2d concrete design - en1992!1!1

8/10/2019 2D Concrete Design - En1992!1!1

http://slidepdf.com/reader/full/2d-concrete-design-en199211 1/119

2D Concrete design-EC2



2

All information in this document is subject to modification without prior notice. No part or this manualmay be reproduced, stored in a database or retrieval system or published, in any form or in any way,electronically, mechanically, by print, photo print, microfilm or any other means without prior writtenpermission from the publisher. Scia is not responsible for any direct or indirect damage because ofimperfections in the documentation and/or the software.

© Copyright 2008 Scia Group nv. All rights reserved.



Table of contents

3

Abstract ..............................................................................................................................................1

2 Global settings ........................................................................................................................2

2.1 Project data ......................................................................................................................2

2.2

Setup manager .................................................................................................................3

2.3 Manager of National Annexes ........................................................................................4

2.4

Concrete solver setup .....................................................................................................6

2.5

Design Defaults ...............................................................................................................7

2.6

Concrete Setup action button ........................................................................................7

2.7 Tips & tricks .....................................................................................................................8

2.7.1 Filters .........................................................................................................................8

2.7.2 User defined defaults ............................................................................................... 11

2.7.3 Save and loading of global settings to different project ........................................... 13

2.7.4 Colour orientation .................................................................................................... 14

2.7.5 Description pictures in setup dialog ......................................................................... 14

3

Concrete tree ......................................................................................................................... 16

3.1 Member data .................................................................................................................. 16

3.1.1 In general ................................................................................................................. 16

3.1.2

Type ......................................................................................................................... 18

3.1.3 Different layers per side ........................................................................................... 19

3.1.4 Layers in the centre ................................................................................................. 20

3.1.5 Advanced mode ....................................................................................................... 20

3.1.5.1 Basic data ........................................................................................................ 21

3.1.5.2 Longitudinal ...................................................................................................... 23

3.1.5.3 Concrete minimal cover ................................................................................... 28

3.1.5.4 Creep coefficient .............................................................................................. 29

3.1.5.5 Position of reinforcement direction arrows ....................................................... 29

3.1.5.6

Action buttons .................................................................................................. 29

3.1.3

Tips & tricks ............................................................................................................. 30

3.1.3.1

Member data labels ......................................................................................... 30

3.2 Member Design .............................................................................................................. 32

3.2.1 Design properties ..................................................................................................... 32

3.2.2 Internal Forces ULS ................................................................................................. 44

3.2.2.1 In general ......................................................................................................... 44

3.2.2.2 Tips & tricks ...................................................................................................... 46

3.4.3 ULS .......................................................................................................................... 59

3.4.3.1 Theoretical background ................................................................................... 59

3.4.3.2 2D Structures detailing ..................................................................................... 65

3.4.3.3 Reinforcement design workflow ....................................................................... 67

3.4.4 ULS+SLS ................................................................................................................. 75

3.4.4.1

Theoretical background ................................................................................... 75

3.4.4.2 Limit bar distances ........................................................................................... 79

3.4.4.3 Reinforcement design workflow ....................................................................... 80

3.5 Section on 2D member ................................................................................................. 84

3.6 2D Reinforcement .......................................................................................................... 86

3.6.1 Reinforcement from 2D Member Data ..................................................................... 86

3.6.2 New Reinforcement¨ ................................................................................................ 87

3.6.3 Tips and tricks .......................................................................................................... 89

3.6.3.1 Substraction from Required reinforcement ...................................................... 89

3.6.3.2 Labels ............................................................................................................... 91

3.6.3.3 Editing the reinforcement parameters .............................................................. 93

3.6.3.4

Editing the shape of the reinforcement region ................................................. 93

3.6.4 Free bars.................................................................................................................. 94

3.6.4.1 New Free bars .................................................................................................. 94



4

3.6.4.2 Explode to free bars ......................................................................................... 96

3.6.4.3 Free bars user reinforcement ........................................................................... 97

3.7 Averaging strip .............................................................................................................. 99

3.8

Code Dependent Deflections (CDD) ..........................................................................104

3.8.1 Introduction ............................................................................................................104

3.8.2 In general ...............................................................................................................104

3.8.3 Example .................................................................................................................109

3.8.3.1

Stiffness presentation ....................................................................................112

3.8.3.2 Deformations ..................................................................................................113

References .....................................................................................................................................115



1

Abstract

Scia Engineer software enables design and check of 2D member reinforcement. Mainpossibilities of design and checks are presented in table below.

Steps of design and checks for 2D members Concrete tree for 2D members

The aim of this document is to describe each step of design and check of 2D member and todescribe some of tips and tricks, which might be important and useful in each part.



2

2 Global settings

Global setting is a set of parameters which are default values for design of whole structure inthe project. User can use default values, change them or simply create his own set of parameters,according to his preferences and needs. General settings can be accessed via several dialogs:

o Project data

o Manager of National annexes

o Setup manager

o Concrete solver

o Design defaults in Concrete tree

o By pressing action button Concrete setup in Concrete tree > Member design

2.1 Project data

The first possibility to change global setting of the project is possible in project dialog. You canswitch between national annexes by National annex button. Each annex has some differencesaccording to the Standard EN.

After clicking the Edit button next to the name of the annex, Manger of National annexes dialogis displayed, containing all implemented national annexes. Project data dialog for Code EN 1992-1-1and Standard EN annex is displayed below



3

Default reinforcement and concrete material for EN Code

Since Scia Engineer version 2010, is default reinforcement and concrete material set directly inProject data dialog. After checking concrete material check box, possibility to choose default concreteand reinforcement material is activated.

Only one default common material is defined for beams, columns, walls or slabs, in contrast toother Codes where for each mentioned member must be separate default material defined in globalsettings. If we want to change any material for some specific member, we need to define local settingsomehow. We can do this by creating Member data or Punching Data on this member.

2.2 Setup manager

Since Scia Engineer 2010 version, there is a new library called Setup manager created. It canbe accessed from:

o Main tree > Libraries > Setup

o Menu > Libraries > Setup

Tree Menu

User can edit default settings for all materials in Setup manager dialog. Each country has itspredefined set of parameters. User is able create his own set of values with default values he requires.He might also change the appearance and the number of items in settings of each material. It ispossible to work with the items as with items of a library, so user can edit, copy, save and load to/fromfile, etc. It is not possible to switch national annex here, this action can be done only in Project dialogor in Manager of national annexes dialog.



4

After clicking a Concrete edit button in Setup manager dialog, Concrete setup dialog appears.This dialog displays all global parameters for concrete, without parameters specified by nationalannex.

2.3 Manager of National Annexes

It is possible to edit national annexes parameters only by using this dialog in Scia Engineer.Manager of national annexes dialog can be displayed in three ways:

o Main tree > Project > National annex

o Menu > Tree > Project > National annex

By pressing second flag icon, representing the country of the annex, in down right corner ofthe screen

Tree Menu Flag icon (Czech)



5

Manger of National annexes dialog is a library too. Content of items is the same as the contentof items in Setup manager. It is the same library and the only difference is that parameters are filteredaccording some filter applied. It is also possible to get more detailed information about implementedCodes and national annexes in Manager of National annexes. This can be done via buttonReferences.

By pressing Edit button ( ) for example for editing national annex parameters in EN 1992-1-1(Genera rules and rules for buildings), another dialog appears, where all appropriate implementedparameters are displayed.



6

2.4 Concrete solver setup

Code dependant values (except for national annexes parameters) and Code independentvalues, which influence design and check of concrete structures, are possible to edit in Concrete setup

dialog which can be displayed through Menu > Setup.> Concrete solver.



7

2.5 Design Defaults

This is the first item in concrete tree, and it is possible to set default values for member design(such as concrete cover, reinforcement diameters, direction angles, etc.), and also parameters fordrawing of user reinforcement.

2.6 Concrete Setup action button

Global settings for design of the reinforcement are adjustable through Concrete setup actionbutton too, which is located in Properties window of both concrete tree and in service for defining localparameters.



8

The main advantages of this action button dialog are:

o Only parameters for actual design are displayed

o Parameters from all dialogs are displayed

o NA parameters from Manager of national annexes dialog

o Code independent/dependent values from Concrete solver setup dialog

o Default parameters from Design default dialog

2.7 Tips & tricks

Here are some tips and tricks, which might some users find useful and which should providebetter overview in the global settings.

2.7.1 FiltersThere are quite a many global concrete parameters which influence reinforcement design. To

simplify the overview of the global settings, user may use filters, which will restrict the number ofdisplayed parameters. Parameters are able to sort according to these filters:

Type of members

This filter is activated only in case, that both 1D and 2D members are defined in the project.Then user may choose from 2 possibilities below:

o 1D members (only parameters that influence 1D member design are displayed)

o 2D members (only parameters that influence 2D member design are displayed)



9

Type of values

Displayed filters depend on where the dialog was displayed from.

o Design defaults (parameters of default design, such as cover, reinforcement diameters,etc.)

o

Code independent valueso Code dependent values (parameters from Code, without national annex parameters)

o Drawing settings (parameters for drawing of the reinforcement)

o NA building (national annex parameters from Code EN 1992-1-1)

o NA fire resistance (national annex parameters from Code EN 1992-1-2)

o NA bridges (national annex parameters from Code EN 1992-2)

o NA hollow core (national annex parameters from Code EN 1168)

Type of functionality

Displayed filters depend on functionality checked in Project data dialog, folder Functionality.o Prestressing (parameters for pre-stressed members design, functionality Prestressing

must be activated)

o Fire resistance (parameters for fire resistance design, functionality Fire resistance mustbe activated)

o Hollow core slab (parameters for hollow core slabs design, functionality Hollow core slabsmust be activated)

Type of checks



10

Parameters of checked check are displayed.

o Member data

o Cross-section characteristics

o Internal forces

o Design

o Automatic reinforcement design

o ULS response

o ULS design

o Crack

o CDD Check

o Detailing

o Allowable stress

o SaT

o Punching check

Displayed filters depend on location where the Concrete setup dialog was displayed from. As itis known, the dialog can be started from:

Setup manager (see 2.2)

All filters are displayed and active. Only national annex filters are not visible in Type of valuesfolder.

Manger of National annex (see 2.3)

o Type of members filters

o Type of values filters(only one, non active, national annex filter is displayed, this filterdepends on selected Code )

o Type of functionality filters (active only for EN 1992-1-1 Code)

NA for EN 1992-1-1 NA for EN 1992-1-2

NA for EN 1992-2 NA for EN 1168

Concrete solver setup (see 2.4)

o Type of member filters

o Type of values filters(only Code dependent/independent filters are displayed



11

o Type of functionality filters

Design defaults (see 3.1)

o Type of members filters

o Type of values filters(only Design defaults and Drawing setup filters are displayed

o

Type of functionality filters

Concrete setup action button

This filter depends on design service, which is currently active and may differ from each other.Only one Design filter is displayed in SLS design, Crack design filter is added in SLS+ULS design.

Setup manager Concrete solver setup

Design defaults

Concrete setup action button (SLS)

2.7.2 User defined defaults

The big advantage of new global settings is the possibility to adjust the global settings to theneeds of each user. Global parameters layout is possible to edit in Concrete setup dialog by right-clicking of mouse button on the window with the parameters (the window on the right side). Afterselecting Edit layout properties, the only possibility from shown menu, Property layout managerdialog is displayed.



12

We have created a new user layout named User1, where we copied all available parametersand switched off some parameters in group Concrete > Design defaults > Concrete cover. User mayadjust default layout or simply create a new one on his own by using edit buttons in the middle. Afterthe editing is finished, it is necessary to have check box Show current layout checked. Then thislayout will be added in form of folder Concrete setup dialog. User may also create more layouts andswitch among them. He still may use the default layout by checking check box Show native layout.



13

2.7.3 Save and loading of global settings to different project

As it was mentioned in different chapter above, global settings for Code EN is since Scia

Engineer 2010 version implemented as library, which enables to transfer global settings of one projectto another. Export and import of global settings is possible through these two icons in Setup manager or in Manger of National annexes dialogs.

o Save to file

o Read from file

The result of export or import will be the same in both dialogs, because the library is still thesame and the only difference is in applied filter in each dialog.

Note

Default global setting (SetupManager.db4 file) is placed in Scia/db folder, with all other db4 files.



14

2.7.4 Colour orientation

For better overview and simplified orientation in global settings are some of the parametersmarked with colour, where:

Blue coloured parameters are those which might be changed by using local setting through

o Member Data

o Punching Datao Green coloured parameters are National annex parameters

2.7.5 Description pictures in setup dialog

Pictures in global settings dialogs are very useful and might be important for more enhanceddescription of desired parameter. On the other hand these pictures take some space in the dialog andmight not be so important especially for more experienced users. To avoid any disturbance by

displaying those pictures it is possible to turn them off. This can be done in Options dialog (Menu >Setup > Options > Environment), by unchecking marked check box. Pictures in Properties will beturned off too.



15



16

3 Concrete tree

3.1 Member data

3.1.1 In general

By creating member data will user over change default global settings with local settings definedfor selected members. Simply said, where user doesn‟t want use global concrete settings, usercreates local concrete settings by defining member data. We recognize two types of this local settings,for 2D concrete members:

o Member data

o Punching data

These member data may be created by selecting these two items in Concrete tree andchoosing the proper 2D member, where this data want to be defined. These newly created settings willbe loaded from default global settings and are possible to be changed to fit user needs.

After selection of a 2D member or 2D sub region is Concrete 2D data dialog displayed and localsettings may be defined and confirmed.



17

When member data are created, a new folder will appear in member properties and will beshown in Attributes of the member too.

After definition of Member data is graphical mark (label) displayed together with the arrowsdescribing reinforcement directions on the member as well. After clicking on these marks is userallowed editing the appropriate attributes in member properties window. Content of the label is also

possible to edit through Concrete folder in View parameters setting dialog.



19

Plate Wall Shell

From the table above it is obvious that type:

o Plate enables to define different parameters for each member surface (upper, lower) bycheck box Different layers per side, but it is not possible to define only one layer of the

reinforcement in the centre by check box Layers in the centre.

o Wall does not enable to define different parameters for each member surface (upper, lower)by check box Different layers per side, but it is not possible to define only one layer of thereinforcement in the centre by check box Layers in the centre.

o Shell enables to define different parameters for each member surface (upper, lower) bycheck box Different layers per side and it is also possible to define only one layer of thereinforcement in the centre by check box Layers in the centre.

