General Explanations for the Use of MAXIMA - Action Combinations in order to get Design Forces or Load Case Combinations#

Introduction#

This document provides some explanations for the use of the program MAXIMA.

Theoretical Background#

In the several design codes different action combinations are given for the ultimate limate states as well as the serviceabiltiy limit states. For the European countries the several action combinations are defined in the EN 1990 and their corresponding National Annexes, for Switzerland in the SIA 260 and for Russia in SP 20.13330. These design codes superimpose the actions according to the partial factor method.

The task of the structural engineer is to assign the individual different loads (e.g. dead load, variable loads, accidental and seismic loads) to the actions and to perform superpositions to determine the appropriate load case combinations with their results.

The superpositions are done with the internal forces and moments, support reactions, displacements aso. of the individual initial loads.

This procedure is absolutely necessary because different load case combinations result for different superimposed values at different points in the structure. E.g. for a two-span girder the decisive result load case combinations are different for the bending moment and the shear force. In addition, the resultant load case combinations for the bending moment depends on the position in the girder. For the sagging moment in the spans result another load case combination than for the hogging moment in the middle support.

The two-span girder has load case 1 as permanent load and two span-wise variable loads in load case 2 and 3:

The bending moments My are:

The decisive load case combination for the maximum My in span 1 is:

factor ∙ LC 1 + factor ∙ LC 2

On the other hand the minimum My for the middle support results as follows:

factor ∙ LC 1 + factor ∙ LC 2 + factor ∙ LC 3

EN 1990 and its National Annexes#

For the fundamental combination for the ultimate limit state the EN 1990 gives several possibilities:

Use of the equation 6.10
Or use of the equations 6.10a and 6.10b.

Additionally, the equations 6.10a and 6.10b are different in the several National Annexes due to the defined use of the reduction factor Xsi and the reliability (consequences class) factor Kfi.

For the accidental combination, the EN 1990 gives also two possibilities dependent on the corresponding accidental action (impact or fire).

SIA 260#

The Swiss code defines a fundamental action combination for the ultimate limit state, however, only similar to equation 6.10 of the EN 1990.

SP 20.13330#

The Russian definition is very complex for the general case. A detailed description with an example file can be found in the tutorial: Superposition according to Russian SP 20.13330.2016: Loads and Actions

Other Codes#

Other design codes, e.g. ACI 318 (American Concrete Institute) or BS 8110 (British Standard), define several combinations with different fixed defined unfavourable factors for the used actions.

All codes have in common that there is a corresponding general specification of action combinations. The task of the engineer is now to apply these general specifications for his project and to determine the appropriate internal forces or load case combinations for the corresponding design task.

Basics of the Program MAXIMA#

Using the program MAXIMA, SOFiSTiK offers various options for determining automatically or manually the design internal forces or load case combinations.

Requirements#

The actions have to be defined with the program SOFiLOAD record ACT or with the SSD task Action Manager. For each design code SOFiSTiK offers default actions with all necessary information which can be select in SOFiLOAD only with their designation or in the task Action Manager. Of course, user-specific actions can also be defined. There have to be initial load cases with loads and their assignment to an action. These load cases should be calculated and results have to be available in the database.

The procedure in the program MAXIMA can be divided into two parts:

1st Part: Definition of the Action Combinations#

This part depends on the design code which was defined by the user in program AQUA record NORM or in the task System Information. Here the appropriate design code for the specific design task of the structural system should be defined. The default actions and action combinations are then according to the associated code or definitions for the basics of structural design.

The default actions combinations are only valid for the use of default actions. In the case of manually defined actions, the action combinations have to be checked and adapted by the user.

Important

Please note that default action combinations for the selected design code are only available for buildings and not for bridges. The SOFiSTiK workflow for the more complex action combinations for bridges is done with the program CSM - Construction Stage Manager or the CSM task in the SSD. This is not a part of this tutorial.

Necessary definitions:

Definition of the combination rule for actions - MAXIMA record COMB or task Combination Rules for Actions
Assignment of the used actions - MAXIMA records ADD and ADA (or ACT) in dependence on the selected combination rule

The corresponding initial load cases are assigned automatically to the actions by the program MAXIMA.

2nd Part: Definition of the Superposition Values#

This part is independent on any design codes and only dependent on the structure. Here it is defined what is to be superimposed.

