concreteproperties.design_codes.nzs3101.NZS3101#
- class NZS3101[source]#
Bases:
DesignCode
Design code class for the New Zealand concrete design standard NZS3101:2006. Also implements the requirements of the NZSEE C5 assessment guidelines for probable strength design.
Note
Note that this design code currently only supports
Concrete
andNZS3101.SteelBarNZ
material objects. MeshedSteel
material objects are not supported as this falls under the composite structures design code.Inits the NZS3101 class.
Methods
Scaling factor relating the nominal 28 day concrete compressive strength to the effective concrete compressive strength used for design purposes within the concrete stress block.
Assigns the appropriate concrete section to be analysed depending on the analysis type requested.
Assigns a concrete section and the section type for the concrete section to the design code.
Scaling factor relating the depth of an equivalent rectangular compressive stress block (\(a\)) to the depth of the neutral axis (\(c\)).
Generates a biaxial bending with capacity factors to NZS3101:2006 or the NZSEE C5 assessment guidelines dependant on analysis type.
Calculates cracked section properties.
Calculates stresses within the reinforced concrete section assuming a cracked section.
Calculates service stresses within the reinforced concrete section.
Calculates ultimate stresses within the reinforced concrete section.
Calculates stresses within the reinforced concrete section assuming an uncracked section.
Returns the appropriate NZS3101:2006 or NZSEE C5 assessment guidelines capacity reduction factor dependant on the type of analysis specified.
Checks that the specified axial load is within the maximum tensile and compressive capacity of the concrete cross section.
Checks that the density is within the bounds outlined within NZS3101:2006 CL 5.2.2 for the elastic modulus expression within NZS3101:2006 CL 5.2.3(b) to be valid.
Checks that a valid Potential Plastic Hinge Region (PPHR) classification has been specified, and that the specified compressive strengths for all defined concrete geometries comply with NZS3101:2006 CL 5.2.1 for the specified PPHR classification.
Checks that the specified steel reinforcement strengths for all defined steel geometries comply with NZS3101:2006 CL 5.3.3.
Function to return the nominal, overstrength or probable concrete capacity capacity of a concrete section.
Calculates the lower characteristic tensile strength of concrete (\(f_t\)) in accordance with NZS3101:2006 CL 5.2.4, or calculates the probable tensile strength of concrete in accordance with NZSEE C5 assessment guidelines C5.4.2.4.
Returns a concrete material object to NZS3101:2006.
Creates a concrete section with likely maximum material strength properties for a cross section analysis to NZS3101:2006.
Creates a concrete section with probable strength material properties for a cross section analysis to NZS3101:2006 & NZSEE C5 assessment guidelines.
Returns a steel material object specific to the NZS3101:2006 code.
Calculates Youngs Modulus (\(E_c\)) for concrete in accordance with NZS3101:2006 CL 5.2.3(b).
Returns the gross section properties of the reinforced concrete section.
Transforms gross section properties.
Modification factor reflecting the reduced mechanical properties of lightweight concrete relative to normal weight concrete of the same compression strength.
Function to return the nominal, overstrength or probable axial load compressive strength of a concrete section when the load is applied with zero eccentricity.
Function to return the nominal axial load tension strength of a concrete section when the load is applied with zero eccentricity.
Calculates the average modulus of rupture of concrete (\(f_r\)) in accordance with NZS3101:2006 CL 5.2.5 for deflection calculations.
Performs a moment curvature analysis.
Generates a moment interaction diagram with capacity factors and material strengths to NZS3101:2006 or the NZSEE C5 assessment guidelines dependant on analysis type.
Returns a list of predefined material properties for steel grades for design to NZS3101:2006 & NZSEE C5 assessment guidelines.
Calculate the probable compressive strength of concrete in accordance with NZSEE C5 assessement guidelines C5.4.2.2.
Function to return the nominal, overstrength or probable steel reinforcement capacity of a concrete section.
Calculates the ultimate bending capacity with capacity factors to NZS3101:2006 or the NZSEE C5 assessment guidelines dependant on analysis type.
- class SteelBarNZ(name, density, stress_strain_profile, colour, steel_grade, phi_os)[source]#
Bases:
SteelBar
Class for a steel bar material to NZS3101, treated as a lumped circular mass with a constant strain.
- Parameters
name (
str
) – Steel bar material namesteel_grade (
str
) – Designation of the grade of reinforcement bar to be analysed, included predefined current and historic grades are detailed in theNZS3101.create_steel_material()
methoddensity (
float
) – Steel bar density (mass per unit volume)phi_os (
float
) – Overstrength factor depending on reinforcement grade (\(\phi_{o,f_y}\)), refer to NZS3101:2006 CL 2.6.5.5 or NZSEE C5 assessment guidelines C5.4.3stress_strain_profile (
StressStrainProfile
) – Steel bar stress-strain profilecolour (
str
) – Colour of the material for rendering
- assign_concrete_section(concrete_section, section_type='column')[source]#
Assigns a concrete section and the section type for the concrete section to the design code.
