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User Manual for SAFlR A Computer Program for Analysis of Structures at Elevated Temperature Conditions
Daniel I. Nwosu,V.K.R. Kodur, J.M. Franssen, J.K. Hum
Internal Report 782
October 1999
NATIONAL RESEARCH COUNCIL OF CANADA INSTITUTE FOR RESEARCH IN CONSTRUCTION
USER MANUAL FOR SAFlR A COMPUTER PROGRAM FOR ANALYSIS OF STRUCTURES AT ELEVATED
TEMPERATURE CONDITIONS
Daniel I. Nwosu, V.K.R Kodur, J.M. Franssen, J.K. Hum
October 1999
TABLE OF CONTENTS
List of Figures ............................................................................................... iii ... List of Tables ...................................................................................................... 111
1.0 INTRODUCTION ................................................................................................. I .................................................................................................... . 1 1 General I
.................................................................................. 1.2 Analysis Procedure I I . 2.1 Thermal analysis ........................................................................... I 1.2.2 Analysis of torsional stiffness of BEAM elements ......................... 2 1.2.3 Structural analysis at elevated temperature .................................. 2
1.3 Capabilities of SAFIR ............................................................................... 2 1.3.1 Capabilities based on temperature analysis .................................. 2 1.3.2 Capabilities based on torsion analysis .......................................... 3 1.3.3 Capabilities based on structural analysis ...................................... 3
1.4 Common Features in all Analyses ............................................................ 3 ..................................................................................... 1.5 Sign Conventions 4
1.5.1 Global and local axes ................................................................... 4 1.5.2 Stresses ....................................................................................... 4
......................................................................................... 2.0 INPUT DESCRIPTION 5 ........................................................................................ 2.1 Input for SAFlR 5 . .
2.2 Problem Defin~tlon .................................................................................... 5 2.3 General Data for Thermal Analysis .......................................................... 6
........................................................ 2.4 General Data for Structural Analysis 7 ................................................................................. 2.5 Material Properties 10
2.5.1 Stress-strain relations of concrete and steel ............................... 10 ................................................. 2.5.2 Parameters of the material laws I 0 . . ............................................................................. 2.6 Convergence Crlterla 11
3.0 DETAILED INPUT DATA AND FORMAT ........................................................... 12 3.1 Description and Format for Thermal Analysis Files ................................ 12
3.1 . 1 The . DAT file for thermal analysis ............................................... 12 3.1.2 The . STR file for thermal analysis ............................................... 17
3.2 Description and Format for Structural Analysis Files .............................. 27 ............................................ 3.2.1 The . DAT file for structural analysis 27
3.2.2 The . STR file for structural analysis ............................................ 37 3.3 Description and Format for Torsional Analysis Files ............................... 48
3.3.1 The . DAT file for torsional analysis ............................................. 48 ............................................. 3.3.2 The . STR file for torsional analysis 52
4.0 ELEMENT THEORY AND FORMULATIONS .................................................... 58 4.1 The TRUSS Element .............................................................................. 58
4.1 . 1 Geometry .................................................................................... 58 4.1.2 Integration on the volume ........................................................... 58 4.1.3 Strain .......................................................................................... 58 4.1.4 Nodal forces ............................................................................... 58 4.1.5 Stiffness matrix ........................................................................... 59
4.2 The BEAM Element ................................................................................ 59 4.3 The SHELL Element ............................................................................... 60
4.3.1 Geometry .................................................................................... 60 4.3.2 Points of integration .................................................................... 61 4.3.3 Rebar .......................................................................................... 62
4.4 The SOLID Element ............................................................................... 63 4.4.1 Internal voids .............................................................................. 63 4.4.2 Convection .................................................................................. 63 4.4.3 Radiation .................................................................................... 65 . .
4.5 Convergence Cr~ter~a ............................................................................. 65 4.6 Storage of Stiffness Matrix ..................................................................... 66
NOMENCLATURE ........................................................................................................ 68
REFERENCES .............................................................................................................. 69
iii
Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13
List of Figures
NDIM ...................................................................................................... 20 Solid elements for a 2-D structure .......................................................... 22 Solid element with 6 nodes ..................................................................... 23 Solid element with 8 nodes ..................................................................... 23 Internal void ........................................................................................... 25
.................................................................................... Coordinate order 54 Truss element ........................................................................................ 58 Beam element ........................................................................................ 60 Shell element ......................................................................................... 61 Points of integration ............................................................................... 61 Rebar element ........................................................................................ 62 Void frontier ............................................................................................ 63 Convergence iterations .......................................................................... 66
List of Tables
Table 1 Files and steps ......................................................................................... 5 Table 2 Input data file (.DAT) format for temperature analysis .............................. 6 Table 3 Input data file (.STR) format for temperature analysis .............................. 7 Table 4 Input data file (.DAT) format for structural analysis ................................... 8 Table 5 Input data file (STR) format for structural analysis ................................... 9
1.0 INTRODUCTION
1.1 General
SAFIR is a special purpose computer program for the analysis of structures under ambient and elevated temperature conditions. The program, which is based on the Finite Element Method (FEM), can be used to study the behav~our of one, two and three-dimensional structures. The program (SAFIR) was developed at the University of Liege, Belgium, and is today v~ewed as the second generation of structural fire codes developed in Liege, the first generation being another computer program called Computer Engineering of the Fire design of Composite and Steel Structures (CEFICOSS)'~.
As a finite element program, SAFIR accommodates various elements for different idealization, calculation procedures and various material models for incorporating stress- strain behaviour. The elements include the 2-D SOLID elements, 3-D SOLID elements, BEAM elements, SHELL elements and TRUSS elements. The stress-strain material laws include multi-linear or linear-elliptic for steel and non-linear for concrete.
The analysis procedure and the program capability are presented in this Chapter. Details of the data files, material properties and cross sectional shapes are presented in Chapter 2. The detail input and format used in the program are given in Chapter 3, while Chapter 4 presents the theory and formulations of the elements available in the program.
1.2 Analysis Procedure
Using the program, the analysis of a structure exposed to fire may consist of several steps. The first step involves predicting the temperature distribution inside the structural members, referred to as thermal analysis. The torsional analysis may be necessary for 3-0 BEAM elements, a section subject to warping and where the warping function table and torsional stiffness of the cross section are not available. The last part of the analysis, termed the structural analysis, is carried out for the main purpose of determining the response of the structure due to static and thermal loading. The various stages of analysis are briefly outlined In the following sections.
1.2.1 Thermal analvsis
This analysis is usually performed while the structure is exposed to fire. For a complex structure, the sub-structur~ng technique is used, where the total structure is divided into several substructures and a temperature calculation is performed successively for each of the substructures. This kind of situation does arise in a structure where the members are made of different sections. For example, a frame structure wlth reinforced concrete columns, pre-stressed main beams and structural steel secondary beams, will require separate temperature analyses for each of the section types. From these analyses, the temperatures across the cross section are obtained and are stored for subsequent structural analysis where these sections are present.
The thermal analysis is made using 2-D SOLID elements, to be used later, on cross sections of BEAM elements or on the thickness of SHELL elements.
1.2.2 Analvsis of torsional stiffness of BEAM elements
This analysis is usually performed when analyzing structures with 3-D BEAM elements, either because non-uniform torsion and beam cross section were subject to warping (warping function is not equal to zero) or because the torsional stiffness is not available from tables or formulas. The 2-0 SOLID elements are used to calculate the warping function and the torsional stiffness of the cross section. The torsional properties obtained from this calculation are added to the results obtained from the temperature analysis of the same cross section for subsequent structural analysis. In cases where the warping function is not necessary, such as in the case of uniform torsion or a cross section with a warping function equal to zero, and if the torsional stiffness can be found in standard tables or by analytical formula, then this analysis need not be performed. In such situations, the torsional stiffness is simply introduced as a property of the cross section for the structural analysis.
1.2.3 Structural analvsis at elevated temoerature
For each calculation, the loads are applied to the structure, described as BEAM, TRUSS and SHELL elements. The temperature history of the structure, due to fire, is read from the files created during the temperature analysis. As the computation strategy is based on a step-by-step procedure, the following information can be obtained until failure occurs in the structure:
Displacement at each node of the structure. Axial and shear forces and bending moments at integration points in each finite element. Strains, stresses and tangent modulus in each mesh at integration points of each finite element.
1.3 Capabilities of SAFIR
SAFIR can be used for performing three different types of calculations, namely, thermal, torsional and structural analysis. The capabilities of the program based on these three analysis types are outlined in this section.
1.3.1 Capabilities based on temoerature analvsis
Plane sections as well as three-dimensional structures can be analyzed. Plane sectlons are discretized by triangular andlor quadrilateral (rectangular and non-rectangular) elements, allowing representation of virtually all cross sectional shapes. Three-dimensional structures are discretized by sol~d elements (prismatic and non- prismatic) with 6 or 8 nodes. This allows the representation of virtually all structure shapes. Variation of material from element to element is possible.
The f~re temperature, defined as a function of time, can either be the standard curves predefined in the code (IS0 834, ASTM E l 19, ULC S-101) or any other curve can be introduced through data points. Cooling down phases can be considered. Variation of material properties with temperatures, as well as the evaporation of moisture, can be considered. Can analyze thermal performance of materials such as steel, reinforced concrete and composite steel-concrete sections. Other materials can also be analyzed provided their physical properties at elevated temperatures are known.
1.3.2 Ca~abilities based on torsional analysis
Allows virtually all cross section shapes to be represented. Materials are considered to be in the elastic stage.
1.3.3 Ca~abilities based on structural analvsis
Plane or 3-D structures can be analyzed. The structure is discretized by means of four different elements: Truss elements, made of one single material with one uniform temperature per element; beam elements, either pure steel, reinforced concrete or composite-steel sections; solid elements in which only thermo-elastic material laws are possible; and shell membrane elements. Large displacements are considered for truss, beam and shell elements. The effects of thermal strains (thermal restraint) can be accounted for. Material properties are non-linearly temperature dependent. Unloading of material is parallel to the elastic-loading branch. Local failure of a structural member that does not endanger the safety of the whole structure can be handled by means of the arc length technique. Nodal coordinates can be introduced in the Cartesian or cylindrical system of axes. Imposed displacement (prescribed degrees of freedom) can be introduced. Structures with external support inclined at an angle to the global axes can be analyzed. Residual stresses (initial strains) can be accounted for. Pre-stressed structures can be analyzed.
Automatic adaptation of time step is possible and structural calculation continues until failure. This means that there are no deflection criteria to actually make the failure point.
1.4 Common Features in all Analyses
The common features in all computations are listed as follows:
Optimization of the matrix bandwidth to reduce the computer storage and calculation time can be performed by the program using internal re-numbering of the system equations. This re-numbering is transparent to the user. The same temperature or the same displacement can be imposed at two different nodes by the use of master-slave relations.
