Redistribution of Bending Moments

8/13/2019 Redistribution of Bending Moments

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Redistribut ion of bending moments and plastic analysisaccording to provision 5.5 and 5.6 of EN 1992-1-1

Manual


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Table of contents

3

Obsah1 Abstract .......................................................................................................................................... 12 Definition of continuous beam .................................................................................................... 23 Combination and construction stages ....................................................................................... 3

3.1 Changes in combinations ...................................................................................................... 33.2 Changes in construction stages ........................................................................................... 43.3 Generation of redistributed combination ............................................................................. 5

4 Definition or change of input parameters in concrete setup .................................................... 84.1 Concrete setup > General > National annex ........................................................................ 84.2 Concrete setup > General > Calculation > tab-sheet Beams .............................................. 9

5 Definition of additional data for redistribution ......................................................................... 116 New properties in services for evaluate the results ............................................................... 167 Calculation of redistributed bending moment ......................................................................... 18

7.1 Method according to EN 1992-1-1, clause 5.5(4) ............................................................... 197.2 Method according to French DTU, clause 3.2.2.5 .............................................................. 207.3 Method - moment of resistance ........................................................................................... 227.4 User input .............................................................................................................................. 238 Check of redistributed bending moment .................................................................................. 248.1 Check according to 5.5(4) .................................................................................................... 27

8.1.1 Partial checks .................................................................................... 288.1.2 Output table ....................................................................................... 30

8.2 Check according to 5.6.2(2) ................................................................................................. 328.2.1 Partial checks .................................................................................... 328.2.2 Output table ....................................................................................... 35

9 XML and parameterization ......................................................................................................... 3710 Definition of new terms .............................................................................................................. 3811

Examples ...................................................................................................................................... 39

11.1 Example 1 ......................................................................................................................... 39


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Input manually the Name of My first chapter

1

1 Abstract

The target of this project is the calculation and check of the redistribution of bending moment My(moment around the local y-axis). Moment Mz (moment around the local z-axis) is not redistributed.The redistribution means decreasing bending moments above supports and increasing bendingmoments in mid-spans where distribution of moments remains in equilibrium with the applied loads.

The user can select four methods for the calculation of redistributed bending moment My:

method according to EN 1992-1-1, clause 5.5, moment resistance (redistributed bending moment = moment of resistance),

user method.

After the calculation of redistributed bending moment according to the above-mentioned methods,the user can check the value of redistributed bending moment according to EN 1992-1-1, clause 5.5(4)or 5.6.2(2). The moment can be redistributed, only if:

a new type of member - continuous beam - is defined,

additional data for redistribution are defined on continuous beam,

a combination for redistribution is prepared.

The following steps for the calculation and check of redistributed bending moment have to beperformed:

Definition of new type of member - continuous beam (chapter 2)

Selection of combination or construction stages for which redistribution will be calculated(chapter 3)

Definition or change of input parameters in concrete setup (chapter 4)

Definition of additional data for redistribution on continuous beam (type of method, selection ofsupport...), chapter 5

Calculation of redistributed bending moment for selected member and selected method(chapter 7)

Check of redistribution bending moment in ULS checks (chapter 8)

Limitations:

Supported direction: only bending moment My(around the local y-axis)Supported code: only EN 1992-1-1Supported member: straight continuous beamSupported cross-sections: all cross-sections

Mred,max

Mlin,max

Mlin,min

Mred,min


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Redistribution of bending moments and plastic analysis according to provision 5.5 and 5.6 of EN 1992-1-1

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2 Definition of continuous beam

Bending moment can be redistributed only if continuous beam is defined. Continuous beam can bedefined via item Continuous beam(tree Structure > Model data).

After clicking on this item the user selects the type of continuous beam:

standard only one option is available.

Then the user allocates the existing 1D members (by selection in graphical window) to continuous

beam. The allocation of 1D members can be changed in the properties of Continuous beam via actionbuttons Select Allocationand Remove inactive entities from allocation.

Note:

the continuous beam cannot be copied,

graphical presentation and label for continuous beam can be set in dialog View parameterssetting > Model > Other model data > Continuous beam.


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3 Combination and construction stages

The user has to define for which combination or construction stages the redistribution should becalculated.

3.1 Changes in combinations

There is a new check box Redistribution of bending momentsin the manager of combinations andin the dialog for editing of combination. This check box is active only for ULS combination and in casethat:

concrete material is defined in project,

code EN 1992-1-1 is selected,

continuous beam is defined in project.

The check box Redistribution of bending moments can be parameterized via parameter Boolean.


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3.2 Changes in construction stages

There is a new check box Redistribution of moment in properties of each construction stage. If thischeck box is ON, then:

the redistributed moment will be calculated for all ULS combinations from the selectedconstruction stage (the check box Redistribution of bending moment in properties of eachULS combination will be ON)

supports for selected construction stage can be taken into account for redistribution.

The check box Redistribution of moment can be parameterized via parameter Boolean.


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3.3 Generation of redistributed combination

A new load case is generated and added to each combination with switching ON check boxRedistribution of bending moment. This load case contains moment reduction in each result-section.Using one of the methods described below, the program calculates moment reduction above support.For the calculation of redistributed bending moments in all sections, the program uses the followingprocedure:

moment reductions are recalculated in sections (a linear distribution is assumed along the lengthof span),

loop for all sections in span: run cross-section solver, calculate stress, integrate forces in phasesof cross-sections and the tendons,

test the material of beams (only concrete + internal tendons in cross-sections can be calculated),

E modulus increase over time (ageing, E modulus changes, ) is respected in calculations offorces in phases of cross-sections.

fill in new LC by moment reduction (forces in phases of cross-sections and tendons).