- Parameters
concrete_section (
ConcreteSection
) – Concrete section object to analysesection_type (
str
, default:'column'
) –The type of member being analysed:-
column - Analyses assigned concrete section object as a column (or beam) member in accordance with NZS3101:2006 Chapter 9 or 10 as appropriate
wall - Analyses assigned concrete section object as a doubly reinforced wall member in accordance with NZS3101:2006 Chapter 11
wall_sr_s - Analyses assigned concrete section object as a singly reinforced wall member in accordance with NZS3101:2006 Chapter 11 for design actions causing bending about the strong axis
wall_sr_m- Analyses assigned concrete section object as a singly reinforced wall member in accordance with NZS3101:2006 Chapter 11 for design actions causing bending about the minor axis
- Raises
ValueError – If the concrete section contains meshed reinforcement
ValueError – If section type for the analysis of the concrete section is not valid
- Return type
None
- assign_analysis_section(analysis_type='nom_chk')[source]#
Assigns the appropriate concrete section to be analysed depending on the analysis type requested.
- Parameters
analysis_type (
str
, default:'nom_chk'
) – The type of cross section analysis to undertake on the defined concrete section, by default a normal nominal strength design check is undertaken, refer toNZS3101.capacity_reduction_factor()
for further information on analysis types.- Raises
ValueError – If analysis type is not valid
- Returns
ConcreteSection
– Returns the appropriate concrete section object for the analysis depending on the analysis type
- e_conc(compressive_strength, density=2300)[source]#
Calculates Youngs Modulus (\(E_c\)) for concrete in accordance with NZS3101:2006 CL 5.2.3(b).
\(E_c=\displaystyle{4700\sqrt{f'_c}\frac{\rho}{2300}}\)
- Parameters
compressive_strength (
float
) – 28 day compressive concrete strength (MPa)density (
float
, default:2300
) – Concrete density \(\rho\) in accordance with NZS3101:2006 CL 5.2.2, defaults to 2300 kg/m3 for normal weight concrete
- Returns
float
– \(E_c\), Youngs Modulus (MPa)
- check_density_limits(density, low_limit, high_limit)[source]#
Checks that the density is within the bounds outlined within NZS3101:2006 CL 5.2.2 for the elastic modulus expression within NZS3101:2006 CL 5.2.3(b) to be valid.
- Parameters
density (
float
) – Concrete density \(\rho\) in accordance with NZS3101:2006 CL 5.2.2low_limit (
float
) – Lower limit for density from NZS3101:2006 CL 5.2.2high_limit (
float
) – Upper limit for density from NZS3101:2006 CL 5.2.2
- Raises
ValueError – If density is outside of the limits within NZS3101:2006 CL 5.2.2
- Return type
None
- alpha_1(compressive_strength)[source]#
Scaling factor relating the nominal 28 day concrete compressive strength to the effective concrete compressive strength used for design purposes within the concrete stress block. For an equivalent rectangular compressive stress block it relates the 28 day concrete compressive strength (\(f'_c\)) to the average concrete compressive design strength (\(f_{ave}\)). A function of the concrete compressive strength.
\(\quad\alpha_1=\displaystyle{\frac{f_{ave}}{f'_c}}\)
Where:-
\(\quad\alpha_1=0.85-0.004(f'_c-55)\quad:0.75\leq\alpha_1\leq0.85\)
- Parameters
compressive_strength (
float
) – 28 day compressive design strength (MPa)- Returns
float
– \(\alpha_1\) factor
- beta_1(compressive_strength)[source]#
Scaling factor relating the depth of an equivalent rectangular compressive stress block (\(a\)) to the depth of the neutral axis (\(c\)). A function of the concrete compressive strength.
\(\quad\beta_1=\displaystyle{\frac{a}{c}}\)
Where:-
\(\quad\beta_1=0.85-0.008(f'_c-30)\quad:0.65\leq\beta_1\leq0.85\)
- Parameters
compressive_strength (
float
) – 28 day compressive design strength (MPa)- Returns
float
– \(\beta_1\) factor
- lamda(density)[source]#
Modification factor reflecting the reduced mechanical properties of lightweight concrete relative to normal weight concrete of the same compression strength.
\(\quad\lambda=0.4+\displaystyle{\frac{0.6\rho}{2200}}\leq1.0\)
- Parameters
density (
float
) – Saturated surface dry density of concrete material- Returns
float
– \(\lambda\) factor
- concrete_tensile_strength(compressive_strength, density=2300, prob_design=False)[source]#
Calculates the lower characteristic tensile strength of concrete (\(f_t\)) in accordance with NZS3101:2006 CL 5.2.4, or calculates the probable tensile strength of concrete in accordance with NZSEE C5 assessment guidelines C5.4.2.4.
