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2D Concrete design-EC2



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© Copyright 2008 Scia Group nv. All rights reserved.



Table of contents

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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 ........................................................................................................20 3.1.5.2 Longitudinal ......................................................................................................24 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 ..........................................................................................................................58 3.4.3.1 Theoretical background ...................................................................................58 3.4.3.2 2D Structures detailing .....................................................................................63 3.4.3.3 Reinforcement design workflow .......................................................................66 3.4.4 ULS+SLS .................................................................................................................73 3.4.4.1 Theoretical background ...................................................................................73 3.4.4.2 Limit bar distances ...........................................................................................78 3.4.4.3 Reinforcement design workflow .......................................................................79 3.5 Section on 2D member .................................................................................................83 3.6 2D Reinforcement ..........................................................................................................85 3.6.1 Reinforcement from 2D Member Data .....................................................................85 3.6.2 New Reinforcement¨ ................................................................................................85 3.6.3 Tips and tricks ..........................................................................................................88 3.6.3.1 Substraction from Required reinforcement ......................................................88 3.6.3.2 Labels ...............................................................................................................90 3.6.3.3 Editing the reinforcement parameters ..............................................................92 3.6.3.4 Editing the shape of the reinforcement region .................................................92 3.6.4 Free bars..................................................................................................................92 3.6.4.1 New Free bars ..................................................................................................92



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3.6.4.2 Explode to free bars .........................................................................................94 3.6.4.3 Free bars user reinforcement ...........................................................................95 3.7 Averaging strip ..............................................................................................................97 3.8 Code Dependent Deflections (CDD) ..........................................................................102 3.8.1 Introduction ............................................................................................................102 3.8.2 In general ...............................................................................................................102 3.8.3 Example .................................................................................................................106 3.8.3.1 Stiffness presentation ....................................................................................109 3.8.3.2 Deformations ..................................................................................................110 References .....................................................................................................................................112



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Abstract

Scia Engineer software enables the user to design and check 2D member reinforcement. Themain possibilities of the design and checks are presented in the 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 the design and check of a 2D member andto describe some of the tips and tricks which might be important and useful in each part.



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2 Global settings

Global settings represent a set of parameters which are default values for the design of thewhole structure in the project. The user can use these default values, change them or simply createhis own sets of parameters reflecting his preferences and needs. General settings can be accessed inseveral ways:

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 the global settings of the project is through the project dialog. Youcan switch between national annexes by National annex button. Each annex has some differencesfrom the Standard EN.

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

Default reinforcement and concrete material for EN Code

Starting from Scia Engineer version 2010, the default reinforcement and concrete material is setdirectly in Project data dialog. After checking the concrete material check box, the possibility to choosethe default concrete and reinforcement material is activated.



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For Eurocodes only one default common material is defined for beams, columns, walls or slabs.This is different from other Codes where for each mentioned member type a separate default materialmust be defined in the global settings. If we want to change any material for some specific member, weneed to define its local settings somehow. We can do this by creating Member data or Punching Dataon the member.

2.2 Setup managerStarting with Scia Engineer 2010, a new library called Setup manager is created. It can be

accessed from:

o Main tree > Libraries > Setup

o Menu > Libraries > Setup

Tree Menu

The user can edit the default settings for all materials in the Setup manager dialog. Eachcountry has its predefined set of parameters. The user is able to create his own set of values withdefault values he requires. He might also change the appearance and the number of items in thesettings of each material. It is possible to work with the items as with any items of a library, so the usercan edit, copy, save and load to/from file, etc. It is not possible to switch the national annex here; this

action can be done only in the Project dialog or in the Manager of national annexes dialog.

After clicking the Concrete edit button in the Setup manager dialog, the Concrete setup dialogappears. This dialog displays all global parameters for the concrete without parameters specified bythe national annex.



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2.3 Manager of National AnnexesIt is possible to edit national annex parameters only through this dialog in Scia Engineer. The

Manager of national annexes dialog can be displayed in three ways:

o Main tree > Project > National annex

o Menu > Tree > Project > National annex

o By pressing second flag icon representing the country of the annex in the bottom right cornerof the screen

Tree Menu Flag icon (Czech)

The Manger of National annexes dialog is a library. The content of items is the same as thecontent of items in Setup manager. It is the same library and the only difference is that parameters arefiltered according to some filter applied. It is also possible to get more detailed information about

implemented Codes and national annexes in the Manager of National annexes. This can be done viabutton References.



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By pressing the Edit button ( ) for example for editing of national annex parameters in EN1992-1-1 (General rules and rules for buildings), another dialog appears, where all appropriateimplemented parameters are displayed.



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2.4 Concrete solver setupCode dependent values (except for national annexes parameters) and Code independent

values which influence design and check of concrete structures can be edited in the Concrete setupdialog which can be displayed through Menu > Setup.> Concrete solver.



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2.5 Design DefaultsThis is the first item in the concrete tree, and it is possible to set here the default values for

member design (such as concrete cover, reinforcement diameters, direction angles, etc.), and alsoparameters for drawing of user reinforcement.

2.6 Concrete Setup action buttonGlobal settings for design of the reinforcement are adjustable through Concrete setup action

button too, which is located in Properties window of both concrete tree and service for defining localparameters.

The main advantages of this action button dialog are:

o Only parameters for actual design are displayed



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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 & tricksHere are some tips and tricks, which might some users find useful and which should provide

better overview in the global settings.

2.7.1 Filters

There are quite a many global concrete parameters which influence reinforcement design. Tosimplify the overview of the global settings, the user may use filters which will restrict the number ofdisplayed parameters. Parameters can be sorted according to these filters:

Type of membersThis filter is activated only in the case that both 1D and 2D members are defined in the project.Then the 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)

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 values

o Code dependent values (parameters from Code, without national annex parameters)



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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 the functionality checked in the Project data dialog, folderFunctionality.

o Prestressing (parameters for pre-stressed members design, functionality Prestressingmust 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

Parameters of selected check are displayed.

o Member data

o Cross-section characteristics

o Internal forces

o Design

o Automatic reinforcement design

o ULS response

o ULS designo Crack

o CDD Check



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o Detailing

o Allowable stress

o SaT

o Punching check

Displayed filters depend on the location where the Concrete setup dialog was displayed from.

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.

Manager 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)

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 the design service that is currently active and may differ from each other.Only one Design filter is displayed in the SLS design, Crack design filter is added in the SLS+ULSdesign.

Setup manager Concrete solver setup



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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. The layout of the Global parameters can be edited in the Concrete setup dialogby right-clicking on the window with the parameters (the window on the right side). After selecting Editlayout properties, the only possibility from the opened menu, the Property layout manager dialog isdisplayed.



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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. The usermay adjust the default layout or simply create a new one using the edit buttons in the middle. After theediting is finished, it is necessary to have check box Show current layout selected. Then this layoutwill be added to the form of folder Concrete setup dialog. The user may also create more layouts andswitch among them. He still may use the default layout by checking check box Show native layout.



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2.7.3 Saving and loading of global settings to different projects

As it was mentioned in a chapter above, the global settings for Code EN are since the SciaEngineer 2010 version implemented as a library, which enables the user to transfer global settings of

one project to another. Export and import of global settings is possible through the following two iconsin 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 the applied filter in each dialog.

Note

Default global setting (SetupManager.db4 file) is placed in Scia/db folder, together with all otherdb4 files.



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2.7.4 Colours

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

Blue coloured parameters are those which might be changed 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 the global settings dialogs are very useful and might be important for more enhanceddescription of the desired parameter. On the other hand these pictures take some space in the dialogand might not be so important especially for more experienced users. To avoid any disturbance bydisplaying those pictures it is possible to turn them off. This can be done in Options dialog (Menu >

Setup > Options > Environment), by unchecking the indicated check box. Pictures in the Propertieswill be turned off too.



