Shear Resistance of RC Beam Calculator

Shear Resistance of an RC Beam — Interactive Calculator

Enter beam and reinforcement data. Results show intermediate calculations (units shown). Based on typical IRC and Eurocode-like design equations illustrated in your example.

Beam width, b_w (mm)

Effective depth, d (mm)

Characteristic concrete strength f_ck (N/mm²)

Characteristic steel strength f_yk (N/mm²)

Stirrup/bar diameter (single leg), Ø (mm) — for info

Number of legs (per link)

Area of one bar A_bar (mm²) — leave blank to auto-calc from Ø

Stirrup spacing, s (mm)

Ultimate uniformly distributed load, w_u (kN/m)

Span length L (m)

Support width (used as contact width) b_supp (m)

Computed values / actions:

Results & Detailed Steps

🏗️ RCC Beam Shear Design Calculator – User Guide

📌 Introduction

This tool is used to perform shear design checks for reinforced concrete (RCC) beams based on applied loads and provided shear reinforcement.

The calculator helps you:

• Compute shear forces at critical sections
• Check concrete shear capacity
• Evaluate shear resistance of stirrups
• Determine strut angle (θ)
• Calculate additional longitudinal tension
• Assess overall shear safety

⚙️ Step 1: Input Beam & Material Properties

📐 Geometry Inputs

• b_w – Beam width (mm)
• d – Effective depth (mm)
• L – Span length (m)
• b_supp – Support width (m)

🧱 Material Properties

• f_ck – Characteristic compressive strength of concrete (N/mm²)
• f_yk – Yield strength of steel (N/mm²)

💡 Tip: Ensure units are consistent (mm, m, kN).

🔩 Step 2: Input Shear Reinforcement Details

• Stirrup Diameter (Ø) – Bar size in mm
• Number of Legs – Usually 2 or 4
• Area of Bar (A_bar) – Optional (auto-calculated if not provided)
• Spacing (s) – Distance between stirrups (mm)

The tool calculates:

Asw = Number of legs × Area of one bar

📉 Step 3: Input Loading Details

• w_u – Ultimate uniformly distributed load (kN/m)

The tool automatically computes:

• Total load
• Support reactions
• Shear at support face
• Shear at distance d from face

▶️ Step 4: Run the Calculation

Click the Calculate button to perform the analysis.

The tool executes:

• Shear force calculations
• Concrete crushing check
• Strut angle (θ) determination
• Shear capacity of stirrups
• Final safety verification

📊 Step 5: Shear Force Calculations

The following are computed:

• Total Load: w_u × L
• Reaction: (w_u × L) / 2
• Shear at face: V_Ef
• Shear at distance d: V_Ed

🧱 Step 6: Concrete Shear Capacity Check

The maximum shear capacity of concrete is:

VRd,max = C × bw × d × (1 − fck/250) × fck

• Check performed at θ = 22° and θ = 45°
• Ensures concrete does not fail in crushing

💡 If this check fails → redesign is required.

📐 Step 7: Strut Angle (θ) Calculation

Angle θ is calculated using:

θ = 0.5 × sin⁻¹ (VEf / VRd,max)

This determines internal stress flow direction.

🔗 Step 8: Shear Resistance of Stirrups

Shear capacity provided by reinforcement:

VRd,s = (Asw / s) × 0.78 × fyk × d × cotθ

• Compared against V_Ed
• Ensures reinforcement is sufficient

📈 Step 9: Additional Longitudinal Force

Additional tensile force:

ΔFtd = 0.5 × VEd × cotθ

This must be properly anchored in design.

📊 Step 10: Final Results & Interpretation

The tool provides:

• Shear forces at key locations
• Concrete capacity check (OK / NOT OK)
• Shear reinforcement capacity
• Strut angle θ
• Final safety status (SAFE / UNSAFE)

⚠️ Input Validation Rules

• All inputs must be positive numbers
• Spacing must be non-zero
• Material strengths must be valid
• Geometry values must be realistic

⚠ Missing or invalid inputs will stop calculation.

📐 Engineering Significance

• Shear Design → Prevents brittle failure
• Stirrups → Provide ductility and safety
• Strut Angle → Governs internal force path
• Concrete Check → Ensures crushing does not occur

💡 Practical Tips

• Use appropriate stirrup spacing for safety
• Avoid very high shear stress near supports
• Ensure proper anchorage of reinforcement
• Follow design codes (IS 456 / Eurocode)
• Always verify with detailed structural design

🖨️ Additional Features

• Print – Generate printable design report
• Reset – Clear all inputs and restart