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Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,7 @@


class Form5Dot1Imperfections(Formula):
"""Class representing formula 5.1 for the calculation of initial inclination imperfections, Θi."""
r"""Class representing formula 5.1 for the calculation of initial inclination imperfections, [$$\Theta_i$$]."""

label = "5.1"
source_document = NEN_EN_1992_1_1_C2_2011
Expand All @@ -21,21 +21,21 @@ def __init__(
alpha_h: DIMENSIONLESS,
alpha_m: DIMENSIONLESS,
) -> None:
"""[Θi] Initial inclination imperfections, Θi, is a ratio between height and inclination of the member [-].
r"""[$$\\Theta_i$$] Initial inclination imperfections, [$$\\Theta_i$$], is a ratio between height and inclination of the member [-].

NEN-EN 1992-1-1+C2:2011 art.5.2(5) - Formula (5.1)

Parameters
----------
theta_0 : float
[Θ0] Basic value [-].
Note: The value of Θ0 for use in a Country may be found in its National Annex.
[$$\\Theta_0$$] Basic value [-].
Note: The value of [$$\\Theta_0$$] for use in a Country may be found in its National Annex.
The recommended value is 1/200
alpha_h : float
[αh] Reduction factor for length or height [-].
[$$\alpha_h$$] Reduction factor for length or height [-].
Use your own implementation of this value or use the SubForm5Dot1ReductionFactorLengthOrHeight class.
alpha_m : float
[αm] Reduction factor for number of members [-].
[$$\alpha_m$$] Reduction factor for number of members [-].
Use your own implementation of this value or use the SubForm5Dot1ReductionFactorNumberOfMembers class.
"""
super().__init__()
Expand Down Expand Up @@ -65,7 +65,7 @@ def latex(self) -> LatexFormula:


class SubForm5Dot1ReductionFactorLengthOrHeight(Formula):
"""Class representing sub-formula 5.1 for the calculation of the reduction factor for length or height, αh."""
r"""Class representing sub-formula 5.1 for the calculation of the reduction factor for length or height, [$$\alpha_h$$]."""

label = "5.1"
source_document = NEN_EN_1992_1_1_C2_2011
Expand All @@ -74,16 +74,16 @@ def __init__(
self,
length: M,
) -> None:
"""[αh] Reduction factor for length or height [-].
r"""[$$\alpha_h$$] Reduction factor for length or height [-].

The calculated value of αh is between 2/3 and 1.0.
The calculated value of [$$\alpha_h$$] is between 2/3 and 1.0.

NEN-EN 1992-1-1+C2:2011 art.5.2(5) - Formula (5.1)

Parameters
----------
length : M
[length] Length or height, see art.5.2(6) [m].
[$$\text{length}$$] Length or height, see art.5.2(6) [$$m$$].
"""
super().__init__()
self.length = length
Expand Down Expand Up @@ -114,7 +114,7 @@ def latex(self) -> LatexFormula:


class SubForm5Dot1ReductionFactorNumberOfMembers(Formula):
"""Class representing sub-formula 5.1 for the calculation of the reduction factor for number of members, αm."""
r"""Class representing sub-formula 5.1 for the calculation of the reduction factor for number of members, [$$\alpha_m$$]."""

label = "5.1"
source_document = NEN_EN_1992_1_1_C2_2011
Expand All @@ -123,14 +123,14 @@ def __init__(
self,
members: int,
) -> None:
"""[αm] Reduction factor for number of members [-].
r"""[$$\alpha_m$$] Reduction factor for number of members [-].

NEN-EN 1992-1-1+C2:2011 art.5.2(5) - Formula (5.1)

Parameters
----------
members : int
[m] Number of vertical members contributing to the total effect [-].
[$$m$$] Number of vertical members contributing to the total effect [-].
"""
super().__init__()
self.members = members
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -7,28 +7,28 @@


class Form5Dot10aRedistributionOfMomentsLowerFck:
r"""Class representing formula 5.10a for the redistribution of moments in continuous beams or slabs when :math:`f_{ck} \leq 50 MPa`."""
r"""Class representing formula 5.10a for the redistribution of moments in continuous beams or slabs when [$$f_{ck} \leq 50 MPa$$]."""

label = "5.10a"
source_document = NEN_EN_1992_1_1_C2_2011

def __init__(self, delta: DIMENSIONLESS, k1: DIMENSIONLESS, k2: DIMENSIONLESS, xu: M, d: M) -> None:
r"""[:math:`δ`] Redistribution of moments in continuous beams or slabs when :math:`f_{ck} \leq 50 MPa`.
r"""[$$\delta$$] Redistribution of moments in continuous beams or slabs when [$$f_{ck} \leq 50 MPa$$].

