calcsheet
Concrete shear friction
Verified against CSA A23.3-24, 2026-10-01
Interface shear transfer by shear friction, to CSA A23.3. Calculate shear capacity at concrete-to-concrete interfaces using the shear-friction method. Applicable to cold joints, composite topping slabs, precast connections, and construction joints. Input interface conditions, reinforcement crossing the joint, and concrete strength to determine factored shear resistance. Full calculation output for design records.
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/concrete-shear-friction.pdf.
Checks
| Check | D/C | Utilisation | Result |
|---|---|---|---|
| Rebar adequate\(\htmlClass{sym-A_vf}{A_{\mathrm{vf}}} \geq \htmlClass{sym-As_req}{\mathrm{As}_{\mathrm{req}}} \quad \Rightarrow \quad \htmlClass{sym-A_vf}{600\ \mathrm{mm}^{2}} \geq \htmlClass{sym-As_req}{521.2\ \mathrm{mm}^{2}}\) | 0.87 | PASS | |
| Stress adequate\(\htmlClass{sym-v_f}{v_{f}} \leq \htmlClass{sym-upsilon_r}{\upsilon_{r}} \quad \Rightarrow \quad \htmlClass{sym-v_f}{2.333\ \mathrm{MPa}} \leq \htmlClass{sym-upsilon_r}{2.652\ \mathrm{MPa}}\) | 0.88 | PASS |
Results
| Quantity | Description | Value | Unit |
|---|---|---|---|
| \(\htmlClass{sym-As_req}{\mathrm{As}_{\mathrm{req}}}\) | Minimum reinforcement required across the interface | 521.2 | \(\mathrm{mm}^{2}\) |
| \(\htmlClass{sym-sigma}{\sigma}\) | Compressive stress clamping the slip plane | 2.2 | \(\mathrm{MPa}\) |
| \(\htmlClass{sym-upsilon_r}{\upsilon_{r}}\) | Factored shear stress resistance of the interface | 2.652 | \(\mathrm{MPa}\) |
| \(\htmlClass{sym-upsilon_allow}{\upsilon_{\mathrm{allow}}}\) | Cap on the cohesion and friction term | 4.062 | \(\mathrm{MPa}\) |
Derivation
A23.3 Cl. 11.5.4, Eq. 11.28
\[\begin{aligned} \htmlClass{sym-rho_v}{\rho_{v}} &= \frac{\htmlClass{sym-A_vf}{A_{\mathrm{vf}}}}{\htmlClass{sym-A_cv}{A_{\mathrm{cv}}}} \\ &= \frac{\htmlClass{sym-A_vf}{600\ \mathrm{mm}^{2}}}{\htmlClass{sym-A_cv}{90000\ \mathrm{mm}^{2}}} \\ &= 0.006667 \end{aligned}\]A23.3 Cl. 11.5.4, Eq. 11.27
\[\begin{aligned} \htmlClass{sym-sigma}{\sigma} &= \htmlClass{sym-rho_v}{\rho_{v}} \cdot \htmlClass{sym-f_y}{f_{y}} \cdot \sin\left(\frac{\htmlClass{sym-alpha}{\alpha} \cdot \pi}{180}\right) + \frac{\htmlClass{sym-N}{N}}{\htmlClass{sym-A_cv}{A_{\mathrm{cv}}}} \\ &= \htmlClass{sym-rho_v}{0.006667} \cdot \htmlClass{sym-f_y}{400\ \mathrm{MPa}} \cdot \sin\left(\frac{\htmlClass{sym-alpha}{90} \cdot \pi}{180}\right) + \frac{\htmlClass{sym-N}{-42\ \mathrm{kN}}}{\htmlClass{sym-A_cv}{90000\ \mathrm{mm}^{2}}} \\ &= 2.2\ \mathrm{MPa} \end{aligned}\]A23.3 Cl. 11.5.1, Eq. 11.25, cohesion and friction
\[\begin{aligned} \htmlClass{sym-upsilon_c}{\upsilon_{c}} &= \htmlClass{sym-lamb}{\lambda} \cdot \htmlClass{sym-phi_c}{\phi_{c}} \cdot \left(\htmlClass{sym-c}{c} + \htmlClass{sym-mu}{\mu} \cdot \htmlClass{sym-sigma}{\sigma}\right) \\ &= \htmlClass{sym-lamb}{1} \cdot \htmlClass{sym-phi_c}{0.65} \cdot \left(\htmlClass{sym-c}{1\ \mathrm{MPa}} + \htmlClass{sym-mu}{1.4} \cdot \htmlClass{sym-sigma}{2.2\ \mathrm{MPa}}\right) \\ &= 2.652\ \mathrm{MPa} \end{aligned}\]A23.3 Cl. 11.5.1, cap on the cohesion and friction term
