19. [eng] new concrete 15
TRANSCRIPT
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Topic Training – New Concrete
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All information in this document is subject to modification without prior notice. No part of this manualmay be reproduced, stored in a database or retrieval system or published, in any form or in any way,electronically, mechanically, by print, photo print, microfilm or any other means without prior writtenpermission from the publisher. SCIA is not responsible for any direct or indirect damage because ofimperfections in the documentation and/or the software.
© Copyright 2015 SCIA nv. All rights reserved.
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Table of contents
3
Table of contents
Introduction ................................................................................................................................... 5
Concrete in SCIA Engineer 15 ..................................................................................................... 6
Settings ......................................................................................................................................... 8
Concrete settings (structure) ........................................................................................................... 8
Concrete settings dialogue............................................................................................................. 8
Setting per member ......................................................................................................................... 12
1D member data .......................................................................................................................... 12 Reinforcement design ................................................................................................................ 14
Internal forces .................................................................................................................................. 15
Parameters which influence the calculation ................................................................................. 16
Shifting of bending moments........................................................................................................ 19
Determination whether member is in compression ...................................................................... 19
First order bending moments with imperfection ........................................................................... 20
Calculation of second order effects .............................................................................................. 22 Slenderness ..................................................................................................................................... 27
Buckling data ................................................................................................................................ 27 Creep coefficient .......................................................................................................................... 27
Estimation of ratio of longitudinal reinforcement .......................................................................... 27
Calculation of slenderness ........................................................................................................... 28
Calculation of limit slenderness.................................................................................................... 28 Reinforcement design – theory ..................................................................................................... 31
Parameters ................................................................................................................................... 31
Design of longitudinal reinforcement ............................................................................................ 34
Design of shear reinforcement ..................................................................................................... 40
Torsional longitudinal reinforcement ............................................................................................ 46 Practical reinforcement ............................................................................................................. 47
Check ........................................................................................................................................... 48
Stiffness ........................................................................................................................................... 48
Theory .......................................................................................................................................... 50 Capacity - response (ULS) ............................................................................................................. 52
Theoretical background................................................................................................................ 52
Effective depth of cross-section ................................................................................................... 54
Inner lever arm ............................................................................................................................. 55 Capacity - diagram (ULS)................................................................................................................ 56
Theoretical background................................................................................................................ 56
Setup ............................................................................................................................................ 61 Shear + torsion (ULS) ..................................................................................................................... 62
Equivalent thin-walled closed cross-section ................................................................................ 62
Shear reinforcement ..................................................................................................................... 65
Shear check ................................................................................................................................. 66
Torsion check ............................................................................................................................... 71
Check interaction shear and torsion ............................................................................................ 73 Stress limitations (SLS) .................................................................................................................. 75
Theoretical background................................................................................................................ 78
Setup ............................................................................................................................................ 79 Check width (SLS) ........................................................................................................................... 81
Value of strength for calculation of cracking forces ..................................................................... 81
Check of normal stresses (occurring of crack width) ................................................................... 81
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Topic Training – New Concrete
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Type of strength for calculation of cracking forces....................................................................... 81
Use of effective modulus of concrete ........................................................................................... 82
Type of maximal crack width ........................................................................................................ 82
Calculation of mean strain in the reinforcement and concrete ..................................................... 82
Calculation of maximum crack spacing ........................................................................................ 83
Calculation of crack width ............................................................................................................ 83 Deflections (SLS) ............................................................................................................................. 84
Theory .......................................................................................................................................... 85
Setup ............................................................................................................................................ 87 Detailing provisions ........................................................................................................................ 89
Minimal clear spacing of bars 8.2(2) ............................................................................................ 90
Maximal percentage of shear reinforcement (6.2.3(3)) ................................................................ 90
Minimal mandrel diameter (8.3(2)) ............................................................................................... 91
Minimal reinforcement area 9.2.1.1(1) ......................................................................................... 91
Maximal area of reinforcement 9.2.1.1(3) .................................................................................... 91
Minimal percentage of shear reinforcement (9.2.2(5)) ................................................................. 92
Maximal longitudinal spacing of stirrups based on shear (9.2.2(6)) ............................................ 92
Maximal longitudinal spacing of stirrups based on shear (9.2.3(3)) ............................................ 92
Maximal centre-to-centre bar distance based on torsion (9.2.3(4)) ............................................. 93
Maximal clear spacing of bars (Code independent) .................................................................... 93
Unity check calculation ................................................................................................................. 93
Minimal bar diameter of longitudinal reinforcement 9.5.2(1) ........................................................ 94
Minimal area of longitudinal reinforcement 9.5.2(2) ..................................................................... 94
Maximal area of longitudinal reinforcement 9.5.2(3) .................................................................... 94
Minimal number of bars in circular column 9.5.2(4) ..................................................................... 94
Minimal bar diameter of transverse reinforcement 9.5.3(1) ......................................................... 95
Maximal longitudinal spacing of stirrups (9.5.3(3)) ...................................................................... 95
Maximal centre-to-centre bar distance (9.3.1.1(3)) ...................................................................... 95 Annex 1: List of parameters ...................................................................................................... 96
Annex 2: National Annexes ..................................................................................................... 104
Annex 3: Concrete settings – Values ..................................................................................... 109
Solver settings ............................................................................................................................... 109
General ....................................................................................................................................... 109
Internal forces............................................................................................................................. 112
Design As ................................................................................................................................... 114
Interaction diagram .................................................................................................................... 116
Shear .......................................................................................................................................... 117
Torsion ....................................................................................................................................... 120
Stress limitation .......................................................................................................................... 120
Cracking forces .......................................................................................................................... 120
Deflection ................................................................................................................................... 121
Detailing provisions .................................................................................................................... 122
Design defaults.............................................................................................................................. 133
Minimal concrete cover .............................................................................................................. 133
Beam .......................................................................................................................................... 136
Beam slab .................................................................................................................................. 139
Column ....................................................................................................................................... 142
Default sway type ....................................................................................................................... 144
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Introduction
5
Introduction
SCIA Engineer 15 brings a completely new solution for 1D concrete members. New technologies of theOpen design, powered by our SCIA Design Forms platform, have allowed for a complete revision of thedesign and checking of reinforced concrete 1D members. This allows us the use of all well knownfeatures of this platform such as very nice and detailed layouts of calculation, using equations in outputetc. Beside this, we offer more - rearrangement of the service tree, new concrete setup and memberdata and a couple of new checks. The described solution works for all kind of shapes of non-prestressed cross-section (e.g. with holes) subjected to all types of loading (e.g. biaxial shearcombined with torsion). Generally this new module provides the following advantages:
• high performance - design and checks run very fast using a parallel process providing resultsin a very small calculation time
• transparency - detailed output enables to verify each intermediate steps of check usingformulas with values and proper units; assisting in dealing with EN 1992-1-1
• dynamic figures - drawing of stress-strain state of cross-section, reinforcement pattern orinteraction diagram
• smart settings - new revised global and member settings, including 'quick search' function
• general solution
• supporting interaction of all internal forces (N, My, Mz, Vy, Vz, T)• supporting arbitrary cross-section shapes including openings & arbitrary reinforcement
positions
• revised and updated generic functions for design & checking of reinforced concrete columns &beams
• code compliance - supporting compliance with EN 1992-1-1:2004/AC:2010-11, corrigendumincluding National Annexes (currently 18 NA´s)
The revised design and checks functions are developed within the SCIA Design Forms environment.This platform is linked as post-processor to SCIA Engineer. The new reporting style makes use of itsadvantages regarding the presentation of results. Next to text and tabular output, also formulas, codereferences, dynamic images and diagrams are included to increase the insight in the calculation!