For design to NZS3101:2006:-
\(\quad f_t=0.38\lambda({f'_c})^{0.5}\)
For design to NZSEE C5 assessment guidelines:-
\(\quad f_{ct}=0.55({f'_{cp}})^{0.5}\)
- Parameters
compressive_strength (
float
) – 28 day compressive design strength (MPa)density (
float
, default:2300
) – Saturated surface dry density of concrete materialprob_design (
bool
, default:False
) – True if the probable tensile strength of concrete is to be calculated in accordance with NZSEE C5 assessment guidelines
- Returns
float
– Lower characteristic (\(f_t\)) or probable (\(f_{ct}\)) tensile strength of concrete
- modulus_of_rupture(compressive_strength, density=2300)[source]#
Calculates the average modulus of rupture of concrete (\(f_r\)) in accordance with NZS3101:2006 CL 5.2.5 for deflection calculations.
\(\quad f_r=0.6\lambda({f'_c})^{0.5}\)
- Parameters
compressive_strength (
float
) – 28 day compressive design strength (MPa)density (
float
, default:2300
) – Saturated surface dry density of concrete material
- Returns
float
– Modulus of rupture (\(f_r\))
- prob_compressive_strength(compressive_strength)[source]#
Calculate the probable compressive strength of concrete in accordance with NZSEE C5 assessement guidelines C5.4.2.2.
Taken as the nominal 28-day compressive strenght of the concrete specified for the original construciton, multiplied by 1.5 for strengths less than or equal to 40 MPa, and 1.4 for strengths greater than 40 MPa.
- Parameters
compressive_strength (
float
) – 28 day compressive design strength (MPa)- Returns
float
– Probable comopressive strength of concrete (\(f'_{cp}\))
- concrete_capacity(os_design=False, prob_design=False, add_compressive_strength=15)[source]#
Function to return the nominal, overstrength or probable concrete capacity capacity of a concrete section.
Note for a column section type outputs the unfactored concrete yield force for a column member designed in accordance with NZS3101:2006 Chapter 10 based on net concrete area:-
\(\quad N_c = \alpha_1A_nf'_c\)
Note for a wall section type outputs the unfactored concrete yield force for a doubly or singly reinforced wall member designed in accordance with NZS3101:2006 Chapter 11 based on gross concrete area:-
\(\quad N_c = A_gf'_c\)
- Parameters
os_design (
bool
, default:False
) – True if an overstrength capacity of a concrete section is required, then the material properties for concrete are scaled to reflect the likely maximum material strength propertiesprob_design (
bool
, default:False
) – True if the probable capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the probable material strength propertiesadd_compressive_strength (
float
, default:15
) – The increase in compressive strength of the specified 28 day compressive strength of concrete to reflect the likely maximum material strength, defaults to an additional 15 MPa as per NZS3101:2006 CL 2.6.5.5(c)
- Raises
ValueError – If section type for the analysis of the concrete section is not valid
- Returns
float
– Nominal, overstrength or probable concrete yield force (N) for the defined section/member type provided
- steel_capacity(os_design=False, prob_design=False)[source]#
Function to return the nominal, overstrength or probable steel reinforcement capacity of a concrete section.
- Parameters
os_design (
bool
, default:False
) – True if an overstrength capacity of a concrete section is required, then the material properties for lumped reinforcement are scaled to reflect the likely maximum material strength propertiesprob_design (
bool
, default:False
) – True if the probable capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the probable material strength properties
- Raises
ValueError – If concrete section contains a steel material that is not
NZS3101.SteelBarNZ
- Returns
float
– Nominal, overstrength or probable steel yield force (N)
- max_comp_strength(cpe_design=False, os_design=False, prob_design=False)[source]#
Function to return the nominal, overstrength or probable axial load compressive strength of a concrete section when the load is applied with zero eccentricity.
For column members, the maximum design load in compression is as follows:-
For non-capacity design situations, refer to NZS3101:2006 CL 10.3.4.2:-
\(\quad\displaystyle{\frac{N^*}{\phi} < 0.85N_{n,max}}\)
For capacity design situations, refer to NZS3101:2006 CL 10.4.4:-
\(\quad N^*_o < 0.7N_{n,max}\)
Where:-
\(\quad N_{n,max} = \alpha_1f'_c(A_g-A_{st})+f_yA_{st}\)
For doubly reinforced wall members, the maximum design load in compression is as follows:-
For non-capacity design situations, refer to NZS3101:2006 CL 11.3.1.6:-
\(\quad\displaystyle{\frac{N^*}{\phi} < 0.3A_gf'_c}\)
For ductile wall design situations within potential plastic regions, refer to NZS3101:2006 CL 11.4.1.1:-
\(\quad N^*_o < 0.3A_gf'_c\)
For singly reinforced wall members, the maximum design load in compression depends on the axis the design actions are causing bending about:-
Warning
Note singly reinforced walls are only allowed in nominally ductile structures designed in accordance with NZS3101:2006.
Refer NZS3101:2006 Chapter 2 & 11 for other limitations on the use of singly reinforced walls.
Note because of the different maximum axial compression load limits and strength reduction factors for singly reinforced walls depending upon the bending axis, care should be taken to only analyse a singly reinforced wall member about the appropriate axis. Engineering judgement should be exercised when analysing a singly reinforced wall about non-principal axes.
