ArcelorMittal A3CSoftware Manual PDF
ArcelorMittal A3CSoftware Manual PDF
ArcelorMittal A3CSoftware Manual PDF
INTRODUCTION
SCOPE
Presentation
The A3C software allows the designer to perform the detailed verification of a single steel member or a composite
steel-concrete column (partially encased or fully encased in concrete) according to the rules of the Eurocodes.
A3C has been designed and developed by the cticm (Centre Technique Industriel de la Construction Mtallique France).
Scope
This software deals with uniform, simply supported or cantilever members (only for steel members).
Steel members are subjected to axial force, axial bending about strong axis or weak axis (axial force and/or bending
moment). Composite columns may be subjected to axial compression force, biaxial bending (axial force and/or
bending moments about strong axis and week axis).
Simply supported member
Sections
The cross-section is doubly symmetric.
Warning
A3C may be used for working out technical solutions during preparatory engineering studies. Because of the
complexity of the calculations involved, A3C is only for users who are able to make themselves an accurate idea of its
possibilities, its limitations and adequacy to the various practical applications. The user is responsible for its use at his
own risk.
Licence
This version of A3C is available free of charge. No right is conferred to the user of the present software, except the
possibility to use it. The use of this software involves no guarantee for the profit of the user who renounces all direct
or indirect recourse in case of damages resulting from an incorrect or improper use.
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A3C
INTRODUCTION
UPDATES OF THE SOFTWARE
New version update
It is possible to check if a more recent version of A3C is available. This checking requires an access to internet. If a
more recent version is found, a hyperlink will be proposed to download this new version. In this case, it will be
necessary to previously uninstall the old version before installing the new one.
It is also possible to check if a more recent database of ArcelorMittal profiles (Sections.dbb) is available. This checkin
requires also an access to internet. If a more recent database is found, it is possible to download and to use this new
database file. This handling doesn't need to reinstall the software.
Checkings
The updates checkings can be carried out by the two following ways:
- either each time A3C is launched, if the associated parameters are activated in the Configuration form;
- or by clicking on the button "Check updates now" in the Configuration form.
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A3C
GRAPHICAL USER INTERFACE
MAIN WINDOW
The main window of the A3C has common characteristics and functionalities as usual Windows applications. The following elements are provided, from the top
to the bottom:
- a Menus bar
- a Standard toolbar
- a Tab bar
- a Graphical zone
- a View toolbar
- a Status bar
Menus bar
The following menus and sub-menus are available:
Menu File
New
Duplicate
Open
Save
Save As
Close
Close All
Recent files
Exit
When the user creates a new project, the software asks to choose the element type form the following list :
- Steel element (beam or column);
- Partially encased composite steel-concrete column;
- Fully encased composite steel-concrete column.
Status
Menu Project
The Project menu displays all the modules for input and treatment. The logical order to go through these modules is from top to bottom.
References
Main data
Section
to define parameters of the cross-section of a composite column (this menu is not available for steel
members)
Lateral restraints
to define intermediate lateral restraints (this menu is not available for composite columns)
Loads
Fire resistance
Design parameters
Combinations
Calculation
to select profiles that are checked against ULS, SLS and Ultimate Limite States in Fire situation
Calculation sheet
Menu Tools
Default design parameters
this tool is quiet the same as the one of Design parameters in the menu Project; furthermore, its allows to define
design parameters as the default ones;
Menu ?
Help
About A3C
0.
Standard toolbar
The Standard toolbar repeats all the required modules displayed in the File menu and the Project menu in order to facilitate the use.
New
Open
Save
References
Main data
Section (this button is not available for steel members)
Lateral restraints (this button is not available for composite columns)
Loads
Fire resistance
Design parameters
Combinations
Calculation
Calculation sheet
Tab bar
Several projects may be opened at the same time. Their names are displayed in the tab bar. A project can be selected when clicking on its associated name in
the tab bar.
By clicking with the right button of the mouse on the selected tab. It is possible to have the following actions:
"Duplicate Selected project"
"Close All"
Graphical zone
The graphical zone displays information concerning the selected project : references, bending axis, drawing of the member involving its length, supports,
lateral restraints and load cases. The information may be shown or hidden by clicking on the associated button in the View toolbar.
View toolbar
The following tools allow to select options for representation in the graphical zone for the selected project.
to show/hide references of the selected project
to show/hide the member length
to show/hide the member supports
to show/hide lateral restraints of the member
to show/hide load cases
to show/hide internal force and bending moment diagram for the selected load case
"Load case"
Status bar
The status bar contains :
The website of ArcelorMittal (www.arcelormittal.com) will be opened by clicking on this logo;
The website of CTICM (www.cticm.com) will be opened by clicking on this logo;
to display the language of the user interface through an associated flag (
on the flag, the user interface language will be changed;
for English,
"Length Unit"
to display the length unit. Three length units are available : m, cm, mm. The length unit may be changed by clicking on this button;
"Dimension Unit"
to display the dimension unit. Three dimension units are available : m, cm, mm. The dimension unit may be changed by clicking on
this button;
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"Force Unit"
to display the force unit. Three force units are available : KN, daN, N. The force unit may be changed by clicking on this button.