The Concrete Toolbox is the new 'calculation heart', used by SCIA Design Forms. It contains a set ofcode-independent functions for the design and checking of reinforced concrete members. It makes useof advanced generic algorithms, however in full compliance with e.g. the Eurocode assumptions. Thismeans they are valid for arbitrary cross-section shapes and reinforcement positions. They also supportthe interaction of any mixture of internal forces (N, My, Mz, Vy, Vz, T).
There are also some limitations. New concrete checks do not support the following items:
• numerical cross-section
• cross-section with more components
• phased cross-section
• member or cross-section with different material than concrete material – composite cross-
section• different reinforcement materials in one section
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Topic Training – New Concrete
Concrete in SCIA Engineer 15
The new version of the Concrete module is placed in a completely different part of the main program
tree. This module is situated in the new command ‘Concrete 15’ in the tree.
Nevertheless, the existing old solution for concrete design and check is still available. The functionalityof existing concrete checks is activated in Project data - Functionality - Old concrete checks.
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Concrete in SCIA Engineer 15
When we go into the concrete tree we can also see a completely different arrangement of the tree. Theconcrete tree is split into four parts:
• Settings - global and local settings
o Concrete settings (structure)
o Reinforcement drawing settings
o Settings per member
1D member data
1D buckling data
• Reinforcement design - 1D members
o Internal forces
o Slenderness
o Reinforcement design - design oflongitudinal and shear reinforcement
• Input of real reinforcement
• Checks
o Internal forces
o Slenderness
o Stiffnesses
o Capacity - response (ULS)
o Capacity - diagram (ULS)
o Shear + Torsion (ULS)
o Stress limitation (SLS)
o Crack width (SLS)
o Deflection (SLS)
o Detailing provisions
Each part will be explained more in detail in the following chapters.
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Topic Training – New Concrete
Settings
Concrete settings (structure)
There is a brand new Concrete settings (structure) setup for concrete members, which contains allneeded settings coming from the code or calculation routines. The global settings located in Concretesettings (structure) are by default valid for all members in the project, unless they are overwritten bySettings per member - 1D member data. A lot of input parameters and calculation settings are
collected here, reflecting the complexity of the Eurocode.
In Annex 3, the available settings are described more in detail.
Concrete settings dialogue
This dialogue is split into two main parts. The left part contains the values themselves and the rightside includes an explanatory figure with a description of the value. Additionally there are severalbuttons for searching, filtering, mode selection and default settings.
The Concrete settings dialogue is presented as a kind of table with 9 columns (description, symbol,value, default, unit, chapter, code, structure and check type). Each column has enabled the possibilityfor searching. The user can easily start typing in the first row of a column and see the intermediate
output of the search.
Find
There is also a 'Find' function, where the user can insert a search term. It brings some kind of filteringof items in the setup. This function enables the search of the defined value anywhere in the Concretesetting dialogue.
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Settings
View
Furthermore, a very useful new option is the possibility of switching the type of view of items of thesetup - concrete commands view, code chapter view or list view.
The first view is according to the commands (Concrete commands view) used for design and check.
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Topic Training – New Concrete
Another view is based on numbering of form design code as mentioned on the following figure.
The last predefined view is the List view where all items are listed and could be alphabetically sorted.
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Settings
Additionally, the user has also the possibility to create his own view based on fi ltered items and usethem for some quick changes afterwards. The user defined view can be created using Save actualview where the new view name can be written.
Afterwards, this view is possible to select in User item. It is possible to save or import this user viewfrom the file using Save views into file, and Import views from file.
Finally, there is a possibility to see only changed items using Show only changed items in thesettings, and not the defaults.
Filters
The user can choose between a Standard or Advanced level, which filters the amount of data.
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Topic Training – New Concrete
Default
Finally, when the user wants go back to the predefined values it is possible to press the button Default and all settings are restored.
Setting per member
1D member data
These settings overwrite the global settings for a specific member. Member data can easily be copy-pasted to similar members. There is a differentiation based on type of member (beam, column, beamslab). As in the case of the concrete settings, member data has also been restyled. Local settingscontains about the same input parameters and calculation settings as the global settings in the setup.Moreover, the user can set his/her own value of limit deflection and limit width of crack, define moreenvironmental classes than just one as in the previous version.
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Settings
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Properties of 1D Member data
1D Member data are arranged similarly as Concrete settings (structure). Generally, there are thefollowing items.
• Name – name of the member data
• Member - name of the associated member
• Member type - generally member data can be set for Beam, Columns and Beam Slab
differently.
• Advanced mode - some items are visible only in advanced mode
• Solver settings
• Design defaults
The available settings for the Solver settings and Design Defaults are described in Annex 1.
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Topic Training – New Concrete
Reinforcement design
First you get an overview of the input data for the design:
• Internal forces, displaying the characteristic and design values.
o For member type 'column', the design values of the bending moments include the2nd order bending moments (if required) and the moments due to geometric
imperfections.o For member type 'beam', the design values of the bending moments include the
shifting of the moment line - to take the additional tensile force due to shear intoaccount.
• Slenderness calculation (for member type 'column'), determining if 2nd order effects need betaken into account.
The design of longitudinal reinforcement to resist N, My and Mz is done according to the Ultimate LimitState requirements. Design method is selected based on type of member (beam x column) andaccording to the acting load. There is not any limit for type of cross-section (formerly for columnsrectangle and column) nor for load type (formerly for beams - My OR Mz).
In case the required area of reinforcement exceeds the available space on one layer, more layers (withadapted lever arm) are automatically generated. Designed reinforcement is automatically recalculatedto real bars afterwards.
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Design
The design of shear reinforcement to resist Vy and Vz is done according to the ULS requirements.Formerly, there was possibility to design shear reinforcement just for Vy or Vz.
Internal forces
The internal forces, which are used for design and checks of concrete members, can be different asthe internal forces calculated from FEM analysis. The differences may be caused by:
• for compression member (column)
o taken into account eccentricities caused by imperfections
o taken into account second order eccentricity
• for beams and beams as slab
o taken into account additional tensile forces caused by shear and torsion (shifting ofbending moments)
The following preconditions are used for the calculation:
• The shifting of bending moments is taken into account only for beams and beams as slab andin both directions
• The second order effect and geometrical imperfection are calculated only for column incompression
• Cross-section with one polygon and one material is taken into account for calculation secondorder effect and imperfection in version SEN 15
• The material of all reinforcement bars have to be same in SEN 15
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Topic Training – New Concrete
Parameters which influence th
Coefficient for calculation o
Coefficient for calculation of effecsettings (Advanced level). The dedeformation, this value will be cal
Coefficient for calculation o
Coefficient for calculation of inner(Advanced level). The default valdeformation, this value will be cal
Angle between concrete co
Angle between concrete comprescalculated automatically or inputtangle of compression strut. Thismember data is not defined) or in
• Auto - angle of compressbetween qmin and qmax
• User(angle) - angle of co
inputted value is outsidetaken into account for cal
• User(cotangent) - angleangle. If the inputted valuvalue is taken into accou
Minimal and maximal angle of cothe Manager of national annex.
Angle of shear reinforceme
There are differences in using threinforcement and check.