NEN-EN 1992-1-1+C2:2011 art.5.5(4) - Formula (5.10a)

Parameters
----------
delta : DIMENSIONLESS
[:math:`δ`] is the ratio of the redistributed moment to the elastic moment.
[$$\delta$$] is the ratio of the redistributed moment to the elastic moment.
k1 : DIMENSIONLESS
[:math:`k1`] is a coefficient for redistribution.
[$$k_1$$] is a coefficient for redistribution.
k2 : DIMENSIONLESS
[:math:`k2`] is a coefficient for redistribution.
[$$k_2$$] is a coefficient for redistribution.
xu : M
[:math:`x_u`] is the depth of the compression zone in the ultimate limit state after redistribution.
[$$x_u$$] is the depth of the compression zone in the ultimate limit state after redistribution.
d : M
[:math:`d`] is the effective depth of the section.
[$$d$$] is the effective depth of the section.
"""
super().__init__()
self.delta = delta
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -7,28 +7,28 @@


class Form5Dot10bRedistributionOfMomentsUpperFck:
r"""Class representing formula 5.10b for the redistribution of moments in continuous beams or slabs when :math:`f_{ck} > 50 MPa`."""
r"""Class representing formula 5.10b for the redistribution of moments in continuous beams or slabs when [$$f_{ck} > 50 MPa$$]."""

label = "5.10b"
source_document = NEN_EN_1992_1_1_C2_2011

def __init__(self, delta: DIMENSIONLESS, k3: DIMENSIONLESS, k4: DIMENSIONLESS, xu: M, d: M) -> None:
r"""[:math:`δ`] Redistribution of moments in continuous beams or slabs when :math:`f_{ck} > 50 MPa`.
r"""[$$\delta$$] Redistribution of moments in continuous beams or slabs when [$$f_{ck} > 50 MPa$$].

NEN-EN 1992-1-1+C2:2011 art.5.5(4) - Formula (5.10b)

Parameters
----------
delta : DIMENSIONLESS
[:math:`δ`] is the ratio of the redistributed moment to the elastic moment.
[$$\delta$$] is the ratio of the redistributed moment to the elastic moment.
k3 : DIMENSIONLESS
[:math:`k3`] is a coefficient for redistribution.
[$$k_3$$] is a coefficient for redistribution.
k4 : DIMENSIONLESS
[:math:`k4`] is a coefficient for redistribution.
[$$k_4$$] is a coefficient for redistribution.
xu : M
[:math:`x_u`] is the depth of the compression zone in the ultimate limit state after redistribution.
[$$x_u$$] is the depth of the compression zone in the ultimate limit state after redistribution.
d : M
[:math:`d`] is the effective depth of the section.
[$$d$$] is the effective depth of the section.
"""
super().__init__()
self.delta = delta
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@


class Form5Dot11nShearSlendernessCorrectionFactor(Formula):
"""Class representing formula 5.11N for the calculation of the shear slenderness correction factor [:math:`k_{λ}`]."""
"""Class representing formula 5.11N for the calculation of the shear slenderness correction factor [$$k_{λ}$$]."""

label = "5.11N"
source_document = NEN_EN_1992_1_1_C2_2011
Expand All @@ -17,15 +17,15 @@ def __init__(
self,
lambda_factor: DIMENSIONLESS,
) -> None:
"""[:math:`k_{λ}`] Shear slenderness correction factor.
r"""[$$k_{λ}$$] Shear slenderness correction factor.

NEN-EN 1992-1-1+C2:2011 art.5.6.3(4) - Formula (5.11N)

Parameters
----------
lambda_factor : DIMENSIONLESS
[:math:`λ`] ratio of the distance between point of zero and maximum moment after redistribution and
effective depth, d [:math:`-`]
[$$λ$$] ratio of the distance between point of zero and maximum moment after redistribution and
effective depth, d [$$-$$]

Use your own implementation for this value or use :class:`Form5Dot12nRatioDistancePointZeroAndMaxMoment`.
"""
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -12,7 +12,7 @@ class Form5Dot12nRatioDistancePointZeroAndMaxMoment(Formula):

Note:
Ratio of the distance between point of zero and maximum moment after redistribution and
effective depth, d. [:math:`λ`]
effective depth, d. [$$λ$$]
"""

label = "5.12N"
Expand All @@ -24,19 +24,19 @@ def __init__(
v_sd: KN,
d: M,
) -> None:
"""[:math:`λ`] ratio of the distance between point of zero and maximum moment after redistribution and
effective depth, d [:math:`-`].
r"""[$$λ$$] ratio of the distance between point of zero and maximum moment after redistribution and
effective depth, d [$$-$$].

