Eurocode 2 - Raw functions

streng.codes.eurocodes.ec2.raw.ch3.concrete.elastic_deformation Concrete elastic deformation
streng.codes.eurocodes.ec2.raw.ch3.concrete.strength Concrete strength
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain Concrete stress-strain relation
streng.codes.eurocodes.ec2.raw.ch4.concrete_cover Concrete cover
streng.codes.eurocodes.ec2.raw.ch5.geometric_data.effective_width Beams effective width
streng.codes.eurocodes.ec2.raw.ch6.shear Shear
graph LR A-->B click A callback "Tooltip" click B "#streng.codes.eurocodes.ec2.raw.ch3.concrete.elastic_deformation.Ecm" "This is a link"

Chapter 3 - Materials

concrete

elastic_deformation

Concrete elastic deformation

streng.codes.eurocodes.ec2.raw.ch3.concrete.elastic_deformation.Ecm(fck)[source]

Modulus of elasticity

Parameters:fck (float) – Characteristic (5%) compressive strength of concrete [MPa]
Returns:Given using the expression:
\[E_{cm}=22 (\dfrac{f_{cm}}{10})^{0.3}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.elastic_deformation.ν(cracked)[source]

Poisson’s ratio

Parameters:cracked (bool) – True for cracked, False for uncracked
Returns:0.0 for cracked, 0.2 for uncracked
Return type:float

strength

Concrete strength

streng.codes.eurocodes.ec2.raw.ch3.concrete.strength.fcd(acc, fck, γc)[source]

Design value for the compressive strength of concrete

Parameters:
  • acc (float) – Coefficient taking account of long term effects on the compressive strength and of unfavourable effects resulting from the way the load is applied
  • fck (float) – Characteristic (5%) compressive strength of concrete
  • γc (float) – Safety factor
Returns:

Given using the expression:

\[f_{cd}=a_{cc}\dfrac{f_{ck}}{γ_c}\]

Return type:

float

streng.codes.eurocodes.ec2.raw.ch3.concrete.strength.fcm(fck)[source]

Mean compressive strength at 28 days

Parameters:fck (float) – Characteristic (5%) compressive strength of concrete [MPa]
Returns:Given using the expression:
\[f_{cm}=f_{ck} + 8\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.strength.fctk005(fck)[source]

Characteristic (5% fractile) tensile strength of concrete [MPa]

Parameters:fck (float) – Characteristic (5%) compressive strength of concrete [MPa]
Returns:Given using the expression:
\[f_{ctk,0.05}=0.7\cdot f_{ctm}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.strength.fctk095(fck)[source]

Characteristic (95% fractile) tensile strength of concrete [MPa]

Parameters:fck (float) – Characteristic (5%) compressive strength of concrete [MPa]
Returns:Given using the expression:
\[f_{ctk,0.95}=1.3\cdot f_{ctm}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.strength.fctm(fck)[source]

Mean tensile strength at 28 days

Parameters:fck (float) – Characteristic (5%) compressive strength of concrete [MPa]
Returns:Given using the expression:
\[ \begin{align}\begin{aligned}f_{ctm} = 0.30\cdot f_{ck}^{2/3} for f_{ck}\le 50MPa\\f_{ctm} = 2.12\cdot ln(1+f_{cm}/10) for f_{ck}> 50MPa\end{aligned}\end{align} \]
Return type:float

stress_strain

Concrete stress-strain relation

streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.n(fck)[source]
Parameters:fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
Returns:Given using the expressions:
\[\begin{split}\begin{eqnarray} n & = & 2.0 & for & f_{ck} \le 50MPa \\ n & = & 1.4 + 23.4 \cdot ((90 - f_{ck})/100)^4 & for & f_{ck} \ge 50MPa \end{eqnarray}\end{split}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.εc1(fck)[source]

Compressive strain in the concrete at the peak stress (‰)

Parameters:fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
Returns:Given using the expression:
\[ε_{c1} = min(0.7\cdot f_{cm}^{0.31}, 2.8)\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.εc2(fck)[source]

The strain at reaching the maximum strength (‰)

Parameters:fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
Returns:Given using the expressions:
\[\begin{split}\begin{eqnarray} ε_{c2} & = & 2.0 & for & f_{ck} \le 50MPa \\ ε_{c2} & = & 2.0 + 0.085(f_{ck}-50)^{0.53} & for & f_{ck} \ge 50MPa \end{eqnarray}\end{split}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.εc3(fck)[source]

(‰)

Parameters:fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
Returns:Given using the expressions:
\[\begin{split}\begin{eqnarray} ε_{c3} & = & 1.75 & for & f_{ck} \le 50MPa \\ ε_{c3} & = & 1.75 + 0.55(f_{ck}-50)/40 & for & f_{ck} \ge 50MPa \end{eqnarray}\end{split}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.εcu1(fck)[source]
Parameters:fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
Returns:Given using the expressions:
\[\begin{split}\begin{eqnarray} ε_{cu1} & = & 3.5 & for & f_{ck} \le 50MPa \\ ε_{cu1} & = & 2.8 + 27 \cdot ((98 - f_{cm})/100)^4 & for & f_{ck} \ge 50MPa \end{eqnarray}\end{split}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.εcu2(fck)[source]