• Design - angle of shear fconcrete member data isthe angle of shear reinfor
• Check - angle of stirrupsinput shear reinforcemen
Type of member can be defined imember data
e calculation
effective depth of cross-section
tive depth of cross-section can be set and loaded frfault value is 0.9. If the value cannot be calculated fculated by a simplified formula:
lever arm
lever arm can be set and loaded from the concretee is 0.9. If the value cannot be calculated from the
culated by a simplified formula:
pression strut and beam axis
sion strut and beam axis perpendicular to the sheard by the user in SEN depending on parameter Typarameter can be changed in Concrete setting (if 1D1D concrete member data. There are the following
ion strut is calculated automatically as minimal valuto condition according to equation 6.29 in EN 1992-
mpression strut be input directly by the user as an a
f the interval qmin and qmax , the minimal or maxiculation
f compression strut be input directly by the user ase is outside of the interval qmin and qmax , the minit for calculation.
mpression strut is a parameter of national annex an
t
angle of shear reinforcement in calculation betwee
rce for member = Beam, can be set directly in Connot defined) or in 1D concrete member data. For mcement is always 90 degrees and cannot be chang
is loaded from inputted shear reinforcement. It is onlt with an angle of 90 degrees in SEN 15.
n properties of member via parameter Type or direc
m the concreterom the plane of
settingsplane of
force can becalculation/inputconcreteptions:
1-1
ngle. If the
um value is
otangent of themal or maximum
can be edited in
n design of
rete setting (if 1Dmber = Column,d.
ly possible to
tly in 1D concrete
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Use equivalent first order v
This setting allows to the user to1-1 will be taken into account forConcrete setting for Advanced morder moments, therefore this val
Coefficient for calculation o
Coefficient for calculation of forceconcrete settings (Advanced levemember is in compression, whichminimal eccentricity. Member is i
Isolated member
Check box for determination if thautomatic determination by the p
others members. This setting canColumn (Advanced mode). Thisgeometrical imperfection, clause
Buckling data
The detailed description of inputtidescribed in Topic Training – Buconcrete members there are addi
These additional data are import5.2(5) in EN 1992-1-1) and theyrelative lengths (member proper
There are following additional dat• Combo box Tot. height
or length of the isolated c
o Calculate – the tmembers in the
o User – the valueaccount if Calcul
• edit box Tot. height – thiisolated columns directlyset in combo box Tot. He
lue
et, if equivalent bending moment according to 5.8.he calculation of first order eccentricity. This settingde. The code EN 1992-1-1 recommends the use of
ue is set to Yes by default.
force at which member is in compressi
s, when member is in compression, can be set andl). Default value is 0.1. This coefficient is used for dis necessary for calculation second order effect, imcompression, if condition below satisfies:
member is an isolated member or not. Default settiogram and the member is isolated, if the member is
be changed in 1D concrete member data for Meetting is used for calculation length of the member
5.2(6) in EN 1992-1-1.
ng buckling data and the way of calculating bucklingkling lengths. There is described the general functiotional parameters for definition of buckling data.
nt for calculation of eccentricities caused by imperfan be defined in tab-sheet Buckling data in dialog
ties > parameter Buckling and relative length > butt
a:this combo allows to set type of calculation of total
olumns. There are two items in the combo box:
ot height. will be calculated automatically as sum ofuckling system
can be inputted directly by the user. The input valuate = User
s edit box allows to input total height of building or lby the user. The input value will be taken into accoight
Design
.2(2) in EN 1992- can be done in
equivalent first
n
loaded fromtermination, if
perfection and
ng is thenot linked the
ber type =or calculation of
data arenality, but for
ction (see clausee Buckling andn Edit ).
height of building
lengths of all the
will be taken into
ngth of thent if item User is
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Topic Training – New Concrete
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• edit box my - is the number of vertical members contributing to the total effect of theimperfection perpendicular to y axis of LCS. It means that the value is used for recalculation ofbending moment around y axis. Only one value can be set for all columns in a buckling system
• edit box mz - is the number of vertical members contributing to the total effect of theimperfection perpendicular to z axis of LCS. It means that the value is used for recalculation ofbending moment around z axis. Only one value can be set for all columns in a buckling system
The important parameter for calculation of buckling data is the type of structure (braced or unbraced).
The global type of structure can be set in Concrete Setting (Design defaults > Default sway type). Forexample, the structures is braced perpendicular to y axis of GCS, if parameter Sway around y axis =NO (it means that the structure is not prone to sway perpendicular to y axis).
Use geometric imperfection
This setting allows the user to set, if geometrical imperfection will be taken into account of ULS or SLS.This setting can be done in Concrete settings (if 1D concrete member data is not defined) or directly in1D concrete member data for Member type = Column.
The imperfection shall be taken into account in ultimate limit states and need not to be considered forserviceability limit states, see clause 5.2(2P) and 5.2(3) in EN 1992-1-1, therefore default setting inSEN is:
• ULS - use geometric imperfection = Yes , it means geometric imperfection will be taken intoaccount
• SLS - use geometric imperfection = No , it means geometric imperfection will not be taken intoaccount
Use minimum eccentricity
User can set if minimum first order eccentricity, calculated according to clause 6.1(4) in EN 1992-1, wil lbe taken into account in the calculation of first order eccentricity including geometrical imperfection forULS. This setting can be done in Concrete settings (if 1D concrete member data is not defined) ordirectly in 1D concrete member data for Member type = Column by using Advanced mode/level.
Use second order effect
This setting allows the user to set if second order effect will be taken into account. This setting can bedone in Concrete settings (if 1D concrete member data is not defined) or directly in 1D concretemember data for Member type = Column.
If check box Use second order effect = Yes, then the second order effect will be taken into account, ifconditions below are satisfied:
• the combination for ULS is used
• Member type = Column and it in case, that column is in compression
• calculated slenderness is greater than limit slenderness
Design defaults
Design defaults is a special group of properties where the user can define the basic parameters(diameter of longitudinal and shear reinforcement, type of value of concrete cover...) for design oflongitudinal and shear reinforcement. This setting can be done in Concrete settings (if 1D concretemember data is not defined) or directly in 1D concrete member data.
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Determination of unfavoura
This setting allows the user to seimperfection wil l be taken into acmember data is not defined) or diof Advanced mode/level.
Shifting of bending momentsAdditional tensile forces causedsimplified calculation based on sbending moment is calculated onl
Distance for shifting is calculated
• for beams
• for beams as slab
Automatic calculation of angle besimplified method for shifting with
• shear of member for calcat whole cross-section p
• value Ak and u k for calculwhich has the same cros
Determination whether memb
The second order effect, minimalfor member = Column, which is isatisfied:
le direction
in which direction the second order moment and th ount. This setting can be done in Concrete settings
rectly in 1D concrete member data for Member type
y shear and torsion is taken into account in SEN15ifting of bending moments according to clause 9.2.1
ly for beams and beams as slab.
around for both axes dependent on type of member
tween the concrete compression strut and beam axithe following simplifications:
ulation value V Rd.max is calculated as minimum widthrpendicular to direction of shear forces
ation of T Rd.max is calculated for effective rectangulas-sectional area and same perimeter as inputted cr
r is in compression
eccentricity and geometrical imperfection are takencompression. Column is in compression if conditio
Design
e geometrical(if 1D concrete= Column in case
by using a.3(2). Shifting of
s is calculated by
of cross-section
cross-section,ss-section
into account onlys below are
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Topic Training – New Concrete
First order bending moments
The calculation of first order mocolumn is in compression it runs
• first order eccentricity wit
• eccentricity caused by im
• first order eccentricity inc
Calculation of first order ec
There are two options for calculacheck box Use equivalent first
• the equivalent first ordermoments will be the sambox Use equivalent firstis not defined) or in 1D c
• the first order eccentricitythat bending moments inequivalent first order vdefined) or in 1D concret
The 1st order equivalent moment
M0,ey = max (0,6*M02,y +0,
M0,ez = max (0,6*M02,z +0, where
• M01y(z) is the first end benthe second end bendingcalculation of limit slende
• M02y(z) is the second endas the first end bendingcalculation of limit slende
The user (real) reinforcement defcalculation effective depth of cro ULS in service Internal forces)
Calculation of eccentricity d
The imperfection in SEN is repreThe imperfection shall be taken iserviceability limit states, see claindependently if the imperfection
The inclination is calculated arou
where
ith imperfection
ent is calculated only for Member type = Column anccording to the following procedure:
hout effect of imperfection is calculated,
perfection is calculated,
luding effect of imperfection is calculated.