NEN-EN 1992-1-1+C2:2011 art.5.6.3(4) - Formula (5.12N)

Parameters
----------
m_sd : KNM
[:math:`M_{sd}`] Design moment at the section [:math:`kNm`].
[$$M_{sd}$$] Design moment at the section [$$kNm$$].
v_sd : KN
[:math:`V_{sd}`] Design shear force at the section [:math:`kN`].
[$$V_{sd}$$] Design shear force at the section [$$kN$$].
d : M
[:math:`d`] Effective depth [:math:`m`].
[$$d$$] Effective depth [$$m$$].
"""
super().__init__()
self.m_sd = m_sd
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@


class Form5Dot14SlendernessRatio(Formula):
"""Class representing formula 5.14 for the calculation of the slenderness ratio, :math:`λ`."""
r"""Class representing formula 5.14 for the calculation of the slenderness ratio, [$$\lambda$$]."""

label = "5.14"
source_document = NEN_EN_1992_1_1_C2_2011
Expand All @@ -18,18 +18,18 @@ def __init__(
l_0: M,
i: M,
) -> None:
"""[:math:`λ`] Slenderness ratio [:math:`-`].
r"""[$$\lambda$$] Slenderness ratio [$$-$$].

NEN-EN 1992-1-1+C2:2011 art.5.8.3.2(1) - Formula (5.14)

Parameters
----------
l_0 : M
[:math:`l_{0}`] Effective length [:math:`m`].
[$$l_{0}$$] Effective length [$$m$$].
Use your own implementation of this value or use :class: `Form5Dot15EffectiveLengthBraced`
or :class: `Form5Dot15EffectiveLengthUnbraced`.
i : M
[:math:`i`] Radius of gyration of the uncracked concrete section [:math:`m`].
[$$i$$] Radius of gyration of the uncracked concrete section [$$m$$].
"""
super().__init__()
self.l_0 = l_0
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -10,24 +10,24 @@


class Form5Dot15EffectiveLengthBraced(Formula):
"""Class representing formula 5.15 for the calculation of the effective length of braced members, :math:`l_0`."""
r"""Class representing formula 5.15 for the calculation of the effective length of braced members, [$$l_0$$]."""

label = "5.15"
source_document = NEN_EN_1992_1_1_C2_2011

def __init__(self, k_1: DIMENSIONLESS, k_2: DIMENSIONLESS, height: M) -> None:
"""[:math:`l_{0}`] Effective length for braced members [:math:`m`].
r"""[$$l_{0}$$] Effective length for braced members [$$m$$].

NEN-EN 1992-1-1+C2:2011 art.5.8.3.2(3) - Formula (5.15)

Parameters
----------
k_1 : DIMENSIONLESS
[:math:`k_{1}`] Relative flexibility of rotational constraint at end 1 [:math:`-`].
[$$k_{1}$$] Relative flexibility of rotational constraint at end 1 [$$-$$].
k_2 : DIMENSIONLESS
[:math:`k_{2}`] Relative flexibility of rotational constraint at end 2 [:math:`-`].
[$$k_{2}$$] Relative flexibility of rotational constraint at end 2 [$$-$$].
height : M
[:math:`l`] Clear height of compression member between end restraints [:math:`m`].
[$$l$$] Clear height of compression member between end constraints [$$m$$].
"""
super().__init__()
self.k_1 = k_1
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -10,24 +10,24 @@


class Form5Dot16EffectiveLengthUnbraced(Formula):
"""Class representing formula 5.16 for the calculation of effective length of unbraced members, :math:`l_0`."""
"""Class representing formula 5.16 for the calculation of effective length of unbraced members, [$$l_0$$]."""

label = "5.16"
source_document = NEN_EN_1992_1_1_C2_2011

def __init__(self, k_1: DIMENSIONLESS, k_2: DIMENSIONLESS, height: M) -> None:
"""[:math:`l_{0}`] Effective length for unbraced members [:math:`m`].
r"""[$$l_{0}$$] Effective length for unbraced members [$$m$$].