The program MAXIMA superimposes the results of the calculation of initial load cases. These can be the following values:

Internal forces and moments
Support and boundary forces
Displacements and rotations
Bedding values
Spring values
Storey results for seismic design

These possibilities correspond to the program MAXIMA record SUPP or the SSD task Superpositions for Combination Rules.

For special cases it is also possible to define objective functions for the superpositions. Here preset objective functions can be selected or they can be defined manually as formula by the user. Preset objective functions are:

Normal and shear stresses in specific points of the cross sections for beams or design elements
Equivalent stress (Von Mises) for QUAD elements

Here the superposition is done according the objective function, however, only the corresponding internal forces are saved.

Internal Process in Program MAXIMA#

Please note that the program MAXIMA calculates for each single superposition value at all positions of the structure the leading variable action and the accompanying variable actions with their relevant load cases. This means that, depending on the system and the loads, there are many resultant load case combinations with their relevant result.

Important

In the database only the results of the superpositions are stored in order to use for the corresponding design task.

The resultant load case combinations are not stored in the database. It is possible to automatically determine load case combinations only for girder systems or columns in the SSD tasks Combine Loads or Combine Results with the Button ‘Automatic’. This automatic determination is done internally with the MAXIMA Engine. The resultant load case combinations of the task Combine Loads can be used for non-linear calculations of girder systems or columns. A detailed description of this internal process is available in the tutorial: Determination of Decisive Load Case Combinations with Superposition of Normal Stresses in Cross Section Points

Possibilities for the Printout to Check the Results#

The preset printout information and tables are:

Number, title, equation of the action combination and type of the resultant load cases as necessary information for the design task
Tables of the combinations including the corresponding initial load cases
Table of the resultant load cases numbers and titles

There are also various output options for checking individual results on a random basis -> MAXIMA manual record ECHO or in the SSD task Superpositions for Combination Rules

Hint

It is recommended to request the detailed printout only for individual values for specific elements (nodes, beam etc.). A full printout for everything may generate thousands of pages, needs a lot of time and is cancelled by MAXIMA from a certain size with a warning.

The following small examples show these possibilities for input definitions and printout.

Another option to check the results is the Tracer - MAXIMA record TRAC. Here the resultant load case combination with the determined factor can be printout for a specific superosition value at a specific position in the structure.

Examples#

Principle Workflow of all Examples#

Generate the system inclusive the design code, materials, cross sections
Generate the actions with the task Action Manager or with the program SOFiLOAD
Generate loads with the program SOFiLOAD
Run linear analysis
Generate action combinations in program MAXIMA (or in SSD task Combination Rules for Actions)
Generate superpositions (or SSD task Superpositions for Combination Rules)
Generate decisive load case combinations using SSD task Combine Loads (or task Combine Results) with button Automatic

Basic Definitions of all Examples#

The following four examples have the same system (or in the case of the example US ACI318-19 similar system due to the units): a two-span girder

A simple rectangular concrete beam is defined as cross section. The picture shows the cross section with the reinforcement layers and the default stress points Z+ and Z- which are used later for the superposition of the normal forces in beam sections.

The system is loaded with the dead load, an additional dead load for both spans, a variable load on the first span and a snow load on the second span:

Dead load G (or D for US ACI318-19) with load cases 1 and 2
Variable load for offices Q_B (or L for US ACI318-19) with load case 3
Snow load S with load case 4

The possibilities of MAXIMA are explained below using the four examples with following design codes:

DIN EN 199x-200x: National Annexes of the DIN EN 1992-1-1/NA, DIN EN1993-1-1/NA, DIN EN1994-1-1/NA for Germany including the information of the National Annex of the DIN EN 1990/NA with equation 6.10
SS EN 199x-200x: National Annexes (EKS 12:2022) of the SS EN 1992-1-1/NA, SS EN1993-1-1/NA, SS EN1994-1-1/NA for Sweden including the information of the National Annex of the SS EN 1990/NA with equation 6.10a and 6.10b
SIA 26x: Swiss Codes SIA 262, SIA 263, SIA 264 including the information of SIA 260
US ACI318-19: American Concrete Institute (2019)

Since the generation of the action combinations is extensive, only the possibilities and results for the action combinations of the ultimate limit state is explained here. As a default, the action combinations of the serviceability limit state are of course also available and included in the data files.

There are two data sets for each example: an DAT file with MAXIMA definitions and the same information as an SSD file with the graphical definitions.