entricity without effect of imperfection
ing first order moments and eccentricity in SEN deprder value.
bending moments are taken into account. It means,e at the whole length of the member. This option isorder value = Yes in Concrete settings (if 1D concncrete member data
is calculated from bending moments in the currenteach section can be different. This option is used iflue = No in Concrete settings (if 1D concrete memmember data
is calculated according to clause 5.8.8.2 (2) in EN 1
4*M01,y; 0,4* M02,y)
4*M01,z; 0,4*M02,z)
ding moments around y(z) axis of LCS with lesser aoment. |M01y(z)| < |M02y(z)| The same values ar
rness
bending moments around y(z) axis of LCS with greaoment. |M02y(z)| ≥ |M01y(z)| The same values are
rness
ined via REDES and free bars are not taken into acs-section for design reinforcement to column (Type
ue to imperfection
ented by an inclination according to clause 5.2(5) ito account in ultimate limit states and need not to bse 5.2(2P) and 5.2(3) in EN 1992-1-1. The user ca
will be taken into account for ULS or SLS.
d both axis (axis y and z) of LCS according to form
d in the case that
ending on the
that bendingsed if check
rete member data
ection. It follows,check box Useer data is not
992-1-1
bsolute value asused for the
ter absolute valueused for the
ount forof check = Design
EN 1992-1-1.e considered for
set
ula:
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• θ0 is the basic value of incan be different for eachEN 1992-1-1 > General
• αh is the reduction factorcalculated according to f
• αm,y(z) is the reduction fac
• l is the length of a columor not
o isolated member
o not isolated memThis height can b
• my(mz) is the number of
perpendicular to y(z) of Lmoment around y(z) axis
The effect of imperfection for an ieccentricity according to clause 5
The direction (sign) of the valuedirection (sign) of first order ecce
Minimum first order eccentr
The minimum first order eccentri
The minimum eccentricity is takeYes
The direction (sign) of minimum feccentricity
Calculation of first order ec
First order eccentricity including
eoEd,y(z) = e0,y(z) + ei,y(z) >
After calculation of the first orderincluding the effect of imperfectio
M0Ed,y(z) = NEd* eoEd,z(y)
lination. The value is a National parameter; it meancountry. The value can be set in the Manager for n
ULS > General > Theta_0
for the length of a column or the height of a structurrmula
or for the number of members calculated according
or the height of a structure depending on, if the me
l = L, where L is the length of the member
ber l = H, where H is the total height of the buildinge defined in Buckling data
ertical members contributing to the total effect of th
CS. It means, that this value is used for recalculatioof LCS. These value can be defined in Buckling dat
olated column and for a structure is always taken i.2(7a) in EN 1992-1-1.
f eccentricity caused by imperfection has to be thetricity.
icity
ity is calculated according to clause 6.1(4) in EN 19
into account, if check box Use minimum value of
rst order eccentricity has to be same as direction (s
entricity including effect of imperfectio
ffect of imperfection is calculated according to the f
e0,min,y(z)
eccentricity including the effect of imperfection, thens around y (z) axis of LCS is calculated:
Design
s that this valuetional annex >
. The value is
to formula
mber is isolated
(buckling system).
imperfection
of the bendinga
to account as an
ame as the
92-1-1.
eccentricity =
gn) of first order
rmula below
st order moment,
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Topic Training – New Concrete
Calculation of second order ef
The EN 1992-1-1 defines several(general method, simplified methcurvature...). SEN allows makingmethods:
• General method - equilibcalculated taking into acc
and creep, see clause 5.• Simplified method based
The second order effect by the si
• for the ultimate limit state
• only for Member type = C
• check box Use second or
• calculated slenderness is
Calculation of second order
Nominal second order moment is
M2,y(z) = NEd* e2,z(y)
The second order eccentricities a
lz(y) >lz(y),lim Use sec
YES YES
YES NO
NO YES
NO NO
The direction (sign) of final valueorder eccentricity
Calculation of curvature
The curvature for the calculationin EN 1992-1-1.
(1/r)y(z) = Kr*Kf,y(z)*(1/r0 It follows that the calculation of cimportant are the following:
• relative normal force
• mechanical ratio of reinfo
• effective creep ratio
• slenderness of the colum
• effective depth of cross-s
• basic value of curvature
fects
methods for the analysis of second order effects wid based on nominal stiffness, simplified method bathe analysis of the second order effect by using the
ium and resistance is verified in the deformed stateount the relevant effects of cracking, non-linear mat
.2(2) in EN 1992-1-1,on nominal curvature according to EN 1992-1-1, cla
mplified method is taken into account:
olumn and it in case that the column is in compress
der effect in switched ON
greater than limit slenderness
moment
calculated according to clause 5.8.8.2(3) in EN 199
re calculated according to formulas below
nd order effect Second order eccentricity
e2y(z) = 0
of second order eccentricity has to be same as dire
f second order eccentricity is calculated according
y(z)
rvature depends on many parameters and factors,
rcement
n
ection
h axial loaded on nominal
following
deformations areerial properties
use 5.8.8
ion
2-1-1
tion (sign) of first
o clause 5.8.8.3
ut the most
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Coefficient Beta
Slenderness of the column for calwhich is calculated according to f
Effective depth of cross-sec Effective depth of cross-section icalculated according to clause 5.the reinforcement is not symmetriDesign of concrete structures” th
• for symmetrical reinforcesides, but part of it is dist
• for other cases (design o
• for other cases (check) -simplified calculation, if t
The calculation of the radius of greinforcement from tensile edgeare calculated for design of reinfodesign of reinforcement and for c The user (real) reinforcement defcalculation of effective depth of c
Design of reinforcement f
Total area of reinforcement
As =μs.Ac
Calculation of ratio of reinforcem
if σy= 0 MPa and σz=0, then ratioy Calculation area of reinforcement
As,y(z) = ratioy(z)*As
Distance of centre of tensile reinf
Posit ion of reinforcement from ce
lculation of factor Kf,y(z) is taken into account by pararmula:
tionused for the calculation of basic value of curvature.8.3(2) in EN 1992-1-1. The EN 1992-1-1 is not givi
cal, but according to “Designers’ guide to EN 1992-following rules are used for the calculation of effec
ent and in case if all reinforcement is not concentrributed parallel
reinforcement)
the effective depth is calculated from plane of equlibis value cannot be calculated from this plane
ration of the total reinforcement and distance of ceepends on the shape of the cross-section and, if thrcement or for checks. It means that this value canhecks.
