Shear Center — Definition, Channel Twist & Centroid Comparison
The shear center (also called the center of twist or flexural center) is the point in a cross-section through which a transverse shear force must pass to produce bending without twisting. If the resultant shear force passes through any other point, the section experiences combined bending and torsion — a critical consideration for singly-symmetric and asymmetric shapes.
Shear center eccentricity: e = distance from centroid to shear center
Torsional moment if loaded at centroid: T = P × e
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Shear Center Location by Section Type
| Section Type | Shear Center Location | Eccentricity from Centroid |
|---|---|---|
| Doubly-symmetric (W, I) | At centroid | e = 0 |
| Channel (C, MC) | Outside section, opposite flange side | e > 0 (away from web) |
| Equal-leg angle (L) | At intersection of leg centerlines | e = 0 in principal axes* |
| Unequal-leg angle | Intersection of leg centerlines | Near heel |
| Z-shape (purlin) | At centroid | e = 0 |
| Tee (WT, ST) | At intersection of stem and flange | At flange-web junction |
*For angles, bending about geometric axes (x-x, y-y) produces twist unless loaded through the shear center.
The Channel Twist Problem
Channels are the most common section where shear center eccentricity causes problems in practice. The shear center of a channel lies outside the section on the far side of the web, away from the flanges. Its location is:
e = (h² × b² × t) / (4 × Ix)
For a C8x11.5 (h = 8.0 in, b = 2.26 in, t = 0.390 in, Ix = 32.6 in⁴):
e = (8.0² × 2.26² × 0.390) / (4 × 32.6) = (64 × 5.11 × 0.390) / 130.4
= 127.5 / 130.4 = 0.98 in outside the web
If a vertical load is applied at the centroid (in the web), the eccentricity is 0.98 inches — producing a torque that can cause significant twist in a member with low torsional rigidity. For a 10-ft channel with a 5-kip load at midspan, the twisting moment is 5 × 0.98 = 4.9 kip-in, and the resulting rotation depends on the channel's torsional stiffness (very low for open sections).
Shear Flow and the Physical Reason
The shear center exists because of how shear stress flows through thin-walled open sections. Consider a channel bent about its strong axis (x-x):
- The vertical shear force is carried primarily by the web (vertical shear flow)
- The flanges carry horizontal shear flow that changes direction at the web-flange junction
- The resultant of all shear flows passes through a point offset from the centroid
- For doubly-symmetric sections, horizontal shear flows in opposite flanges cancel — resultant at centroid
- For channels, the flanges are on one side only — the resultant shifts away from the centroid
This is why I-beams can be loaded through their centroid without twisting, while channels cannot.
Design Implications
| Situation | Consequence | Mitigation |
|---|---|---|
| Channel loaded through centroid (web) | Twist + lateral displacement | Load through shear center, add bracing |
| Channel used as spandrel beam | Torsion from eccentric load | Check combined bending + torsion |
| Angle lintel loaded on horizontal leg | Twist unless restrained | Provide lateral-torsional restraint |
| WT-section chord in truss | Prying if loaded eccentric | Align load through shear center |
| Purlin (Z or C) with roof sheeting | Twist restrained by sheeting | Sheeting provides rotational restraint |
AISC 360 Section H3.2 addresses singly-symmetric members subject to bending — the moment capacity is reduced when the shear center and centroid do not coincide, because lateral-torsional buckling is influenced by the asymmetry.
Shear Center of Common Channel Sizes (Approximate)
| Channel | Depth h (in) | Flange b (in) | e (in from web) |
|---|---|---|---|
| C3x4.1 | 3.0 | 1.41 | 0.42 |
| C6x8.2 | 6.0 | 1.92 | 0.57 |
| C8x11.5 | 8.0 | 2.26 | 0.98 |
| C12x20.7 | 12.0 | 2.94 | 1.21 |
| C15x33.9 | 15.0 | 3.40 | 1.52 |
Frequently Asked Questions
How does the shear center differ from the centroid?
The centroid is the geometric center of area (first moment of area = 0). The shear center is the point where shear forces cause no twist. In doubly-symmetric sections they coincide. In channels, the shear center lies outside the section. The two points are fundamentally different properties: centroid relates to axial and bending behavior; shear center relates to torsional behavior.
Does the shear center move under load?
No — the shear center is a geometric property of the cross-section shape, independent of load magnitude. It does shift, however, if the cross-section is partially yielded or if the material is nonlinear. But for linear-elastic analysis, it is a fixed section property tabulated in section property tables.
Why doesn't the AISC Manual list shear center locations for W-shapes?
Because for doubly-symmetric W-shapes, the shear center is at the centroid — e = 0. There is nothing to list. The Manual tabulates shear center locations only for channels (C and MC shapes), where the eccentricity is non-zero and design-relevant.
Related Terms and Pages
- Warping Torsion — Vlasov Theory & Bimoment
- Lateral Torsional Buckling — LTB Explained
- Torsional Buckling — Flexural-Torsional Instability
- Moment of Inertia — Definition & Calculation
- Steel Section Properties — Full Database
- Beam Capacity Calculator — Free Online Tool
Educational reference only. Torsion-sensitive members must be designed per AISC 360 Section H3 and verified by a licensed Professional Engineer. The shear center is a linear-elastic concept; nonlinear behavior may modify effective eccentricity.
Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.