Thermal and mechanical properties of the steel and concrete according to Eurocodes 2,3 and 4 are embedded in the code and can be used directly. Graphic pre-processing and post-processing capabilities are by the PREPRO and DIAMOND97 codes, respectively. When needed, SAFIR could be adapted so as to give the results in a format compatible with commercial graphic softwaie, such as I-DEAS.
1.5 Sign Conventions
The following sign conventions are applied.
1.5.1 Global and local axes
Global axes are employed when defining a structure that is to be analyzed using SAFIR. This is done using the Cartesian system of coordinates. For the 2-0 (plane) problems, the axes are named G I and G2, while the local axes are named L1 and L2. Applied force and the displacements are positive in the direction of G I and G2; the applied moments and rotations are positwe in a counter-clockwise direction. For the 3-D problem, the global axes are named GI , G2 and G3 and the local axes are named L1, L2 and L3. The movement GI-G2-G3 is dextrorsum; the applied force and moments, displacements and rotations are all positive in the GI , G2 and G3 directions.
1.5.2 Stresses
The stresses are positive in tension. Axial forces, obtained as a summation of the stresses, are also positive in tension. Bending moments in the beam elements, obtained as a summation of y, o,, with y, measured on the local axis L1, are positive when fibres having a positive local coordinate are in tension.
2.0 INPUT DESCRIPTION
2.1 Input for SAFIR
For analysis using SAFIR, data files acting as input files to the program are prepared. For each analysis type (thermal, torsional and structural analysis), the user prepares two data files. These are ASCII files, created with a text editor in a word processor, or by PREPRO (for special cases only), and have names w~th the extensions .DAT and .STR. Each file is divided into sections with one blank line between each section to indicate that input for the preceding section is complete.
The data file with a .DAT extension contains information such as calculation strategy, time discretization, loads and the name of the file with the .STR extension where the structure is specified. The file with the .STR extension is where the structural parameters are defined. Information specified in this file include node coordinates, types of finite elements used, material properties, etc. For structural analysis, the .STR file specifies the name of the .TEM files created during thermal and torsional analyses and in which the temperature data is stored. This method of input is adopted so that calculations on the same structure with different components can be made just by changing the name of the .TEM files in the .STR file. Table 1 shows a schematic representation of the different steps and files that may be involved in the case of a frame structure comprised of two types of columns, one type of beam, one floor and one bracing system. The user must create the .STR and .DAT files. The detailed structure of these files is given in Chapter 3.
Table 1: Files and steps
2.2 Problem Definition
The problem to be solved is described in files as mentioned above. Depending on the type of structure to be analyzed, data is sectioned into these input files. The first few lines are used as comment statements, where the problem title can be specified by up to 80 alphanumeric characters in each line. The rest of the sections contain general data definition, such as the total number of integration points (NPTTOT), the total number of nodes (NNODE) in the structure and the material dimension (NDIMMATER). A blank line is used to indicate the end of the previous section in the input files. The
commands, format and number of lines required for a section in the input files are briefly given in the following sections.
2.3 General Data for Thermal Analysis
The general data for thermal analysis is briefly described in Table 2 .DAT file and Table 3 .STR file. Each input line is comprised of a command followed by parameters for the command. Both the command and the parameters are written in a predetermined format. Commands follow a 10-character (A1 O), right justified format. Full details of all the commands and their parameters are given in Chapter 3.
Table 2: Input data file (.DAT) format for temperature analysis
" TO," STEP'," NDDL", follow five character
RENUMPEW Only RENWMGEO needs a parameter
" RENUMGEO"
" RENUM"
Table 3: Input data file (.STR) format for temperature analysis
Parameter Format
2.4 General Data for Structural Analysis
The general data for structural analysis is briefly presented in Table 4 .DAT file, and Table 5 .STR file. In each input line, a command is given followed by the parameters for the command. Both the command and the parameters are written in a predetermined format that is also given. Full details of all the commands are given in Chapter 3.
8
Table 4: Input data file (.DAT) format for structural analysis
Only REWMGEO needs a p-tete
Table 5: Input data file (.STR) format for structural analysis
Parameter Format
2.5 Material Properties
Material names are provided in the program by command CMAT(NM) and the values of the parameters associated with this command by PARACOLD(1,NM). There is a maximum of eight values of PARACOLD(1,NM) available in the program depending on the material name introduced in the CMAT(NM). Valid material names are: INSULATION (does not carry any load), ELASTIC, BILIN, RAMBOSGOOD (only at room temperature), STEELEC3, STEELEC2, SILCONEC2 and CALCONEC2 (at elevated temperatures).
2.5.1 Stress-strain relations of concrete and steel
The relations in these materials are non-linear and are temperature dependent. In structures exposed to fire loads, the materials are subjected to initial strains (E,), thermal effects (E,) and stress related effects (E,). The stresses are, therefore, caused by the difference between the total strain (E,,), obtained from the nodal displacements, and the initial and thermal strains.
2.5.2 Parameters of the material laws
Both the steel and concrete materials can be modelled in the program by different material laws. For example, if CMAT(NM) is RAMBOSGOOD, the Ramberg-Osgood stress-strain relationship is used in the program to model both steel and concrete. For Ramberg-Osgood stress-strain relationships for unheated structures only, with material valid at 20°C, five parameters must be introduced by the user:
(a) PARACOLD(1 ,NM) =the Young's modulus (E) (b) PARACOLD(2,NM) = any value or leave as blank space (c) PARACOLD(3,NM) = limit of proportionality (Ip) (d) PARACOLD(4,NM) =exponent of the law (e) (e) PARACOLD(5,NM) =the factor of the law (D)
Ramberg-Osgood strain:
If Stress (S) < Ip then Strain = SIE Else Strain = S/E + ((S-lp)/D)"
For steel materials (STEELEC3, STEELEC2, STEELE3DC and PSTEELAIG), three parameters, according to the Eurocodes, must be introduced by the user:
(a) PARACOLD(1 ,NM) = E, the Young's modulus (b) PARACOLD(2,NM) = any value or leave as blank space (c) PARACOLD(3,NM) = fy, the yield strength
For concrete materials that behave at elevated temperatures (CALCONCEC2 and SILCONCEC2) and Schneider model3 (CALCONSCH, SILCONCSCH and LWCONCSCH), four parameters, according to the Eurocodes, must be introduced by the user:
(a) PARACOLD(1 ,NM) =any value or leave as blank space (b) PARACOLD(2,NM) = any value or leave as blank space (c) PARACOLD(3,NM) = f,, compressive strength (d) PARACOLD(4,NM) = f,, the tensile strength
2.6 Convergence Criteria
In order to converge to a solution, a tolerance value has to be specified in the program. SAFlR uses an iterative procedure to converge on the correct solution for each increment. The precision given in the data file is a small value that must be reached at different tlmes in SAFlR calculations in order to have convergence. A good precision value is dependent on the type of structure that is being analyzed and information from preliminary runs. However, if the user does not know which to choose, a value of 0.001 can be used as a starting point. After the first run, an examination of the out-of-balance forces in the output can help the user to modify the corresponding precision value to obtain an acceptable value.
3.0 DETAILED INPUT DATA AND FORMAT
3.1 Description and Format for Thermal Analysis Files
Parameter formats are specified as fixed length strings containing alphanumeric, integer or decimal values. Most labels and parameters are right justified with extra blank spaces for padding. Most commands are left justified.
Example: <A10 > Represents a ten-character string of alphanumeric characters. <I52 Represents a five-character string containing an integer value. <G10.0> Represents a ten-character string containing a decimal value. <30b> Represents a thirty-character string containing only blank spaces.
3.1 .I The .DAT file for thermal analvsis
SERIES 1: Comments. Any number of lines for comments. Format A80 Follow with one blank line to indicate the end of comments.
SERIES 2: Number of integration points of the structure. One line. Format <A1 0>,<110> ' NPTTOT', NPTTOT The user makes an estimate for this number and SAFlR verifies to ensure that NPTTOT is not too small. If the number is found to be small, SAFlR prompts the user to increase the value and indicates which value is to be used.
SERIES 3: Number of nodes of the structure One line. Format <A1 0>,<15> ' NNODE', NNODE
SERIES 4: Number of global coordinate axes. One line. Format <A10>,<15> ' NDIM', NDIM NDlM = 2 for plane structures. NDIM = 3 for 3-D structures.
SERIES 5: Dimension of the material laws. One line. Format <A10>,<15> ' NDIMMATER', NDIMMATER NDIMMATER = 1 for thermal analysis
SERIES 6: Maximum degrees of freedom per node. One line, first line of series. Format <A1 0>,<15> ' NDDLMAX', NDDLMAX NDDLMAX = 1 for thermal analysis.
Degrees of freedom for all nodes. One line, second line series. Format <A10>,<308>,<15> 'EVERY NODE ', NNDL
Degrees of freedom for specific nodes. Multiple lines possible. Format <A10>,<15>,<A5>,<15>,<A5>,<15>,<A5>,<15> ' FROM', NNOI , ' TO', NN02, 'STEP', NN03, ' NDDL', NDDL NNOI = First node of this group of nodes. NN02 = Last node of this group of nodes. NN03 = Node step. NDDL = Number of D.0.F. for group of nodes, 0 or 1.
Note: ' i h e nodes: NNO1, NN01sNN03, NNOIi2xNN03, ...... NN02-2xNN03, NNO~-NNO~,/ I NN02 have NDDL D.0.F.
Degrees of freedom for specific nodes by repeating existing ones. Multiple lines possible. One line for each set of nodes. Format <A1 0>,<15>,<A5>,<15>,<A5>,<l5>,<A5>,<15> ' REPEAT', NNOI, ' TO', NN02, ' STEP', NN03, ' TIME', NT NNOI = First node to be repeated. NN02 = Last node to be repeated. NN03 = Node step. NT = Number of times that the nodes are repeated.
SERIES 7: Thermal calculation. One line for header, first line of four-line series. Format CAI O> ' TEMPERAT'
Thermal calculation time parameter. One line for time integration, second line of four-line series. Format <A1 0>,<G10.0> ' TETA', TETA TETA = Parameter for the time integration, 0 c TETA 1 (0.90
recommended).
Thermal calculation initial time. One line for initial time, third line of four-line series. Format <A1 0>,<G10.0> ' TINITIAL', TlNlTlAL TlNlTlAL =Temperature in the structure at time t = 0, normally taken as
20°C.
Thermal calculation output file type. One line of three possible choices, fourth line of four-line series. Format <A1 O> ' MAKETEM' Store average element temperatures for beam fibres.
' MAKE.TSH' Store first NNODEl2 node temperatures describing shell element temperatures.
' NOter ' Oniy one of the above possibilities can be chosen. i
SERIES 8: Band width. One Ilne, flrst line of two-line series. Format <A1 0>,<110> ' LARGEURI l', ILARGEURI 1 ILARGEURI I = Maximum length of K l 1 in the stiffness matrix K.