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3 Concrete tree

3.1 Member data

3.1.1 In general

By creating the member data, the user will overwrite default global settings with local settingsdefined for selected members. Simply said, where the user doesn’t want to use the global concretesettings, the user creates local concrete settings by defining member data. We recognize two types ofthese local settings for 2D concrete members:

o Member data

o Punching data

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

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



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

After the definition of Member data a graphical mark (label) is displayed together with thearrows describing reinforcement directions on the member. After clicking on these marks the user canedit the appropriate attributes in the member properties window. Content of the label can also beedited through the Concrete folder in the View parameters setting dialog.

Orthogonal.,2 directions, same layers User .,3 directions, different layers



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The local settings were changed since Scia Engineer version 2010 into attributes. This changeenables the user to edit these settings directly through the properties of the selected member. It ispossible to manipulate with these settings as with all others attributes by functions Copy attributes andMove attributes in:

o geometry manipulations toolbar

o member menu after choosing attribute and right clicking

It is possible to edit these parameters in Member data.

3.1.2 Type

This represents the 2D member type. Default value depends on the type defined in the

member’s properties.

There are three types supported for this attribute (plate, wall, shell). The change of type of theattribute does not influence the analysis model, but influences only the presentation and definition ofthe parameters in the member data properties. In the table below Member data properties for eachtype selected are displayed, without the advance mode being activated.

Plate Wall Shell



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From the table above it is obvious that the type:

o Plate enables the user 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 layerof the reinforcement in the centre by check box Layers in the centre.

o Wall does not enable the user to define different parameters for each member surface

(upper, lower) by check box Different layers per side, but it is not possible to define onlyone layer of the reinforcement 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 side

This attribute enables the user to define different parameters for upper and lower surfaces andits reinforcement layers. By activating this attribute the user will be able to define differentreinforcement material, different directions and different diameters for each surface. This attribute isavailable only when the Type is set to Plate or Shell.

Different layers per side off Different layers per side on

As you can see the original tree item Longitudinal is divided into item Upper and Lower . If an

advanced mode will be activated too, then another items Number of reinforcement layers and theirdirections will be added.



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3.1.4 Layers in the centre

In the real life project we come across 2D members which have very small thickness, whichdoes not allow for defining reinforcement layers for both surfaces. It is necessary to design only onelayer of reinforcement which lies in the centre of gravity of the member. It is possible to design onlyone layer of reinforcement by activating attribute Layers in the centre. This attribute is available onlywhen Type is set to Wall or Shell and when it is checked, many parameters in the member data aredeactivated.

It is not possible to change the attribute type of reinforcement geometry attribute. Onlyorthogonal direction 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 the global settings (Design defaults) are displayed together with

reinforcement material parameters which might be edited. Groups Longitudinal and Minimal concretecover with the very basic parameters are displayed.

When it is activated then the user may edit all available parameters. Those parameters aresorted to a few groups:

3.1.5.1 Basic data

In this group basic attributes and parameters for reinforcement design are located. As you cansee from the picture the user can edit reinforcement geometry, type of concrete cover andreinforcement materials here. Also Different layers per side, User reinforcement and User inputthickness attributes are here.



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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 reinforcementlayer. The second reinforcement layer direction will always be perpendicular to the first one.The default value for the first direction angle is loaded from the 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 the same parameter in the Longitudinalfolder.

Orthogonal User2 directions

User3 directions

Note

Minimal difference between two reinforcement directions defined directly by user, must be 30degrees. If the difference is smaller, then the reinforcement design will end up with Error 61 (Generalerror in input data).



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Type of cover

It is possible to change the way concrete cover is calculated. Two basic types of cover aresupported:

o Use minimal cover enables Scia Engineer software to evaluate all appropriate parametersand calculates minimal possible cover according to the selected Code. This will be theminimal value possible.

o User , where Concrete cover parameters in Longitudinal folder will be activated and user isallowed to use his own values

User reinforcement

User reinforcement is defined by new parameter Basic distance in Longitudinal folder, whereuser defines the axial distance of reinforcement bars. It is possible to define different value for eachreinforcement direction.

It is possible to set this attribute ON only in the case that there is no user reinforcement definedby 2D region or Free bars on selected 2D member or its sub region.

Note

User reinforcement defined by Member data is the same for the whole 2D member surface. Ifthe user wants to change the Basic distance value only on a part of the 2D member, then he needs tocreate sub region where this parameter may be defined separately.

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

User input thickness

Scia Engineer software enables to set different thickness for 2D member or its sub region thanis defined in the model. The big advantage of this feature is that it is possible to run reinforcementdesign for different thickness, without the need of deleting calculation results together with internalforces. The importance of this function is directly proportional to the size of the structure, as thecalculation of internal forces for large projects may take very long time. What is important is that the



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user must remember the fact that the self weight of the changed member is not adjusted by thechanged thickness by this function and remains the same as originally defined.

The user defined thickness of a 2D member or its sub region can be edited by new parameterThickness. This parameter will be displayed after switching on the attribute User input thickness.



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3.1.5.2 Longitudinal

In this group there are parameters for each reinforcement direction such as number of layers ineach direction, their angles, bar diameters and eventually the distances between them. Also veryimportant parameter which influences concrete cover for each layer is here. The Longitudinal group,which defines parameters for both surfaces, may be split into Upper and Lower group if the attributeDifferent layers per side is switched on. The appearance of this folder may differ quite a lot depending

on activated attributes and defined parameters

Longitudinal2 directions, 2 layers, user cover

Upper3 directions, 4 layers, minimal cover

Number of directions

By setting attribute Type of geometry to User, a new parameter Number of directions will bedisplayed in the Longitudinal group. The user is able to choose from two or three directions wherereinforcement will be created. Depending on the choice, the user is able to define appropriate number

of direction angles

Direction angles

As it was mentioned before, these are the values with direction angles. It may be one up tothree. The default value for the first direction angle is loaded from the global settings. These directionangles are used only for reinforcement layers angles definition. It does not mean that this is the angleof the first, second or third reinforcement layer. The user selects the direction for each layerafterwards.

Number of reinforcement layers

The user is allowed to define more reinforcement layers for each member or sub region surfacethrough member data. The minimal amount of reinforcement layers is set by the number of defined

directions (see above). The maximal number of reinforcement layers for one surface is 10.

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



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Diameter

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



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Layer angle

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

Orthogonal geometry

2 directions

User geometry

3 directions

Type of cover

Concrete cover, which is the distance from the outer reinforcement surface to the closer surfaceof the member, is determined by this parameter. This value can be automatically calculated by thesoftware for the first reinforcement layer. This calculation will respect values from group Minimalconcrete cover. The user may also define his own value of the concrete cover. For this feature,attribute Type of cover in Basic data group must be switched on.

The location of other reinforcement layers depends on the Type of cover for each of them. It is

possible to define different Type of cover for each reinforcement layer. The user can choose fromthese 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 the 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 otherbar.

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



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

Concrete cover (cu)

Shows or provides place for input of the cover value.

Basic distanceIf the attribute User reinforcement from Basic data group is switched on, then the Basic distance

parameter is active and the user may define and edit its value. As it was mentioned before, itrepresents the axial distance between two reinforcement bars and it is defined only for every firstreinforcement layer in each direction. For other reinforcement layers in already defined direction thesoftware sets the same value.

During the 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 the following is input for the needs of the design:

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

, ∑ ,



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o User reinforcement area calculated from the first reinforcement layer (after assigningreinforcement layer to the direction which has already one layer defined, it is possible toedit only the concrete cover of this new layer)

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

Note

If the average concrete cover value for the upper or lower surface is equal or even bigger thanhalf of the member thickness, the design will not be possible and it will end up with Error 61 (Generalerror in input data).

3.1.5.3 Concrete minimal cover

In this group there are parameters that influence the value of the minimal cover calculated bythe software. It is also possible to define different parameters for the upper and lower surfaceseparately by switching on attribute Input for side. The user can edit Exposure and Abrasion classes,Type of concrete and its surface, control attributes and values for determination of Delta;cdur.



