PyFEA is a finite element analysis (FEA) software written in Python language. It is divided into separate analyses for different structural engineering calculations. There are several available modules for different engineering calculations.
This a general purpose finite element analysis module, which could be used to derive element bending moments and axial forces. Please note, that geometric non-linearity is not available.
The external loads, including dead, live or wind forces, are resisted by internal energy stored in the structure. Depending on the distribution of forces, varying strains develop across the section. This results in a member to be subjected to bending moments and/or axial forces, which can be found using global analysis.
Section analysis allows to generate a M-N interaction curve, which defines the boundaries for combined bending moment and axial forces. Non-linear material properties are available, which enables to analyse variety of steel and concrete models.
This section defines how to incorporate material classes from material.py module.
For each model, the parameters plotting and title can be used to generate plots showing stress vs. strain diagrams.
materials.con1(Ec1,fc1,Ec2,fc2,Et1,ft,Et2,alphac,alphat,pset=0,crks=0)| Parameter | Type | Description |
|---|---|---|
| Ec1 | float in range [0,∞] | secant compressive stiffness |
| fc1 | float in range [-∞,0] | peak compressive strength |
| Ec2 | float in range [-∞,0] | secant compressive softening stiffness |
| fc2 | float in range [-∞,0] | residual compressive strength |
| Et1 | float in range [0,∞] | secant tensile stiffness |
| ft | float in range [0,∞] | peak tensile strength |
| Et2 | float in range [-∞,0] | tensile softening secant stiffness |
| alphac | float in range [-1,1] | compressive response parameter |
| alphat | float in range [-1,1] | tensile response parameter |
| pset | float | plastic strain in compression |
| crks | float | cracking strain in tension |
This is a trilinear concrete model, with optional quadratic and cubic overlays.
The input parameters for con1 material can be cumbersome to obtain. Therefore, con1gen subclass can be used to generate concrete properties based on its compressive strength
It is assumed that the input strength
Most of the other parameters are calculated according to CEB-FIP Model Code 1990 (MC 1990), CEB-FIP Model Code 2010 (MC 2010) as well as Rijkswaterstaat Technical Document: Guidelines for Nonlinear Finite Element Analysis of Concrete Structures (RTD 2010). These formulas are based on the uniaxial compressive cylinder strength.
| Parameter | Formula | Units | Reference |
|---|---|---|---|
| Compressive cylinder strength | MPa | NA | |
| Characteristic compressive cylinder strength | MPa | NA | |
| Mean compressive strength | MPa | MC 1990 Eq. 2.1-1 | |
| Peak compressive strength | MPa | NA | |
| Residual compressive strength | MPa | NA | |
| Tensile strength |
|
MPa | MC 2010 Eq. 5.1-3a |
| Fracture energy | N/mm | MC 2010 Eq. 5.1-9 | |
| Initial compressive modulus | MPa | MC 2010 Eq. 5.1-21 | |
| Poisson's ratio | - | MC 2010 5.1.7.3 | |
| Compressive fracture energy | N/mm | RTD 2010 p. 11 | |
| Compressive strain at peak strength | - | RTD 2010 p. 21 | |
| Secant compressive modulus | MPa | NA | |
| Initial tensile modulus | MPa | NA | |
| Compressive failure strain | - | RTD 2010 p. 21 | |
| Tensile strain at peak strength | - | NA | |
| Tensile failure strain |
|
- | RTD 2010 p. 17 |
| Compressive response factor | - | ||
| Tensile response factor | - |
materials.epm1(E1, fy, fu, epsilon_u,tension=True,compression=True)| Parameter | Type | Description |
|---|---|---|
| E1 | float/int | initial elastic stiffness |
| fy | float/int | yield strength |
| fu | float/int | ultimate strength |
| epsilon_u | float | ultimate strain |
| tension | bool | calculate the response in tension if True |
| compression | bool | calculate the response in compression if True |
This is a bilinear elasto-plastic model with kinematic strain hardening, typically used for a uniaxial modelling of mild steel. The curve can be defined for compression and/or tension by setting the parameters compression, tension to True or False.
materials.esb1(fu, lamb, epsilon_u, tension=True, compression=True)| Parameter | Type | Description |
|---|---|---|
| fu | float/int | ultimate strength |
| lambda | float | ratio of the depth of the equivalent stress block to NA |
| epsilon_u | float | ultimate strain |
This is a material based on an equivalent stress block for reinforced concrete sections design. This is
For Eurocode 2 design the following properties are recommended:
- The strength of the material is equal to the compressive strength reduced by 0.85
$f_u=\alpha f_{cd}=0.85f_{cd}$ . - The ratio of the depth of the equivalent stress block to NA is taken as
$\lambda =0.8$ . - The peak compressive strain is
$\epsilon_u = 0.0035$ .