First Example according to DIN EN199x-200x#

Files: din_en1992-2004_girder.dat and ssd2026-din_en1992-2004_girder.sofistik

After the definition of the material, the cross section and the system generation the actions and the loads are input.

Hint

For the default actions it is only necessary to input the action name. All other information about the default actions are generated automatically.

+PROG SOFILOAD
HEAD Actions
ECHO ACT
ACT  'G'   TITL "dead load"                        ! default action G
ACT  'Q_B' TITL "Pay load offices cat. B"          ! default action Q category B offices
ACT  'S'   TITL "snow loading"                     ! default action S
END

+PROG SOFILOAD
HEAD Loads
ECHO ACT FULL   ! table of the actions with associated load cases
LC   1 'G' 1 FACD 1 TITL "dead load"

LC   2 'G' 1 TITL "add dead load"
LINE SLN '1' WIDE 0 TYPE PG P1 15 0 0 0 P2 15 10 0 0
LINE SLN '2' WIDE 0 TYPE PG P1 20 10 0 0 P2 20 20 0 0

LC   3 'Q_B' 1 TITL "variable load"
LINE SLN '1' WIDE 0 TYPE PG P1 25 0 0 0 P2 25 10 0 0

LC   4 'S' 1 TITL "snow load"
LINE SLN '2' WIDE 0 TYPE PG P1 10 10 0 0 P2 10 20 0 0
END

The input of the actions in the SSD task Action Manager is:

In context with the input of the loads it is possible to set ECHO ACT FULL for the printout table of the used actions and the corresponding load cases:

../../_images/din_en-ssd-actions-out.png

After the calculation of the initial load cases the superpositions are done in order to get the necessary design values (e.g. internal forces and moments, support reactions etc.).

In the first MAXIMA the default action combinations and their default superposition values are calculated. In order to get these defaults only the following simple MAXIMA should run:

+PROG MAXIMA
HEAD Default action combinations
CTRL COMB YES      ! generates the default combination rules
CTRL SUPP YES      ! generates the default associated superpositions
ECHO TABS YES
ECHO LC   YES
END

Or in the SSD the default action combinations are shown in the task Combination Rules for Actions and the superposition values are shown in the task Superpositions for Combination Rules - default superpositions:

../../_images/din_en-ssd-comb-default.png

../../_images/din_en-ssd-supp-default.png

Please note that all for a 3D system possible superposition values are preset. For this small system e.g. for the beam forces only Vz and My are interesting.

Hint

If you want to get the MAXIMA (CADINP) input of the default action combinations, you can use the export from CDB to MAXIMA inside TEDDY or SSD (Button Database Tools -> Export to DAT).

The printout contains the general information about the action combinations and the table of the generated resultant load cases:

The National Annex Germany of the EN 1990 demands the equation 6.10 for the action combination of the ultimate limit state. This corresponds to following MAXIMA input (DAT file second MAXIMA or SSD combination 2 or 103):

COMB NO 2 EXTR EXPL BASE 4100 TYPE DESI TITL "ULS fundamental combination"
ADD TYPE G     FACU GAMU  FACF GAMF                      ! permanent action G
ADD TYPE {Q1}  FACU GAMU  FACF 0                         ! leading action
  ADA Q_B,S
ADD TYPE {QI}  FACU PSIU  FACF 0                         ! accompanying action
  ADA Q_B,S

Or in the SSD example:

It follows the definition of the superposition values, here only the bending moment My, the shear forces Vz and the support reaction Pz.

In the second part a superposition for the normal forces should be done in the cross section points Z+ or Z- (see also screenshot of the cross section above) for beam end no. 10005 (middle of the first span) or for beam end no. 10010 (middle support). OPT S means, that only for these points the values are calculated. If OPT S is not input, the superposition is done for all beam sections and the input of the beam number at FROM and beam position at X is only valid for the selected ECHO option ECHO LOAD,FACT - full printout. OPT S is not available in the SSD task Superpositions for Combination Rules.

