calcsheet
Bolt capacity
Verified against CSA S16-19, 2026-09-29
Factored shear and tensile resistance of a structural bolt to CSA S16-19. Calculate factored shear and tensile resistance of structural bolts per CSA S16-19. Includes bearing capacity on the connected plate and bolt tear-out at the plate edge. Full hand-calculation output shows every step for review and 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/bolt-capacity.pdf.
Checks
| Check | D/C | Utilisation | Result |
|---|---|---|---|
| Edge distance adequate\(\htmlClass{sym-e}{e} \geq \htmlClass{sym-e_min}{e_{\mathrm{min}}} \quad \Rightarrow \quad \htmlClass{sym-e}{40\ \mathrm{mm}} \geq \htmlClass{sym-e_min}{34\ \mathrm{mm}}\) | 0.85 | PASS |
Results
| Quantity | Description | Value | Unit |
|---|---|---|---|
| \(\htmlClass{sym-V_rb}{V_{\mathrm{rb}}}\) | Factored shear resistance, smallest of the three modes | 87.08 | \(\mathrm{kN}\) |
| \(\htmlClass{sym-T_rb}{T_{\mathrm{rb}}}\) | Factored tensile resistance | 155.5 | \(\mathrm{kN}\) |
| \(\htmlClass{sym-e_min}{e_{\mathrm{min}}}\) | Minimum edge distance required | 34 | \(\mathrm{mm}\) |
Derivation
Cl. 13.12.1.2 (c), phi_b = 0.80 per Cl. 13.1 c)
\[\begin{aligned} \htmlClass{sym-V_rb1}{V_{\mathrm{rb}1}} &= \frac{0.6 \cdot 0.8 \cdot \htmlClass{sym-m_shear}{m_{\mathrm{shear}}} \cdot \htmlClass{sym-k}{k} \cdot \htmlClass{sym-F_ub}{F_{\mathrm{ub}}} \cdot \pi \cdot \htmlClass{sym-d}{d}^{2}}{4} \\ &= \frac{0.6 \cdot 0.8 \cdot \htmlClass{sym-m_shear}{1} \cdot \htmlClass{sym-k}{0.7} \cdot \htmlClass{sym-F_ub}{825\ \mathrm{MPa}} \cdot \pi \cdot \left(\htmlClass{sym-d}{20\ \mathrm{mm}}\right)^{2}}{4} \\ &= 87.08\ \mathrm{kN} \end{aligned}\]Cl. 13.12.1.2 (a), phi_br = 0.80 per Cl. 13.12.1.2
\[\begin{aligned} \htmlClass{sym-V_rb2}{V_{\mathrm{rb}2}} &= 3 \cdot \htmlClass{sym-t}{t} \cdot \htmlClass{sym-d}{d} \cdot 0.8 \cdot \htmlClass{sym-F_u}{F_{u}} \\ &= 3 \cdot \htmlClass{sym-t}{10\ \mathrm{mm}} \cdot \htmlClass{sym-d}{20\ \mathrm{mm}} \cdot 0.8 \cdot \htmlClass{sym-F_u}{450\ \mathrm{MPa}} \\ &= 216\ \mathrm{kN} \end{aligned}\]Cl. 13.11, phi_u = 0.75 per Cl. 13.1 a)
\[\begin{aligned} \htmlClass{sym-V_rb3}{V_{\mathrm{rb}3}} &= \frac{2 \cdot 0.6 \cdot \htmlClass{sym-e}{e} \cdot \htmlClass{sym-t}{t} \cdot 0.75 \cdot \left(\htmlClass{sym-F_u}{F_{u}} + \htmlClass{sym-F_y}{F_{y}}\right)}{2} \\ &= \frac{2 \cdot 0.6 \cdot \htmlClass{sym-e}{40\ \mathrm{mm}} \cdot \htmlClass{sym-t}{10\ \mathrm{mm}} \cdot 0.75 \cdot \left(\htmlClass{sym-F_u}{450\ \mathrm{MPa}} + \htmlClass{sym-F_y}{300\ \mathrm{MPa}}\right)}{2} \\ &= 135\ \mathrm{kN} \end{aligned}\]Cl. 13.12.1.3, phi_b = 0.80 per Cl. 13.1 c)
\[\begin{aligned} \htmlClass{sym-T_rb}{T_{\mathrm{rb}}} &= \frac{0.75 \cdot \htmlClass{sym-F_ub}{F_{\mathrm{ub}}} \cdot 0.8 \cdot \pi \cdot \htmlClass{sym-d}{d}^{2}}{4} \\ &= \frac{0.75 \cdot \htmlClass{sym-F_ub}{825\ \mathrm{MPa}} \cdot 0.8 \cdot \pi \cdot \left(\htmlClass{sym-d}{20\ \mathrm{mm}}\right)^{2}}{4} \\ &= 155.5\ \mathrm{kN} \end{aligned}\]Branch: \(d \leq 36\ \mathrm{mm}\) held
Cl. 22.3.2, Table 5
\[\begin{aligned} \htmlClass{sym-e_min}{e_{\mathrm{min}}} &= 34\ \mathrm{mm} \quad \left(\text{Sheared edge, 20 mm bolt}\right) \end{aligned}\]Questions
Why does tear-out govern V_rb at a small edge distance e?
Tear-out, V_rb3 from Cl. 13.11, is the only one of the three resistances that depends on e: it shears the plate along two planes of length e, so it falls in proportion as the bolt moves toward the edge. Bolt shear V_rb1 and bearing V_rb2 do not change with e, so below some edge distance tear-out is the smallest. At the declared values bolt shear governs, and a larger or stronger bolt moves the crossover out to a larger e.
Which clause of CSA S16-19 sets e_min, and how does the edge type change it?
Cl. 22.3.2, through its Table 5. A sheared edge takes the Table 5 value for the bolt size, 34 mm for a 20 mm bolt, reading the next larger listed bolt between sizes and 1.75d above 36 mm; a rolled, sawn or cut edge takes 1.25d. e_min is a detailing minimum, checked on its own, so a bolt can meet it and still have tear-out govern its shear.
What does k do when the bolt threads are intercepted?
k multiplies bolt shear V_rb1 only: 0.70 when a shear plane passes through the threads, whose root area is smaller than the shank, and 1.00 when every shear plane is in the shank. It does not enter the tension resistance T_rb, whose 0.75 factor already allows for the threads.
Does T_rb from Cl. 13.12.1.3 cover a bolt in combined shear and tension?
No. T_rb is the tension resistance on its own, reported beside the shear side and not combined with it. A bolt carrying both needs the interaction check of Cl. 13.12.1.4, and a bolt in tension through a flexible flange also needs prying, which the Bolt prying action calc works out.