Calculation
xT = 3·b²/(6·b+h)
A transverse force applied through the shear centre rather than the centroid does not add a twisting moment in the idealized U-section.
Schubmittelpunkt des dünnwandigen U-Profils · xT = 3b²/(6b+h)
Calculate the Shear Centre of a Thin-Walled U-Section
A transverse force applied through the shear centre rather than the centroid does not add a twisting moment in the idealized U-section.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Shear-centre offset xT — Distance from the vertical web centreline along the symmetry axis, positive toward the closed side opposite the open mouth. A vertical transverse force must act there to avoid shear-induced twist.
- Flange width b — Length of each equal horizontal flange from the web centreline to its free edge, from the section drawing. Wall thickness must be small compared with b.
- Web height h — Distance between the two flange midlines along the vertical web, from the section drawing. The same uniform wall thickness must also be small compared with h.
Example
Two 100 mm flanges and a 200 mm web give xT = 3·100²/(6·100+200) = 37.5 mm from the web centreline toward the closed side.
Assumptions and limits
Ideal open U-section with two identical flanges and uniform wall thickness much smaller than b and h; thin-wall shear-flow approximation. The output is only an offset on the symmetry axis, not a torsion or strength check. Corner radii, unequal flanges or thicknesses and cutouts are excluded.
Understand Shear centre of a U-section
A U-section can twist under a transverse load. The shear centre locates the force line needed to avoid an extra shear-induced torque.
What does this quantity describe?
The shear centre is the point through which a transverse force acts for bending without shear-induced twist. In a U-section with two equal horizontal flanges and a vertical web, it lies on the horizontal symmetry axis but generally differs from the area centroid. Thin-wall shear-flow analysis gives offset xT = 3b²/(6b+h) from the web centreline toward the closed web side. b is flange length from web centreline; h is the spacing of flange midlines.
Formula and variables
xT = 3·b²/(6·b+h)
Offset from web: xT = 3b²/(6b+h)Origin: moment balance between shear flow and external transverse force
| Symbol / input | Meaning |
|---|---|
| Shear-centre offset xT | Distance from the vertical web centreline along the symmetry axis, positive toward the closed side opposite the open mouth. A vertical transverse force must act there to avoid shear-induced twist. |
| Flange width b | Length of each equal horizontal flange from the web centreline to its free edge, from the section drawing. Wall thickness must be small compared with b. |
| Web height h | Distance between the two flange midlines along the vertical web, from the section drawing. The same uniform wall thickness must also be small compared with h. |
Choose the inputs correctly
b and h are lengths measured on wall midlines from the profile drawing; practical profiles range from millimetres to decimetres. Both must be nonnegative and h positive. Uniform wall thickness much smaller than b and h is assumed; it cancels from this formula and is not an input. xT is an offset in mm, not a second moment of area; it locates the vertical force line for avoiding shear-induced twist.
How to use the calculator
Orient the open section with vertical web and two equal horizontal flanges. Measure b from web centreline to free edge and h between flange midlines. From the web, measure the result toward the closed web side along the symmetry axis. Check torsion from other loads and section strength separately.
Worked example
With b = 100 mm and h = 200 mm, xT = 3·100²/(6·100+200) = 37.5 mm. Apply a vertical transverse load on that force line rather than through the area centroid when avoiding an additional shear-induced twist.
Understand the result and units
Wider flanges increase the offset. As b approaches zero it vanishes; scaling all lengths by one factor scales xT by that factor. The location applies only to the specified U-section.
b and h convert internally to metres; xT is displayed in the selected length unit. In xT = 3b²/(6b+h), b and h must have the same unit.
Typical applications
Positioning loads and hangers on open-section beams, lifting frames and thin-walled machine frames before torsion checks.
Assumptions, limits and common mistakes
Thin-wall approximation for an open U-section with identical flanges, uniform thickness and negligible corner radii. Unequal legs or wall thicknesses, large radii, cutouts and multiple cells require a separate shear-flow analysis. The calculator does not give the centroid, torsional stiffness or a strength verification.
Common mistake: Do not double-count b as full profile width: b is one flange from the web centreline to its free edge. h is between wall midlines, not the outside height. Do not confuse shear centre with area centroid.
Frequently asked questions
What is “Shear centre of a thin-walled U-section” used for?
Positioning loads and hangers on open-section beams, lifting frames and thin-walled machine frames before torsion checks.
Where do the input values come from?
b and h are lengths measured on wall midlines from the profile drawing; practical profiles range from millimetres to decimetres. Both must be nonnegative and h positive. Uniform wall thickness much smaller than b and h is assumed; it cancels from this formula and is not an input. xT is an offset in mm, not a second moment of area; it locates the vertical force line for avoiding shear-induced twist.
What does the result not cover?
Thin-wall approximation for an open U-section with identical flanges, uniform thickness and negligible corner radii. Unequal legs or wall thicknesses, large radii, cutouts and multiple cells require a separate shear-flow analysis. The calculator does not give the centroid, torsional stiffness or a strength verification.