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3.1.5.4 Creep coefficient

Here in this group there are parameters related to creep.

3.1.5.5 Position of reinforcement direction arrows

Only two parameters are in this group. By editing the default values, the user can move thelocation of the direction arrow marks along the 2D member or its sub region. It is not possible to setcoordinates outside 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 theuser might sometimes find useful:

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

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

Note

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



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3.1.3 Tips & tricks

3.1.3.1 Member data labels

If Member data are defined for a certain 2D member or its sub region, then a graphical mark

(label) is displayed together with the arrows describing reinforcement directions and layers on themember. Only the name of the attribute is displayed by default (Concrete 2D data), but this descriptioncan be edited or modified in the View parameters setting dialog. It might be accessed by:

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

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

After that the View parameters setting dialog, affecting whole model, is displayed and the usercan find parameters for concrete structure in folder Concrete



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Member data can be switched on or off in two ways:

o by checking and unchecking the check box Display label from the dialog above

o by selecting Concrete label button in Fast adjustment of view parameters on whole modelmenu (see picture below)



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3.2 Member Design

3.2.1 Design properties

Design properties layouts for internal forces ULS, Member design ULS and Member designULS + SLS differ from the chosen design and attributes selected by user.

Internal forces ULS ULS + SLS design

ULS design

See the description and possibilities for each of the attributes below.

3.2.1.1 Name

The user is allowed to name the design. It might be very useful for better specification andorientation, especially in the Document.

3.2.1.2 Selection

This attribute influences the total amount of members that will be taken into the specific 2Dmember design. There are four possibilities to be chosen from:

o All (all active 2D members will be designed)

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

o Advanced (the user may alter the previous selection)



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o Named selection (only 2D members from a certain named selection will be designed.new attribute “Named selection” will appear in the properties)

3.2.1.3 Type of loads

By this attribute the user defines the type of the load for the design generation. There are threepossibilities to choose from:

o Combinations (the user may choose from all combinations)

o Load cases (the user may choose from all load cases)

o Class (the user may choose from all result classes)

Depending on the selected type of the load, a new attribute Combination or Load cases orClass will appear on the right under this attribute. The user may select the desired Combination, Loadcase or Class from the filtered list here.

Note

Only the Class type can be selected for ULS+SLS design.

3.2.1.4 Filter

It is possible to define the filter for adjusting the already selected type of selection. This will

affect the number of 2D members taken into the design. The user may select one from six possibilities:o No (no filter will be applied)

o Wildcard (the user may define the attributes for selection)

o Material (the user may select a specific material)

o Layer (the user may select the desired layer)

o Thickness (the user may define the desired thickness)

Again, after selecting one possibility a new appropriate attribute will be displayed on the right.

3.2.1.5 System

This attribute defines the used coordinate system. It is not possible to adjust this attribute. It isset to Local.

3.2.1.6 Output

This parameter affects the appearance and detail-level of the table with results which may beshown either in the preview or in the Document. There are three predefined layouts which will displaydifferent number and types of parameters and results:

o Brief



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o Advanced

o Detailed

Note

The output parameter may be defined only for Type values attribute set to Required areas.

3.2.1.7 Show Errors

If this attribute is active, then error marks with appropriate numbers will be displayed in thegraphical window after a non successful design. More information about the error may be found in theCalculation info dialog that opens through the Calculation info action button.

3.2.1.8 Show warnings

If this attribute is active, then warning marks with appropriate numbers will be displayed in thegraphical window after a non successful design. More information about the warning may be found inthe Calculation info dialog that opens through Calculation info action button.

3.2.1.9 Print explanation of errors and warnings

If this attribute is active, then a table with all errors and warnings will be displayed in the previewwindow. In fact two tables will be displayed. The first one will display the number of error or warning foreach reinforcement type. The second one will display the error/warning description. This is the sametable as in the Calculation info dialog.

3.2.1.10 Use user scale iso lines

This feature enables the user to define his own scale which will affect the view of the graphicalresults. Simply said, the user may define his own key points on the scale. This might be very helpfulfor better orientation in the used types and amounts of reinforcement. By switching this attribute on,another attribute User scale isolines will appear on the right and the user may define his scale throughthe dialog shown below:



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Name Specifies the name of the user scale.

New level group In this group the user can input a new level for the isolines palette. Thelevel is defined by the diameter of the reinforcement bar and by thedistance between 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 level is defined, it can be added to the legend using thisbutton. The new level is positioned in the legend according to totalreinforcement area of 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 all This button clears the whole legend.



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If this User scale is used, the scale in the top right corner of the graphical window will look likethis:

Note

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

The user may also use the possibility to draw isolines together with labels. Together with exportof the slab picture it might be very useful to transfer these pictures to different CAD systems and

reinforce the entity using exported picture as reference layer. This might be used also for meshreinforcement. Also note that the setting in the 2D result display dialog will be overwritten to User scale isolines

and the possibility to choose different type of result representation will be disabled. To change this, theuser must deactivate the possibility Use user scale isolines.

3.2.1.11 Averaging of peak

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



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3.2.1.12 Location

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

o In centres, (results represented in the centre of gravity of each element, the design valueis 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 based for all other design location possibilities)

o In nodes, avg., (results represented in mesh nodes, but contrary to the “no avg.” values,all values from all adjacent 2D members in each node are recalculated by Scia Engineerbefore 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.

In centres In nodes, no avg.

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



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3.2.1.13 Type values

By this attribute the user may define the type of the value he wants to be calculated anddisplayed. The user may choose from a drop down menu, but the content of this menu differs forInternal forces ULS, Member design ULS and Member design ULS+SLS.

Internal forces ULS Member design ULS+SLS

Member design ULS

o Basic magnitudes (magnitudes of internal forces from the FEM analysis)

o Design magnitudes (magnitudes of forces used for member design)

o

Required areas (amount of reinforcement)o Reinforcement ratio (this is the rate between the amount of required reinforcement and

concrete area)

o Maximal diameters (value of maximal reinforcement bar diameter which might be usedfor member design)

o Maximal distances (value of maximal distance between two reinforcement bars)

o Shear stresses (design and capacity stresses in concrete)

o Weight (weight of the designed reinforcement)

3.2.1.14 Envelope

The user may choose from two options here. He chooses from minimum and maximumenvelope for displaying.

Note

This attribute is displayed only when the Type of load attribute is set to Combination or Class.

3.2.1.15 Reinforcement

The user may choose to design different types of required reinforcement area. There are fourpossibilities:

o Required reinforcement (this is the amount of reinforcement needed for successfulmember design)

o User reinforcement (this is the amount of reinforcement defined by the user. eitherpractical reinforcement already defined on 2D member or reinforcement defined byconcrete member data when the User reinforcement check box is active)

o Additional reinforcement (this is the difference between the amount of requiredreinforcement and the amount of user reinforcement, i.e. this is the reinforcement neededin addition to user reinforcement to fulfil the required reinforcement)

o Total reinforcement (this is the larger value of the required reinforcement and userreinforcement)



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Note

This Reinforcement attribute is displayed only in Member design ULS or Member designULS+SLS when the 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 graphical window. Ifthis attribute is checked, then the designed values will be displayed in the centres of gravity ofselected 2D members.

3.2.1.17 Section

This attribute is used to determine where the design will be shown in the graphical window. Ifthis attribute is checked, then the 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 graphical window. Ifthis 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 elemento Element plane

o X direction

o Y direction

o Z direction

Note

This attribute is displayed only when the possibility to draw designed values on Section or Edgeis checked.

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

3.2.1.20 Course

The user may also define the way of interpretation of the designed values. It is possible tochoose from three possibilities.

o Precise (the precise interpretation based on the mesh)

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

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

Note

This attribute is displayed only when the possibility to draw the designed values on Section orEdge is checked.



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3.2.1.21 Values

This attribute defines the final value to be displayed. The content of this drop down menu differsaccording to selected design and attribute.