For design situations where the design actions cause bending about the strong axis of a singly reinforced wall, refer to NZS3101:2006 CL 11.3.1.6:-
\(\quad N^* < 0.015A_gf'_c\)
For design situations where the design actions cause bending about the minor axis of a singly reinforced wall, refer to NZS3101:2006 CL 11.3.5:-
\(\quad N^* < 0.06A_gf'_c\)
- Parameters
cpe_design (
bool
, default:False
) – True if the capacity protected element capacity of a concrete section is required (i.e. design capacity being checked against O/S actions)os_design (
bool
, default:False
) – True if the overstrength capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the likely maximum material strength propertiesprob_design (
bool
, default:False
) – True if the probable capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the probable material strength properties
- Returns
float
– Returns the nominal, overstrength or probable axial load compressive strength of a concrete section \(N_{n,max}\)
- max_ten_strength(os_design=False, prob_design=False)[source]#
Function to return the nominal axial load tension strength of a concrete section when the load is applied with zero eccentricity.
\(\quad N_{t,max} = f_yA_{st}\)
- Parameters
os_design (
bool
, default:False
) – True if an overstrength capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the likely maximum material strength propertiesprob_design (
bool
, default:False
) – True if the probable capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the probable material strength properties
- Returns
float
– Returns the nominal, overstrength or probable axial tension strength of a concrete section \(N_{t,max}\)
- check_axial_limits(n_design, phi, cpe_design=False, os_design=False, prob_design=False, n_scale=0.001)[source]#
Checks that the specified axial load is within the maximum tensile and compressive capacity of the concrete cross section.
- Parameters
n_design (
float
) – Axial design force (\(N^*\))phi (
float
) – Strength reduction factor \(\phi\)cpe_design (
bool
, default:False
) – True if the capacity protected element capacity of a concrete section is required (i.e. design capacity being checked against O/S actions)os_design (
bool
, default:False
) – True if the overstrength capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the likely maximum material strength propertiesprob_design (
bool
, default:False
) – True if the probable capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the probable material strength propertiesn_scale (
float
, default:0.001
) – Scaling factor to apply to axial load
- Raises
ValueError – If the supplied axial load is less than or greater than the the tensile or compressive strength of a concrete section
- Return type
None
- check_f_y_limit()[source]#
Checks that the specified steel reinforcement strengths for all defined steel geometries comply with NZS3101:2006 CL 5.3.3. :rtype:
None
Note
Note this check does not apply to predefined steel materials based on probable strength properties.
- Raises
ValueError – If concrete section contains a steel material that is not
NZS3101.SteelBarNZ
ValueError – If characteristic steel reinforcement yield strength is greater than the 500MPa limit in NZS3101:2006 CL 5.3.3
- check_f_c_limits(pphr_class)[source]#
Checks that a valid Potential Plastic Hinge Region (PPHR) classification has been specified, and that the specified compressive strengths for all defined concrete geometries comply with NZS3101:2006 CL 5.2.1 for the specified PPHR classification.
- Parameters
pphr_class (
str
) –Potential Plastic Hinge Region (PPHR) classification, NDPR/LDPR/DPR.
NDPR = Nominally Ductile Plastic Region
LDPR = Limited Ductile Plastic Region
DPR = Ductile Plastic Region
- Raises
ValueError – If specified Potential Plastic Hinge Region (PPHR) classification is not NDPR, LDPR or DPR
ValueError – If specified compressive strength for a concrete geometry is not between 20 MPa and 100 MPa for NDPR PPHR’s, or is not between 20 MPa and 70 MPa for LDPR or DPR PPHR’s
- Return type
None
- create_concrete_material(compressive_strength, ultimate_strain=0.003, density=2300, colour='lightgrey')[source]#
Returns a concrete material object to NZS3101:2006.
Material assumptions
Density: Defaults to 2300 kg/m3 unless supplied as user input
Elastic modulus: Calculated from NZS3101:2006 Eq. 5-1
Serviceability stress-strain profile: Linear with no tension
Ultimate stress-strain profile: Rectangular stress block, parameters from NZS3101:2006 CL 7.4.2.7, maximum compressive strain of 0.003
Lower characteristic tensile strength of concrete: Calculated from NZS3101:2006 Eq. 5-2
- Parameters
compressive_strength (
float
) – 28 day compressive design strength (MPa)ultimate_strain (
float
, default:0.003
) – Maximum concrete compressive strain at crushing of the concrete for designdensity (
float
, default:2300
) – Saturated surface dry density of concrete materialcolour (
str
, default:'lightgrey'
) – Colour of the concrete for rendering, defaults to ‘lightgrey’
- Returns
Concrete
– Concrete material object
- predefined_steel_materials()[source]#
Returns a list of predefined material properties for steel grades for design to NZS3101:2006 & NZSEE C5 assessment guidelines.
Refer to
NZS3101.create_steel_material()
for details of predefined steel grades.- Returns
Tuple
[Dict
,List
[str
],List
[str
]] – Returnsdict
with standard predefined steel material properties based on current steel grade 300E & 500E material properties in accordance with NZS3101:2006, and based on historic steel grade material properties in accordance with NZSEE C5 assessment guidelines.Returns
list
with predefined material grades that have been defined on characteristic strength material properties andlist
of predefined material grades that have been defined based on probable strength material properties.
