calcsheetSteelBolt prying action
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CSA S16 Cl. 13.12.1.3

Bolt prying action

Prying action on a bolted tee or angle flange: flange, connection, bolt and web checks. Check bolt capacity against prying forces in flange-type connections such as tee-stubs and end-plate joints. The calculator determines the additional tensile demand on bolts caused by flange flexibility and compares it to available bolt strength. Input flange geometry, bolt layout, and applied load to verify adequacy. Produces detailed hand-calculation output.

Given

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\(F_{\mathrm{ub}}\) \(\mathrm{MPa}\) 300-1,200
\(d\) \(\mathrm{mm}\) 10-50
\(n\) 1-40
\(g\) \(\mathrm{mm}\) 50-400
\(p\) \(\mathrm{mm}\) 60-500
\(\mathrm{section}\)
\(L\) \(\mathrm{mm}\) 50-3,000
\(f_{y}\) \(\mathrm{MPa}\) 200-700
\(P_{f}\) \(\mathrm{kN}\) 1-5,000
\(\phi\) 0.5-1
\(\phi_{b}\) 0.5-1
t = 23.9 mm g = 80 mm a = 40.06 mm b = 32.05 mm w = 15.9 mm Pf = 273 kN
Section through the tee, with the two prying lever arms as the calc computes them.
b0 = 304 mm g = 80 mm L = 300 mm p = 100 mm
Plan on the flange: the bolt pair and the tributary length the calc divides by.

Title block

Optional. Printed under the title of the PDF.

This printed copy omits the derivation. The full report, with every step, is the PDF at https://calc.struct.work/calc/bolt-prying.pdf.

Checks

Check D/C Result
Geometry valid\(\htmlClass{sym-g}{g} \leq \htmlClass{sym-b_0}{b_{0}} \quad \Rightarrow \quad \htmlClass{sym-g}{80\ \mathrm{mm}} \leq \htmlClass{sym-b_0}{304\ \mathrm{mm}}\) 0.26 PASS
Flange adequate\(\htmlClass{sym-t_p_min}{t_{p,\mathrm{min}}} \leq \htmlClass{sym-t}{t} \quad \Rightarrow \quad \htmlClass{sym-t_p_min}{11.19\ \mathrm{mm}} \leq \htmlClass{sym-t}{23.9\ \mathrm{mm}}\) 0.47 PASS
Connection adequate\(\htmlClass{sym-P_f}{P_{f}} \leq \htmlClass{sym-F_r}{F_{r}} \quad \Rightarrow \quad \htmlClass{sym-P_f}{273\ \mathrm{kN}} \leq \htmlClass{sym-F_r}{699.4\ \mathrm{kN}}\) 0.39 PASS
Bolt adequate\(\htmlClass{sym-T_fb}{T_{\mathrm{fb}}} \leq \htmlClass{sym-T_rb}{T_{\mathrm{rb}}} \quad \Rightarrow \quad \htmlClass{sym-T_fb}{68.25\ \mathrm{kN}} \leq \htmlClass{sym-T_rb}{156.5\ \mathrm{kN}}\) 0.44 PASS
Web adequate\(\htmlClass{sym-P_f}{P_{f}} \leq \htmlClass{sym-P_r}{P_{r}} \quad \Rightarrow \quad \htmlClass{sym-P_f}{273\ \mathrm{kN}} \leq \htmlClass{sym-P_r}{1.288\ \mathrm{MN}}\) 0.21 PASS

Results

Quantity Description Value Unit
\(\htmlClass{sym-t_p_min}{t_{p,\mathrm{min}}}\) Minimum flange thickness, with prying fully developed 11.19 \(\mathrm{mm}\)
\(\htmlClass{sym-t_p_max}{t_{p,\mathrm{max}}}\) Flange thickness at which prying can be disregarded 14.93 \(\mathrm{mm}\)
\(\htmlClass{sym-F_r}{F_{r}}\) Factored connection capacity 699.4 \(\mathrm{kN}\)
\(\htmlClass{sym-T_rb}{T_{\mathrm{rb}}}\) Factored bolt tensile resistance 156.5 \(\mathrm{kN}\)
\(\htmlClass{sym-P_r}{P_{r}}\) Factored web tensile resistance 1.288 \(\mathrm{MN}\)

