# 3D results - Displacements & stresses

14.0

## Introduction

SCIA Engineer 14.0 brings the presentation of results to a new level: 3D! Displacements and stresses can now be displayed on the 3D rendered surface of columns and beams. On top of that, the results may be projected on the initial as well as the deformed structure. This feature improves the insight in the global behaviour of the structure to assist you in quickly discovering issues and their causes.

Highlights
Displacements and stresses on 3D rendered surfaces of 1D members
Results displayed as isobands or isolines ('patch grid'), on original or deformed structure
Calculation of results in cross-section fibres; linear interpolation in between them

New result magnitude: Utotal = √ux²+uy²+uz²

Combination key legend included in the print preview

## Detailed information

The 3D results are accessible at the top of the Results service.

##### Results properties

The user selects in the Properties menu the result parameters as well as how they are displayed. This is very similar to other result types. For envelope combinations and result classes it is possible to switch between the minimum or the maximum 'envelope'. This means that in every fibre along the member surface, either the minimal or the maximal value of the chosen magnitude is displayed.

##### Calculation points

3D results are calculated in all cross-section fibres, in a number of sections distributed equally along the member’s length. To obtain a smooth result distribution, linear interpolation in between the fibres is used.

The number of fibres is automatically set for all predefined cross-section types from the Cross-section library. The fibres are located in each cross-section corner, and on the intersection with the principal axes.

The number of sections along the member is defined in the Setup menu > Solver. The default value is 10, but can of course be increased to increase the accuracy of the results.

### 3D displacements

#### Result magnitudes

Available values are

• ux, uy, uz: displacements of fibres, according to the member's local co-ordinate system
• φx, φy, φz: rotations of fibres, according to the member's local co-ordinate system
• Utotal: resulting displacement of fibres, i.e. Utotal = √ux²+uy²+uz²

#### Calculation background

Displacements are calculated in SCIA Engineer using the small displacement theory. This assumption implies linear translation of fibres, caused by a rotation of the section. For example, as presented in the image below, the rotation φ causes a translation of point '0' to point '2'.

Pure torsion causes rotation of the section an thus displacement of the fibres!

#### Initial or deformed structure

The results may be displayed on the original structure or on the deformed surface of the members.

When 'Deformed structure' is selected, together with an envelope combination or a result class, also the type of 'member deformation' needs to be selected.

• For member maximum: The rendered surface is displayed as it deforms under the load combination that causes the extreme value of the selected magnitude on the member. The evaluation is thus executed for each member separately! Per member, the extreme may be caused by another critical combination so there are possibly discontinuities in connecting nodes.
• For global maximum: The rendered surface is displayed as it deforms under the load combination that causes the extreme value of the selected magnitude on the whole structure.The evaluation is done for one single critical combination, resulting in a continuous deformation.

#### Special case: Torsion

Especially in case of torsion, the display of the deformed surface enables the user to better understand the behaviour of the model. These torsional deformations were not easily noticed in the 'old' result type Deformations of 1D members.

If the check box 'For drawing use linear rotation' is activated, the displayed deformation is consistent with the small displacement assumption during analysis. If de-activated, the displayed deformation is based on circular translations of fibres, maintaining the original shape of the cross-section. The result may look better, but keep in mind that it's inconsistent with the analysis assumption.

### 3D stresses

#### Result magnitudes

Available values are

• σx: orthogonal normal stress, perpendicular to the section plane
• τxy, τxz: orthogonal shear stresses, according to the principal axes of the cross-section, resulting from Vy, Vz and Mx
• τxs = √τxy² + τxz²

#### Calculation background

A linear stress-strain relationship is assumed. This means the results are valid as long as a physical linear analysis is executed (e.g. a linear, geometrical non-linear or dynamic analysis).

The normal stress σx is thus derived from the strain in the cross-section fibres using Hooke's law.

The shear stresses τxy, τxz contain different components in case of thin-walled or thick-walled cross-sections. For more information, refer to the Help article.

##### Limitation

The interpolation of stress values in between cross-section fibres is done in a linear way. This may cause misinterpretation in case of shear stresses, as there are not always enough fibres for an accurate evaluation. Some local extremes may be omitted, as is shown in the example below.

#### Initial or deformed structure

The principle is exactly the same as described for 3D displacements.

#### Special case: Composite cross-section

In case a cross-section is composed of multiple materials (e.g. steel and concrete), the normal stress σx clearly shows how the different material stiffness is taken into account.

### Graphical presentation

#### Drawing setup

3D results may be displayed as coloured or monochrome isobands or isolines, or as numerical values in the fibres. The default is a smoothened isoband result. The selection of your liking can be made in the Drawing setup.

The legend to the colours is automatically generated. Just select 'User adjustable palette values' in the Drawing setup if you want to create you own legend.

#### Animation of results

Choose a 3D result magnitude, select the option 'Deformed structure' and then open the Animation window. This is carefully hidden in the View menu. Press the 'Start animation' icon and the structure will move back and forth between its initial and deformed shape.

### Print preview

The 'Extreme' property influences the amount of data printed in the output table. The extreme values of the chosen magnitude are printed for each section, each member or only for the structure as a whole. The concomitant values of the other magnitudes are printed as well.

#### Combination key

Very useful is the combination key included directly in the print preview!

This legend of decisive combinations is printed as a separate table at the bottom of the preview window.

Sonja Asselbergh

03/04/2014