2.1.2 Shear Force

Shear Force

The check of shear force resistance is to be performed only in the ultimate limit state (ULS). The actions and resistances are considered with their design values. The general design requirement according to EN 1992-1-1, clause 6.2.1 is the following:

• V_Ed ≤ V_Rd

where

• V_Ed : design value of applied shear force
• V_Rd : design value of shear force resistance

Depending on the failure mechanism, the design value of the shear force resistance is determined by one of the following three values.

• V_Rd,c : design shear resistance of a structural component without shear reinforcement
• V _Rd,s : design shear resistance of a structural component with shear reinforcement, limited by the yield point of shear reinforcement (failure of tie)
• V_{Rd, max} : design shear resistance limited by strength of concrete compression strut

If the acting shear force V_Ed remains below the value of V_Rd,c, no calculated shear reinforcement is necessary and the check is verified.

If the applied shear force V_Ed is higher than the value of V_Rd,c, a shear reinforcement must be designed. The shear reinforcement must resist the entire shear force. In addition, the bearing capacity of the concrete compression strut must be analyzed.

• V_Ed ≤ V_Rd,s and V_Ed ≤ V_Rd,max

The various types of shear force resistance are determined according to EN 1992-1-1 as follows.

The design value for the design shear resistance V_Rd,c may be determined with:

$V_{Rd,c} = \left[C_{Rd,c} · k {\left(100{\sigma }_l · f_{ck}\right)}^{\frac{1}{3}} - k_1 · {\sigma }_{cp}\right] b_w · d$

Equation 2.1 EN 1992-1-1, Eq. (6.2a)

where

It is allowed, however, to apply a minimum value of the shear force resistance V_Rd,c,min.

$V_{Rd,c,\text{min}} = \left[v_{\text{min}} + k_1 · {\sigma }_{cp}\right] · b_w · d$

Equation 2.2 EN 1992-1-1, Eq. (6.2b)

where

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

$V_{Rd,s} = \frac{A_{sw}}{s} · z · f_{ywd} ·\text{ cot} \theta$

Equation 2.3 EN 1992-1-1, Eq. (6.8)

where

The inclination of the concrete compression strut θ may be selected within certain limits depending on the loading. This way, the equation can take into account the fact that a part of the shear force is resisted by crack friction and the virtual truss is thus less stressed. The following limits are recommended in equation (6.7) of EN 1992-1-1:

• 1 ≤ cot θ ≤ 2.5

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

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

$V_{Rd,\text{max}} = \frac{{\alpha }_{cw} · b_w · z · {\nu }_1 · f_{cd}}{\text{cot} \theta + \text{tan} \theta }$

Equation 2.4 EN 1992-1-1, Eq. (6.9)

where