Calculation
τmax = 1.5·Q/(b·h)
Shear stress is distributed parabolically over a rectangular section; its maximum at the neutral axis is 1.5 times the average stress Q/A.
Dubbel Festigkeitslehre C 2.4.6 Schubspannungen am geraden Träger: max τ = 1,5·FQ/A (Rechteck, parabolische Verteilung)
Maximum shear stress in a rectangular cross-section
Shear stress is distributed parabolically over a rectangular section; its maximum at the neutral axis is 1.5 times the average stress Q/A.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Maximum shear stress τmax — Peak shear stress in the cross-section, at the neutral axis.
- Shear force Q — Shear force at the considered location from the internal-force analysis.
- Section width b — Width of the rectangular section perpendicular to the force direction.
- Section height h — Height of the rectangular section in the direction of the force.
Example
Q=5,000 N, b=50 mm and h=100 mm give A=5,000 mm² and τmax=1.5·5,000/5,000=1.5 MPa.
Assumptions and limits
Homogeneous, linear-elastic rectangular section and pure transverse shear with no simultaneous torsion; thin-walled or composite sections follow a different distribution.
Understand Maximum shear stress in a rectangular cross-section
This calculator determines the maximum transverse shear stress in a rectangular cross-section, complementing existing beam and bending-stress calculators that report bending stress but not transverse shear stress.
What does this quantity describe?
For a rectangular section, transverse shear stress is distributed parabolically over the height and peaks at the neutral axis: τmax=1.5·Q/A with A=b·h.
Formula and variables
τmax = 1.5·Q/(b·h)
τmax = 1.5·Q/(b·h)τaverage = Q/(b·h)
| Symbol / input | Meaning |
|---|---|
| Maximum shear stress τmax | Peak shear stress in the cross-section, at the neutral axis. |
| Shear force Q | Shear force at the considered location from the internal-force analysis. |
| Section width b | Width of the rectangular section perpendicular to the force direction. |
| Section height h | Height of the rectangular section in the direction of the force. |
Choose the inputs correctly
Q is the shear force at the considered location, b the section width and h the section height in the direction of the force.
How to use the calculator
Take Q from the beam's internal-force analysis, b and h from the actual rectangular cross-section.
Worked example
Q=5,000 N, b=50 mm and h=100 mm give A=5,000 mm² and τmax=1.5·5,000/5,000=1.5 MPa.
Understand the result and units
The 1.5 factor distinguishes the actual peak stress from the often first-computed average shear stress Q/A; other section shapes (I-beam, circle) use a different factor.
Q is a force, b and h are lengths. τmax is output as a stress.
Typical applications
Checking shear stress alongside bending stress for short, heavily loaded beams and brackets with rectangular sections, where shear can govern.
Assumptions, limits and common mistakes
Homogeneous, linear-elastic rectangular section and pure transverse shear with no simultaneous torsion; thin-walled, composite or non-rectangular sections follow a different distribution and shape factor.
Common mistake: Do not forget the 1.5 factor and do not equate τmax with the average shear stress Q/A.
Frequently asked questions
What is “Maximum shear stress in a rectangular cross-section” used for?
Checking shear stress alongside bending stress for short, heavily loaded beams and brackets with rectangular sections, where shear can govern.
Where do the input values come from?
Q is the shear force at the considered location, b the section width and h the section height in the direction of the force.
What does the result not cover?
Homogeneous, linear-elastic rectangular section and pure transverse shear with no simultaneous torsion; thin-walled, composite or non-rectangular sections follow a different distribution and shape factor.