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Warping Constant Calculator

Structural Section Properties — Cw • J • Shear Center

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Section Input

mm
mm
mm
mm
mm (optional)

Web height = total height minus flange thickness. Only top flange is used.

mm
mm

Common Sections

W360x33 (W14x22)
bf=127 tf=6.6 hw=299 tw=5.8 • Cw=6.92e8 mm6
W460x52 (W18x35)
bf=152 tf=10.3 hw=355 tw=7.2 • Cw=1.85e9 mm6
C150x12 (C6x8.2)
bf=48 tf=5.2 hw=140 tw=3.6 • Cw=1.28e7 mm6
W530x66 (W21x44)
bf=180 tf=10.9 hw=453 tw=7.5 • Cw=3.21e9 mm6
C200x17 (C8x11.5)
bf=50 tf=6.4 hw=190 tw=4.3 • Cw=3.15e7 mm6

Unit Converter

mm
inch
mm²
in²
mm⁴
in⁴

Results & Visualization

Warping Constant Cw
mm⁶
Torsion Constant J
mm⁴
Shear Center Xs
mm from web center
Cross Section View

How It Works — Formulas

01

Warping Constant Cw (I-Beam)

Cw = (Iy * h²) / 4

Where Iy is the minor axis moment of inertia and h is the distance between flange centroids (hw + tf). For doubly-symmetric I-sections, warping is resisted by flange bending out-of-plane.

02

Warping Constant Cw (Channel)

Cw = (Iy * h²) / 4 * (3b² / (b² + 6b*c + c²))

For singly-symmetric channels, Cw depends on the flange width b, the distance h between flange centroids, and the warping factor c. The shear center offset increases warping effects.

03

Torsion Constant J

J = Σ (bi * ti³) / 3 (open sections)

For thin-walled open sections, J is approximated as the sum of each segment's (length × thickness³) divided by 3. For closed (box) sections, Bredt's formula applies: J = 4A²m / (∮ds/t).

04

Shear Center

Xs = -e0 (on axis of symmetry, measured from web centerline)

The shear center is the point where applied shear forces cause no twisting. For channels: Xs = -b²h²tf / (4Ix). It always lies on the axis of symmetry, outside the web for channels.

05

Box Section (Closed)

J = 4A²m / Σ(bi/ti)    Cw = 0 (closed sections)

Closed box sections have negligible warping (Cw ≈ 0). Their torsional resistance comes from circulating shear flow. Am is the area enclosed by the centerline of the wall.

06

T-Section

Cw = (Iy * h²) / 4 (approx, where h = hw)

T-sections are singly-symmetric. Cw is calculated using the web height as the effective distance. The shear center is at the web-flange junction for symmetric T-sections.

WARPING CALC v2.1 • STRUCTURAL ANALYSIS