\[\begin{aligned} \htmlClass{sym-upsilon_allow}{\upsilon_{\mathrm{allow}}} &= 0.25 \cdot \htmlClass{sym-phi_c}{\phi_{c}} \cdot \htmlClass{sym-f_c}{f_{c}} \\ &= 0.25 \cdot \htmlClass{sym-phi_c}{0.65} \cdot \htmlClass{sym-f_c}{25\ \mathrm{MPa}} \\ &= 4.062\ \mathrm{MPa} \end{aligned}\]A23.3 Cl. 11.5.1, Eq. 11.25, dowel term
\[\begin{aligned} \htmlClass{sym-upsilon_s}{\upsilon_{s}} &= \htmlClass{sym-phi_s}{\phi_{s}} \cdot \htmlClass{sym-rho_v}{\rho_{v}} \cdot \htmlClass{sym-f_y}{f_{y}} \cdot \cos\left(\frac{\htmlClass{sym-alpha}{\alpha} \cdot \pi}{180}\right) \\ &= \htmlClass{sym-phi_s}{0.85} \cdot \htmlClass{sym-rho_v}{0.006667} \cdot \htmlClass{sym-f_y}{400\ \mathrm{MPa}} \cdot \cos\left(\frac{\htmlClass{sym-alpha}{90} \cdot \pi}{180}\right) \\ &= 0\ \mathrm{Pa} \end{aligned}\]A23.3 Cl. 11.5.1, Eq. 11.25
\[\begin{aligned} \htmlClass{sym-upsilon_r}{\upsilon_{r}} &= \min\left(\htmlClass{sym-upsilon_c}{\upsilon_{c}}, \htmlClass{sym-upsilon_allow}{\upsilon_{\mathrm{allow}}}\right) + \htmlClass{sym-upsilon_s}{\upsilon_{s}} \\ &= \min\left(\htmlClass{sym-upsilon_c}{2.652\ \mathrm{MPa}}, \htmlClass{sym-upsilon_allow}{4.062\ \mathrm{MPa}}\right) + \htmlClass{sym-upsilon_s}{0\ \mathrm{Pa}} \\ &= 2.652\ \mathrm{MPa} \end{aligned}\]Questions
Where do c and mu come from for each interface case?
CSA A23.3 Cl. 11.5, by surface: concrete placed monolithically takes c = 1.0 MPa and mu = 1.4; hardened concrete intentionally roughened to at least 5 mm takes 0.5 MPa and 1.0; hardened concrete clean but not intentionally roughened takes 0.25 MPa and 0.6; concrete anchored to as-rolled steel by studs or bars takes 0 and 0.6. A cold joint that was not deliberately roughened belongs in the third case, however rough it looks.
Which way round is N, and why is it unfactored?
Negative is tension and positive is compression. CSA A23.3 Cl. 11.5.4 takes N as the unfactored permanent load perpendicular to the plane, so only compression that is always there is credited with clamping the joint. N / A_cv adds to the clamping stress sigma, so a tension force raises the reinforcement the joint needs and lowers the shear stress it can carry.
What does 0.25 phi_c f_c limit?
The cohesion and friction term of Cl. 11.5.1, lambda phi_c (c + mu sigma). It grows with every bar crossing the plane, and the cap stops added clamping being credited past the point where the concrete itself crushes. Going over it is not a failure: upsilon_r takes the lesser of the two, plus the phi_s rho_v f_y cos(alpha) dowel term, and stress_adequate compares V_f / A_cv with that. With the bars perpendicular to the plane the dowel term is zero, so if V_f / A_cv is near the cap only a larger interface or stronger concrete helps.
Why does a raked bar, alpha under 90, need less As_req?
A bar at alpha to the plane clamps it with f_y sin(alpha), which enters sigma, and also carries shear directly with phi_s f_y cos(alpha), the last term of Eq. 11.25. Cl. 11.5.5 counts only bars raked so that the shear puts them in tension, which is the sense the figure draws.