fagus6__materials and analysis parameters

Materials andAnalysis

Parameters

Manualfor generation 6 of

cubus programsCopyright Cubus AG, Zurich

1. Materials1.1 Material Management

1Materials / Analysis Parameters

Materials and Analysis ParametersIn the different CUBUS programs all members have allocated construction materials,whose properties are needed for static analysis and in reinforcement design procedures.The handling and management of theses materials and their properties are defined uni-formly in the programs CEDRUS-6, STATIK-6, FAGUS-6 and PYRUS-6 and described below.

1. MaterialsAt the outset of a new project all construction materials and their relevant propertiesshould be defined or reviewed. This can be done through the material management dialo-gues.

1.1 Material Management

1.1.1 Overview dialogueThe overview dialogue for the material management is accessed through the menu 'Op-tions' >'Materials'. All the available construction materials are shown as follows:

The columns in the overview have the following meaning:

ID

This is the name allocated to each individual material in the components. It is composedof three parts:

a: character identifying the material type (see below), i.e. 'C' for concreteb: character identifying the component type (see below) i.e. 'C' for columnc: a freely selectable designation of nil to two capital letters or numbers

The reason for prefering the ID over the class name is that construction materials haveadditional properties also listed in the overview. In addition there are advantages in the al-location to the components, as the following example shows. A bridge contains su-perstructures of concrete CB and columns of concrete CC. If you are forced to change theconcrete class of the superstructure, the class of the material CB can be adjusted accordin-gly, otherwise a new class would have to be allocated to all cross sections of the superstruc-ture.

Type

The type of construction material defines amongst other things the one dimensional mate-rial relationship and can only be chosen with the initial input of the construction material.

1.1 Material Management 1. Materials

2 Materials / Analysis Parameters

Certain structural elements allow only certain construction material types. A reinforcementbar cannot be type 'concrete'. The following construction material types and their identifi-cation in the Material ID are available:

C Concrete

R Reinforcment

P Posttensioning

S Steel

W Timber (Wood)

U Aluminium

F FRP

M Masonry

X Special

Member

Here a member (component) type, to which the construction material has initially been as-signed, has to be chosen. The following component types and their identification in the Ma-terial ID are available:

General '_' if there are no subsequent characters in the ID, '_' is omitted.

B Beam

C Column

P Slab

W Wall

F Foundation

E,G

The modulus of elasticity and the shear modulus are used for the evaluation of deflectionsand forces in th FE-model (stiffnesses in CEDRUS and STATIK). The default values are in-itialised with from selected material class but can be overwritten.

,,

: Density (e.g used for dead-load): Coefficient for thermal effects: Poisson's ratio ;There is no relation between G and ;

in STATIK G is used; in CEDRUS used

Color / Hue

The colour for the display on screen and for the printed output can be chosen from the listof the colours for construction materials. These can be changed in the menu 'Representa-tion' > 'Colours/Line types'.

Different hues may be chosen varing in intensity and brightness.

Classes

Subject to the code chosen, several predefined construction material classes cannot bechanged by the user. However, user defined classes may be introduced.

The properties of the class are code specific with regards to terms and extent. They are usedin cross section analysis and are irrelevant for the linear elastic structual analysis withCEDRUS and STATIK. Further information can be found under 1.1.1.2 and 1.2.

1. Materials1.1 Material Management


1.1.2 Introducing, changing and deleting materials

The material overview dialogue offers three buttons for introduction, modification and de-letion of construction material.

Only construction material not used in the current calculation may be deleted.

The following dialog appears when introducing a new construction material:

Type and member shown above are the first two characters of the construction material ID.Nil to two characters (numbers or capital letters) may be used as designation. Please usewisely as this input cannot be changed later on.

After pressing [OK], the same construction material dialog is shown, as used when editingan existing construction material:

Button for the material classdialogue (. 1.1.3)

Here all properties of construction material may be adjusted, as specified above.

Please note that the above-mentionned values for E,G are predefined according to the classchosen. However, they may be changed later and will stand in wanted discrepancy to theclass properties. The two values are used for the determination of the stiffnesses in linearelastic structural analysis in STATIK (E,G) and CEDRUS (E, ).