Derivation

S.1 \[\begin{aligned} \htmlClass{sym-b_0}{b_{0}} &= 304\ \mathrm{mm} \quad \left(\text{Width of flange or horizontal leg}\right) \end{aligned}\]
S.2 \[\begin{aligned} \htmlClass{sym-t}{t} &= 23.9\ \mathrm{mm} \quad \left(\text{Thickness of flange}\right) \end{aligned}\]
S.3 \[\begin{aligned} \htmlClass{sym-w}{w} &= 15.9\ \mathrm{mm} \quad \left(\text{Thickness of web}\right) \end{aligned}\]
S.4 \[\begin{aligned} \htmlClass{sym-b}{b} &= \frac{\htmlClass{sym-g}{g} - \htmlClass{sym-w}{w}}{2} \\ &= \frac{\htmlClass{sym-g}{80\ \mathrm{mm}} - \htmlClass{sym-w}{15.9\ \mathrm{mm}}}{2} \\ &= 32.05\ \mathrm{mm} \end{aligned}\]
S.5 \[\begin{aligned} \htmlClass{sym-b_prime}{{b'}} &= \htmlClass{sym-b}{b} - \frac{\htmlClass{sym-d}{d}}{2} \\ &= \htmlClass{sym-b}{32.05\ \mathrm{mm}} - \frac{\htmlClass{sym-d}{20\ \mathrm{mm}}}{2} \\ &= 22.05\ \mathrm{mm} \end{aligned}\]
S.6 \[\begin{aligned} \htmlClass{sym-a}{a} &= \min\left(\frac{\htmlClass{sym-b_0}{b_{0}} - \htmlClass{sym-g}{g}}{2}, 1.25 \cdot \htmlClass{sym-b}{b}\right) \\ &= \min\left(\frac{\htmlClass{sym-b_0}{304\ \mathrm{mm}} - \htmlClass{sym-g}{80\ \mathrm{mm}}}{2}, 1.25 \cdot \htmlClass{sym-b}{32.05\ \mathrm{mm}}\right) \\ &= 40.06\ \mathrm{mm} \end{aligned}\]
S.7 \[\begin{aligned} \htmlClass{sym-a_prime}{{a'}} &= \htmlClass{sym-a}{a} + \frac{\htmlClass{sym-d}{d}}{2} \\ &= \htmlClass{sym-a}{40.06\ \mathrm{mm}} + \frac{\htmlClass{sym-d}{20\ \mathrm{mm}}}{2} \\ &= 50.06\ \mathrm{mm} \end{aligned}\]
S.8 \[\begin{aligned} \htmlClass{sym-d_prime}{{d'}} &= \htmlClass{sym-d}{d} + 2\ \mathrm{mm} \\ &= \htmlClass{sym-d}{20\ \mathrm{mm}} + 2\ \mathrm{mm} \\ &= 22\ \mathrm{mm} \end{aligned}\]
S.9

CISC HSB Cl. 6.3

\[\begin{aligned} \htmlClass{sym-P_fb}{P_{\mathrm{fb}}} &= \frac{\htmlClass{sym-P_f}{P_{f}}}{\htmlClass{sym-n}{n}} \\ &= \frac{\htmlClass{sym-P_f}{273\ \mathrm{kN}}}{\htmlClass{sym-n}{4}} \\ &= 68.25\ \mathrm{kN} \end{aligned}\]
S.10

CISC HSB Cl. 6.3 (net over gross section)

\[\begin{aligned} \htmlClass{sym-delta}{\delta} &= 1 - \frac{\htmlClass{sym-d_prime}{{d'}}}{\htmlClass{sym-p}{p}} \\ &= 1 - \frac{\htmlClass{sym-d_prime}{22\ \mathrm{mm}}}{\htmlClass{sym-p}{100\ \mathrm{mm}}} \\ &= 0.78 \end{aligned}\]
S.11