A3C
GRAPHICAL USER INTERFACE
REFERENCES OF THE PROJECT
Call
This form is called through the button
Object
This form is used to define references of the selected project.
References
References of a project involve :
- User's name
- Company name
- Project name
- Project reference
The references will be stated in the calculation sheet.
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A3C
GRAPHICAL USER INTERFACE
MAIN DATA OF THE MEMBER
Call
This form is called through the button
Object
This form is used to define : member length (L), member orientation, support conditions, bending axis and distance
between members.
For steel members, it is possible to change : member orientation, support conditions and bending axis.
On the contrary, for composite steel-concrete columns, the user cannot change these three parameters because : 1
the column is vertical; 2) only simply supported columns are considered; 3) loads may be defined in to perpendicula
planes.
Orientation
For composite columns, the user cannot change the member orientation. On the contrary, for steel members, it i
possible to choose the member orientation : vertical (columns) or horizontal (beams).
The choice of the member orientation has an influence on the member weight calculation. When the member i
vertical, the software automatically calculates the member weight and adds it to the axial force of the permanent load
case. When the member is horizontal, the software considers the member weight as a permanent distributed load (in
the permanent load case) over the member length.
Support conditions
For composite columns, the software considers only the case of simply supported member. For steel members, the
user can choose one of two types of support conditions :
- Simply supported member
- Cantilever
Bending axis
For composite columns, the user can define loads in two perpendicular planes. On the contrary, for steel members, the
software doesn't consider the biaxial bending. In this case, it is possible to choose one of two types of bending axis :
- Bending about the strong axis of the cross-section (y-y)
- Bending about the weak axis of the cross-section (z-z)
The distance between members is required in order to determinate the associated uniform load applied on the
member, resulting from a surface load :
D1
D2
The associated uniform applied on the selected member is determined by : qu = qs (D1+D2) / 2, where qs is the surface
load.
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A3C
GRAPHICAL USER INTERFACE
FIRE DESIGN OF A STEEL MEMBER
Call
This form is called through the button
Object
This form is used to define options for the fire design of a steel member. The fire calculation can only be carried out
when the checkbox "Calculation of the standard fire resistance" is checked.
Calculation options
The user can choose between two fire calculation options :
Option 1 : Standard fire resistance
The thickness of protection material required for the selected standard fire resistance (R15, R30, R60, R90, R180
or R240) will be determined.
Option 2 : Thickness of protection material
The highest standard fire resistance rate will be assessed from the selected thickness of the fire protection
material. This thickness depends on the selected fire protection type and material (see below).
The buckling length is multiplied by a buckling coefficient related to the member position in the structure. This
coefficient has a fixed valued for a column located in the top storey or in an intermediate storey of a braced
frame, and a user-defined value otherwise.
Discret or continuous lateral restraints
This option enables to keep the discrete or continuous lateral restraints between the ends of the member in the
fire calculation. It is up to the user to make sure that these restraints have a sufficient fire resistance to be kept in
the fire calculation of the member.
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A3C
GRAPHICAL USER INTERFACE
FIRE DESIGN OF A COMPOSITE COLUMN
Call
This form is called through the button
Object
This form is used to define options for the fire design of a composite column (fully encased or partially encased in
concrete). The fire calculation can only be carried out when the checkbox "Calculation of the standard fire resistance"
is checked.
Calculation options
The fire verification of a composite column can be performed following two methods, which depend on the type of
encasement (total or partial).
For composite columns with a totally encased steel section, the verification is performed following the tabulated
values method.
For composite columns with a partially encased steel section, there are two methods depending on the mechanical
load. The simple calculation method can only be applied for buckling about the minor axis of the cross-section.
Otherwise, the verification is performed according to the tabulated values method.
Depending on the verification method, the user can choose between two fire calculation options :
Option 1 : Standard fire resistance
The cross-sectional dimensions of the composite column will be compared to the minimum values recommended
by the method to meet the selected standard fire resistance rate.
For totally encased steel sections, this standard fire resistance rate can be equal to R30, R60, R90, R120, R180 or
R240.
For partially encased steel sections, it can be equal to R30, R60, R90 or R120. Besides, it depends on the applied
load.
Option 2 : Dimensions of the cross-section
The highest standard fire resistance rate the column can meet will be determined from the cross-sectional
dimensions. For partially encased steel sections, the standard fire resistance rate also depends on the applied
load.
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A3C
GRAPHICAL USER INTERFACE
LATERAL RESTRAINTS OF A STEEL MEMBER
Call
This form is called through the button
Object
This form is used to define intermediate lateral restraints for a steel member.
For composite columns, only the sections located at both ends of the member are restrained against the lateral displacement and the
torsion. For this reason that the form cannot be displayed.
- Either both flanges are assumed to be continuously restrained along the member. In this case, no Lateral Torsional Buckling verification
carried out;
- Or both flanges of the member is laterally restrained at some discrete sections along the member.
to add a lateral restraint. By default, all restrained sections are assumed to be equally spaced when
adding a new lateral restraint,
to uniformise spacings between restrained sections when they are not equally spaced,
). The displayed spacing evolves according to the movement of the selected restraint.