3.1.3 Different layers per sideThis attribute enables to define different parameters for upper and lower surfaces and its

reinforcement layers. By activating this attribute user will be able to define different reinforcementmaterial, different directions and different diameters for each surface. This attribute is available onlywhen Type is set to Plate or Shell.

Different layers per side off Different layers per side on



20

As you can see original tree item Longitudinal is divided into item Upper and Lower . If anadvanced mode will be activated too, then another items Number of reinforcement layers and itsdirections will be added.

3.1.4 Layers in the centre

In the real life project we come across with 2D members which have very small thickness, which

does not allow defining reinforcement layers for both surfaces. It is necessary to design only one layerof reinforcement which lies in the centre of gravity of the member. It is possible to design only onelayer of reinforcement by activating attribute Layers in the centre. This attribute is available only whenType is set to Wall or Shell and when it is checked, many parameters in member data are deactivated.

It is not possible to change attribute type of reinforcement geometry attribute. Only orthogonaldirection of reinforcement layers is supported.

Only two reinforcement layers are allowed. One lies just above the centre of gravity location andthe other one lies just bellow it.

Layers in the centre withAdvanced mode off

Layers in the centre withAdvance mode on

3.1.5 Advanced mode

This attribute is a filter for displaying the parameters in member data properties. If it is switchedoff, then only basic parameters from global settings (Design defaults) are displayed together withreinforcement material parameters, which might be edited. Groups Longitudinal and Minimal concretecover with the very basic parameters are displayed.

When it is activated then user may edit all available parameters. Those parameters are sortedto a few groups:



21

3.1.5.1 Basic data

In this group are basic attributes and parameters for reinforcement design. As you can see fromthe picture user can edit reinforcement geometry, type of concrete cover and reinforcement materialshere. Also Different layers per side, User reinforcement and User input thickness attributes are here.

Type of reinforcement geometry

There are two types of reinforcement geometry in Scia Engineer:

o Orthogonal (default) where user can define only one direction angle for first reinforcement

layer. The second reinforcement layer direction will always be perpendicular to the first one.Default value for first direction angle is loaded from global settings.

o User where it is allowed to define two or three direction angles for each reinforcement layerseparately. Number of directions may be edited by same parameter in Longitudinal folder.

Orthogonal User2 directions

User3 directions



23

If user reinforcement is already active on a certain member and then user defines userreinforcement by 2D region or by free bars, then the user reinforcement defined in Member data willbe deleted.

User inpu t thickness

Scia Engineer software enables to set different thickness for 2D member or its sub region, than

in model is defined. The big advantage of this feature is that it is possible to run reinforcement designfor different thickness, without the need of deleting calculation results together with inner forces. Theimportance of this function is directly proportional to the size of the structure in the project, wherecalculation of inner forces may take very long time. What is important is, that user must remember thefact, that self weight of the changed member is not adjusted by changed thickness by this function andremains the same as originally defined.

User defined thickness of 2D member or its sub region is possible to edit by new parameterThickness. This parameter will be displayed after switching on attribute User input thickness.

3.1.5.2 Longitudinal

In this group are parameters for each reinforcement direction such as number of layers in eachdirection, their angles, bar diameters and eventually distances between them. Also very importantparameter which influences concrete cover for each layer is here. Longitudinal group, which definesparameters for both surfaces may be split into Upper and Lower group, when attribute Different layersper side is switched on. The appearance of this folder may differ quite a lot depending on activatedattributes and defined parameters



24

Longitudinal2 directions, 2 layers, user cover

Upper3 directions, 4 layers, minimal cover

Numb er of di rect ionsBy setting attribute Type of geometry to User, a new parameter Number of directions will be

displayed in Longitudinal group. User is able to choose from two or three directions, wherereinforcement will be created. According to the choice, user is able to define appropriate number ofdirection angles

Direct ion angles

As it was mentioned before, these are the values with direction angles. It may be one up tothree. Default value for first direction angle is loaded from global settings. These direction angles areused only for reinforcement layers angles definition. It does not mean that this is angle of first, second

or third reinforcement layer. User selects direction for each layer afterwards.

Numb er of reinforcement layers

User is allowed through member data to define more reinforcement layers for each member orsub region surface. Minimal amount of reinforcement layers is set by number of defined directions (seeabove). Maximal number of reinforcement layers for one surface is 10.

For each reinforcement layer is necessary to define its bar diameter, direction angle, type ofcover, eventually Basic distance parameter.



25

Diameter

Reinforcement bar diameter is defined only for every first reinforcement layer in each direction.Default value is loaded again from global settings. The other layers in same direction has thisparameter disabled (not possible to edit)

Layer angle

It is possible to choose from defined direction angles in this combo box. These angles weredefined in root of Longitudinal group, eventually in root of Upper or Lower groups.



26

Orthogonal geometry

2 directions

User geometry

3 directions

Type of cover

Concrete cover, which is a distance from outer reinforcement surface to closer surface of themember, is determined by this parameter. This value can be automatically calculated by the softwarefor the first reinforcement layer. This calculation will respect values from group Minimal concrete cover.User may also define his own value for concrete cover. For this feature, attribute Type of cover inBasic data group must be switched on.

Location of other reinforcement layers depends on Type of cover for each of them. It is possibleto define different Type of cover for each reinforcement layer. User can choose from these types:

o Layer on previous layer: One layer is laid on the other one.

o Cover from previous: The user defines the cover from the previous layer. The cover ismeasured from a surface of one reinforcement bar to the surface of the other bar.

o Cover from edge: The user defines the cover from the edge of the slab.

o Distance from previous: The user defines the distance from the previous layer. Thedistance is measured from the centre of one reinforcement bar to the centre of the other

bar.



27

o Distance from edge: The user defines the distance from the edge of the slab.

Here is the description picture for all Types of cover. Turquoise line at the top represents 2D

member surface.

Conc rete cov er (cu)

Shows or provides place for the input of cover value itself .

Basic distance

If the attribute User reinforcement from Basic data group is switched on, than Basic distanceparameter is active and user may define and edit its value. As it was mentioned before, it representsaxial distance between two reinforcement bars and it is defined only for every first reinforcement layerin each direction. For other reinforcement layers in already defined direction software sets the samevalue.

During reinforcement design only certain number of reinforcement layers is being input. Thiscertain number equals to the number of defined directions. This means that if more reinforcementlayers are defined in one defined direction, then for design is being input:

o Average concrete cover calculated from all reinforcement layers in that direction



28

o User reinforcement area calculated from the first reinforcement layer (after assigning

reinforcement layer to direction which has already one layer defined, it is possible to editonly concrete cover of this new layer

The conclusion from this is that more layer reinforcement model may be substituted with onlyone layer with adjusted value of concrete cover.

Note

If average concrete cover value for upper or lower surface is equal or even bigger than half ofmember thickness, design will not be possible and it will end up with Error 61 (General error in inputdata).

3.1.5.3 Concrete minimal cover

Here in this group are parameters which influence the value of minimal cover calculated by thesoftware. It is also possible to define different parameters for upper and lower surface separately byswitching on attribute Input for side. User can edit Exposure and Abrasion classes, Type of concreteand its surface, control attributes and values for determination of Delta;cdur.



29

3.1.5.4 Creep coefficient

Here in this group are parameters for setting or influencing determination of creep coefficient.

3.1.5.5 Position of reinforcement direction arrows

Only two parameters are in this group. By editing default values, user can move the location ofthe direction arrow marks, along the 2D member or its sub region. It is not possible to set coordinatesout of the 2D member or sub region.

3.1.5.6 Action buttons

Just bellow all Member data attributes and parameters, there are two action buttons, which usermight sometimes find useful:

o Load default values, which will restore default settings from global settings forappropriate parameters such as, diameter, angle, etc.

o Concrete Setup, which will open dialog with global settings, while items in this dialog arefiltered according to the member type and member check.



30

Note

Parameters in member data, with the grey background, are parameters visible only when Advanced mode is switched on.

3.1.3 Tips & tricks

3.1.3.1 Member data labels

If a Member data are defined for certain 2D member or its sub region, then graphical mark(label) is displayed together with the arrows describing reinforcement directions and layers on themember. Only name of the attribute is displayed by default (Concrete 2D data), but this description ispossible edit or modify in View parameters setting dialog. It might be accessed by:

o clicking by right mouse button on graphical window, and choosing item Set viewparameters for all

o using an icon Fast adjustment of view parameters on whole model, which is abovecommand prompt, and selecting Setup dialog possibility

After that View parameters setting dialog, affecting whole model, is displayed and user can findparameters for concrete structure are in folder Concrete



32

3.2 Member Design

3.2.1 Design properties

Design properties layouts for Inner forces ULS, Member design ULS and Member design ULS +SLS differs from chosen design and attributes selected by user.

Inner forces ULS ULS + SLS design

ULS design

See description and possibilities for each of the attribute below.

3.2.1.1 Name

User is allowed to name the design. It might be very useful for better specification andorientation, especially in document.

3.2.1.2 Selection

This attribute influences the total amount of members, which will be taken into the specific 2D

member design. There are four possibilities to be chosen from:o All (all active 2D members will be designed)

o Current (only selected 2D members will be designed)



35

Where buttons:

Name Specifies the name of the user scale.

New level group in this group you can input a new level for the isolines palette. The level isdefined by the diameter of the reinforcement bar and by the distancebetween individual bars. The program then calculates the area ofreinforcement and mean diameter and distance. One level can contain oneto three different diameters, each of them with a separate spacing.

Copy to legend when a new is defined, it can be added to the legend using this button. Thenew level is positioned in the legend according to total reinforcement areaof the level.

Clear level this button clears all the edit boxes in the New level group.

Legend group this group displays the defined levels sorted according to the total area ofreinforcement in the level.

Delete active level if required, any defined level can be removed from the legend.

Delete this entire button clear the whole legend.



36

When this User scale will be used, then the scale in the top right corner of the graphical windowwill look like this:

Note

User scale isolines feature may be used only for parameter Location set to In nodes, avg., andfor Type values set to Required areas only.

User may also use possibility to draw isolines together with labels. Together with export of the

slab picture it might be very useful to transfer these pictures to different CAD systems and reinforcethe entity using exported picture as reference layer. This might be used also for mesh reinforcement.

Also note that setting in 2D result display dialog will be overwritten to User scale isolines andthe possibility to choose differently type of result representation will be disabled. To change this, usermust deactivate possibility Use user scale isolines.

3.2.1.11 Av eraging of peak

See more information about this feature in chapter 3.7 Averaging strip.



37

3.2.1.12 Location

This parameter defines the location, where the design will be calculated. This is based on FEMresults. If user changes this attribute, then Scia Engineer needs to make internal calculation of designforces. User may choose from four possibilities:

o In centres, (results represented in centre of gravity of each element, the design value fordesign is calculated directly from no avg. values by arithmetic average)

o In nodes, no avg. (results represented in mesh nodes, for each element separately,these are the main results which are base for all other design location possibilities)

o In nodes, avg., (results represented in mesh nodes, but on the opposite of no avg.values, all values from all adjacent 2D members in each node are recalculated by SciaEngineer before design and only one value for each node will be represented)

o In nodes, avg. on macro (the same as In nodes, avg. possibility with one importantdifference. the recalculation is done only on each 2D member separately, this means thatone 2D member will not be influenced by another 2D member, also note that there mightbe more same values)

We can show the differences of the designs for example on required reinforcement amount(As1-) calculated on example from chapter ULS and ULS+SLS design, which will follow.

In centres In nodes, no avg.

In nodes, avg. In nodes, avg. on macro



39

Note

This Reinforcement attribute is displayed only in Member design ULS or Member designULS+SLS, when Type value attribute is set to Required areas.

3.2.1.16 Standard

This attribute is used to determine where the design will be shown in the graphic window. Whenthis attribute is checked, then designed values will be displayed in the centres of the gravity ofselected 2D members.

3.2.1.17 Section

This attribute is used to determine where the design will be shown in the graphic window. Whenthis attribute is checked, then designed values will be displayed on predefined sections, which aredefined on selected 2D members.

3.2.1.18 Edge

This attribute is used to determine where the design will be shown in the graphic window. Whenthis attribute is checked, then designed values will be displayed on the edges of selected 2Dmembers.

3.2.1.19 Draw

This attribute defines the direction the designed values will be displayed. It is possible to selectone of the following possibilities:

o Upright to element

o Element plane

o X direction

o Y direction

o Z direction

Note

This attribute is displayed only when possibility to draw designed values on Section or Edge ischecked.

Also note that to make this feature functional, user have to set attribute Draw for each 2Dsection to “Draw similar as for setting in section properties” possibility.

3.2.1.20 Course

User may also define the way of interpretation of designed values. It is possible to choose fromthree possibilities.

o Precise (the precise interpretation based on mesh)

o Uniform (this will display the average value for whole edge)

o Trapezoidal (this will display trapezoidal progression of the value)



40

Note

This attribute is displayed only when possibility to draw designed values on Section or Edge ischecked.

3.2.1.21 Values

This attribute defines the final value to be displayed. Content of this drop down menu differs onselected design and attribute.

Internal forces ULS

Basic magnitudes Design magnitudes

, where values

o mx, my, mxy, vx, vy, nx, ny, nxy represent inner forces from FEM analysis

o n1-, n2-, n1+, n2+, vd, nc+ and nc- represent design forces.

For more information about these values see chapter 3.2.2 Internal Forces ULS.

Member design ULS

Required areas Reinforcement ratio Shear stresses Weight

, where values

o As1-, As2-, As1+, As2+ represents amount of longitudinal reinforcement for upper or

lower surface in certain direction. Asw value represents amount of shearreinforcement. These amounts are designed for ULS state.

o As,perc(1/2,+/-) represents rate between amount of required longitudinalreinforcement and concrete area. Asw,perc represents rate between amount ofrequired shear reinforcement and concrete area

o tauD represents shear stress in concrete, tauR is shear capacity of the concrete 2Dmember with longitudinal reinforcement involved.

o Mass (+/-) is the weight of the upper/lower reinforcement. Mass l is the total weight ofthe reinforcement.