The load case with moment reduction can be presented in the services Internal forces on beam(treeResults > Beams) and Internal forces(tree Concrete > 1D member), where a new item Load cases -moment reductionis available in combo box Type of loads.

ForType of loads = Load cases - moment reductiona new combo box Load cases - momentreductionis active with the list of all load cases with moment reduction for all combinations for whichRedistribution of bending moment isON. The name of load case is derived from the name of thesource redistributed combination, for example name of LC for combination F1-MAX is F1-MAX/1. Thenumber behind the name of the combination means the number of the load case, because forenvelope combination several load cases with moment reduction can be generated.


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Basic principles for the generation of redistributed combination are:

The redistributed combination can be created only for ULS combination depending on the typeof calculation (analysis):

for TDAand Construction stages analysisthe combinations are generated automatically .Thecheck box Redistribution of bending momentis ON for all ULS combinations inconstruction/serviceability stage in which the check box Redistribution of momentis on.

for other type of analysis the check box Redistribution of bending momenthas to be switchedON directly by the user in the dialog for the definition of combination.

for linear combination only one load case with moment reduction is generated

for envelope combination the following procedure is used

o the envelope combination is exploded to linear combinations in the background,

o for the selected member (only a member with redistribution data defined) and envelopecombination the dangerous combinations from linear combinations are created,

o for each dangerous combination a new load case with moment reduction is created andfilled in,

o the new created load cases are stored.

the envelope combination is found from all dangerous combinations with load case momentreduction directly in the current result/concrete service

the contents of the redistributed combination can be presented only using the Combination key

Mlin

snj

M

snj

Mj,lMi,p

sni snj

Mred

Elastic bending moment ( linear or dangerous combination)

Moment reduction ( LC moment reduction)

Redistributed bending moment ( redistributed combination)

sni

sni


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redistributed combination is taken into account if check box Redistribution of momentinselected service (type of check) is ON


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4 Definition or change of input parameters in concrete setup

The new parameters influencing the calculation and check of the redistribution of bending moment arein:

Concrete setup > General > National annex

Concrete setup > General > Calculation > tab-sheet Beams.

4.1 Concrete setup > General > National annex

There are parameters for calculation of value according to EN 1992-1-1, clause 5.5.4 in nationalannex. The value is used for calculation of redistributed bending moment according to EN 1992-1-1and check of redistributed bending moment according to chapter 5.5 (4).


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4.2 Concrete setup > General > Calculation > tab-sheet Beams

There are parameters for the check of compression member and for selection method which is used forthe check of redistribution of bending moment My.

check boxNormal force to calculationo if this check box is ON, then normal forces in beam is taken into account for the design

of reinforcement, otherwise the beam is designed for the pure bending moment. Thischeck has no influence on checks of the member. This parameter is codeindependent.

o default value is ON

check boxCheck compression of membero is active only if check box Normal force to calculation is ONo is code independent and is used for the definition of member predominantly subject to

flexure or compression.

o if check box is ON then program checks the formula

in design reinforcement (service Design As)

in calculation of redistributed bending moment according to EN 1992-1-1


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in check of redistribution according to chapter 5.5(4) (services for ULS checks,value Redistribution check)

phn

i

icdicpEd fAxNN1

,,

where

NEd is normal force caused by external load

Np is normal force caused by prestressing

x is relative number sets in Concrete setup, default value is 0,1

nph is number of phases of cross-section

Ac,i is area of concrete of i- th phase of cross-section

fcd,i is design value of concrete compressive strength of i- th phaseof cross-section

Design of reinforcement:

if formula is satisfied, then program gives warning 60 (The member is notconsidered to be in compression) and calculation is OK

if formula is not satisfied, then program gives warning 61 (The member isconsidered to be in compression) and calculation is not ok and the beam shouldbe calculated as a column. The user must switch the type of member to columnmanually

Calculation of redistributed bending moment according to EN 1992-1-1:

if formula is satisfied, then redistributed moment may be calculated if formula is not satisfied, then program gives error 851 (The member is not

predominantly subject to flexure) and redistributed bending moment is notcalculated

Check of redistribution according to chapter 5.5(4):

if formula is satisfied, then check is OK if formula is not satisfied, then program gives error 851 (The member is notpredominantly subject to flexure) and check is not ok

o if check box is OFF, the previous formula is checked only :

in calculation of redistributed bending moment according to EN 1992-1-1 in check of redistribution according to chapter 5.5(4),

because only member predominantly subject to flexure can be used in these cases.

group Check of redistributed momentso user can select type of method for check of redistributed momentso two methods are supported

Check according to 5.5(4) - is method in EN 1992-1-1, clause 5.5 (4) Check according to 5.6.2(2) - is method in EN 1992-1-1, clause 5.6.2(2)


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5 Definition of additional data for redistribution

Calculation and check of redistributed moment is not possible without redistribution data, becausesupports and method for calculation have to be selected. Additional data for redistribution (RM data)can be input via item Redistribution datain Concrete tree > 1D member. The item is active only, if:

code EN is selected in Project > Basic data

concrete material is selected in Project > Basic data one or more continuous beams are defined in the project

After clicking on item Redistribution data, the user has to select one Continuous beam and methodand supports for the calculation in dialog Redistribution moment.

