Non-linear combinations

Definition, application

Non-linear combinations are similar to standard combinations and are used for non-linear calculations. A nonlinear combination MUST be defined if a nonlinear calculation is supposed to be carried out. Without a nonlinear combination defined, the program is NOT CAPABLE of running the nonlinear calculation of any kind.

Where to find in SCIA Engineer

All non-linear combinations are stored in Load cases, Combinations / Nonlinear combinations in main tree. It is possible go there in menu Tree / Load cases, Combinations / Nonlinear combinations too.

How to create a new one

In 'Nonlinear combinations' dialog there are possibilities 'New' or 'New from combination'. For modification it is possible to use buttons 'Insert', 'Edit' and 'Delete'. 'New' starts dialog 'Nonlinear combinations - NCX' where it is possible to define new one and add some LCs to it .

'New from combination' allows to create nonlinear combination from standard linear and envelope combinations saved in 'Combination' dialog. After click on this button 'Make selection' dialog will appear.

In dialog there are several properties:

Type of combination	Linear / Envelope According this choice available combinations are displayed in left window. it means one nonlinear combination will be created from one selected linear combination, several nonlinear combinations will be created from one envelope combination because it contain several linear ones. Note: 'Envelope' choice means all code depended combinations like ULS, SLS, Characteristic., Seismic...
Used filter	All / All dangerous / Most dangerous All = is set as default value. It means envelope combination will be decomposed on the background on linear ones and from every linear combination one nonlinear combination will be created. Approximate number of generated nonlinear combinations is displayed in right bottom corner of dialog. If linear analysis is successfully passed and results are available, other two possibilities are available in combobox. All dangerous = nonlinear combinations will be generated only from dangerous combinations from the selected envelope combination. Dangerous combination is a combination which causes a stress extreme on FE in the envelope. Detection of dangerous combinations is based on stress evaluation after a linear analysis. The number of generated combinations will be lower. Most dangerous = it is possible to chose how many most frequent dangerous combination from envelope combination will be transformed to nonlinear ones. Note: See schema below the table.
Number of dangerous	Number of most frequent dangerous combination from envelope combination which will be transformed to nonlinear ones.
Create class	From all generated nonlinear combinations the result class will be automatically created. So this result class from nonlinear combinations generated from envelope combination will behave for nonlinear analysis as envelope combination for linear analysis.

Explanation of theoretical background on an example :

Descriptions for five tables in five columns :

Model of structure covered by 10 FEs ---> Envelope combination contains 12 linear ones --->Analysis of extreme stress for every FE ---> Calculated frequency ---> Sorted as most dangerous

Initial imperfection

The non-linear combination may be defined with a specific kind of initial imperfection in shape of the modelled structure. There are several ways to define the initial imperfection. In general, the imperfections are divided into two groups:

bow imperfection,
global imperfection.

Bow imperfection

None

No initial imperfection is imposed.

Simple curvature

f	Curvature of one 1D member
1/f	Radius of curvature

According to buckling data

The imperfection is derived from the buckling data. For standard sections the buckling curves are determined according to the appropriate national standard (e.g. for EC3 Table 5.5.3 is used ). For other sections, the buckling curves are taken from the user input made in cross-section definition.

Global imperfection

None

No initial imperfection is imposed.

Simple inclination

dx	The inclination per one meter of height in the direction of global X-axis
dy	The inclination per one meter of height in the direction of global Y-axis

Inclination functions

dx inclination function: Z	The inclination in the direction of the global X-axis. The inclination dependent on the Z-direction, i.e. on the height of the structure.
dx inclination function: Y	The inclination in the direction of the global X-axis. The inclination dependent on the Y-direction, i.e. on the length of the structure.
dy inclination function: Z	The inclination in the direction of the global Y-axis. The inclination dependent on the Z-direction, i.e. on the height of the structure.
dy inclination function: X	The inclination in the direction of the global Y-axis. The inclination dependent on the X-direction, i.e. on the length of the structure.
dz inclination function: X	The inclination in the direction of the global Z-axis. The inclination dependent on the X-direction, i.e. on the height of the structure.
dz inclination function: Y	The inclination in the direction of the global Z-axis. The inclination dependent on the Y-direction, i.e. on the length of the structure.

Note 1: The inclinations in both X- and Y-direction are evaluated as a sum of inclination components dependent on vertical and horizontal direction. I.e. the final inclination in X-axis is equal to the sum of (dx inclination function: Z) and (dx inclination function: Y), and the final inclination in Y-axis is equal to the sum of (dy inclination function: Z) and (dy inclination function: X).

Deformation from load case

Load case

The results obtained for the specified load case are imposed as the initial imperfection for further calculations. It means that the results for the specified load case must be calculated first. Only then the further calculations may be performed.

Note: The results for the given load case must be already calculated. Otherwise the program issues a warning.

See the theoretical background chapter for more details about the calculation of imperfections in the nonlinear analysis.

Nonlinear composite analysis

Stage for composite analysis model

This setting is available in case the composite analysis model is enabled in the project. It defines the reference stage for the analysis of the structure in case composite members are present in the model. For more details, see Nonlinear & Stability analysis of composite structures.