1.1.3 Management of material classes

This button next to the class box in the construction material dialog opens the summary ofconstruction material classes:

This dialog contains the assigned construction material classes of the construction materialcurrently in use. The columns are dependent on the code used and the construction mate-

1.2 One Dimensional Stress-Strain-Diagrams 1. Materials


rial type. The dimmed values shown are defined by the code and cannot be changed by theuser.

1.1.4 Attributes of material classes

In general in the national codes the default values are given as characteristic values Xk:

A certain design value Xd is then calculated with

Xd=xkM

= characteristic material strength= partial factor

xkM

Depending on the type of material Xk is

fck, fyk, fpk Charact. values for concrete, reinforcing steel, prestressing steel

an for M

c, s, p, a Partial factors for concrete, reinforcement, prestressing steel

The partial factors are defined in a separate tabsheet ('Analysis Parameters'). For concretethere is an additional value taking into account long term effects on the tensile strengthand unfavourable effects, resulting from the way the load is applied.

fcd= fckc

For SIA262 the input value is directly given as fc fck and is set to 1.00.

fcd=fc fckc

1.2 One Dimensional Stress-Strain-Diagrams

The form of the -diagram usually depends on both the code and the analysis typeand therefore has to be input with the analysis parameters.

1.2.1 Concrete Compressive Stresses

For bending with axial force the uniaxial stress-strain relationship in each point of the crosssection is described by one of the diagrams shown below.

Fig. 1 Stress--strain diagrams for compressive stresses in concrete

Type 1: bilinear Type 2: quadratic parabola Type 3: according to EC2

fc fc

cu cu c1u2.0 ooo c1

EcEcm

0.4 fcEcoEc

fc

c1d

Type 4: SIA262

For the determination of the cross section resistance and for design tasks most codes spe-cify a diagram of Type 2, whereby for the first part of the curve a quadratic parabola is used,which is defined by the two parameters 2.0= 2.00 oooand fc . Thus the tangential E-modulus at the start of loading is Eco= 1000fc. For analyses in which the deformation ofthe concrete plays an important part, this value is too small, which is why for stress analyses

1. Materials1.3 Concrete Tensile Stresses


and stiffness considerations as a rule the diagram of Type 1 is used. Ecand fccan be definedas parameters in the input of the material.

As an alternative, Type 3 in FAGUS together with the stress-strain curves defined in EC2 un-der Point 4.2.1.3.3 are available, which are in fact closest to the actual behaviour, but are notsuitable for hand calculations. It is described by the following equation:

c= fc k 2

1+ (k 2) where:

= c/c1 (both are specified as negative)

c1 = - 0.0022 (crushing on reaching the max. value of the concrete compressivestress fc)

k = 1.1 . Ec,nom . c1 /fc ( fc negative)

Ec,nom = either mean value Ecm (Table 3.2 EC2) or corresponding design value Ecd ofthe elastic modulus

. Note on sign convention:Analogous to the axial forces in a member, the tensile stresses in FAGUS are also positive.The above representation of the stress-strain diagram for concrete and that adopted in theprogram conform to the usual conventions.

1.3 Concrete Tensile Stresses

In the standard case concrete is assumed to be cracked in tension (State II), i.e. it cannotresist tensile stresses. However, for special investigations, e.g. if the stiffness of the crosssection is an important factor, a diagram of Types 1 to 3 can be chosen:

Fig. 1- 1 Tensile behaviour of concrete

1 2 3

ct= f (r , fct)fctfct fct

fct

0

Tensile behaviour of concrete of zero strength is described by Type 0. Whereas for concreteof Type 1 after reaching fct no stresses can be resisted, while for Type 3 they remainconstant at the level= fct. fct can be input as a parameter in the material input or modified.The shape of the curves always corresponds to that for the compressive stresses of the cor-responding type (mirror-imaging with respect to the zero point). A somewhat more reali-stic material behaviour is given by Type 2, in which the magnitude of the concrete stressis made to depend on the current maximum (edge) strain.

For Type 2 the following assumption was made:

0 c= fct (1 (r0.2%)

2)

where:

ct : concrete tensile strength

fct : input concrete tensile strength

r : current maximum strain on the tensile side of the cross section

0.2 % strain at elastic limit of conventional reinforcing steel (S500)

With this model the concrete tensile strength at the start of loading is= fct and decreasesquadratically with increasing curvature. After reaching the yield stress at the edge on thetensile side (or at r= 0.2 %) no further concrete tensile strength is available.

