## Introduction¶

This document provides a short introduction in the use of the program MAXIMA using load groups with an internal procedure of intermediate superpositions. The given generic example is only for demonstation purposes. The used design code is therefore not decisive. For comparison the second file includes the input definiton for the analog intermediate and final superpositons without load groups.

### Theoretical Background¶

It is mainly necessary in bridge construction that several variable loads are exclusive each other. E.g. for road bridges according to EN 1990 and EN 1991-2 the traffic loads are divided into load groups gr1 till gr5 which should not be simultaneously taken into account.

### Objectives¶

• Generate the system inclusive the design code, materials, cross sections

• Generate the actions with the task Action Manager or with the program SOFiLOAD using load goups for an variable action and its categories

• Run linear analysis

• Generate action combinations in program MAXIMA (SSD please use a TEDDY task, task ‘Define Combinations’ is not able to process load groups)

• Generate superpositions

• Alternative workflow for bridge design: use of program CSM, SSD task ‘CSM Bridge Design - Superpositioning’

## Project Description¶

In the given files a two span girder is generated.

Files:

two-span-girder_intermediate-superposition.dat for comparison with intermediate superposition

### Geometry¶

A simple two-span girder, which has beam cuts every 1 m, is presented. The direction of gravity is the Z direction.

### Materials¶

Number

Notes

1

C 30 (EN 1992)

concrete fc = 30.0 MPa

2

S 500B (EN 1992)

reinforcing steel fy = 500 MPa, ft = 540 MPa

### Cross Section¶

A simple T-beam is generated.

Action and its Category

Title

G_1

11,12

GR

action GR for variable traffic loads

GR_1

Q_1 (group 1)

101 - 111

GR_2

Q_1 (group 1)

201 - 211

GR_3

Q_2 (group 2)

301 - 311

GR_4

Q_3 (group 3)

401 - 411

The SOFiLOAD input for the actions is:

+prog sofiload
ACT  TYPE  PART  SUP   GAMU GAMF  PSI0 PSI1 PSI2  TITL
G_1   G     PERM  1.35 1.00  1.00 1.00 1.00  'permanent'

$Feature load groups -> in an action with categories GR Q EXCL 1.50 0.00 0.90 0.60 0.40 'exclusive' GR_1 Q_1 EXCL 1.50 0.00 0.90 0.60 0.40 'exclusive' GR_2 Q_1 EXCL 1.50 0.00 0.80 0.50 0.30 'exclusive' GR_3 Q_2 EXEX 1.50 0.00 0.90 0.60 0.40 'exclusive+category 1' GR_4 Q_3 EXEX 1.50 0.00 0.90 0.60 0.40 'exclusive+category 2' END  The actions and the loads are defined with the program SOFiLOAD. The printout of the table Actions inclusive the corresponding load cases is as follows: In the file two-span-girder_intermediate-superposition.dat for comparison purposes the categories for GR are not assigned to load groups and uses only PART Q - variable action. ### Action Combination in Program MAXIMA¶ In MAXIMA the necessary action combination and the desired superposition values have to be defined as usual. Here the combination DESI according to equation 6.10 EN 1990 is used. As superposition value the beam bending moment MY is defined. The MAXIMA input is: +prog maxima HEAD Combination 10 ECHO LOAD,FACT FULL COMB NO 10 EXTR desi TYPE desi BASE 3100 ACT G_1 ACT GR_1 LC -1 ACT GR_2 LC -1 ACT GR_3 LC -1 ACT GR_4 LC -1 SUPP 10 EXTR MAX ETYP BEAM TYPE MY FROM 105 X 0.00$ FROM and X only for printout
END


As a second variant the combination 11 is shown in the file for demonstration. Here the explicit defined combination EXPL is used with action groups. It is the same defintion as for combination 10 with DESI.

### Results of the Superposition¶

The following scheme shows the procedure of the internal pre- and final superpositions:

E.g. for the maximum bending moment in span 1 beam no. 105 position X 0.0 m the load cases 103 and 203 of the categories GR_1 and GR_2 of the load group 1 are decisive:

The results max MY of the comparison example with intermediate and final superpositon is equal:

In an own MAXIMA run with record TRAC it is possible to keep the loadcase tracing of the initial load cases for a superposition value at a specific structure position.

For the maximum bending moment My in beam no. 105 at start point the MAXIMA input is as follows:

+PROG MAXIMA