41

o Member design ULS+ SLS

Required areasReinforcement ratio

Maximal diameters Maximal distances

, where values

o As1-, As2-, As1+, As2+ represents amount of longitudinal reinforcement for upper orlower surface in certain direction. Asw value represents amount of shearreinforcement. These amounts are designed for SLS state.

o fr1-, fr2-, fr1+, fr2+ are maximal possible reinforcement bar diameters

o sr1-, sr2-, sr1+, sr2+ are maximal possible distances between two reinforcement bars

allowed

In Member design ULS+SLS is also possible to design Reinforcement ratio, Shear stressesand Weight values. They are already displayed and described in Member ULS.

Note

Numbers 1 and 2, eventually 3 indicates the direction of X axis and Y axis of selected 2Dmember‟s LCS. Marks + and – indicates positive and negative direction of Z axis of selected 2Dmember‟s LCS.

Also note that by selecting possibility More comp is user able to display more values at thesame time in the preview window or in the document.

3.2.1.22 Extreme

Simply said, this attribute defines what results to show in Preview window or document. Usermay choose from three possibilities:

o No (results for all elements will be displayed on selected 2D members)

o Member (only elements with maximum results on each of selected 2D member will bedisplayed)

o Global (only elements with maximum results on selected 2D members will be displayed)



42

3.2.1.23 Drawing setup

By selecting edit button for this parameter, a 2D results display dialog will be open. Here usermay specify the representation of design results on 2D member. We can split this dialog into a fourzones.

o Display = red (here user may define the main type of 2D design representation, he maychoose to select one possibility from the list below)

o blue (where user may adjust type of representation selected in Display zone, the view ofthis zone may differ consequently to each type)

o green (here user may define to show or not to show local extremes and their appearance)

o yellow (it is possible to adjust the range of the scale and user defined isolines)



43

3.2.1.24 Ac t ion butto ns

In the lower part of the Properties dialog are a few action buttons placed. User may find thesebuttons very useful.

o Refresh (this button is probably most important from all of them. It will start the process ofdesign itself and it is needed to pres this button to refresh previous design results and toget new results, based on chosen attributes)

o Calculation info (this button will open Calculation info dialog, where errors and warningsrelated to the design are displayed together with their description)

o Concrete setup (see more info in chapter 2.6 Concrete Setup action button)

o New reinforcement (see more info in chapter 3.6.2 New reinforcement)

o Export reinf. Area to CAD program (by pressing this button will be user asked to saveactual finished design to an *.ASF file, which might be loaded in others CAD program,such as Allplan, for further reinforcement design)

o Preview (this button will open Preview window with tables containing results of finisheddesign, it might be also used for refreshing the results)



45

Tension force from shear stress is also dependent on inclination of shear strut. In Scia Engineerit is possible to set two types of shear strut inclination calculation. This can be done in Concrete setupdialog through attribute Shear strut inclination control 6.2.3, which is placed at the same location inConcrete setup dialog as Shear effect control 6.2.3(7).

o Variable strut inclination method (inclination is calculated automatically and the aim isto find minimal value of angle , which lies in interval min and max, and condition vd ≤

vRd.max is true, This method optimises variable strut inclination to determine the minimalamount of shear reinforcement)

o Fixed strut inclination method (with this method set, user defines the inclination bydefining angle . Default value is set to 40 degrees.)

Values, which will be available in value list for Type values attribute set to Design magnitudesdepend on:

o Type of the structure set during definition of the project itself. For 2D members project ispossible to set three options, Plate XY, Wall XY and general XYZ.

o Layers in the centre attribute placed in 2D concrete data. If all 2D members in the projecthave 2D concrete member data defined with attribute Layers in the centre active, then

only n1-, n2-, nc- values will be displayed the list of values in General XYZ project.o Number of reinforcement directions. If all 2D members have only 2 reinforcement

direction defined, then values with index 3 will not be displayed in the list of values.

Plate XY Wall XY General XYZ

Description of the values above:

m1-,m2-,m3-,m1+,m2+,m3+ Design bending moment in reinforcement direction 1,2 and 3 forlower surface (-) or upper surface (+). These values are used forreinforcement design.

n1-,n2-,n3-,n1+,n2+,n3+ Design normal force in reinforcement direction 1,2 and 3 for lowersurface (-) or upper surface (+). These values are used forreinforcement design.



46

n1,n2,n3 Design normal force in reinforcement direction 1,2 and 3 placed inthe centre of gravity of 2D member. These values are used forreinforcement design.

mc-, mc+ Design bending moment in concrete compression strut for lowersurface (-) or upper surface (+), which must be covered byconcrete. If the concrete strut is not able to cover this moment,design will end up with error message.

nc-, nc+ Design normal force in concrete compression strut for lowersurface (-) or upper surface (+), which must be covered byconcrete. If the concrete strut is not able to cover this force, designwill end up with error message.

nc Design normal force in concrete compression strut placed in the

centre of gravity of 2D member, which must be covered byconcrete. If the concrete strut is not able to cover this force, designwill end up with error message.

vd Resultant shear force, which takes effect perpendicular to 2Dmember plane.

Note

Upper and lower surface of 2D member is determined by the Z axis direction of local coordinatesystem (LCS). Upper surface is in the positive direction of the Z axis and on the other hand Lowersurface is in negative direction of Z axis. Upper surface values are marked with + and lower values aremarked with -.

3.2.2.2 Tips & tricks

3.2.2.2.1 Inner forces in Resu lt tree

It is possible to check inner forces directly in Results through Member 2D – Internal Forces item.Here, user can also view design magnitudes, if attribute Type of the force is set to Elementary design

magnitudes possibility.

http://slovnik.seznam.cz/?q=resultant%20force&lang=en_cz

http://slovnik.seznam.cz/?q=resultant%20force&lang=en_cz



47

Elementary design magnitudes in tree Results are determined differently than in Concrete tree.The difference is that Elementary design forces are reached for X and Y axis of local coordinatesystem of the 2D member, not for reinforcement directions as it is done for determination of designmagnitudes in Concrete tree. In Elementary design forces is also torsion moment mxy taken into acount, however tension force from shear stress is not. These Elementary design forces might be usedonly for presentation. For design of the amount of reinforcement are Design magnitudes fromConcrete tree used.

Values displayed in value list, when attribute Type forces is set to Elementary designmagnitudes possibility are only dependent to type of the structure set during definition of the projectitself. For 2D members project is possible to set three options, Plate XY, Wall XY and general XYZ.

Plate XY Wall XY General XYZ

Description of the values above:

mxD+, mxD- Design bending moment in X axis direction of local coordinatesystem (LCS) for lower surface (-) or upper surface (+).

myD+, myD+ Design bending moment in Y axis direction of local coordinatesystem (LCS) for lower surface (-) or upper surface (+).

nxD+, nxD- Design normal force in X axis direction of local coordinate system(LCS) for lower surface (-) or upper surface (+).

nyD+, nyD+ Design normal force in Y axis direction of local coordinate system(LCS) for lower surface (-) or upper surface (+).

mcD+, mcD- Design bending moment in concrete compression strut for lowersurface (-) or upper surface (+), which must be covered by concrete.

ncD-, ncD+ Design normal force in concrete compression strut for lower surface(-) or upper surface (+), which must be covered by concrete.

Note

Upper and lower surface of 2D member is determined by the Z axis direction of local coordinatesystem (LCS). Upper surface is in the positive direction of the Z axis and on the other hand Lowersurface is in negative direction of Z axis. Upper surface values are marked with + and lower values aremarked with -.



48

3.2.2.2.2 Compariso n of desig n inner forc es in Concrete and Resul ts trees

Design inner forces magnitudes, in Concrete tree and Results tree, have same values onlywhen on selected 2D member:

o has only two reinforcement directions defined and are perpendicular to each other

o is first reinforcement direction angle is identical with the value of rotation, defined inproperties of Member 2D – Internal Forces, in Results tree.

Member Data in Concrete tree Member 2D - Internal Forces in Results tree

o influence of tension force is not considered for shear reinforcement,. That means that forattribute Shear effect control 6.2.3(7) is set to no shear effect is considered possibilityin concrete setup dialog

Comparison of results in Results and Concrete trees will be done for type of the structure PlateXY. Structure is simple 2D concrete member, which diameters are 6 x 8 meters with thickness 200mm. It has defined concrete C25/30 and it is supported on three sides. It is loaded with constantsurface load of 10kN/m2 .No member data are defined on this 2D member.



49

3.2.2.2.2.1 Two p erpend icular reinfo rcement direct io ns , ident ical with X and Y

axes of LCS

First direction angle in Member data is set to 0 (zero) degrees and Rotation attribute in 2DMembers – internal Forces properties in Results tree is 0 (zero) as well. Influence of tension force isnot considered for shear reinforcement. That means that for attribute Shear effect control 6.2.3(7) isset to no shear effect is considered possibility in concrete setup dialog.

Reinforcement and LCS directions Member 2D - Internal Forces attributes

Graphical comparison of moment for lower surface for direction 1 (direction of X axis of LCS)

Results, moment mxD- Concrete, moment m1-



50

Numerical comparison of moment for both surfaces and directions for elements 1-24 (half of the2D member)

Moments Results tree Concrete tree

Case Elem. mxD- myD- mcD- mxD+ myD+ mcD+ m1- m2- mc- m1+ m2+ mc+

LC1 1 0 5,37 -15,73 17,04 8,78 -15,46 0 5,37 -15,73 17,04 8,78 -15,46

LC1 2 15,32 19,72 -34,61 19,29 14,89 -34,61 15,32 19,72 -34,61 19,29 14,89 -34,61LC1 3 20,37 24,31 -37,97 17,6 13,66 -37,97 20,37 24,31 -37,97 17,6 13,66 -37,97

LC1 4 20,38 25,18 -35,29 14,91 10,11 -35,29 20,38 25,18 -35,29 14,91 10,11 -35,29

LC1 5 18,58 25,07 -31,73 13,16 6,67 -31,73 18,58 25,07 -31,73 13,16 6,67 -31,73

LC1 6 16,58 25,62 -30,36 13,78 4,74 -30,36 16,58 25,62 -30,36 13,78 4,74 -30,36

LC1 7 0 -2,47 -27,44 32,06 9,85 -11,99 0 0 0 32,06 9,85 -11,99

LC1 8 7,47 18,18 -27,91 20,45 9,74 -27,91 7,47 18,18 -27,91 20,45 9,74 -27,91

LC1 9 18,85 27,48 -31,53 12,68 4,05 -31,53 18,85 27,48 -31,53 12,68 4,05 -31,53

LC1 10 21,79 32,58 -29,65 5,42 0 -30,14 21,79 32,58 -29,65 5,42 0 -30,14

LC1 11 20,33 35,78 -26,79 1,07 0 -30,4 20,33 35,78 -26,79 1,07 0 -30,4

LC1 12 16,07 38,62 -25,51 2,98 0 -32,16 16,07 38,62 -25,51 2,98 0 -32,16

LC1 13 0 -5,77 -38,35 41,67 9,81 -7,36 0 0 0 41,67 9,81 -7,36

LC1 14 0 11,56 -17,93 19,42 4,57 -17,63 0 11,56 -17,93 19,42 4,57 -17,63

LC1 15 13,87 24,57 -20,49 3,7 0 -21,66 13,87 24,57 -20,49 3,7 0 -21,66

LC1 16 19,31 32,66 -19,57 -5,33 0 -27,06 19,31 32,66 -19,57 0 0 0

LC1 17 18,47 38,52 -17,79 -6,91 0 -32,3 18,47 38,52 -17,79 0 0 0

LC1 18 12,78 43,14 -16,85 -2,31 0 -36,76 12,78 43,14 -16,85 0 0 0

LC1 19 0 -7,29 -44,11 45,31 8,56 -2,47 0 0 0 45,31 8,56 -2,47

LC1 20 0 4,7 -13,69 15,23 0 -6,25 0 4,7 -13,69 15,23 0 -6,25

LC1 21 7,2 18,76 -7,07 -2,85 0 -16,04 7,2 18,76 -7,07 0 0 0

LC1 22 14,1 28,37 -6,82 -10,23 0 -25,43 14,1 28,37 -6,82 0 0 0

LC1 23 13,95 35,89 -6,22 -10,54 0 -33,08 13,95 35,89 -6,22 0 0 0

LC1 24 7,78 41,62 -5,87 -4,62 0 -38,9 7,78 41,62 -5,87 0 0 0

It is obvious from the table, that design forces are identical in both trees.

3.2.2.2.2.2 Two p erpend icular reinfo rcement direct io ns , ident ical with X and Y

axes of LCS, shear effect cons idered

Same settings as in previous chapter will be used here with one exception. Influence of tensionforce is considered for shear reinforcement. That means that for attribute Shear effect control 6.2.3(7)is set to shear effect considered unconditionally possibility in concrete setup dialog.



51






LC1 1 0 5,37 -15,73 17,04 8,78 -15,46 1,14 12,19 -19,1 16,11 10,66 -11,83

LC1 2 15,32 19,72 -34,61 19,29 14,89 -34,61 16,36 19,66 -34,49 20,44 14,96 -34,73

LC1 3 20,37 24,31 -37,97 17,6 13,66 -37,97 20,01 25,22 -36,8 18,42 15,74 -39,14

LC1 4 20,38 25,18 -35,29 14,91 10,11 -35,29 20,09 27,35 -34,63 15,29 12,94 -35,95

LC1 5 18,58 25,07 -31,73 13,16 6,67 -31,73 18,47 27,86 -31,52 13,27 9,68 -31,95

LC1 6 16,58 25,62 -30,36 13,78 4,74 -30,36 16,7 31,28 -30,59 13,66 10,15 -30,12

LC1 7 0 -2,47 -27,44 32,06 9,85 -11,99 0 1,36 -25,5 33,34 8,98 -6,64LC1 8 7,47 18,18 -27,91 20,45 9,74 -27,91 10,84 18,74 -28,88 22,85 9,33 -26,95

LC1 9 18,85 27,48 -31,53 12,68 4,05 -31,53 19,83 27,09 -30,23 14,96 4,95 -32,82

LC1 10 21,79 32,58 -29,65 5,42 0 -30,14 21,52 32,98 -28,07 8,29 0 -31,29

LC1 11 20,33 35,78 -26,79 1,07 0 -30,4 20,08 37,19 -26,18 2,19 0 -29,74

LC1 12 16,07 38,62 -25,51 2,98 0 -32,16 16,42 42,86 -26,16 3,76 0 -28,99

LC1 13 0 -5,77 -38,35 41,67 9,81 -7,36 0 0 0 45,64 8,54 -3,65

LC1 14 0 11,56 -17,93 19,42 4,57 -17,63 2,78 13,57 -18,56 23,08 4,16 -16,69

LC1 15 13,87 24,57 -20,49 3,7 0 -21,66 16,19 24,35 -20 6,64 0 -22

LC1 16 19,31 32,66 -19,57 -5,33 0 -27,06 19,92 32,35 -18,31 0 0 0

LC1 17 18,47 38,52 -17,79 -6,91 0 -32,3 18,27 38,92 -16,98 0 0 0

LC1 18 12,78 43,14 -16,85 -2,31 0 -36,76 13,31 45,87 -17,74 0 0 0

LC1 19 0 -7,29 -44,11 45,31 8,56 -2,47 0 0 0 51,31 7,98 -1,19

LC1 20 0 4,7 -13,69 15,23 0 -6,25 0 5,24 -9,48 19,71 0 -5,98

LC1 21 7,2 18,76 -7,07 -2,85 0 -16,04 10,16 18,7 -6,95 0,18 0 -16,07

LC1 22 14,1 28,37 -6,82 -10,23 0 -25,43 15,52 28,19 -6,4 0 0 0

LC1 23 13,95 35,89 -6,22 -10,54 0 -33,08 14,18 35,77 -5,73 0 0 0

LC1 24 7,78 41,62 -5,87 -4,62 0 -38,9 8,49 42,69 -6,72 0 0 0

It is obvious from the table, that design forces are different in both trees. It is due to the fact thatin Concrete tree is tension force from shear stress considered. In this case it is necessary to make

check of inner forces only in Concrete tree.



