ACI Theory to Practice

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ACI

WEB SESSIONS

Andy Scanlon Symposium on

Serviceability and Safety of

Concrete Structures: Theory to

Practice, Part 4

ACI Fall 2011 Convention

October 16 20, Cincinnati, OH ACIWEB SESSIONS

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ACI

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This ACI Web Session includes 2 speakers presenting at the

ACI fall convention held in Cincinnati, OH, October 16 20,

2011.

Additional presentations will be made available in future ACI

Web Sessions.

Please enjoy the presentations.

ACI

WEB SESSIONS

Andy Scanlon Symposium on

Serviceability and Safety of

Concrete Structures: Theory to

Practice, Part 4

ACI Fall 2011 Convention

October 16 20, Cincinnati, OH

ACI

WEB SESSIONS

Jonathan Hirsch, PE, is a Development Manager at

Bentley Systems, Inc. He is a member of PTI Committee

DC-20, Building Design. He earned his Bachelor of

Science in Civil Engineering from Old Dominion

University and Master of Science in Civil Engineering from the

Georgia Institute of Technology. He is a licensed Professional

Engineer in Georgia.

ACI

WEB SESSIONS

PracticalDeflectionPredictionof

ConcreteSlabs

JonathanHirsch

FloraCalabrese

EamonnConnolly

AllanBommer

ACI

WEB SESSIONS

InfluencingFactors

ConcreteProperties

Cracking/TensionStiffening

Creep Shrinkage

Externallyrestrained

Internallyrestrained

LoadHistory

ACI

WEB SESSIONS

DeflectionPredictionMethods

Method1 2Dequivalentframeanalysisusing

effectivemomentofinertia

Effectivemomentofinertiaoverentireframe

width

Loadhistorystiffness

Multipliersforcreepandshrinkage

Summingofstripresults


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ACI

WEB SESSIONS


Method2 Spreadsheetconsideringcracking,

creep,andloadhistoryCoefficientsforloaddistribution/tension stiffening

CreepandshrinkageusingACI318/209curves

Ageofconcreteaccountedfor

Loadhistory

Summingofstripresults

ACI

WEB SESSIONS


Method3 3Dfiniteelementanalysisusing

elementstiffnessadjustmentEC2tensionstiffeningmodel

Creepandshrinkagestrainstrackedandsuperimposed

Loadredistribution

Restrainedshrinkage

ACI

WEB SESSIONS

TestSlabs

UniversityofNewSouthWales(Guo and

Gilbert)

215WestWashingtonStreet

Aqua

ACI

WEB SESSIONS

UniversityofNewSouthWales

ACI

WEB SESSIONS


ACI

WEB SESSIONS



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WEB SESSIONS


ACI

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ACI

WEB SESSIONS

Aqua

ACI

WEB SESSIONS

Aqua

ACI

WEB SESSIONS

SlabS6

ACI

WEB SESSIONS

3-D Finite Element predicted def lect ions very wel l no externalres t ra in t was m ode ledSpreadsheet p red ic t ed de f lec t i ons very we l l

Charac te r i st i c s o f t h i s t es t :

No rest ra in t due to ro l le rs a t t he co lumn baseNo co lumn c rack ingLoads near s lab c rack ing loads

Slab c racks p ropagated over t ime

2-D Equivalent Frames s igni f icant l y underest imat ed

def lec t i ons due t o under p red ic t i on o f c rack ing

SlabS6


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ACI

WEB SESSIONS

SlabS7

ACI

WEB SESSIONS

SlabS7


Same s lab load as S6

Rest rained column baseSim i la r f i na l s lab c rack pa t t e rn t o S62-D Equivalent Frames s igni f icant l y underest imat eddef lec t i ons due t o under p red ic t i on o f c rack ingSpreadsheet overes t imated de f lec t i ons , t o a r easonab ledegree