ined via REDES and free bars are not taken into acoss-section for design reinforcement of a column
or rectangular section
nt in y and z direction
= ratioz=0.5
in direction of y(z) axis of LCS
rcement from tensile
ntroid of concrete cross-section in direction of y (z)
Design
meter (βy(z)) ,
and it isng rules where
Eurocode 2:ive depth:
ted on opposite
rium or by
tre of tensileinternal forcese different for
ount for
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Topic Training – New Concrete
Second moment of reinforcemen
Radius of gyration of the total rei
Design of reinforcement f
Total area of reinforcement
As =μs.Ac
Distance of centre of tensile reinf
Posit ion of reinforcement from ce
Second moment of reinforcemen
Radius of gyration of the total rei
Design of reinforcement f
Total area of reinforcement
As =μs.Ac
Area of reinforcement in each ed
Asi = As /nedge
Distance of centre of tensile reinf
area
forcement area
or circular section
rcement from tensile
ntroid of concrete cross-section in direction of y (z)
area
forcement area
or other cross-sections
e
rcement from tensile
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Posit ion of reinforcement from ce
Second moment of reinforcemen
Radius of gyration of the total rei
Checks for all type of cro
Total area of reinforcement
Second moment of reinforcemen
Radius of gyration of the total rei
Basic value of curvature
There is a rule for the calculationsymmetrical reinforcement. in EN
For unsymmetrical cross-section“Designers’ guide to EN 1992-2should be used
ntroid of concrete cross-section in direction of y (z)
area
forcement area
s-sections
area
forcement area
of basic curvature only for symmetrical cross-sectio1992-1-1, where the formula below should be used
with unsymmetrical reinforcement according to recourocode 2: Design of concrete structures” the follo
Design
n with:
mmendation ofing formula
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Topic Training – New Concrete
Calculation of unfavourable
The minimum eccentricity, geomcalculated in both directions. Thelimit slenderness and can be calcof the first-order moments and thoccur in the direction where the dlength of the column, is greatest.
moment and second-order momeTherefore it is possible in SEN, tsecond order moment and geom
There are 3 possibilities:
• Auto - the direction for thdetermined automatically
The uniaxial calculation fare satisfied, otherwise b
• Uniaxial - second order
direction (more unfavourassigned (accidental benboth direction), the seconin both directions.
• Biaxial - second order efdirections.
There are no rules for the determused the procedure described inDesign of concrete structures, Gunfavourable direction is determi
ηy > ηz - unfavourableηy < ηz - unfavourableηy = ηz - both direction
direction
trical imperfection and first order moments includinsecond order effect depends on the comparison ofulated too in both directions. The column will deflect
accidental moment. It proposes that the second or eflection, due to first-order moment as a proportion
It is assumed, though this is not stated in the code,
nts will only occur in one direction and not in both di define the unfavourable direction; it means the diretrical imperfection will be taken into account.
e calculation of second order effect and geometricalaccording to conditions 5.38a and 5.38b in EN 199
r automatic determination is taken into account; if ciaxial calculation will be used.
ffect and geometrical imperfection is taken into acc
ble direction). In case that the more unfavourable dding moments, effective length and css properties ad order effect and geometrical imperfection will be t
fect and geometrical imperfection is always taken in
ination of unfavourable direction in EN 1992-1-1, th“Designers’ guide to EN 1992-1-1 and EN 1992-1-2:neral rules for buildings and structural fire design” ,ed according to the equation below:
direction is around y axisdirection is around z axiss are taken into account
imperfection arelenderness andunder the actioner moments willf the effectivehat the accidental
rections at once.ction in which the
imperfection is-1-1
onditions below
unt only in one
irection cannot bere the same inken into account
o account in both
refore in SEN isEurocode 2:here the
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Design
Slenderness
Slenderness and limit slenderness of a column should be checked before the design or check of themembers. Using the second order effect in the calculation depends on the check of slenderness,because if the check of slenderness is greater than the limit slenderness, the second order effect hasto be taken into account for the column calculation.
Conditions Calculation of second order effect
YESNO
The slenderness and limit slenderness is calculated according to clause 5.8.3.1 and 5.8.3.2 in EN1992-1-1. The following preconditions are used for calculation:
• The slenderness is calculated for beams and columns and for general load (N+My+Mz)
• The limit slenderness is calculated only if the axial forces is smaller than zero (N < 0 kN)
• Cross-section with one polygon and one material is taken into account in version SEN 15
• The material of all reinforcement bars has to be same in SEN 15
Buckling data
The detailed description of inputting buckling data and the way of calculating buckling data aredescribed in Topic Training – Buckling lengths. There is described the general functionality, but for thecalculation of slenderness and limit slenderness the following properties are important:
• properties for the calculation of effective length of the member around y and z axis
• if the member is braced (Sway = NO) or unbraced (Sway = YES ) around y and z axis
The important parameter for calculation of buckling data is type of structure (braced or unbraced). Theglobal type of the structure can be set in Concrete Settings (Design defaults > Default sway type) .For example, the structure is braced perpendicular to y axis of GCS, if parameter Sway around y axis= NO (it means the structure is not prone to sway perpendicular to y axis).
Creep coefficientThis value can be set in the Concrete settings by using Advanced level or in 1D memberdata (advanced mode is ON), if it is defined. The creep coefficient can be calculated automatically byusing the input of ages of concrete and relative humidity (see annex B.1 in EN 1992-1-1), if the Typeinput of creep coefficient = Auto. If the Type input of creep coefficient = User value, the creepcoefficient can be inputted directly by the user.
Estimation of ratio of longitudinal reinforcement
There are some values in the design of reinforcement, which are dependent on the area ofreinforcement, for example:
• mechanical reinforcement ratio (μ) in the calculation of limit slenderness (clause 5.8.3.1(1) in
EN 1992-1-1)
• mechanical reinforcement ratio (μ) in the calculation of second order eccentricity (clause5.8.8.3(3) in EN 1992-1-1)
• radius of gyration of the total reinforcement area (is) in the calculation of second ordereccentricity (clause 5.8.8.3(2) in EN 1992-1-1)
• calculation of the exponent of interaction formula x in the biaxial bending calculation (clause5.8.9.(4) in EN 1992-1-1)
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Topic Training – New Concrete
These values should be calculated before the design of reinforcement, but before the design we do notknow the area of reinforcement. It follows that for calculation of this value:
• area of reinforcement will be neglected,
• iterative calculation will be used,
• area of reinforcement will be estimated.
The third solution is implemented in SEN via the parameter Estimation ratio of longitudinalreinforcement for recalculation internal forces, where the user can set the ratio of reinforcement, whichwill be used for calculation of the values above. This value can be set in the Concrete settings byusing Advanced level or in 1D member data (advanced mode is ON), if it is defined. Total area ofreinforcement is calculated according to formula:
As = μs.Ac
Calculation of slenderness
The slenderness (slenderness ratio) is calculated according to clause 5.8.3.2(1) in EN 1992-1-1.
The simplified values and formulas for calculation of effective length for isolated columns, braced andunbraced frames are described in clauses 5.8.3.2(2-4) in EN 1992-1-1
The slenderness is calculated in each section, it follows that for an arbitrary member and member witha haunch, the slenderness can be different along the length of the member
Calculation of limit slenderness
The limit slenderness is calculated according to clause 5.8.3.1(1) in EN 1992-1-1. The limitslenderness and the slenderness are always checked separately for each direction according to5.8.3.1(2) in EN 1992-1-1. The formula for the calculation of limit slenderness in EN 1992-1-1 is anational parameter, it means, that a different formula, method or value can be used in some countries,see concrete setup (Manager for national annex > EN 1992-1-1 > General > ULS > General >lambda_lim)
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Design
There are changes in the calculation of limit slenderness for some national annex, see the table below:
National annex Calculation of limit slenderness
Standard EN 1992-1-1 λ _lim = (20*A*B*C) ⁄ √n
DIN EN 1992-1-1 NAλ _lim = 25 ... for |n| ≥ 0,41λ _lim = 16 ⁄√n ... for |n| < 0,41
CSN 1992-1-1 NA
STN 1992-1-1 NAλ _lim = (20*A*B*C)
⁄ √n ≤ 75
The limit slenderness calculated according to standard EN 1992-1-1 depends on:
• effective creep ratio φeff (coefficient A),
• mechanical reinforcement ratio w (coefficient B),
• shape (ratio) of bending moment rm (coefficient C),
• relative normal force n.