Bandwidth of K12. One line, second line of two-line series. Format <A1 0>,<110> ' LARGEUR12', ILARGEUR12 ILARGEUR12 = Maximum length of K12 in the stiffness matrix K.
SERIES 9: Renumbering strategy. One line, choose from five possibilities. Format <A1 0>,[<15>] ' NORENUM' No renumbering of the equations.
' RENUMPERM' Renumbering of equations by logical permutations.
' RENUMGEO', NNOl Renumbering of equations by geometrical method
' RENUM' = RENUMGEO + RENUMPERM
READRENUM' Renumbering previously done, reread renumbering from .REN file.
NNOl = Node number where geometrical renumbering will start. NNOl = 0 Then renumbering started successively from all the nodes.
Note: If RENUM or RENUMPERM is used, SAFlR stops after the renumbering. A subsequent run using READRENUM is required.
SERIES 10: File name. One line, first line of two line series. Format <A202 Left justified. 'CFILENAME' CFILENAME = Name of .STR file where the structure is described.
File name for temperature file. One line, second line of two line series. Format <A202 Left justified. 'CFILENAME' CFILENAME = Name of file .TEM or .TEM or .TSH, where temperatures
are stored.
SERIES 11 : Precision. One line. Format <AlOz,<GIO.O> ' PRECISION', PRECISION PRECISION = Small value which must be reached to have convergence.
SERIES 12: Time discretization. One line, first line of several in series. Format <A1 0> ' TIME'
Time discretization time steps. One line for each time step of multiple line series. Max of IDlMTlMESTEP
lines. Format <10bz,<GI O.O>,<G10.0> 10 blank characters, TIMESTEP, UPTIME TIMESTEP = T~me step in seconds. UPTIME = Limit of validity of this time step.
Time discretization last line. One line, last line in series. Format <A1 02 ' ENDTIME'
SERIES 13: Output results desired. Program running time increased with additional outputs requested.
One line, first line of possible multiple line series. Format <A1 O> 'IMPRESSION'
Output results desired choice. One line, second line of possible multiple line series. Format <A1 0>,<G10.0> ' TIMEPRINT', TIMEPRINT TIMEPRINT = Output results time. Results written if Mod (TIME,
TIMEPRINT) = 0, that is, if TIME is a product of TIMEPRINT.
Output results multiple possible lines. One line added to series for each choice. Format <A1 O> ' PRINTDEPL' Write temperature variation each iteration (large amount
of results).
' PRINTFHE' Write out of balance forces each iteration (large amount of results).
'PRINTREACT' Write reactions. One blank line, last line of series. Format <A80>
3.1.2 The .STR file for thermal analvsis
SERIES I: Comments. Any number of lines for comments. Format <A80> Follow with one blank line to indicate the end of comments.
SERIES 2: Number of materials. One line. Format<Al0>,<15>
NMAT', NMAT NMAT = Number of different materials.
i Note: If two materials have the same material law but different characteristics, it creates two different materials. e.g. 5235 and S355 steel.
SERIES 3: Number of different elements. One line, first line of series. Format<Al O> ' ELEMENTS'
Number of solid elements. One line, second line of series. Format <A1 0>,<15> ' SOLID', NSOLID NSOLID = Number of solid elements in the structure.
Number of integration points. One line, third line of series. ForrnatcAl0>,<15> ' NG', NG NG = Number of integration points in each direction in the element. Not
less than 1. Greater than 3 is not recommended.
Number of voids. One line, fourth line of series. Format <A1 0>,<15> ' NVOID', NVOID NVOID = Number of internal voids.
Number of elements around voids. One line, optional line of series. Used when NVOID > 0 Format <A10>,<15> 'FRTIERVOID', NFRONTIERVOID NFRONTIERVOID = Maximum number of elements enclosing the internal
voids. One blank line, last line of series. Format <A80>
SERIES 4: The nodes. One line, first line of series. Format <A1 O>,[<Al O>] ' NODES', [' CYLINDRIC'] ' CYLINDRIC' Parameter is used if the cylindrical coord~nate system is
chosen instead of the Cartesian system. Cylindrical input as (r,B,Z)
and transformed to (X,Y,Z) for the internal solution process by X = r cos(8), Y = r sin(8). 0 is in degrees.
The Nodes position. One line for a node added to series. Format <A1 O>,<lS>,<NDlM*Gl 0.0>,<15> ' NODE', NNO, RCOORDG(I,NNO), ..., RCOORDG(NDIM,NNO),
KGENE NNO = Number of the node. Each node will have one positional entry along each global axis from one to
NDIM.
Example:
RCOORDG(1 ,NNO) = First global coordinate of the node NNO. RCOORDG(2,NNO) = Second global coordinate of the node NNO. RCOORDG(ND1M-2,NNO) = Node NNO coordinate on global axis NDIM-2 RCOORDG(ND1M-1 ,NNO) = Node NNO coordinate on global axis NDIM-1 RCOORDG(NDIM,NNO) = Node NNO coordinate on global axis NDIM KGENE = Automatic generation between previous defined node and the
node NNO. KGENE = 0 or left blank ~f no generation KGENE = I if equidistant generation from the last defined node.
One line for a repeated series added to series. Format <AIO>,<NNO>,<DELTAC(l), ..., <DELTAC(NDIM)>, <KGENE> ' REPEAT', NNO, DELTAC(I), ..., DELTAC(NDIM), KGENE NNO = Number of nodes to be repeated. Each DELTAC( ) increment represents one of the global axis. DELTAC(1) = Increment on the first coordinate. DELTAC(2) = lncrement on the second coordinate.
. . . DELTAC(ND1M-2) = lncrement on the coordinate NDIM-2. DELTAC(ND1M-I) = lncrement on the coordinate NDIM-I. DELTAC(NDIM) = lncrement on the coordinate NDIM. KGENE = Number of times that this command has to be repeated
1' 1st mrd.. y 'r 1 st coord., y
NDIM = 2 NDIM = 3
Figure 1 : NDIM
SERIES 5: Torsional centre.
One line, first line of two line series. Format <A1 0>,<5b>,<GlO.O>,<GlO.O> 'NODELINE', Yo, Zo Yo = First global coordinate of the node line which joins the beam
elements. Zo = Second global coordinate of the node line.
One line, second line of two line series. Format <A1 0>,<5b>,<G1O.Oz,<G10.0> ' YC zc', Yc, Zc Yc = First global coordinate of the centre of torsion. Zc = Second global coordinate of the centre of torsion.
SERIES 6: Supports and imposed displacements. One line, first line of a possible multiple line series. Format <A1 O> 'FIXATIONS'
Supports and imposed fixations. One line for each node as a f~xed block. Format <A1 0>,<15>,<5b>,<AI O> ' BLOCK', NNO, ' ', CBLOCK(I(NN0) NNO = Node where the solution is not be calculated. CBLOCK(1 ,NNO) = Function name describing the evolution of the solution
at this node with respect to tlme. The temperature is the solut~on.
Supports and lmposed displacements optional slave nodes Optional line for each slave node. Format <A1 0>,<15>,<15>,<AI 0>
SAME', NNOI , NN02, CTRAV(1) NNOI = Number of the slave node. NN02 = Number of the master node. CTRAV(1) = ' YES'
One line to repeat a previous SAME command. Format <A1 0>,<15>,<15>,<AI 0> ' REPEAT', NUMBER, INC, CTRAV(1) NUMBER = Number of times the preceding SAME command is repeated. INCR = Increment on NNOI and NN02. CTRAV(1) = ' YES'
Support and imposed displacements end of series. One blank line as last line of series. Format <A80>
SERIES 7: SOLID elements. One line, first line of possible multiple line series. Format <A1 O> 'NODOFSOLID'
Solid elements. One line for each element. Format <A1 O>,<(NUMBEROFNODESINSOLID+2)'15>,<G10.0>,<15> ' ELEM', NSOL, NODESOFSOLID( ..., NPL), MATSOLID, EPSRSOLID,
KGENE NSOL = Number of this element. NODESOFSOLID(1 ,NPL) = First node of this element. NODESOFSOLID(2,NPL) = Second node of this element. . . . . . . . . . NODESOFSOLID(NUMBEROFNODESINSOLID,NPL) = Last node of this
element. MATSOLID = Material of this element. EPSRSOLID = Residual stress in this element. KGENE = Generate from previously element up to this one, increment by
node number.
One line to repeat previous element structure. Format <AlO>,c(NODESOFSOLID+2)*l5>,<G10.0>,~15> ' REPEAT', ILAST, INCR, NODESOFSOLID( ,NPL), MATSOLID,
EPSRSOLID, KGENE ILAST = Number of elements to repeat. INCR = Increment in node number. NODESOFSOLID(2,NPL) =Any value ( can be 0 ). ... . . . ... NODESOFSOLID(NUMBEROFNODESINSOLID,NPL) = Any value
(can be 0). MATSOLID = Any value (can be 0). EPSRSOLID = Residual stress in this element. KGENE = Number of times to repeat th~s command. Increase element
number by 1.
' GI, = L2 of a beam element
NDIM = 2
node 3 node 4 face 3 node 3 A 2 node 1
face l node 2 node 1
face 1 node 2
G2, = L3 of a beam element > Figure 2: Solid elements for a 2-D structure
A node 5
3
node 6
node 1
Gl,G2.G3 is dextrorsum
node 3
G2
Figure 3: Solid element with 6 nodes
'l' node 6 G I NDIM = 3
face 3
face 6
face 5 --.----.-------------
face 1
node I node 4
Figure 4: Solid element with 8 nodes
Solid element heated surfaces. One line of multiple line series. Format <A1 O> ' FRONTIER'
Solid element heated elements. One line for each heated surface of each heated element. Format <15>,<NUMBEROFFRONTlER*AS>,[<I5>] NSOL, CFRONTIERSOLID( ..., NSOL), KGENE NSOL = Number of the element. CFRONTIERSOLID(1 ,NSOL) =Temperature curve on the first face of the
element.
... CFRONTIERSOLID(NUMBEROFFRONTIER,NSOL) = Temperature curve
on the last face of the element. KGENE = Increment the number of the elements.
Note ! Temperature curve can be a predefined function (e.g., "FISO"), or a file name.
I I
Solid element separator line. One blank line as separator line in series. Format <A80>
Solid element sub-series for voids among heated elements. One line, first line of possibly repeated sub series. Format <A1 O>. ' VOID'
Solid element sub-series for heated elements and voids. One line for each heated element adjacent to a void. Format <Al0>,<15>,<15>,<15> ' ELEM', NSOL, NFRONTIER, KGENE NSOL = Number of the element. NFRONTIER = Number of the frontier exposed to the internal void. KGENE = Generate elements from the previous element. Can be positive
or negative.
