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The Jourawski relation estimates transverse shear stress from beam shear force and section geometry.
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Formula
τ in Pa; V in N; Q in m3; I in m4; b in m
| Symbol | Meaning | Unit |
|---|---|---|
| Local shear stress at the evaluated height | Pa | |
| Internal shear force | N | |
| First moment of the selected partial area about the neutral axis | m3 | |
| Second moment of area of the full section | m4 | |
| Local section width | m |
\tau=\frac{VQ}{I b}This classical beam relation assumes a prismatic section and an appropriate shear distribution. Q is the first area moment of the partial section, not volume flow. Shear stress generally varies over the section depth. Short beams, open thin-walled sections and local load introduction may need more detailed models.
This classical beam relation assumes a prismatic section and an appropriate shear distribution. Q is the first area moment of the partial section, not volume flow. Shear stress generally varies over the section depth. Short beams, open thin-walled sections and local load introduction may need more detailed models.
The Jourawski relation estimates transverse shear stress from beam shear force and section geometry.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Beam shear stress” and check its unit and magnitude.
For a rectangle b=0.04 m, h=0.12 m and V=12 kN, τmax=3V/(2bh)=3.75 MPa.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: τ in Pa; V in N; Q in m3; I in m4; b in m.
Formula cluster
The Jourawski relation estimates transverse shear stress from beam shear force and section geometry.
For a rectangle b=0.04 m, h=0.12 m and V=12 kN, τmax=3V/(2bh)=3.75 MPa.
Assess transverse shear in beams and understand its distribution.
Here is how to work through a typical Beam shear stress (τ = VQ/(Ib)) task step by step:
Task
Work through the numerical example for “Beam shear stress” and check its unit and magnitude.
Solution path
For a rectangle b=0.04 m, h=0.12 m and V=12 kN, τmax=3V/(2bh)=3.75 MPa.
Here Q is the first area moment of the section portion above or below the point, about the neutral axis. It is not volume flow, although the same letter is used in fluid mechanics. Its unit is m3. Compute partial area times its centroid distance from the axis. Beam shear stress varies through the section depth and depends on the first area moment of the partial section. Define the evaluation position and local width b. Not every beam or profile satisfies the classical derivation; thin-walled and short components require particular care.
For a rectangular section, the Jourawski relation gives a parabolic distribution. Shear stress is zero at the free surfaces, rises toward the neutral axis and reaches 3V/(2A) there. This is a classical beam approximation for a rectangular section, not a universal profile formula. Beam shear stress varies through the section depth and depends on the first area moment of the partial section. Define the evaluation position and local width b. Not every beam or profile satisfies the classical derivation; thin-walled and short components require particular care.
V/A is at most an average shear stress over an appropriately loaded area; it does not describe the distribution in a beam section. The beam relation includes geometry through Q, I and b. Connections or thin-walled sections may require other models for the shear flow. Beam shear stress varies through the section depth and depends on the first area moment of the partial section. Define the evaluation position and local width b. Not every beam or profile satisfies the classical derivation; thin-walled and short components require particular care.
Write the quantity and unit from the variable list next to every value: τ in Pa; V in N; Q in m3; I in m4; b in m. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For a rectangle b=0.04 m, h=0.12 m and V=12 kN, τmax=3V/(2bh)=3.75 MPa. 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. Beam shear stress varies through the section depth and depends on the first area moment of the partial section. Define the evaluation position and local width b. Not every beam or profile satisfies the classical derivation; thin-walled and short components require particular care.
The background states this starting condition: This classical beam relation assumes a prismatic section and an appropriate shear distribution. Q is the first area. 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. Beam shear stress varies through the section depth and depends on the first area moment of the partial section. Define the evaluation position and local width b. Not every beam or profile satisfies the classical derivation; thin-walled and short components require particular care.
Quanta exam set
Curated exam set for "Beam shear stress":
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Which formula describes Beam shear stress?
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How do you rearrange Beam shear stress for Base equation for the target quantity?
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Which common mistake happens with Beam shear stress?
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