NEN-EN 1992-1-1+C2:2011 art.5.8.3.2(3) - Formula (5.16)

Parameters
----------
k_1 : DIMENSIONLESS
[:math:`k_{1}`] Relative flexibility of rotational constraint at end 1 [:math:`-`].
[$$k_{1}$$] Relative flexibility of rotational constraint at end 1 [$$-$$].
k_2 : DIMENSIONLESS
[:math:`k_{2}`] Relative flexibility of rotational constraint at end 2 [:math:`-`].
[$$k_{2}$$] Relative flexibility of rotational constraint at end 2 [$$-$$].
height : M
[:math:`l`] Clear height of compression member between end restraints [:math:`M`].
[$$l$$] Clear height of compression member between end constraint [$$m$$].
"""
super().__init__()
self.k_1 = k_1
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -10,25 +10,25 @@


class Form5Dot17EffectiveLengthBucklingLoad(Formula):
"""Class representing formula 5.17 for the calculation of effective length of unbraced members, in the
case where criteria (2) and (3) do not apply such as by variable loading, :math:`l_0`.
r"""Class representing formula 5.17 for the calculation of effective length of unbraced members, in the
case where criteria (2) and (3) do not apply such as by variable loading, [$$l_0$$].
"""

label = "5.17"
source_document = NEN_EN_1992_1_1_C2_2011

def __init__(self, ei: KN_M2, n_b: KN) -> None:
"""[:math:`l_{0}`] Effective length for unbraced members [:math:`m`].
r"""[$$l_{0}$$] Effective length for unbraced members [$$m$$].

NEN-EN 1992-1-1+C2:2011 art.5.8.3.2(6) - Formula (5.17)

Parameters
----------
ei : KN_M2
[:math:`EI`] is a representative bending stiffness [:math:`kN/m^2`].
[$$EI$$] is a representative bending stiffness [$$kN/m^2$$].
n_b : KN
[:math:`N_{b}`] is the buckling load expressed in terms of EI (in equation (5.14) i should correspond
to this EI). [:math:`kN`].
[$$N_{b}$$] is the buckling load expressed in terms of EI (in equation (5.14) i should correspond
to this EI). [$$kN$$].
"""
super().__init__()
self.ei = ei
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -14,25 +14,25 @@ class Form5Dot18ComparisonGeneralSecondOrderEffects:
source_document = NEN_EN_1992_1_1_C2_2011

def __init__(self, f_ved: KN, k_1: DIMENSIONLESS, n_s: DIMENSIONLESS, length: M, e_cd: MPA, i_c: MM4) -> None:
"""[:math:`CHECK`] Criteria met, based on damage accumulation.
r"""[$$CHECK$$] Criteria met, based on damage accumulation.

NEN-EN 1992-1-1+C2:2011 art.5.8.3.3(1) - Formula (5.18)

Parameters
----------
f_ved : KN
[:math: F_{v,ed}`] Total vertical load (on braced and bracing members) [:math:`kN`].
[$$F_{v,ed}$$] Total vertical load (on braced and bracing members) [$$kN$$].
k_1 : DIMENSIONLESS
[:math: k_1`] The value of k1 for use in a Country may be found in its National Annex. Recommend value is
0.31 [:math:`-`].
[$$k_1$$] The value of k1 for use in a Country may be found in its National Annex. Recommend value is
0.31 [$$-$$].
n_s : DIMENSIONLESS
[:math: `n_s`] is the total number of storeys [:math:`-`].
[$$n_s$$] is the total number of storeys [$$-$$].
length : M
[:math: `L`] is the total height of the building above level of moment restraint. [:math:`m`].
[$$L$$] is the total height of the building above level of moment restraint. [$$m$$].
e_cd : MPa
[:math: `E_{cd}`] is the design value of the modulus of elasticity of concrete. [:math:`MPa`].
[$$E_{cd}$$] is the design value of the modulus of elasticity of concrete. [$$MPa$$].
i_c : MM4
[:math: `l_c`] is the second moment of area (uncracked concrete section) of bracing member(s). [:math:`mm^4`].
[$$I_c$$] is the second moment of area (uncracked concrete section) of bracing member(s). [$$mm^4$$].
"""
self.f_ved = f_ved
self.k_1 = k_1
Expand All @@ -54,7 +54,7 @@ def left_hand_side(self) -> KN:

@property
def right_hand_side(self) -> KN:
"""Calculate the left hand side of the comparison.
"""Calculate the right hand side of the comparison.

Returns
-------
Expand Down
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