52

3.2.2.2.2.3 Two p erpend icular reinforc ement d irect ions , rotated w ith 45 degrees

according to the LCS

First direction angle in Member data is set to 45 degrees and Rotation attribute in 2D Members – internal Forces properties in Results tree is 45 degrees as well. Influence of tension force is notconsidered for shear reinforcement. That means that for attribute Shear effect control 6.2.3(7) is set tono shear effect is considered possibility in concrete setup dialog.

Reinforcement and LCS directions Member 2D - Internal Forces attributes






LC1 1 0 3,87 -14,23 17,04 1,58 -8,25 0 3,87 -14,23 17,04 1,58 -8,25

LC1 2 0 17,8 -17,37 17,37 0 -17,8 0 17,8 -17,37 17,37 0 -17,8

LC1 3 0 22,59 -15,88 15,8 0 -22,52 0 22,59 -15,88 15,8 0 -22,52

LC1 4 0 23,24 -12,97 12,76 0 -23,03 0 23,24 -12,97 12,76 0 -23,03

LC1 5 0 22,88 -10,97 10,39 0 -22,3 0 22,88 -10,97 10,39 0 -22,3

LC1 6 0 23,31 -11,46 10,23 0 -22,07 0 23,31 -11,46 10,23 0 -22,07

LC1 7 0 -3,08 -26,84 32,06 20,07 -22,21 0 0 0 32,06 20,07 -22,21

LC1 8 0 14,72 -16,99 17,33 0 -15,06 0 14,72 -16,99 17,33 0 -15,06



54



In this case results will be different in both trees. Results in Result tree can‟t be “fixed“ with LCSrotation or by adjusting Rotation attribute. General transformation would must have been used .In thiscase it is necessary to make check of inner forces only in Concrete tree.

3.2.2.2.3 Determinat ion of design inn er forces in Resul ts and Concrete tree

As it was mentioned before, different methods are used for determination of design inner forcesin these two trees. For determination of design values in Results tree is used method described inliterature [2], while method described in literature [3] is used for determination of design values inConcrete tree. Demonstration of this determination will be presented on the same structure as wasused in chapter 3.2.2.2.2.1. It will be done for element number 10, where is the moment m1- (mxD-)

has the largest value.

3.2.2.2.3.1 Determinat ion of desig n inner forc es in Resul ts tree

Value Conditions and formulas Calculation

mxD-

(1) mxymx if mymx and mxymx

(2) mxymx if mymx and mxymy

(3) 0 if mymx a mxymx

(4) my

mxy

mx

2

if mymx and mxymy

mx =6,96 kNm < my = 17,75 kNmmx =6,96 kNm > -|mxy| = -14,83 kNmmy =17.75 kNm > -|mxy| = -14,83 kNm

Condition (1) fulfilled, then:

8314956 ,, mxy mx mxD

mxD- =21,78 kNm

myD-

(1) mxymy if mymx and mxymx

(2) mxymy if mymx and mxymy

(3)mx

mxymy

2

if mymx and mxymx

(4) 0 if mymx and mxymx



83147517 ,, mxy my myD

myD- =32,58 kNm

mcD-

(1) mxy*2 if mymx and mxymx

(2) mxy*2 if mymx and mxymy

(3)mx

mxymx

2

if mymx and mxymx



831422 , mxy mcD



55

(4)my

mxymy

2

if mymx and mxymx mcD- =-29,66 kNm

mxD+

(1) mxymx if mymx and mxymy

(2) mxymx if mymx and mxymx

(3)my

mxymx

2

if mymx and mxymy

(4) 0 if mymx and mxymx

mx = 6,96 kNm < my = 17,75 kNmmx = 6,96 kNm < |mxy| = 14,83 kNmmy = 17.75 kNm > |mxy| = 14,83 kNm


7517

8314966

22

,

,

,

my

mxy mx mxD

mxD+ = 5,43 kNm

myD+

(1) mxymy if mymx and mxymy

(2) mxymy if mymx and mxymx

(3) 0 if mymx and mxymy

(4)mx

mxymy

2

if mymx and mxymx


Condition (3) fulfilled, then:myD+ =0 kNm

mcD+

(1) mxy*2 if mymx and mxymy

(2) mxy*2 if mymx and mxymx

(3)my

mxymy

2

if mymx and mxymy

(4)mx

mxymx

2

if mymx and mxymx



7517

83147517

22

,

,

,

my

mxy my mcD

mcD+ = 30,14 kNm

3.2.2.2.3.2 Determinat ion of desig n inner forc es in Conc rete tree

According to this method basic inner forces and their directions must be determined first. In SciaEngineer are these magnitudes presented in Results in 2D Members – Inner forces item, if the type ofthe value is selected to Basic magnitudes possibility.

Value Formulas Calculation

zDetermination of effective height and lever arm.z = 0,9d

dlo = dup= 200-45 = 155mmz = 0,9·d = 0,9·155== 139,5mm

nx,lo(up) ny,lo(up)

nxy,lo(up)

Determination of normal forces for lower and uppersurface in LCS

nx.up = -49,89kNny.up = -127,24kNnxy.up = 106,38kN

nx.lo = 49,89kNny.lo = 127,24kNnxy.lo = -106,38kN

n1,lo(up)

n2,lo(up)

Determination of principal forces for lower surface n1,lo = 201,7 kNn2,lo = -24,55 kNn1,up = 24,55 kNn2,up = -201,37 kN



56

α,lo(up)

Determination of principal forces directions αlo = -55 degαup = 35 deg

αlc,lo(up) Determination of compression strut angle in concrete. Theangle of compression strut is optimised to allow thesmallest force in compression strut.

αlc,lo = 45degαlc,up = 129deg

α j,lo(up)

Determination of angle between the reinforcementdirection and the direction of principal forces.α1,lo = αr1,lo - αlo

α2,lo = αr2,lo - αlo

α3,lo = αrc,lo - αlo

α1,lo = 0 - (-55) = 55deg

α2,lo = 90 - (-55) = 145degα3,lo = 45 - (-55) = 100degα1,up = 0 - 35 = -35deg

α2,up = 90 - 35 = 55degα3,up = 129 - 35 = 94deg

n j,-(+)

Determination of design forces in reinforcement‟sdirection, i.e. in direction of compression strut. Baumanntransformation formula, adjusted for two reinforcementdirections, is used.

n1- =156,2 kNn2- =233,5 kNnc- =-212,6 kNn1+ =39 kNn2+ =-0,09 kNnc+ =-216,03 kN

m j,-(+)

While type of the structure is set to Plate, design forceswill be transformed into moments by formula

m =n·z

m1- = 21,79 kNmm2- = 32,58 kNmmc- =-29,66 kNm1+ = 5,44 kNmm2+ = -0,014 kNm

mc+ =-30,14 kN

Note

Formulas in the tables are usually named for lower surface only, but same formulas withchanged indexes stands good for the upper surface.

3.2.2.2.4 Determinat ion of design inn er forces for General XYZ stru cture

Normal forces in reinforcement and compression strut directions for both surfaces are presentedwhen structure type is set to General XYZ possibility. Sometimes, for further checks, it is necessary toreplace these normal forces with the effect of moment and normal force, which are located in the



57

centre of gravity of the member. If reinforcement directions for both surfaces are identical, then it ispossible for determination of these effect use formulas bellow.

m j =(d j- – 0,5h)·n j- + (0,5h - d j+)·n j+

n j =n j- + n j+

Where j stands for reinforcement directiond j-(+) stands for effective height in j reinforcement direction for lower (-) and upper (+)surfacen j-(+) stands for values of normal forces in reinforcement direction for lower (-) andupper (+) surface, presented in numerical values

If reinforcement directions for both surfaces are not identical, then the determination is moredifficult, because it is necessary to calculate normal forces for upper surface (nvj+) and lower surface(nvj-) separately. Then the determination uses formulas bellow.

m j- =(d j- – 0,5h)·n j- + (0,5h - d j+)·nvj+ (moment in lower reinforcement direction)

m j+ =(0,5h - d j+)·n j+ + (d j- – 0,5h)·nvj- (moment in upper reinforcement direction)

n j- =n j- + nvj+ (force in lower reinforcement direction)

n j+ =n j+ + nvj- (force in upper reinforcement direction)

Recalculation will be done for identical reinforcement directions for both upper and lowersurface and structure from chapter 3.2.2.2.2.1. Only Structure type of this project will be changed fromPlate XY to General XYZ. After the change, these design magnitudes will be displayed in Concretetree.

Recalculation of normal forces for both surfaces to forces which take place in the centre of thegravity will be done for mesh element number 10.


d j

Determination of effective height.d j = h- c j – 0,5dsj

d1= d1- = d1+= 200-35-0,510 =160mmd2= d2- = d2+= 200-45-0,510 =150mm



58

m1

n1

Determination of normal forces in reinforcementdirection 1 (0 degree).m1 =(d1 – 0,5h)·n1- +(0,5h- d1)·n1+

n1 =n1+ + n1-

n1+= 146,5kN/mn1-= 53,1kN/mm1 = 5,6kNm/mn1 = 199,6kN/m

m2

n2

Determination of normal forces in reinforcementdirection 2 (90 degree).

m2 =(d2 – 0,5h)·n2- +(0,5h- d2)·n2+n2 =n2+ + n2-

n2-= 219,8kN/mn2+= -19,73kN/m

m2 = 11,97kNm/mn2 = 200,1kN/m

3.2.2.2.5 Determinat ion of inner forces with inf luence of shear force

As it was mentioned in previous chapters, values of design magnitudes in Concrete tree aredependable whether the influence of tension force from shear is taken into consideration. Thisinfluence may be changed in Concrete setup dialog under Concrete > ULS > Shear > 2D Structures. Ifthis influence is taken into consideration, then resultant of tension force from shear (value Ftdj) isincremented to the resultant of principal forces. More on this issue can be found in chapter 3.2.2.1.

Again, calculation will be done for structure from chapter 3.2.2.2.2.1 for mesh element number10, where the design moment m1- (mDx-) reaches its maximum.


vd Determination of resultant shear force.

vd = 10,79 kN

Determination of resultant shear force direction.

β = 56,53 deg

vdj,lo(up)

Recalculation of resultant shear force to the principal

forces directions, where 50% will be added to upperand 50% to lower surface.

vd1,lo = -1.98kN

vd2,lo = -5kNvd1,up = 5kNvd2,up = -1,98kN

Ftdj,lo(up)

Determination of tension force increment from shear.

Ftd1,lo= -4,95 kNFtd2,lo= 12,55 kNFtd1,up= 12,55 kNFtd2,up= -4,95 kN

n1,lo(up)

n2,lo(up)

Principal inner forces with shear increment

For recalculation of principal force is compression strutangle determined and design values calculated.

n1,lo = 199,7 kNn2,lo = -12 kNn1,up = 37,1 kNn2,up = -206,32 kN

Note

During calculation of tension force from shear according to the EN 1992-1-1, chapter 6.2.3 (7) iscondition MEd/z + Ftd ≤ MEd,max/z being checked.

Resultant shear force is presented directly in Design magnitudes in Concrete tree as vd andalso in Results tree in 2D Members – Inner forces, for attribute type forces set to Principal magnitudespossibility. It is named as qmax-b.



59

Resultant shear force angle is presented in Results tree under 2D Members – Inner forces, forattribute type forces set to Principal magnitudes possibility. It is named as beta. In Concrete tree it canbe found under Member design ULS, for attribute output set to Advanced or Detailed, for Asw value.

Shear strut inclination (angle ) is displayed in Concrete tree it can be found under Memberdesign ULS, for attribute output set to Advanced or Detailed, for Asw value.

3.4.3 ULS

3.4.3.1 Theoretical background

Reinforcement concrete 2D structures handled by Scia Engineer (Walls, Plates and Shells) areusually reinforced by two systems of steel reinforcement nets consisting of 2 or 3 reinforcementcourses situated more or less close to both faces of the 2D structure. Scia Engineer puts no principalrestrictions upon the absolute position of reinforcement courses within the cross-section, its axialconcrete cover describes the position of each reinforcement course. However, there are relativerestrictions: all concrete covers must fulfil some rules to prevent ambiguousness of the geometric

definition of the design task. These rules are described in the part of the Scia Engineer manual. Yet itmust not be forgotten that there might be other, more complex situations in the cross-section thansymbolised by the figure 1:

o The crossing reinforcement bars of individual layers do not need to touch each other; theymight be placed at larger distances from each other within the cross sections.

o The surfaces of bars are usually corrugated so that there is, as a rule, a greater distancebetween two crossing bars than expressed by their characteristic bar diameters.

o Last but not least, in very thick plates, e.g. foundation slabs, two layers or bars bundles inone layer are used, so that the representative axial distance (of the point of gravity) and therepresentative bar diameter itself are two independent quantities and qualities, which mustbe defined independently on input in order to carry out reliable analysis.