Note:

The redistribution data cannot be input to a continuous beam if the graphical presentation ofcontinuous beam is OFF. This presentation can be set ONvia View parameters setting >Model > Other model data > Continuous beam

Only input parameter for bending moment Myand for supports in direction of z-axis of LCS canbe set

There is a list of all supports in the direction of the local z-axis (name of supports) for all constructionstages in the dialog. All types of support are supported (standard supports, columns, crossing ofmember). Each support has the following properties:

x [m]

o non editable value, the position of the support on the continuous beam ispresented


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Reduce

o if check box is ON, the moment M above this support is redistributed,

o default value is ON

o the value can be parameterized using a Boolean parameter

Redistribution

o combo box for selection of the type of method for the calculation ofredistributed bending moment, user can select these methods:

EN 1992-1-1,5.5(4), default method Moment of resistance User input

o is active only if Reduce = ON

Construction stages

o the supports can be defined in more construction stages and this propertyallow the user to select for which construction stages the moment abovesupport will be redistributed

o is active if construction stages are defined and the check box Redistributionmomentis ON for one construction stage, see chapter 3.2.

o the list of construction stages for which the moment above support will beredistributed. Only construction stages with Redistribution moment = Onare listed.

o the list of construction stages can be edited via button . The user canselect construction stages for which the moment above support will beredistributed. Only construction stages with Redistribution moment = Onare listed in the dialog Construction stages selection.

There are additional properties for user input (redistribution = User input)

Same input of internal support

o is active only for internal support

o if the check box is OFF, then input values for left and right side of the supportcan be different.

o if check box is ON, theninput values for both side of support are same

o the value can be parameterized via parameter Boolean


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Same input of internal support = ON Same input of internal support = OFF

Equilibrium of Mred

o is active only for an internal support and if Same input of internal supportis

OFFo combo box for selection of the method for equilibrium of redistributed moment

above internal support. Three possibilities are supported: None (defualt value), the redistributed bending moment on the left

and right side of the support can be different Min, the redistributed bending moment on the left and right side of the

support are the same, minimum from both Max, the redistributed bending moment on the left and right side of

the support are the same, maximum from both

Equlibriumo

fMred

None

Min

Max

Type of input

o combo box for selection of the type of input, two types are supported

Delta ,the user inputs the value of M (moment reduction) which issubtracted from elastic bending moment

Total (defualt), the user inputs directly the value of redistributedmoment above support


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Type of input= Total Type of input= Delta

Value

o different type can be set for both sides of internal supports

o only value for bending moment My(around y-axis of LCS) can be input

o combo box for selection of the type of value with two items. Abs (default) the value is input as real value and the values Mr(l),

delta Mr(l), Mr(r), delta Mr(r) can be parameterized via parameterMoment

Rel the relative value is input and the values Mr(l), delta Mr(l), Mr(r),delta Mr(r) can be parameterized via parameter Relative.

Mr(l) or delta Mr(l)

o edit box for inputting the value on the left side of the support

o is inactive for support in the beginning of a continuous beam

o type of the value depends on properties Type of inputand Value Type of input = Total and Value = Abs, user inputs directly the

absolute value of redistributed moment (Mr(l) ). The final value ofredistributed moment is the same as the input value. The negativevalue should be input.

Type of input = Total and Value = Rel, user inputs the relative valueof redistributed moment (Mr(l) ) with limitations from 0 to 1. The finalvalue of redistributed moment depends on the value of elasticbending moment.

Type of input = Delta and Value = Abs, user inputs the absolutevalue of moment reduction (deltaMr(l)) which is subtracted from theelastic bending moment. It means that the final value of redistributedmoment depends on the value of the elastic bending moment. The

positive value should be input. Type of input = Delta and Value = Rel, user inputs the relative value

of moment reduction (deltaMr(l)). Moment reduction depends on thevalue of elastic bending moment .Final value of redistributed momentis calculated by subtracting the value of moment reduction from theelastic bending moment.

Mr(r) or delta Mr(r)

o edit box for input of the value on the right side of the support

o is inactive for support at the end of continuous beam and for internal supportif check box Same input of internal support is ON

o the type of the value depends on properties Type of inputand Value Type of input = Total and Value = Abs, the user inputs directly the

absolute value of redistributed moment (Mr(r)). The final value of


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redistributed moment is the same as the input value. The negativevalue should by input.

Type of input = Total and Value = Rel, the user inputs the relativevalue of redistributed moment (Mr(r)) with limitations from 0 to 1. Thefinal value of redistributed moment depends on the value of elasticbending moment.

Type of input = Delta and Value = Abs, the user inputs the absolutevalue of moment reduction (deltaMr(r)) which is subtracted from theelastic bending moment. It means that the final value of redistributedmoment depends on the value of elastic bending moment. Thepositive value should by input.

Type of input = Delta and Value = Rel, the user inputs the relativevalue of moment reduction (deltaMr(r)). Moment reduction dependson the value of elastic bending moment. The final value ofredistributed moment is calculated by subtracting the value ofmoment reduction from the elastic bending moment.

The input values of RM data can be presented in numerical output in the Document via itemRedistribution data.