Internal forces ULS

Basic magnitudes Design magnitudes

, where values

o mx, my, mxy, vx, vy, nx, ny, nxy represent internal 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 the amount of longitudinal reinforcement for upperor lower surface in a certain direction. Asw value represents the amount of shearreinforcement. These amounts are designed for ULS.

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

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

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

o Member design ULS+ SLS

Required areasReinforcement ratio

Maximal diameters Maximal distances



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, where values

o As1-, As2-, As1+, As2+ represents the amount of longitudinal reinforcement for upperor lower surface in a certain direction. Asw value represents the amount of shearreinforcement. These amounts are designed for SLS.

o

fr1-, fr2-, fr1+, fr2+ are maximal possible reinforcement bar diameterso sr1-, sr2-, sr1+, sr2+ are maximal possible distances between two reinforcement bars

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

Note

Numbers 1 and 2, eventually 3 indicates the direction of the X axis and Y axis of the selected2D member’s LCS. Marks + and – indicate the positive and negative direction of the Z axis of theselected 2D member’s LCS.

Also note that by selecting possibility More comp the user is 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 which results will be shown in the Preview window or in theDocument. The user may 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)

3.2.1.23 Drawing setup

By selecting the edit button for this parameter, a 2D results display dialog will be open. Here theuser may specify the representation of the design results on a 2D member. We can split this dialoginto four zones.



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

o blue (where the user may adjust the type of the representation selected in the Displayzone, the view of this zone may differ for each type)

o green (here the user may define whether to show or not the local extremes and theirstyle)

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

3.2.1.24 Act ion but tons

In the lower part of the Properties dialog there are a few action buttons. The user may find thesebuttons very useful.



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o Refresh (this button is probably the most important from all of them. It will start theprocess of design itself and it must be pressed to refresh the previous design results andget new results based on the chosen attributes)

o Calculation info (this button will open the Calculation info dialog where errors andwarnings related 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 the user will be asked to

save actual finished design to an *.ASF file which might be loaded into anothers CADprogram, such as Allplan, for further reinforcement design)

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



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3.2.2 Internal Forces ULS

3.2.2.1 In general

Before starting the design process itself, it might be useful to check internal forces which willenter the design. It is possible to do so in Internal forces ULS service in Concrete > 2D Member >Member design > Internal forces ULS.

In this service there are presented these types of internal forces which might be changedthrough the attribute Type value:

o Basic magnitudes (internal forces directly from FEM analysis, presented in the localcoordinate system of the appropriate 2D member)

o Design magnitudes (design forces in reinforcement, calculated for reinforcementdirections and design force in concrete compression strut)

As mentioned above, design magnitudes are recalculated into reinforcement directions,moreover in these values also torsion moment mxy is taken into account. It is also possible to calculatewith the influence of tension force caused by shear stress. This can be set in Concrete setup dialogwith attribute Shear effect control 6.2.3(7), under Concrete > ULS > Shear > 2D structures. Thisattribute can be set in three ways:

o No shear effect considered (the tension force from shear stress will not be consideredin the design forces calculation)

o Shear effect considered in R2 (the tension force from shear stress will be considered inthe design forces calculation only on elements where the shear force is not covered bythe concrete capacity, i.e. on elements where shear reinforcement is needed)

o Shear effect considered unconditionally (the tension force from shear stress will beconsidered in the design forces calculation on all elements, regardless whether the shearreinforcement is needed or not)



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The tension force from shear stress is also dependent on the inclination of the shear strut. InScia Engineer it is possible to set two types of shear strut inclination calculation. This can be done inConcrete setup dialog through attribute Shear strut inclination control 6.2.3 which is placed at thesame location in the Concrete setup dialog as Shear effect control 6.2.3(7).

o Variable strut inclination method (inclination is calculated automatically and the aim isto find the minimal value of angle which lies in interval min and max, and condition vd ≤ vRd.max is true, This method optimises the variable strut inclination to determine the

minimal amount of shear reinforcement)

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

The values that will be available in the value list for Type values attribute set to Designmagnitudes depend on:

o Type of the structure set during definition of the project itself. For 2D members project it 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, thenonly n1-, n2-, nc- values will be displayed in the list of values in General XYZ project.

o Number of reinforcement directions. If all 2D members have only 2 reinforcementdirection 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.

n1,n2,n3 Design normal force in reinforcement direction 1, 2 and 3 placed in

the centre of gravity of 2D member. These values are used forreinforcement design.

mc-, mc+ Design bending moment in concrete compression strut for lower



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surface (-) or upper surface (+) which must be covered by concrete.If the concrete strut is not able to cover this moment, the design willend up with error message.

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

nc Design normal force in concrete compression strut placed in thecentre of gravity of 2D member which must be covered byconcrete. If the concrete strut is not able to cover this force, thedesign will 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 the localcoordinate system (LCS). The upper surface is in the positive direction of the Z axis and on the other

hand the Lower surface is in negative direction of Z axis. The upper surface values are marked with +and the lower values are marked with -.

3.2.2.2 Tips & tricks

3.2.2.2.1 Internal forces in Result tree

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

The Elementary design magnitudes in tree Results are determined differently than in theConcrete tree. The difference is that the Elementary design forces are expressed for the X and Y axisof local coordinate system of the 2D member, not for reinforcement directions as it is done fordetermination of the design magnitudes in Concrete tree. In the Elementary design forces the torsionmoment mxy is also taken into account, however the tension force from shear stress not. TheseElementary design forces might be used only for presentation. For design of the amount ofreinforcement the Design magnitudes from Concrete tree are used.

The values displayed in the value list when attribute Type forces is set to Elementary designmagnitudes possibility are only dependent on the type of the structure set during the definition of theproject itself. For 2D members project it is possible to set three options, Plate XY, Wall XY and generalXYZ.



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Plate XY Wall XY General XYZ

Description of the values above:

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

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

nxD+, nxD- Design normal force in the X axis direction of the local coordinate

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

system (LCS) for lower surface (-) or upper surface (+).

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

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

Note

The upper and lower surface of 2D member is determined by the Z axis direction of the localcoordinate system (LCS). The upper surface is in the positive direction of the Z axis and on the otherhand the Lower surface is in negative direction of Z axis. The upper surface values are marked with +and the lower surface values are marked with -.

3.2.2.2.2 Comparison of design in ternal forces in Concrete and Results t rees

The Design internal forces magnitudes in Concrete tree and Results tree have the same valuesonly when the selected 2D member:

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

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

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



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

Comparison of the results in the Results and Concrete trees will be done for the type of thestructure set to Plate XY. The structure is a simple 2D concrete member which dimensions are 6 x 8meters and the thickness is 200 mm. It has defined concrete C25/30 and it is supported on threesides. It is subject to a constant surface load of 10kN/m2. No member data are defined on this 2Dmember.

3.2.2.2.2.1 Two perpendicular reinforcement directions, identical with X and Yaxes 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. The influence of tension forceis not considered for shear reinforcement. That means that attribute Shear effect control 6.2.3(7) is setto no shear effect is considered possibility in the concrete setup dialog.



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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-

Numerical comparison of the moment for both surfaces and directions for elements 1-24 (half ofthe 2D 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 -34,61

LC1 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 -21,66LC1 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



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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 perpendicular reinforcement directions, identical with X and Yaxes of LCS, shear effect considered

The same settings as in the previous chapter will be used here with one exception. Theinfluence of the tension force is considered for shear reinforcement. That means that attribute Sheareffect control 6.2.3(7) is set to shear effect considered unconditionally possibility in the concretesetup dialog.



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



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 -6,64

LC1 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



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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 -16,07LC1 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 the design forces are different in both trees. It is due to the factthat in Concrete tree the tension force from shear stress is considered. In this case it is necessary tomake check of internal forces only in the Concrete tree.