The ultimate strain

Parameters:fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
Returns:Given using the expressions:
\[\begin{split}\begin{eqnarray} ε_{cu2} & = & 3.5 & for & f_{ck} \le 50MPa \\ ε_{cu2} & = & 2.6 + 35 \cdot ((90 - f_{ck})/100)^4 & for & f_{ck} \ge 50MPa \end{eqnarray}\end{split}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.εcu3(fck)[source]
Parameters:fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
Returns:Given using the expressions:
\[\begin{split}\begin{eqnarray} ε_{cu2} & = & 3.5 & for & f_{ck} \le 50MPa \\ ε_{cu2} & = & 2.6 + 35 \cdot ((90 - f_{ck})/100)^4 & for & f_{ck} \ge 50MPa \end{eqnarray}\end{split}\]
Return type:float
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.σc_bilin(fck, αcc, γc, εc)[source]
Parameters:
  • fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
  • αcc (float) – Coefficient taking account of long term effects on the compressive strength and of unfavourable effects resulting from the way the load is applied
  • γc (float) – Safety factor
  • εc (float) – concrete strain (‰)
Returns:

Return type:

float

streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.σc_design(fck, αcc, γc, εc)[source]

Stress-strain relations for the design of cross-sections

Parameters:
  • fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
  • αcc (float) – Coefficient taking account of long term effects on the compressive strength and of unfavourable effects resulting from the way the load is applied
  • γc (float) – Safety factor
  • εc (float) – concrete strain (‰)
Returns:

Given using the expression:

\[\begin{split}\begin{eqnarray} σ_{c} & = & f_{cd}\cdot(1-(1-\dfrac{ε_c}{ε_{c2}})^n) & for & 0\le ε_c \le ε_{c2} \\ σ_{c} & = & f_{cd} & for & ε_{c2}\le ε_c \le ε_{cu2} \end{eqnarray}\end{split}\]

Return type:

float

streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.σc_nl(fck, εc)[source]

Stress-strain relation for non-linear structural analysis

Parameters:
  • fck (float) – Characteristic compressive cylinder strength of concrete at 28 days
  • εc (float) – concrete strain (‰)
Returns:

Given using the expression:

\[\begin{split}\begin{eqnarray} σ_{c} & = & f_{ctm}\dfrac{kη-η^2}{1+(k-2)η} \\ where: & \\ η & = & \dfrac{ε_c}{ε_{c1}} \\ k & = & 1.05\cdot E_{cm} \cdot ε_{c1} / f_{cm} \end{eqnarray}\end{split}\]

Return type:

float

Chapter 4 - Durability and cover to reinforcement

concrete cover

Concrete cover

streng.codes.eurocodes.ec2.raw.ch4.concrete_cover.cmindur(cat, env)[source]

Minimum cover cmin,dur with regard to durability for reinforcement steel

Struct. Class X0 XC1 XC2/XC3 XC4 XD1/XS1 XD2/XS2 XD3/XS3
S1 10 10 10 15 20 25 30
S2 10 10 15 20 25 30 35
S3 10 10 20 25 30 35 40
S4 10 15 25 30 35 40 45
S5 15 20 30 35 40 45 50
S6 20 25 35 40 45 50 55
Parameters:
  • cat (str) – Structural Class
  • env (str) – Exposure Class
Returns:

Taken from the table above

Return type:

int

Chapter 5 - Structural analysis

geometric_data

effective_width

Beams effective width

streng.codes.eurocodes.ec2.raw.ch5.geometric_data.effective_width.beff(bw, beff1, beff2, b)[source]

Effective flange width

http://repfiles.kallipos.gr/html_books/1284/images/Fig_09_14.png
Parameters:
  • bw (float) – Width of the web
  • beff1 (float) – Side 1 effective flange width
  • beff2 (float) – Side 2 effective flange width
  • b (float) – bw + b1 + b2
Returns:

Given using the expression:

\[b_{eff}=\sum{b_{eff,i}} + b_w \le b\]

Return type:

float

streng.codes.eurocodes.ec2.raw.ch5.geometric_data.effective_width.beffi(bi, l0)[source]

Side i effective flange width

http://repfiles.kallipos.gr/html_books/1284/images/Fig_09_14.png
Parameters:
  • bi (float) – half net length between adjacent beams
  • l0 (float) – Distance between points of zero moment
Returns:

Given using the expression:

\[b_{eff,i}=0.2\cdot b_i +0.1\cdot l_0 \le 0.2\cdot l_0\]

Return type:

float

streng.codes.eurocodes.ec2.raw.ch5.geometric_data.effective_width.l0(l1=0, l2=0, l3=0, zero_moments_case=0)[source]

Distance between points of zero moment

http://repfiles.kallipos.gr/html_books/1284/images/inter_09_01_2.png
Parameters:
  • l1 (float) – μήκος αμφιέρειστης ή ακραίου ανοίγματος
  • l2 (float) – μήκος μεσαίουν ανοίγματος
  • l3 (float) – μήκος προβόλου
  • zero_moments_case (int) – συνθήκες στήριξης. 0: αμφιέρειστη, 1: ακραίο άνοιγμα, 2: μεσαίο άνοιγμα, 3: μεσαία στήριξη, 4: στήριξη προβόλου
Returns:

Υποπεριπτώσεις σύμφωνα με το σχήμα

Return type:

float

Chapter 6 - Ultimate limit states (ULS)

shear

Shear

streng.codes.eurocodes.ec2.raw.ch6.shear.VRdc(CRdc, Asl, fck, σcp, bw, d, units='N-mm')[source]

The design value for the shear resistance \(V_{Rd,c}\) [N]

Units are ‘N-mm’, unless specified otherwise. Alternative options are: ‘kN-m’

1
2
3
4
5
6
7
 vrdc = shear.VRdc(CRdc=0.12,
                        Asl=308,
                        fck=20.,
                        σcp=0.66667,
                        bw=250.,
                        d=539.,
                        units='N-mm')
Parameters:
  • CRdc (float) – 0.18/γc
  • Asl (float) – [mm2] is the area of the tensile reinforcement
  • fck (float) – [N/mm2]
  • σcp (float) – \(σ_{cp}=N_{Ed}/A_c \lt 0.2f_{cd}\) [N/mm2]
  • bw (float) – The smallest width of the cross-section in the tensile area. [mm]
  • d (float) – Effective depth of the cross-section. [mm]
Returns:

Result value in [N], unless specified otherwise. Intermediate results are always ‘N-mm’

Given using the expressions

\[\begin{split}V_{Rd,c} = max \left\{\begin{matrix} [C_{Rd,c} \cdot k \cdot(100\cdot ρ_l\cdot f_{ck})^{1/3} + k_1 \cdot σ_{cp}] \cdot b_w \cdot d \\ (v_{min} + k_1 \cdot σ_{cp}) \cdot b_w \cdot d \end{matrix}\right.\end{split}\]

where:

  • \(k=1 + \sqrt{\dfrac{200}{d}} <= 2.0\)
  • \(ρ_l=\dfrac{A_{sl}}{b_w \cdot d}<=0.02\)
  • \(k_1 = 0.15\)

Return type:

VRdc (dict)

streng.codes.eurocodes.ec2.raw.ch6.shear.VRdmax(bw, d, fck, fyk, fywk, θ, αcw=1.0, γc=1.5, units='N-mm-rad')[source]

Maximum value for the shear resistance \(V_{Rd,max}\) [N]

Units are ‘N-mm’, unless specified otherwise. Alternative options are: ‘kN-m-rad’

1
2
3
4
5
6
7
8
9
 vrdmax = shear.VRdmax(bw=250.,
                       d=539.,
                       fck=20.,
                       fyk=500.,
                       fywk=500.,
                       θ=np.pi/4,
                       αcw = 1.0,
                       γc = 1.5,
                       units='N-mm-rad')
Parameters:
  • bw (float) – The smallest width of the cross-section in the tensile area. [mm]
  • d (float) – Effective depth of the cross-section. [mm]
  • fck (float) – [N/mm2]
  • fyk (float) – [N/mm2]
  • fywk (float) – [N/mm2]
  • θ (float) – Τhe angle between the concrete compression strut and the beam axis is the angle between the concrete compression strut and the beam axis [rad]
  • αcw (float) – Coefficient taking account of the state of the stress in the compression chord
Returns:

Result value in [N], unless specified otherwise. Intermediate results are always ‘N-mm’

Given using the expression

\[V_{Rd,max} = \dfrac{α_{cw}\cdot b_w \cdot z \cdot ν_1 \cdot f_{cd}}{\cot θ + \tan θ}\]

Return type:

VRdmax (dict)

streng.codes.eurocodes.ec2.raw.ch6.shear.VRds(nw, diaw, d, fyk, fywk, θ, s, γs=1.15, units='N-mm-rad')[source]

Shear resistance for members with vertical shear reinforcement \(V_{Rd,s}\) [N]

Units are ‘N-mm-rad’, unless specified otherwise. Alternative options are: ‘kN-m-rad’

1
2
3
4
5
6
7
8
9
 vrds = shear.VRds(nw=2.,
                   diaw = 8,
                   d=539,
                   fyk=500.,
                   fywk=500.,
                   θ=np.pi/4,
                   s = 169,
                   γs = 1.15,
                   units='N-mm-rad')
Parameters:
  • nw (float) – number of hoop legs.
  • diaw (float) – hoop bars diameter. [mm]
  • d (float) – Effective depth of the cross-section. [mm]
  • fyk (float) – [N/mm2]
  • fywk (float) – [N/mm2]
  • θ (float) – Τhe angle between the concrete compression strut and the beam axis is the angle between the concrete compression strut and the beam axis [rad]
  • s (float) – the spacing of the stirrups [mm]
Returns:

Result value in [N], unless specified otherwise. Intermediate results are always ‘N-mm’

Given using the expression

\[V_{Rd,max} = \dfrac{A_{sw}}{s} \cdot z \cdot f_{ywd} \cdot \cot θ\]

Return type:

VRds (dict)