All properties of redistribution data are presented in default table. The input values can be changeddirectly in the Document (double click on the value) or via XML


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6 New properties in services for evaluate the results

The possibility of calculation and check of redistributed bending moment produced some changes inseveral services in comparison with previous versions of Scia Engineer:

new check box Redistribution of moment

o is in following services

Internal forces on beam ( tree Results > Beams ) Reinforcement design ( tree Concrete > 1D member > Automatic member

reinforcement design ) Cross-section characteristics ( tree Concrete > 1D member ) Internal forces ( tree Concrete > 1D member ) Design As ( tree Concrete > 1D member > Member design ) Design of non-prestressed reinforcement in prestressed css ( tree Concrete > 1D

member > Member design ) Check response ( tree Concrete > 1D member > Member check > Check on non-

prestressed concrete) Check capacity ( tree Concrete > 1D member > Member check > Check on non-

prestressed concrete) Check response ( tree Concrete > 1D member > Member check > Check on -

prestressed concrete) Check capacity ( tree Concrete > 1D member > Member check > Check on

prestressed concrete) Allowable stress of concrete ( tree Concrete > 1D member > Member check >

Check on prestressed concrete) Allowable stress of concrete ( tree Concrete > 1D member > Member check >

Check on prestressed concrete) Allowable principal stresses

o is active only for ULS combination for which Redistribution of bending moment is ON Class with one or more ULS combination for which Redistribution of bending

moment isON, see chapter 3

o if it is ON, the redistributed bending moment (with LC moment reduction) is taken intoaccount, else elastic bending moment (without LC moment reduction) is taken intoaccount

new type of loads Load cases - moment reductions

o is in following services Internal forces on beam ( tree Results > Beams ) Internal forces ( tree Concrete > 1D member )

o is active if one or more combinations are redistributed (check box Redistribution ofbending moment in properties of combinationisON), see chapter 3

o if this type of load is selected, then the new combo boxLoad cases - moment reductionis active with the list of all load cases with moment reduction for all combinations forwhichRedistribution of bending moment isON. The name of load case is derivedfrom the name of source redistributed combination.


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new value Check redistribution

o is in the following services Check response ( tree Concrete > 1D member > Member check > Check on non-

prestressed concrete) Check capacity ( tree Concrete > 1D member > Member check > Check on non-

prestressed concrete) Check response ( tree Concrete > 1D member > Member check > Check on -

prestressed concrete) Check capacity ( tree Concrete > 1D member > Member check > Check on

prestressed concrete)

o is active only if check box Redistribution of momentis ONo if it is ON or selected, the value of redistributed bending moment is checked according to

the settings in concrete setup (Concrete setup > General > Calculation > tab-sheetBeams > group Check of redistributed moments )


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Mred,n,l is redistributed bending moment above left support of the span n

Mred,n,p is redistributed bending moment above right support of the span n

Mi,p is moment reduction above i-support on the right side

Mj,l is moment reduction above j-support on the left side

Mn,l is moment reduction above left support of the span n

Mn,p is moment reduction above left support of the span n

Note:

The value of redistributed bending moment and moment reduction are input to the left or rightside of support, and not to the left/right support of the span

The moment Mz(around the local z-axis of the member is not redistributed)

Four types of method for calculation of two ends moment reduction in span are supported:

EN 1992-1-1,5.5(4), default method

Moment of resistance

User input

7.1 Method according to EN 1992-1-1, clause 5.5(4)

It is linear elastic analysis with limited redistribution calculated according to EN 1992-1-1, clause 5.5.The moment reduction above support is calculated according to formula

M = ( 1 - )Mlin

and it follows that redistributed bending moment is calculated from formula

Mred= Mlin-M= Mlin- ( 1 - )Mlin= Mlin

where

M is moment reduction above support

Mlin is elastic bending moment from linear analysis

Mred is redistributed bending moment

is a ratio of redistributed bending moment to the elastic bending momentcalculated according to formulas 5.10a and 5.10 b in EN 1992-1-1

= max (1;2) < 1,0

1= k1+ k2xu/d for fck50 MPa= k3+ k4xu/d for fck> 50 MPa

2= k5 for class B or C of non prestressed reinforcement

= k6 for class A of non-prestressed reinforcement and forprestressed reinforcement

xu is the depth of neutral axis at the ULS calculated for redistributed bendingmoment calculated after second step of iterative calculation

d is the effective depth of the cross-section

k1-k6

are parameters for calculation of value , the values can be set in Concretesetup > General > National annex. Some of them are dependent on the value

cu2cu2 is the ultimate strain of the concrete. This value is automatically determined by

the program from the properties of concrete in compression


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Limitations:

non-prestressed user real reinforcement or prestressed reinforcement are input in continuousbeam

equilibrium for ULS was found

ratio of the length of adjacent spans of continuous beam in the range 0.5 to 2 (program have to

check the ratio of spans)

the beam is predominantly subject to flexure, it means that above support the condition below isfulfilled, see chapter 4

phn

i

icdicpEd fAxNN

1

,,

the ratio of redistributed bending moment to the elastic bending moment is lower than 1

if the limitations are not fulfilled, then the moment is not redistributed and the program gives awarning or error

Note:

the lowest quality of concrete of all phases of the cross-section is used for calculation of value (values fckand cu2) for calculation of cross-section with more phases

the value k6 (class A) is used for calculation of value for cross-section with only prestressedreinforcement

the lowest quality of all reinforcement (k6 for class A) is used for calculation of value for cross-section with different classes of reinforcement

the depth of neutral axis at the ULS is calculated for redistributed bending moment that iscalculated after second step of iterative calculation, because calculation of redistributed bendingmoment leads to an iterative calculation. Full iteration is not used because the calculation wouldtake a lot of time.

7.2 Method according to French DTU, clause 3.2.2.5

For calculation of moment reduction according to French DTU clause 3.2.2.5c is used. Redistribution isestimated on the basis of a localized rotation above the support equal to 0.003 rad. The momentreduction, redistributed towards the neighbouring spans, can be calculated in the 1st approximation as:

p

p

l

l

L

EI

L

EIM

3300075,0

where


EIl is flexural stiffness of the left span of continuous beam at the support

Ll is length of the left span of continuous beam at the support (the value ispresented in properties of continuous beam, see chapter 2)

EIp is flexural stiffness of the right span of continuous beam at the support

Lp is length of the right span of continuous beam at the support (the value ispresented in properties of continuous beam, see chapter 2)

For usual floor beam stiffness, this value leads generally to a moment reduction around a 10th of theelastic moment of the neighbouring spans.