3.2.2.2.2.3 Two perpendicular reinforcement directions, rotated with 45 degreesaccording 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. The influence of the tension force isnot considered for shear reinforcement. That means that attribute Shear effect control 6.2.3(7) is set tono shear effect is considered possibility in the concrete setup dialog.




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



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 -23,03LC1 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

LC1 9 0 25,39 -10,6 9,17 0 -23,97 0 25,39 -10,6 9,17 0 -23,97

LC1 10 2,92 32,58 -10,79 3,54 0 -28,25 2,92 32,58 -10,79 3,54 0 -28,25

LC1 11 8,99 35,78 -15,45 0,86 0 -30,18 8,99 35,78 -15,45 0,86 0 -30,18

LC1 12 13,11 38,62 -22,55 2,82 0 -31,99 13,11 38,62 -22,55 2,82 0 -31,99

LC1 13 0 -8,52 -35,6 41,67 34,31 -31,86 0 0 0 41,67 34,31 -31,86

LC1 14 0 10,22 -16,59 19,42 1,8 -14,85 0 10,22 -16,59 19,42 1,8 -14,85

LC1 15 4,08 24,57 -10,7 2,76 0 -20,71 4,08 24,57 -10,7 2,76 0 -20,71

LC1 16 13,09 32,66 -13,36 -4,69 0 -27,7 13,09 32,66 -13,36 0 0 0

LC1 17 20,73 38,52 -20,05 -7,18 0 -32,03 20,73 38,52 -20,05 0 0 0

LC1 18 26,29 43,14 -30,36 -2,87 0 -36,2 26,29 43,14 -30,36 0 0 0

LC1 19 0 -11,93 -39,47 45,31 42,84 -36,75 0 0 0 45,31 42,84 -36,75

LC1 20 1,02 7,01 -17,01 15,99 10,01 -17,01 1,02 7,01 -17,01 15,99 10,01 -17,01

LC1 21 11,69 18,76 -11,55 -3,34 0 -15,55 11,69 18,76 -11,55 0 0 0

LC1 22 21,55 28,37 -14,27 -12,02 0 -23,63 21,55 28,37 -14,27 0 0 0

LC1 23 29,67 35,89 -21,95 -13,87 0 -29,75 29,67 35,89 -21,95 0 0 0

LC1 24 35,75 41,62 -33,84 -7,24 0 -36,29 35,75 41,62 -33,84 0 0 0

It is obvious from the table that design forces are identical in both trees. It is due to the fact thatonly two perpendicular reinforcement directions are defined and the first reinforcement direction angle



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is identical with the rotation angle defined in 2D Member – Internal Forces attributes, in Results tree. Ifdifferent reinforcement direction angles were defined in 2D Member data for lower and upper surfaces,then the results in the Results tree would have to be recalculated separately for each surface.

3.2.2.2.2.4 Two non-perpendicular or three reinforcement directions

Three angles of 0, 45 and 90 degrees are defined in Member data. Rotation attribute in 2DMembers – Internal Forces, in Results tree, has 0 (zero) value. The influence of the tension force is

not considered for shear reinforcement. That means that attribute Shear effect control 6.2.3(7) is set tono shear effect is considered possibility in the concrete setup dialog




In this case the results will be different in both trees. Results in Result tree can’t be “fixed“ withLCS rotation or by adjusting Rotation attribute. General transformation would have to be used. In thiscase it is necessary to make the check of internal forces only in Concrete tree.

3.2.2.2.3 Determination of design internal forces in Results and Concrete tree

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



54

3.2.2.2.3.1 Determination of design internal forces in Results 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

mxymx

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


Condition (1) fulfilled, then:

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

(4)my

mxymy

2

if mymx and mxymx



831422 , mxy mcD

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



55

3.2.2.2.3.2 Determination of design internal forces in Concrete tree

According to this method the basic internal forces and their directions must be determined first.In Scia Engineer these magnitudes are presented in Results in 2D Members – Inner forces item, if thetype of the value is set to Basic magnitudes possibility.

Value Formulas Calculation

z

Determination of effective height and lever arm.

z = 0,9d

dlo = dup= 200-45 = 155mm

z = 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 = 106,38kNnx.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

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 for 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.

, ∙ sin, ∙ sin, , ∙ cos, ∙ cos,sin, ,∙sin, ,

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

n2+ =-0,09 kNnc+ =-216,03 kN



56

, ∙ sin, ∙ sin, , ∙ cos, ∙ cos,sin, , ∙ sin, ,

, ∙ sin , ∙ sin, , ∙ cos, ∙ cos,sin, , ∙ sin, ,

m j,-(+)

While type of the structure is set to Plate, design forces

will be transformed into moments by formula

m =n·z

m1- = 21,79 kNm

m2- = 32,58 kNmmc- =-29,66 kNm1+ = 5,44 kNmm2+ = -0,014 kNmmc+ =-30,14 kN

Note

Formulas in the tables are usually named for lower surface only, but the same formulas with

changed indexes stands good for the upper surface.

3.2.2.2.4 Determination of design internal forces for General XYZ structure

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 thecentre of gravity of the member. If reinforcement directions for both surfaces are identical, then it ispossible to determine these effect using the 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 the values of normal forces in reinforcement direction for lower (-)and upper (+) 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 calculation uses the 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.



57

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

m1

n1

Determination of normal forces in reinforcement

direction 1 (0 degree).m1 =(d1 – 0,5h)·n1- +(0,5h- d1)·n1+

n1 =n1+ + n1-

n1+= 146,5kN/m

n1-= 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/mm2 = 11,97kNm/mn2 = 200,1kN/m

3.2.2.2.5 Determination of inner forces with influence of shear force

As it was mentioned in previous chapters, values of design magnitudes in Concrete tree dependon whether the influence of tension force from shear is taken into consideration. This influence may bechanged in Concrete setup dialog under Concrete > ULS > Shear > 2D Structures. If this influence istaken into consideration, then resultant of tension force from shear (value Ftdj) is incremented to theresultant 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



58

vdj,lo(up)

Recalculation of resultant shear force to the principalforces directions, where 50% will be added to upperand 50% to lower surface.

, 0.5 ∙ ∙ cos , 0,5 ∙ ∙ sin

vd1,lo = -1.98kNvd2,lo = -5kNvd1,up = 5kNvd2,up = -1,98kN

Ftdj,lo(up)

Determination of tension force increment from shear.∆, , ∙ cot

∆, , ∙ cot

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

Ftd1,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 the calculation of tension force from shear according to the EN 1992-1-1, chapter 6.2.3(7) condition MEd/z + Ftd ≤ MEd,max/z is being checked.

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

Resultant shear force angle is presented in Results tree under 2D Members – Internal forces,for attribute type forces set to Principal magnitudes possibility. It is named as beta. In Concrete tree itcan be 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 and it can be found under

Member design ULS, for attribute output set to Advanced or Detailed, forAsw

value.

3.4.3 ULS

3.4.3.1 Theoretical background

Reinforced 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 surfaces of the 2D member. Scia Engineer puts noprincipal restrictions upon the absolute position of reinforcement courses within the cross-section, itsaxial concrete cover describes the position of each reinforcement course. However, there are relativerestrictions: all concrete covers must fulfil some rules to prevent ambiguousness of the geometricdefinition of the design task. These rules are described in the part of the Scia Engineer manual. Yet it

must 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.



59

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 influence the effective static

height 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,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 the

mathematical formulation replaced by assigning them the ordinal numbers 1, 2 and 3 (if threereinforcement courses are specified). The same double identification may be given to other associatedterms like reinforcement angles, design forces, effective static heights, internal forces levers, etc. Sowe can say, e.g., about reinforcement angle α, β, γ meaning the same, when alternately indicating α1,α2, α3. There is no indication that this ambiguity of terms should cause confusion; as a fact, there isno ambiguousness for the correspondence of both systems of denotation is clearly defined.

