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 |
Chapter 3 - Materials¶
concrete¶
elastic_deformation¶
Concrete elastic deformation
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: Returns: Given using the expression:
\[f_{cd}=a_{cc}\dfrac{f_{ck}}{γ_c}\]Return type:
-
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:
-
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:
-
streng.codes.eurocodes.ec2.raw.ch3.concrete.stress_strain.
σc_nl
(fck, εc)[source]¶ Stress-strain relation for non-linear structural analysis
Parameters: 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:
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: Returns: Taken from the table above
Return type:
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
Parameters: Returns: Given using the expression:
\[b_{eff}=\sum{b_{eff,i}} + b_w \le b\]Return type:
-
streng.codes.eurocodes.ec2.raw.ch5.geometric_data.effective_width.
beffi
(bi, l0)[source]¶ Side i effective flange width
Parameters: 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:
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: 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)