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Limitations:

there are no limitations for this method

Note:

the lowest quality of concrete of all phases of the cross-section is used for calculation (value Ec)of cross-section with more phases

the flexural stiffness EIl is calculated on the left side of the support (just in front of the section)

the flexural stiffness EIp is calculated on the right side of the support (just behind the section)

the secant module of elasticity from properties of material is used for the calculation


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7.3 Method - moment of resistance

The redistributed bending moment above support equals the moment of resistance of the cross-section. Moment of resistance is determined from the interaction diagram for the method Mu (momentof resistance is calculated as an intersection of parallel line with axis of MRdcrossing the point[NEd;MEd,y;MEd,z] ) and interaction diagram ). The axis MRd is resultant of vectors MRd,yand MRd,z

Interaction diagram Linear bending moment

Redistributed bending moment

Note: The line for calculation of intersection with interaction diagram is parallel with line My in this

case, because moment Mz is zero.

The redistributed bending moment and moment reduction are calculated according to procedure below

Mred= MRd,min(Vu,min) if Mlin(V) < 0 kNmMred= MRd,max(Vu,max) if Mlin(V) 0 kNm

M = Mlin- Mred

where




MRd,min(Vu,min)

is minimum value of moment of resistance determined from interactiondiagram of the cross-section. The value in brackets is symbol used in theprogram

MRd,max(Vu,max)

is maximum value of moment of resistance determined from interactiondiagram of the cross-section. The value in brackets is symbol used in theprogram


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Limitations:

non-prestressed user real reinforcement or prestressed reinforcement are input in continuousbeam

if the limitations are not fulfilled, then the moment is not redistributed and the program gives awarning or error

7.4 User input

The redistributed bending moment or moment reduction is directly input by the user in redistributeddata, see chapter 5. The value of redistributed bending moment and moment reduction depends onproperties Type of valueand Valuein redistribution data and they are calculated according to tablebelow

Properties in redistribution data Formulas for calculation

Type of input Value Redistributed moment Moment reduction

Total Abs Mred= Input M = Mlin- InputTotal Rel Mred = InputMlin M = Mlin(1-Input)Delta Abs Mred= Mlin- Input M = InputDelta Rel Mred= Mlin(1-Input) M = MlinInput

where




Input is input value in properties Mr(l)or delta Mr(l)and Mr(r)or delta Mr(r)inredistribution data

Limitations:

there are no limitations for this method


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8 Check of redistributed bending moment

The user can check calculated redistributed bending moment My(around the local y-axis of themember) using two methods:

Check according to 5.5(4) - is method in EN 1992-1-1, clause 5.5 (4)

Check according to 5.6.2(2) - is method in EN 1992-1-1, clause 5.6.2 (2)

Type of the method can be set in Concrete setup > General > Calculation > tab-sheetBeams >groupCheck of redistributed moments(no, one or more method can be ON). The redistributedbending moment can be checked in the following services:

Check response ( tree Concrete > 1D member > Member check > Check on non-prestressedconcrete)

Check capacity ( tree Concrete > 1D member > Member check > Check on non-prestressedconcrete)

Check response ( tree Concrete > 1D member > Member check > Check on -prestressedconcrete)

Check capacity ( tree Concrete > 1D member > Member check > Check on prestressedconcrete)

For check of redistribution some conditions have to be fulfilled:

the check box Redistribution of moment is ON

the check boxes Check according to 5.5(4) or Check according to 5.6.2(2) are ON in Concretesetup

value Check redistributionis ON or selected.


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The redistributed bending moments are checked only in sections above supports. The maximum checkvalue from all selected methods is presented graphically. In numerical output the following is presented

Summary table - is presented always

Table for Check according to 5.5(4) , if this method is ON in Concrete setup

Table Check according to 5.6.2(2), if this method is ON in Concrete setup

Note:

if redistributed bending moment in some section does not satisfy, the other check where bendingmoment is taken into account (check capacity, check stress, check strain....) is not doneandprogram gives error 898(The check of redistributed bending moment does not satisfy. Uselinear internal forces only).

if equilibrium for ULS is not found in the section above support, the check redistribution will notbe done, program gives error 583(Forces are zero or no equilibrium found ) and there is noresults for this section in tables for check according to 5.5(4) and 5.6.2(2).

The check of redistribution is performed according to the diagram below

Method5.5(4)

Check 1

Check 5.5(4) = OFF

Check 5.5(4) = OK Check 5.5(4) = NOT OK

Method

5.6.2(2)

Check 1

Check 5.6.2(2) = OFF

Check 5.6.2(2) = OK Check 5.6.2(2) = NOT OK

Check 5.6.2(2) = NOT DONE

ON OFF

OFF

YES

YES

NO

NO

Equilibriumis found

YES

Check 5.5 (4) = NOT DONE

Check 5.6.2(2) = NOT DONE

NO

ON


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The results of all checks are presented in Summary tablein the member check or in the single check

Member check

There are the following values in tables and in table composer

Member the name and number of the member

dx position of standard result section

Case type and name of extreme load case/combination/class

N normal force

Nlim limit normal force to be considered predominantly subject to flexure

My linear bending moment before redistribution calculated for source

combination of redistributed combinationMred redistributed bending moment calculated for redistribution combination

ratio of redistributed moment to the elastic bending moment

lim limit ratio of redistributed moment to the elastic bending moment calculatedaccording to formula 5.10

