calcsheet
Steel web shear capacity
Verified against CSA S16-19, 2026-09-29
Shear stress capacity of an unstiffened steel web to CSA S16 Cl. 13.4.1.1. Determine the shear stress capacity of an unstiffened structural steel web to CSA S16 Clause 13.4.1.1. The web slenderness h/w decides which of three limit states governs: shear yielding for a stocky web, inelastic shear buckling for an intermediate one, and elastic shear buckling for a slender one. The calculator reports both slenderness limits alongside the governing capacity, so the arm it used is visible rather than assumed. The factored shear resistance V_r = phi A_w F_s follows, with A_w taken as the clear web depth times its thickness.
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This printed copy omits the derivation. The full report, with every step, is the PDF at https://calc.struct.work/calc/steel-shear.pdf.
Checks
| Check | D/C | Utilisation | Result |
|---|---|---|---|
| Web reaches shear yield\(\htmlClass{sym-h_w}{h_{w}} \leq \htmlClass{sym-h_w_1}{h_{w,1}} \quad \Rightarrow \quad \htmlClass{sym-h_w}{50} \leq \htmlClass{sym-h_w_1}{54.2}\) | 0.92 | PASS | |
| Web below elastic limit\(\htmlClass{sym-h_w}{h_{w}} \leq \htmlClass{sym-h_w_2}{h_{w,2}} \quad \Rightarrow \quad \htmlClass{sym-h_w}{50} \leq \htmlClass{sym-h_w_2}{76.7}\) | 0.65 | PASS |
Results
| Quantity | Description | Value | Unit |
|---|---|---|---|
| \(\htmlClass{sym-h_w}{h_{w}}\) | Web slenderness | 50 | |
| \(\htmlClass{sym-h_w_1}{h_{w,1}}\) | Slenderness limit for shear yielding | 54.2 | |
| \(\htmlClass{sym-h_w_2}{h_{w,2}}\) | Slenderness limit for inelastic buckling | 76.7 | |
| \(\htmlClass{sym-F_s}{F_{s}}\) | Shear stress capacity | 231 | \(\mathrm{MPa}\) |
| \(\htmlClass{sym-A_w}{A_{w}}\) | Web shear area | 5000 | \(\mathrm{mm}^{2}\) |
| \(\htmlClass{sym-V_r}{V_{r}}\) | Factored shear resistance | 1.04 | \(\mathrm{MN}\) |
Derivation
Cl. 13.4.1.1 a) i)
\[\begin{aligned} \htmlClass{sym-h_w_1}{h_{w,1}} &= 1014 \cdot \frac{1\ \mathrm{MPa}}{\htmlClass{sym-root_F_y}{\mathrm{root}_{F,y}}} \\ &= 1014 \cdot \frac{1\ \mathrm{MPa}}{\htmlClass{sym-root_F_y}{18.71\ \mathrm{MPa}}} \\ &= 54.2 \end{aligned}\]Cl. 13.4.1.1 a) ii), iii)
\[\begin{aligned} \htmlClass{sym-h_w_2}{h_{w,2}} &= 1435 \cdot \frac{1\ \mathrm{MPa}}{\htmlClass{sym-root_F_y}{\mathrm{root}_{F,y}}} \\ &= 1435 \cdot \frac{1\ \mathrm{MPa}}{\htmlClass{sym-root_F_y}{18.71\ \mathrm{MPa}}} \\ &= 76.7 \end{aligned}\]Branch: \(h_{w} \leq h_{w,1}\) held
Cl. 13.4.1.1 a) i), shear yielding
\[\begin{aligned} \htmlClass{sym-F_s}{F_{s}} &= 0.66 \cdot \htmlClass{sym-F_y}{F_{y}} \\ &= 0.66 \cdot \htmlClass{sym-F_y}{350\ \mathrm{MPa}} \\ &= 231\ \mathrm{MPa} \end{aligned}\]Cl. 13.4.1.1, girder form
\[\begin{aligned} \htmlClass{sym-A_w}{A_{w}} &= \htmlClass{sym-h}{h} \cdot \htmlClass{sym-w}{w} \\ &= \htmlClass{sym-h}{500\ \mathrm{mm}} \cdot \htmlClass{sym-w}{10\ \mathrm{mm}} \\ &= 5000\ \mathrm{mm}^{2} \end{aligned}\]Cl. 13.4.1.1, phi = 0.90 per Cl. 13.1 a)
\[\begin{aligned} \htmlClass{sym-V_r}{V_{r}} &= 0.9 \cdot \htmlClass{sym-A_w}{A_{w}} \cdot \htmlClass{sym-F_s}{F_{s}} \\ &= 0.9 \cdot \htmlClass{sym-A_w}{5000\ \mathrm{mm}^{2}} \cdot \htmlClass{sym-F_s}{231\ \mathrm{MPa}} \\ &= 1.04\ \mathrm{MN} \end{aligned}\]Questions
Why does Cl. 13.4.1.1 cover unstiffened webs only here?
Unstiffened webs only. The constants in Clause 13.4.1.1 assume a shear buckling coefficient of 5.34, which is the unstiffened value; a stiffened web's coefficient depends on the spacing of its transverse stiffeners.
What is h/w, and which F_s does it select?
The web slenderness, clear depth h over thickness w. At or below 1014 / sqrt(F_y) the web reaches shear yield and F_s = 0.66 F_y; up to 1435 / sqrt(F_y) it buckles inelastically, and beyond that elastically, with F_s falling as (w/h) squared. For 350 MPa steel the two limits are about 54 and 77.
Is F_s a factored resistance?
No. F_s is a shear stress. The factored shear resistance is V_r = phi A_w F_s, with A_w the web area h w and phi = 0.90 (Cl. 13.1). For a rolled shape the clause takes d w, so h w is slightly conservative.