3-D F in i t e E lement (w i t h ex te rna l sh r inkage res t ra in t

mode led) underes t imated de f lec t i ons , t o a reasonab ledegree

ACI

WEB SESSIONS

SlabS4

ACI

WEB SESSIONS

SlabS4


Slab load ing f a r i n excess o f c rack ing load and sus ta inedRest rained column baseHeavy s lab c rack ing w h ich p ropagated over t ime

Ex tens ive co lumn c rack ing

Heavier re inforcem ent than S6/S7

2-D Equivalent Frames s igni f icant l y underest imat ed

def lec t i ons due t o under p red ic t i on o f c rack ingSpreadsheet s ign i f ican t l y overest imated de f lec t i ons3-D Fini te Element predic t ions were excel lent

ACI

WEB SESSIONS

SlabS5

ACI

WEB SESSIONS

SlabS5


Slab loading far in excess of c r ack ing load and rem ovedRest rained column base

Heavy s lab c rack ing w h ich p ropagated over t imeSame re in fo rcement as S42-D Equivalent Frames s igni f icant l y underest imat eddef lec t i ons due t o under p red ic t i on o f c rack ingSpreadsheet overes t imated de f lec t i ons t o a reasonab ledegree

3-D F in i t e E lement p red ic t i ons (w i t hou t cons ider ing ex te rna l

res t ra in t ) were overes t imated t o a reasonab le degree . E f fec t so f ex te rna l res t ra in t t o shr inkage were overes t imated


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ACI

WEB SESSIONS

SlabS3

ACI

WEB SESSIONS

SlabS3


Slab loading s imi lar to S6/S7 sustained, then reduc ed

Rest rained column baseSame reinforc ement as S4/S52-D Equivalent Frames s igni f icant l y underest imat eddef lec t i ons due t o under p red ic t i on o f c rack ing

Spreadsheet overest imated ear ly sustained def lec t ions, but

also overest imated elast ic and creep rec overy , g iv ingreasonab le f i na l resu l t s3-D F ini te Element predic t ions wer e reasonable, but e last icand c reep recovery w ere overes t imated

ACI

WEB SESSIONS

Aqua

3D f i n i t e e lement (method 3 ) underes t imated shor t

t e rm de f lec t i ons , w i t h s ign i f i can t improvements w i t hsmal l o f f se t s i n t ime

2D Equ iva len t f ram es s ign i f i can t l y underes t imated

def lec t i ons

Spreadsheet (method 2 ) s ign i f i can t l y overes t imated

def lec t i ons

ACI

WEB SESSIONS

ACI

WEB SESSIONS

PerformanceComparison

2Dequivalentframes(method1)significantlyunderestimateddeflectionsinallcases

Spreadsheet(method2)overestimateddeflectionsinallcases,dependentupontheactuallevelsofcracking

3Dfiniteelements(method3)predictedmostofthetestslabsreasonablywithexternalshrinkagerestraintadjustment,underestimatedrealworldslabs

ACI

WEB SESSIONS

DesignRecommendations

Maintainrealisticexpectations

Usespreadsheetmethodinsteadof

span/depthratios

Neverusefullframesectionsfordeterminingcrackingandeffectivemomentsofinertia

ACI

WEB SESSIONS

DesignRecommendations

Beconservativewithcracking

Considerloadhistory

Considerusinglargerdeflectionmultipliersfor

creepandshrinkage


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ACI

WEB SESSIONS

Questions

ACI

WEB SESSIONS

Robert L. Vollum, is a Reader in Concrete Structures in the Civil

Engineering Department at Imperial College London. He received his

M.Sc. and PhD degrees from Imperial College London. His research

interests are related to the design of reinforced concrete structures.

He is a member of British Standards Committee 525/2; StructuralUse of Concrete, the Concrete Society Design Group and fib task

force 4.2 which considers ultimate limit state models for the design of

concrete structures.