Alternatively, the spacing between two adjacent restrained sections can be directly imposed by modifying the displayed value as shown
in the following figure :
Finally, the spacing between a selected restrained section and the left end of the member can also be modified by editing its horizontal
spacing as :
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A3C
GRAPHICAL USER INTERFACE
CROSS-SECTION OF A COMPOSITE STEEL-CONCRETE COLUMN
Call
This form is called through the button
Object
This form is used to define the cross-section of a composite steel-concrete column (partially encased of fully encased in
concrete).
Partially encased composite steel-concrete section
Steel profile
To define the steel profile, it should be proceeded as follows :
Select a serie of profiles;
Select a profile;
Select a steel grade.
The database of rolled profiles (ArcelorMittal's catalogue) is stored in binary files AM_HRProfiles.dbb and
AM_HRSteels.bdb located in the databases directory.
All the geometrical properties of the selected profile are shown in the table located on the right side of the form.
For partially encased composite columns, profile dimensions (width and height) are those of the section. For full
encased composite columns, section dimensions are defined by the user.
Concrete covers
To define concrete covers, it is necessary to :
Select a structural class : S1, S2, S3, S4, S5 et S6;
Select an exposure class : X0, XC1, XC2, XC3, XC4, XD1, XD2, XD3, XS1, XS2 et XS3;
For partially encased composite columns : enter the vertical distance between internal edge of the flange and
the transverse bars (ef);
For fully encased composite columns : enter the vertical distance between the external edge of the concrete
section and the transverse bars (cs,z);
Enter the horizontal distance between the external edge of the concrete section and the transverse bars (cs,y);
By choosing a structural class and an exposure class, the sortware automatically calculates the minimum concrete
cover (cnom). For fully encased composite columns, distances between the external edge of the concrete section and
the external edge of the steel profile (ca,y et ca,z) are calculated and shown in the frame "Concrete covers".
Concrete parameters
The frame "Concrete" allows the user to define : concrete class, age of concrete at loading (t0) and relative humidit
(RH). These last two parameters are necessary for the concrete creep calculation.
Diameter of bars
The diameter and the steel grade of reinforcing bars are selected from :
Diameter of transverse bars : 6, 8, 10 and 12mm;
Diameter of longitudinal bars : 8, 10, 12, 14, 16, 20, 25, 28, 32 and 40mm;
Steel grade : B420 and B500.
The position of the reinfocing bars is such that the composite section remains symmetric about both axes. So, when
the user changes the position of a layer, the position of the associated layer which is symmetric about an axis i
automatically calculated.
It is possible to define up to 8 layers about both axes. By default, layers are equidistant. The user can change the
position of any layer by fulfilling the eurocode requirements on the bars spacing.
Layer of longitudinal bars
It consists in defining the position of layers of longitudinal bars about the z-z axis (vertical axis).
First layer of longitudinal bars
It consists in defining the position of longitudinal bars in the first layer.
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A3C
GRAPHICAL USER INTERFACE
DEFINITION OF LOADS
Call
This form is called through the button
Object
This form is used to define the load cases applied on the member.
It is possible to define up to four elementary load cases:
- 1 permanent load case (symbol G) : The title and the symbol of this load case are unmodified,
- Up to 3 live load cases (symbol Qi by default): The title and the symbol of these load cases may be modified.
For each load case, it is possible to define:
- A symbol ("Q1", "Q2", ... ) : Up to 3 characters (only for variable load cases),
- A label ("Permanent", "Snow",...) : Up to 25 characters (only for variable load cases),
- 0,i, 1,i, 2,i factors (only for variable load cases),
- An axial force at the member ends (assumed to be constant along the member),
- Up to 6 concentrated loads for each plane,
- Up to 3 distributed loads for each plane,
- A surface load for each plane,
- End moments for each plane.
to add a force. By default, the new added force of intensity F = 1kN applies on the middle of the member (x = L/2)
"Remove"
to remove a selected force. The last one has the red color label in the grid and its representing arrow in the graphical zone is orange.
A concentrated load is defined by the two following parameters as shown in the grid "Concentrated loads":
x
location of the force, defined as the horizontal spacing of the point of application to the left end of the member; this value can be modified by moving horizontally the ass
directly the associated text-box in the grid;
intensity of the force; it is considered as a positive one when acting towards the bottom and its value can only be modified by editing the associated textbox in the grid ;
Position
vertical position of the load : Top, Bottom and Gravity centre (only for steel members under bending about y-y axis).
Distributed loads
Up to 3 distributed loads can be defined. Their positions and intensities are displayed in the grid "Distributed loads". It is possible to have two following actions :
"Add"
to add a load. By default, the new added distributed load is the uniform one of intensity q = 1kN/m and applies on all the member length.
"Remove"
to remove a selected load. The last one has the red color label in the grid and its two representing arrows in the graphical zone are orange.
A distributed load is defined by the four following parameters as shown in the grid "Distributed loads":
x1 and x2
locations of the load, all defined as the horizontal spacing to the left end of the member; their values can be modified by moving associated arrows in the graphical zone or
editing associated text-boxes in the grid;
q1 and q2
intensities of the load at locations x1 and x2 respectively, a positive value being considered as acting towards the bottom; their values can only be modified by editing
associated text-boxes in the grid ;
Position
vertical positions of the load at locations x1 and x2 respectively : Top, Bottom and Gravity centre (only for steel members under bending about y-y axis).
