Flowchart for Punching Shear Check

Punching Shear Verification Manual

Ultimate Limit State (ULS) Two-Way Shear Calculations for Reinforced Concrete Slabs

1. Overview of Punching Shear Behavior

Punching shear is a critical two-way shear failure mechanism observed in flat plates, slab-column connections, and reinforced concrete footings. It is characterized by a column punching truncated cone- or pyramid-shaped shear cracks through the slab under concentrated vertical loading. The algorithm mapped in the flowchart below structures the assessment procedure based on standard code principles (such as Eurocode 2 / EN 1992-1-1).

flowchart TD %% Start A([START]) --> B[Determine the value of β] B --> C["Compute Vₑd,ₘₐₓ = β × Vₑd / (u₀ × dₑff)"] C --> D["Where:
u₀ = Perimeter at column face
dₑff = Effective depth"] D --> E["Determine Vᵣd,ₘₐₓ = 0.134 × f꜀ₖ × (1 − f꜀ₖ / 310)"] E --> F{"Is Vᵣd,ₘₐₓ > Vₑd,ₘₐₓ ?"} F -->|No| G["Redesign the section"] F -->|Yes| H["Determine vₑd = β × Vₑd / (u₁ × dₑff)
(for control perimeter between d and 2d)"] H --> I["Allowable shear stress:
vᵣd = 0.12 × k × (80 × ρₗ × f꜀ₖ)^(1/3) ≥ vₘᵢₙ × (2d / a)"] I --> J{"Is vₑd < vᵣd ?"} J -->|No| K["Redesign the section:
• Increase slab thickness
• Increase concrete grade
• Increase reinforcement"] J -->|Yes| L["No shear reinforcement required"] %% Styling classDef startEnd fill:#4CAF50,stroke:#388E3C,color:white,font-weight:bold classDef process fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px classDef decision fill:#FFF3E0,stroke:#FF9800,stroke-width:2px classDef output fill:#F1F8E9,stroke:#689F38,stroke-width:1.5px classDef note fill:#FFEBEE,stroke:#D32F2F,color:#B71C1C,font-size:11px class A,L startEnd class B,C,D,E,H,I process class F,J decision class G,K output

2. Step-by-Step Engineering Verification

Step 1: Moment Transfer Factor ($\beta$) Determination

Unbalanced moments transmitted between flat slabs and columns create localized stress concentrations. The factor $\beta$ magnifies nominal shear load to account for these eccentricities. Standard values depend on column location (e.g., internal, edge, or corner positions).

Step 2: Maximum Applied Shear Stress at Column Perimeter ($v_{Ed,max}$)

Shear stress is evaluated directly along the column perimeter $u_0$. This check prevents direct crushing of the concrete matrix adjacent to the column face:

v_Ed,max = (β × V_Ed) / (u₀ × d_eff)

Step 3: Concrete Diagonal Compression Failure Limit ($v_{Rd,max}$)

The applied shear stress $v_{Ed,max}$ is checked against maximum allowable concrete capacity ($v_{Rd,max}$). If $v_{Ed,max} \ge v_{Rd,max}$, the concrete section fails by diagonal compression crushing regardless of internal link provision, requiring an immediate section redesign.

v_Rd,max = 0.134 × f_ck × (1 − f_ck / 310)

Step 4: Shear Stress at Basic Control Perimeter ($v_{Ed}$)

For sections that clear the column face crushing check, shear stress ($v_{Ed}$) is calculated at the basic control perimeter $u_1$ (typically located at a distance $2d_{eff}$ from the column face):

v_Ed = (β × V_Ed) / (u₁ × d_eff)

Step 5: Design Punching Shear Resistance Verification ($v_{Rd,c}$)

The calculated stress $v_{Ed}$ is compared against concrete shear capacity without transverse reinforcement ($v_{Rd,c}$), incorporating scale effects ($k$), flexural reinforcement ratio ($\rho_l$), and concrete strength ($f_{ck}$):

v_Rd,c = 0.12 × k × (80 × ρ_l × f_ck)^1/3 ≥ v_min × (2d / a)

• If $v_{Ed} < v_{Rd,c}$: Concrete alone is sufficient against punching shear failure; no transverse shear reinforcement is mandatory.
• If $v_{Ed} \ge v_{Rd,c}$: The section requires engineering intervention—either redesigning dimensions/materials or sizing shear studs/drop panels.

3. Design Variable Definitions

Symbol	Parameter Description	Standard Units
VEd	Ultimate design vertical force applied to column connection	kN
β	Eccentricity magnification factor for shear loading	Dimensionless
u0	Perimeter of the column cross-section face	mm
u1	Basic control perimeter (typically at 2d from column face)	mm
deff	Mean effective depth of slab tension reinforcement: (dx + dy) / 2	mm
fck	Characteristic compressive strength of concrete	MPa (N/mm²)
ρl	Mean longitudinal flexural steel ratio: √(ρlx × ρly) ≤ 0.02	Dimensionless
k	Size effect factor: 1 + √(200 / deff) ≤ 2.0	Dimensionless

Yogendra Gopal Borse

Civil Engineer | Assistant Engineer Grade-I, Maharashtra PWD

B.Tech (Civil) from VJTI Mumbai. Experienced in bridge design, road works, estimation, project monitoring and digital engineering tools. Creator of YogiPWD – practical technical resources for civil engineers.

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