Dictionary keys
Dict key
Description
1
Charateristic yield strength (\(f_y\)) or probable yield strength (\(f_{yp}\))
2
Fracture strain (\(\varepsilon_{su}\))
3
Overstrength factor (\(\phi_{o,f_y}\) or \(\phi_o\)) (note if probable strength based material property is specified then the true O/S factor to be applied against the characteristic yield strength is 1.08 times this value).
4
True if probable strength based yield strength & overstrength factor. False if lower characteristic strength based yield strength & overstrength factor.
- create_steel_material(steel_grade=None, yield_strength=None, fracture_strain=None, phi_os=None, colour='red')[source]#
Returns a steel material object specific to the NZS3101:2006 code.
Material assumptions
Density: 7850 kg/m3
Elastic modulus: 200000 MPa
Stress-strain profile: Elastic-plastic, fracture strain \(\varepsilon_{su}\) from AS/NZS4671 Table 7.2(A) or NZSEE C5 assessment guidelines (for historic reinforcement grades)
- Parameters
steel_grade (
Optional
[str
], default:None
) – Designation of the grade of reinforcement bar to be analysed, included predefined current and historic grades are as follows:-
Note
By using a valid steel grade designation the required input parameters are initiated with the required values for current reinforcement grades from the AS/NZS4671 standard or for historic grades from the NZSEE C5 assessment guidelines. Note user may overwrite any parameter of a predefined material by providing that parameter as input to
NZS3101.create_steel_material()
.Note if no predefined steel grade is provided, a steel grade name of ‘user_’ + yield strength is utilised.
NZS3101:2006 & NZSEE C5 asessment guidelines predefined steel materials
NZS3101:2006 characteristic yield strength based predefined materials
300e - Use for design to NZS3101:2006 provisions
Characteristic yield strength \(f_y\) = 300 MPa
Fracture strain \(\varepsilon_{su}\) = 15% or 0.15
Overstrength factor \(\phi_{o,f_y}\) = 1.35
500e - Use for design to NZS3101:2006 provisions
Characteristic yield strength \(f_y\) = 500 MPa
Fracture strain \(\varepsilon_{su}\) = 10% or 0.10
Overstrength factor \(\phi_{o,f_y}\) = 1.35
NZSEE C5 guidelines probable yield strength based predefined materials
pre_1945 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 280 MPa
Fracture strain \(\varepsilon_{su}\) = 10% or 0.10
Overstrength factor \(\phi_{f_o}\) = 1.25
33 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 280 MPa
Fracture strain \(\varepsilon_{su}\) = 10% or 0.10
Overstrength factor \(\phi_{f_o}\) = 1.25
40 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 324 MPa
Fracture strain \(\varepsilon_{su}\) = 15% or 0.15
Overstrength factor \(\phi_{f_o}\) = 1.25
275 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 324 MPa
Fracture strain \(\varepsilon_{su}\) = 15% or 0.15
Overstrength factor \(\phi_{f_o}\) = 1.25
hy60 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 455 MPa
Fracture strain \(\varepsilon_{su}\) = 12% or 0.12
Overstrength factor \(\phi_{f_o}\) = 1.5
380 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 455 MPa
Fracture strain \(\varepsilon_{su}\) = 12% or 0.12
Overstrength factor \(\phi_{f_o}\) = 1.5
430 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 464 MPa
Fracture strain \(\varepsilon_{su}\) = 12% or 0.12
Overstrength factor \(\phi_{f_o}\) = 1.25
300 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 324 MPa
Fracture strain \(\varepsilon_{su}\) = 15% or 0.15
Overstrength factor \(\phi_{f_o}\) = 1.25
500n - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 500 MPa
Fracture strain \(\varepsilon_{su}\) = 5% or 0.05
Overstrength factor \(\phi_{f_o}\) = 1.5
500 - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 540 MPa
Fracture strain \(\varepsilon_{su}\) = 10% or 0.10
Overstrength factor \(\phi_{f_o}\) = 1.25
cd_mesh - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 600 MPa
Fracture strain \(\varepsilon_{su}\) = 1.5% or 0.015
Overstrength factor \(\phi_{f_o}\) = 1.2
duc_mesh - Use for probable strength design to NZSEE C5 assessment guidelines
Probable yield strength \(f_{yp}\) = 500 MPa
Fracture strain \(\varepsilon_{su}\) = 3% or 0.03
Overstrength factor \(\phi_{f_o}\) = 1.2
- Parameters
yield_strength (
Optional
[float
], default:None
) –Steel characteristic yield strength (MPa)
Note for a predefined steel grade based on probable strength properties this is interpreted as the probable yield strength.
