calcsheet
Weld capacity
Factored shear resistance of a fillet weld to CSA S16 Cl. 13.13. Calculate fillet weld resistance for structural steel connections per CSA S16 Clause 13.13. Input weld size, length, electrode strength, and loading direction to get factored resistance. The calculator checks both base metal and weld metal failure paths and reports the governing capacity. Full hand-calculation output for engineering documentation.
Given
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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/weld-capacity.pdf.
Results
| Quantity | Description | Value | Unit |
|---|---|---|---|
| \(\htmlClass{sym-A_w}{A_{w}}\) | Effective weld throat area | 848.4 | \(\mathrm{mm}^{2}\) |
| \(\htmlClass{sym-V_r1}{V_{r1}}\) | Base metal resistance, Cl. 13.13.2.1 (a), conservative extra check | 242.4 | \(\mathrm{kN}\) |
| \(\htmlClass{sym-V_r2}{V_{r2}}\) | Weld metal resistance, Cl. 13.13.2.2 | 186.6governs | \(\mathrm{kN}\) |
| \(\htmlClass{sym-V_r}{V_{r}}\) | Governing factored shear resistance | 186.6 | \(\mathrm{kN}\) |
Derivation
Cl. 13.13.2.1 (a), conservative extra check
\[\begin{aligned} \htmlClass{sym-V_r1}{V_{r1}} &= 0.67 \cdot \htmlClass{sym-phi_w}{\phi_{w}} \cdot \htmlClass{sym-A_m}{A_{m}} \cdot \htmlClass{sym-F_u}{F_{u}} \\ &= 0.67 \cdot \htmlClass{sym-phi_w}{0.67} \cdot \htmlClass{sym-A_m}{1200\ \mathrm{mm}^{2}} \cdot \htmlClass{sym-F_u}{450\ \mathrm{MPa}} \\ &= 242.4\ \mathrm{kN} \end{aligned}\]Cl. 13.13.2.2
\[\begin{aligned} \htmlClass{sym-k_theta}{k_{\theta}} &= 1 + \frac{\sin\left(\htmlClass{sym-theta}{\theta}\right)^{1.5}}{2} \\ &= 1 + \frac{\sin\left(\htmlClass{sym-theta}{0}\right)^{1.5}}{2} \\ &= 1 \end{aligned}\]Cl. 13.13.2.2
\[\begin{aligned} \htmlClass{sym-V_r2}{V_{r2}} &= 0.67 \cdot \htmlClass{sym-phi_w}{\phi_{w}} \cdot \htmlClass{sym-A_w}{A_{w}} \cdot 490\ \mathrm{MPa} \cdot \htmlClass{sym-k_theta}{k_{\theta}} \\ &= 0.67 \cdot \htmlClass{sym-phi_w}{0.67} \cdot \htmlClass{sym-A_w}{848.4\ \mathrm{mm}^{2}} \cdot 490\ \mathrm{MPa} \cdot \htmlClass{sym-k_theta}{1} \\ &= 186.6\ \mathrm{kN} \end{aligned}\]Questions
Why is V_r the lesser of V_r1 and V_r2?
V_r1 is the base metal at the fusion face, on A_m = D L with the plate's F_u. Cl. 13.13.2.1 (a) is the groove weld clause and the fillet clause has no base metal check, so V_r1 is a conservative extra check. V_r2 is the weld metal on the throat, Cl. 13.13.2.2, on A_w = 0.707 A_m with the electrode's X_u. At the declared values, E49XX on a 450 MPa plate, the weld metal governs for a longitudinal weld and the base metal for a transverse one.
What does theta_deg do to V_r2?
It sets the directional factor 1 + 0.5 sin^1.5 theta: 1.0 for a longitudinal weld, loaded along its axis, rising to 1.5 for a transverse one. It does not change V_r1, so at the declared values the base metal takes over as governing once theta passes about 45 degrees. Cl. 13.13.2.2 does not allow the factor for a single-sided fillet weld connected to an element in tension: answer Yes to that input and the factor is taken as 1.0 whatever theta is.
Which electrode strengths X_u are available?
E43XX, E49XX, E55XX, E62XX and E82XX. The electrode ultimate strength X_u follows the classification and is substituted into the weld metal check.
Which CSA S16 Cl. 13.13 rules does this calculator not apply?
It checks one weld segment. For a concentrically loaded group of segments at different angles, Cl. 13.13.2.2 multiplies each segment by M_w, 1.0 for the largest theta and 0.85 for the others, which is not applied here. Welds to HSS must also satisfy Cl. 13.13.4.3. Choose the electrode that matches the joined steel per CSA W59: for an overmatched electrode Cl. 13.13.2.2 caps X_u at that of the matching electrode, and this calculator does not apply the cap.