The limit slenderness is not calculated if normal force (relative normal force) is compressive.
The limit slenderness is calculated in each section, it follows that for an arbitrary member or a memberwith a haunch, the normal force is not uniform at the length of the member or the reinforcement is notconstant at the length, the limit slenderness can be different along the length of the member.
Effective creep ratio
In SCIA Engineer, for the calculation of limit slenderness the creep ratio is used loaded from theconcrete settings (if member data is not defined ) or concrete member data. It means that if the userwants to take into account the effective creep ratio according to clause 5.8.4 in EN 1992-1-1, the valueof this creep ratio has to be directly inputted in the concrete settings or the concrete member data.Otherwise, the final creep ratio will be taken into account.
The coefficient A is calculated according to formula:
A = 1/1+0,2•φ.
Mechanical reinforcement ratio
Check
The mechanical reinforcement ratio depends on total area of longitudinal reinforcement. For checks,the total area of reinforcement is calculated from inputted reinforcement via REDES or Free bars. Themechanical reinforcement can be different at the whole length of the column and in each section of themember and it is calculated according to formula below:
The coefficient B is calculated according to formula:
B = √(1+2∙ω)
Design
The mechanical reinforcement ratio depends on total area of longitudinal reinforcement. For design ofreinforcement, total area of reinforcement is calculated from estimation ratio loaded from Concretesettings (if concrete member data is not defined ) or concrete member data. The mechanical
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Topic Training – New Concrete
reinforcement ratio is the same aformula:
The coefficient B is calculated ac
B = √(1+2∙ω)
Shape of bending moment
Shape of bending moment is expinfluence of imperfection aroundon the type of member and on th
• if type of member is unbr
• if type of member is bracfrom or predominantly dualong the member is not
• otherwise, value rm is cal
where
• M01y(z) is first end bendinsecond end bending moof limit slenderness.
• M02y(z) is second end benfirst end bending momenlimit slenderness.
• rm.y(z) is ratio of bending
limit slenderness around
The coefficient C is calculated ac
Relative normal force
Relative normal force is calculate
n = NEd / Ac•fcd
If normal force is not uniform at lmember with haunch), the maxibe taken into account.
the whole length of the column and it is calculated
ording to formula:
ressed by the ratio of first order end bending momehe selected local axis. The ratio of these moments (shape of shear force.
aced around local axis (sway = YES), then rm = 1,0
d around local axis (sway = NO) and first order moe to imperfections or transverse loading (maximumat the beginning or at the end of the member), then
ulated according to formula
moment around y(z) axis of LCS with lesser absolent. | M01y(z) |< | M02y(z) | The same values are used
ing moment around y(z) axis of LCS with greater a. | M02y(z) |≥ | M01y(z) | The same values are used for
oment around y(z) axis of LCS which is used for th
y(z) axis of LCS.
ording to formula:
d according to formula
ngth of column or part of the column (for arbitraryum value of normal force at length of column or par
according to
ts without thevalue rm) depends
ents arise onlybending momentrm= 1,0
te value asfor the calculation
bsolute value ashe calculation of
calculation of
ember andof the column will
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Design
31
Reinforcement design – theory
SEN 15 allows to design reinforcement for a general cross-section which is loaded by general forces(N, My,Mz,Vy,Vz, Mx) . It is possible to design:
• statically required longitudinal reinforcement
• longitudinal reinforcement including detailing provisions
• statically required shear reinforcement
• shear reinforcement including detailing provisions
• torsional longitudinal reinforcement
The following preconditions are used for calculation:
• additional tensile forces caused by shear is taken into account by shifting of bending moments,see clause 9.2.1.3(2)in EN 1992-1-1,
• cross-section with one polygon and one material is taken into account,
• practical (user defined) reinforcement is not taken into account.
Parameters
Design defaults
Design defaults is a special group of properties where the user can define the basic parameters(diameter of longitudinal and shear reinforcement, type of value of concrete cover...) for design oflongitudinal and shear reinforcement. This setting can be done in Concrete settings (if 1D concretemember data is not defined) or directly in 1D concrete member data.
Three types of 1D members with different design defaults parameter are supported in SEN 15:
• Beam - member predominantly loaded by bending moments, for which longitudinal and shearreinforcement can be designed. There are the following parameters:
o Longitudinal reinforcement
diameter of upper/lower reinforcement type of cover of upper and lower reinforcement (auto or user defined value)
type of cover of side reinforcement (upper, lower or user defined value)
material of longitudinal reinforcement (only in 1D concrete data)
o Stirrups
diameter of stirrups
number of cuts (number of shear links)
angle of shear reinforcement
material of shear reinforcement (only in 1D concrete data)
basic (user defined stirrup) – the user can define user value of area of shear
reinforcement per meter with some angle and material of this reinforcement
• Beam as slab - member predominantly loaded by bending moments for which shearreinforcement is not designed (for example cut of 2D member). There are the followingparameters:
o Longitudinal reinforcement
diameter of upper/lower reinforcement
type of cover of upper and lower reinforcement (auto or user defined value)
type of cover of side reinforcement (upper, lower or user define value)
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Topic Training – New Concrete
material of longitudinal reinforcement (only in 1D concrete data)
• Column - member predominantly in compression for which longitudinal and shearreinforcement can be designed. There are the following parameters:
o Longitudinal reinforcement
diameter of upper/lower reinforcement
type of cover of upper and lower reinforcement (auto or user defined value)
type of cover of side reinforcement (upper, lower or user define value)
material of longitudinal reinforcement (only in 1D concrete data)
o Stirrups
diameter of stirrups
number of cuts (number of shear links)
material of shear reinforcement (only in 1D concrete data)
Design defaults in concrete settings:
• there is a possibility to define design defaults for all types of 1D member (beam, column, beamslab)
• it is not possible to input/edit the material of longitudinal and shear reinforcement in this setting,but material is loaded from project data and it is the same for all type of members
Design defaults in 1D concrete member data
• only design defaults of selected type of member can be edited in this setting
• material of shear and longitudinal reinforcement can be edited directly in the concrete memberdata
Design method
The user can set the type of method for design of reinforcement for columns and beams This settingcan be done in Concrete settings (if 1D concrete member data is not defined) or directly in 1D concrete
member data for Member type = Column or beams by using Advanced mode/level.
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Design
Four types of methods for design statically required reinforcement are supported for beams andcolumns:
• auto
• uniaxial around y
• uniaxial around z
• biaxial
Uniaxial method around y axis is always used for type of member = beam as slab.
Biaxial method independently on selected method is always used for circular and oval columns.
Limit ratio of bending moments for uniaxial method
The automatic method for design of reinforcement is based on the ratio of bending moments around yand z axis and on the value of limit ratio of bending moments for using uniaxial method. This limit valuecan be set and loaded from concrete setting (Advanced level). Default value is 0.1. It follows, if ratio ofmaximal bending moments around y and z axis for all combinations in current section is lesser thanlimit ratio of bending moments, uniaxial method is used for design, otherwise biaxial method is used.
