Concrete Shear Capacity — One-Way & Two-Way (ACI 318)
Finds the shear strength the concrete itself provides, by ACI CODE-318-25 [1]. One-way shear is for beams and one-way slabs. Two-way (punching) shear is for flat slabs and footings around a column. Enter a required shear and the page checks it. Designers use it to decide whether a beam needs stirrups or a slab is thick enough at its columns.
One-way shear
Vc = 2λ√f′c·bw·d (psi, in.)
Vc is the concrete shear strength, λ the lightweight concrete factor (1.0 for normalweight), f′c the concrete strength, bw the web width and d the effective depth. This is Code Table 22.5.5.1(a) with no axial load, for members with at least the minimum shear reinforcement Av,min. A beam needs Av,min where Vu > φλ√f′c·bwd (9.6.3.1); some beams listed in Table 9.6.3.1 need it only where Vu > φVc. Above φVc, stirrups carry Vs = Vu/φ − Vc, and the section must keep Vu ≤ φ(Vc + 8√f′c·bwd) (22.5.1.2).
Two-way shear
vc = least of 4, (2 + 4/β) and (2 + αsd/bo), times λsλ√f′c
λs = √(2/(1 + d/10)) ≤ 1 (d in in.)
φVc = φ·vc·bo·d
bo is the perimeter of the critical section, d/2 from the column faces, β the ratio of the column’s long side to its short side, and αs 40, 30 or 20 for an interior, edge or corner column (Table 22.6.5.2). λs is the size-effect factor, 1 up to d = 10 in. (254 mm). √f′c is not taken above 100 psi. φ = 0.75 for shear in both modes. The Code’s expressions are in psi and inches, so the page converts the inputs exactly.
Limits and common mistakes
- The two-way strength is for slabs and footings without shear reinforcement and with no moment transferred to the column. An edge or corner column usually transfers moment, which raises the shear stress; check it separately.
- For an edge column, c1 is the dimension perpendicular to the slab edge.
- For the two-way check, d is the average effective depth of the two bar layers.
- Openings near the column shorten bo; the page does not deduct them.
Worked example
A flat slab with an average effective depth of 220 mm sits on 500 mm square interior columns. The factored column reaction is 700 kN, and the concrete is 4000 psi. Check punching shear.
- Choose Shear Type Two-way (punching) shear.
- Choose Concrete Strength 4000 psi (27.6 MPa) and enter Effective Depth (d) 220 mm.
- Enter Column Dimension c1 500 mm and Column Dimension c2 500 mm, and keep Column Location Interior (αs = 40).
- Keep normalweight concrete (λ = 1.00) and enter Required Shear Vu 700 kN.
- Press Solve. The Solution shows:
Critical perimeter bo: 2,880 mm
Size-effect factor λs: 1
vc (a) 4λsλ√f′c: 1.74425 MPa
vc (b) (2 + 4/β)λsλ√f′c: 2.61638 MPa
vc (c) (2 + αs·d/bo)λsλ√f′c: 2.20454 MPa
Governing vc: 1.74425 MPa
φVc (φ = 0.75): 828.868 kN
Demand-capacity ratio Vu/φVc: 0.844525
Result: OK
Check: bo = 4 × (500 + 220) = 2,880 mm. 4√4000 = 253.0 psi = 1.744 MPa, and 0.75 × 1.744 × 2,880 × 220 = 828.9 kN, more than 700 kN.