!*!Label Superpositions
ECHO LOAD,FACT
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE VZ,MY FROM 10010 X 1[-] TITL "Forces and moments"
ECHO LOAD,FACT NO
SUPP COMB 2 EXTR MAMI ETYP NODE TYPE PZ TITL "Support reactions"

!*!Label Superposition Normal Stress in Cross Section Point Z+
ECHO LOAD,FACT
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE SIG SELE Z+  FROM 10005 X 1[-] OPT S    ! printout: end of beam no. 10005
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE SIG SELE Z-  FROM 10010 X 1[-] OPT S    ! printout: end of beam no. 10010

Or in the SSD example 2nd task Superpositions for Combination Rules:

Finally, the full printout will be explained for the minimum bending moment My at middle support for the combination 2:

../../_images/din_en-output-comb2-min-my.png

The first table shows the values of the initial load cases. In the second table ‘Determination of Sums and Leading Variable Action’ the calculated sums and the possible resultant factors are printed. Here the decision for the leading or accompanying action is shown with a * at the corresponding sum value:

Leading action is Q_B: Act Q_B: SumQ1 = -233.2999* SumQI = -163.3100
Accompanying action is S: Act S: SumQ1 = -93.3200 SumQI = -46.6600*

Hint

Please note that the leading action is that with the largest difference between the two sums.

It follows the table of the determined load case combination with the determined factors for minimum MY. At least the resultant beam forces min MY = -708.3 kNm is shown in the table ‘Relevant Forces in Beam Elements’

In the SSD file the task Combine Loads is included. Here the resultant load case combinations for the ultimate limit state are determined automatically via the button ‘Automatic’. A click on ‘Automatic’ opens a subdialog. For the determination of the load case combinations action combinations which are stored in the database should be selected. During the calculation the program MAXIMA runs internally and then the found load case combinations are shown in the dialog for further processing.

A detailed description of this internal process is available in the tutorial: Determination of Decisive Load Case Combinations with Superposition of Normal Stresses in Cross Section Points

Second Example according to SS EN1992-2004 with the Particularities of the Equations 6.10a and 6.10b#

Files: ss_en1992-2004-cat-A2_girder.dat and ssd2026-ss_en1992-2004-cat-A2_girder.sofistik

The selected building class for the design code is CAT A2 or in the SSD for buildings ‘Konstruktion og säkerhetsklass: A2 (Byggnader klass 2)’. Due to this definition the actions values and action combinations are generated automatically. The Swedish National Annex of the EN 1990 (EKS 12:2022) prescribes the use of the equations 6.10a and 6.10b for the fundamental combinations of the ultimate limit state. Here the reduction factor Xsi is given with 0.89 and the reliability (consequences class) factor Kfi called in this National Annex as Gamma-d with 0.91 for the safety class 2.

Literature: Boverket mandatory provisions amending the board’s mandatory provisions and general recommendations (2011:10) on the application of European design standards (Eurocodes) , EKS (BFS 2022:4 EKS 12)

../../_images/ss_en-eks12-comb-table.png

After the definition of the material, the cross section and the system generation the actions and the loads are input in program SOFiLOAD. These input definitions are analogous to the first example according to DIN EN1992-2004.

In the input of the actions in the SSD task Action Manager and also in the printout table these two factors reduction factor Xsi and the reliability factor Kfi are shown:

In context with the input of the loads it is possible to set ECHO ACT FULL for the printout table of the used actions and the corresponding load cases:

Hint

The reduction factor Xsi and the reliability factor Kfi are boxed values and stored in the database. They can be modified in the program AQUA record TVAR or in the SSD task System Information subdialog boxed values.

After the calculation of the initial load cases the superpositions the default action combinations and superpositions are used in the first MAXIMA run as described in the first example.

In the SSD the default action combinations are shown in the task Combination Rules of Actions and the superposition values are shown in the task Superpositions for Combination Rules - default superpositions:

../../_images/ss_en-ssd-comb-default.png

../../_images/ss_en-ssd-supp-default.png

Please note that all for a 3D system possible superposition values are preset. For this small system e.g. for the beam forces only Vz and My are interesting.

Hint

If you want to get the MAXIMA (CADINP) input of the default action combinations, you can use the export from CDB to MAXIMA inside TEDDY or SSD (Button Database Tools -> Export to DAT).

The printout contains the general information about the action combinations and the table of the generated resultant load cases:

The National Annex Sweden of the EN 1990 demands the equation 6.10a and 6.10b for the action combinations of the ultimate limit state. The input definitions for these action combinations are shown in the following MAXIMA input (DAT file second MAXIMA or SSD combination 2 and 3 or 103 and 104): The input ADD TYPE {Q1} demands the determination of the leading action and the input ADD TYPE {QI} the accompanying actions. The factors and factor combinations which should be used for the unfavourable and favourable factors are defined with literals. The literals are described in the MAXIMA manual chapter 3.6 ADD – Actions for an Explicit Defined Action Combination.

