advanced topics in analysis and design of normal and high strength concrete structures volume 2...

8/17/2019 Advanced Topics in Analysis and Design of Normal and High Strength Concrete Structures Volume 2 Lecture Notes.…

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FACULTY OF ENGINEERING ANDINFORMATION TECHNOLOGY

The Institution of Engineers, Malaysia

Short Course on Advanced Topics in Analysis and Design of

Normal and High Strength ConcreteStructures

4 to 5 May 2006, Kuala Lumpur, Malaysia

Course MaterialsVolume 2: Lecture Notes

EIT2006


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PREFACE

The Short Course on “Advanced Topics in Analysis and Design of Normal andHigh Strength Concrete Structures” is delivered on the invitation of TheInstitution of Engineers, Malaysia. Held in Kuala Lumpur on 4 and 5 May2006, its primary objective is to acquaint the participants with the researchwork conducted in the topical areas by the researchers at Griffith Universitymainly over the last decade. The Short Course also provides the backgroundand technical details which inform the Keynote Address to be presented at the9 th International Conference on Concrete Engineering and Technology(CONCET 2006) to be held from 8 to 10 May 2006. It is hoped that thediscussion over the next two days will be helpful to the Malaysian engineeringcolleagues in their future work.

To assist the participants, the Short Course materials are given in twovolumes: “Selected Published Papers”, which is an up-to-date collection ofrelevant publications in the areas to be covered in the discussion; “LectureNotes”, which contains the hardcopy of all the PowerPoint slides to bepresented.

I wish to take this opportunity to acknowledge the contributions of all myconcrete research colleagues and students at Griffith School of Engineeringwithout which many of the advances made would not have been possible. Inparticular, I would like to thank my close collaborators

• Dr Sam Fragomeni, Associate Professor and Deputy Head of School• Dr Hong Guan, Senior Lecturer in Structural Engineering and Mechanics• Dr Sanaul Chowdhury, Lecturer in Structural Engineering, and• Dr Jeung-Hwan Doh, Associate Lecturer in Structural Engineering

for their invaluable work over the years. Special thanks are also due to DrsChowdhury and Doh for their meticulous efforts in compiling, developing andupdating these two volumes of materials.

The invitation of the Organising Committee of CONCET 2006 to present theKeynote Address and the help of its members in particular Ir. M.C. Hee, Mr.Thang Fai Li and Mr. Jamie Kheng are greatly appreciated.

Professor Yew-Chaye LooDean, Faculty of Engineering and Information TechnologyGriffith University

4 May 2006


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Section 1: Overview


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SERVICEABILITY AND STRENGTH OFNORMAL AND HIGH STRENGTHCONCRETE BEAMS, COLUMNS,

SLABS AND WALLS

Yew-Chaye LooPhD, FICE ,FIStructE, FIEAust

Professor of Civil Engineering andHead, School of Engineering

SERVICEABILITY AND STRENGTH OFNORMAL AND HIGH STRENGTH CONCRETE

STRUCTURES- OVERVIEW

Professor Yew-Chaye LooPhD, FICE ,FIStructE, FIEAust

DeanFaculty of Engineering & Information Technology

Faculty of Engineering & Information Technology

CONTENTSCONTENTSSERVICEABILITY

STRENGTH

LAYERED FINITE ELEMENTMETHOD (LFEM)

COLUMN & WALLSHORTENING

SUMMARY


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CRACK WIDTH

DAMPING CHARACTERISTICS

DEFLECTION

SERVICEABILITY

ULTIMATE STRENGTH OF WALLS

PUNCHING SHEAR STRENGTH OF FLATPLATES

STRENGTH


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CRACK WIDTHCrack width formulas for beams

Crack Width Formula*Average crack width:

wcr = (f s /E s) [0.6(c - s) + 0.1 ( Φ / ρ )] (1)

Maximum crack width:

wmax = 1.5 wcr (2)

__________________________________________________ *Chowdhury, S.H., Loo, Y.C. & Wu, T.H. 1995; Chowdhury, S.H. & Loo, Y.C. 1997, 2001, 2002, 2003,

2004a, 2004b; Chowdhury, S.H. 2001; Chowdhury, S.H. & Fragomeni, S. 2001

clear cover

spacing between bars

average bar diameter

steel ratiosteel stress

elastic modulus


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ComparisonComparison (30 test beams)(30 test beams) **

w cr, calculated in mm

0.40.30.20.1 0.0

w c r , m

e a s u r e

d i n m m

0.4

0.3

0.2

0.1

0.0

- 30% line

+ 30% linePartially prestressedconcrete beamsReinforced concretecontinuous beamsReinforced concretesolid beams

Reinforced concrete box beams

*Chowdhury, S.H. & Loo, Y.C. 1997, 2001, 2002; Chowdhury, S.H. 2001

Published data

34 PC beams Nawy (1986), Rutgers University

Fully prestressed T-beamsPPC T-beamsPPC I-beamsPost-tensioned PPC T-beams

6122

14

59 RC beams Clark (1956), ACI, USA 26

Chi & Kirstein (1958), ACI, USA 16

Hognestad (1962), PCA, USA 8

Kaar & Mattock(1963), PCA, USA 9


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Equation 1 or 2 in mm

.9.8.7.6.5.4.3.2.10.0

M e a s u r e

d c r a c

k w

i d t h s

i n m m

.9

.8

.7

.6

.5

.4

.3

.2

.1

0.0

Legend

+ 30% line

- 30% line

Kaar & Mattock's bea

Hognestad's beams

Naw y's beams

(14 post-tensioned)

