Calculation
q = T/(2Am); τmax = q/tmin
In a closed thin-walled cell, torsional shear flow is constant around the wall; the largest stress occurs at the thinnest wall.
Bredtsche Torsion einer geschlossenen dünnwandigen Einzelzelle · q = T/(2Am), τmax = q/tmin
Calculate Bredt Shear Flow and Stress
In a closed thin-walled cell, torsional shear flow is constant around the wall; the largest stress occurs at the thinnest wall.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Shear flow q — Force per unit length along the wall midline; constant around a single closed cell under pure torque. Divide by local wall thickness to obtain local shear stress.
- Maximum shear stress τmax — Highest torsional shear stress at the thinnest wall; compare with material limits and safety requirements. Select as result quantity.
- Applied torque T — Magnitude of pure torque about the section longitudinal axis from loading or measurement; transverse-force shear is excluded.
- Enclosed midline area Am — Area enclosed by the closed wall midline, not outside area or material area; obtain from section drawing.
- Minimum wall thickness tmin — Smallest actual wall thickness around the closed perimeter from drawing or measurement; needed for τmax only.
Example
At T = 1,000 N·m and Am = 100 cm² = 0.01 m², q = 50,000 N/m = 50 N/mm. With tmin = 2 mm, τmax = 25 MPa.
Assumptions and limits
One closed thin-walled cell, Saint-Venant torsion and free warping. Torque is carried by circulating shear flow alone. Multicell sections, openings, transverse shear, restrained warping, local stress peaks and strength checks are excluded. Wall thickness must be small relative to section dimensions.
Understand Bredt shear flow in a closed section
A closed thin-walled section carries torque by circulating shear flow. This calculator gives the flow and, when selected, the largest wall shear stress.
What does this quantity describe?
Shear flow q is shear force per unit length of section wall. For one closed thin-walled cell under pure torque T it is constant around the perimeter. The area Am enclosed by the wall midline sets its lever arm: q = T/(2Am). Local shear stress is τ(s) = q/t(s) for local thickness t(s), so τmax = q/tmin at the thinnest wall.
Formula and variables
q = T/(2Am); τmax = q/tmin
Constant shear flow: q = T/(2Am)Local shear stress: τ(s) = q/t(s)Maximum wall stress: τmax = q/tmin
| Symbol / input | Meaning |
|---|---|
| Shear flow q | Force per unit length along the wall midline; constant around a single closed cell under pure torque. Divide by local wall thickness to obtain local shear stress. |
| Maximum shear stress τmax | Highest torsional shear stress at the thinnest wall; compare with material limits and safety requirements. Select as result quantity. |
| Applied torque T | Magnitude of pure torque about the section longitudinal axis from loading or measurement; transverse-force shear is excluded. |
| Enclosed midline area Am | Area enclosed by the closed wall midline, not outside area or material area; obtain from section drawing. |
| Minimum wall thickness tmin | Smallest actual wall thickness around the closed perimeter from drawing or measurement; needed for τmax only. |
Choose the inputs correctly
T is nonnegative applied torque magnitude about the section axis in N·m, from loading or measurement. Am is the area enclosed by the closed wall midline, in cm² or m², from a section drawing; it is neither outer area nor material area and must be positive. tmin is smallest wall thickness around the cell, from drawing or measurement, and must be positive. q is constant shear flow in N/mm, and τmax is stress at the thinnest wall in MPa; select the desired result above the input fields.
How to use the calculator
Confirm that the section has exactly one closed thin-walled cell. Find its midline area, enter T and measure the smallest wall thickness for the stress output. Calculate q first; selecting τmax divides that same q by tmin. Check the stress against permitted material values and other load cases separately.
Worked example
For Am = 100 cm² and T = 1,000 N·m, q = 1000/(2·0.01) = 50,000 N/m = 50 N/mm. With tmin = 2 mm, τmax = 50/2 = 25 N/mm² = 25 MPa.
Understand the result and units
Doubling T doubles q and τmax. Doubling enclosed midline area halves both. For fixed q, stress is inversely proportional to local thickness and peaks at the thinnest wall.
Internal units are N·m for T, m² for Am, m for t, N/m for q and Pa for τ. The common SI registry converts cm², mm and N/mm. 1 N/mm equals 1,000 N/m; 1 N/mm² equals 1 MPa.
Typical applications
Early analysis of closed box sections, thin tubes and hollow beams in torsion; locating the governing wall for later strength checks.
Assumptions, limits and common mistakes
One fully closed thin-walled cell under Saint-Venant torsion with free warping. Open or multicell sections, thick walls, restrained warping, local notches and superimposed transverse shear are outside the model. There is no safety factor or complete strength verification.
Common mistake: Do not calculate Am from outer dimensions without locating the wall midline. τmax occurs at tmin even though q is constant. A slit makes the section open and changes its torsional behaviour fundamentally.
Frequently asked questions
What is “Bredt shear flow in a closed thin-walled section” used for?
Early analysis of closed box sections, thin tubes and hollow beams in torsion; locating the governing wall for later strength checks.
Where do the input values come from?
T is nonnegative applied torque magnitude about the section axis in N·m, from loading or measurement. Am is the area enclosed by the closed wall midline, in cm² or m², from a section drawing; it is neither outer area nor material area and must be positive. tmin is smallest wall thickness around the cell, from drawing or measurement, and must be positive. q is constant shear flow in N/mm, and τmax is stress at the thinnest wall in MPa; select the desired result above the input fields.
What does the result not cover?
One fully closed thin-walled cell under Saint-Venant torsion with free warping. Open or multicell sections, thick walls, restrained warping, local notches and superimposed transverse shear are outside the model. There is no safety factor or complete strength verification.