Surface load
A surface load can be applied on the surface (deck or roof for example) supported by a system of members. The surface load is defined by the parameter :
p
intensity of the surface load (unit of force per unit of area), a positive value being considered acting towards the bottom.
The width of application of this surface load is calculated through spacings between members (see Main Data) and is displayed in the form. The surface load is then converted into an equivalent
uniform distributed load applying on the member length :
qs = p.(D1 + D2) / 2
Two arrows of the equivalent uniform load are of the green color in order to make a difference with distributed loads defined by the User:
Axial force
It is possible to define a constant axial force applying at ends and in the direction of the member axis :
intensity of the axial force, a positive value being considered as a compressive force.
End moments
A moment can be defined at each end of the member. The directions for positive values of moment are given in the figure below.
For cantilever members, only the moment at the right end can be defined.
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A3C
GRAPHICAL USER INTERFACE
DESIGN PARAMETERS OF A STEEL MEMBER
Call
This form is called through the button
Object
This form is used for the selection of certain options to be used for the calculation of a steel member. The default values are
defined in the menu Tools / Default design parameters.
Parameters
Combinations according to EN 1990
The checkbox "Maximum 2 variable actions" indicates if automatique combinations according to EN 1990 take into
account up to two variable actions (EN 1990 A1.2.1 (1)).
Partial factors for loads
G.sup, G.inf and Q are used for the combinations of loads.
Partial factors for resistances
M0
M1
"Application of the f-factor for LTB, according to EN to indicate if the factor f is taken into account in the calculation of
1993-1-1 6.3.2.3(2)"
the LTB resistance according to EN 1993-1-1 6.3.2.3(2).
(*) : the LTBeamN modulus - developped by CTICM - deals with the elastic stability of beams in bending and/or
compression towards the lateral torsional buckling phenomenon (lateral torsional buckling, lateral flexural buckling) by
calculating the critical factor cr .
Limite States of Seviceability checking
wmax = L / n; w3,max = L / n3
fmin
Minimum value of the natural frequency of vibration (for example, in the case of a floor b
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A3C
GRAPHICAL USER INTERFACE
DESIGN PARAMETERS OF A COMPOSITE COLUMN
Call
This form is called through the button
Object
This form is used for the selection of certain options to be used for the calculation of a composite column. The defaul
values are defined in the menu Tools / Default design parameters.
Parameters
Partial factors for loads
G.sup, G.inf and Q are used for the combinations of loads.
Partial factors for resistances
M0
M1
M,fi,a
M,fi,s
The yield strength can be determined from the material thickness, either according to EN 1993-1-1 table 3.1, o
according to EN 10025-2.
Ultimate Limite States
"National Annexes"
At any moment, all the parameters defined in this form may be reset with their default values by using the button
"Reset with default values".
Set as default values
By clicking on the menu Tools / Default design parameters, the form is changed. In this case, the button "Reset with
default values" is replaced by a check-box "Set as default values". When the last one is checked, all the values o
parameters defined in the form will be considered as the default ones.
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A3C
GRAPHICAL USER INTERFACE
LOAD COMBINATIONS
Call
This form is called through the button
Object
This form is used to define the combinations of loads for: Ultimate Limit States (ULS), Serviceability Limit States (SLS)
and Fire design situation (FIRE), according to EN 1990.
For each combination, it is possible to define :
-
A label
A description
combinations arised from the rules EN 1990, called Autocombinations. Associated coefficients displayed in the grid
cannot be modified by the user;
Any combination may be removed by clicking on the button "Remove". A combination is taken into account in the
calculationwhen the check box on the left is checked.
Ultimate Limit States (ULS)
ULS combinations can be automatically generated by using equation 6.10 of EN 1990, for persistent or transient
design situations. So, the number of combinations depends on the number of load cases.
For example, for three load cases :
- Pernament load case (G)
- Live load case (Q1)
- Live load case (Q2)
8 ULS combinations are generated :
ULS01 = G.sup G + Q Q1
ULS02 = G.inf G + Q Q1
Permanent actions;
Qi
Variable actions. Their names may be modified in the form "Definition of loads";
G.sup, G.inf, Q
Partial factors for permanent and variable actions. They are defined in the form
"Design parameters of a steel member" or "Design parameters of a composite
column" ;
0,i
Combination factors for variable actions. They are defined in the form "Definition of
loads".
Designed by
Combination factors for variable actions. They are defined in the form "Definition of
loads".
A3C
GRAPHICAL USER INTERFACE
CALCULATION OF A STEEL MEMBER
Call
This form is called through the button
Object
This form is used to select profiles and perform resistance verifications for the Ultimate Limit States (ULS), the
Serviceability Limit States (SLS) and the Fire design situation (FIRE) according to the Eurocode 3.
Selection of profiles
Rolled profiles database is directly read from binary files AM_HRProfiles.bdb and AM_HRSteels.bdb that can be found
in the database directory of the A3C. To select a group of rolled profiles, the following logical order is to go :
- Select a type of profile in the list-box "Types of profiles";
- Select a group of profiles in the the list-box "Profiles";
- Select the steel grade for all the group of profiles in the form "Grade".