In Walls, being (theoretically) subjected to forces acting in their planes, the (by definitionsymmetric) positions of reinforcement nets are of no static interest; however, the cross-sectiongeometry (concrete covers and bar diameters) is of interest for the Crack Proof algorithm (ifimplemented). Thus, the Wall design branch comprises the same cross-section input dialog as thePlate and Shell models.

In Plates and Shells, on the contrary, the reinforcement covers estimate the effective staticheight of the reinforcement courses in the cross-section subjected (also) to bending, thus havingfundamental meaning for the design process. The covers are related to the faces. Thus, it isnecessary to distinguish them clearly from each other. Because Plates are (still) the structural typemost frequently used in the practice, Scia Engineer use originally common terms distinguishing thetwo faces: upper and lower face. These concepts have to be given mathematically exact meaning,

which makes them acceptable for Shells, too: the lower face is the structural plane edge in direction ofthe positive planar axis Zp; the upper face is opposite to it. Finally, the symbol -Zp appears generallyin the output protocol instead of the term upper face; the symbol +Zp symbolises lower face. In Walls,



60

there is no need of distinguishing both structural edges; nevertheless, out of formal reasons(simplification), if the concept of upper face appears in connection with Walls it means both faces.

The reinforcement courses are, correspondingly to their relative position in the cross-section,called the outer(most), middle (if any) and inner(most) ones. This verbal distinguishing is in themathematical formulation replaced by assigning them the ordinal numbers 1, 2 and 3 (if threereinforcement courses are specified at all). The same double identification may be given to otherassociated terms like reinforcement angles, design forces, effective static heights, inner forces levers,etc. So we can say, e.g., about reinforcement angle α, β, γ meaning the same , when alternatelyindicating α1, α2, α3. There is no indication that this ambiguity of terms should cause confusion; as afact, there is no ambiguousness for the correspondence of both systems of denotation is clearlydefined.

Note that each reinforcement course can hold up to 10 reinforcement layers.

The terms of the reinforcement concrete theory are used in accordance with the generalstructural use or they strictly follow the rules postulated by the Norms implemented in Scia Engineer.However, for Scia Engineer deals with several national codes, it is probable that this or that term orformulation would appear somewhat unfamiliar to some readers focused onto the use of one codebranch only. It is hardly possible to create a manual text on such special topic for international use

being in all respects verbally fully conform to every country‟s verbal usage. In doubts, the terminologyof Eurocode will be given preference.

The design task and the output of results are performed in basic and derived units of the SIsystem.

3.4.3.1.1 Wall Desig n

Once a positive design force is assigned to its associated reinforcement course, thecorresponding statically required reinforcement amount ai is calculated from the elementary relation:

a i = n i /σsd (i = 1,2 (,3)) [m²/m] (6)

(6) has symbolic meaning only, as we do not want write down at this stage all exact calculationrules for Norms implemented in NEDIM. The symbol σsd stands for effective design steel strength.Both ni and σsd may be, according to the actual Norm, charged with security coefficients. We are notgoing to discuss the problem of 1D reinforcement design; the NEDIM algorithm strictly follows specialrules stipulated by national Norms and associated Standards, as far as they are applicable to the 2Ddesign.

The virtual stiffening strut of the heterogeneous concrete-steel continuum represents quite asubstantial issue of the design process. While it is possible (unless the upper reinforcementpercentage limit has been exceeded) to improve the bearing capacity of the cross-section on the sideof the reinforcement by augmenting its amount, the bearing limit of the concrete strut is given by theheight of the cross-section and the quality of concrete only; thus its limits are predestined by the input

data. The concrete strut bearing capacity condition is described by the following relation:

–n3 <Ac σcd (9)

In (9) σcd represents the effective concrete design pressure strength and Ac – the concretearea of reference. In NEDIM it is generally assessed on the base of 80% of the standard designconcrete pressure strength. This reduction follows the recommendation of Schleich and Schäfer inliterature [2] : the compression strength of concrete is unfavourably affected by transversal tensionstresses which produce cracks, parallel to the direction of pressure; this is typically the stress situationof the stiffening strut. For cracks parallel to the direction of strut, the reduction coefficient kc = 0.80 isstipulated, which is identical with the NEDIM default, whereas for cracks crossing the strut directionthe value kc = 0.60 is specified! The cross-section area Ac in (9) is for Walls taken as the full unityrectangular cross-section h × 1.

Once a design pressure force ni, assigned to a reinforcement direction i, is known thecompression reinforcement is calculated acc. to the following general formula:



61

ai = ( –ni –Ac σcd) / σscd (i = 1,2 (,3)) [cm2/m] (10)

In (10) σscd represents the effective design compression strength of reinforcement steeldifferently to (6), where σsd denotes the design tension strength; Ac is the gross section area. NEDIMchecks if the steel attains the pressure yield strain; if not, σscd reflects the actual strain level. SomeNorms (ÖNORM B 4200, CSN/STN 73 1201, GBJ 10-89) stipulate different values of steel strength intension and pressure. NEDIM follows this idea by enabling different definitions of tension and pressuresteel strength to all Norm branches.

3.4.3.1.2 Plate Desig n

In the Wall model, dealt with in the preceding paragraph, the inner design forces produceconstant stresses all over the cross-section; thus, there is no necessity to examine the stressdistribution within the cross-section. In contrast to the Wall model, for bending in Plates it is afundamental characteristic that the stresses are non-linearly and discontinuously distributed over thecross-section. Since all of the national Norms implemented in NEDIM exclude the tensional bearingcapacity of concrete (ULS), in the tension zone (below“ the neutral axis) the only bearing material isthe reinforcement steel. The resistance of concrete is exploited in the pressure bending zone only.

Figure 3 shows symbolically one possible equilibrium situation in the reinforcement courses 1

and 2 (Fig. 3a,b) as well as in the concrete stiffening strut, i.e. in virtual course 3 (Fig. 3c). In Fig. 3,the face subscript is generally omitted, for the discussion is equally valid for both faces. Thedistribution of the concrete pressure stress in Fig. 3 is not related to a special Norm. However, theNorms implemented introduce different basic notions of the concrete pressure stress distribution. Theassumption of the pressure stress distribution is in affinity to the σ-ε diagram of the concrete material.

EUROCODE 2 allows for all national Norm assumptions. Actually, NEDIM keeps to theparabola-constant concrete pressure stress distribution assumption. EC 2 introduces a new approachto the shear proof, which explicitly operates with the notion of the virtual (shear) strut. It alsoformulates a new approach to the consideration of the interaction (m/n) ⇔ v. In compliance with thisnotion, the shear force may cause an increase of the required net reinforcement. This phenomenonwas investigated by the Author of NEDIM and 1999 implemented into the EC 2 design branch as wellas into all other design branches following the same (or similar) approach. For more detail on this

phenomenon, named Shear Effect by the Author of NEDIM, see paragraph Advanced notes on"Shear Effect".

EN 1992-1-1:2004 is the EC 2 novella of the preliminary European Norm ENV 1992-1-1:1991.Extensive modifications to the original text have been taken in all sections. Especially the paragraphson shear proof, crack control and minimum reinforcement control have been expanded and diversified,e.g. (a) all "reasonable" assumptions of concrete stress-strain diagram are allowed, namely the threebasic cases: pressure block, linear-constant and parabola-constant. For the block distribution,restrictions to height and stress have been introduced: λx and η fcd ; (b) the recommended value ofthe strength reduction coefficient in f cd = αcc f ctk,0.005 / γc is αcc = 1.0 (for the EC2 Norm family is typicallyαc = 0.85); (c) the strength reduction coefficient ν1 in the formula for the shear strut resistance vRd,max ismore diversified and the coefficient αcw of the same formula expresses the effect of normal stress uponvRd,max on three intensity levels; (d) the crack calculation formula (direct control) resembles that of DIN

1045-1, however, the crack distance formula depends here on 4 parameters.

In Plate models the statically required tension reinforcement of a design course is calculated bythe basic formula :

ai =mi /(zi σs,eff ) (i = 1,2 (,3)) [cm²/m] (11)

In (11) the special moment symbol mi for the design moment associated with the reinforcementcourse is substituted for the common symbol n i for design force in order to avoid confusion. The stresssymbol σs,eff has a quality comparable with that introduced by (6) for Walls; it again represents theeffective design steel strength for all Norms.

The inner forces lever zi in (11) makes out the formal difference of (6) and (11); factually, thereis no difference between them, since the quotient mi /zi equals the steel design force Zi, whichconstitutes with the opposing concrete pressure zone resultant force Di the force couple representingthe design bending moment mi; thus, we formally obtain (6) by substituting ni = Zi =mi /zi into (11).



62

(11) reveals the fundamental meaning of the inner forces lever z for the design algorithm. As afact, by introducing the transformation formulae (3) for Shells it was made clear enough that theknowledge of the proper value of inner forces lever is indispensable for correct reinforcement design.

In NEDIM the inner forces lever z is calculated by the following procedures:

o For DIN 1045 and ÖNORM B 4200 interpolation formulae for the value of z weredeveloped. The maximum approximation error amounts up to 2%, however.

o For all other Norms (following the first two on the time scale) analytic integrationprocedures for the basic assumptions of stress block, linear-constant and parabolaconstant stress function were devised; they yield exact pressure integrals.

The stiffening function of the concrete medium is not as transparent in Plates as in Walls. InPlates we have to do with force couples representing inner bending moments. The concrete pressurestresses are not constantly distributed over the cross-section. Thus, a direct application of theconcrete strut bearing capacity limit condition (9) is not possible in Plates. NEDIM had used someapproximate approaches until the best and perhaps most simply formulation of the strut bearingcapacity limit was found. Instead of describing the strut control by mathematical terms, a verbalexplanation of the matter relating to Fig. 3c and Fig. 3d is preferred :

o

In Plates the strut design force n3 means the force couple of m3. From Fig. 3c it is obviousthat m3 causes basically the same kind of stresses in its direction as the other two reinforcementdesign moments m1 and m2, however, with exchanged faces (i.e. m3 is of opposite sign). In this casewe are not interested in analysing the situation on the opposite face; the state of stress in the stiffeningstrut bending pressure zone is of interest. What is the limit condition of the strut bearing capacity?What calculation value of stress integral force D3 is to be taken into account?

o The answer to this fundamental question is given by Fig. 3d : NEDIM allows for themaximum height of the bending pressure zone xmax in compliance with the design algorithm applied. Ifat this state of stress the equilibrium in the cross-section is not yet attained, i.e. would strengthening ofthe pressure zone by (pressure) reinforcement be formally required, then this is considered by NEDIMas an unambiguous indication of the bearing capacity of the stiffening strut being exceeded. Thecross-section is non-designable due to concrete failure.

Till the mid of 2007 it had not been known to the Author of NEDIM that any competing softwarewould deal with this problem at all. Neither Norms nor theoretical publications on reinforced concretedesign do not care about the state of concrete in a heterogeneous concrete-steel 2D medium. SomeNorms give “standardized” recommendations as to the geometrical arrangement of reinforcement inreference to the directions of the principal moments. They are concerned with stress situations whichare typical for corners of floor slabs etc.

Figure 3 Equilibrium of design inner forces in a Plate cross-section : (a) reinforcement course1; (b) reinforcement course 2; (c) concrete stiffening strut – course 3; (d) strain situation in thestiffening strut (bearing ability proof).



63

3.4.3.1.3 Shell Desig n

In the design of Shells, the ideas and procedures of both the design of Walls and the design ofPlates are combined. The Norm requirements and restrictions, which seldom are formulatedindividually for Shells, must both be considered both for Walls and Plates. Thus, the Shell design isthe most complex design model dealt with by NEDIM.

From the mechanical point of view, the stress-strain situation in cross-sections of Shells may

develop from a typical "Wall pattern" with constant stress distribution to a "Plate pattern" withcharacteristic non-linear concrete pressure stress distribution over the bending pressure zone alongwith a cracked region "below" the neutral axis where there the reinforcement resists the stresses frominner forces. The special situation depends, however, on the character of external load as well as onthe boundary conditions of the analysis model.

NEDIM has to manage all possible stress situations arising between the Wall type and the Platetype state of stress using one unique design model to be able to produce results consistent also withquantitatively slowly yet qualitatively abruptly changing states of stress. It would be unacceptable tohave a Shell design model which, on one side, yields results fully identical with a Plate solution whenthere is pure bending acting, i.e. the membrane forces being zero, yet produces, on the other side,obviously distorted results whenever the membrane forces differ slightly from zero. Little change inloading must imply little change in the reinforcement design results.

As a fact, all Norms were drafted focusing to the problems of 1D structural members, i.e. beamsand columns. In NEDIM, many requirements and restrictions had to be given a reasonableengineering interpretation or extrapolation to fit to the special character of the 2D structures. Thereinforcement at both faces consists of two mutually independent nets with 2 or 3 reinforcementcourses in generally different directions. Thus, in Shells it is not possible to proceed by simply usingthe solutions of the reinforcement concrete design of beams.

NEDIM creates two sets of transformed design forces assigned to individual reinforcementcourses and/or the stiffening concrete strut at both faces of the analysis model. The procedure goesacc. to the formulae (4). In the assessment of the inner forces lever z the Shell design procedureresembles the Plate design. By creating equivalent inner forces {nx, ny, nxy}±Zp and their transforms{n1d, n2d, n3d} NEDIM follows a typical Wall design approach. Formally, we get two systems of design

situations at both Shell faces which must be managed in two algorithmic steps in every cross-sectionby considering the situation on the other face. In this sense, the Shell design is organized like thePlate design.

Fig. 4c symbolizes the Shell design : there is a design force nd (subscript i = 1,2,3 is omitted)assigned to a reinforcement course at the upper face (the same procedure applies to the lower face).The symbol nd,opp is used for the virtual design force at the opposite face acting in the same directionas at the actual face; it is unimportant if there is a congruent reinforcement course parallel to that atthe actual face or not. The normal force in this cross-section is in Fig. 4c denoted as nvirt (virtualnormal force). The virtual bending moment mvirt is defined complementary to nvirt. Thus, the virtualnormal force eccentricity (241), (242) can be estimated.

Fig. 4c demonstrates also the fact that the design at a Shell face is typically Wall design;

however, the design force nd is not applied to the total cross-section area as in Walls (Fig. 4a), yet tosome portion of it : Ac,eff = heff × 1.0. NEDIM assigns Ac,eff basically in accordance with thesuggestions of Baumann.