Cl. 13.12.1.3

\[\begin{aligned} \htmlClass{sym-T_rb}{T_{\mathrm{rb}}} &= \frac{0.75 \cdot \htmlClass{sym-phi_b}{\phi_{b}} \cdot \htmlClass{sym-F_ub}{F_{\mathrm{ub}}} \cdot \pi \cdot \htmlClass{sym-d}{d}^{2}}{4} \\ &= \frac{0.75 \cdot \htmlClass{sym-phi_b}{0.8} \cdot \htmlClass{sym-F_ub}{830\ \mathrm{MPa}} \cdot \pi \cdot \left(\htmlClass{sym-d}{20\ \mathrm{mm}}\right)^{2}}{4} \\ &= 156.5\ \mathrm{kN} \end{aligned}\]
S.12

CISC HSB Eq. 6.13

\[\begin{aligned} \htmlClass{sym-K}{K} &= \frac{4 \cdot \htmlClass{sym-b_prime}{{b'}} \cdot 1\ \mathrm{GPa}}{\htmlClass{sym-phi}{\phi} \cdot \htmlClass{sym-p}{p} \cdot \htmlClass{sym-f_y}{f_{y}}} \\ &= \frac{4 \cdot \htmlClass{sym-b_prime}{22.05\ \mathrm{mm}} \cdot 1\ \mathrm{GPa}}{\htmlClass{sym-phi}{0.9} \cdot \htmlClass{sym-p}{100\ \mathrm{mm}} \cdot \htmlClass{sym-f_y}{300\ \mathrm{MPa}}} \\ &= 3.267 \end{aligned}\]
S.13

CISC HSB Eq. 6.13

\[\begin{aligned} \htmlClass{sym-t_p_min}{t_{p,\mathrm{min}}} &= \sqrt{\frac{\htmlClass{sym-K}{K} \cdot \htmlClass{sym-P_fb}{P_{\mathrm{fb}}}}{\left(1 + \htmlClass{sym-delta}{\delta} \cdot 1\right) \cdot 1\ \mathrm{GPa}}} \\ &= \sqrt{\frac{\htmlClass{sym-K}{3.267} \cdot \htmlClass{sym-P_fb}{68.25\ \mathrm{kN}}}{\left(1 + \htmlClass{sym-delta}{0.78} \cdot 1\right) \cdot 1\ \mathrm{GPa}}} \\ &= 11.19\ \mathrm{mm} \end{aligned}\]
S.14

CISC HSB Eq. 6.13

\[\begin{aligned} \htmlClass{sym-t_p_max}{t_{p,\mathrm{max}}} &= \sqrt{\frac{\htmlClass{sym-K}{K} \cdot \htmlClass{sym-P_fb}{P_{\mathrm{fb}}}}{\left(1 + \htmlClass{sym-delta}{\delta} \cdot 0\right) \cdot 1\ \mathrm{GPa}}} \\ &= \sqrt{\frac{\htmlClass{sym-K}{3.267} \cdot \htmlClass{sym-P_fb}{68.25\ \mathrm{kN}}}{\left(1 + \htmlClass{sym-delta}{0.78} \cdot 0\right) \cdot 1\ \mathrm{GPa}}} \\ &= 14.93\ \mathrm{mm} \end{aligned}\]
S.15 \[\begin{aligned} \htmlClass{sym-t_utilization}{t_{\mathrm{utilization}}} &= \frac{\htmlClass{sym-t_p_min}{t_{p,\mathrm{min}}}}{\htmlClass{sym-t}{t}} \\ &= \frac{\htmlClass{sym-t_p_min}{11.19\ \mathrm{mm}}}{\htmlClass{sym-t}{23.9\ \mathrm{mm}}} \\ &= 0.4683 \end{aligned}\]
S.16