1.3 Concrete Tensile Stresses 1. Materials


1.3.1 Tension stiffening effects

Normally a cracked cross section ( section A) is considered in cross section analyses.

A

Procedure for a FRP analysis according to SwisscodeCertain correction possibilities were shown in the previous chapter. Another approach ta-king into consideration the participation of the concrete between the cracks is describedin code SIA E 166 'Fibre reinforcement polymers':

For the determination of the strains mean tensions are considered but the cracked sectionis used to check equilibrium (more details can be found in the manual of CEDRUS). The re-lationship between mean and maximum values are described by a bond factor.

= : mean value ": where the peak value occurs

Is the corresponding check box activated (tabsheet 'Miscellaneous'), the cross sectionanalysis is executed under consideration of the factor .

Generally is dependent on:- conditions in basic material cracked / uncracked- type of reinforcement (internal steel bar or external glued fibre reinforcement)

In the current version of the program the following values, that cannot be changed, areused:

Bond ratio for reinforcing steel : s = 0.7Bond ratio for the fibre reinforcement (lamelle): l = 0.9

1. Materials1.3 Concrete Tensile Stresses


1.3.2 Reinforcing Steel, Structural Steel and Prestressing Steel

For reinforcing and structural steel a bilinear and for prestressing steel a trilinear stress-strain diagram is used:

Fig. 2 Stress--strain diagram for steel

bilinear (reinforcing andstructural steel) trilinear (prestressing steel)

fy

Es Es

ET

y uk

fpk (ftk)

0.9fpk (fy)

In brackets notation of SIA 162

For most cases the same value is assumed for tensile and compressive strength. For specialinvestigations (e.g. British Standard BS5400), however, different values can be chosen.

If at the same time fy < ftk was chosen, ET is the same for tension and compression with:

ET=ftk fyuk y

In the material tables of FAGUS for prestressing steel also, for all codes, some suggestionsare made. In the choice of a prestressing steel, however, it is very important to check thatthe predefined values in the program agree with the manufacturer's information, i.e.usually they have to be adjusted.

The initial prestressing force is given by means of the input of an initial strain. Further expla-nations on this are to be found in section B 1.8.4 Tendons > Initial strain.

1.3 Concrete Tensile Stresses 2. Analysis parameters


2. Analysis parametersAll parameters that influence the analysis behaviour and are not already contained in thecross section geometry or the material parameters, are designated as analysis parameters.

. Example: An M-N interaction diagram can be created either for the Serviceability LimitState or for the Ultimate Limit State" by selecting the corresponding analysis parametername.

Usually for the different analyses the following assignment is used:

Type of analysis

!SLS Service limit stateReinforcement-Design for Serviceabilty, Crack-with etc.

!ULS Ultimate limit state

!NLS Nonlinear (second order) analysis in PYRUS

These three default analysis set are available in every project. The user may change pa-ramaters or add new sets.

2.1 Dialogue 'Analysis parameters'

This dialogue is needed for the management of several analysis parameter sets. In mostprograms the dialogue can be opened with the menu > 'Options' > 'Analysis Parameters'.

In the dialogue there are several tabsheets

Management of Analysis Pa-rameters Sets(common tools)

2.1.1 Tabsheet 'Strain- / Stress- Limits'

The limiting resistance of a cross section, i.e. the cross section resistance, is assumed to bereached if the strain in the extreme fibre of the cross section on the compression side or inthe extreme reinforcement position on the tension side has reached a certain value. Thelimit strains are different for axial compression and for bending, as shown in the figurebelow:

For the parameters cu.c, cu.b, su there are no standard notations. Thus a definition waschosen which should be more or less acceptable for all supported codes. Here the first in-

2. Analysis parameters1.3 Concrete Tensile Stresses


Tension Compression

Fig. 3 Limit strain planes

cu.b

su

cu.c

sy

1 23

45

d h

= strain in steel at elastic limitsy

dex c stands for concrete" and s for steel", u for ultimate state" and the letter after thepoint for c=centric (axial) or b=bending.