Check 5.5(4) Check redistributed bending moment according to EN 1992-1-1, chapter5.5(4). The result of check can be:OK - if check satisfiesNOT OK - if check does not satisfyOFF - if check is OFF in Concrete setupNOT DONE - if equilibrium is not found

Check 5.6.2(2) Check redistributed bending moment according to EN 1992-1-1, chapter

5.6.2(2). The result of check can be:OK - if check satisfiesNOT OK - if check does not satisfyOFF - if check is OFF in Concrete setupNOT DONE - if check is ON in Concrete setup and check according to

5.5(4) satisfy or if equilibrium is not found

Check 5.6(3) Check redistributed bending moment according to EN 1992-1-1, chapter5.6(3). This check is not implemented, therefore status of this check isalways OFF

Checkcal The value of unit check of all partial checks

Checklim The limit value of unit check.

Check The results of check (OK or NOT OK)

W/E the number of warning or error


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Single check

The tables for check detailing provisions are presented in the Document, if

the check box Check results in dialog Change of setupis ON

section above support is selected

The summary table in single check contains the following values:

8.1 Check according to 5.5(4)

This check is performed according to EN 1992-1-1, clause 5.5(4) and it contains three partial checks:

if the member is predominantly subject to flexure

ratio of adjacent spans


If the check is satisfied, linear elastic analysis with limited redistribution can be used at ULS. The checksatisfies only in case that all partial checks are fulfilled. The unit check is calculated as maximum valueof all partial checks

);;max( 2,2,1, calcalcalcal CheckCheckCheckCheck ,

If the check does not satisfy, the redistributed bending moment does not satisfy too and should bechecked using plastic analysis or the linear elastic bending moment has to be used for the calculation.


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8.1.1 Partial checks

Check if the member is predominantly subject to flexure

The EN 1992-1-1 code does not define when the member is predominantly subject to flexure, thereforewas added to the concrete setup a new check box Check of compression of member(see chapter 4)which is used for this check too.

The member is predominantly subject to flexure if the condition below is fulfilled

phn

i

icdicpEd fAxNNNN

1

,,lim

where

N is normal force caused by external load and prestressing

NEd is normal force caused by external load

Np is normal force caused by prestressing

Nlim is limit normal force to predominantly subject to flexure

x is relative number set in Concrete setup, default value is 0,1nph is number of phases of cross-section

Ac,i is area of concrete of i- th phase of cross-section

fcd,i is design value of concrete compressive strength of i- th phase of cross-section

The unit check is calculated as ratio of normal force caused by external load and by prestressing tolimit normal force.

lim

1,N

NCheckcal

Note:

this check is performed always independently on activity of check box Check of compressionin Concrete setup > General >Calculation > tab-sheet beam,

if unit check ( N/Nlim) is greater than 1, the program gives warning 884(The member is notpredominantly subject to flexure).

Check ratio of adjacent spans

The check is performed only for the internal support of a continuous beam for which the followingcondition has to be satisfied

2,0 Lleft/Lright0,5

The condition can be also written as

lim

right

left

right

left

L

L

L

L

where

Lleft is the length of span on the left side of support

Lright is the length of span on the right side of support


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Lleft/Lright is ratio of adjacent spans

(Lleft/Lright)lim is limit ratio of adjacent spansif LleftLright, then (Lleft/Lright)lim= 2if Lleft< Lright, then (Lleft/Lright)lim= 0,5

The unit check is calculated according to formulas bellow

LleftLright Lleft< Lright

lim

2,

right

left

right

left

cal

L

L

L

L

Check

right

left

right

left

cal

L

L

L

L

Check lim2,

Note:

this check is provided only for the internal support of a continuous beam,

if this check is not fulfilled the program gives warning 885(Ratio of the length of adjacent spansis out of the range (0.5-2.0)).

Ratio of redistributed moment to the elastic bending moment

The following condition is checked in this check:

lim1

where

is ratio of redistributed moment to elastic bending moment

lin

red

M

M



lim is a limit ratio of redistributed bending moment to the elastic bending moment calculated

according to formulas 5.10a and 5.10 b in EN 1992-1-1lim= max(k1+ k2xu/d; k5) for fck50MPa and for class B and C of non-prestressed reinf.= max(k1+ k2xu/d; k6) for fck50MPa and for class A of non-prestressed reinf. and for

prestressed reinforcement

= max(k3+ k4xu/d; k5) for fck> 50MPa and for class B and C of non-prestressed reinf.

= max(k3+ k4xu/d; k6) for fck> 50MPa and for class A of non-prestressed reinf. and forprestressed reinforcement

xu is the depth of compression zone at the ULS calculated for redistributed bending moment

d is the effective depth of the cross-section

k1-k6

are parameters for calculation of value , the values can be set in Concrete setup > General

> National annex. Some of them are dependent on the value cu2cu2 is the ultimate strain of concrete. This value is automatically determined by the program from

the properties of concrete in compression


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The unit check is calculated according formula below

1 1

lim3, calCheck

,max lim3,calCheck

Note:

the lowest quality of concrete of all phases of cross-section is used for calculation of value lim(values fckand cu2) for calculation of the cross-section with more phases

the value k6 (class A) is used for calculation of value lim for cross-section with only prestressedreinforcement

the lowest quality of all reinforcement (k6 for class A) is used for calculation of value limforcross-section with different classes of reinforcement

the depth of neutral axis at the ULS is calculated after redistribution (for redistributed bendingmoment).

if this check is not fulfilled the program gives warning 886(Ratio of redistributed bendingmoment to elastic is lower than the limit value or greater than 1.0)

8.1.2 Output table

Numerical output can be presented in member check or in single check.