All the characteristics of the selected profile are displayed in the table and the figure located on the right of the form.
All the selected profiles are then added in the table "Selected profiles". In this table, the last column "Satisfied"
indicates the result of the calculation procedure: the corresponding profile is "satisfied" or "Not satisfied" the
resistance, deflection and vibration criteria. All the profiles can be sorted in the ascending or descending order of :
Name, Steel grade, Mass (per length unit) and Criteria by clicking on the header of the corresponding column.
For the table "Selected profiles", it is possible to have the following actions :
"Verify"
Some parameters or the member may be modified after the checking procedure of profiles
has been done, 0,i in the form Load combinations for example. This leads to a modification
of the Criteria column . So, when the calculation form is recalled, all the profiles in the table
"Selected profiles" become "Not verified". It suffices to click on the button "Verify" ;
"Remove"
"Remove All"
"Calculation
sheet"
to display the calculation sheet for the selected profile. Alternatively, by double clicking on a
profile, the associated calculation sheet will display.
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A3C
GRAPHICAL USER INTERFACE
CALCULATION SHEET
Call
This form is called through the button
Object
This form is used to edit the calculation sheet of the selected profile. The calculation procedure is carried out when
the sheet is displayed.
Editing tools
Some functions are proposed to navigate, print or save the calculation sheet. They are available from the toolbar and
associated to the following buttons:
Close the sheet
Go to the first page of the sheet
Go to the previous page
Go to the next page
Go to the last page of the sheet
Print the calculation sheet. This function allows the user to save the sheet in PDF format by
selecting a "PDF Printer".
Language
Select the language used to edit the calculation note. This may not be the same as the language
of the User Interface. The default language for editing the notes of the calculations is defined in
the settings configuration software.
Summary
Options
Four options are available to define the detail level of the sheet (Synthesis, Intermediate sheet,
Detailed sheet and Customized sheet).
Status bar
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A3C
GRAPHICAL USER INTERFACE
CUSTOMIZATION OF THE CALCULATION SHEET
Call
This dialogue box is called in the dialogue box " Calculation sheet", the level of detail customized.
Object
This dialogue box is used to select options in the calculation sheet of the active project.
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A3C
GRAPHICAL USER INTERFACE
CONFIGURATION OF THE SOFTWARE
Call
This form is called through the menu Tools / Configuration.
Object
This dialog box defines the configuration, directories of the software and some steel constants through three tabs :
General, Environment and Constants.
General parameters
The following general parameters may be defined by the User:
- Language of the User Interface and of the Calculation Sheet, to be chosen among the available languages
installed on the computer.
- Length, dimension and Force Units. Three length and dimension units are available : m, cm, mm. Three force
units are available : kN, daN, N. These units may be selected by clicking directly on the associated button in
the status bar.
- Automatical checkings of the available updates (new version of the Member Module and database of
ArcelorMittal profiles) to be carried out at the launch of the software. These checkings require an access to
internet.
Environment
This tab displays : installation directory, configuration directory, working directory and ArcelorMittal profiles
database. Only the working directory can be modified by the User.
Constants
This tab displays some constants used in the software : gravity, density, Young's modulus, Shear modulus and Poisson
factor of the steel.
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A3C
CATALOGUES
CATALOGUE OF FIRE PROTECTION MATERIALS
Call
This form is called through the menu Tools / Catalogue of protection materials.
Object
This form is used to show or change the catalogue of protection materials. The last one is stored in the file
MATERIAUPROTECTION.DB located in the database directory of the software.
The paramaters of a protection material are : Name, Type, Minimum thickness, Variation of the specific heat (CP
according to the temperature (TC), Variation of the thermal conductivity () according to TC, Variation of the volumi
mass () according to TC.
"Add" and "Remove" buttons allow the user to add a new material or remove a selected material. The material name
material type and minimum thickness may be directly edited in the associated cell of the table.
Material type
The type of protection materials is selected from the list : Contour encasement, Hollow encasement, Intumescen
paint.
Variation of the specific heat (CP) according to the temperature
This variation is defined by the set of specific heat values which are associated to a given temperature. The drawin
located below the table shows this variation.
"Add" et "Remove" buttons allow to add a new value of the specific heat or remove a selected value.
Variation of the thermal conductivity () according to the temperature
This variation is defined by the set of thermal conductivity values which are associated to a given temperature. The
drawing located below the table shows this variation.
"Add" and "Remove" buttons allow the user to add a new value of the thermal conductivity or remove a selected
value.
Variation of the volumic mass () according to the temperature
This variation is defined by the set of volumic mass values which are associated to a given temperature. The
drawing located below the table shows this variation.
"Add" and "Remove" buttons allow the user to add a new value of the volumic mass or remove a selected value.
Designed by
A3C
CALCULATION PROCEDURES
ULTIMATE LIMITE STATES (ULS) VERIFICATIONS OF A STEEL MEMBER
General
A cross-section of a steel member is generally subjected to :
- An axial force NEd;
- A shear force VEd;
- A bending moment MEd.
For each ULS combination, A3C performs the following verifications :
- Resistance of cross-sections;
- Web resistance to shear buckling;
- Buckling resistance of member (flexural buckling, lateral torsional buckling and M-N interaction).
