2.4.4.2 Shear force resistance with shear reinforcement

Shear force resistance with shear reinforcement

The following applies for structural components with shear reinforcement perpendicular to the component's axis (α = 90 °):

$V_{Rd,s} = \left(\frac{A_{SW}}{s}\right) · z · f_{ywd} ·cot \theta \text{(6.8)}$

where

The inclination of the concrete compression strut θ may be selected within certain limits depending on the loading. This takes into account the fact that a part of the shear force is resisted by the crack friction and thus does not stress the virtual truss. These limits are specified in EN 1992-1-1, Equation (6.7N).

$1.00 \le cot \theta \le 2.5 \left(\text{6.7N}\right)$

Thus, the compression strut inclination θ can be between the following values:

DIN EN 1992-1-1/NA:2010 specifies the following:

$1.00 \le cot \theta \le \left(1.2 + 1.4 · \frac{{\sigma }_{cd}}{f_{cd}}\right) / \left(1 - \frac{V_{Rd, cc}}{V_{Ed}}\right) \le 3.0 \left(\text{6.7aDE}\right)$

where

$V_{Rd,cc} =\hspace{0.17em}c · 0.48 · {f_{ck}}^{\frac{1}{3}} · \left(1 - 1.2 · \frac{{\sigma }_{cd}}{f_{cd}}\right) · b_w · z \left(\text{6.7bDE}\right)$

Thus, the compression strut inclination θ can be between the following values:

A flatter concrete compression strut means smaller tension forces within the shear reinforcement and thus a smaller required reinforcement area. In RF-CONCRETE Surfaces, the inclination of the compression strut is controlled in the EN 1992-1-1 tab of window 1.4 Reinforcement.

The size of the minimum compression strut inclination angle θ also depends on the applied internal forces V_Ed that can only be taken into account during the calculation. If the minimum compression strut angle is too small, a corresponding message is displayed.

In the calculation, the specified minimum value of the concrete compression strut inclination is first used to determine the shear resistance V_Rd,max of the concrete compression strut (see Equation 2.37). If it is smaller than the acting shear force V_Ed, a steeper strut inclination must be chosen. Then, the strut inclination θ is increased until the following applies:

$V_{Ed} \le V_{Rd,\text{max}}$

This compression strut inclination angle leads to the smallest shear reinforcement.