Member check

There are two types of table for presentation of results for check redistribution bending moment

according to 5.5 (4) default

detailed


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dx position of result section


N normal force

Nlim limit normal force to be considered predominantly subject to flexure

My linear bending moment before redistribution calculated for source combination ofredistributed combination

Mred redistributed bending moment calculated for redistribution combination


lim limit ratio of redistributed moment to the elastic bending moment calculatedaccording to formula 5.10

Lleft/Lright ratio of adjacent spans

(Lleft/Lright)lim limit ratio of adjacent spans

Lleft length of span on the left side of support (effective span)

Lright length of span on the right side of support (effective span)

xu depth of compression zone axis after redistribution

d effective depth of cross-section

Class.reinf class of reinforcing steelfck characteristic compressive cylinder stress of concrete in the compressed zone

Checkcal the value of unit check of all partial checks

Checklim the limit value of unit check.

Check the results of check (OK or NOT OK)


Single check

Tables for check of detailing provisions are presented in the Document if:

check box Check results in dialog Change of setupis ON



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The table for check according to 5.5(4) in single check contains the following values:

8.2 Check according to 5.6.2(2)

It is a method of check using a plastic analysis without direct calculation of rotation capacity. Plasticanalysis is an extreme case of moment redistribution, where moment is distributed in accordance withthe structure's ability to resist them.This check is performed according to EN 1992-1-1, clause 5.6.2(2) and it contains three partial checks

check of depth of compression zone after redistribution

check of class of reinforcement

check of ratio of the moments at intermediate support to the moment in the span

The check satisfies only in case that all partial checks are fulfilled. The unit check is calculated as themaximum value of all partial checks

);;max( 2,2,1, calcalcalcal CheckCheckCheckCheck

If the check does not satisfy, the redistributed bending moment does not satisfy and should be checkedusing plastic analysis with direct calculation of rotation capacity (EN 1992-1-1, clause 5.6.3) or linearelastic bending moment has to be used for the calculation.

8.2.1 Partial checks

Check of depth of compression zone

Adequate rotation capacity for plastic analysis is deemed to be achieved if depth of compression zoneis restricted to depth as follows (EN 1992-1-1, clause 5.6.2(2)):

lim

d

x

d

xuu

where

xu is depth of compression zone axis after redistribution

d is effective depth of cross-section

xu/d is calculated ratio of xu/d

(xu/d)lim is limit ratio of xu/d(xu/d)lim= 0,25 for fck50 MPa (strenght classes C50/60)(xu/d)lim= 0,15 for fck> 50 MPa (strenght classes C55/67)

fck is characteristic compressive cylinder stress of concrete in thecompressed zone


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The unit check is calculated according to formula below

lim

1,

d

x

d

x

Checku

u

cal

Note:

the lowest quality of concrete of all phases of cross-section is used for calculation of limit ratioxu/d for calculation of cross-section with more phases

if this check is not fulfilled, the program gives error 887(Depth of neutral axis after redistributiondoes not satisfy)

if value xu> d, then the check is not performed (value xu/d is not calculated and appeared innumerical output ) and the program gives warning 288 (The check xu/d is not performed, becausexu > d (member in compression))

Check of class of reinforcement

Only reinforcement with a big ductility can be used for plastic analysis, therefore class A of non-prestressed reinforcement and prestressed reinforcement cannot be used for this check due to its lowductility.

The value for unit check for class A of non-prestressed reinforcement and for only prestressedreinforcement is loaded from Concrete setup > Errors and warning > group Check value for section,where the value cannot be calculated. For other classes of reinforcement, the unit check is not

calculated.

Note:

this check is not fulfilled and program gives error 863(Reinforcement of class A or prestressed

reinforcement is not recommended for this check) if:o only Class A of non-prestressed reinforcement is defined in the checked section,

o only prestressed reinforcement is defined in the checked section

o prestressed reinforcement and class A of non-prestressed reinforcement is defined in thechecked section


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Check of ratio of the moment at intermediate support to the moment in the span

The ratio of moments at intermediate supports to those in adjacent span must lie between 0.5 and 2.0(EN 1992-1-1, clause 5.6.2(2). It means that

lim,,

lpos

left

lpos

left

M

M

M

M

, lim,,

rpos

right

rpos

right

M

M

M

M

where

Mleft is elastic bending moment on the left side of the support

Mpos,l is the maximal elastic bending moment in the left span

Mright is elastic bending moment on the right side of the support

Mpos,r is the maximal elastic bending moment in the right span

Mleft/Mpos,l is ratio of elastic bending moment on the left side of the support tothe elastic moment in the left span

(Mleft/Mpos,l)lim is limit ratio of bending moment on the leftif MleftMpos,l, then (Mleft/Mpos,l)lim= 2if Mleft> Mpos,l, then (Mleft/Mpos,l)lim= 0,5

Mright/Mpos,r is ratio of elastic bending moment on the right side of the support tothe elastic moment in the right span

(Mright/Mpos,r)lim is limit ratio of bending moment on the rightif MrightMpos,r, then (Mright/Mpos,r)lim= 2if Mlright> Mpos,r, then (Mright/Mpos,r)lim= 0,5

