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Ultimate limit state - shear

The verification of the shear resistance is performed according to the chapter 6.2 of EN 1992-1-1.

Members not requiring design shear reinforcement

The design value for the shear resistance VRd,c is given according to the chapter 6.2.2(1):

Where is:

ρ|

  • The reinforcement ratio for longitudinal reinforcement

fck

  • The characteristic compressive cylinder strength of concrete at 28 days

bw

  • The smallest width of the cross-section in the tensile area

d

  • The effective depth of a cross-section

The minimum value of the shear resistance VRd,c is given by expression (6.2b):

The coefficient k is given by

Where is:

d

  • The effective depth of a cross-section

The reinforcement ratio ρ| is calculated using following formula

Where is:

As|

  • The area of the tensile reinforcement

The concrete compressive stress at the centroidal axis due to axial loading σcp is given by expression

Where is:

NEd

  • The design value of the applied axial force

Ac

  • The cross sectional area of concrete

fcd

  • The design value of concrete compressive strength

The value of CRd,c is given by formula

The value of vmin is calculated using the formula (6.3N):

Members requiring design shear reinforcement

The shear resistance is calculated with the help of formula (6.8):

Where is:

Asw

  • The cross-sectional area of the shear reinforcement

s

  • The spacing of the stirrups

fyd

  • The design yield strength of the shear reinforcement

z

  • The inner lever arm. This value may be obtained from the analysis or specified by the user.

Θ

  • The angle between the concrete compression strut and the beam axis perpendicular to the shear force

The shear resistance for members with inclined shear reinforcement is calculated with the help of formula (6.13):

The maximum shear force limited by crushing of the compression struts is calculated using formula (6.9):

Where is:

αcw

  • The coefficient taking account of the state of the stress in the compression chord, value is 1.0

bw

  • The minimum width between tension and compression chords

ν1

  • The strength reduction factor for concrete cracked in shear

fcd

  • The design value of concrete compressive strength

Θ

  • The angle between the concrete compression strut and the beam axis perpendicular to the shear force

The maximum shear force limited by crushing of the compression struts for members with inclined shear reinforcement is calculated using formula (6.14):

The strength reduction factor for concrete cracked in shear is calculated using formula (6.6N):

The minimum of values VRd,s and VRd,max is considered as the design shear resistance VRd.

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