64

Fig. 4 Comparison of design situations in three NEDIM design models : (a) Wall : totalcross-section under tension/compression design force nd; (b) Plate : design bending moment mdacting over the effective height d; (c) Shell : combined action of bending moments/membrane forcesexpressed by nd : design normal force at active face; nd,opp : design normal force at passive face;nvirt : total virtual normal force in cross-section; mvirt : virtual bending moment conjugated with nvirt

In the area assignment formula

Ac,eff = kAAc (12)

the value of the coefficient k A varies in the range [0.35, 0.42] in stress situations with neutralaxis within the cross-section. Principally, this approach may be compared with the approximation ofthe stress distribution in the bending pressure zone by the pressure block (see above). Recenttheoretical and algorithmic enhancements of NEDIM made it possible to distinguish efficiently betweenbending-like and membrane-like stress situations in Shells, thus enabling to apply the full cross-section, i.e. k A = 0.50, to the virtual strut proof when the strut cross-section is over-pressed.

The proof of the virtual strut resistance is formally governed by (9), like for Walls. However,instead of the total cross-section area Ac , the effective one-face area Ac,eff (12) is to substitute into (9).

Note

For more information about this chapter see literature [3], where more detailed description maybe found.



65

3.4.3.2 2D Structures detailing

Sometime amount of statically needed reinforcement is not determining for finally designedreinforcement and different check come in place. These checks may be switched off/on or adjusted inconcrete setup dialog in Detailing provisions chapter and under Calculation chapter.

Minimum transverse reinforcementMinimal amount of transverse reinforcement, determined as a percentage of mainreinforcement. This check has two options.

o Inactive reinforcement excluded (amount of transverse reinforcement is calculated onlyfrom statically needed reinforcement)

o Inactive reinforcement included (amount of transverse reinforcement is calculated from

whole reinforcement)

Default value = 20%.

Minimum constructive reinforcementMinimum percentage of longitudinal reinforcement, unconditionally. Default value = 0%.

Minimum pressure reinforcementMinimal part of concrete cross-section that should act as compression reinforcement. Defaultvalue = 0%.

Maximum percentage in bending pressure zonePlates only. Definition of the maximum percentage of reinforcement in the bending pressure

zone related to the concrete pressure force. Default value = 50%.



66

Min tension reinforcement at face +ZpShells and Plates only. Minimum percentage of tension reinforcement at the surface withpositive Z co-ordinate (in the local coordinate system of the 2D member). This check has twooptions.

o Automatic calculation of minimal tension reinforcement (evaluated with equation to 9.1N)

o Min. tension reinforcement percentage (direct percentage of area of concrete cross-

section, new input option Min. tension reinf. Appears, when his option is selected).Default value = 1%.

Min tension reinforcement at face -ZpMinimum percentage of tension reinforcement at the surface with negative Z coordinate (in thelocal coordinate system of the 2D member), or at each of the Wall faces. This check has twooptions.

o Automatic calculation of minimal tension reinforcement (evaluated with equation to 9.1N)

o Min. tension reinforcement percentage (direct percentage of area of concrete cross-section, new input option Min. tension reinf. Appears, when his option is selected).Default value = 1%.

Max degree of reinforcementMaximal part of concrete cross-section that should act as reinforcement. Default value = 4%.

Min shear reinforcementMinimal part of concrete cross-section that should act as shear reinforcement. Default value =0%.

Minimal bar distanceDisplays and determines minimal bar distance. Default value = 0,05m.

Maximal bar distanceDisplays and determines maximal bar distance. Default value = 0,2m.

There are two more reinforcement amount control checks. They are located under Concrete >General > Calculation > 2D structures.

Req,shear reinforcement > c –s height >= 20cm A 2D member is provided with shear reinforcement only if the thickness of the member is higherthan 200mm. If it is less, then the shear reinforcement will not be designed and calculation

finishes with error message. (EN 1992-1-1:2004, §9.3.2(1))



67

Structural reinforcement of deep beamsIf the check is active, then construction reinforcement for deep beams will be taken intoaccount. (EN 1992-1-1:2004, §9.7.1)

3.4.3.3 Reinforcement design workflow

We can demonstrate the basic possible workflow for reinforcement design on example similar tothe previously used for demonstrating internal forces. It is a concrete plate defined in XY project,supported according to the picture. It is made from concrete C25/30 and is 200 mm thick. It is loadedwith self weigh in LC 1 and with constant surface load of 10KN/m 2 in LC2. Results will be described oncombinations which contain both previous load cases.

The reinforcement design will be shown only for lower reinforcement in direction of y axis of themember LCS, where we expect more amount of reinforcement. We need also redefine design defaultssettings, where the reinforcement 1 direction is similar with the X axis of the member LCS. This will bedone by defining member data and setting Layer angle parameter for first direction to 90 degrees. Thislayer will be now closer to the surface and will decrease amount of designed reinforcement little bid.We could change the reinforcement direction also by adjusting first direction angle and rotating thewhole reinforcement system.



68

On the picture below is magnitude of m1-, which will be determining for reinforcement design.We will use location In nodes, avg. on macro and for presentation isobands will be used.

Now we are ready to run ULS reinforcement design by adjusting ULS service properties andpressing Refresh action button. After this dialog with progress bar will appear and then final messagewith conclusion of the design will be displayed. After confirmation of this dialog, results will bedisplayed.



70

As we can see, no user reinforcement is defined yet. Therefore amounts of required, additionaland total reinforcement are equal.

We can also check the design values in preview window. User may switch to brief, detailed oradvanced mode, as we did in this example. We can see that maximal amount of reinforcement forlower surface and direction 1 is designed to 1295mm2/m.

Now user has to decide how he wants to reinforce the designed member. Whether he wants todefine each reinforcement layer manually or if he wants to use automatic definition of reinforcementfrom concrete member data. The second possibility is much common and more useful, so we will

show this one. User has to activate User reinforcement check box in concrete data first. This willenable him to define Basic distance of bars.

After this, amount of user reinforcement is determined directly from concrete member data anduser may simply adjust it by changing appropriate parameters (diameter, basic distance). Defaultvalues are loaded from Concrete setup dialog, which might be changed in Design defaults. Let‟s seethe differences in designed amounts of reinforcement just after activating the user reinforcementcheck box.



71

Required reinforcement User reinforcement

Additional reinforcement Total reinforcement

Now user reinforcement has non-zero values and accordingly to this change, amount ofdesigned additional reinforcement has been changed too. However the reinforcement amount definedis not sufficient enough, so we have to adjust the concrete data to fulfil the requirements. Before thiswe can check the preview window for more information.

It is clear from here, that additional amount of 902mm2/m has to be added to fulfil the requiredamount. Let‟s redefine the reinforcement diameter to 12mm and basic distance to 100mm. Now we

get these results.



72



From this results we can see, that defined reinforcement is sufficient on mostly whole 2Dmember area. However there is requirement for additional 174 mm2/m of reinforcement on the rightside of the designed member. We don‟t want to define more reinforcement for whole member areaand we will handle this requirement afterwards, by crating separate reinforcement polygon.

We can now proceed to crating practical reinforcement from user reinforcement. We have Userreinforcement check box active, so we can simply double click the Reinforcement 2D item in concrete

tree. Dialog below will be displayed and new practical reinforcement will be created from the userreinforcement previously defined by concrete 2D data.



73

After confirmation of this dialog, practical reinforcement is created and input into 2D member.Now we will also define additional reinforcement to cover the requirement on the right side of themember. Let‟s double click the 2D Reinforcement again and define it.

The designed 2D member has now two reinforcement polygons defined for lower surface anddirection 1. One is on whole 2D member and second one is only on the mentioned right side. Seepicture below.



74



At this time we have fulfilled the requirements for direction 1 in lower surface. No additionalreinforcement is needed and we are done. The upper surface and other directions might be handle thesimilar way, we have shown here.



76

Figure 13 Assumptions about crack propagation in 2D continuum : (a) Cracks perpendicular tothe direction of principal tension (trajectory reinforcement); (b) Cracks perpendicular to the direction ofprincipal tension, yet non-perpendicular to reinforcement courses; (c) Cracks perpendicular toreinforcement courses

The basic Problem of the 2D crack proof is obvious from the only formula dedicated by theNorms of the Eurocode family, here exemplary EN 1992-1-1:2004, formula (7.15)), to 2D structures:

sr,max = 1 / {cos φ / sr,max,1 + sin φ / sr,max,2} [mm] (271)



77

In (271) the symbols sr,max denote the maximum allowable or calculated, respectively, crackdistances, which play a distinguished role in most Norm proof theories (besides the crack widthwmax). The indices 1, 2 in (271) refer to 1st and 2nd reinforcement course, here assumingorthogonality.

Formula (271) and the following discussion refers to Fig. 13a,b. It relates the crack distancessr,max,1 und sr,max,2 to the direction of principal tension. The relation is, however, contradictory,what is obvious from Fig. 13b : the principal direction divides symmetrically the right angle betweenthe reinforcement directions 1 and 2, i.e. φ = 45°. From (271) follows thus sr,max = sr,1 / √2 ≈ 0,707 sr,1

(where sr,1 ≡ sr,max,1 = sr,max,2).

The announced contradiction consists in the fact that this most ineffective reinforcementgeometry, which causes about 200% of required as in ULS compared with the correspondingtrajectory reinforcement is assigned a significantly lower design crack distance sr,max (about 71%). Thisconclusion is unacceptable, obviously defective.

Thus, the NEDIM approach, as symbolized by Fig. 13c, proves, also from this point of view, tobe the most realistic in a 2D reinforced concrete continuum.

The proof methods are based on similar assumptions of crack propagation mechanism:

o High tension stress in a reinforcement bar causes high steel strain. The adhesion betweenconcrete and the reinforcement bar is disturbed, and cracks arise in the concrete continuum. Thehigher is the ratio of steel stress and the adhesion resistance, the wider become the cracks along thereinforcement bar. Thus, the higher the representative reinforcement diameter ϕ, the higher the ratio ofthe steel stress and the adhesion resistance, since the cross-section area of a bar grows with thesquare of ϕ whereas the surface of (unit length) of bar depends linearly on ϕ.

o Cracks arise not only close to the reinforcement bars yet merely between them. Thus, thetransversal distance s of reinforcement bars may also become a crucial factor of the cracks widthdevelopment. However, some Norms, like ÖNORM B 4700, do not introduce the distance s asindependent factor of the crack proof at all.

To limit or reduce, respectively, crack widths (as a fact, not the number of cracks but therepresentative crack width is of interest for the crack proof) the following measures have to be taken:

o Specification of as small reinforcement diameters ϕ as possible.

o Reduction of the representative (transversal) reinforcement bar distance s. However,there is a dependence between ϕ and s : with given ϕ and provided as, s is determined by

s = 0.25 × π × ϕ ² / as [mm] (272)

o Augmenting the statically required reinforcement amount. Due to this provision the steelstress in the serviceability state is lowered, thus the crack widths are reduced as direct

consequence. This steel amount control (augmenting of reinforcement amount from theULS design) is the basic concern of the NEDIM crack proof algorithm.

Practically, NEDIM follows a two-step thread : (a) ULS design, yielding statically requiredreinforcement amount; (b) SLS design, referring to the characteristic bar diameter ϕk and/or acharacteristic bar distance sk as specified by the user on input. NEDIM carries out the crack proofaccording to the Norm proof approach and increases the statically required reinforcement amountwhere it is needed to meet completely the crack proof requirements.

NEDIM, however, allows for merging of load cases for the ultimate and serviceability stateswithin a calculation process in order to enable the crack proof procedure outlined above. In thefollowing paragraphs it is shown that different attributes may be assigned to the load cases, inaccordance with the individual stipulations of the Norms.

In Chapter Program Theory and Algorithm in literature [1] the notion of the virtual cross-sectiondesign force nvirt was introduced. The effect of this algorithmic enhancement is, along with thatdiscussed with the shear proof and the minimum compression reinforcement, a consistent description



78

of the state of stress in the cross-section, especially in case of non-congruent reinforcement at bothfaces. Since most Norms consider the stress distribution pattern (bending ↔ centric tension) asimportant a factor of the crack development, the knowledge of nvirt is indispensable to reliable crackproof design. Upon the analysis types dealt with by NEDIM it has the following impact:

o Walls : the general inner forces vector (3) degenerates to

{ nx, ny, nxy } (281)

There is no use of nvirt, since nvirt ≡nd in this model. All design forces are membrane forces withzero eccentricity, causing either tension or pressure in the cross-section.

o Plates : the general inner forces vector (3) degenerates to

{ mx, my, mxy, vx, vy } (282)

Thus, instead of the design forces nd, design moments md and shear force vd are active in Platedesign. There is effectively no (virtual) normal force nvirt in pure flexural members, even if hyperbolic

cases suggest that such an interpretation of the rather complicated type of stress state may bediscussible: both reinforcement courses at upper/lower face appear to be under tension, thus theconclusion seems to be justified that there is a normal force action upon the cross-section. However,in such hyperbolic cases, the prevailing stress is shear, not tension, and that also the reinforcement is,effectively, subject to shear rather than to tension; the representative stress pattern in the designsection is thus the shear stress triangle. As a fact, it was made an attempt in NEDIM to deal with suchstates of stress as with “prevailing tension”. This had, however, serious consequences to the crackand shear proof results unacceptable crack reinforcement increments to statically requiredreinforcement were casually obtained.

o Shells : the general inner forces vector (3) applies to Shell design, rewritten here :

{ mx, my, mxy, vx, vy, nx, ny, nxy } (283)

Although the two-step reinforcement design (running separately for both faces) assigns a halfcross-section to each reinforcement course, the crack proof must take into consideration the totalcross-section, even if there is no congruent reinforcement at opposite (actually inactive) face. Theinformation needed is delivered by the virtual normal force nvirt and the complementary virtual bendingmoment mvirt.

All possible states of stress have to be correctly interpreted and managed by the NEDIM crackproof algorithm. As symbolized by Fig. 14, for the crack proof procedure it is not enough to determinetensile stresses at the actual face, yet also the stress pattern over the cross-section is of eminentimportance; especially, the s. c. “disconnection cracks” are of interest.