The unit check is calculated according to formulas bellow

MleftMpos,land MrightMpos,r MleftMpos,land Mright< Mpos,r

lim,

,

lim,

,,max

rpos

right

rpos

right

lpos

left

lpos

left

M

M

M

M

M

M

M

M

rpos

right

rpos

right

lpos

left

lpos

left

M

M

M

M

M

M

M

M

,

lim,

lim,

,,max

Mleft< Mpos,land MrightMpos,r Mleft< Mpos,land Mright< Mpos,r

lim,

,

,

lim, ,max

rpos

right

rpos

right

lpos

left

lpos

left

M

M

M

M

M

M

M

M

rpos

right

rpos

right

lpos

left

lpos

left

M

M

M

M

M

M

M

M

,

lim,

,

lim, ,max

Note:

this check is provided for intermediate support of continuous beam, where elastic bendingmoment Mleftor Mrightare non zero

for outside support only one side of support is checked, if elastic bending moment above this

support in non-zeroo support at the beginning of the member (right side of support is checked, if Mright 0)

o support at the end of the member (left side of support is checked, if Mleft 0)


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if unit check of this check is greater than 1, the check is not fulfilled and the program gives error888(Ratio of the elastic moments at the supports to elastic moment in the span is out of therange (0.5-2.0))

8.2.2 Output table

Numerical output can be presented in member check or in single check.

Member check

There are two types of table for presentation of results for check redistribution bending moment accordingto 5.5 (4)

default

detailed



dx position of result section


N normal forceMy linear bending moment before redistribution calculated for source

combination of redistributed combination

Mred redistributed bending moment calculated for redistribution combination

Mleft is elastic bending moment on the left side of the support

Mpos,l is the maximal elastic bending moment in the left span

Mright is elastic bending moment on the right side of the support

Mpos,r is the maximal elastic bending moment in the right span

Mleft/Mpos,l is ratio of elastic bending moment on the left side of the support to the elasticmoment in the left span

(Mleft/Mpos,l)lim is limit ratio of bending moment on the left

Mright/Mpos,r is ratio of elastic bending moment on the right side of the support to the

elastic moment in the right span(Mright/Mpos,r)lim is limit ratio of bending moment on the right

xu depth of compression zone axis after redistribution

d effective depth of cross-section


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xu/d is calculated ratio of xu/d

(xu/d)lim is limit ratio of xu/d

fck is characteristic compressive cylinder stress of concrete in the compressedzone

Class.reinf class of reinforcing steel

fck characteristic compressive cylinder stress of concrete in the compressedzone

Checkcal The value of unit check of all partial checksChecklim The limit value of unit check.

Check The results of check (OK or NOT OK)


Single check

The tables for check of detailing provisions are presented in the Document if

the check box Check results in dialog Change of setupis ON


The table for check according to 5.6.2(2) in single check contains the following values:


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9 XML and parameterization

Almost all values for redistribution data for the user method can be parameterized (see chapter 5) andchanged via XML. In addition, the following check boxes are parameterized

Redistribution of bending moments in definition of combination (see chapter 3.1)

Redistribution of moment in properties of each construction stages (see chapter 3.2)


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10 Definition of new terms

REDES a module of SCIA Engineer for the definition and drawing of realnon-prestressed reinforcement


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11 Examples

11.1 Example 1

Six non-prestressed continuous beams with two spans, with same load, but with different number ofupper bars above support and different method for redistribution of bending moment

B1: upper bars above support =716, method according to EN 1992-1-1, 5.5(4) B2: upper bars above support =716, method Moment of resistance

B3: upper bars above support =716, user input, delta Mr= 30kNm

B4: upper bars above support =616, method according to EN 1992-1-1, 5.5(4)

B5: upper bars above support =616, method Moment of resistance

B6: upper bars above support =616, user input, delta Mr= 30kNm

Linear internal forces along continuous beam

Required area

User defined reinforcement via REDES (real bars)


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Check member in extreme sections for linear bending moment

Cross-section with reinforcement Interaction diagram

SectionabovesupportforB1,B

2,B

3(x=6,0

Sectionabovesu

pportforB4,B

5,B

6(x=6,0m)

Sectionatmidspan(x=2,4man

dx=9,6m)

Section above support with 616 (member B4-B6) does not satisfy for linear bending moment,therefore we used functionality for redistribution.


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The redistributed bending moment was calculated for three different methods and for two numbers ofupper bars above support, see table below

The redistributed bending moment

above support Mred[kNm]

Upper reinforcement above support

716 616

EN 1992-1-1,5.5(4) -232,8 (B1) -240,4 (B4)

Moment of resistance -252 (B2) -219,6 (B5)

User input (Abs,Delta Mr= 30 kNm) -210,4 (B3) -210,4 (B6)

Note:

the method according to EN 1992-1-1, clause 5.5(4)

o for upper reinforcement 616 the moment was not redistributed (is the same as the linear

elastic moment) because equilibrium was not found the method Moment of resistance

o for upper reinforcement 716 redistributed bending moment is bigger than the linearelastic bending moment, therefore this redistribution is not usable

o support at the end of the member (left side of support is checked, if Mleft 0)

the User method

o the redistributed bending moment is independent on reinforcement

The detailed evaluation will be done only for configurations in the table below

Method Mred[kNm]

Upperbars

Internal forces after redistribution

EN1992-1-

1,5.5(4)

-232,8

(B1)

716

Mo

mentof

res

istance

-21

9,6

(B5)

616

Userinput

(Abs,DeltaMr

=30kNm)

-210,4

(B6)

616


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Check of redistributed bending moment for member B1,B5 and B6

Check of capacity of critical section for member B1,B5 and B6

Conclusion:

Date post:	04-Jun-2018
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Redistribution of Bending Moments

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