Under axial force and/or bending moment, the resistance of a cross-section depends on the class as mentionned in the
following table :
Class
Type of resistance
1, 2
Plastic resistance
Elastic resistance
Resistance of cross-sections
The following criteria for the resistance of cross-sections are calculated in different points along the member :
-
Axial force:
N = NEd / Nc,Rd
Shear force:
V = VEd / Vpl,Rd
Bending moment:
M = MEd / Mc,Rd
Interaction M+N:
MN
Interaction M+V:
MV = MEd / MV,Rd
Interaction M+N+V:
Vb = VEd / Vbw,Rd 1
where Vbw,Rd is calculated according to EN 1993-1-5 5.2(1) and assuming non-rigid end posts.
If the shear criterion Vb is higher than 0.5, the criterion MNb is calculated whatever the class is :
MNVb 1
is calculated according to EN 1993-1-5 7.1(1).
Buckling resistance of member (flexural buckling, lateral torsional buckling and M-N interaction)
General
For members under bending about the strong axis only, when at least one section is restrained at the top flange or
bottom flange. The general method for lateral and lateral torsional buckling ( EN 1993-1-1 6.3.4) is used. In other cases,
the verification of the member resistance is carried out according to EN 1993-1-1 6.3.1, 6.3.2 and 6.3.3 for each
segment delimited by two consecutive restrained sections. It covers :
- In-plane flexural buckling;
- Out-of-plane flexual buckling;
- Lateral torsional buckling;
- M-N interaction.
Simple compression
The in-plane buckling length is taken equal to the system length for simply supported members and to double system
length for cantilever members.
The out-of-plane buckling length is taken equal to the distance between two consecutive restrained sections.
The flexural buckling criteria are calculated for each segment delimited by two consecutive restrained sections :
LT = My,Ed / Mb,Rd 1
where : Mb,Rd is calculated according to one of the following options :
- EN 1993-1-1 6.3.2.2 (General case)
- EN 1993-1-1 6.3.2.3 (Rolled sections or equivalent welded sections)
The options can be selected in the form "Design parameters of a steel member".
M-N interaction
The buckling criteria in case of M-N interaction are given by EN 1993-1-1 6.3.3 :
op = (ult,k / cr,op)1/2
with :
cr,op
the minimum amplifier for the in plane design loads to reach the elastic critical resistance of the member
with regards to lateral or lateral torsional buckling without accounting for in plane flexural buckling. This factor is
determined using the LTBeamN modulus - developed by the CTICM - that deals with the elastic stability of beams in
bending and/or compression with respect to the out-of-plane elastic buckling phenomenon (lateral flexural bucking,
torsional and flexural-torsional buckling, lateral torsional buckling);
ult,k
the minimum load amplifier of the design loads to reach the characteristic resistance of the most critical
cross section of the member considering its in plane behaviour without taking lateral or lateral torsional buckling into
account however accounting for local imperfection and local 2nd order effects. This factor is determined by :
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The value of e0 / L is chosen according to the table5.1 of EN 1993-1-1. When sections are of class 3 or 4 and when the
french National Annex is chosen, e0 / L is determined by the formula given in the french National Annex.
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CALCULATION PROCEDURES
SERVICEABILITY LIMIT STATES (SLS) VERIFICATIONS OF A STEEL MEMBER
Deflections
Deflections of the member are calculated for all the SLS combinations defined in the form "Load combinations",
according to a 1st order elastic analysis via analytical fomulae. No imperfection is taken into account.
The deflection criterion is :
wmax L / n1
where :
wmax is the maximum deflection along the member;
L is the member length;
n1 is a factor defined by the user in the form "Design parameters of a steel member".
Vibrations
The natural frequency of the member is calculated for each SLS combination by using the following formula :
f = 15,81 / (wmax)1/2
where : wmax is the maximum deflection along the member.
The vibration criterion is :
f flim
where flim is the minimum natural frequency defined by the user in the form "Design parameters of a steel member".
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CALCULATION PROCEDURES
VERIFICATIONS OF A STEEL MEMBER IN FIRE DESIGN SITUATION (FIRE)
General
A cross-section of a steel member in fire design situation is generally subjected to :
- An axial force Nfi,Ed;
- A shear force Vfi,Ed;
- A bending moment Mfi,Ed.
For each fire combination, the software performs the following verifications :
- Resistance of cross-sections;
- Buckling resistance of the member (flexural buckling, lateral torsional buckling).
Under axial force and/or bending moment, the resistance of a cross-section depends on the class as mentioned in the
following table :
Class
Type of resistance
1, 2
Plastic resistance
Elastic resistance
The resistance of a cross-section also depends on its heating, which is determined by a heat transfer calculation.
Heating of cross-sections
The increase of temperature a,t of an insulated steel member during the time interval t is obtained in accordance with
EN 1993-1-2 4.2.5.2 (1), assuming a uniform heating of the cross-section. The value of is equal to 3 s.
The fire design temperature is determined by iterating on t, until the sum of the time intervals t corresponds to the fire
resistance duration to be checked.