The five strain regions are characterised by the following terms:Region 1: axial tension and tensile force with small eccentricityRegion 2: bending (with axial force), full exploitation of reinforcementRegion 3: bending (with axial force), full exploitation of reinforcement and of

concreteRegion 4: bending (with axial force), full exploitation of concreteRegion 5: axial force within middle region of cross section, compression through

centroid

In the limit state the strains at the edges of the cross section are also shown on the followingclosed figure:

Bending

Tension

Comp.

Bending

Fig. 4 Strain at the top and bottom edges of the cross section at the limit state

2= strains at top edge

1 =hd(su.c cu.b)+ cu.b

1 =hdsu.c

1 = cu.b

2 = cu.b

1= strains at bottom edge

1 = 2 = cu.c

1

23,4

5

A verification for permissible steel stresses is also possible (these are converted into a limi-ting strain internally by the program using the E-modulus for steel).

Therefore the cross section resistance is never determined purely statically from thecharacteristic values of the material strengths, but a strain state is always sought, for whichthe strains just reach the admissible limit value at least in one position on the cross section.For an exact determination of the plastic moment (with complete plastification of the crosssection) it must be possible to prescribe an infinitely large edge strain, which is not possiblein FAGUS for computational reasons.

In an analysis with biaxial-bending these conditions are checked with respect to the currentposition of the neutral axis.

1.3 Concrete Tensile Stresses 2. Analysis parameters


Fig. 5 Cross section resistance defined by means of limit strains

tension critical:limit strain reached at theextreme reinforcementposition

compression critical:limit strain reached atedge of cross section

cu.b

su

Special cross sections

Above all, FAGUS is a program for reinforced concrete cross sections. Nevertheless, compo-site beams or purely steel sections can be analysed.

If there is no untensioned reinforcement on the tension side, the input maximum value su(or the input maximum steel stress) applies at the edge of the cross section.

2.1.2 Tabsheet 'Partial factor'

The characteristic material strength is defined through the assignment of a certain materialclass. For each analysis a different partial safety factors (c , s , .. ) can be selected.

2.1.3 Tabsheet 'Stress-strain-relation for concrete'

In this tabheet the desired stress-strain-relation for compression and tension can be selec-ted. A more detailed description is given in Chap. 1.2.

2.1.4 Tabsheet 'Prestressing'

For the possible diagram types see Fig. 2.

In FAGUS and STATIK there is an additional check box for the control of long term losses.

2.1.5 Tabsheet 'Reinforcement'

In this tabsheet various factors for minimum and maximum reinforcement areas can be de-fined:

S Minimum amount of longitudinal reinforcement for columns

S Maximum amount (for all member types)Acts as an iteration stop during reinforcement design

S Minimum area for shear reinforcement

2.1.6 Tabsheet 'Miscellaneous'

In this tabsheet all residual parameters can be found

2. Analysis parameters1.3 Concrete Tensile Stresses


- Creep coefficient

- Angle between the concrete compression strut and the beam axis

- Maximum steel stress in stirrups(for an SLS analysis a stress below the yield stress can be defined here)

- Checkbox for tensions stiffening effects described in Chap 1.3.1

2.1.7 Tabsheet 'Additional Parameters

The parameters in this tabsheet are shown as a simple list and may vary upon the selectednational code. At the moment some values for crack calculations can be found here.


Materials and Analysis Parameters 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1. Materials 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1 Material Management 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.1 Overview dialogue 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.2 Introducing, changing and deleting materials 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.3 Management of material classes 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.4 Attributes of material classes 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2 One Dimensional Stress-Strain-Diagrams 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.1 Concrete Compressive Stresses 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3 Concrete Tensile Stresses 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.3.1 Tension stiffening effects 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.3.2 Reinforcing Steel, Structural Steel and Prestressing Steel 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2. Analysis parameters 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1 Dialogue 'Analysis parameters' 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.1 Tabsheet 'Strain- / Stress- Limits' 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2 Tabsheet 'Partial factor' 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.3 Tabsheet 'Stress-strain-relation for concrete' 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.4 Tabsheet 'Prestressing' 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.5 Tabsheet 'Reinforcement' 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.6 Tabsheet 'Miscellaneous' 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.7 Tabsheet 'Additional Parameters 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

fagus6__materials and analysis parameters

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