Eurocode 2 Shear Design Calculator (EN 1992‑1‑1)

Check shear resistance of reinforced concrete beams according to Eurocode 2: calculate concrete shear resistance \(V_{Rd,c}\), shear reinforcement resistance \(V_{Rd,s}\), required links, and minimum shear reinforcement.

Input Data

Beam type

For T‑beams, use web width \(b_w\) and effective depth \(d\).

Concrete strength \(f_{ck}\) (MPa)

Cylinder strength (e.g. C30/37 → 30 MPa).

Beam width \(b_w\) (mm)

Effective depth \(d\) (mm)

Longitudinal tension steel area \(A_{sl}\) (mm²)

Area of bottom reinforcement at the section.

Design shear force \(V_{Ed}\) (kN)

Design bending moment \(M_{Ed}\) (kNm)

Used only for approximate longitudinal strain check (optional).

Steel yield strength \(f_{yk}\) (MPa)

Concrete partial factor \(\gamma_c\)

Steel partial factor \(\gamma_s\)

Link bar diameter \(\phi_w\) (mm)

Number of legs per link \(n_l\)

E.g. 2 for single‑leg stirrup, 4 for double‑leg.

Link spacing \(s\) (mm)

Concrete density

Shear reinforcement angle \(\theta\)

Eurocode 2 allows \(1.0 \le \cot\theta \le 2.5\). Default 2.0.

Shear Design Results (EN 1992‑1‑1)

Concrete shear resistance \(V_{Rd,c}\)

\(V_{Rd,c}\): kN

Shear stress \(v_{Ed}\): MPa

Shear stress \(v_{Rd,c}\): MPa

Shear reinforcement \(V_{Rd,s}\)

Provided \(V_{Rd,s}\): kN

Required shear steel \(A_{sw,req}/s\): mm²/m

Provided \(A_{sw}/s\): mm²/m

Minimum shear reinforcement

Minimum \(A_{sw,min}/s\): mm²/m

Recommended maximum spacing: mm

Design summary

Show intermediate values & formulas

Effective depth: d = mm

Effective width: b_w = mm

Longitudinal reinforcement ratio: ρ_l =

Size factor: k =

Concrete factor: C_Rd,c =

k₁:

v_min: MPa

Design steel strength: f_yd = MPa

\(\cot\theta\):

Link area per leg: A_sw,leg = mm²

Provided A_sw/s: mm²/m

How this Eurocode 2 shear design calculator works

This tool follows EN 1992‑1‑1:2004 (Eurocode 2) for the shear design of reinforced concrete beams using the variable‑strut‑inclination method. It checks:

Concrete shear resistance without shear reinforcement \(V_{Rd,c}\)
Shear resistance of links \(V_{Rd,s}\)
Minimum shear reinforcement and spacing limits
Whether the provided links are sufficient for the design shear force \(V_{Ed}\)

1. Concrete shear resistance \(V_{Rd,c}\)

For members with shear reinforcement, Eurocode 2 (6.2.2) gives:

\( v_{Rd,c} = \left[ C_{Rd,c} \cdot k \cdot (100 \rho_l f_{ck})^{1/3} \right] \ge v_{min} \) (MPa)

where:

\(C_{Rd,c} = 0.18 / \gamma_c\) (≈ 0.12 for \(\gamma_c = 1.5\))
\(k = 1 + \sqrt{\dfrac{200}{d}}\) with \(d\) in mm, limited to \(k \le 2.0\)
\(\rho_l = \dfrac{A_{sl}}{b_w d}\) (longitudinal tension reinforcement ratio, limited to \(\rho_l \le 0.02\))
\(v_{min} = 0.035 \cdot k^{3/2} \cdot f_{ck}^{1/2}\) (MPa)

The design shear resistance is then:

\( V_{Rd,c} = v_{Rd,c} \cdot b_w \cdot d / 1000 \) (kN, with \(b_w, d\) in mm)

2. Shear resistance of links \(V_{Rd,s}\)

For vertical links (stirrups) with angle \(\alpha = 90^\circ\), Eurocode 2 (6.2.3) gives:

\( V_{Rd,s} = \dfrac{A_{sw}}{s} \cdot z \cdot f_{yd} \cdot \cot\theta / 1000 \) (kN)

where:

\(A_{sw}\) – total area of shear reinforcement within spacing \(s\) (mm²)
\(s\) – spacing of links (mm)
\(z \approx 0.9 d\) – internal lever arm (mm)
\(f_{yd} = f_{yk} / \gamma_s\) – design yield strength of shear reinforcement (MPa)
\(\cot\theta\) – cotangent of the compression strut angle, limited to \(1.0 \le \cot\theta \le 2.5\)

The calculator assumes vertical links and lets you choose \(\cot\theta\) (default 2.0).

3. Required shear reinforcement

If \(V_{Ed} > V_{Rd,c}\), shear reinforcement is required. The required steel per unit length is:

\( \dfrac{A_{sw,req}}{s} = \dfrac{V_{Ed} - V_{Rd,c}}{z \cdot f_{yd} \cdot \cot\theta} \cdot 10^6 \) (mm²/m)

The provided reinforcement is computed from your bar diameter \(\phi_w\), number of legs \(n_l\), and spacing \(s\). The tool compares provided \(A_{sw}/s\) with both the required and minimum values.

4. Minimum shear reinforcement and spacing

Eurocode 2 (9.2.2) specifies a minimum shear reinforcement ratio. A common expression is:

\( \dfrac{A_{sw,min}}{s} = 0.08 \cdot \dfrac{\sqrt{f_{ck}}}{f_{yk}} \cdot b_w \cdot 10^3 \) (mm²/m)

The calculator also checks a typical maximum spacing limit:

\(s \le 0.75 d\)
\(s \le 600\) mm

These are indicative; always confirm against your National Annex.

5. Design check

The design is considered adequate if:

\(V_{Ed} \le V_{Rd,c} + V_{Rd,s}\)
Provided \(A_{sw}/s \ge A_{sw,req}/s\)
Provided \(A_{sw}/s \ge A_{sw,min}/s\)
Link spacing satisfies code limits

Engineering notes & limitations

Designed for prismatic beams in bending with shear; torsion and axial force are not included.
Assumes vertical shear links and a constant \(\theta\) along the design region.
For deep beams, discontinuity regions (D‑regions), openings, or highly prestressed members, a full strut‑and‑tie model is recommended.
National Annexes may modify coefficients \(C_{Rd,c}\), \(k_1\), minimum reinforcement, and spacing rules.

This calculator is intended as a design aid for qualified engineers. Always verify results against the current version of EN 1992‑1‑1 and your National Annex, and apply professional judgement.