Resistance of cross-sections
The following criteria for the resistance of cross-sections are calculated at different points along the member, in accordance
with EN 1993-1-2 4.2.3 :
-
Axial force:
Shear force:
Bending moment:
M-V interaction:
Axial force
The resistance criterion of the cross-section of a member subjected to an axial force is :
Top storey:
Lfi = 0,7 L
Intermediate storey:
Lfi = 0,5 L
The flexural buckling criteria are calculated for each segment delimited by two consecutive restrained sections :
where : fi - reduction factor for flexural buckling in the fire design situation
ky, - reduction factor for the yield strength of steel fy at temperature
kp0,2, - reduction factor for the yield strength of steel fy at temperature
A - area of the cross-section
Aeff - effective area of the cross-section
Simple bending
The lateral torsional buckling (LTB) verification applies to members under bending about the strong axis only.
The elastic critical moment Mcr is calculated using the formula of the French National Annex with the following
assumptions :
- Free rotation in the plane parallel to the flanges is assumed at both ends (kz = 1,0);
- Free warping is assumed at both ends of the segment (kw = 1,0);
- The transverse loads are assumed to apply above the upper flange (zg = +h/2) towards the shear centre;
- Coefficients C1 and C2 are calculated according to NF EN 1993-1-1/NA - Annex MCR - 3.5.
The LTB criterion is :
where : Mb,fi,,Rd is calculated according to EN 1993-1-2 4.2.3 and its French National Annex :
Mb,fi,,Rd = LT,fi Wpl ky,,com fy / M,fi Mpl,Rd
M-N interaction
For M-N interaction, the buckling and lateral torsional buckling criteria are those given in EN 1993-1-2 4.2.3.5 for Class
1, 2 or 3 cross-sections, and its French National Annex for Class 4 cross-sections:
fi,MN1 1 (criterion 4.21a for Class 1 or 2 cross-sections and criterion 4.21c for Class 3 or 4 cross-sections)
fi,MN2 1 (criterion 4.21b for Class 1 or 2 cross-sections and criterion 4.21d for Class 3 or 4 cross-sections)
For class 4 cross-sections, verification criteria are :
Bending about the strong axis
These criteria are calculated for each segment delimited by two consecutive restrained sections if they have a sufficient
fire resistance to be kept in the fire calculation.
The factors kij are caculated according to EN 1993-1-2 or its French National Annex for Class 4 cross-sections. In the latter
case, these factors are in conformity with EN 1993-1-1 6.3.3 and its Annex A.
The factors M,y, M,z and Cmy (French National Annex for Class 4 cross-sections) are calculated according to the form of
the bending moment diagram along the total length of the member, while the factors M,LT and CmLT (French National
Annex for Class 4 cross-sections) are calculated according to the form of the bending moment diagram along the total
length of the segment delimited by two consecutive restrained sections if they have a sufficient fire resistance to be kept
in the fire calculation.
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CALCULATION PROCEDURES
ULTIMATE LIMITE STATES (ULS) VERIFICATIONS OF A COMPOSITE COLUMN
General
A cross-section of a composite steel-concrete column (partially encased or fully encased) is generally subjected to :
- An axial force NEd ;
- Shear forces : Vz,Ed (loads applied in the plane z-z) and Vy,Ed (loads applied in the plane y-y);
- Bending moment about two main axes : My,Ed and Mz,Ed.
For each ULS combination, the software performs the following verifications :
- Resistance of cross-sections;
- Buckling resistance of the column (flexural buckling, M-N interaction).
According to EN 1994-1-1 6.7.1 (9), the effects of local buckling may be neglected for a fully encased I-profile as
well as a partially encased I-profile with the width-thickness ratio satisfying the condition : b / tf 44 (235 / fy)1/2.
Resistance of cross-sections
The following criteria for the resistance of cross-sections are calculated in different points along the member :
-
Axial force:
N = NEd / Nc,Rd
Shear force:
V = VEd / Vpl,Rd
Interaction M+N+V:
Some criteria are calculated for both axes : shear force (Vy and Vz), interaction (My,N , Mz,N and My,Mz,N).
restraint is considered.
The flexural buckling criteria are calculated for :
where : NG,Ed is the axial force due to permanent loads (under G G); Ecm is the secant modulus of elasticity
for the concrete; t is the creep coefficient of the concrete, calculated according to EN 1992-1-1 3.1.4.
Interaction N-My-Mz
The second order effects and the local imperfection effects are taken into account to calculate bending moments
about botth axes via the following formulas :
My,Ed = ky [My,Ed(I) + NEd e0,y sin(x/L)]
Mz,Ed = kz [Mz,Ed(I) + NEd e0,z sin(x/L)]
where : My,Ed(I), Mz,Ed(I) - bending moments resulting from 1st order elastic analysis
e0,y, e0,z - amplitude of imperfections along two axes : e0,y = L/200 and e0,z = L/150 (EN 1994-1-1 table 6.5)
ky, kz - factors introducing the 2nd order effects (EN 1994-1-1 6.7.3.4 (5))
The criteria (My,N , Mz,N et My,Mz,N) are calculated by using effective flexural stiffness as follows:
Effective flexural stiffness of a composite column under combined actions
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CALCULATION PROCEDURES
VERIFICATIONS OF A COMPOSITE COLUMN IN FIRE DESIGN SITUATION (FIRE)
General
A cross-section of a composite in fire design situation is generally subjected to :
- An axial force Nfi,Ed;
- A bending moment Mfi,Ed.