79

Figure 14 Typical stress patterns considered by NEDIM‟s crack proof procedure : (a) bendingcrack – neutral axis within cross-section; (b) disconnection crack due to tension force with loweccentricity; (c) over-pressed cross-section – no crack proof

According to the basic notion of EC 2 [9], §4.4.2 two possible crack proof strategies are atchoice :

o §4.4.2.3 : crack limiting without direct calculation. This method is almost identical to the

elementary crack limiting method stipulated by DIN 1045 [5]. By meeting therequirements of §4.4.2.3 the mean crack width will be limited to the value wk = 0.30 [mm].

o §4.4.2.4 : method of calculating mean crack width wk by formula (4.80) :

wk = β srm εsm (30)

with wk – calculation value of the crack width; β – security factor distinguishing force inducedcracks (β = 1.7) and cracks induced by imposed deformations (β = 1.3); srm – mean crack distance incase of fully developed crack pattern; εsm – mean steel strain, considering tension stiffening betweenthe cracks. Formula (30) represents a sophisticated procedure taking several factors into account. Theprocedure by Heft 400 [23] as enhancement of the DIN 1045 [5] crack proof is almost identical to thatdescribed by formula (30) of EC 2.

The enhanced procedure acc. to formula (30) enables to control the mean crack width w k in thestructure by varying bar diameter ϕ or bar distance s. However, the NEDIM procedure, with given inputvalues of ϕinp or sinp, is aimed at controlling the statically required reinforcement as,ULS : if required bycrack proof, as,ULS is augmented in order to lower the steel stress σs, which is the crucial factoraffecting the value of mean strain εsm in (30). This procedure is called crack reduction, since generallycracks wk < 0.30 [mm] are aspired to.

NEDIM controls the crack proof procedure of the EC 2 branch by distinguishing four differentload case attributes acc. to the same principles as described in the paragraph on the DIN 1045 7/88branch.

Note

For more information about this chapter see literature [3], where more detailed description maybe found.

3.4.4.2 Limit bar distances

ULS+SLS design is also affected with reinforcement amount control checks mentioned inchapter 3.4.3.2. But here, another two checks are to be introduced. They are located underLimit bar distances chapter.



80

Limit bar distance on face Zp+Maximal allowable distance between reinforcement bars at the surface with positive Z co-ordinate (in the local co-ordinate system of the 2D member). Default value = 200mm.

Limit bar distance on face Zp-Maximal allowable distance between reinforcement bars at the surface with negative Z co-ordinate (in the local co-ordinate system of the 2D member). Default value = 200mm.

3.4.4.3 Reinforcement design workflow

To describe the basic workflow, we can use the structure already used in ULS design

3.4.3.3 chapter and continue with it. We will also focus only on lower surface and direction 1. Atthe end of ULS design, two reinforcement regions are defined on the 2D member. See thepicture below for recapitulation.

Now we will run the ULS+SLS reinforcement design for lower surface and direction 1 withthe settings below. Location will be set to In nodes, avg. on macro possibility again. Previouslycreated reinforcement for ULS design will take effect here as well.



81





83


Now we have successfully fulfilled the requirements for both ULS and ULS+SLS design and nofurther steps are needed at the moment.

Note

For reinforcement design of structures without any additional layer of hydroizolation, user wouldlike to calculate reinforcement amount with crack width converting to 0mm (zero). It is not possible inScia Engineer to use direct zero value and user has to input minimal value of 0,01mm in Concretesetup dialog, to successfully finnish the ULS+SLS design.



84

3.5 Section on 2D member

Sometimes user might find useful or necessary to display his results in specified position of 2Dmember. Then he is allowed to define his own section on 2D member, where designed result valuesmay be displayed separately or n addition to other drawing styles. Definition of 2D member sectioncan be done through Section on 2D member service.

In this Section on 2D member dialog user defines name of the section, vector of direction of thesection and the way, results will be graphically represented. User may choose from few possibilities to

draw results:

o Upright to element – values will be drawn upright to the element

o Element plane – values will be drawn in the element plane

o X Direction – values will be drawn in X direction

o X Direction – values will be drawn in Y direction

o X Direction – values will be drawn in Z direction

o Draw similar as for setting in section properties – when this possibility is chosen, thenthe values will be drawn the way it is already defined in appropriate service by Draw parameter.

After definition of the section parameters, user confirms the dialog and manually defines theposition itself. When this is done, also coordinates of definition points will be displayed in previousdialog and user may also edit them either there or in section properties. Section geometry may be alsoagain adjusted in graphical window and all geometry functions may be used together with it.

To display results on already defined 2D member section, it is necessary that user checks themarked check box Section in properties of appropriate service. Then after the refresh, results will bedisplayed on defined section as well (or only).



85

Note

Also note that by activating Section check box, Drawing setup 1D option appears in the serviceproperties. Here user may adjust the view of the values representation. This will be the same for Edgerepresentation too.



86

3.6 2D Reinforcement

Generally there are two ways, how to define practical reinforcement for 2D concrete members inScia Engineer. The first and very often used way is to use previously defined 2D Concrete data. Thesecond way is to define each reinforcement area manually and separately from each other.

3.6.1 Reinforcement from 2D Member DataThis is very useful feature which will create reinforcement layers according to the settings which

are already defined in 2D Member data on 2D member. To use this feature it is necessary to haveattribute User reinforcement checked. If so, then it is possible to input and edit Basic distanceattribute for each reinforcement layer.

Now if settings in Member data attributes fit the user‟s needs, user may double-click the 2DReinforcement service. After that a decision dialog will appear and user may choose to use thisfeature, or not. If Yes possibility is chosen, then all reinforcement layers are automatically defined. IfNo possibility is chosen, then nothing is created and ordinary Reinforcement 2D dialog for manualdefinition of reinforcement is displayed.



88

Material Defines the material for the reinforcement.

Surface Specifies the surface: lowed, upper.

Number of directions The reinforcement can be defined in one or two perpendiculardirections.

Direction closest to surface Defines in which direction the layer of the reinforcement is closer tothe surface.

Angle of the first direction Specifies possible inclination of the first direction.

Diameter Defines the diameter of the reinforcement bars.

Concrete cover Defines the thickness of the cover.

Bar distance Defines the distance of individual bars.

Offset The zero offset means that the first bar is put directly along the edge of thereinforced region (usually a slab of sub region). Nonzero offset means that there is agap between the first bar and the edge of the reinforced region.

Reinforcement area This is informative attribute. It shows the total reinforcement areaper one-metre-section of the slab.

Total weight This is informative attribute. It shows the total weight of the reinforcement in thereinforced region. This item has no meaning in the input dialogue. It gives thecorrect value only when the existing reinforcement region is edited.

Mesh Selects the required mesh from the library of reinforcement meshes.

The reinforcement is always defined for a particular region. The reinforcement is distributed

uniformly over this region. It is not possible to input separate bars of reinforcement. The shape ofthe reinforced region is defined by means of the following parameters.



89

o Geometry defined by Point - reinforcement region is defined by its centre, width, lengthand possible inclination.

o Line - reinforcement region is defined by its centre line and width.

o Polygon - reinforcement region is defined by the polygon outlining the region.

3.6.3 Tips and tricks

3.6.3.1 Substraction from Required reinforcement

Normally, as shown in chapters above, for example, when Additional reinforcement is needed, itis calculated as simple difference between required and user defined reinforcement. Simillarly theother reinforcement types calculates with it. User may come across two possible situations when thisis declined:

o If there is already defined practical reinforcement (the one, which physically exist in the

model), which has different material, than the material defined in Member data. If thishappens, then user will be warned by error message below and this user reinforcement isnot recognized.

o Second situation may happen, when user has also practical reinforcement defined on themember and has activated the possibility “Check of concrete cover for substracting2D user reinforcement from required reinforcement”. This can be done underConcrete > General > Calculation > 2D user reinforcement. When this check box isactivated, new input parameter appears just below and user may define required value. All renforcement layers within this range will be ignored by the design. The error dialog isalso displayed and design will end up in same results as in the first case.



90

Let‟s demonstrate this on an example from chapter ULS design, when only main reinforcementon the whole slab was defined. There is diameter of 12mm used and the distance between the bars isset to 100mm. We can change the material of this reinforcement polygon for example to B500Acontrary to B400A, which is defined in member data for first option. Activating the mentioned checkbox, together with setting the value to 0.1 and changing concrete cover of the reinforcement to forexample 60mm. Then we will get these results:




91

3.6.3.2 Labels

The user may control the display style of the reinforcement through a set of view parameters,which can be found in View parameters setting dialog. These parameters are located under Concretefolder > Reinforcement regions 2D.

Display This parameter must be ON if the reinforcement is to be displayed.

Display style This will define the way, reinforcement will be displayed. There are fourdifferent types of display.

o Simple – only the main symbol of the reinforcement directions will bedisplayed.




92

o Distribution - the main symbol of the reinforcement directions will bedisplayed together with the indication of the distance between individualbars.

o Distribution full - The "real" distribution of the reinforcement isdisplayed. That will be displayed in the central plane.

o Real positions - All the option mentioned above draw the reinforcementschematically into the middle plane of the reinforced slab. Option Realpositions displays the reinforcement in its real (actual) position.



93

Upper layer Switches ON/OFF the layer of the reinforcement at the upper surface.

Lower layer Switches ON/OFF the layer of the reinforcement at the lower surface.

Display label This parameter must be ON if the reinforcement labels are to be displayed.

Name Shows the name of the bars.Diameter+distance Shows the diameter and distance of the reinforcement bars.

3.6.3.3 Editing the reinforcement parameters

If user wants to change some existing reinforcement parameters he might simply edit andmodify parameters in the reinforcement attributes.

1. Select the reinforcement that needs editing.2. The properties of the selected reinforcement are shown in the Property Window.3. Modify the required parameters.4. Clear the selection.

3.6.3.4 Editing the shape of the reinforcement region

If the reinforced region was input as a polygon, you can later modify its shape by followingprocedure below:

1. Select the reinforcement the region of which is to be modified.2. The properties of the selected reinforcement are shown in the Property Window.3. Click action button Edit geometry.4. You can use the right-mouse button to invoke the pop-up menu and insert or deletevertices.5. Or you can drag-and-drop the vertices by mouse.6. To finish the editing, invoke the pop-up menu and select End polygon edit.

If the reinforced region was input as point or line object, you can simply modify its shape by

adjusting appropriate parameters in the properties.

Note

Any function for geometric manipulations can be used to modify the reinforced area. Thatmeans that functions like Move, Copy, Stretch, Rotate, etc. can be used.



94

3.6.4 Free bars

3.6.4.1 New Free bars

The normal way in Scia Engineer is to define the reinforcement in 2D members through 2Dmember data or by placing some kind of polygon directly using 2D reinforcement service. On the otherhand, it may be sometimes more convenient to input separate bars. This feature is also necessary

when the reinforcement is imported from a third party program (e.g. Allplan).

The principle is that the user defines the shape of the reinforcement bars and then selects themembers into which these bars are included. Free bars are considered in all calculations (design andchecks). On the other hand, free bars are not included in the bill of material and scheme ofreinforcement.

Name Specifies the name of the reinforced region.

Layer Defines the layer into which the entity is located.

Position number Informative parameter, which defines the position number of the bar.

Diameter Specifies the diameter of the bar.

Mandrel Specifies the mandrel.

Material Specifies the material of the bar.

Long/Stirrup Determines if the bar is a longitudinal bar or a stirrup.

Detailing If ON, the bar is ignored in design and checks. It is just a structural bar.

Number It is possible to input a set of bars at a time. This parameter specifies the totalnumber of the bars in one set.

Dir X This parameter defines the distance between individual bars in the set in X direction.

Dir Y This parameter defines the distance between individual bars in the set in Y direction.



96

4. Alternatively, you may click button [Edit free bar geometry] to be able to edit graphically theshape of the bar. When this option is activated, the vertices of the selected free bar arehighlighted and can be moved, etc.

5. Clear the selection when everything is done.

3.6.4.2 Explode to free bars Any standard reinforcement can be exploded into free bars. Once this is done, the

reinforcement bars lose all their original properties and become free bars. This operation isirreversible. To go through the procedure follow the steps bellow:

1. Open service Concrete.2. Start function New free bars > Explode to free bar .3. Select the required reinforcement. End the selection with ESC4. You are asked if the reinforcement elements are to be deleted or not.

5. Select YES if you want to have just the free bars (the original reinforcement is transformedinto free bars.)

6. Select NO f you want to keep the original reinforcement and have its copy converted into thefree bars.



97

3.6.4.3 Free bars user reinforcement

Free bar is a different entity than reinforcement polygon and displaying user reinforcementconsisting from free bars may, and usually does, look differently. We can show the difference onsimple slab, already used in previous chapters. We will display one-directional user reinforcement forlower surface of the slab. Reinforcement is defined in global x-axis direction. On the first picture, thereis standard reinforcement polygon defined with bars (diameter 10mm) and 500mm spacing. On the

second picture, there are free bars created from the reinforcement polygon, which are on the firstpicture. Reinforcement amounts are on both slabs the same. We are displaying user reinforcementdefined on the slabs.

Reinforcement polygon Free bars reinforcement

As it is clear from the pictures, displayed amounts of reinforcement are NOT equal, althoughamounts of reinforcement defined on those two slabs are identical. This is due to the inner algorithm offree bar recalculation. This algorithm may be described in a few steps:

o software checks the free bar diameter and calculates the free reinforcement bar area. Inour case it is π (10/2)2 = 78,5mm2.

o then “virtual reinforcement polygon” is internally created on 300mm long section of theslab (virtual reinforcement polygon area equals 300*free bar length)

o the intensity of this „virtual reinforcement polygon‟ is calculated from arithmetic product offree reinforcement bar area and hardcoded value of (1/0,3). In our case it is 78.5 * 1/0,3 =262 mm2

o the last step is to assign the appropriate intensity of reinforcement into each mesh

element which lies (even a part of it) under our internal virtual reinforcement polygon. Thevalue will be proportional to this area under the virtual reinforcement polygon. As we haveset 2D mesh element size to 200mm, there are a few “situations” on our slab”

Let‟s delete a few free bars to analyze different possible free bar layouts. Virtual reinforcementarea is represented by red area and free bars are highlighted by purple line:

o the edge – mesh element size is 200mm, virtual reinforcement area width above theelement is 300/2 = 150mm. User reinforcement amount in adjacent mesh element is262 * 150/200 = 196mm2

http://slovnik.seznam.cz/?q=arithmetic%20product&lang=en_cz





98

o free bar on mesh line – similar to the previous case. mesh element size is 200mm,virtual reinforcement area width above the elements is 300/2 = 150mm. Userreinforcement amount in both adjacent mesh elements is 262 * 150/200 = 196mm2

o free bar in the middle of mesh element –. mesh element size is 200mm, virtualreinforcement area width above the middle element is 200mm and virtual reinforcementarea width above the adjacent elements is (300-200)/2 = 50mm. User reinforcementamount in middle mesh element is 262 * 200/200 = 262mm2 User reinforcementamount in both adjacent mesh elements is 262 * 50/200 = 65mm2.

