Flowchart - Shear Design

Beam Shear Design Verification Guide

Ultimate Limit State (ULS) Concrete Shear Calculation Workflow (V_Ed known)

1. Overview of the Calculation Workflow

In structural concrete design (e.g., Eurocode 2 / EN 1992-1-1), shear verification ensures that a beam element possesses adequate structural capacity against diagonal tension failure and concrete strut crushing. The flowchart below visualizes the algorithm required to analyze section capacity, determine if shear links are necessary, and calculate required transverse steel reinforcement (A_sw / s).

flowchart TD A(["START"]) --> B{"Is VRd,min >= VEd ?"} B -->|Yes| C["No shear reinforcement required"] B -->|No| D["Determine x/d = (As * fyd) / (0.8 * fck * bw * d)"] D --> E{"Is x/d <= 0.25 ?"} E -->|No| F["Redesign section"] E -->|Yes| G["Calculate lever arm: z = d*(1 - 0.5*x/d) or z = MEd/(As*fyd)"] G --> H{"Is z/d >= 0.85 ?"} H -->|Yes| I["Use z = 0.9d"] H -->|No| J["Use calculated z"] I --> K["Calculate VRd,max = 0.6*(1 - fck/250)*fck*bw*z / (cot THETA + tan THETA)"] J --> K K --> L{"Is VEd <= VRd,max ?"} L -->|No| M["Redesign section"] L -->|Yes| N["Check min strut capacity: VRd,min = 0.035 * sqrt(fck) * bw * d"] N --> O{"Is VRd,min >= VEd ?"} O -->|Yes| P["No shear reinforcement required"] O -->|No| Q["Calculate VRd,c = 0.12 * (100 * p_l * fck)^(1/3) * bw * d"] Q --> R{"Is compression flange length >= l_min ? (where l_min = 0.67 * z / tan THETA)"} R -->|No| S["Redesign section"] R -->|Yes| T["Calculate b_eff = bw + 2 * 0.67z * tan(30 deg)"] T --> U["TAU = VEd / (z * b_eff) - Check TAU <= 0.135 * fck * (1 - fck/250)"] U --> V{"Is TAU within limit ?"} V -->|Yes| W["Provide stirrups: Asw/s = VEd / (0.9 * d * fywd * cot THETA)"] V -->|No| X["Redesign section or increase flange width"] style A fill:#4CAF50,stroke:#388E3C,stroke-width:2px,color:#ffffff style C fill:#4CAF50,stroke:#388E3C,stroke-width:2px,color:#ffffff style P fill:#4CAF50,stroke:#388E3C,stroke-width:2px,color:#ffffff style W fill:#4CAF50,stroke:#388E3C,stroke-width:2px,color:#ffffff style B fill:#FFF3E0,stroke:#FF9800,stroke-width:2px style E fill:#FFF3E0,stroke:#FF9800,stroke-width:2px style H fill:#FFF3E0,stroke:#FF9800,stroke-width:2px style L fill:#FFF3E0,stroke:#FF9800,stroke-width:2px style O fill:#FFF3E0,stroke:#FF9800,stroke-width:2px style R fill:#FFF3E0,stroke:#FF9800,stroke-width:2px style V fill:#FFF3E0,stroke:#FF9800,stroke-width:2px style D fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style G fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style I fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style J fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style K fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style N fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style Q fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style T fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style U fill:#E3F2FD,stroke:#1976D2,stroke-width:1.5px style F fill:#FFEBEE,stroke:#D32F2F,stroke-width:1.5px style M fill:#FFEBEE,stroke:#D32F2F,stroke-width:1.5px style S fill:#FFEBEE,stroke:#D32F2F,stroke-width:1.5px style X fill:#FFEBEE,stroke:#D32F2F,stroke-width:1.5px

2. Key Stages of the Verification Process

Stage 1: Initial Capacity Check

The procedure checks if unreinforced concrete can safely carry the applied ultimate shear design load (V_Ed).

Stage 2: Section Geometry & Lever Arm (z) Evaluation

The neutral axis depth ratio (x/d) is checked against ductility limits (x/d ≤ 0.25).

Stage 3: Maximum Concrete Strut Crushing Limit (V_Rd,max)

V_Rd,max = [ 0.6 × (1 − f_ck / 250) × f_ck × b_w × z ] / (cot θ + tan θ)

Stage 4: Flange Shear Stress Verification

For flanged sections, the algorithm calculates effective flange width (b_eff) and checks local shear stress against concrete crushing limits.

Stage 5: Shear Link Sizing

A_sw / s = V_Ed / (0.9 × d × f_ywd × cot θ)

3. Variable Notation & Design Definitions

Symbol	Design Parameter	Standard Units
VEd	Design shear force at ultimate limit state (ULS)	kN
VRd,max	Maximum design shear capacity limited by concrete strut crushing	kN
VRd,c / VRd,min	Design shear resistance of member without shear reinforcement	kN
bw / beff	Web width / Effective flange compression width	mm
d / z	Effective flexural depth / Internal lever arm	mm
fck	Characteristic compressive cylinder strength of concrete	MPa (N/mm²)
fywd	Design yield strength of shear reinforcement	MPa (N/mm²)
θ	Angle of concrete compression strut (21.8° ≤ θ ≤ 45°)	Degrees
Asw / s	Cross-sectional area of shear links per unit longitudinal spacing	mm²/mm