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 standards implemented in SciaEngineer. However, for Scia Engineer deals with several national codes, it is probable that this or thatterm or formulation would appear somewhat unfamiliar to some readers focused on the use of one

code branch only. It is hardly possible to create a manual text on such special topic for internationaluse being in all respects verbally fully conform to every country’s verbal usage. In doubts, theterminology of 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 Design

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

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

(6) has symbolic meaning only, as we do not want to write down at this stage all the exactcalculation rules for codes implemented in NEDIM (the original development name of the 2D designmodule system, used internally by SCIA developers, testers and supporters for quick communication).



60

The symbol σsd stands for the effective design steel strength. Both ni and σsd may be, according tothe actual code, charged with security coefficients. We are not going to discuss the problem of 1Dreinforcement design; the NEDIM algorithm strictly follows special rules stipulated by national codesand associated Standards, as far as they are applicable to the 2D design.

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 inputdata. 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 is

stipulated, 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:

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 sectional area.NEDIM checks if the steel reaches the compression yield strain; if not, σscd reflects the actual strainlevel. Some codes (ÖNORM B 4200, CSN/STN 73 1201, GBJ 10-89) stipulate different values of steelstrength in tension and compression. NEDIM follows this idea by enabling different definitions of

tension and compression steel strength to all code branches.

3.4.3.1.2 Plate Design

In the Wall model dealt with in the preceding paragraph, the internal 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 codes implemented in NEDIM exclude the tensile bearingcapacity of concrete (ULS), the only bearing material in the tension zone (“below” the neutral axis) isthe reinforcement steel. The resistance of concrete is exploited in the compression 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 compressive stress in Fig. 3 is not related to a specific code. However, thecodes implemented introduce different basic notions of the concrete compressive stress distribution.The assumption of the compressive stress distribution is in affinity to the σ-ε diagram of the concretematerial.

EUROCODE 2 allows for all national code assumptions. Actually, NEDIM keeps to theparabola-constant concrete compressive stress distribution assumption. EC 2 introduces a newapproach for 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 in 1999 it was implemented into the EC 2 design branchas well as into all other design branches following the same (or similar) approach. For more detail onthis phenomenon, named Shear Effect by the Author of NEDIM, see paragraph Advanced notes on"Shear Effect".



61

EN 1992-1-1:2004 is the EC 2 amendment of the preliminary European Norm ENV 1992-1-1:1991. Extensive modifications to the original text have been made in all sections. Especially theparagraphs on shear proof, crack control and minimum reinforcement control have been expandedand diversified, e.g. (a) all "reasonable" assumptions of concrete stress-strain diagram are allowed,namely the three basic cases: pressure block, linear-constant and parabola-constant. For the blockdistribution, restrictions to height and stress have been introduced: λx and η fcd ; (b) therecommended value of the strength reduction coefficient in f

cd = α

cc f

ctk,0.005/ γ

c is α

cc = 1.0 (for the EC2

code family is typically αc = 0.85); (c) the strength reduction coefficient ν1 in the formula for the shearstrut resistance vRd,max is more diversified and the coefficient αcw of the same formula expresses theeffect of normal stress upon vRd,max on three intensity levels; (d) the crack calculation formula (directcontrol) resembles that of DIN 1045-1, however, the crack distance formula depends here on 4parameters.

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 m i for the design moment associated with the reinforcement

course 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 codes.

The internal forces lever z i in (11) makes out the formal difference of (6) and (11); factually,there is no difference between them, since the quotient m i /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).

(11) reveals the fundamental meaning of the internal forces lever z for the design algorithm. Asa fact, 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 internal forces lever z is calculated by the following procedures:

o For DIN 1045 and ÖNORM B 4200 interpolation formulae for the value of z were

developed. The maximum approximation error amounts up to 2%, however.

o For all other codes (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 middle of 2007 it had not been known to the Author of NEDIM that any competingsoftware would deal with this problem at all. Neither codes nor theoretical publications on reinforced



62

concrete design care about the state of concrete in a heterogeneous concrete-steel 2D medium.Some codes give “standardized” recommendations as to the geometrical arrangement ofreinforcement in reference to the directions of the principal moments. They are concerned with stresssituations which are typical for corners of floor slabs etc.

Figure 3 Equilibrium of design internal forces in a Plate cross-section : (a) reinforcementcourse 1; (b) reinforcement course 2; (c) concrete stiffening strut – course 3; (d) strain situation in thestiffening strut (bearing ability proof).

3.4.3.1.3 Shell Design

In the design of Shells, the ideas and procedures of both the design of Walls and the design ofPlates are combined. The code 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 maydevelop from a typical "Wall pattern" with constant stress distribution to a "Plate pattern" with

characteristic 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 codes 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 meshes 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 designsituations at both Shell faces which must be managed in two algorithmic steps in every cross-section

by considering the situation on the other face. In this sense, the Shell design is organized like thePlate design.



63

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.

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.

3.4.3.2 2D Structures detailing

Sometime amount of statically required reinforcement is not determining for finally designedreinforcement and different check come in place. These checks may be switched off/on or adjusted in

the concrete setup dialog in Detailing provisions chapter and under Calculation chapter.



64

Minimum transverse reinforcementMinimal amount of transverse reinforcement, determined as a percentage of the main

reinforcement. This check has two options.o Inactive reinforcement excluded (amount of transverse reinforcement is calculated only

from statically required reinforcement)

o Inactive reinforcement included (amount of transverse reinforcement is calculated from allthe 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 compressionzone related to the concrete compressive force. Default value = 50%.

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)



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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 two

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

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)



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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 the direction of the yaxis of the member LCS, where we expect more amount of reinforcement. We need also redefinedesign defaults settings, where the reinforcement 1 direction is identical with the X axis of the member

LCS. This will be done by defining member data and setting Layer angle parameter for first direction to90 degrees. This layer will be now closer to the surface and will decrease the amount of designedreinforcement little bit. We could change the reinforcement direction also by adjusting the first directionangle and rotating the whole reinforcement system.

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



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

For better orientation in the design process, all types of reinforcement will be shown in the tablebelow.



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Required reinforcement User reinforcement

Additional reinforcement Total reinforcement

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. The user may switch to brief, detailedor advanced mode, as we did in this example. We can see that maximal amount of reinforcement for

lower surface and direction 1 is designed to 1295mm

2

/m.

Now the user has to decide how he wants to reinforce the designed member. Whether he wantsto define each reinforcement layer manually or if he wants to use automatic definition of reinforcement

from concrete member data. The second possibility is much common and more useful, so we willshow this one. The user has to activate User reinforcement check box in the concrete data first. Thiswill enable him to define Basic distance of bars.



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After this, the amount of user reinforcement is determined directly from concrete member dataand the user may simply adjust it by changing appropriate parameters (diameter, basic distance).Default values are loaded from Concrete setup dialog, which might be changed in Design defaults.Let’s see the differences in designed amounts of reinforcement just after activating the userreinforcement check box.




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Now the user reinforcement has non-zero values and accordingly to this change, amount of

designed 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 weget these results.




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From this results we can see that the defined reinforcement is sufficient on mostly whole 2D

member 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 creating a separate reinforcement polygon.

We can now proceed to creating practical reinforcement from user reinforcement. We have theUser reinforcement check box active, so we can simply double click the Reinforcement 2D item in theconcrete tree. The dialog below will be displayed and a new practical reinforcement will be createdfrom the user reinforcement previously defined by concrete 2D data.

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.



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



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At this time we have fulfilled the requirements for direction 1 at the lower surface. No additionalreinforcement is needed. The upper surface and other directions might be handled in a similar way wehave shown here.

3.4.4 ULS+SLS

3.4.4.1 Theoretical background

The most important serviceability proof is the Crack Proof. As first implementation in NEDIM thecrack proof was introduced in 1997.