ACI

WEB SESSIONS

InfluenceofLoadHistoryonLong

termslabdeflections

DrRobertVollum

ReaderinConcreteStructures

ImperialCollegeLondon

ACI

WEB SESSIONS40

Influenceofloadhistory

EC2doesnotaddressinfluenceofpreviousloadingondeflection

Thisisimportantsincecrackingisirreversible

Aimofresearch

Todeterminetheeffectofpreviousshorttermpeaksinloadonlongtermslabdeflections

ACI

WEB SESSIONS41

Influenceofearlyagestrikingandconstruction

loadingonslabdeflections

ACI

WEB SESSIONS42

CardingtonEuropeanConcreteBuilding


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ACI

WEB SESSIONS43

Cardingtoninsitu concretebuildingThe structure is 7 storeys high with 250 mm thick flatslabs spanning 7.5 m in each direction. It wasdesigned in accordance with EC2.

7500 7500 7500 7500

7500

7500

7500

ACI

WEB SESSIONS44

DesignersbriefforCardingtonslabs

Slab thickness = 250 mm

Design imposed load: 2.5 kN/m2Superimposed dead load: 2 kN/m

2ceiling,

services, access floor and partitions

ACI

WEB SESSIONS45

TableformsatCardington

Backprops

Props

ACI

WEB SESSIONS46

ConstructionofCardingtonslabs

The Cardington slabs were constructed withprops and one level of backprops with theexception of slab 4 where 2 levels ofbackprops were used.

Loads were measured with load cells in theprops and backprops in 2 bays.

The slabs were essentially cast in a singlepour from around 8 am to 5 p.m.

ACI

WEB SESSIONS47

Stage Time Operation1 0 Concrete floor 1

2 2 Strike floor 1

3 2-12 Erec t formwork and fix

reinforcement for floor2

4 Backprop floor 1

5 13 Concrete floor 2

1

1

1

1

FloorcycleatCardingtonwithonelevelbackprops

ACI

WEB SESSIONS48

Stage Time Operation

5 13 Concrete floor 26 14 Strike floor 2 and

remove backpropsfloor 1

7 14-24

Erect formwork and fixreinforcement for floor3

8 Backprop floor 2


2

1

3

2

1

3

2

1


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ACI

WEB SESSIONS49


10 27 Strike floor 3 andremove backpropsfloor 2

11 27-38

Erect formwork andfix reinforcement for

floor 4

12 Backprop floor 3


3

2

1

3

2

1

4

3

2

1

4

ACI

WEB SESSIONS50

LoadinghistoryforthirdflooratCardington

Time(days)

Load(kN/m2)

2

8.75 9

337

6

26 2812 14

10.74

6.75

0

2

4

6

8

10

12

1 10 100 1000

Time from casting: days

LoadkN/m2

ACI

WEB SESSIONS51

LoadedareaforCardingtonslabs

Loaded area

ACI

WEB SESSIONS52

SandbagsonCardingtonslabs

ACI

WEB SESSIONS53

Slab deflections were measured by precise levelling:

After striking

At end of construction of building

approximately 8 months after construction started

Further measurements were not taken until February 99 dueto a lack of funding. In March 1999, floors 1 to 6 were loadedwith sandbags to give a uniform load of 3 kN/m2 betweengrids 2 and 4.

The imposed load is at the upper end of that which mightoccur in a typical office. The service load includes allowancesof 1 kN/m2 for ceiling, raised floor and services and 1 kN/m 2

for partitions.

Measurementofdeflection

ACI

WEB SESSIONS54

Comparisonofdeflectionsinexternalbaysoffloors1to6atCardington

There was a significant variation in deflectionsbetween floors as shown below. Why?

0

5

10

15

20

25

300 100 200 300 400 500 600 700 800 900

Deflectionmm

Time,days

Average deflection external panels

floor 1 floor 2

Floor 3 Floor 4

floor 5 Floor 6


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ACI

WEB SESSIONS55

The table shows that the variation between the deflectionsin each floor is not attributable to differences in thereinforcement weight between floors.