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Topic Training – New Concrete
Design of longitudinal reinfor
The design of statically required ruses an iteration routine to calculmaterial properties and position ointeraction of the normal force (N
There are the following assumpti
• Plane sections remain pl• Strain in bonded reinforc
the concrete at the same
• Tensile strength of the co
• The stresses in the concr(bilinear or parabola-rect
• The stresses in the reinfo(bilinear with or without i
Four methods are supported in S
• uni-axial around y axis
• uni-axial around z axis
• biaxial
• auto
Uniaxial method around y axis is
Biaxial method independently on
Designed required area is for a bdirections of axis’s of LCS of the
Except of statically required longilongitudinal reinforcement (As.prov
recalculated to real bars, where:
• diameter of longitudinal rinput diameter)
• minimal number of bars
• number of bars is rounde
• corner bars are taking intedge, and half of a bar fo
ement
einforcement is based on the calculation equilibriumate equilibrium based on the internal forces, the cro
f reinforcement. Generally, this iterative method worwith uni-axial or bi-axial bending moments (My + M
ns:
ne.ment, whether in tension or compression, is the salevel
ncrete is ignored.
ete in compression are given by the design stress–ngular stress-strain diagram)
rcing steel are given by the design stress–strain relclined horizontal branch stress-strain diagram)
EN 15 for design of reinforcement for beams and co
always used for type of member = beam as slab.
selected method is always used for circular and ova
tter overview and graphical presentation recalculatross-section (member).
udinal reinforcement (As.req), the program calculates. It is the statically required longitudinal reinforceme
inforcement is taken into account (cross-sectional
er edge is 2
d to whole number
o account for all edges (half of a bar is taken into acr second edge)
. This methods-section,ks for thez).
e as the strain in
train relationships
tionships
lumns:
l columns.
d to the
also the providednt area
rea of bars with
count for one
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Uniaxial method for design
This method allows designing the(MEd). In case, that the cross-secmoment is ignored:
• for method uniaxial aroureinforcement is designe
• for method uniaxial aroureinforcement is designe
The results of uniaxal method de
• for beams and beam as
o reinforcement isrequired or cross
o the reinforcemen
o the reinforcemen
• for columns
o reinforcement is
o reinforcement is
The position of reinforcement is
reinforcement only for normal force (NEd) and oneion is loaded by bending moments around both axe
nd y, the bending moment MEdz is ignored, it followonly for normal forces NEd and bending moment M
nd z, the bending moment MEdy is ignored, it followonly for normal forces NEd and bending moment M
end on type of member:
lab
esigned only at one or two edges (if compressive r-section is loaded only by normal force)
t can be unsymmetrical
t can be designed in more layers
esigned always at two edges and the reinforcemen
esigned always at one layer
alculated from parameters defined in Design defaul
Design
ending moment, one bending
that the
Edy
that theEdz
inforcement is
t is symmetrical
s.
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Topic Training – New Concrete
Calculation position of reinf
The position of reinforcement is cDesign defaults. The position of roffset of current cross-section indifferent for each edge and it is c
• beam
• beam as slab
• column
The edge, for which the parametcrossed by the line in direction ofthe biggest linear stress in the cr The edge, for which the parametcrossed by the line in direction ofthe biggest linear stress in the cr
Design for several layers
The program is able to design reifollowing procedure is used:
• the reinforcement is desi
• designed area at each ereinforcement calculatedplaced along the edge
• if designed area at somelayer is done where:
orcement
alculated from parameters, which are defined in Coeinforcement is always in the middle of the edge, wistance as. This distance and diameter of reinforcelculated in dependence on type of member accordi
r of upper reinforcement is used, is the edge abovebending moment resultant for dangerous combinatiss-section.
r of lower reinforcement is used, is the edge underbending moment resultant for dangerous combinatiss-section.
nforcement for more layers. It is an iterative calculati
ned at the first layer for the selected method
ge is checked with maximum area of reinforcementfrom minimum surface to surface distance of bars),
edge is bigger than maximum area, then new desig
crete settings >ich is created byent can be
ng to formulas:
axis which isn, which causes
axis which isn, which causes
ion, where the
(area ofwhich can be
n for the next
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o the area of reinfo
o the position of rei
o design with newreinforcement fro
Maximal number of layers which ierror, when maximum number of
Design for more layers is support
rcement As,max is inputted to the previous layer
inforcement for the next layer is calculated
positions of reinforcement is run with taking into accm the previous layer
s taken into account is 5 in SEN 15. The program filayer (nmax = 5) is inefficient.
ed only for beams and beams as slab.
Design
unt
ishes with some
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Topic Training – New Concrete
Recalculation reinforcemen
Longitudinal reinforcement can bsection. Designed required area idirections of axes of LCS of the cdepends on the angle of the edgfollows, that 4 areas of reinforce
Asz.req+
requiplacefromassiglesse
Asz.req-
requiplacefromassiglesse
Asy.req+
requiplacefromassiggreat
Asy.req-
requiplacefromassiggreat
to directions
designed to more edges of a cross-section and fors for a better overview and a graphical presentationross-section (member). The recalculated area of reifrom y-axis and the angle of bending moment resulent can be presented in graphical and numerical o
red area of reinforcement (mostly designed for bendd on edges above axis y with angle of edges lessery- axis. The edges with angle 45 degree and abovened to this direction if direction of bending moment rr or equal than 45 degree.
red area of reinforcement (mostly designed for bendd on edges under axis y with angle of edges lessery- axis.The edges with angle 45 degree and underned to this direction if direction of bending moment rr or equal than 45 degree.
red area of reinforcement (mostly designed for bendd on edges above axis z with angle of edges greatey- axis.The edges with angle 45 degree and abovened to this direction if direction of bending moment rer than 45 degree.
red area of reinforcement (mostly designed for bendd on edges under axis z with angle of edges greatey- axis. The edges with angle 45 degree and underned to this direction if direction of bending moment rer than 45 degree.
a general cross- recalculated to
forcementltant from y-axis. Ittput:
ing moment My)than 45 degreeaxis y areesultant (αM) is
ing moment My)han 45 degreexis y areesultant (αM) is
ing moment Mz)r than 45 degreexis z areesultant (αM) is
ing moment Mz)than 45 degree
axis z areesultant (αM) is
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Biaxial method for design
This method allows designing theThis method is based on interacti
Procedure of calculation:
• program designs initial arcross-section
• program increases areaand checks interaction fo
• if interaction formula is fuof reinforcement , if the p
The results of biaxial method dep
• for beam and beam as sl
o the reinforcemen
o exponent of inter
o the reinforcemen
• for column
o reinforcement is
o exponent of inter
o reinforcement is
Automatic method for desig
There is a possibility to use the auniaxial or biaxial method accordi
• uniaxial method is used i
reinforcement for normal force (NEd) and biaxial beon formula, equation 5.39 in EN 1992-1-1.
ea of reinforcement according to linear stress on th
f reinforcement, generates interaction diagram arormula in iterative calculation, till interaction formula i
lfilled, then program checks plane of deformation anlane of deformation is not found
end on type of member:
ab
t can be unsymmetrical
action formula is 1
t can be designed in more layers
ymmetrical, if the cross-section is symmetrical
action formula depends on shape of cross-section
esigned always at one layer
n
tomatic method for design. The program automaticng to the values of bending moments around y and
Design
ding moments.
edges of the
nd y and z axesnot satisfied
d increases area
ally selects thez axis. It follows:
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Topic Training – New Concrete
• biaxial method is used in
Different method for design of reidependence on values of bendin
Design of shear reinforcement
Design of shear reinforcement in
• design for biaxial shear f
• design for torsion
• design for interaction she
Design is provided according to ctorsion is commonly based on thmodel is imagined in a concretehorizontal and diagonal membersbars are the main reinforcement
There are the following assumpti
• The shear forces in bothdone for resultant of she
• The parameters of planeshear force resultant
• The design shear resistaaccording to clause 6.2.212.6.3 in EN 1992-1-1 is
• Design value of maximuand 6.2.3 (3,4) (VRd,max) i
• Design value of shear re
• The number of shear link
concrete data
• The angle of compressio
• The torsional cracking m
• Design value of maximuclause 6.3.2(4) in EN 19
• The angle of stirrups for
• There are 5 possibilities f
With the following limitations
other cases
forcement can be used in each section along themoments around y and z axis from all combination
ludes:
rce
ar force and torsion
lause 6.1 -6.3 in EN 1992-1-1. Design reinforcementheory of the concrete truss-model too. In this theoeam. This truss-model has a set of vertical (or sligh. The vertical bars are considered to be the stirrups;nd the diagonal bars are the concrete struts.