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The contemporary theories of crack development in a concrete-steel compound medium havebecome very complex. Practical engineers, confronted with a plenitude of contradictory ideas andformulae, may feel doubts on the reliability of such calculations. However, it should be understand thatall crack theories have probabilistic a nature. They try more or less successfully to give analyticalexplanation to empirical data of the crack behaviour of real structures. In 2D structures even thefundamental question, in what direction the main (first) cracks arise, has not been decided uniquely:

o perpendicular to the direction of 1st principal forces nI or mI (Fig. 13a,b)

o perpendicular to the reinforcement courses (Fig. 13c)

o parallel to the virtual stiffening concrete strut

o erratic (combined) crack patterns etc. This assumption comes, no doubt, most closely tothe reality; on the other hand, it is obviously least productive in stimulating efficient,simply crack control methods.

The NEDIM crack proof algorithm follows formally the assumption of Fig. 13c. However, itappears contradictory to the Baumann transformation theory, which prefers the assumption of crackparallel to the virtual stiffening concrete strut. Nevertheless, the NEDIM approach to the crack proofmay be defended by following considerations:

o The design forces ndim, assigned to the reinforcement courses, attain, as a rule, valuescomparable with the governing principal forces n I,II (mI,II), since the strut force n3d is negative (n3d denotes, strictly speaking, the strut force in 2-course nets; as a fact, in 3-course reinforcement netsthe strut force need not to be assigned the subscript ‘3’). Only in three-course nets the relation max|nd| < nI,II may become true under elliptic states of stress. However, such states of stress are the lesscritical for the cross-section resistance, and the cracks may the more tend to erratic patternsdistributed over all three courses.

o The NEDIM crack proof algorithm is able, as will be demonstrated below, to distinguishqualitatively between different states of stress of the structure. Thus the formal “linearization” of thecrack proof process does not ignore the 2D character of the reinforcement concrete medium.

o All codes stipulate crack control formulae primarily for a 1D state of stress. The NEDIMcalculation assumption of cracks developing perpendicular to reinforcement courses enables to

organise the crack proof in quasi 1D steps running over individual reinforcement courses, in the samemanner like with the ULS design.



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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)



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

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 (27

1) follows thus s

r,max = s

r,1/ √2 ≈ 0,707 s

r,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 between

concrete 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 codes, 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 directconsequence. 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 code 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 codes.

In Chapter Program Theory and Algorithm in literature [1] the notion of the virtual cross-section

design 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 descriptionof the state of stress in the cross-section, especially in case of non-congruent reinforcement at bothfaces. Since most codes consider the stress distribution pattern (bending ↔ centric tension) as



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important 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 hyperboliccases 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. The

information 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.

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 low

eccentricity; (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 at

choice :



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

cracks 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 distancesULS+SLS design is also affected by the reinforcement amount checks mentioned in

chapter 3.4.3.2. But here, another two checks are to be introduced. They are located underLimit bar distances chapter.

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.



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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 design3.4.3.3 chapter and continue with it. We will also focus only on the lower surface and direction1. At the 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.



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As we can see in the pictures above, the required reinforcement is a little bit larger thanreinforcement provided for ULS design. It is clear that additional 165mm2/m has to be defined andreinforcement polygon has to be enhanced, in order to ensure that cracks at the lower surface indirection 1 will not be larger than 0.2mm (for the XC3 exposure class). We can delete thereinforcement and create a new one which will be sufficient for both ULS and ULS+SLS design, butwe will adjust already defined practical reinforcement to fulfil the ULS+SLS design requirements. The

changes may be checked at the



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Then if we run the reinforcement amount design of the 2D member, we will get these results.




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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, the userwould like to calculate reinforcement amount with crack width converging to 0mm (zero). It is notpossible in Scia Engineer to use direct zero value and user has to input minimal value of 0.01mm inthe Concrete setup dialog, to successfully finish the ULS+SLS design.



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3.5 Section on 2D memberSometimes the user might find useful or necessary to display his results in specified position on

the 2D member. Then he is allowed to define his own section across the 2D member where thedesigned result values may be displayed separately or in addition to other drawing styles. Definition of2D member section can 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 todraw 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, the user confirms the dialog and manually defines theposition itself. When this is done, also coordinates of the 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).



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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.



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3.6 2D ReinforcementGenerally there are two ways, how to define practical reinforcement for 2D concrete members in

Scia 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 Data

This is very useful feature which will create reinforcement layers according to the settings whichare 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 the ordinary Reinforcement 2D dialog for manualdefinition of reinforcement is displayed.

3.6.2 New Reinforcement¨

Sometimes the user may find manual definition of the Reinforcement more useful. To do so, theuser may simply use the item Reinforcement 2D in concrete tree or click action button New



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reinforcement. This will display the Reinforcement 2D dialog where the user may define reinforcementparameters. Only one layer may be defined at a time.

Attributes in Reinforcement 2D or Reinforcement 2D mesh dialog are similar to 2D Member dataproperties.

Name Specifies the name of the reinforced region.

2D member Shows the name of the member, where the reinforcement is placed.

Type

o Bars User defines numbers, diameters, etc. of bars in individual layers.

o Mesh User selects a pre-defined reinforcement mesh (usually made by a stainlesssteel mesh manufacturer) from a library of reinforcement meshes. After selection of thispossibility the user may define his own reinforcement mesh or choose already predefinedone from library.



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Material Defines the material for the reinforcement.

Surface Specifies the surface: lower, 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 of thereinforced region is defined by means of the following parameters.



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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 Subtraction 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. Similarly theother reinforcement types calculate with it. The user may come across two possible situations whenthis is declined:

o If there is already defined practical reinforcement (the one, which physically exist in themodel), which has different material, than the material defined in Member data. If thishappens, then user will be warned by the error message below and this userreinforcement is not recognized.

o Second situation may happen when the user has also practical reinforcement defined onthe member and has activated the possibility “Check of concrete cover for subtracting2D user reinforcement from required reinforcement”. This can be done underConcrete > General > Calculation > 2D user reinforcement. When this check box is

activated, new input parameter appears just below and the user may define requiredvalue. All reinforcement layers within this range will be ignored by the design. The errordialog is also displayed and design will end up in same results as in the first case.



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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:




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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.




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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.



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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 the 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 delete

vertices.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 a point or line object, you can simply modify its shape byadjusting 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.

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 other

hand, it may be sometimes more convenient to input separate bars. This feature is also necessarywhen 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 the

members into which these bars are included. Free bars are considered in all calculations (design and



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checks). 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.Dir Z This parameter defines the distance between individual bars in the set in Z direction.

Horizontal Defines the horizontal position of the description (label) of the reinforcement bar.

Vertical Defines the vertical position of the description (label) of the reinforcement bar.

Location Defines if anchorage length is to be defined with the bar or not. It is possible todefine these five locations:

o None No anchorages will be defined.

o Begin Anchorage will be possible to be defined at the beginning of the free bar.



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o End Anchorage will be possible to be defined at the end of the free bar.

o Both Anchorage will be possible to be defined both at the beginning and at the end of thefree bar.

o Both separated Anchorage will be possible to be defined both at the beginning andat the end of the free bar independently.

Add/subtract Specifies whether the specified anchorage length is to be added to the input bar orwhether the effective length of the bar is obtained from the defined bar bysubtracting the specified anchorage length.

Length Specifies the anchorage length.

Curve type Defines the type of the curve in bents of the reinforcement.

Curve parameter Defines the parameter of the selected curve.

Once a free bar is input, it represents a standalone entity that has no relation to any of thedefined beams, columns, plates, etc. in the model. It is necessary to allocate the bar to requiredmembers. The allocation can be done through the corresponding action buttons.

o Manual allocation The user manually selects the members where thereinforcement free bar is allocated. To do so, select the required free bar and click actionbutton [Select allocation]. Then follow with the selection of appropriate members.

o Automatic allocation The program automatically selects the members where thereinforcement free bar is allocated. To allocate bars automatically, click action button[Allocate automatically]. The program does the allocation on its own.

3.6.4.1.1 Editing the reinforcement parameters

If user want to change some existing free bar parameters he might simply edit and modifyparameters in the reinforcement attributes.