Solid element sub-series end. One line, last line in sub-series. Format <A1 O> ' ENDVOID'
Figure 5: Internal void
The following group of lines on symmetry is necessary if symmetry is accounted for. If not, only the ENDSYM line is present.
Solid element symmetry. One line of series. Format <A1 0> ' SYMMETRY'
Solid elements axis of symmetry. One line for each axis of symmetry in series. Format <A10>,<15>,</5> ' REALSYM', N1, N2 Axis is drawn from node N1 to node N2.
Sol~d element Y axis of symmetry. One line. Format <A1 O> ' YSYM' If the first axis of coordinate, i.e. the local y axis for the beam element, is a
thermal and structural axis of symmetry.
Solid elements last line in series. One line as last line in series. Format <A1 O> ' ENDSYM'
SERIES 8: Material description. One line, first line of series. Format <A1 O> ' MATERIALS'
Material description sub-series, one sub-series for each different type of material used. One line, first line of two line sub-series. Format <A1 0>[<15>] CMAT(NM), X CMAT(NM) = Name of the material. Stored in array of NM items, Number
Materials. X = For user defined materials with temperature dependent properties only.
Indicates number of temperature ranges with linear interpolation between temperatures.
1 Note: I
Vai~d mater~al names are: 'INSULATION', 1
STEELEC3, ' STEELEC2, or ' PSTEELAI 6' I 'CALCONCEC2'. 'SILCONCECZ, 'CALCONCSCH', 'SILCONCSCH' 'LWCONCSCH' " USER?'
Material description sub-series, material properties. One line, second line of two line sub-series. Format <8'G10.0> Values of eight possible parameters depend on the material:
If CMAT(NM) = INSULATION PARACOLD(1 ,NM) blank. PARACOLD(2,NM) Thermal conductivity k (WImK), if 0 then k = 0.04 +
0.00025 T. PARACOLD(3,NM) Specific heat (JIkgK). PARACOLD(4,NM) Specific mass (kg/m3). PARACOLD(5,NM) blank. PARACOLD(6,NM) Convection coefficient on hot surfaces, if 0 then
default value 25. PARACOLD(7,NM) Convection coefficient on cold surfaces, if 0 then
default value 9. PARACOLD(8,NM) Relatlve emissivity, if 0 then default value 0.50.
For the steel materials in temperature analysis PARACOLD(1 ,NM) blank. PARACOLD(2,NM) blank. PARACOLD(3,NM) blank. PARACOLD(4,NM) blank. PARACOLD(5,NM) blank. PARACOLD(6,NM) Convectlon coefficient on hot surfaces, if 0 then
default value 25. PARACOLD(7,NM) Convectlon coefficient on cold surfaces, if 0 then
default value 9. PARACOLD(8,NM) Relative emissivlty, if 0 then default value 0.50. Thermal conductivity, specific heat, and specific mass are according to
Eurocode 3.
For the concrete materials in temperature analysis PARACOLD(1 ,NM) blank. PARACOLD(2,NM) blank. PARACOLD(3,NM) blank. PARACOLD(4,NM) blank. PARACOLD(5,NM) Moisture content ( kg/m3), if 0 then default value 92. PARACOLD(6,NM) Convection coefficient on hot surfaces, if 0 then
default value 25. PARACOLD(7,NM) Convection coefficient on cold surfaces, if 0 then
default value 9. PARACOLD(8,NM) Relative emissivity, if 0 then default value 0.50. Thermal conductivity, specific heat, and specific mass are according to
Eurocode 2.
For user defined materials for thermal analysis only PARACOLD(1 ,NM) Temperature ("C). PARACOLD(2,NM) lambda. PARACOLD(3,NM) C. PARACOLD(4,NM) rho. PARACOLD(5,NM) Moisture content ( kg/m3). PARACOLD(6,NM) Convection coefficient on hot surfaces. PARACOLD(7,NM) Convection coefficient on cold surfaces. PARACOLD(8,NM) Relative emlssivity.
3.2 Description and Format for Structural Analysis Files
Structural input files follow the same general format as those used for thermal analysis.
3.2.1 The .DAT file for structural analysis
SERIES 1: Comments. One line for each comment. Format <Ago> One blank line to mark end of comments. Format <A80>
SERIES 2: Number of integration points. One line. Format <A1 0>,<110z ' NPTTOT', NPTTOT NPTTOT = Number of integration points in the structure
SERIES 3: Number of nodes. One line. Format <A1 0>,<15> ' NNODE', NNODE NNODE = Number of nodes of the structure.
SERIES 4: Number of axes. One line. Format <A10>,<15> ' NDIM', NDlM NDlM = Number of global axes, 2 for plane structures, 3 for 3-D structures.
SERIES 5: Dimension of the material laws. One line. Format <A1 0>,<15> 'NDIMMATER', NDIMMATER NDIMMATER = 1 if all the materials used in the structure have uni-axial
mechanical law = 2 if one of the materials used in the structure has bi-axial
mechanical law (e.g. plane stress).
SERIES 6: Degrees of freedom. One I~ne, first line in series. Format <A10>,<15> ' NDDLMAX', NDDLMAX NDDLMAX = Maximum number of degrees of freedom per node. if NDlM = 2 for truss elements, NDDLMAX 2
for solid elements, NDDLMAX 2 for beam elements, NDDLMAX 3
if NDlM = 3 for truss elements, NDDLMAX 3 for solid elements, NDDLMAX 3 for shell elements, NDDLMAX 6 for beam elements, NDDLMAX 7
Degrees of freedom for specif~c nodes. One line added for each node. Format <A10>,<30b>,<15> 'EVERY NODE', NDDL NDDL = Number of degrees of freedom for a specific node.
Degrees of freedom for a series of nodes. One line added for each series of nodes. Format <A1 0>,<15>,<A5>,<15>,<A5>,<152,<A5>,<15>
FROM', NNOI, ' TO', NN02, ' STEP', NN03, ' NDDL', NDDL NNOI = First node of this group of nodes. NN02 = Last node of this group of nodes. NN03 = Node step. NDDL = Number of degrees of freedom for group of nodes.
1 Note: ' The nodes: NNOI, NNOI+NN03, NN01+2~NN03, ...... NN02-2xNN03, NN02-NN03, NN02
of freedom.
One line added for a repeating series of nodes, repeated copies get the same degrees of freedom as the original.
Format <A1 0>,<15>,cA5>,<I5>,<A5>,<l5>,<A5>,<15> REPEAT', NNOI , ' TO', NN02, ' STEP', NN03, ' TIME', NT
NNOI = First node to be repeated. NN02 = Last node to be repeated. NN03 = Node step. NT = Number of times that the nodes are to be repeated.
N o k 1 The command will create the following groups: I
1
f NNOl +NN03, NNOI+NN03+1, ... NN02+NN03 . NN01+2xNN03, NN01+2xNN03+1, ... NN02+2NN03
..... ... ..... I ..... ... .-..- / NNOI+NTxNN03, NNOI +NTxNN03+1, ... NN02+NTxNN03
If NDlM = 2: The nodes supporting truss and solid elements must have NDDL 2:
translation in the global axis 1 translation in the global axis 2
The end nodes supporting beam elements must have NDDL 3: translation in the global axis 1 translation in the global axis 2 rotation about virtual global axis
The internal node of beam elements must have NDDL = 1: 2nd order component of the longitudinal displacement, no other elements must be linked to this node
If NDlM = 3: The nodes supporting truss and solid elements must have NDDL 3:
translation in the global axis 1 translation in the global axis 2 translation in the global axis 3
The end nodes supporting beam elements must have NDDL 7 : translation in the global axis 1 translation in the global axis 2 translation in the global axis 3. rotation about global axis 1. rotation about global axis 2. rotation about global axis 3. warping.
The internal node of beam elements must have NDDL = 1 : 2nd order component of the longitudinal displacement, only shell elements are allowed to be linked to this node. The angle nodes of shell elements must have NDDL 6: translation in the global axis 1 translation in the global axis 2 translation in the global axis 3 rotation about global axis 1 rotation about global axis 2 rotation about global axis 3
The mid-side nodes of shell elements must have NDDL 1 : 2nd order component of the longitudinal displacement, only beam elements are allowed to be linked to this node.
SERIES 7 : Loads. One line, first line of two line series. Format <A1 O> ' STATIC'
Load number of vectors. One line, second line of two line series. Format <A10>,<15> ' NLOAD', NLOAD NLOAD = Number of load vectors. One load vector is made of the load
that will vary with time according to the same function.
SERIES 8: Inclined supports. One line. Format <A1 0>,<15>
OBLIQUE', NOBLIQUE NOBLIQUE = Number of inclined supports.
SERIES 9: Convergence strategy. One line, first line of two line series, choice of two possible settings. Format <AlO>,[<GI 0.0>] 'COMEBACK', TlMESTEPMlN
'NOCOMEBACK' TlMESTEPMlN = Minimum value for the time step in case of comeback
only.
Convergence strategy. One line, second line of two line series, choice of two settings. Format <AIO>,<GI 0.0> 'ARCLENGTH', X
'NARCLENGTH', X X not used for NARCLENGTH.
32
SERIES 10: Bandwidth. One Ilne, first line of two llne series. Format <A1 0>,<11 O> 'LARGEURI l', ILARGEURI 1 ILARGEURI I = Maximum length of K11 in the stiffness matrix K.
Bandwidth. One line, second line of two line series. Format <A10>,<110> 'LARGEUR12', ILARGEUR12 ILARGEUR12 = Maximum width of K12 in the stiffness matrix K.
SERIES I I: Renumbering strategy. One line, choice of five options. Format <A1 0>,[<15>] ' NORENUM' = No renumbering of the equations
RENUMPERM' = Renumbering of equations by logical permutations.
or
RENUMGEO', NNOl = Renumbering of equations by geometrical method.
or
RENUM' = RENUMGEO + RENUMPERM
READRENUM' = Read a previous renumbering from a .REN file. NO1 = Node number where the geometrical renumbering w~l l start. Only
used by RENUMGEO. If NNOl = 0 renumbering is started successively from all the nodes.
Note: /If RENUM or RENUMPERM is used SAFIR stops after the renumbering. A subsequent' irun has to be made using READRENUM
SERIES 12: File name. One line. Format <A20> 'CFILENAME' Left justified name of the .STR file where the structure is described.
SERIES 13: Precision. One line. Format <A1 O>,cG10.0> 'PRECISION', PRECISION PRECISION = Small value that must be reached for convergence.
SERIES 14: Loading. One line, first line of possible multiple line series. Format <A1 O> ' LOADS'
Loading function. One line, second line of possible multiple line series. Format <A1 O>,<A10> ' FUNCTION', CFORCE(NL0) CFORCE(NL0) = Function showing how load vector NLO varies as a
function of time.