!*!Label Action Combinations
COMB NO 2 EXTR EXPL BASE 4100 TYPE DESI TITL "equation 6.10a"
  ADD TYPE G  FACU KFG  FACF GAMF

COMB NO 3 EXTR EXPL BASE 4200 TYPE DESI TITL "equation 6.10b"
  ADD TYPE G     FACU XKGU  FACF GAMF                      ! leading action
    ADA Q_B,S
  ADD TYPE {QI}  FACU KFG0  FACF 0                         ! accompanying action
    ADA Q_B,S

Or in the SSD example combination 3 manually defined:

It follows the definition of the superposition values, here only the bending moment My, the shear forces Vz and the support reaction Pz.

!*!Label Superpositions
ECHO LOAD,FACT NO
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE VZ,MY TITL "Forces and moments"
SUPP COMB 2 EXTR MAMI ETYP NODE TYPE PZ TITL "Support reactions"
ECHO LOAD,FACT
SUPP COMB 3 EXTR MAMI ETYP BEAM TYPE VZ,MY FROM 10010 X 1[-] TITL " Forces in Beam Elements"
ECHO LOAD,FACT NO
SUPP COMB 3 EXTR MAMI ETYP NODE TYPE PZ TITL "Support reactions"

!*!Label Superposition Normal Stress in Cross Section Point Z+
ECHO LOAD,FACT
SUPP COMB 3 EXTR MAMI ETYP BEAM TYPE SIG SELE Z+  FROM 10005 X 1[-] OPT S    ! printout: end of beam no. 10005
SUPP COMB 3 EXTR MAMI ETYP BEAM TYPE SIG SELE Z-  FROM 10010 X 1[-] OPT S    ! printout: end of beam no. 10010

Or in the SSD example 2nd task Superpositions for Combination Rules:

Finally, the full printout will be explained for the minimum bending moment My at middle support for the combination 3:

../../_images/ss_en-output-comb3-min-my.png

Leading action is Q_B: Act Q_B: SumQ1 = -212.3029* SumQI = -148.6121
Accompanying action is S: Act S: SumQ1 = -84.9212 SumQI = -50.9527*

Hint

Please note that the leading action is that with the largest difference between the two sums.

It follows the table of the determined load case combination with the determined factors for minimum MY. At least the resultant beam forces min MY = -610.2 kNm is shown in the table ‘Relevant Forces in Beam Elements’

As in the first example in the SSD file the task Combine Loads is included. Here the resultant load case combinations for the ultimate limit state are determined automatically via the button ‘Automatic’. A click on ‘Automatic’ opens a subdialog. For the determination of the load case combinations action combinations which are stored in the database should be selected. During the calculation the program MAXIMA runs internally and then the found load case combinations are shown in the dialog for further processing.

Third Example according to SIA 262 with the Particularities of SIA 260#

Files: sia262_girder.dat and ssd2026-sia262_girder.sofistik

The Swiss code SIA 260 contains following particularity: The combination coefficients of the action snow are determined using formulas depending on the height over sea level according to table 2. In order to get the default combination coefficients for snow it is necessary to input the height over sea lever at the definition of the design code:

Program AQUA record NORM with literal ALT

NORM 'SIA' '26X' ALT 555.[m] UNIT 0     ! ALT 555.[m] height over sea level

SSD task ‘System Information’ subdialog ‘Location’

After the definition of the material, the cross section and the system generation the actions and the loads are input in program SOFiLOAD. These input definitions are the analogous to the first example according to DIN EN199X-200X.

In the input of the actions in the SSD task Action Manager and also in the printout table ‘Actions’ the combination coefficients for snow which were calculated by the program SOFiLOAD are shown:

In context with the input of the loads it is possible to set ECHO ACT FULL for the printout table of the used actions and the corresponding load cases:

After the calculation of the initial load cases the superpositions the default action combinations and superpositions are used in the first MAXIMA run as described in the first example.

In the SSD the default action combinations are shown in the task Combination Rules for Actions and the superposition values are shown in the task Superpositions for Combination Rules - default superpositions:

Please note that all for a 3D system possible superposition values are preset. For this small system e.g. for the beam forces only Vz and My are interesting.