Now it should be clear how the algorithm works and also two possible solutions for improvingthe displaying results, should be introduced.

o minimising free bar distances will cause that virtual reinforcement polygons will overlaythe ones laying next to it and will provide more continuous results

o as user may not want to change the distance between reinforcement bars, increasing the

2D mesh element size will result in more continuous results as well.

On the picture below, there is the same slab with the 2D mesh element size set to 400mm.These results are much more consistent then the results on the beginning.



99

3.7 Averaging strip

This functionality provides automatic averaging of peak results around defined points or alongdefined line strips on slabs. The users can define several styles how to calculate the averaged values.The averaging can be applied to internal forces on slabs and to required reinforcement areas used inthe design of reinforcement in concrete slabs.

The averaging algorithm uses only the FE nodes that are located inside the averaging strip.This may cause certain inaccuracies especially in the combination with larger finite elements.Therefore, it is recommended to redefine mesh or define internal edges along the averaging strips.This ensures that finite element nodes are generated along the edge of the averaging strip, which maysignificantly improve the accuracy.

The averaging algorithm can be applied to internal forces in slabs and required reinforcementareas in slabs. Each of the averaging is performed separately. It means that averaging internal forcesare calculated from non-averaged internal forces and averaged required reinforcement areas arecalculated from non-averaged required reinforcement areas. Thus it is NOT true that the averagedrequired reinforcement areas are calculated from averaged internal forces.

The averaging strips are defined as what is termed additional data. This fact together with someother characteristics of the averaging strips leads to the following rules concerning the manipulationwith the already defined strips:

o No geometrical manipulation is supported (i.e. the averaging strip cannot be copied, moved,etc.) The only exception is the direct editing of the coordinated of the definition points in theProperty Window.

o The averaging strip can be normally deleted.

o The removal or editing of the defined averaging strip DOES NOT influences the results.

o If the slab that contains the averaging strip is moved, copied, etc. the averaging strip "goeswith" its master slab.

o The averaging strips react to the activity of the slabs. It means that only averaging strips thatare defined on active slabs are visible.

o Check of data verifies the position of the strips and all invalid strips (e.g. located out of themaster slab) are deleted.

For creating a new averaging strip user may simply double click item Averaging strip inconcrete tree. Dialog below appears where user may define a few parameters which will determine theaveraging strip location and its parameters. After confirmation user defines averaging strip location ingraphic window.



100

Name Specifies the name of the strip.

Type Specifies the averaging strip input type

o Strip The averaging strip is defined by a line with a specified width.

o Point The averaging strip is defined by a point, width, length, and angle (that specifies thedirection of the strip).

Width Defines the width of the averaging strip.

Length Active only if Type = Point. Defines the length of the averaging strip

Angle Active only if Type = Point. Defines the direction of the averaging strip.

Direction Specifies the direction in which the averaging is to be calculated

o Longitudinal The averaging is done along the defined strip. We can imagine that the striprepresents a 1D member and we want the program to smooth the distribution of the resultalong that 1D member.

o Perpendicular The averaging is performed in the direction that is perpendicular to thelength of the strip. This option is for special purposes only.

o Both The averaging is made in both directions. Again, this option is for special purposesonly, e.g. heads of columns.

o None No averaging is made. This option may be useful if one (or several) definedaveraging strip(s) should be temporarily ignored while other strips are still required to beused.



103

Non averaged result of moment my on 2D sections with location parameter set to In nodes, noavg. Parameter course changed to Uniform possibility.

The conclusion is, that in 2D section A has moment my value -1,38 KNm, in 2D section B -4,45KNm and in 2D section C -7 KNm.

Numerical results of moment my averaged with averaging strip, with location parameter set to Innodes, no avg.

Conc lus ionNow if we compare this averaged numerical results in mesh nodes and the non averaged

results on 2D sections, we come to the conclusion, that the values are equal.



105

coefficient equals to the deflection due to creep. Then, we add the long-term deflection to the short-term deflection and get the total deflection that can be assessed in accordance with the standards.

This calculation of the effects of creep is simplified and can be used for a limited set ofsituations. In fact, in case of reinforced concrete it covers most possible situations, as the history ofassembly does not have to be followed. In other words, if the history of assembly steps does not haveto be followed, this procedure can be applied.

The solution consists of a simplified method of calculation. An equivalent flexural stiffness isused taking into account effects of cracking, material nonlinearity and creep. Creep is taken into theanalysis using an effective modulus of elasticity for concrete according expression 7.20 of EN 1992-2-2

The deformation for other codes than NEN 6720 is calculated by reducing the stiffness‟s usingthe following so-called Stiffness/Moment diagram:

Where: Mr is the cracking momentMu is the ultimate moment

The physical non-linear deformations are calculated based on the concept of “quasi”-non-linearity. This means that linear calculations are used to model non-linear behaviour of theconstruction. Four steps are used to perform the calculation.

o Using the short-term stress and strain diagram for concrete, the deformations for „creep‟-load is determined. The „creep‟-load is commonly the quasi-permanent load (1.0 × DEADLOAD + FACTOR × LIFE LOAD). The factor is in most cases around 30%.

o Using the long-term stress and strain diagram for concrete the deformations for „creep‟-load is determined.

o Subtracting the short-term deformation from the long-term deformation the „creep‟-deformation is obtained.

o Adding the creep-deformation to the linear deformation caused by the representativeload (1.0 × DEAD LOAD + 1.0 × LIFE LOAD), the total quasi-non-linear deformation isobtained.

To calculate the immediate deformation, the deformation of the permanent load is calculatedusing the short-term stress and strain diagram. Additionally by subtracting the immediate deformationfrom the total deformation, the program determines the additional deformation.



106

The calculated deformations in Scia Engineer are:

o Elastic deformation: Using the short-term stress and strain diagram and representativeload combinations. (1.0 × DEAD LOAD + 1.0 × LIFE LOAD)

o Creep deformation: Using the long- and short-term stress and strain diagrams andmomentaneous load combinations. (1.0 × DEAD LOAD + X × LIFE LOAD)

o Total deformation: Elastic deformation + Creep deformation.

o Immediate deformation: Using the short-term stress and strain diagram and permanentcombination.(1.0 × DEAD LOAD)

o Additional deformation: Elastic deformation + Creep deformation – Immediatedeformation.

The short- and long-term stiffness‟s are calculated using a so-called creep factor. This creep-factor is dependent on the relative humidity, outline of the cross-section, reinforcement percentage,concrete class, etc. is used to divide the short-term stiffness and obtain the long-term stiffness.

There are two check boxes for determining key concrete combinations, for determining thecreep factor, in the dialog below.

Use to determine Code Dependent Deflections (CDD) caused by creep If thisoption is ON, combination will be used for calculation with creep.

Use to determine permanent Code Dependent Deflections (CDD) If thisoption is ON, selected combination will be used for calculation of permanent deformation. Only onepermanent combination may be defined.

Following steps must be performed in advance of running CDD calculation:

o Special load concrete combinations must be created. These combinations must contain staticloads only.

o Practical reinforcement should be defined and this reinforcement should fulfil the ultimate statedesigns



107

o If no practical reinforcement is input, then at least some required reinforcement must becalculated

o If no required reinforcement is designed, calculation is determined without changes of stiffness

As it is clear from what is mentioned above, calculation can be performed using both theoreticaleither practical reinforcement

The using of practical reinforcement, .e.g. the reinforcement which is really assumed in theconcrete member is a more realistic assumption to perform the analysis. However, the programdoesn‟t warn the user in case he doesn‟t use the practical reinforcement.

In general setup of concrete, part general calculation, the user can set the default assumptionfor the reinforcement steel in the CDD calculation

As,designed The total area of reinforcement is used for the calculation on condition thatthe design function has been already run and that the program has already calculated the requiredarea of reinforcement. Otherwise, zero value is used (even if the user has manually inserted somereinforcement bars). The total area of reinforcement is the sum of the user-defined reinforcement(through basic reinforcement, through reinforcement zones/regions or through free bars) andcalculated additional required reinforcement. The additional required reinforcement may be zero, if theuser has already inputted enough user-defined reinforcement.

IMPORTANT: Keep in mind that the function calculating the required areas of reinforcementMUST HAVE BEEN run before. Otherwise, the user-defined reinforcement is ignored and ZERO valueis used.



108

As, user The user-defined reinforcement is used for the calculation. The term user-defined reinforcement covers the basic reinforcement specified in member data, reinforcement barsinputted through reinforcement templates in reinforcement zones (1D members) or regions (2Dmembers), and free bars of reinforcement.

In order: [ As, user ]; [ As,designed] If there is any user-defined reinforcement, it isused, otherwise, the total reinforcement is used (which in fact means the calculated required area ofreinforcement). Remember, that for the second option, the design function must have been alreadyrun.

In order: [ As,designed]; [ As, user] If the design of reinforcement has been alreadyperformed and the required area of reinforcement has been already calculated, it is used. Otherwise,the user-defined reinforcement is used.

The reduced stiffness for Walls is not calculated when a CDD – deformations calculation isperformed. Deformations of beams, plates and shells are calculated by integrating the non-linearcurvatures over the length of beam or slab. However if some element has a value of Md larger thanMu, than the stiffness according Mu is taken. Since the finite element method can give large internalforces due to singularities, etc. the calculation is allowed to continue without an error message, but

supplies messages after the calculation has finished.The program always converges to a solution. The program does not warn the user when the

loading is bigger than the capacity of the cross section. Here is assumed that the user did in a firststep a proper design of the reinforcement in the concrete members.

Note

The user can define the creep coefficient, or let the program evaluate the following the ECappendix B. Please find the setting in the concrete setup at the SLS settings

An error message concerning about not sufficient mesh may appear during the CDDcalculation. If so, mesh should be improved and then linear and CDD calculations should be startedagain.

In the solver setup, the user can change the amount of reinforcement for the CDD. This optionis intended to correct the theoretical reinforcement by this coefficient. Default value is 1. Let‟s remarkthat the program doesn‟t display a warning when you use this option when concrete member isprovided with practical reinforcement.



109

3.8.3 Example

To demonstrate this functionality we can continue with the example used in previous chapters ofULS and ULS+SLS designs.

As a first step we need to create concrete combinations necessary for calculation of codedependent deflections. We will set Load case 1, where only self weight is defined, for determiningpermanent code dependent deflections and Load case 2, where all load are defined, for determiningthe code dependent deflection caused by creep.

We will also define reinforcement for second direction and also for upper surface. User

reinforcement for both surfaces and both direction will fulfil ULS design only. For information aboutinput reinforcement see table below:

User reinforcement As1- User reinforcement As2-

User reinforcement As1+ User reinforcement As2+



110

After the reinforcement design of user reinforcement for ULS state, it is a time to definereinforcement determining the Code dependent deflections. It can be done in Setup dialog in Menu >Setup > Concrete solver. Picture of this dialog is shown in the previous chapter. We will set thisparameter to User reinforcement possibility. Then we must run the design nonce again to regain theamounts of reinforcement once again.

Now if we start the FE analysis dialog, possibility Concrete – Code Dependent Deflections(CDD) is activated and may be chosen. After selection of this option we can proceed to calculationitself by pressing Ok button.

After confirmation of FE analysis dialog warning error may appear. This will warn the user aboutnon-consistent location parameter of 2D design.



111

If user accepts the dialog above, the calculation itself is started and process of determining thedeflections should be finished with informational End of analysis dialog. Here maximal values oftranslation and rotation is displayed.

Now if we go back to concrete service, two new items Stiffness presentation andDeformations, may be found here. They are both under Member check item. See picture below.



112

3.8.3.1 Stiffness presentation

In this service user may choose to display two types of results. Location is set permanently to“In centres” possibility. The parameter type of values may be set to:

o Required area

As1- longitudinal reinforcement for lower surface and direction 1

As2- longitudinal reinforcement for lower surface and direction 2

As1+ longitudinal reinforcement for upper surface and direction 1

As2+ longitudinal reinforcement for upper surface and direction 2

As1 overall longitudinal reinforcement for both surfaces and direction 1

As2 overall longitudinal reinforcement for both surfaces and direction 2

o

StiffnessEI1,s bending stiffness from short term load in direction 1

EA1,s normal stiffness from short term load in direction 1

EI2,s bending stiffness from short term load in direction 2

EA2,s normal stiffness from short term load in direction 2

EI1,l bending stiffness from long term load in direction 1

EA1,l normal stiffness from long t term load in direction 1

EI2,l bending stiffness from long term load in direction 2

EA2,l normal stiffness from long term load in direction 2

There may be also displayed values for required areas and stiffness for the thirddirection, but it must be defined in advance.

Here is an example of the bending stiffness from short-term load in direction 1.



113

3.8.3.2 Deformations

In this service, user may display the code dependent deflection, calculated from the settingsalready defined in whole process. User may choose to set parameter Deformation to three possibleoptions:

o linear will display linear deformation

o nonlinear will display nonlinear deformations

o nonlinear with creep will display nonlinear deformations including creep

Parameter type of values may be set to another three options:o Uz deformation in Z-axis direction

o Fix rotation around X-axis direction

o Fiy rotation around X-axis direction

In the table below, we can compare the deformation in the Z-axis direction with differentDeformation parameter.

Linear Nonlinear



114

Nonlinear with creep

As it is clear from the table, the largest values of Code Dependent Deflections are for Nonlinearwith creep deformations.



References

[1] EN 1992-1-1: 2004 Eurocode 2 : design of concrete structures – Part 1: General rules andrules for building

[2] ENV 1992-1-1: 1991 Eurocode 2 : design of concrete structures – Part 1: General rules andrules for building

[3] Hobst, Ed.: ESA-PRIMA WIN & SCIA.ESA PT REINFORCED CONCRETEDESIGN OF 2DSTRUCTURES, Theoretical background

[4] Internal Scia Engineer manuals

2d concrete design - en1992!1!1

Documents