Loading function possible multiple node loads. One line added for each point load directed at a node. Format <A1 0>,<110>,<6*G10.0> ' NODELOAD', NNO, LOAD(?), LOAD(2), ..., LOAD(NDDL) NNO = Number of nodes where loads are applied. LOAD(1) = Load at degrees of freedom 1. LOAD(2) = Load at degrees of freedom 2.
LOAD(NNDL) = Load at degrees of freedom NDDL
Loading on beam elements. One line added for each element with a distributed load applied. Format <A1 O>,<ll O>,<NDIM'Gl 0.0>,<110> 'DISTRBEAM', NBM, TRAV(I), TRAV(2), ..., TRAV(NDIM), KGENE NBM = Number of the specific BEAM under a distributed load. TRAV(1) = Uniformly distributed load in the direction of the first global axls. TRAV(2) = Uniformly distributed load in the direction of the second global
axis.
. . . TRAV(NDIM) = Uniformly distributed load in the direction of the final global
axis. KGENE = If not equal to zero, distributed loads are generated between the
previous element and the present element
Loading on shell elements. One line added for each loaded shell element. Format <AIO>,<IIO>,<NDIM*GI O.O>,cllO> 'DISTRSHELL', NSH, TRAV(I), TRAV(2), ..., TRAV(NDIM), KGENE NSH = Number of the specific SHELL element under distributed load. TRAV(1) = Uniformly distributed load in the direction of the first global axis. TRAV(2) = Uniformly distributed load in the direction of the second global
axis.
... TRAV(NDIM) = Uniformly distributed load in the direction of the final global
axis. KGENE = If not equal to zero distributed loads are generated between the
previous element and the present element.
Loading on solid elements. One l~ne added for each loaded solid element. Format <AIO>,<Il O>,<NDIMeGI 0.0>,<110> 'DISTRSOLID', NSOL, TRAV(I), TRAV(2), ..., TRAV(NDIM), KGENE NSOL = Number of the specific SOLID element under distributed load. TRAV(1) = Uniformly distributed load in the direction of the first global axis. TRAV(2) = Uniformly d~stributed load in the direction of the second global
axis.
. . . TRAV(NDIM) = Uniformly distributed load in the direction of the final global
axis. KGENE = If not equal to zero distributed loads are generated between the
previous element and the present element.
Loading end of series. One blank line, last line of series. Format <Ago>
SERIES 15: Time discretization. One line, first line of possible multiple line series. Format <A1 O> ' TIME'
Time frames. One line added for each time frame added. Maximum of IDIMTIMESTEP
lines. Format < I Ob>,<GI O.O>,<GI 0.0> 10 blanks characters, TIMESTEP, UPTIME TIMESTEP =Time step in seconds. UPTIME = Limit of validity of this time step.
Time last line. One line, end of time discretization series. Format <A1 O> ' ENDTIME'
SERIES 16: Large displacements. One line. Format <A1 0> 'LARGEDISPL' Indicates that large displacements are taken into account.
SERIES 17: Thermal elongation. One line, choice of two options. Format <A1 O> ' NOEPSTH' If thermal elongation is not considered.
' EPSTH' If thermal elongation is considered.
SERIES 18: Output results. One line, first line of multiple line series Format <A1 O> 'IMPRESSION'
Output results. One line, second line of multiple line series. Format <A1 O>,<G10.0> ' TIMEPRINT', TlMEPRlNT TlMEPRlNT = Time for the output of the results.
Output optional results. Add one line for each option chosen. Format <A10>,[<15>],[~15>] ' PRINTDEPL' The displacement variation is written at every iteration.
or
'PRINTTMPRT' The temperatures in the fibres of the beam elements are written.
' PRINTFHE' The out of balance forces are written at every iteration.
'PRINTREACT' The reactions are written.
' PRINTMN' Print the internal forces of the beam elements. or
'PRINTSOLID' Print the stresses in the solid elements.
'PRNSIGMABM', NBM, NG Print the stresses in a beam element. NBM Number of the beam element where stresses are printed. NG Integration point of the beam element where stresses are
printed.
' PRINTET', NBM, NG Print the tangent modul~ in a beam element. NBM Number of beam element where moduli are printed. NG Integration point of the beam element where moduli are printed.
'PRNSIGMASL', NSOL Print the stresses in a solid element. NSOL Number of the solid element where the stresses are printed.
Output results last line. One blank line as last line of series. Format <A80>
3.2.2 The .STR file for structural analvsis
SERIES 1: Comments. One line for each comment added. Format <A80>
Comments end line. One blank line as end to comment series. Format <A80>
SERIES 2: Number of materials. One line. Format <Al0>,<15> ' NMAT', NMAT NMAT = Number of different materials.
If two materials have the same material law but dierent characteristics, it makes two
SERIES 3: Number of different elements. One line, first line of multiple line series. Format <A1 O> ' ELEMENTS'
Different elements, beam elements sub-series. One line added to sub-series if beams are used in the structure. Format <A1 0>,<15>,<15> ' BEAM', NBEAM, NGEOBEAM NBEAM = Number of BEAM elements in the structure. NGEOBEAM = Number of different groups of geometrical properties.
Different elements, integration points, beam elements sub-series. One line. Format <A10>,<15> ' NG', NG NG = Number of longitudinal points of integration in elements. Cannot be
less than 2. Greater than 3 is not recommended.
Dierent elements, fibres of beam elements, beam elements sub-series. One line. Format <A1 0>,<15> ' NFIBER', NFIBERBEAM NFIBERBEAM = Number of longitudinal fibres in the beam elements (the
maximum value for all the different groups of geometrical properties).
Different elements, truss elements. One line added to series if truss elements are used. Format <A1 0>,<15>,<15> ' TRUSS', NTRUSS, NGEOTRUSS NTRUSS = Number of TRUSS elements in the structure. NGEOTRUSS = Number of different groups of geometrical properties.
1 Note: ! One group of geometrical properties comprised elements that had the same materials, the same cross sectional area and the same temperature history.
Different elements, shell elements sub-series. One line, first line of four line sub-series. Format <A1 0>,<15>,<15> ' SHELL', NSHELL, NGEOSHELL NSHELL = Number of SHELL elements in the structure. NGEOSHELL = Number of different groups of geometrical properties.
Different elements, Shell elements sub-series shell thickness. One line, second line of four l~ne sub-series. Format <Al0>,<15> ' NGTHICK', NGSHELLTHICK NGSHELLTHICK = Number of points of integration on the thickness of the
elements. Cannot be less than 2.
Different elements, shell element sub-serges shell area. One line, third line of four line sub-series. Format <A1 0>,<15> ' NGAREA', NGSHELLAREA NGSHELLAREA = Number of points of ~ntegration in each direction of the
surface of the elements.
Note: If NGSHELLAREA = 1 integration point(s) = I 5 = 1/3 q = 113 If NGSHELLAREA = 2 integration point(s) = 3 q = 116 q = 116
5 = 416 q = 1/63 ! ;= 1/6 q = 416
If NGSHELLAREA = 3 integration @nt(s) = 4 ; = 113 q=1/3, 5 = 115 5=35 rl=1/5i q=1/5 < = 7/5 q=3/5/
where and q are the natural coordinate systems of the shell surface. I
Different elements, shell element sub-series rebar. One line, fourth line of four line sub-series. Format <A1 0>,<15> ' NREBARS', NREBARS NREBARS = Number of REBAR layers in the shell elements.
Different elements, solid elements. One line, first line of two line sub-series. Format <A1 0>,<15> ' SOLID', NSOLID NSOLID = Number of SOLID elements in the structure.
Different elements, solid elements integration points. One line, second line of two line sub series. Format <A1 0>,<15> ' NG', NGSOLID NGSOLID = Number of points of integration in each direction in the
elements. Cannot be less than 1. Greater than 3 is not recommended.
Last line of series. One blank line as last line of series. Format <A80>
SERIES 4: The nodes. One line, first line of multiple line series. Format <A1 O>,[<AI Oz]
NODES'
or
' NODES CYLINDRIC'
Adding ' CYLINDRIC' allows use of cylindrical coordinates (r,0,Z) instead of Cartesian coordinates (X,Y,Z). Cylindrical coordinates are processed by the formulas X = r cos(0) and Y = r sin(8).
Nodes. One line added for each node. Format <Al0>,<15>,<NDIM*G10.0>,<15> ' NODE', NNO, RCOORD(I,NNO), ..., RCOORD(NDIM,NNO), KGENE NNO = Number of the specific node. RCOORD(1 ,NNO) = First global coordinate of the node NNO.
... RCOORD(NDIM,NNO) = Last global coordinate of node NNO of NDIM
global axis. KGENE =Generate nodes between the previous node and the current
node NNO. KGENE = 0 if no generation KGENE = 1 if equidistant generation from the last defined node.
Format <Al0>,<15>,cNDIM*GI0.0>,<15> ' REPEAT', NNO, DELTAC(I), ..., DELTAC(NDIM), KGENE NNO = Number of nodes to be repeated. DELTAC(1) = Increment on the first coordinate.
. . . DELTAC(NDIM) = lncrement on the coordinate NDIM. KGENE = Number of times that this command has to be repeated.
SERIES 5: Supports and imposed displacements. One line, first line of possible multiple line series. Format <A10> 'FIXATIONS'
I Note: (In ths series, two lines are present instead of one if NDDLMAX > 6 1
Supports and imposed displacements fixed blocks. One line for each node where solution follows a defined function of time
and the reaction must be calculated for up to six degrees of freedom. Format <Al0>,<15>,<5b>,<6*A10> ' BLOCK', NNO, ' ', CBLOCK(1 ,NNO), ..., CBLOCK(NDDLMAX,NNO) If NDDLMAX > 6 then an addit~onal line follows the previous one to specify
bounds on other degrees of freedom.
One additional line for more degrees of freedom for a node. Format <20b>,<6*AI 0>
', CBLOCK(7,NNO), ..., CBLOCK(NDDLMAX,NNO) NNO = Number of the specific node where the solution must not be
calculated. CBLOCK(1 ,NNO) = Function describing displacement for first D.0.F. at this
node with respect to time. CBLOCK(2,NNO) = Function describing displacement for second D.0.F. at
this node with respect to time
. . . CBLOCK(NDDLMAX,NNO) = Function describing displacement for last
D.0.F. at this node with respect to time
Supports and imposed displacements slave nodes. One line added for each slave node up to six degrees of freedom. Format <A1 0>,<15>,<15>,<6'AI 0> ' SAME', NNOI, NN02, CTRAV(I), ..., CTRAV(NDDLMAX) If NDDLMAX > 6 add a line to specify functions for additional degrees of
freedom. One line added for other degrees of freedom for a slave node. Format <20b>,<6*A10>
', CTRAV(7), ..., CTRAV(NDDLMAX)
NNOI = Number of the specific slave node. NN02 = Number of the master node. CTRAV(1) = ' YES' If the solution is the same as at node NN02 and as
at node NNOI for the D.0.F. 1.