ns:
directions are taken into account and design of sher forces
of equilibrium (value d, z and h) are recalculated to
ce of the member without shear reinforcement (VRd (1) in EN 1992-1-1, if section is cracked in f lexure, o
used
shear force will be calculated according to clauseEN 1992-1-1
istance is calculated according to 6.2.3 (3,4) (VRd,s)
s is loaded directly from Design defaults from concr
strut can be calculated automatically or defined by
ment (TRd,c) is calculated according to clause 6.3.2(
of torsional resistance moment (TRd,max) is calculat2-1-1
esign of shear reinforcement for torsion has to be p
or calculation of thin-walled closed section
ember ins
t for shear andry a virtual truss-
ly diagonal),the horizontal
r reinforcement is
he direction of
,c) is calculatedtherwise clause
.2.2(6) (VEd,max)
in EN 1992-1-1
te settings or
the user
5) in EN 1992-1-1
ed according to
erpendicular
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• Cross-section with one p
• The user (practical) reinf
• Design should be done othe resultant of shear for
• Inclined compression ch
• The widths of cross-secti
There is no possibility for
Except of statically required sheashear reinforcement (Aswm.prov ). Itstirrups in longitudinal direction is
Design shear reinforcement
As was mentioned above, thereshear effects in concrete. In thisthe compressive concrete and terepresented by the diagram belo
lygon and one material is taken into account in ver
rcement is not taken into account
nly in case, that the angle between gradient of the ses is not greater than 15 degrees
rd or inclined tensile chord are not taken into accou
n for shear checks (value bw and bw1) are calculate
definition of user value in SEN 15
r reinforcement per meter (Aswm.req ), the program calis statically required shear reinforcement, where therounded to 25 mm.
for shear forces
xists the general concept of “strut-and-tie” model foodel, the top compression and bottom tensile memsile reinforcement, respectively. The procedure for:
Design
ion SEN 15
rain plane and
nt
d automatically.
culates providedspacing of the
the prediction ofbers representdesign can be
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Topic Training – New Concrete
The formulas which are used for
Generally, there are two possibiliexistence of cracked in bending:
Shear concrete capacity in regio
Shear concrete capacity in regio
Additionally, there is calculated twhere load is applied in the uppe
Maximal capacity of concrete co1992-1-1, because as has beenthe member axis.
Statically required cross-sectionaformula 6.13 in EN 1992-1-1
Design value of shear force sust
6.13 in EN 1992-1-1
Design value of shear force sust6.13 in EN 1992-1-1
Final design value of shear forceformulas depending on type of m
• for beam as slab and for
• for other cases
For a member with inclined chorcheck according to clause 6.2.1(chords. Nevertheless the calcula explained in the following figure.
he calculation of each component of this model are
ies for the calculation of shear capacity of concrete
cracked in bending – formula 6.2.a, b in EN 1992-1
uncracked in bending – clause 12.6.3(3) in EN 199
e maximal shear force (VEd,max) without reduction by r side of the member (see formula 6.5 in EN 1992-1
pressive strut (VRd,max) is determined according to fentioned before, the angle of stirrups (θ) is always
l area of the shear reinforcement per meter is calcul
ined by shear reinforcement (VRd,s ) is calculated ac
ined by shear reinforcement (VRd,s ) is calculated ac
(VRd) carried by the member is calculated based onmber and area of shear reinforcement.
other member with only detailing stirrups (Aswm.req =
s the additional forces have to be taken into accoun ). The calculation is prepared for taking into accounion itself is not implemented yet. The partial compo
the following.
ependently on
-1
2-1-1
b for member1).
rmula 6.9 in ENperpendicular to
ated from the
cording to formula
cording to formula
the following
0)
t for the sheart also inclinedents are
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Design shear reinforcement
As was mentioned above, thereof torsion effects in concrete. In trepresent the compressive concr
design can be represented by th
The formulas which are used for
for torsion
xists a general concept of the “strut-and-tie” modelis model, the top compression and bottom tensilete and tensile reinforcement, respectively. The pro
diagram below:
he calculation of each component of this model are
Design
or the predictionembersedure for the
the following.
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Topic Training – New Concrete
Torsional cracking moment is calstress caused by the torsional mfctd). It follows:
Maximum of torsional resistance1-1.
Statically required cross-sectionathe formula below:
Design torsional resistance momformula below
Final design value of torsional mfollowing formulas:
• for member without or wi
• for other cases
ulated according to equation 6.26 in EN 1992-1-1,ment is equal to the design axial tensile strength of
moment (TRd,max) is determined according to formula
l area of the shear reinforcement per meter is calcul
nt of torsional reinforcement (TRd,st) is calculated ac
ment (TRd) carried by the member is calculated bas
h only detailing stirrups for torsion (Aswm.req = 0)
rovided that theconcrete (value
6.30 in EN 1992-
ated according to
cording to the
d on the
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Design shear reinforcement
As was mentioned above, thereof shear and torsional effects in cinteraction shear and torsion can
Only minimum reinforcement is r1992-1-1) is satisfied:
The maximum resistance of a meconcrete struts. In order not to ex
1992-1-1) should be satisfied:
Statically required cross-sectionaformulas
for interaction shear and torsion
xists a general concept of the “strut-and-tie” modeloncrete. The procedure for design of shear reinforcbe represented by the diagram below:
quired, provided that the following condition (equati
mber subjected to torsion and shear is limited by thceed this resistance the following condition (equatio
l area of the shear reinforcement per meter is calcul
Design
or the predictionment for
on 6.31 in EN
capacity of then 6.29 in EN
ated according to
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Topic Training – New Concrete
The force in shear reinforcementformula
The maximum force which, can b
Torsional longitudinal reinforc
Additional tensile forces caused
The required cross-sectional arewhen sum of design axial forces(bigger than 0). This area is calcpreconditions:
• reinforcement is designe
• longitudinal reinforcemen
In a simplified way said, the longibelow:
Additional tensile forces causedrequired reinforcement by shiftin
caused by shear and torsion effect can be calculate
e carried by shear reinforcement is given by formula
ement
y torsion are calculated from the equation 6.28 in E
of the longitudinal reinforcement for torsion is calcNEd) and Additional tensile forces caused by torsionlated by using the biaxial method for design, with fol
only for pure tension
t is equally distributed on each edge of the cross-se
udinal reinforcement for torsion is designed accordi
y shear forces is taken into account in the design oof the bending moments.
according to
:
N 1992-1-1:
lated in the case,(Fsdt) is tensile
llowing
ction
ng to the formula
statically
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Design
47
Practical reinforcement
As in the past, a practical reinforcement layout can be defined for each 1D concrete member.Longitudinal bars, stirrups and free-form bars are available for manual input by the user. Additionally,also anchorage types may be chosen and their properties may be manipulated by the user.
This practical reinforcement layout forms the basis for several ULS and SLS checks of reinforcedconcrete members.
The input of practical reinforcement is explained more in detail in the Advanced Concept Training – 1Dconcrete members.
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Topic Training – New Concrete
Check
Stiffness
The behaviour of reinforced concand it is therefore necessary to aaddition concrete is subject to sigthe curvature and stiffness of a r
and stiffness of a reinforced conc
Stiffness presentation command ifor calculation of stiffness is baseGenerally, two states of cross-se
I. uncra