However, the fire verification of a composite column with a totally encased steel section only takes into account it
cross-sectional dimensions, regardless of the applied forces (see EN 1994-1-2 4.2.3.2).
In return, regarding partially encased steel sections, the fire verification is conducted using either the simple
calculation method or the tabulated values method depending on the actions on the column.
If the column is not subject to flexural bending, or if the column is subject to flexural bending about its cross-sectiona
minor axis only, the simple calculation method is applied. Otherwise, the tabulated values method is applied.
The verification covers flexural buckling about the weak axis of the cross-section, whether the axial load has an
eccentricity or not. The applied simple calculation method is defined in EN 1994-1-2 Annex G.
Simple compression
The buckling length Lcr,y is taken equal to the length of the column.
For a column in a braced frame, this buckling length is multiplied by the reduced factor related to the location o
the column in the structure :
-
Top storey:
Lfi = 0,7 L
Intermediate storey:
Lfi = 0,5 L
where : Nfi,pl,Rd - design value of the plastic resistance to axial compression, determined by summing up the plasti
resistances of the different parts of the cross-section (Notation : f - flanges of the profile, w - web of the profile, c
concrete, s - longitudinal reinforcing bars) :
Nfi,Rd,z = Nfi,pl,Rd,f + Nfi,pl,Rd,w + Nfi,pl,Rd,c + Nfi,pl,Rd,s
- the reduction factor for flexural buckling in the fire design situation, determined from the c buckling curve
where : Nfi,pl,Rk - characteristic value of the plastic resistance to axial compression; Nfi,cr,z - critical
normal force for the flexural buckling about z-z axis : Nfi,cr,z = 2 (EI)fi,eff,z / Lfi2 with : (EI)fi,eff,z is
determined by summing up the flexural stiffness of the different parts of the cross-section :
(EI)fi,eff,z = (EI)fi,f,z + (EI)fi,w,z + (EI)fi,c,z + (EI)fi,s,z
Bending and axial force
The buckling criterion becomes :
This method can only be applied for a load level less or equal to 0.66 and structral steel grades S235, S275 and S355
For each FIRE combination, this load level is calculated as follows (see EN 1994-1-2 2.4.2 (3)):
o :
NRd
My,pl,N,Rd
is the design value of the bending resistance about the strong axis at normal temperature;
Mz,pl,N,Rd
is the design value of the bending resistance about the weak axis at normal temperature;
The axial buckling resistance is determined considering a buckling length twice as great as the buckling length in fire
situation (cf. EN 1994-1-2 4.2.3.1 (3)).
The bending resistances My,pl,N,Rd and Mz,pl,N,Rd, calculated according to EN 1994-1-1, take account of the axial load
Nfi,Ed, and of the vertical shear force Vfi,Ed if the latter is greater than or equal to half the vertical shear resistance a
normal temperature.
For a give standard fire resistance rate, the minimum cross-sectional dimensions are determined from fi,t.
NB: In case of a partially encased column made of structural steel grade S460 and subject to flexural bending about it
cross-sectional major axis, a warning message indicates to the user that the column characteristics are out of scope o
both fire verification methods. However, the two methods are subsequently used for information purposes only in the
following order:
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REFERENCES
[1]
[2]
EN 1993-1-1: Eurocode 3 - Design of steel structures - Part 1-1: General rules and rules for buildings. AFNOR. O
2005.
[3]
NF EN 1993-1-1/NA: Eurocode 3 - Design of steel structures - Part 1-1: General rules and rules for buildings National Annex. AFNOR. May 2007.
[4]
EN 1993-1-5: Eurocode 3 : Design of steel structures - Part 1-5: Plated structural elements. AFNOR. March 2007.
[5]
NF EN 1993-1-5/NA: Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elements - French Na
Annex. AFNOR. October 2007.
[6]
EN 1993-1-2: Eurocode 3 - Design of steel structures - Part 1-2: General rules - Structural fire design. AFNOR. Nov
2005.
[7]
NF EN 1993-1-2/NA: Eurocode 3 - Design of steel structures - Part 1-2: General rules - Structural fire design National Annex. AFNOR. October 2007.
[8]
EN 1994-1-1: Eurocode 4 - Design of concrete steel and concrete structures - Part 1-1: General rules and ru
buildings. AFNOR. June 2005.
[9]
NF EN 1994-1-1/NA: Eurocode 4 - Design of concrete steel and concrete structures - Part 1-1: General rules and ru
buildings - French National Annex. AFNOR. April 2007.
[10]
EN 1994-1-2: Eurocode 4 - Design of concrete steel and concrete structures - Part 1-1: General rules - Structur
design. AFNOR. February 2006.
[11]
NF EN 1994-1-2/NA: Eurocode 4 - Design of concrete steel and concrete structures - Part 1-1: General rules - Stru
fire design - French National Annex. AFNOR. October 2007.
[12]
[13]
EN 10025-2: Hot rolled products of structural steels - Part 2: Technical delivery conditions for non-alloy structural s
[14]
EN 10025-4: Hot rolled products of structural steels - Part 4: Technical delivery conditions for thermomechanical
weldable fine grain structural steels
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