CTRAV(NDDLMAX) = ' YES' If the solution is the same as at node NN02 and as at node NNOI for the D.0.F. 1.
NNOl for the D.0.F. 1. ' ' If there is no master-slave relation for this D.0.F.
NNOl for the last D.0.F. ' ' If there is no master-slave relation for this D.0.F.
One line added for repeating series of slave node nodes up to six degrees of freedom.
Format <Al0>,<15>,<15>,<6*AlO> ' REPEAT', NUMBER, INCR, CTRAV(I), ..., CTRAV(NDDLMAX)
If NDDLMAX > 6 add a line to specify values for other degrees of freedom for repeated nodes
One line added for specifying additional degrees of freedom. Format <20b>,<6*A10>
', CTRAV(I), ..., CTRAV(NDDLMAX)
NUMBER = Number of times that the preceding SAME command must be repeated.
INCR = Increment on NNOl and NN02. CTRAV(1) = ' YES' If the solution is the same as at node NN02 as at
node NNOI for the D.0.F. 1. ' ' If there is no master-slave relation for this D.0.F.
... CTRAV(NDDLMAX) = ' YES' If the solution is the same as at NN02 as
at NNOI for the last D.0.F.
SERIES 6: BEAM elements.
'Note: [This series is skipped if no BEAM element is present in the structure.
One line, first line of possible multiple line series. Format <A1 O> 'NODOFBEAM'
Beam elements file name sub-series. One sub-series for each type of element. One line, first line of sub-series. Format <A202 'CFILENAME' CFILENAME = Full name of the file where the information on this section
type can be found. Usually the extension is .TEM. File name is left justified.
Beam elements sub-series material translation. One llne added for each different material used in the section. Format <Al0>,<15>,<15> ' TRANSLATE', MATL, MATG MATL = Local number of thls material in this section type. MATG =Global number of this mater~al in the structure.
Beam element sub series last line. One blank line to mark end of sub-series. Format <A80>
Beam elements list. One line for each beam element. Format <15>,~15>,~15>,<15>,[<15>],<15>,[<l5>] NE, NODOFBEAM(1 ,NE), ..., NODOFBEAM(4,NE), ITYPEBEAM(NE),
KGENE NE = Number of this element. NODOFBEAM(1 ,NE) = F~rst end node of this element. NODOFBEAM(3,NE) = Third (i.e. central) node of this element. NODOFBEAM(2,NE) = Second end node of this element. NODOFBEAM(4,NE) = Fourth node of this element (present only if
NDlM = 3). ITYPEBEAM(NE) =The section type of this element. KGENE = Allows the generation from the previously defined element up to
this one. KGENE gives the increment on the first 3 nodes.
SERIES 7: SOLID elements
Note: ,This series is skipped if no SOLID element is present in the structure.
One line, first line of multiple line series for solid elements. Format <A1 O> 'NODOFSOLID'
Sol~d elements file names. One line for each solid element *.TEM file. Format <A20> left justified. 'CFILENAME' CFILENAME = Name of the file where the temperatures concerning the
solid elements are read. Usually, this file has the extension .TEM.
Solid element list. One line for each solid element. Format <AlO>,<(NUMBEROFNODESINSOLID+2)*15>,<G10.0>,<15> ' ELEM', NS, NODE(I,NS), ..., NODE(8,NS), SMAT, EPSRSOLID,
KGENE NS = Number of this element. NODE(1,NS) = First node of this element. NODE(2,NS) = Second node of this element.
. . . NODE(8,NS) = Last node of this element. SMATS = Material of this element. EPSRSOLID =Any value, preferably 0. KGENE = Allows the generation from the previously defined element up to
this one. KGENE gives the increment on the node number.
Format ~AlO>,<NUMBEROFNODESINSOLID+2)'15>,cG10.0>,<15> ' REPEAT', NE, INC, NODE(2,NS), ..., NODE(8,NS), MAT,
EPSRSOLID, KGENE NE = Number of elements to repeat. INC = Increment on the node number. NODE(2,NS) =Any value ( can be 0 ).
... NODE(8,NS) Any value ( can be 0 ). MAT = Any value ( can be 0 ). EPSRSOLID = Any value, preferably 0. KGENE = Number of times that this command has to be repeated. The
element numbers increase by 1. For triangular based elements NODE(7,NS) = NODE(8,NS) = 0.
Solid element last line. One line. Format <A1 O> ' ENDSYM'
SERIES 8: SHELL elements.
Note: ,This series is skipped if no SHELL element is present in the structure.
One line, first line of possible multiple line series. Format <A1 0> 'NODOFSHELL'
Shell elements file list. One line, first part of shell element sub-series, one sub-series for each
element type. Format <A202 left justified 'CFILENAME' CFILENAME = File name where the information concerning this section
type is read.
Shell element material translation. One line for each different material in section, second part of shell element
sub-series. Format <A10>,<15>,<15> ' TRANSLATE', N l , N2 N1 = Local number of this material in this section type. N2 = Global number of this material in the structure.
Shell element series end of translation. One line. Format <A1 O> 'ENDTRANSLA'
Shell element list. One line for each shell element. Format <A1 0>,<9*15> ' ELEM', NSH, N1, N2, N3, N4, N5, N6, ITYPESHELL(NSH), KGENE NSH = Number of the element. N1 = Node 1 (first corner). N4 = Node 4 (first side). N2 = Node 2 (second corner). N5 = Node 5 (second side). N3 = Node 3 (third corner). N6 = Node 6 (third side). ITYPESHELL(NSH) = Type of geometrical section. KGENE = Automatic generation on the element number.
Format <A1 0>,<15>,<15>,<30b>,<l5> ' REPEAT', NSH, N1, ' ', NUMBER NSH = Number of elements to be repeated. N1 = Node increment. NUMBER = Number of times that the NSH elements have to be repeated
SERIES 9: TRUSS elements.
Note: I This series is skipped if no TRUSS dement is present in the structure.
One line, first line of possible multiple line series. Format <A1 0> 'NODOFTRUSS'
Truss elements files. One line for each different truss section type used. Format <A20>,<3*GI 0.0>,<15> 'CFILENAME', GEOTRUSS(1 ,NGT), GEOTRUSS(2,NGT),
IMATTRUSS(NGT) CFILENAME = Name of the file where the temperatures concerning this
section types are read. Left justified. GEOTRUSS(1 ,NGT) = Cross sectional area of this section type. GEOTRUSS(2,NGT) = Residual stress of this section type. IMATTRUSS(NGT) = Global Number of the material in this section type.
Truss elements list. One line for each truss element. Format <6*15> NTR, NODOFTRUSS(1 ,NTR), NODOFTRUSS(2,NTR),
IGEOTRUSS(NTR), KGENE NTR = Number of the element. NODOFTRUSS(1 ,NTR) = First node of this element. NODOFTRUSS(2,NTR) = Second node of this element. IGEOTRUSS(NTR) = Number of the section type for this element. KGENE = Allows for automatic generation.
SERIES 10: Material description. One line, first line of possible multiple line series. Format <A1 O> ' MATERIALS'
Material description sub-serres. One line, first line of two line material sub-series. Format<Al O> 'CMAT' CMAT = Name of the material.
Material description sub-series parameters. One line, second line of two line material sub-series. Format <8*G10.0> PARACOLD(1 ,NM), PARACOLD(2,NM), ..., PARACOLD(8,NM) The value of eight possible parameters depends on the material name
(CMAT).
If CMAT = 'INSULATION' No parameter is necessary because this material does not carry any stress.
If CMAT = ' ELASTIC' PARACOLD(1 ,NM) = E, the Young's modulus. The stress is proportional
to the strain. The material is valid at 20°C.
If CMAT = ' BILIN' PARACOLD(1 ,NM) = E, the Young's modulus. PARACOLD(2,NM) = Any value. PARACOLD(3,NM) = fp, the limit of proportionality. PARACOLD(4,NM) = E', the slope of the strain hardening branch. Bilinear
stress-strain relationship. The material is valid at 20°C.
If CMAT(NM) = 'RAMBOSGOOD' PARACOLD(1 ,NM) = E, the Young's modulus. PARACOLD(2,NM) = Any value. PARACOLD(3,NM) = Ip, the limit of proportionality. PARACOLD(4,NM) = n, exponent of the law. PARACOLD(5,NM) = K, factor of the law.
Ramberg-Osgood Stress-Strain Relationship. The material is valid at 20°C.
For steel materials. PARACOLD(1 ,NM) = E, the Young's modulus. PARACOLD(2,NM) = Any value. PARACOLD(3,NM) = fy, the yield strength.
Those materials behave at elevated temperature according to the Eurocodes.
For the concrete materials. PARACOLD(1 ,NM) = Any value. PARACOLD(2,NM) = Any value. PARACOLD(3,NM) = fc, the compressive strength. PARACOLD(4,NM) = ft, the tension strength.
Those materials behave at elevated temperature according to: The Eurocodes ( CALCONCEC2 and SILCONCEC2 ). The Schneider Model ( CALCONCSCH, SILCONCSCH and
LWCONCSCH).
If CMAT(NM) = 'ELPLANESTR' PARACOLD(1 ,NM) = E, the Young's modulus. PARACOLD(2,NM) = The Poisson's ratio.
Elastic plane stress material law. The material is valid at 20°C.
3.3 Description and Format for Torsional Analysis Files
Section left out if torsion is not to be considered.
3.3.1 The .DAT file for torsional analvsis
SERIES 1 : Comments. One line for each comment. Format <A80> One blank line to mark end of comments Format <A80>
SERIES 2: Number of integration points. One line. Format <A10>,<110> ' NPTTOT', NPTTOT NPTTOT = 1 For torsion.
SERIES 3: Number of nodes. One line. Format <A10>,<15> ' NNODE', NNODE NNODE = Number of nodes of the section.
SERIES 4: Number of axes. One line. Format <A1 0>,<15> ' NDIM', NDlM NDlM = 2 For torsion.
SERIES 5: Dimension of the material laws. One line. Format <A1 0>,<15> 'NDIMMATER', NDIMMATER NDIMMATER = 1 Because a uni-axial mechanical law is used.
SERIES 6: Degrees of freedom. One line. Format <A1 0>,<15> ' NDDLMAX', NDDLMAX NDDLMAX = 1 For torsion calculations
Degrees of freedom at nodes. One line, optional. Format <A10>,<306>,<15> 'EVERY NODE', ' ', NDDL NDDL used for torsional calculations.
Degrees of freedom at specific nodes. One line for each group of nodes with specific degrees of freedom. Format <A1 0>,<15>,<A5>,<15>,<A5>,<15>,<A5>,<15> ' FROM', NNO1, ' TO', NN02, ' STEP', NN03, ' NDDL', NDDL NNOl = First node of this group of nodes. NN02 = Last node of this group of nodes. NN03 = Node step. NDDL = Number of degrees of freedom for this group of nodes, 0 or 1.