1. Select the required free bar.2. Its properties are displayed in the Property window.3. Make necessary changes.4. Clear the selection.

3.6.4.1.2 Edit ing the free bar geometry

Sometimes the user also needs to adjust or redefine the free bar geometry. This can be doneby following few steps below.

1. Select the required free bar.2. Its properties are displayed in the Property window. A few action buttons are displayed in the

Property window as well.

3. Click button [Table edit geometry] to get a table with bar coordinates. You may modify theshape in this table.4. Alternatively, you may click button [Edit free bar geometry] to be able to edit graphically the

shape 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, thereinforcement 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.



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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.

3.6.4.3 Free bars user reinforcement

Free bar is a different entity than reinforcement polygon and the displayed user reinforcement

consisting of free bars may, and usually does, look differently. We can show the difference on a simpleslab, already used in previous chapters. We will display one-directional user reinforcement for lowersurface of the slab. Reinforcement is defined in the global x-axis direction. In the first picture, there is astandard reinforcement polygon defined with bars (diameter 10mm) and 500mm spacing. In thesecond picture, there are free bars created from the reinforcement polygon that is in the first picture.Reinforcement amounts are the same on both slabs. We are displaying the user reinforcement definedon 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 a “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 the arithmetic

product of the free reinforcement bar area and hardcoded value of (1/0,3). In our case itis 78.5 * 1/0,3 = 262 mm2



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o the last step is to assign the appropriate intensity of reinforcement into each meshelement 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. The virtualreinforcement area 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

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. User

reinforcement 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 reinforcement

area width above the adjacent elements is (300-200)/2 = 50mm. User reinforcementamount in the 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 two possible solutions for improving thedisplaying results can 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 the user may not want to change the distance between reinforcement bars, increasingthe 2D mesh element size will result in more continuous results as well.

In 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 at the beginning.



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3.7 Averaging stripThis functionality provides automatic averaging of peak results around defined points or along

defined 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.

To create a new averaging strip the user may simply double click item Averaging strip inconcrete tree. The dialog shown below appears. The user may define in it a few parameters which willdetermine the averaging strip location and its parameters. After confirmation the user defines

averaging strip location in the graphical window.



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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.

We can demonstrate the functionality on a simple example. Let’s create a 4x4 meters concreteslab with thickness of 200mm, made of concrete C20/25. It will be supported according to the pictureand subject to self weight. The mesh size is set to 1 meter. Two meter wide averaging strip was inputin the Y direction with the averaging direction set to 'Perpendicular'.



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Non-averaged result of moment my with location parameter set to In nodes, no avg.

Results of moment my averaged with averaging strip, with location parameter set to In nodes,no avg.



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Manual verification

Create sections perpendicular to the inputted averaging direction. In this example, theaveraging was set to 'perpendicular' => create sections in longitudinal direction.

o 2D section A is input just outside the strip from (0;3,001) to (4;3,001)

o 2D section B is input just inside the strip from (0;2,999) to (4;2,999)

o 2D section C is input in the middle of the slab from (0; 2) to (4;2)

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

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



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

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

Conclusion

Now if we compare this averaged numerical results in mesh nodes and the non averagedresults on 2D sections, we come to the conclusion that the values are equal.



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Note

Basic size of the averaging strip should be, in general, sum of the width of the support andthickness of the slab doubled. Nevertheless, the final size of the averaging strip should be alwayschecked by an experienced engineer.

If the averaging strip is not in the coordinate system of the macro, then the transformation ofinternal forces to the averaging strip LCS is done before the averaging itself. After that, a backward

transformation of the averaged internal forces back to the macro coordinates is performed. A special view parameter can be found in the View parameters setting dialogue, under folderStructure/Averaging strips. Tick option Display to see the averaging strips (default) or clear the optionto hide them.

3.8 Code Dependent Deflections (CDD)

3.8.1 Introduction

The names PNL calculation (or analysis) (physically non-linear calculation) and PGNLcalculation (or analysis) (physically and geometrically non-linear calculation) are taken from previousversions of the software. These terms are very similar and may be a bit misleading.

Therefore, it is useful to start with a few words about the features and principles of the two types

of analysis. First of all, it may be reasonable to establish more explanatory names.What was known as a PNL calculation should be called calculation of deflections according

to a standard. Starting from version 2008.1 the term PNL was replaced by more suitable

Code Dependent Deflections (CDD)

What was known as a PGNL calculation should be called physically (and geometrically) non-linear calculation.

This fact in turn may lead to shortening of the name of the second calculation type to "physicallynon-linear calculation" which may be abbreviated PNL. Now you can see one of the reasons why amore reasonable naming should be introduced. The second reason is that the old PNL calculation(CDD from 2008.1 on) is not a real physically non-linear calculation in terms of finite element method(contrary to PGNL that is a real nonlinear calculation). It is a two-step solution following exactly the

regulations given in technical standards for design and checking of concrete structures.Both analyses are aimed primarily at concrete structures. The "calculation of deflections

according to a standard" has been designed exclusively for concrete beams and plates, as it is basedon the wording of technical standards for design and checking of concrete structures. The "physically(and geometrically) non-linear calculation" is a general procedure tailored for the analysis of concreteframes (as it takes into account the provided reinforcement), but it is not limited to such structures.

3.8.2 In general

This calculation of deflections depends (is based) on standards. Therefore, it represents astandard-related calculation that is performed in two steps. First, a normal linear calculation is carriedout and the computed internal forces are used to input the reinforcement (the provided reinforcement)or at least to determine the required reinforcement areas. The procedure continues with the

calculation of cracks and their effect on the stiffness of individual elements. This weakening is theninput into the solver. Finally, the calculation (linear one) is run once more with this reduced stiffness’staken into account. Which is exactly what the technical standards require.

The short-term deflection is calculated. This deflection is multiplied by the creep coefficient andthe long-term deflection is obtained. It is known that the elastic deflection multiplied by the creepcoefficient 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 to take into account the effects of cracking, material nonlinearity and creep. Creep is taken into

the analysis using the effective modulus of elasticity for concrete according expression 7.20 of EN1992-2-2



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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 calculated

using the short-term stress and strain diagram. Additionally by subtracting the immediate deformationfrom the total deformation, the program determines the additional deformation.

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.



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The short- and long-term stiffnesses 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.

The following steps must be performed before running the 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 state

designso If no practical reinforcement is input, then at least some required reinforcement must be

calculated

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 theoreticaland practical reinforcement

Use of practical reinforcement, .e.g. the reinforcement which is really assumed in the concretemember is a more realistic assumption to perform the analysis. However, the program doesn’t warnthe user in the case he doesn’t use the practical reinforcement.

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



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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.

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 bars

inputted 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 the CDD – deformations calculation is

performed. 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 the value of Md larger thanMu, than the stiffness according to Mu is taken. Since the finite element method can give large internal



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forces due to singularities, etc. the calculation is allowed to continue without an error message, butsupplies messages after the calculation has finished.

The program always converges to a solution. The program does not warn the user when theloading is bigger than the capacity of the cross section. It is assumed that the user did in a first step aproper design of the reinforcement in the concrete members.

Note

The user can define the creep coefficient, or let the program determine the creep coefficientusing the EC appendix B1. 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 practical reinforcement hasbeen defined in the member.

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. Userreinforcement for both surfaces and both directions will satisfy the ULS design only. For informationabout the input reinforcement see table below:



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User reinforcement As1- User reinforcement As2-

User reinforcement As1+ User reinforcement As2+

After the reinforcement design of the user reinforcement for ULS state, it is time to define thereinforcement 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 this

parameter to User reinforcement possibility. Then we must run the design once again to regain theamounts of reinforcement.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.



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

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



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

3.8.3.1 Stiffness presentation

In this service the user may choose to display two types of results. Location is set permanentlyto “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 Stiffness

EI1,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 2EI1,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.



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3.8.3.2 Deformations

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

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



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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

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