RHCES Punching Shear (Two-Way) Calculator

Inputs

Column c1 (mm)

Column c2 (mm)

Slab d (mm)

Column Position

f'c (MPa)

Vu (kN)

β = c1/c2 (auto)

Method — ACI 318 §22.6

b₀ = 2(c1+d) + 2(c2+d) for interior; reduced perimeter for edge/corner.
vc = min[ 0.33·λ·√f'c, (0.17 + 0.33/β)·λ·√f'c, (0.083 + 0.083·αs·d/b₀)·λ·√f'c ].
φVc = 0.75·vc·b₀·d. Compare with Vu.

Results

b₀ (perimeter)—

vc1 0.33√f'c—

vc2 (β term)—

vc3 (αs term)—

vc governing—

φVc—

DCR Vu/φVc—

Status—

About this calculator

This tool checks two-way (punching) shear at a slab-column connection — interior, edge, or corner — against ACI 318 §22.6. It is meant for engineers designing flat plates, flat slabs, or footings, who need a quick demand/capacity check before deciding whether a drop panel, thicker slab, or shear reinforcement is needed.

Method & formulas

The critical section is a perimeter b_o located d/2 from the column faces. For an interior column:

b_o = 2(c₁+d) + 2(c₂+d)

(edge and corner columns use a correspondingly shorter perimeter, since the critical section is cut off at the slab edge). The nominal shear stress is the smallest of three ACI limits:

v_c = min[ 0.33·λ·√f'c , (0.17 + 0.33/β)·λ·√f'c , (0.083 + 0.083·α_sd/b_o)·λ·√f'c ]

where β = long/short column dimension and α_s = 40 (interior), 30 (edge), or 20 (corner) — the reduced α_s for edge/corner columns reflects their shorter, less-confined critical perimeter. Design capacity and the demand-capacity ratio are then:

φV_c = 0.75·v_c·b_o·d DCR = V_u / φV_c

A DCR ≤ 1.0 is acceptable; above that, the slab needs a thicker section, a drop panel/capital, or punching-shear reinforcement (stirrup cages or headed stud rails).

Worked example

Using the tool's defaults — 400×400 mm interior column, d=180 mm, f'c=28 MPa, V_u=600 kN: b_o = 2(400+180)+2(400+180) = 2320 mm, β=1, α_s=40. √f'c = 5.29 MPa, so v₁=0.33×5.29=1.75 MPa, v₂=(0.17+0.33)×5.29=2.65 MPa, v₃=(0.083+0.083×40×180/2320)×5.29≈1.80 MPa. The governing (minimum) value is v_c≈1.75 MPa, giving φV_c = 0.75×1.75×2320×180 ≈ 547 kN. DCR = 600/547 ≈ 1.10 — slightly over capacity, meaning this default case needs a thicker slab or shear reinforcement.

Assumptions & limitations

Edge and corner critical-perimeter geometry is a simplified approximation of the actual (often U- or L-shaped) ACI critical section — use it to sanity-check, not replace, a detailed layout.

Only concrete shear capacity is reported; the tool flags when reinforcement is needed but does not size stirrups or stud rails.

Unbalanced-moment transfer between slab and column (the added shear stress from γ_v·M_u) is not included — significant for edge and corner columns.

Openings near the column, drop panels, and slab thickness transitions are not modeled.

Verify results against the governing code and a licensed engineer's judgment.

FAQ

What does DCR > 1.0 mean?

Factored shear V_u exceeds the concrete's punching capacity φV_c. Increase slab or drop-panel thickness d, use a larger column or capital, or add punching-shear reinforcement.

Why does the calculator take the minimum of three v_c expressions?

ACI 318 bounds punching stress three ways: an absolute upper limit, a penalty for elongated/rectangular columns (the β term), and a penalty tied to perimeter shape and column position (the α_s term). The smallest of the three always governs so none of the limits is exceeded.

Does column position really change the result that much?

Yes. Edge and corner columns have both a shorter critical perimeter and a lower α_s, so their punching capacity is meaningfully lower than an interior column of identical size — always select the correct position before reading the result.

InputsReset