CISC HSB Eq. 6.12, 6.13

\[\begin{aligned} \htmlClass{sym-alpha_c0}{\alpha_{c0}} &= \frac{\left(\frac{\htmlClass{sym-K}{K} \cdot \htmlClass{sym-T_rb}{T_{\mathrm{rb}}}}{\htmlClass{sym-t}{t}^{2} \cdot 1\ \mathrm{GPa}} - 1\right) \cdot \htmlClass{sym-a_prime}{{a'}}}{\htmlClass{sym-delta}{\delta} \cdot \left(\htmlClass{sym-a_prime}{{a'}} + \htmlClass{sym-b_prime}{{b'}}\right)} \\ &= \frac{\left(\frac{\htmlClass{sym-K}{3.267} \cdot \htmlClass{sym-T_rb}{156.5\ \mathrm{kN}}}{\left(\htmlClass{sym-t}{23.9\ \mathrm{mm}}\right)^{2} \cdot 1\ \mathrm{GPa}} - 1\right) \cdot \htmlClass{sym-a_prime}{50.06\ \mathrm{mm}}}{\htmlClass{sym-delta}{0.78} \cdot \left(\htmlClass{sym-a_prime}{50.06\ \mathrm{mm}} + \htmlClass{sym-b_prime}{22.05\ \mathrm{mm}}\right)} \\ &= -0.0937 \end{aligned}\]
S.17

CISC HSB Cl. 6.3 (0 <= alpha <= 1)

\[\begin{aligned} \htmlClass{sym-alpha_c}{\alpha_{c}} &= \min\left(1, \max\left(0, \htmlClass{sym-alpha_c0}{\alpha_{c0}}\right)\right) \\ &= \min\left(1, \max\left(0, \htmlClass{sym-alpha_c0}{-0.0937}\right)\right) \\ &= 0 \end{aligned}\]
S.18

CISC HSB Eq. 6.13

\[\begin{aligned} \htmlClass{sym-F_r}{F_{r}} &= \frac{\htmlClass{sym-t}{t}^{2}}{\htmlClass{sym-K}{K}} \cdot \left(1 + \htmlClass{sym-delta}{\delta} \cdot \htmlClass{sym-alpha_c}{\alpha_{c}}\right) \cdot \htmlClass{sym-n}{n} \cdot 1\ \mathrm{GPa} \\ &= \frac{\left(\htmlClass{sym-t}{23.9\ \mathrm{mm}}\right)^{2}}{\htmlClass{sym-K}{3.267}} \cdot \left(1 + \htmlClass{sym-delta}{0.78} \cdot \htmlClass{sym-alpha_c}{0}\right) \cdot \htmlClass{sym-n}{4} \cdot 1\ \mathrm{GPa} \\ &= 699.4\ \mathrm{kN} \end{aligned}\]
S.19 \[\begin{aligned} \htmlClass{sym-connection_utilization}{\mathrm{connection}_{\mathrm{utilization}}} &= \frac{\htmlClass{sym-P_f}{P_{f}}}{\htmlClass{sym-F_r}{F_{r}}} \\ &= \frac{\htmlClass{sym-P_f}{273\ \mathrm{kN}}}{\htmlClass{sym-F_r}{699.4\ \mathrm{kN}}} \\ &= 0.3903 \end{aligned}\]
S.20

CISC HSB Eq. 6.13

\[\begin{aligned} \htmlClass{sym-alpha_b0}{\alpha_{b0}} &= \frac{\frac{\htmlClass{sym-K}{K} \cdot \htmlClass{sym-P_fb}{P_{\mathrm{fb}}}}{\htmlClass{sym-t}{t}^{2} \cdot 1\ \mathrm{GPa}} - 1}{\htmlClass{sym-delta}{\delta}} \\ &= \frac{\frac{\htmlClass{sym-K}{3.267} \cdot \htmlClass{sym-P_fb}{68.25\ \mathrm{kN}}}{\left(\htmlClass{sym-t}{23.9\ \mathrm{mm}}\right)^{2} \cdot 1\ \mathrm{GPa}} - 1}{\htmlClass{sym-delta}{0.78}} \\ &= -0.7817 \end{aligned}\]
S.21

CISC HSB Cl. 6.3 (0 <= alpha <= 1)

\[\begin{aligned} \htmlClass{sym-alpha_b}{\alpha_{b}} &= \min\left(1, \max\left(0, \htmlClass{sym-alpha_b0}{\alpha_{b0}}\right)\right) \\ &= \min\left(1, \max\left(0, \htmlClass{sym-alpha_b0}{-0.7817}\right)\right) \\ &= 0 \end{aligned}\]
S.22