Note for a user defined steel grade, this is always entered on the basis of a characteristic yield strength, even if undertaking a probable strength based analysis. The analysis will internally scale the characteristic yield stress by 1.08 as per NZSEE C5 assessment guidelines C5.4.3.
fracture_strain (
Optional
[float
], default:None
) – Lower bound tensile strain (\(\varepsilon_{su}\)), based on characteristic uniform elongation limit from AS/NZS4671 Table 7.2(A) or NZSEE C5 assessment guidelines Table C5.4.phi_os (
Optional
[float
], default:None
) – Overstrength factor depending on reinforcement grade (\(\phi_{o,f_y}\) or \(\phi_o\)), refer to NZS3101:2006 CL 2.6.5.5, or for a probable strength assessment to the NZSEE C5 assessment guidelines refer to NZSEE C5 Table C5.4.colour (
str
, default:'red'
) – Colour of the steel for rendering, if user does not provide a value, characteristic strength based materials will be rendered as red, and probable strength based materials will be rendered as blue.
- Raises
Exception – If a predefined steel grade is not provided and the required material properties have not been provided. For creating a user defined steel material, values for yield_strength, fracture_strain & phi_os are required to define a valid user defined material.
- Returns
SteelBarNZ
– Steel bar material object
- capacity_reduction_factor(analysis_type)[source]#
Returns the appropriate NZS3101:2006 or NZSEE C5 assessment guidelines capacity reduction factor dependant on the type of analysis specified. Refer to NZS3101:2006 CL 2.3.2.2 or NZSEE C5 assessment guidelines C5.5.1.4.
- Parameters
analysis_type (
str
) –The type of cross section analysis to undertake on the defined concrete section, by default a normal nominal strength design check is undertaken:-
nom_chk - Nominal strength design check.
Returns the normal nominal strength section design capacity, i.e. undertakes the cross section analysis based on the following assumptions:-
Using a strength reduction factor of \(\phi\) = 0.85 in accordance with NZS3101:2006 CL 2.3.2.2.
Except that for a singly reinforced wall for in-plane actions (flexure about the strong axis) a strength reduction factor of \(\phi\) = 0.7 applies in accordance with NZS3101:2006 CL 2.3.2.2.
Using the lower 5% characteristic reinforcement yield strengths.
Using the lower 5% characteristic concrete 28 day compressive design strength.
cpe_chk - Capacity Protected Element (CPE) strength design check.
Returns the capacity protected element section design capacity, i.e. undertakes the cross section analysis based on the following assumptions:-
Using a strength reduction factor of \(\phi\) = 1.0 in accordance with NZS3101:2006 CL 2.3.2.2.
Using the lower 5% characteristic reinforcement yield strengths.
Using the lower 5% characteristic concrete 28 day compressive design strength.
os_chk - Overstrength (O/S) strength design check.
Returns the O/S (overstrength) section design capacity, i.e. undertakes the cross section analysis based on the following assumptions:-
Using a strength reduction factor of \(\phi\) = 1.0 in accordance with NZS3101:2006 CL 2.3.2.2.
Using a likely maximum reinforcement yield strength of \(\phi_{o,f_y}f_y\), typically \(\phi_{o,f_y}=1.35\) in accordance with NZS3101:2006 CL 2.6.5.5(a) for grade 300E or grade 500E reinforcement which complies with AS/NZS4671. User may define custom overstrength factors when defining steel reinforcement materials using
NZS3101.SteelBarNZ
.Using a likely maximum compression strength of the concrete based on the lower 5% characteristic concrete 28 day strength plus 15 MPa, i.e. \(f'_c\) + 15 in accordance with NZS3101:2006 CL 2.6.5.5(c).
prob_chk - Probable strength design check to NZSEE C5 guidelines based on NZS3101:2006 analysis provisions.
Returns the probable strength section design capacity, i.e. undertakes the cross section analysis based on the following assumptions:-
Using a strength reduction factor of \(\phi\) = 1.0 in accordance with NZSEE C5 assessment guidelines C5.5.1.4.
Using the probable reinforcement yield strengths in accordance with NZSEE C5 assessment guidelines C5.4.3, typically \(f_{yp}=1.08f_y\) in accordance with NZSEE C5 assessment guidelines C5.4.3. User may define custom probable strengths when defining steel reinforcement materials using
NZS3101.SteelBarNZ
. Note if one of the predefined probable strength based steel grade materials are being utilised, then the yield strength is inclusive of the 1.08 factor noted above.Using the probable compressive strength of the concrete in accordance with NZSEE C5 guidelines C5.4.2.2, typically for specified 28 day concrete compressive strengths of less than or equal to 40 MPa, \(f'_{cp}=1.5f'_c\), and for greater than 40 MPa, \(f'_{cp}=1.4f'_c\).
prob_os_chk - Probable overstrength design check to NZSEE C5 guidelines based on NZS3101:2006 analysis provisions.
Returns the probable O/S (overstrength) strength section design capacity, i.e. undertakes the cross section analysis based on the following assumptions:-
Using a strength reduction factor of \(\phi\) = 1.0 in accordance with NZSEE C5 assessment guidelines C5.5.1.4.
