2.5.6 Shear Design

Shear Design

In the shear design, the applied tensile reinforcement is determined first.

From all reinforcement layers and directions, a total of 1.54 cm²/m of tension reinforcement can be applied. With it, the shear force V_Rd,c that can be resisted without shear reinforcement is determined.

With the applied tensile reinforcement, the longitudinal reinforcement ratio ρ_l is determined:

${\rho }_l = \frac{A_{sl}}{\left(b_w · d\right)} = \frac{1.54}{\left(100 · 125.5\right)} = 0.00012 \le 0.02$

In a 3D model type (in contrast to a plate), an additional axial force can occur. It must be considered via the corresponding concrete longitudinal stress.

${\sigma }_{cp} = \frac{n_{\beta }}{\left(b_w · h\right)} = \frac{-425.783}{\left(100 · 129\right)} = -0.33 {\text{N/m}}^2$

The factor k for considering the plate thickness is calculated as follows:

$k = 1 + \sqrt{\frac{200}{d}} = 1 + \sqrt{\frac{200}{1255}} = 1.399 \le 2.0 d\text{ in }\left[\mathrm{mm}\right]$

The following factors are also included in the design:

Thus, the design shear resistance V_Rd,c without shear reinforcement can be determined according to Equation (6.2a):

$$\begin{gathered} V_{Rd,c} = \left[C_{rd,c} · k {\left(100 · {\rho }_l · f_{ck}\right)}^{\frac{1}{3}} + k_1 · {\sigma }_{cp}\right] · b_w · d = \\ = \left[0.12 · 1.399 {\left(100 · 0.00012 · 30.0\right)}^{\frac{1}{3}} + 0.15 · 0.33\right] · 1000 · 1255 = 212.00 \text{kN/m} \end{gathered}$$

According to Equation (6.2b), the minimum value of the design shear resistance V_Rd,c without shear reinforcement is determined from the minimum reinforcement ratio ν_min:

${\nu }_{\text{min}} = 0.035 · k^{\frac{3}{2}} · {f_{ck}}^{\frac{1}{2}} = 0.035 · 1.{399}^{\frac{3}{2}} · 30.0^{\frac{1}{2}} = 0.317$

$V_{Rd,c} = \left(0.317 · 0.15 · 0.33\right) · 1000 · 1255 = 459.96\text{ kN/m }$

Because the plate's design shear resistance V_Rd,c = 459.96 kN/m is greater than the applied shear force V_Ed = 259.726 kN/m, no shear reinforcement is required in the example.

Should the plate's shear resistance be insufficient, the program first checks if the maximum shear resistance of the concrete compression strut V_Rd,max is sufficient. V_Rd,max is determined with the minimum inclination of the compression strut θ. When the design shear resistance of the concrete compression strut is greater than the applied shear force V_Ed, the statically required shear reinforcement req a_sw can be determined. Then the design for the shear reinforcement V_Rd,sy is carried out.