19. [eng] new concrete 15

8/17/2019 19. [Eng] New Concrete 15

1/144


2/144

Topic Training – New Concrete

2

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.


3/144

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


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


Setup ............................................................................................................................................ 79 Check width (SLS) ........................................................................................................................... 81

Value of strength for calculation of cracking forces ..................................................................... 81

Check of normal stresses (occurring of crack width) ................................................................... 81


4/144


4

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


5/144

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


6/144


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.


7/144

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.


8/144


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.


9/144

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.


10/144


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.


11/144

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.


12/144


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.


13/144

Settings

13

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.


14/144


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.


15/144

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


16/144


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 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


17/144

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 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


18/144


18

• 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.


19/144

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


20/144


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:


21/144

• 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,


22/144


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


23/144

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


24/144


Second moment of reinforcemen

Radius of gyration of the total rei



As =μs.Ac







As =μs.Ac

Area of reinforcement in each ed

Asi = As /nedge


area

forcement area

or circular section



area

forcement area

or other cross-sections

e



25/144




Checks for all type of cro




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


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


26/144


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


27/144

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)


28/144


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)


29/144

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


30/144


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


31/144

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:


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)


32/144



• Column - member predominantly in compression for which longitudinal and shearreinforcement can be designed. There are the following parameters:


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)


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.


33/144

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.


34/144


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


35/144

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.


36/144


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


37/144

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


38/144


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


39/144

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:


40/144


• 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


41/144

• 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


42/144


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


43/144


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.


44/144


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


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


45/144


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


Design

or the predictionment for

on 6.31 in EN

capacity of then 6.29 in EN

ated according to


46/144


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


47/144

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.


48/144


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

19. [eng] new concrete 15

Documents