shift J noticeably, especially in slender webs.
Compare against a trusted steel table, a section‑property calculator, or a simple sensitivity check. If the value changes wildly with tiny input edits, review units and thickness assumptions.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.