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DC EC 01: shear reinforcement in beam


Geometry Cross-section: b=200mm and h=400mm
Material: C25/30
Concrete cover: d_1=d_2=40mm
Load Design shear force: V_{Ed.ULS}=102.9kN
Standard EN 1992-1-1 [–]



EN 1992-1-1 [–] allows the shear reinforcement to be calculated using the variable strut inclination method. In this method, you can choose

  • the inclination of the struts \theta between 1 < \cot (\theta) < 2.5.
    Diamonds starts its calculations with \theta)=31° (more info).
  • and the inclination of the stirrups \alpha. In practice there are 2 options: either you have ‘straight’ stirrup (\alpha=90°) or inclined stirrups (\alpha=45°).  

The variable strut inclination method in EN 1992-1-1 is often mixed up with the standard method used in ENV 1992-1. The standard method always assumes  \theta=45°.

    \[\nu =0.6 \cdot \left ( 1-\frac{f_{ck}}{250MPa} \right )=0.6 \cdot \left ( 1-\frac{25MPa}{250MPa} \right )=0.54\]

    \[V_{Rd.max}=b\cdot h\cdot \nu \cdot f_{cd}\cdot \frac{\cot (\theta )+\cot (\alpha )}{1+\cot (\theta )^2}\]

    \[V_{Rd.max}=200mm\cdot 400mm\cdot 0.54 \cdot 16.67MPa\cdot \frac{\cot (31^{\circ})+\cot (90^{\circ})}{1+\cot (\theta )^2}=257.47kN\]

    \[V_{Ed.ULS}< V_{Rd.max} \Rightarrow OK\]

    \[A_{sw}=\frac{V_{Ed.ULS}}{0.9\cdot d\cdot f_{ywd}\cdot (\cot (31^{\circ})+\cot (90^{\circ}))\cdot \sin (90^{\circ} )}=438mm^2/m\]

    \[A_{sw.min}=\frac{0.08\cdot \sqrt{f_{ck}}}{f_{yk}}\cdot b\cdot 10^3=\frac{0.08\cdot \sqrt{25MPa}}{500MPa}\cdot 200mm\cdot 10^3=160mm^2/m\]


Shear reinforcement calculated by Diamonds

Results Independent reference Diamonds Difference
Maximum shear reinforcement 438 mm²/m 438 mm²/m 0,00%
Minimum shear reinforcement 160 mm²/m 160 mm²/m 0,00%


  • EN 1992-1-1: 2005 + AC: 2010 §6.2.3 en §9.2.2
  • Van Hooymissen, L., Spegelaere, M., Van Gysel, A., & De Vylder, W. (2002). Gewapend beton. Academia Press.
    This reference does not contain this exact example, but it’s a good reference if you want to understand how reinforcement calculations work. However, keep in mind the calculations in this book are made done using the NBN B15-002 which is comparable to ENV 1992-1. The principle is similar to EN 1992-1-1 but some parameters differ slightly.
  • Tested in Diamonds 2023r01.

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