/:&:odes NNO? , NNOl iNN03. NNOl+ZxNN03, .... NNO2-2xNNO3, iNN02-NN03, NNCM have NDDL degrees of freedom i
Format cAl0>,<15>,cA5>,<15>,~A5>,cl5>,<A5>,<l5> ' REPEAT', NNOI, ' TO', NN02, ' STEP', NN03, 'TIME', NT NNOl = First node to be repeated. NN02 = Last node to be repeated. NN03 = Increment. NT = Number of times that the nodes have to be repeated.
Note: This command will create the groups: i
NNO14N03 , NNOl+NN03+7 , ... NNO;I+NN03 NN01+2"NN03 , NN01+2'NN03+1 , ... NN02+2"NN03
.... -...
NNOI 4 T N N 0 3 , NNOliNTNN03I1, ... N N 0 2 4 7 N N 0 3
Degrees of freedom series end. One blank line to mark end of series. Format <A80>
SERIES 7: Torsion. One line. Format CAI O> ' TORSION'
SERIES 8: Band w~dth. One line, flrst line of two line serles. Format <A10>,<110> 'LARGEURI l', ILARGEURI 1 ILARGEURI 1 = Max~mum length of K11 in the stiffness matrix K. An initial
estimate must be made according to the experience of the user. SAFlR will say if this value is too small. The length of K11 cannot be larger than ILARGEURI I
Bandwidth. One line, second line of two llne series. Format <A1 0>,<110> ' LARGEURIT, ILARGEUR12 ILARGEUR12 = Maximum length of K12 in the stiffness matrix K. An initial
estimate must be made according to the experience of the user. SAFlR will say if this value IS too small. The number of fixed D.0.F. cannot be larger than ILARGEUR12
SERIES 9: Renumbering strategy. One line, choice of options. Format <A10>,[<15>] ' NORENUM' No renumbering of the equations.
'RENUMPERM' Renumbering of the equations by logical permutations.
'RENUMGEO', NNOI Renumbering of the equations by geometrical method.
' RENUM' = RENUMGEO + RENUMPERM
'READRENUM' Use previous renumbering from .REN file. NNOl = Number of the node where the geometrical renumbering will start.
Relevant only if using RENUMGEO. If NNOI = 0, the renumbering is started successively from all the nodes.
Note: If RENUM or RENUMPERM is used SAFIR stops after the renumbering. A subsequent run has to be made using READRENUM.
SERIES 10: File name. One line, first line of two-line series. Format <A20>, Left justified 'CFILENAME' CFILENAME = Name of the .STR file where the section is described.
File name for torsion data. One line, second line of two-line series. Format <A20>, Left justified 'CFILENAME' CFILENAME = Name of the .TOR file where the warping function is written.
SERIES 11 : Precision. One line. Format <A1 O>,<G10.0> 'PRECISION', PRECISION PRECISION = Small tolerance value reached to have convergence. A
'good value depends on the type of structure that is analyzed. 10" may be used for the first simulation to look at the incremental displacements and if out of balance forces needs a different value.
SERIES 12: Output results. One line, first line of multiple line series. Format <A1 O> 'IMPRESSION'
Output results. One line, second line of multiple line series. Format <A1 0>,cG10.0> ' TIMEPRINT', TlMEPRlNT TlMEPRlNT = Any value.
Output results. One line, third line of multiple line series, Format <A? O> 'PRINTREACT' Write reactions.
Output results last line. One blank line to mark end of series. Format cA80>
3.3.2 The .STR file for torsional analvsis
SERIES 1 : Comments. One line for each comment. Format cA80>
One blank line. to mark end of comments. Format <A80>
SERIES 2: Number of materials. One line. Format CAI 0>,<15> ' NMAT', NMAT NMAT = Number of different materials.
<
Note: /If two materids have. the m e material law but dierent characteristics, it makes two [different materials. e.g. C20 and C25 concrete.
SERIES 3: Number of different elements. One line, first line of five line series. Format <A1 0> ' ELEMENTS'
Number of different elements, solid elements. One line, second line of five line series. Format <A1 0>,<15> ' SOLID', NSOLID NSOLID = Number of SOLID elements in the section.
Number of points for integration. One line, third line of five line serles. Format <A1 0>,<15> ' NG', NGSOLID NGSOLID = Number of points of integration in each direction in the
elements, cannot be less than 1. Greater than 3 is not recommended.
Number of voids. One line, fourth line of five line series. Format <A1 0>,<15> ' NVOID', NVOID NVOID = 0
Last line of series. One blank line, last of five line series. Format <A80>
SERIES 4: The nodes. One line, of multiple line series. Format <A1 O>,[cAl O>] ' NODES',[' CYLINDRIC']
CYLINDRIC' Is added on to ' NODES' if cylindrical coordinates are used. (r,B,Z) and are transformed to (X,Y,Z) for the internal solution process by the formula:
X = r cos(8) Y = r sin(8)
NODES One line added for each node described. Format <A1 0>,<15>,<G10.O>,<G10.0>,<15>
NODE', NNO, RCOORDG(1 ,NNO), RCOORDG(2,NNO), KGENE NNO = Number of the specific node. RCOORDG(1 ,NNO) = First global coordinate of the node NNO. RCOORDG(2,NNO) = Second global coordinate of the node NNO. KGENE =Automatic generation between previously node and node NNO.
KGENE = 0 if no generation, KGENE = 1 if equidistant generation from the last defined node.
Format cA10>,~15>,cG10.O>,cG10.0>,15> ' REPEAT', NNO, DELTAC(I), DELTAC(2), KGENE NNO = Number of nodes to be repeated. DELTAC(1) = lncrement on the first coordinate. DELTAC(2) = lncrement on the 2nd coordinate. KGENE = Number of times that this command has to be repeated.
T 1st coord., y
2nd coo d., z k NDIM = 2
Figure 6: Coordinate order
,Note: The first coordinate corresponds to the local y axis and the second coordinate 'corresponds to the local z axis of the beam element.
SERIES 5: Torsional centre. One line, first line of two line series. Format ~Al0~,<5b>,cG10.O>,~G10.0>
NODELINE', Yo, Zo Yo = First global coordinates of the node line which joins the beam
elements. Zo = Second global coordinate of the node line.
Torsional centre. One line, second line of two line series. Format <A1 0>,<5b>,<GI O.O>,<Gl 0.0> ' YC ZC', Yc, zc Yc = First global coordinate of the centre of torsion. Zc = Second global coordinate of the centre of torsion.
SERIES 6: Supports and imposed displacements. One line, first line of possible multiple line series. Format <A1 0> ' FIXATIONS'
Supports and imposed displacements. One llne added for every node where no solution is to be calculated. Format cAI0>,<15>,<5b>,<Al O> ' BLOCK', NNO, ' ', ' FO' NNO = Node number where no solution is calculated (for example, lines of
symmetry).
Supports and imposed displacements slave nodes. One line added for each slave node described. Format <A10>,<15>,~15>,<A10~ ' SAME', NNOI , NN02, CTRAV(1) NNOI = Number of the slave node. NN02 = Number of the master node. CTRAV(1) = ' YES'
Supports and imposed displacements repeated slave nodes. One line for repeating previous slave node. Format cA10>,<15>,<15>,<A10> ' REPEAT', NUMBER, INC, CTRAV(1) NUMBER = Number of times that the preceding SAME command must be
repeated. INCR = Increment on NNOI and NN02. CTRAV(1) = ' YES'
Last line of series. One blank line to mark end of series. Format <Ago>
SERIES 7: SOLID elements. One line, first line of possible multiple line series. Format <A1 O> 'NODOFSOLID'
Solid element list. One line added for each solid element. Format <A10>,<6*15>,<G10.0>,<15> ' ELEM', NE, NODE(I,NE), ..., NODE(4,NE), MAT, EPSRSOLID,
KGENE NSOL = Number of this element. NODE(1 ,NE) = First node of this element. NODE(2,NE) = Second node of this element.
... NODE(4,NE) = Last node of this element. MAT = Material of this element. EPSRSOLID = Residual stress in this element. KGENE =Allows the generation from the previously defined element up to
this one. KGENE gives the increment on the nodes number.
Format <A10>,~6*15>,<G10.0>,~15> ' REPEAT', NER, INC, NODE(2,NE), ..., NODE(4,NE), MAT, EPSRSOLID,
KGENE NER = Number of elements to repeat. INC = Increment on the node number. NODE(2,NE) = Any value ( can be 0 ). NODE(4,NE) = Any value ( can be 0 ). MAT = Any value ( can be 0 ). EPSRSOLID = Residual stress in this element. KGENE = Number of times that this command has to be repeated. The
element numbers increase by 1.
For triangular elements, NODE(4,NE) = 0.
1 Note: 1 The following group of lines on symmetry is necessary if symmetry is accounted for. If ,not, only the ENDSYM line is present. t
1
Solid elements symmetry. One line. Format <A1 0> ' SYMMETRY'
Solid element axis of symmetry. One line for each axis, a maximum of six axes can be specified. Format <A1 0>,<15>,<15>
REALSYM', N1, N2 N1 = First node on axis. N2 = Second node on axis.
Solid elements axis of symmetry, symmetric about y axis. One optional line. Format <A1 O>
YSYM'
Solid elements last line. One line to mark end of series and symmetry. Format <A1 O> ' ENDSYM'
SERIES 8: Material description. One line, first line of possible multiple line series. Format <A1 O> ' MATERIALS'
Material description line pair added for each different material used. One line, first line of two line pair. Format <A1 Oz CMAT CMAT = Name of the material.
Valid matw-al names are: ' ELASTIC', ' BILIN', ' STEELEC3'. ' STEELEW or ' PSTEELAI 6',
' 'CALCONCEW, 'SILCONCEW, 'CALCONCSCH', 'SILCONCSCH', ' LWCONCSCH'
Material description properties. One line, second line of two line pair. Format <GIO.O>,<GI O.O>,cGI 0.02
The value of the following three parameters depends on the material name introduced in CMAT
If CMAT(NM) = ELASTIC, BILIN, or for STEEL type materials. PARACOLD(I ,NM) = young's modulus. PARACOLD(2,NM) = Poisson's ratio.
For the CONCRETE type materials PARACOLD(1 ,NM) = Nothing. PARACOLD(2,NM) = Poisson's ratio. PARACOLD(3,NM) = Compressive strength fc.
The Young's modulus for concrete materials is calculated according to the formula:
4.0 ELEMENT THEORY AND FORMULATIONS
4.1 The TRUSS Element
4.1 .I Geometry
The truss element is straight with two end nodes. The geometry is defined by the position of these end nodes. The truss element is completely defined by its cross sectional area and the material type. Only one material, one temperature and one strain is present in each element.