Deflectionsincrease insequence

Weightsteel

(tonnes)

Max deflection

(800 days)

Floor 1 16.9 18.04Floor 4 18.9 (ave) 19.75Floor 2 17.1 22.49Floor 5 19.9 22.84Floor 3 15.3 24.94Floor 6 25.5 26.58

Influenceofreinforcementweighton

deflectionsinexternalpanelsatCardington

ACI

WEB SESSIONS56

CalculationofcurvatureinEC2

Themeancurvatureisgivenby:

1/rm =(1/r2+1/r2cs)+(1 )(1/r1+1/r1cs)

where1/r1 =M/EceffI1 =curvatureofuncracked section

1/r2= M/EceffI2 =curvatureofcrackedsection

whereEceff =Ecm/(1+)

1/r1cs,1/r2cs shrinkagecurvature

=1 (Mr/M)2

where=1.0forshorttermand0.5forlongtermloading

Load

Time

ACI

WEB SESSIONS57

0

5

10

15

0 50 100 150 200 250 300 350 400

days from hydration

kN/m2

Idealized load-time history for Cardington concrete

building

The problem is to predict the slab deflection underthe idealized load-history.

Definitionofproblem

ACI

WEB SESSIONS58

Fundamentalbehaviour

Short termmomentcurvaturediagram

Increaseincurvature

Uncracked

response

Fullycrackedresponse

UltimatemomentMu

Curvature1/r

Moment

Unloading

Mpeak

Mperm

1 2 3

EC2

1 perm2 peak3 *

ACI

WEB SESSIONS59

Influence of previous loading on deflection

EC2 uses= 1-(Mr/M)2todefine the level of cracking.

If =0.5, the level of cracking is governed by:

Mr/M fct/w =K

It follows that the degree of cracking in a slab can bedefined in terms of K where w = load andfct = tensile strength.

Hypothesis: The minimum value of K correspondsto the greatest cracking and hence greatest deflection.

ACI

WEB SESSIONS60

0

2

4

6

8

10

12

14

16

18

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

K (mm-2

x103)

Deflection(mm)

330 mm slab fixed at one end

w = 11 kN/m2, = 2, cs = 500 s

Theoretical influence of K on deflection according toEC2

Linear relationship betweenK and deflection for crackedslab

K

D

eflection

330mmslab=2,cs=500s

RelationshipbetweenKandcurvature

ConstantM:varyfctK=fct/w


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ACI

WEB SESSIONS61

Sequence of

deflectionincrease

Kstrike

=0.5

Kpeak

=0.5

Klong

=0.5fcu28

Kmin

=0.5

Max

deflection(800days)

Floor 1 0.26 0.38 0.33 0.26 18.04Floor 4 0.26 0.29 0.34 0.26 19.75Floor 2 0.25 0.23 0.30 0.23 22.49Floor 5 0.26 0.22 0.29 0.22 22.84Floor 3 0.28 0.24 0.31 0.24 24.94Floor 6 0.21 0.23 0.31 0.21 26.58

Lowest value of K critical

Relationshipbetweenslabdeflections

andKatCardington

ACI

WEB SESSIONS62

Linearrelationshipbetweenslabdeflections

andKatCardington

R2

= 0.7043

0

0.05

0.1

0.15

0.2

0.25

0.3

15 20 25 30

Deflection (mm)

Kmin

Cardington

Linear (Cardington)

ACI

WEB SESSIONS63

Use a modified E value to account forstaged loading

Calculate the mean curvature using the

greatest value of from current orprevious loading.

Time

Load

t0

Proposedsinglestepprocedureforcalculation

ofslabdeflection

ACI

WEB SESSIONS64

Laboratorybasedvalidation

ACI

WEB SESSIONS65

Slabgeometry

ACI

WEB SESSIONS66

Aimsoftestingprogramme

Theprimaryaimswereto:

Determinethevalidity ofthecalculationmethodderivedfrombackanalysisoftheCardingtondata

Todeterminetherateoflossoftensionstiffeningwithtimeunder:

i . Sustainedloading

i i. S ho rttermconstructionloads


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ACI

WEB SESSIONS67

Loadhistoryintests

Time

Mmax

Time(days)

t0=9days

Slab1

Slab2M=M2

Slabs1to3

t=100days

t=100days

Slab3M=M2

t0=9

Mmax

13

ACI

WEB SESSIONS68

Influenceofconstructionloadingonslab

deflections

0

5

10

15

20

25

0.1 1 10 100 1000

Time (days)

