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Shear flow in a thin-walled beam is determined by transverse shear force and the first area moment at the cut.
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Formula
q in N/m; V in N; Q in m3; I in m4
| Symbol | Meaning | Unit |
|---|---|---|
| Shear flow along the wall | N/m | |
| Transverse shear force at the section | N | |
| First moment of the selected partial area | m3 | |
| Second moment of area of the full section | m4 |
q=\frac{VQ}{I}The relation follows by integrating τ=VQ/(Ib) through the local wall thickness for a thin-walled approximation. Q must correspond to the selected cut and neutral axis. Closed cells can also carry a statically indeterminate circulating shear flow, so this open-section expression alone is not sufficient there.
The relation follows by integrating τ=VQ/(Ib) through the local wall thickness for a thin-walled approximation. Q must correspond to the selected cut and neutral axis. Closed cells can also carry a statically indeterminate circulating shear flow, so this open-section expression alone is not sufficient there.
Shear flow in a thin-walled beam is determined by transverse shear force and the first area moment at the cut.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Shear flow in a thin-walled beam section” and check its unit and magnitude.
For V=10 kN, Q=2·10−5 m3 and I=8·10−6 m4, q=25 kN/m.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: q in N/m; V in N; Q in m3; I in m4.
Formula cluster
Shear flow in a thin-walled beam is determined by transverse shear force and the first area moment at the cut.
For V=10 kN, Q=2·10−5 m3 and I=8·10−6 m4, q=25 kN/m.
Estimate shear transfer in thin webs and flanges.
Here is how to work through a typical Shear flow in a thin-walled beam section (q = VQ/I) task step by step:
Task
Work through the numerical example for “Shear flow in a thin-walled beam section” and check its unit and magnitude.
Solution path
For V=10 kN, Q=2·10−5 m3 and I=8·10−6 m4, q=25 kN/m.
Shear stress τ is force per area in pascals. Shear flow q integrates stress through wall thickness and has units N/m. For nearly uniform stress in a thin wall, q≈τt and is useful for force balance along a wall. Use the thin-wall approximation and first moment corresponding to the cut location. Application: Estimate shear transfer in thin webs and flanges. The numerical example For V=10 kN, Q=2·10−5 m3 and I=8·10−6 m4, q=25 kN/m anchors the idea in a concrete measurement case.
Q is the first moment of the partial area on one side of the cut about the neutral axis. It depends on cut location and axis. Do not confuse it with volumetric flow; here its unit is m3. Use the thin-wall approximation and first moment corresponding to the cut location. The corresponding units are q in N/m; V in N; Q in m3; I in m4. For V=10 kN, Q=2·10−5 m3 and I=8·10−6 m4, q=25 kN/m. This checks that the reference quantities are compatible.
A closed thin-walled section can carry circulating shear flow not determined by transverse-force equilibrium alone. Compatibility and torsion add constraints. The relation can give a basic open-section flow but needs augmentation for closed cells. Use the thin-wall approximation and first moment corresponding to the cut location. Scope: The relation follows by integrating τ=VQ/(Ib) through the local wall thickness for a thin-walled approximation. Q must correspond to the selected cut and neutral axis. Closed cells can also carry a statically indeterminate circulating shear flow, so this open-section expression alone is not sufficient there. A practical application is Estimate shear transfer in thin webs and flanges.
Write the quantity and unit from the variable list next to every value: q in N/m; V in N; Q in m3; I in m4. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For V=10 kN, Q=2·10−5 m3 and I=8·10−6 m4, q=25 kN/m. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Use the thin-wall approximation and first moment corresponding to the cut location.
The background states this starting condition: The relation follows by integrating τ=VQ/(Ib) through the local wall thickness for a thin-walled approximation. Q must correspond. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Use the thin-wall approximation and first moment corresponding to the cut location.
Quanta exam set
Curated exam set for "Shear flow in a thin-walled beam section":
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Which formula describes Shear flow in a thin-walled beam section?
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How do you rearrange Shear flow in a thin-walled beam section for Base equation for the target quantity?
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Which common mistake happens with Shear flow in a thin-walled beam section?
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