CISC HSB Eq. 6.12

\[\begin{aligned} \htmlClass{sym-T_fb}{T_{\mathrm{fb}}} &= \htmlClass{sym-P_fb}{P_{\mathrm{fb}}} \cdot \left(1 + \frac{\htmlClass{sym-b_prime}{{b'}} \cdot \htmlClass{sym-delta}{\delta} \cdot \htmlClass{sym-alpha_b}{\alpha_{b}}}{\htmlClass{sym-a_prime}{{a'}} \cdot \left(1 + \htmlClass{sym-delta}{\delta} \cdot \htmlClass{sym-alpha_b}{\alpha_{b}}\right)}\right) \\ &= \htmlClass{sym-P_fb}{68.25\ \mathrm{kN}} \cdot \left(1 + \frac{\htmlClass{sym-b_prime}{22.05\ \mathrm{mm}} \cdot \htmlClass{sym-delta}{0.78} \cdot \htmlClass{sym-alpha_b}{0}}{\htmlClass{sym-a_prime}{50.06\ \mathrm{mm}} \cdot \left(1 + \htmlClass{sym-delta}{0.78} \cdot \htmlClass{sym-alpha_b}{0}\right)}\right) \\ &= 68.25\ \mathrm{kN} \end{aligned}\]
S.23 \[\begin{aligned} \htmlClass{sym-BoltStr_utilization}{\mathrm{BoltStr}_{\mathrm{utilization}}} &= \frac{\htmlClass{sym-T_fb}{T_{\mathrm{fb}}}}{\htmlClass{sym-T_rb}{T_{\mathrm{rb}}}} \\ &= \frac{\htmlClass{sym-T_fb}{68.25\ \mathrm{kN}}}{\htmlClass{sym-T_rb}{156.5\ \mathrm{kN}}} \\ &= 0.4362 \end{aligned}\]
S.24

Cl. 13.2 a) i)

\[\begin{aligned} \htmlClass{sym-P_r}{P_{r}} &= \htmlClass{sym-phi}{\phi} \cdot \htmlClass{sym-L}{L} \cdot \htmlClass{sym-w}{w} \cdot \htmlClass{sym-f_y}{f_{y}} \\ &= \htmlClass{sym-phi}{0.9} \cdot \htmlClass{sym-L}{300\ \mathrm{mm}} \cdot \htmlClass{sym-w}{15.9\ \mathrm{mm}} \cdot \htmlClass{sym-f_y}{300\ \mathrm{MPa}} \\ &= 1.288\ \mathrm{MN} \end{aligned}\]
S.25 \[\begin{aligned} \htmlClass{sym-WebStr_utilization}{\mathrm{WebStr}_{\mathrm{utilization}}} &= \frac{\htmlClass{sym-P_f}{P_{f}}}{\htmlClass{sym-P_r}{P_{r}}} \\ &= \frac{\htmlClass{sym-P_f}{273\ \mathrm{kN}}}{\htmlClass{sym-P_r}{1.288\ \mathrm{MN}}} \\ &= 0.212 \end{aligned}\]

Questions

Why is a capped at 1.25 b?

The prying force falls as a grows, because the reaction at the flange tip acts on a longer lever. The prying procedure in the CISC Handbook does not credit a tip reaction farther out than 1.25 b, so a is the lesser of the real edge distance (b_0 - g) / 2 and 1.25 b. A wider flange is not refused; it earns no further reduction.

What do t_p_min and t_p_max mean for flange_adequate?

t_p_min is the thinnest flange that works with prying fully developed, alpha = 1; t_p_max is the flange thick enough that prying can be disregarded, alpha = 0. flange_adequate compares t with t_p_min only. A flange between the two carries some prying force, which alpha_b estimates and T_fb adds to each bolt.

Why does bolt_adequate compare T_fb rather than P_f / n with T_rb?

T_fb is the bolt load with prying in it: P_fb = P_f / n plus the extra tension the flange tip adds as it bends, which grows with alpha_b. A bolt that passes on P_f / n alone can fail once prying is added, which is the reason to run this sheet rather than the bolt capacity one.

What does geometry_valid rule out?

A gauge g wider than the flange b_0, which puts the bolts off the flange. It is listed first because every later check assumes the bolts are on the flange: past that point a' can reach zero and T_fb would divide by it.

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