# Linear Cracked Analysis (simplified)#

A fast, reliable and efficient way of considering cracked concrete for slabs is by modifying the elements properties and conducting a linear analysis and design on this modified system. This allows to take the effects of cracking into account while remaining linear. One advantage of this method is that the superposition principle remains valid and the standard linear analysis workflow can be applied.

## In the Example Files#

In the example files, this cracked linear analysis is performed by tasks of group *Linear Cracked Analysis (simplified)*.
The results of this simplified cracked analysis are saved in the following load and design cases:

Type |
Nr |
Description |

Load Case |
2500 |
SLS Combination of Results for Cracked Analysis and Design (simplified), Linear with Modified QUAD Stiffness |

Design Case |
25 |
SLS Required Reinforcement Distribution in the Slab according to Cracked Design (simplified, Linear with Modified QUAD Stiffness) |

## Prerequisite Knowledge#

SOFiSTiK provides several methods to modify elements properties. The one presented here allows to reduce locally the stiffness of QUAD Finite Elements and to calculate the behaviour of the modified structure.

### Modifying the Stiffness of QUAD Elements#

To modify the stiffness of QUAD elements, insert SSD’s task *Linear Analysis* and convert it into a User Task to revise its input.

Tip

To convert a task into a User Task, access SSD’s context menu by `Right mouse click`

on the task and selecting Convert to User Task.

In the text input to conduct the linear analysis with module ASE, add records `GRP`

.
This allows, amongst others, to modify the stiffness of QUAD elements:

Define the default behaviour for all elements with

`GRP NO -`

.Define a different behaviour for elements in specific groups:

Provide group number(s) at item

`NO`

, all QUAD elements belonging to these groups will be selected.Modify the stiffness of the selected QUADs with record

`FACS`

.

A detailed description of the options available as well as example of their use can be found in the manual of module ASE,
at chapters 3.11 *GRP - Expanded Group Selection Elements*.

At the end, the calculation input for module ASE should be similiar to this one:

```
+PROG ASE
HEAD Calculation of Forces and Moments with Modified QUAD Stiffness
$Default - all Elements have a 100% Stiffness
GRP NO - FACS 1
$Exception - QUADs belonging to Primary Groups 100 and 150 have a Stiffness reduced by 50%
GRP 100,150 FACS 0.5
LC 1,2
END
```

Attention

All QUAD elements belonging to the indicated groups will have their stiffness modified. Therefore, during modelling, a careful assignation of group numbers to structural areas is required.

It is also important to note, that with `GRP`

, **the modified stiffness is applied only for the current calculation**.
In the report of the linear analysis, a table summarizes which stiffness was used and for which groups.

## Linear Analysis with Modified Stiffness#

To perform the linear analysis of the load cases 1 and 2 with modified QUAD stiffness,
the SSD task *Linear Analysis* is inserted and converted it into a User Task to revise its input.

The following input is used in the example files. It applies the factor of 0.5 to the stiffness of all QUAD elements in groups 100 and 150, and calculates load cases 1 and 2 with this reduced stiffness:

```
+PROG ASE
HEAD Calculation of Forces and Moments with Modified QUAD Stiffness
$Default - all Elements have a 100% Stiffness
GRP NO - FACS 1
$Exception - QUADs belonging to Primary Groups 100 and 150 have a Stiffness reduced by 50%
GRP 100,150 FACS 0.5
LC 1,2
END
```

Note

The reduction factors must be chosen according to the project’s objectives and the normative requirements. The value 0.5 applied here is purely illustrative.

## Combination of Results#

This cracked method is linear, so the principle of superposition remains valid.
The Task *Combine Results* is used to superpose manually the results of the linear analysis with modified QUAD stiffness.
With this task, results for a SLS quasi-permanent combination are generated.
These results are saved in load cases 2500.

After calculating this task, the deformation of the cracked slab (simplified) is available and can be displayed for load case 2500.

Note

Task *Combine Results* is used in this tutorial for simplification purposes.
In general, Tasks *Combination rules* and *Superpositioning for Combination Rules* should be used in a linear analysis to superpose results automatically
according to rules and and combinations from the design code.
Please refer to the Beginners Tutorial - Design of Concrete Building to know more on this topic.

See also

Refer to the online documentation of SOFiSTiK FEA for more information on the task *Combine Results*.

## Design Parameters#

The graphical task *Design Parameters of Areas Elements* allow to adjust
reinforcement direction, concrete cover, rebar diameters and allowable crack width for QUAD Finite Elements.
This task can be placed only once in the project navigation.
In the example files, this information is modified successively to illustrate the different methods available for cracked analysis.
This is why a text input task is used instead of the graphical one.
The text task contains input for module BEMESS, which defines the same design parameters for all QUAD elements in the project.
It sets explicit values for the concrete cover (`GEOM`

), the reinforcement direction (`DIRE`

), the rebar diameters (`PARA`

)
and the minimum reinforcement (`PARA`

) while leaving all other parameter values to their default:

```
+PROG BEMESS
HEAD Default Values of Slab Design Parameters
GEOM HA 35 DHA 10 HB 35 DHB 10
DIRE UPP 0 LOW 0
PARA DU 10 DU2 10 DL 10 DL2 10 ASU 1.13 ASU2 1.13 ASL 1.13 ASL2 1.13
END
```

See also

Please refer to:

the online documentation of SOFiSTiK FEA, task

*Design Parameters of Area Elements*

to know more about design parameter of area elements.

## SLS Design#

The SLS design is performed in the exact same way as for an uncracked linear analysis. As input reinforcement distribution, the required reinforcement from the uncracked ULS design is used (design case 10). The required reinforcement distribution in the slab calculated is saved under design case number 25 (cracked SLS design, simplified).

See also

Please refer to the Beginners Tutorial - Design of Concrete Building to know more about performing ULS and SLS designs in SSD.

## Regenerate Results in Load Cases 1 and 2#

In the example files, task *Linear Analysis (- with Full Stiffness)* is calculated at the end of the Linear Cracked Analysis.
This regenerates the results of load cases 1 and 2 with full stiffness, making them available for all further calculations.

## Evaluation of Results and Additional Resources#

Further information about the evaluation of results and additional resources is common to both methods of this tutorial: Evaluation of Results.