Hint

If you want to get the MAXIMA (CADINP) input of the default action combinations, you can use the export from CDB to MAXIMA inside TEDDY or SSD (Button Database Tools -> Export to DAT).

The printout contains the general information about the action combinations and the table of the generated resultant load cases:

The SIA 260 demands the equation 16 for the action combination of the ultimate limit state. Here this equation has to be defined with COMB EXTR EXPL. This corresponds to following MAXIMA input (DAT file second MAXIMA or SSD combination 2 or 103):

!*!Label Action Combinations
COMB NO 2 EXTR EXPL BASE 4100 TYPE DESI TITL "ULS fundamental combination"
  ADD TYPE G       FACU GAMU FACF GAMF           ! action G
  ADD TYPE {Q1}    FACU GAMU FACF 0              ! leading action
    ADA Q_B,S
  ADD TYPE {QI}    FACU PSI0 FACF 0              ! accompanying actions
    ADA Q_B,S

Or in the SSD example combination 2 manually defined:

It follows the definition of the superposition values, here only the bending moment My, the shear forces Vz and the support reaction Pz.

!*!Label Superpositions
ECHO LOAD,FACT
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE VZ,MY FROM 10010 X 1[-] TITL "Forces and moments"
ECHO LOAD,FACT NO
SUPP COMB 2 EXTR MAMI ETYP NODE TYPE PZ TITL "Support reactions"

!*!Label Superposition Normal Stress in Cross Section Point Z+
ECHO LOAD,FACT
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE SIG SELE Z+  FROM 10005 X 1[-] OPT S    ! printout: end of beam no. 10005
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE SIG SELE Z-  FROM 10010 X 1[-] OPT S    ! printout: end of beam no. 10010

Or in the SSD example 2nd task Superpositions for Combination Rules:

Finally, the full printout will be explained for the minimum bending moment My at middle support for the combination 2:

../../_images/sia-output-comb2-min-my.png

Leading action is Q_B: Act Q_B: SumQ1 = -233.2999* SumQI = -108.8733
Accompanying action is S: Act S: SumQ1 = -93.3200 SumQI = -55.4876*

Hint

Please note that the leading action is that with the largest difference between the two sums.

It follows the table of the determined load case combination with the determined factors for minimum MY. At least the resultant beam forces min MY = -717.13 kNm is shown in the table ‘Relevant Forces in Beam Elements’

As in the first example in the SSD file the task Combine Loads is included. Here the resultant load combinations for the ultimate limit state are determined automatically via the button ‘Automatic’. A click on ‘Automatic’ opens a subdialog. For the determination of the load case combinations action combinations which are stored in the database should be selected. During the calculation a MAXIMA runs internally and then the found load case combinations are made available to the dialog for further processing.

Fourth Example according to ACI 318-19#

Files: us_aci318-19_girder.dat and ssd2026-us_aci318-19_girder.sofistik

The US customary units of the unit set 9 are used here. The cross section and the system are input in inch and the load in kip/ft.

The actions which are given in the ACI 318-19 are different to these of the EN 1990:

Dead load D
Live load L
Snow S

Important

In the different US design codes several action combinations are provided for the design. These action combinations depend on the in the system available actions and have a fixed unfavourable factor for the corresponding action. The safety concept of these design codes is different to the EN codes both on the load side and material side. In this tutorial the load side should be explained.

Literature: Building Code Requirements for Structural Concrete (ACI 318-19)

Hint

In this table, no statement is made about the consideration of initial load cases (whether permanent, variable or exclusive), only about the actions. The programm MAXIMA determines which initial load cases act how for each superposition value at each position of the structure and automatically determines the resultant load case combinations.

SOFiSTiK also offers default actions and action combinations for this code ACI 318-19.

After the definition of the material, the cross section and the system generation the actions and the loads are input in program SOFiLOAD.

Hint

For the default actions it is only necessary to input the action name. All other information about the default actions are generated automatically.

+PROG SOFILOAD
HEAD Actions
ECHO ACT
ACT  'D' TITL "dead load"      ! default action D
ACT  'L' TITL "live load"      ! default action L
ACT  'S' TITL "snow load"      ! default action S
END

In the input of the actions in the SSD task Action Manager and also in the printout table ‘Actions’ these two necessary default factors for the unfavourable and favourable case are shown. Because the factors are changing in the given action combinations the changed factors are defined automatically in the default action combination.

