Shear capacity¶

The following functions are related to calculation of shear capacity with and without shear reinforcement.

Without shear reinforcement¶

structuralcodes.codes.ec2_2004.VRdc(fck: float, d: float, Asl: float, bw: float, NEd: float, Ac: float, fcd: float, k1: float = 0.15, gamma_c: float = 1.5, CRdc: float | None = None) → float[source]¶

Compute the design strength of the shear resistance.

EN 1992-1-1 (2005), Eq. (6.2)

Parameters:

fck (float) – The characteristic compressive strength in MPa.
d (float) – The effective depth of the cross-section in mm.
Asl (float) – The cross-sectional area of the tensile reinforcement, anchored atleast (lbd + d) beyond the considered cross-section, in mm2.
bw (float) – The smallest width of the cross-section in tension in mm.
NEd (float) – The normal force in the cross-section due to loading or prestress (NEd > 0 for compression) in N.
Ac (float) – The cross-sectional area of the concrete in mm2.
fcd (float) – The design compressive strength in MPa.

Keyword Arguments:

k1 (float) – Factor used to include the effect of the normal stress into the shear resistance of the concrete. Default value = 0.15, value might differ between National Annexes.
gamma_c (float) – Partial factor for concrete. Default value = 1.5, value might differ between National Annexes.
CRdc (Optional[float]) – Scaling factor for the shear resistance. Default value is 0.18 / gamma_c.

Returns:

The concrete shear resistance in MPa.

Return type:

float

structuralcodes.codes.ec2_2004.VRdc_prin_stress(Iy: float, bw: float, S: float, fctd: float, NEd: float, Ac: float, L_x: float = None, L_pt2: float = None) → float[source]¶

Calculate the shear resistance in uncracked, prestressed elements without shear reinforcement, value is determined via Mohr’s circle.

The maximal value of the principle tensile stress does no necessarily lay at the centre of gravity. If this is the ase the minimum value of the shear resistance and corresponding stress needs to be found at the relevant location.

EN 1992-1-1 (2005), Eq. (6.4).

Parameters:

Iy (float) – The second moment of area of the considered cross-section in mm4.
bw (float) – The width of the cross-section at the centre of gravity.
S (float) – The first moment of area of the considered cross-section of the part above the centre of gravity, and with respect to the centre of gravity in mm3.
fctd (float) – Design value of the tensile strength of the concrete.
NEd (float) – The normal force in the cross-section due to loading or prestress (NEd > 0 for compression) in N.
Ac (float) – The cross-sectional area of the concrete in mm2.

Keyword Arguments:

L_x (float) – Distance from the considered cross-section until the starting point of the transference length of the prestress steel. This value should be provided when the prestressing steel is prestreched. Default value is None.
L_pt2 (float) – Maximum value of the transference length of the prestress steel, according to Eq. (8.18). This value should be provided when the prestressing steel is prestreched. Default value is None.

Returns:

The maximum allowable shear force in N for an uncracked, prestressed element without shear reinforcement, determined from maximum allowable principle stress.

Return type:

float

structuralcodes.codes.ec2_2004.VEdmax_unreinf(bw: float, d: float, fck: float, fcd: float) → float[source]¶

Calculate the maximum allowable shear force for cross-sections without shear reinforcement.

En 1992-1-1 (2005), Eq. (6.5).

Parameters:

bw (float) – The smallest width of the cross-section in tension in mm.
d (float) – The effective depth of the cross-section in mm.
fck (float) – The characteristic compressive strength in MPa.
fcd (float) – The design compressive strength in MPa.

Returns:

The maximum allowable shear force in the cross-section in N. When a reduced shear force may be considered for the calculations, the unreduced shear force has to comply to this value.

Return type:

float

With shear reinforcement¶

structuralcodes.codes.ec2_2004.VRds(Asw: float, s: float, z: float, theta: float, fyk: float, alpha: float = 90.0, gamma_s: float = 1.15) → float[source]¶

Calculate the shear resistance of vertical shear reinforcement.

EN 1992-1-1 (2005). Eq. (6.8)

Parameters:

Asw (float) – the cross-sectional area of the shear reinforcement in mm2.
s (float) – The centre-to-centre distance of the shear reinforcement in mm.
z (float) – The inner lever arm of internal forces in mm.
theta (float) – The angle of the compression strut in degrees.
fyk (float) – The characteristic strength of the reinforcement steel in MPa.

Keyword Arguments:

alpha (float) – The angle of the shear reinforcement with respect to the neutral axis in degrees. Default value = 90 degrees.
gamma_s (float) – Partial factor of the reinforcement steel. Default value = 1.15. Value might differ between National Annexes.

Returns:

The shear resistance of the shear reinforcement in N.

Return type:

float

Raises:

ValueError – When theta < 21.8 degrees or theta > 45 degrees.

structuralcodes.codes.ec2_2004.VRdmax(bw: float, z: float, fck: float, theta: float, NEd: float, Ac: float, fcd: float, alpha: float = 90.0, limit_fyd: bool = False) → float[source]¶

Calculate the maximum shear strength of the compression strut.

EN 1992-1-1 (2005). Eq. (6.9)

Parameters:

bw (float) – The smallest width of the cross-section in tension in mm.
z (float) – The inner lever arm of internal forces in mm.
fck (float) – The characteristic compressive strength in MPa.
theta (float) – The angle of the compression strut in degrees.
NEd (float) – The normal force in the cross-section due to loading or prestress (NEd > 0 for compression) in N.
Ac (float) – The cross-sectional area of the concrete in mm2.
fcd (float) – The design compressive strength in MPa.

Keyword Arguments:

alpha (float) – The angle of the shear reinforcement with respect to the neutral axis in degrees. Default value = 90 degrees.
limit_fyd (bool) – Flag to indicate if the design yield stress is limited to 0.8 * fyk or not. This controls whether the stress reduction factor of concrete is given by Eq. (6.6) (False) or (6.10) (True).

Returns:

The shear strength of the shear reinforcement in N.

Return type:

float

Raises:

ValueError – When theta < 21.8 degrees or theta > 45 degrees.
ValueError – When sigma_cp > fcd.

structuralcodes.codes.ec2_2004.Asw_max(fcd: float, fck: float, bw: float, s: float, fywd: float, NEd: float, Ac: float, alpha: float = 90.0) → float[source]¶

Calculate the maximum cross-sectional area of the shear reinforcement, based on the assumption 1/tan(theta) == 1.

EN 1992-1-1 (2005). Eq. (6.13)

Parameters:

fcd (float) – The design strength of the concrete in MPa.
fck (float) – The characteristic compressive strength in MPa.
bw (float) – The smallest width of the cross-section in tension in mm.
s (float) – The centre-to-centre distance of the shear reinforcement in mm.
fwyd (float) – The design strength of the shear reinforcement steel in MPa.
NEd (float) – The normal force in the cross-section due to loading or prestress (NEd > 0 for compression) in N.
Ac (float) – The cross-sectional area of the concrete in mm2.

Keyword Arguments:

alpha (float) – The angle of the shear reinforcement with respect to the neutral axis in degrees. Default value = 90 degrees.

Returns:

The maximum allowable cross-sectional area of the shear reinforcement in mm2.

Return type:

float

Raises:

ValueError – When sigma_cp > fcd.