Shear friction
Checks shear transfer across a plane by ACI 318-19 22.9: a crack, a construction joint, new concrete against old, or concrete against steel. A second mode checks the contact surface of a composite concrete flexural member by 16.4, a topping on a beam for instance. Strength design only. The result is the steel across the plane, or the ties, against the shear, with the limits and the development.
Inputs of the shear plane #
- Calculation: a shear plane (22.9) or a composite flexural member (16.4).
- Contact surface: the four rows of Table 22.9.4.2. This is your statement of what will be built: the construction documents must say the same (22.9.1.4).
- Strength reduction factor: 0.75 for shear, Table 21.2.1. Enter less where 21.2.4 applies to a seismic element; that is your decision.
- Materials: f'c, the bar grade and the concrete type. f'c of the other concrete: the lesser sets the limits of Table 22.9.4.4 and each side's development uses its own. Grade 80 bars still count as 60 ksi (Table 20.2.2.4(a)); their development uses their true fy.
- Loads: by load type (the ASCE 7-22 2.3.1 combinations) or factored values from your analysis. Amplification multiplies the shear when a provision says so, for example the factor on a precast diaphragm joint.
- Plane: width b and length L along the shear, so Ac = b L. Angle α: 90 degrees is perpendicular. Under 90 degrees, Eq. 22.9.4.3 applies, and only if the shear puts the bars in tension: if the shear can reverse, use perpendicular bars.
- Bars: size, bars in a row across b, rows along L. Rows are spaced evenly between the covers.
- Eccentricity e: the moment Vu e is checked against the bars past L/2.
- Permanent compression: a credit by 22.9.4.5, only if it is permanent, and only as you enter it: use the lowest factored value. It offsets net tension first.
- φ for tension steel: net tension across the plane adds steel (22.9.4.6). 0.90 is prefilled as tension-controlled (21.2.2). The corbel rule of 16.5 uses 0.75 if you prefer it here.
- Development on both sides: straight, standard hook, or "headed, mechanical or welded", which is your own check and is reported as such. Against structural steel, side 1 is the weld.
- Composite member: Vu at the section with bv d (16.4.3), or the change of the chord force Vuh over a segment with the contact area (16.4.5). Enter Vuh as the factored shear. Ties: bar, legs, spacing, and the least dimension of the supported element for the spacing limit.
Auto-design varies the bar size, the bars in a row and the rows; for a composite member, the tie bar, legs and spacing. The plane, the surface, the loads and the embedment stay yours.
Checks performed #
| Check | Basis |
|---|---|
| Steel across the plane | Eq. 22.9.4.2 Vn = μ Avf fy, or Eq. 22.9.4.3 Vn = Avf fy (μ sin α + cos α); μ by Table 22.9.4.2, λ at most 0.85; φVn ≥ Vu at the combination needing the most steel |
| Net tension | 22.9.4.6: An = Nu / (φ fy), added to Avf |
| Permanent compression | 22.9.4.5: added to the clamping force, as entered |
| Upper limit | Table 22.9.4.4 on the lesser f'c |
| Moment across the plane | R22.9.4.6: the flexural steel for Vu e by the stress block of 22.2, plus the share of An, against the bars in the tension half. No steel is added unless it exceeds them |
| Spacing | 25.2.1 for the bars in a row and the rows |
| Development | 22.9.5.1: ℓd by Eq. 25.4.2.4a, or ℓdh by 25.4.3, on each side |
| Horizontal shear | 16.4.3 or 16.4.5: above φ(500 bv d), 22.9 over the contact length with Table 22.9.4.4; else Table 16.4.4.2 (a) to (d) |
| Ties | 16.4.6.1 Av,min; 16.4.7.2 spacing; 16.4.7.3 development is a note |
Limitations #
- Only the transfer across the plane. Whether the plane is in the right place is your judgment (R22.9.4.2).
- Rows are evenly spaced; with a moment, R22.9.5.1 says to place the steel mainly in the tension zone. If you do, add rows or split the plane into its own calculation.
- The alternative design methods of 22.9.1.2 are not offered.
- Headed studs: their anchorage in the concrete and any shear checks of Chapter 17 are not part of this. Use Anchors in concrete or Embed plate.
- 18.12.9 diaphragm joints use this equation, with their own φ and amplification; enter those.
- The composite mode does not design the member, and ties are not developed by calculation (a note instead). 16.4.5.2 distribution of the ties is a note.
Verification examples #
Verification status: 31 values compared in 20 examples (9 published, 11 hand calculations from the cited equations): 31 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
Published examples for this as a subject of its own are thin. None on disk is written to ACI 318-19. The equations used below read the same in the older editions.
| Example | Source | Published |
|---|---|---|
| Plank diaphragm joints 1, 4, 5 | FEMA P-1051 (2015), Ch. 11, pp. 526, 530, 531 (ACI 318-14) | Avf 2.92, 0.64, 1.41 in² |
| Topped plank joints 4, 5 and the collector bars | FEMA P-1051, pp. 539, 540 | Avf 2.15, 4.03 in²; φVn 120 kips |
| Column base on a footing | VCmaster US catalog, pp. 65 to 66 (ACI 318-11) | Avf 3.11 in²; φ × limit 86.4 kips |
| Plate on lightweight concrete | VCmaster, pp. 73 to 74 | Avf 0.151 in² |
| Composite slab on a precast beam | VCmaster, pp. 90 to 91 | φ500 bv d 71.3 kips; 1.09 in²/ft |
Hand calculations from the equations cover inclined bars, net tension, permanent compression, the grade 80 cap, the lesser f'c, λ from the density, the moment check, Table 16.4.4.2 and 16.4.5. The published set does not exercise the moment check, inclined bars or Table 16.4.4.2 (a): those are hand checked only. ACI MNL-17(21) may hold a 318-19 example; it comes after wave 7.