Using the probable overstrength reinforcement yield strengths in accordance with NZSEE C5 assessment guidelines C5.4.3, typically \(f_o=\phi_of_{yp}\) in accordance with NZSEE C5 assessment guidelines C5.4.3 & C5.5.2.3. User may define custom overstrength factors strengths when defining steel reinforcement materials using
NZS3101.SteelBarNZ
. Note if one of the predefined probable strength based steel grade materials are being utilised, then the overstrength factor being applied to the yield strength is inclusive of the 1.08 factor on the lower bound yield strength.\(\quad\phi_o=\displaystyle{\frac{f_o}{f_{yp}}}\)
Where:-
\(\quad f_{yp}=1.08f_y\)
Using the probable compressive strength of the concrete in accordance with NZSEE C5 guidelines C5.4.2.2, typically for specified 28 day concrete compressive strengths of less than or equal to 40 MPa, \(f'_{cp}=1.5f'_c\), and for greater than 40 MPa, \(f'_{cp}=1.4f'_c\).
Note there is no enhancement to concrete strength for overstrength checks in accordance with the NZSEE C5 assessment guidelines.
- Raises
ValueError – If analysis type is not valid
ValueError – If concrete section contains a steel material that is not
NZS3101.SteelBarNZ
Exception – If a characteristic strength based analysis is specified, but a predefined probable strength based steel grade has been specified. Undertaking a non NZSEE C5 assessment guidelines analysis on a probable strength based steel grade is not consistent with an analysis to NZS3101:2006.
- Returns
Tuple
[float
,bool
,bool
,bool
] – Returns the appropriate strength reduction factor \(\phi\) and variables to indicate the type of analysis being requested.
- create_os_section(add_compressive_strength=15)[source]#
Creates a concrete section with likely maximum material strength properties for a cross section analysis to NZS3101:2006. Concrete and steel reinforcement strength properties are modified in accordance with NZS3101:2006 CL 2.6.5.5 to reflect likely maximum material strengths.
- Parameters
add_compressive_strength (
float
, default:15
) – The increase in compressive strength of the specified 28 day compressive strength of concrete to reflect the likely maximum material strength, defaults to an additional 15 MPa as per NZS3101:2006 CL 2.6.5.5(c)- Raises
ValueError – If concrete section contains a steel material that is not
NZS3101.SteelBarNZ
- Returns
ConcreteSection
– Returns a concrete section with material strengths modified to reflect likely maximum material strengths to enable an overstrength based analysis to be undertaken
- create_prob_section(os_design=False)[source]#
Creates a concrete section with probable strength material properties for a cross section analysis to NZS3101:2006 & NZSEE C5 assessment guidelines. Concrete and steel reinforcement strength properties are modified in accordance with NZSEE C5 assessment guidelines C5.4.2.2 & C5.4.3.
- Parameters
os_design (
bool
, default:False
) – True if an overstrength probable capacity of a concrete section is required, then the material properties for concrete and lumped reinforcement are scaled to reflect the probable overstrength material strength properties, defaults to False which only scales the material properties for concrete to reflec tthe probable material strength properties- Raises
ValueError – If concrete section contains a steel material that is not
NZS3101.SteelBarNZ
- Returns
ConcreteSection
– Returns a concrete section with material strengths modified to reflect probable material strengths or probable overstrength material strengths, to enable a probable strength or probable overstrength based analysis to be undertaken
- ultimate_bending_capacity(pphr_class='NDPR', analysis_type='nom_chk', theta=0, n_design=0)[source]#
Calculates the ultimate bending capacity with capacity factors to NZS3101:2006 or the NZSEE C5 assessment guidelines dependant on analysis type.
- Parameters
analysis_type (
str
, default:'nom_chk'
) – The type of cross section analysis to undertake on the defined concrete section, by default a normal nominal strength design check is undertaken, refer toNZS3101.capacity_reduction_factor()
for further information on analysis types.theta (
float
, default:0
) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))n_design (
float
, default:0
) – Axial design force (\(N^*\))
- Returns
Tuple
[UltimateBendingResults
,UltimateBendingResults
,float
] – Factored and unfactored ultimate bending results objects, and capacity reduction factor (factored_results, unfactored_results, phi)
- moment_interaction_diagram(pphr_class='NDPR', analysis_type='nom_chk', theta=0, control_points=[('fy', 1.0), ('fy', 0.5), ('fy', 0.0), ('N', 0.0)], labels=None, n_points=24, n_spacing=None, max_comp_labels=None, progress_bar=True)[source]#
Generates a moment interaction diagram with capacity factors and material strengths to NZS3101:2006 or the NZSEE C5 assessment guidelines dependant on analysis type.
- Parameters
pphr_class (
str
, default:'NDPR'
) –Potential Plastic Hinge Region (PPHR) classification, NDPR/LDPR/DPR.