All the materials have the same methods available. Any type of material is referred to as materials.type in the code below.
materials.type.plotting(strain)| Parameter | Type | Description |
|---|---|---|
| strain | float | strain at which stress is calculated |
This method calculates the stresses at given strain.
materials.sections.plot(strain,title='',lineType='-',xlim=(None,None),ylim=(None,None))| Parameter | Type | Description |
|---|---|---|
| strain | vector | strain for which stress is plotted |
| title | str | title of the plot |
| lineType | bool | line t C34E ype |
| xlim | tuple | x-axis limits |
| ylim | tuple | y-axis limits |
This method plots the material response for the given strain vector.
materials.sections.basicCurve(title='',lineType='-',xlim=(None,None),ylim=(None,None))| Parameter | Type | Description |
|---|---|---|
| title | str | title of the plot |
| lineType | bool | line type |
| xlim | tuple | x-axis limits |
| ylim | tuple | y-axis limits |
This method is similar to materials.sections.plot() but plot the entire material material response, without the need to specify the strain vector.
This chapter defines how to incorporate section classes from sections.py module.
Reinforced concrete rectangular section.
sections.rss(ID, mat, b, d)| Parameter | Type | Description |
|---|---|---|
| ID | str | name of the section |
| b | float | section width [mm] |
| d | float | section depth [mm] |
| reinf_sect | list | list of reinforcement layers, see below |
Reinforcement layers reinf have to be input as a nested list as follows:
reinf = [layer_1,layer_2,...layer_n]
layer_k = [no_bars, dia, dist]where the layer k has the following parameters:
- no_bars - number of bars
- dia - diamater of the bars [mm]
- dist - distance from the bottom of the section [mm]
Reinforced concrete T-section.
sections.rcts(Df, Dw, Bf, Bw, reinf_sect)| Parameter | Type | Description |
|---|---|---|
| Df | float | flange depth [mm] |
| Dw | float | web thickness [mm] |
| Bf | float | flange depth [mm] |
| Bw | float | web thickness [mm] |
| reinf_sect | list | list of reinforcement layers, see below |
Reinforcement layers reinf have to be input as a nested list as follows:
reinf = [layer_1,layer_2,...layer_n]
layer_k = [no_bars, dia, dist]where the layer k has the following parameters:
- no_bars - number of bars
- dia - diamater of the bars [mm]
- dist - distance from the bottom of the section [mm]
All the sections have the same methods available. Any type of section is referred to as sections.type in the code below.
materials.sections.plotting(title='section layout',reverse=False)| Parameter | Type | Description |
|---|---|---|
| title | str | title of the plot |
| reverse | bool | plots the section upside down |
This method plots the section layout. In case of rc sections, the reinforcement is uniformly distributed across its width and is only informative.
A group is composed of a section and corresponding materials and can be defined using groups module. This allows to carry out a strain / stress analysis.
groups.rc(concr,reinf,section)| Parameter | Type | Description |
|---|---|---|
| concr | object | concrete material instance |
| reinf | object | reinforcement material instance |
| section | object | section instance |
A reinforced concrete section can be instantiated using rc class. This assigns concrete and reinforcement material models to the concrete section.
The rc instance has several methods that allow to extract the section response at the given state. These extract the total axial force and moment applied on the section at the given stain distribution.
| Parameter | Type | Description |
|---|---|---|
| f_tot | float | axial load applied on the section (tension positive) |
| m_tot | float | moment applied on the section |
f_tot,m_tot=groups.rc(concr,reinf,section).calc(eps0,epsH, plotting=True,n_layers=800)| Parameter | Type | Description |
|---|---|---|
| eps0 | float | strain at depth x = 0 (tension positive) |
| epsH | float | strain at depth x = h (tension positive) |
| plotting | bool | plot stresses and strains across the section |
| n_layers | int | number of fibres the section to be discretised into |
f_tot,m_tot=groups.rc(concr,reinf,section).calcX0(eps0,x_NA, plotting=True,n_layers=800)| Parameter | Type | Description |
|---|---|---|
| eps0 | float | strain at depth x = 0 (tension positive) |
| x_NA | float | depth of the neutral axis (tension positive) |
| plotting | bool | plot stresses and strains across the section |
| n_layers | int | number of fibres the section to be discretised into |
f_tot,m_tot=groups.rc(concr,reinf,section).calcXH(epsh,x_NA, plotting=True,n_layers=800)| Parameter | Type | Description |
|---|---|---|
| epsH | float | strain at depth x = h (tension positive) |
| x_NA | float | depth of the neutral axis (tension positive) |
| plotting | bool | plot stresses and strains across the section |
| n_layers | int | number of fibres the section to be discretised into |
groups.rc(concr,reinf,section).mnCurve(xRatio=[0.16,0.2,0.3,0.4,0.5,0.8,0.9,1,1E99],n_layers=100,epsU=-0.0035,reverseMoment=False,points=None,r2kPath=None,legend=False,labels=None)| Parameter | Type | Description |
|---|---|---|
| xRatio | list | neutral axis distances at which the response is calculated |
| n_layers | int | number of fibres the section to be discretised into |
| epsU | float | assumed maximum compressive strain in the section |
| reverseMoment | bool | reverse the moments on the plot (x-axis) |
| points | list | if not None plot points with the given axial force and bending moment in a format points = [[M1,F1],[M2,F2]] |
| r2kPath | int | if not None this provides a path to csv file to plot another M-N curve in a format r2kPath="file.csv" |
| legend | bool | plot a legend |
| labels | list | list of labels for the legend in a format labels = ['label 1','label 2'] |
This method generates the M-N interaction diagram.
There is an option to overplot another M-N curve calculated in a different way using other commercial software, by providing a path to .csv file in r2kPath attribute.