RF-CONCRETE Surfaces – Online Manual Version 5

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RF-CONCRETE Surfaces – Online Manual Version 5

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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 °):

VRd,s = ASWs · z · fywd ·cot θ     (6.8)

where

Asw

cross-sectional area of shear reinforcement

s

spacing of links

z

lever arm of internal forces

fywd

design yield strength of shear reinforcement

θ

inclination of concrete compression strut

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  cot θ 2,5     (6.7N)

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

Table 2.1 Limits of the compression strut inclination according to EN 1992-1-1
Minimum inclination Maximum inclination

θ 

21.8°

45.0°

cot θ 

2.5

1.0

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

       1,00  cot θ  1,2 + 1,4 · σcdfcd / 1 - VRd, ccVEd  3,0     (6.7aDE)

where

VRd,cc = c · 0,48 · fck13 · 1 - 1,2 · σcdfcd · bw · z     (6.7bDE)

Table 2.1

NEd : design value of the longitudinal force in the cross-section due to external actions (NEd > 0 as longitudinal compressive force)

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

Table 2.2 Limits of the compression strut inclination according to DIN EN 1992-1-1/NA:2010
Minimum inclination Maximum inclination

θ

18.4°

45.0°

cot θ

3.0

1.0

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.

Figure 2.42 Window 1.4 Reinforcement, EN 1992-1-1 tab with limits of the variable compression strut inclination

The size of the minimum compression strut inclination angle θ also depends on the applied internal forces VEd 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 VRd,max of the concrete compression strut (see Equation 2.37). If it is smaller than the acting shear force VEd, a steeper strut inclination must be chosen. Then, the strut inclination θ is increased until the following applies:

VEd  VRd,max 

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