NDPR = Nominally Ductile Plastic Region
LDPR = Limited Ductile Plastic Region
DPR = Ductile Plastic Region
analysis_type (
str
, default:'nom_chk'
) – The type of cross section analysis to undertake on the defined concrete section, by default a normal nominal strength design check is undertaken, refer toNZS3101.capacity_reduction_factor()
for further information on analysis types.theta (
float
, default:0
) – Angle (in radians) the neutral axis makes with the horizontal axis (\(-\pi \leq \theta \leq \pi\))control_points (
List
[Tuple
[str
,float
]], default:[('fy', 1.0), ('fy', 0.5), ('fy', 0.0), ('N', 0.0)]
) – List of additional control points to add to the moment interaction diagram. The default control points include the balanced point, the 50% reinforcement strain point, the 0% reinforcement strain point (fy=1
,fy=0.5
,fy=0
), and the pure bending point (N=0
). Control points may lie outside the limits of the moment interaction diagram as long as equilibrium can be found.labels (
Optional
[List
[str
]], default:None
) – List of labels to apply to thelimits
andcontrol_points
for plotting purposes. The first two values inlabels
apply labels to thelimits
, the remaining values apply labels to thecontrol_points
. If a single value is provided, this value will be applied to bothlimits
and allcontrol_points
. The length oflabels
must equal1
or2 + len(control_points)
.n_points (
int
, default:24
) – Number of points to compute including and between thelimits
of the moment interaction diagram. Generates equally spaced neutral axes between thelimits
.n_spacing (
Optional
[int
], default:None
) – If provided, overridesn_points
and generates the moment interaction diagram usingn_spacing
equally spaced axial loads. Note that usingn_spacing
negatively affects performance, as the neutral axis depth must first be located for each point on the moment interaction diagram.max_comp_labels (
Optional
[List
[str
]], default:None
) – Labels to apply to themax_comp
intersection points, first value is at zero moment, second value is at the intersection with the interaction diagram.progress_bar (
bool
, default:True
) – If set to True, displays the progress bar
- Returns
Tuple
[MomentInteractionResults
,MomentInteractionResults
,List
[float
]] – Factored and unfactored moment interaction results objects, and list of capacity reduction factors (factored_results, unfactored_results, phis)
- biaxial_bending_diagram(pphr_class='NDPR', analysis_type='nom_chk', n_design=0.0, n_points=48, progress_bar=True)[source]#
Generates a biaxial bending with capacity factors to NZS3101:2006 or the NZSEE C5 assessment guidelines dependant on analysis type.
- Parameters
pphr_class (
str
, default:'NDPR'
) –Potential Plastic Hinge Region (PPHR) classification, NDPR/LDPR/DPR.
NDPR = Nominally Ductile Plastic Region
LDPR = Limited Ductile Plastic Region
DPR = Ductile Plastic Region
analysis_type (
str
, default:'nom_chk'
) – The type of cross section analysis to undertake on the defined concrete section, by default a normal nominal strength design check is undertaken, refer toNZS3101.capacity_reduction_factor()
for further information on analysis types.n_design (
float
, default:0.0
) – Axial design force (\(N^*\))n_points (
int
, default:48
) – Number of calculation points for neutral axis orientationprogress_bar (
bool
, default:True
) – If set to True, displays the progress bar
- Returns
Tuple
[BiaxialBendingResults
,List
[float
]] – Factored biaxial bending results object and list of capacity reduction factors (factored_results, phis).
- calculate_cracked_properties(**kwargs)#
Calculates cracked section properties.
- Parameters
kwargs – Keyword arguments passed to
calculate_cracked_properties()
- Returns
CrackedResults
– Cracked results object
- calculate_cracked_stress(**kwargs)#
Calculates stresses within the reinforced concrete section assuming a cracked section.
- Parameters
kwargs – Keyword arguments passed to
calculate_cracked_stress()
- Returns
StressResult
– Stress results object
- calculate_service_stress(**kwargs)#
Calculates service stresses within the reinforced concrete section.
- Parameters
kwargs – Keyword arguments passed to
calculate_service_stress()
- Returns
StressResult
– Stress results object
- calculate_ultimate_stress(**kwargs)#
Calculates ultimate stresses within the reinforced concrete section.
- Parameters
kwargs – Keyword arguments passed to
calculate_ultimate_stress()
- Returns
StressResult
– Stress results object
- calculate_uncracked_stress(**kwargs)#
Calculates stresses within the reinforced concrete section assuming an uncracked section.
- Parameters
kwargs – Keyword arguments passed to
calculate_uncracked_stress()
- Returns
StressResult
– Stress results object
- get_gross_properties(**kwargs)#
Returns the gross section properties of the reinforced concrete section.
- Parameters
kwargs – Keyword arguments passed to
get_gross_properties()
- Returns
GrossProperties
– Concrete properties object
- get_transformed_gross_properties(**kwargs)#
Transforms gross section properties.
- Parameters
kwargs – Keyword arguments passed to
get_transformed_gross_properties()
- Returns
TransformedGrossProperties
– Transformed concrete properties object
- moment_curvature_analysis(**kwargs)#
Performs a moment curvature analysis. No reduction factors are applied to the moments.
- Parameters
kwargs – Keyword arguments passed to
moment_curvature_analysis()
- Returns
MomentCurvatureResults
– Moment curvature results object