Deflection(mm)

S1

S2

S3

S2No

construction

loading

ACI

WEB SESSIONS69

Loadhistoryintests

Slabs4to6

Time

(days)

Load

Peakloadtosimulate

constructionloadfrom

castingslabsabove

Slab4:Mpeak=MpermSlab5:Mpeak=1.3MpermSlab6:Nopeakload

AllslabshavesameMperm

t0=7 ~100013 17

S5 S4Mpeak=Mperm

ACI

WEB SESSIONS70

Variationofdeflectioninslab5

Slab 2

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18

Deflection (mm)

Load(KN)

Totalload

20min5days

60days

Deflectionnot

recoveredonunloading

17days

ACI

WEB SESSIONS71

ComparisonofdeflectionsinS4toS6

0

5

10

15

20

25

30

0 200 400 600 800 1000

Time (days)

Deflection

(mm)

S4

S5

S6

Control S6

ACI

WEB SESSIONS72

RelationshipbetweencurvatureandK=Mr/Mpeakat93days(relationshipislinearasatCardington)

y = -2E-05x + 3E-05

R

2

= 0.9971

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

1.0E-05

1.2E-05

1.4E-05

1.6E-05

1.8E-05

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

k* = Mr/Mpeak

(MpermS

1/Mp

erm

)*curvature

S1 to S3

S4 to S6

Linear (S1 to S3)

LinearrelationshipbetweenKandcurvatureasatCardington


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ACI

WEB SESSIONS73

Meanmomentresistedbyconcrete

betweencracks

Fromstrainmeasurements:

Mconcm =MTsm(dxm/3)

AccordingtoEC2themeanresidualmomentresistedbyconcreteintensionbetweenthecracksisgivenby:

Mconcm =(1)Mconc1~(Mr/M)2M

=1 (Mr/M)2 0

dxm/3

Tsm

ACI

WEB SESSIONS

-1.5

-1.0

-0.5

0.0

0.5

1.0

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

M/Mr

Mconcmean

/Mr

4 days from peak

S5 unload

S4 unload

S3 unload

EC2 b=0.8

74

RelationshipbetweenMconcmean andMjust

beforeandafterremovalMpeakEC2

Mconcm =(1)Mwith

=0.8

Mpeak/Mr(CMpeak+(1Mpeak)/MrCMpeak/Mr

M/Mr

ACI

WEB SESSIONS75

Calculationofcurvatureafterunloading

1/rm=*1/r2+(1*)1/r1

where*accountsforthepreviousloadhistory.

Mconc mean =(1*)Mperm = Mpeak(1peak)M(1peak/(1+C))

*=peak(1+CMpeak/Mperm)/(1+C)

whereM=MpeakMperm andC~1.

Take indeflectioncalculationsasthegreatestof*and

calculatedwithwperm orwsls asappropriate.

ACI

WEB SESSIONS76

Comparisonbetweenmeasuredand

predictedcurvaturesS3

ACI

WEB SESSIONS77

Questions

ACI

WEB SESSIONS78


5 13 Concrete floor 26 14 Strike floor 2 and

remove backpropsfloor 1

7 14-24

Erect formwork and fixreinforcement for floor3

8 Backprop floor 2


2

1

3

2

1

3

2

1


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ACI

WEB SESSIONS79

Questions

ACI

WEB SESSIONS

Related Documents

ACI Bookstore

SERVICEABILITY AND SAFETY OF CONCRETE STRUCTURES

SP225-06: Deflection Control by Design

435R-95: Control of Deflection in Concrete Structures (Reapproved 2000)

201.1R-08: Guide for Conducting a Visual Inspection of Concrete in

Service

SP86-07: Deflections of Concrete Slabs Under Construction Loading

SP161-04: Deflection Analysis of Reinforced Concrete Members Using

Finite Element Method

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