Theoretical Background > ULS Shear > Uniaxial check (predefined section)

The design for shear force resistance is only performed in the ultimate limit state. The analyzed rc sections belong to beam or to columns with transverse reinforcement that consist only of stirrups placed orthogonally to the axis of member. Do not use this shear check with opened thin walled sections (section do not stay plane with bending-shear actions).

The general design requirement according to EC2 (EN 1992-1-1) is the following:

VEd ≤ VRd

where

VEd design value of applied shear force

VRd 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:

VRd,c design shear resistance without shear reinforcement

VRd,s design shear resistance limited by yiel shear of shear reinforcement

VRd,max design shear resistance limited by strength of concrete compression struts

Design shear resistance without shear reinforcement

The design value for the design shear resistance VRd,c may be determined by:

VRd,c = [CRd,c k (100 ρl fck)1/3 - k1 σcp ] bw d (6.2a) EC2 σ

For the symbol's meaning please see EC2 /1/.

Program provide in the general data window a special member characteristic defined "Beam without stirrups" that you can choose if no stirrup is is to use.

Design shear resistance with shear reinforcement

Program provide only shear reinforcement perpendicular to the member's axis (α = 90°), then the following is applied:

VRd,s = Asw/s ·z · fywd ·cotϑ (6.8)EC2

where:

Asw cross-sectional area of shear reinforcement

s longitudinal spacing between stirrups (pitch)

z level arm of internal force of bending and axial force acting in the same combination

(program do not assume the simplified value z = 0.9 ·d)

fywd yield strength of shear reinforcement

ϑ inclination of concrete compression struts

The inclination ϑ of struts must comply with the following limit values recommended by EC2:

1 ≤ cot ϑ ≤ 2.5 (6.7)EC2

Those limiting value can be different in the National Annex (see Code and reinforcement options)

The design shear resistance of concrete compression struts (α = 90° always in this ) is:

VRd,max = αcw · bw · z · v1 · fcd /(1+cot2ϑ)

where

αcw = 1 factor for considering stress conditions in compression chord

bw minimum width of cross section (predefined sections)

z lever arm of internal forces

v1 reduction factor for concrete strength (National Annex can change this parameter. See Code and reinforcement options)

fcd design value of concrete strength

ϑ inclination of concrete struts

The procedure followed by the program for shear check is:

If for cotϑ = 1 VRcd < VEd then concrete section dimensions are not sufficient for shear resistance then it is necessary to resize the section.

If for cotϑ = 1 VRcd ≥ VEd then equating design shear VEd to shear resistance (1) VRcd we obtain ϑ value:

ϑ = 0.5 ⋅ arcsin [(2 VEd )/(acw⋅ v1 · fcd ⋅ 0.9 ⋅ d ⋅ bw )]

if cotϑ satisfyes eq. (6.7)EC2 the strictly necessary stirrups area Asw is given by eq. (6.8). The ckeck is OK if the comparison between Asw is less than the actually present area.

If the section was defined (in general data) as internal to a critical region of a beam in seismic zone and its ductility class is DCH then for EC8 program sets cotϑ = 1.

If cotϑ > 2.5 we assume cotϑ = 2.5.

In Code and reinforcement options windows you can optionally assign to cotϑ a max value less than 2.5.

In shear checks program controls all the stirrups detailing specified in § 8 and § 9 of EC2 and in § 5 of EC8.