Figure 7: Truss element - Degrees of freedom at nodes
4.1.2 Intearation on the volume
All integrations are made analytically. Hence, no points of integration are given in the program for truss elements.
The strain is uniform in the element and calculated according to:
where L is the deformed length of the element, and Lo is the un-deformed length of the element.
4.7.4 Nodal forces
In the co-rotational configuration, the two longitudinal forces are calculated according to:
where A is the cross sectional area, and s is the stress.
4.1.5 Stiffness matrix
With the nodal displacements ordered as:
pT=)ul vi W1 U2 V2 w2(
the stiffness matrix has the form:
where
L SYM
and
I SYM I O /
with E, defined by the material model:
4.2 The BEAM Element
The beam element is straight in its un-deformed geometry. Its position in space is defined by the position of three nodes: the two end nodes (NI-N2), and a third node (N4) defin~ng the position of the local y axis of the beam. The node N3 is used to support an addit~onal degrees of freedom.
Px N1 (.--+- x
z 6
(b) nodes N1 ,N2
-J?+-x
(a) node N3 (c)
Figure 8: Beam element: (a) Local axes (b) Degrees of freedom at nodes (c) Cross section
To describe the geometry of the cross section, the fibre model is used. The cross section of the beam is subdivided into small fibres (triangles, quadrilaterals or both). The material behaviour of each fibre is calculated at the centre of the fibre and it is constant for the whole fibre. Each fibre has it's own material, this allows for the building of composite sections made of different materials.
Assumptions for beam elements: the Bernoulli Hypothesis is considered, i.e., the cross section remains plane under bending moment plastifications are only considered in the longitudinal direction of the member, that is uni-axial constitutive models non-uniform torsion is considered
4.3 The SHELL Element
The Constant Strain Triangle is used as a base for the formulation of the membrane part of this element'.
4.3.1 Geometry
The shell element is triangular. Its geometry is defined by the position of the three nodes at the angles. Three other nodes are also present at the middle of each edge. The local system of coordinates is located at node 1. The local y axis is on 1-3. The local 2 axis is on ?A 1 - 2 . The local 2 axis is given by ? A 2 .
ZP N2 :qy N1 N4
4 A
1 X
(a) (b) nodes N1 ,N2,N3 N4,N5,N6
Figure 9: Shell element: (a) Local axes (b) Degrees of freedom at nodes
4.3.2 Points of intearation
The position of the points of integration on the surface are given in parametric coordinates by the figure following:
I NGAREA= 1 NGAREA = 2 NGAREA=3 I
Figure 10: Points of integration
The positions of the points of integration are in the parametric system of coordinates:
NGAREA = I point 1 { = 113 q =I13
NGAREA = 2 point 1 5 = 116 q =I16 point 2 5 = 416 q =?I6 point 3 5 = 116 q = 416
NGAREA = 3 point 1 5 = 113 q = 113 point 2 5=1/5 q = 115 point 3 5 = 315 q = 115 point 4 5 = 115 q = 315
Where NGAREA is the command whose parameter in the .STR file, NGSHELLAREA (see section 3) is the number of integration points in each direction of the surface of the elements.
Different layers of rebars can be present in the element. The rebar layers are horizontal (i.e. parallel to the local x, y plane). The rebars are uniformly distributed (layered rebars). Each layer is parallel to one of the global axes of the structure X, Y or Z and is defined by:
it's local vert~cal coordinate z in the element; it's cross section per unit length of width (m2/m for example); it's material number; and the global axis to which it is parallel.
Assumptions for rebar elements are: the cross section of the rebar is not subtracted from the plane section of the element, that is, a reinforced concrete slab steel and concrete are supposed to be simultaneously present at the location of the bars; the bars resist only axial direction actions, that is, a mesh of perpendicular rebars does not resist shear by itself.
The figure below is made for an element, which is located in the global X, Y plane, and a rebar layer which is parallel to the global X axis:
-
Figure 11: Rebar element
The angle 9 between the rebars and the local x axis is calculated in the un-deformed configuration by the following procedure:
1. Transform the local vector x of the element (i.e. 12) in the global system of coordinates xglob, xglob = R' x with RT being the rotation matrix of the element.
2. 0 = arcsin ( IlaxisAxglobll/ llaxisll IIxglobll ) with axis(? ,0,0) if the bars are parallel to X
(0,1,0) if the bars are parallel to Y (0,0,1) if the bars are parallel to Z
4.4 The SOLID Element
4.4.1 Internal voids
For thermal calculations in 2-D situations, the structure can have internal voids filled with air, as in hollow core concrete slabs, or H-steel sections encased in a box of thermally insulating material.
Each void is surrounded by NFR frontier elements. As far as linear elements are concerned, each element Ex has the two nodes: Ni and Ni,. Each Ni node belongs to two elements : Ej., and Ei.
Figure 12: Void frontier
Convection and radiation are treated separately.
4.4.2 Convection
The hypothesis is that the specific heat of the air is so small that it is neglected. Then, at any time, the fictitious temperature of the air in the void is uniform, determined by the convective fluxes received from all the elements:
with q, : convective heat flux [W/m2] L : length of the frontier surrounding the void [m]
With the FE formulation, we have a linear convective flux:
or, in the particular case of linear elements,
NFR LEi
~,JLE, (T, - TN, + T, - T N + ~ ) = o [Wim], i=l
where n: nip: h": w*: hE,: T,.: T,: LE,: TN,:
point of integration number of integration points on the frontier of an element value of the shape function at point n weight at point n convection factor of the material in element E, fictitious temperature of the air in the void temperature at point i length of the frontier of the element E, temperature at node I
The last equation can be written as:
NFR NFR LEi
NFR
T, x LE, hEi = x h ~ ; (TN, + TN,_~) = TN, LN, [W/m], i=l i=l i=l
hE,-, LEi-l + hEi LEi where w, = 2
[WImK].
It comes:
NFR NFR
TN, LN, xmi m i T, = i=l - - i=l
NFR NFR IKl. x LE, h ~ , m i i=l i=l
The convective heat flux at each node is then given by:
The derivative of the flux, used in the iteration matrix, is given by:
LN, LNj gNi,j = LNi xT,, j = Nm [W/mq.
c. LNr
This matrix is symmetric. This contribution (Equation 9) to the matrix of iteration has not been programmed in SAFlR because it would dramatically increase the bandwidth of the problem. It is perfectly possible to reach the correct equilibrium state, provided Equation 8 is correctly considered, even with an approximate matrix of iteration.
4.4.3 Radiation
The physical phenomena on each frontier element are radiat~on, illumination and net heat flux going out of the surface. They are defined by the following equations:
R, = E I O ~ ; ~ + ~ E H , = E I ~ < + ( ~ - E Z ) H ~ [W/m2]
4.5 Convergence Criteria
Fint Internal forces. Those forces are calculated at the nodes as the result of the internal forces coming from the elements: axial forces, bending forces
du'" incremental displacement at time step i and iteration j NDOF Number of Degrees Of Freedom of the structure NE Norm of the Energy, calculated at each iteration NET Norm of the Total Energy, calculated as the summation of all the previous
N E PRECISION a number, chosen by the user, supposed to be small
At the beginning of the program:
NET = 0
At each iteration of each time step:
NET = NET + NE I F ( j 5 l )THEN CRITER = 1 ELSE IF(NET=O)THEN CRITER = 0 ELSE CRITER = NE / NET ENDlF ENDlF IF ( CRITER < PRECISION ) then convergence has been obtained ELSE convergence has not been obtained ENDlF
Note that NE is neither exactly the energy nor the norm of the energy. It has the d~mension of an energy because forces multiply displacements. This has the advantage of giving equal importance to displacement-force type variables and to moment-rotat~on type variables. The relative importance of these two groups of variables 1s also not dependent on the unit, which has been chosen for length, (metre or mrn, for example) or for force (Newton or KiloNewton, for example). It IS not exactly the energy because a force associated to a negative displacement should be counted as a negative energy, whereas it is counted as positive in Equation 10. Each component of Equation 10 is counted as positive because, if not, the negative components would tend to reduce the energy NE, and if by chance the sum of the negative components is exactly equal to the sum of the positive components, this would give NE = 0, whereas the iteration under consideration has produced a lot of incremental movements. Even if all displacements and forces are positive, NET is not exactly the energy, as can be seen on the next figure, drawn for a system w~th 1 D.o.F., a load applied in two time steps under constant temperature TO, and then the temperature chang~ng from TO to T I in one time step.
1 Force
time step 2
NET
Displacement
Figure 13: Convergence iterations
4.6 Storage of Stiffness Matrix
The stiffness matrix is supposed to be symmetric. Only the upper part is stored.
The matrix K is divided in 3 parts K11, K12=K21 and K22
lndex 1 is related to the undefined D.o.F., where the solution has to be calculated. lndex 2 is related to the fixed D.o.F., where the solution is prescribed. Many of the K11 elements have the value 0, it IS stored by the skyline technique. Matrix K11 is stored in the REAL vector RIGE.
An INTEGER vector, NSTSKY is associated to the vector RIGE to retrieve the position of K l I (i,j) in RIGE. NSTKY(j) is the position of K l l(j,j) in RIGE. The retrieving function is IFCTSKY(iJ,NSTSKY). It calculates the position of K l l(i,j) in RIGE: IFCTSKY(i J,NSTSKY) = NSTSKY(j)+i-j with I j
Example:
If matrix K11 has the following non 0 elements, they are stored in RIG€ in the order 1, 2, 3.
For example: K11(3,4) is stored in RIGE(IFCTSKY(3,4,NSTSKY) = RIGE(NSTSKY(4)+3-4) = RIGE(9+3-4) = RIGE(8)
NUACTIFS is the dimension of K11 and NSTSKY ILARGEURI 1 is the dimension of RIGE
The K12 part is stored in rK12, although it is stored in the manner of K21 K12(i,j) is stored in rK126-NUACTIFS,i) with i.1e.j
NOMENCLATURE
Young's modulus Limit of proportionality Exponent of the law Factor of the law Stress Yield strength of steel Compressive strength of concrete tensile strength of concrete Strain Stress
REFERENCES
1 Franssen, J.M. "hude du Comportement au Feu des Structures Mixtes Ac~er- beton". These de Doctorat en Sciences Appliquees, No. 11 1, Universite de Liege, Belgium, 1987.
2 Schleich, J.B. "REFAO-CAFIR: Computer Assisted Analysis of the Fire Resistance of Steel and Composite Concrete-steel Structures". CEC Research 721 0-SN502, Final Report EUR 10828 EN, Luxembourg, 1987.
3 Schneider, U. "Behaviour of Concrete at High Temperatures". Rilem-Committee, 44-PHT, 1983.
4 Franssen, J.M. "Contributions Modelisation lncendies BCitiments leurs Effets Structures", Universite de Liege, Belgium, 1998.