In context with the input of the loads it is possible to set ECHO ACT FULL for the printout table of the used actions and the corresponding load cases:

../../_images/aci318-19-ssd-actions-out.png

After the calculation of the initial load cases the superpositions are done in order to get the necessary design values (e.g. internal forces and moments, support reactions etc.).

In the first MAXIMA the default action combinations and their default superposition factors are calculated. In order to get these defaults only the following simple MAXIMA should run:

!*!Label Using default action combinations
+PROG MAXIMA
HEAD Default action combinations
CTRL COMB YES      ! generates the default combination rules
CTRL SUPP YES      ! generates the default associated superpositions
ECHO TABS YES
ECHO LC   YES
END

Or in the SSD the default action combinations are shown in the task Combination Rules for Actions’ and the superposition values are shown in the task *Superpositions for Combination Rules - default superpositions:

../../_images/aci318-19-ssd-comb-default.png

../../_images/aci318-19-ssd-supp-default.png

Please note that all for a 3D system possible superposition values are preset. For this small system e.g. for the beam forces only Vz and My are interesting. As already described all possible action combinations are preset for the general case. In this small project only the variable action L and S are used. Therefore, the superpositions were removed manually for the action combinations that are not required.

Hint

If you want to get the MAXIMA (CADINP) input of the default action combinations, you can use the export from CDB to MAXIMA inside TEDDY or SSD (Button Database Tools -> Export to DAT).

The printout contains the general information about the action combinations and the table of the generated resultant load cases:

../../_images/aci318-19-default-output.png

The ACI 318-19 demands several action combinations with different fixed factors. Here these equations have to be defined with COMB EXTR EXPL. As an example the equation (5.3.1b) with S is input manually (DAT file second MAXIMA or SSD combination 2 or 102), whereby the factors are defined as numerical value:

!*!Label Action Combinations
COMB NO 2 EXTR EXPL BASE 4100 TYPE DESI TITL "equation 5.3.1b"
ADD TYPE D  FACU 1.2  FACF 1.0
ADD TYPE L  FACU 1.6  FACF 0
ADD TYPE S  FACU 0.5  FACF 0

Or in the SSD example combination 2 manually defined:

It follows the definition of the superposition values, here only the bending moment My, the shear forces Vz and the support reaction Pz as well as the nodal displacement uz.

!*!Label Superpositions
ECHO LOAD,FACT
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE VZ,MY FROM 10010 X 1[-] TITL "Forces and moments"
ECHO LOAD,FACT NO
SUPP COMB 2 EXTR MAMI ETYP NODE TYPE UZ TITL "Displacements"
SUPP COMB 2 EXTR MAMI ETYP NODE TYPE PZ TITL "Support reactions"

!*!Label Superposition Normal Stress in Cross Section Point Z+
ECHO LOAD,FACT
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE SIG SELE Z+  FROM 10005 X 1[-] OPT S    ! printout: end of beam no. 10005
SUPP COMB 2 EXTR MAMI ETYP BEAM TYPE SIG SELE Z-  FROM 10010 X 1[-] OPT S    ! printout: end of beam no. 10010

Or in the SSD example 2nd task Superpositions for Combination Rules:

Finally, the full printout will be explained for the minimum bending moment My at middle support for the combination 2:

../../_images/aci318-19-output-comb2-min-my.png

The first table shows the values of the initial load cases. In the second table ‘Determination of Sums and Leading Variable Action’ the calculated sums and the possible resultant factors are printed. This second table here not so important due to the safety concept of the ACI 318-19 where no leading or accompanying actions should be determined. The program MAXIMA decides only whether the initial variable load cases are used.

It follows the table of the determined load case combination with the determined factors for minimum MY. At least the resultant beam forces min MY = -5974.96 in-k is shown in the table ‘Forces in Beam Elements’

Remarks#

The several design codes and even the National Annexes of the EN 1990 provide different formulas for the action combinations. SOFiSTiK offers several options for the combination rules for actions and their superpositions automatically or manually using action combinations and for the determination of resultant load case combinations. It is the task of the engineer to check the used combination rules and randomly the results with the extensive output only for a specific element.

If you need a special solution for the topic of the combinations and superpositions of your project, contact us please with an email to support@sofistik.com.