\[e=\frac{T}{V}\]
Variables
eshear center eccentricity (m)
Ttorsional moment caused by eccentric shear load (N·m)
Vapplied shear force (N)
Description
What is this formula?
Shear center eccentricity is the distance between the line of action of a shear force and the shear center of a cross-section. If a shear force does not pass through the shear center, torsion is generated.
When to use it
Use this formula when analyzing unsymmetrical or thin-walled structural sections such as channels, angles, Z-sections, and built-up members where shear loading may induce twisting.
Example
A channel section experiences a shear force of:
V = 80,000 N
The resulting torsional moment is:
T = 4,000 N·m
Formula:
e = T / V
Substitution:
e = 4000 / 80000
Result:
e = 0.050 m
Result:
e = 50 mm
Applications
Channel sections, angle sections, cold-formed steel members, bridge girders, aircraft structures, thin-walled beams, and torsion-sensitive designs.