Naw y's beams

(20 pre-tensioned)

Chi & Kirstein's bea

Clark's beams

93 RC & PC beams

Comparison with Code FormulasComparison with Code Formulas

CRACK WIDTH

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.1 0.2 0.3 0.4

Calculated w cr in mm

M e a s u r e

d w c r

i n m m

Chowdhury & Loo's beams

Chi & Kirstein's beams

Clark's beams- 30% line

+30% line

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.1 0.2 0.3 0.4

Calculated w cr in mm

M e a s u r e

d

w c r

i n m m

Chowdhury & Loo formula Eurocode formula

For average crack width

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Calculated w max in mm

M e a s u r e

d w m a x

i n m m

Chi & Kirtstein's beamsClark's beams

- 30% lne

+ 30% line

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Calculated w max in mm

M e a s u r e

d w m a x

i n m m

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Calculated wmax in mm

M e a s u r e d

w m a x i n

m m

Chowdhury & Loo formula

BS formula

ACI Code formula

For maximum crack width


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DEFLECTION

Deflection

Repeated loading

Impact


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Deflection of RC beams under repeated loading

δT= δda+ δl

δda = k δdi

k = k 1 + R log 10T

number of loading cycle

1.18 + (0.029/ ρ) (M t – Md )/(M y – Mcr )(0.0015/ ρ) (M t – Md )/(M y – Mcr )

Correlation of measured and computed total deflections – proposed formulaREPEATED LOAD


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Hertz’s Contact Law and the relative approach

3/2

s K )t(F

)t,x(y)t(y)t(a ⎥⎦

⎤⎢⎣

⎡=−=

Deformation constant (materials and shapes)

ymax = y’ max [(2/m bω12) (1.25 m s v02 K 2/3)3/5]

ω1 = (π2/L2) √(EI/ ρA)

α = (m b/m s)

β = 1.47 ( ω1/π) (5m s/4Kv 01/2)2/5


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WijewardeneWijewardene ’’ss andand HussainHussain ’’ss beamsbeams

Hughes andHughes and Speir Speir ’’ss beamsbeams

DEFLECTION


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DAMPING CHARACTERISTICS

Damping of RC & PC beams


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DAMPINGDAMPING -- DEFINITIONDEFINITION

Time t

Amplitude A

A1A n+1

n periods

Residual crack width

Lbaw= rcr,

The logarithmic decrement , δ, is obtained as:

A1),(ncycleatamplitude

Acycle1,atamplitudelog(1/n)=

1n

1e

++δ

Time t

Amplitude A

A1 A n+1

n periods

Time t

Amplitude A

A1 A n+1

n periods

Experimental Program• 14 RC beams• 12 PPC beams

Beamlength,L

l

Appliedload

Loadingbeam

100 mm 100 mm

Typcal loadingdiagram

Embedded Polystyrene

asvoid

60 180 60

2 5

1 0 0

Typical RCbox beam

2 8

300mm

3 0 0 m m

mm m m

Stages in a vibration measurement system

Test Procedure

Beam length, L

l

Applied load

Loading beam

100 mm 100 mm

Typcal loading diagram


as void

60 180 60

2 5

1 0 0

Typical RC box beam

2 8

300 mm

3 0 0 m m

mm m m


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Damping prediction formulas*

– For RC beams, δ isδ = 0.048 w cr,r + 0.011 L

– For PPC beams,

δ = 0.054 w cr,r + 0.0104 L __________________________________________________________________________________________________

*Chowdhury, S.H. & Loo, Y.C 1998a, 1998b, 1999, 2001, 2003; Chowdhury,S.H. Loo, Y.C. & Fragomeni, S. 2000

W cr,r = 0.312 w cr, i

w cr, i = (f s /E s) [0.6 (c – s) + 0.1 ( φ/ ρ)]

RC beams

Predicted δ

.16.12.08.040.00

M e a s u r e

d

.16

.12

.08

.04

0.00

+ 30% limits

- 30% limits

Continuous beams

Simply-supported beams


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.16

PPC beams

Predicted δ

.16.12.08.040.00

M e a s u r e

d

.16

.12

.08

.04

0.00

- 30% limits

+ 30% limits

.16

Predicted δ

.16.12.08.040.00

M e a s u r e

d

.16

.12

.08

.04

0.00

- 30% limits

+ 30% limits

.16PPC beams

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Predicted δ

M e a s u r e

d

Beam HSB 1

Beam HSB 2

Beam HSB 3

Beam HSB 4

Beam HSB 5

Beam HSB 6

+ 30% Line

- 30% Line

DAMPING

6 HSC RC beams


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PUNCHING SHEAR STRENGTH OFFLAT PLATES

Typical flat plate with spandrel beams


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Punching Shear Strength

Higher punching shear due tounbalanced bending moment

Balanced bendingmoments

30 –35degrees

LOADLOAD

Bendingcracksappear atlowloading

Test setupTest setup (University of Wollongong, 1987(Univers ity of Wollongong, 1987 --90)90)


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Corner connection Edge connection

21uVVV += 21u V2VV +=

543

corner ,1342431u k k k

)V(k k k k k k V

−+−

=543

edge,1342432u k k k

)V(k k k k k k 2V

−+−

=

ely121u PnVVV −+= ely121u PnV2VV −+=Corner connection Edge connection

543

7342431u k k k

k k k k k k k V

−+−=

543

7342431u k k k

k k k k k k k 2V

−+−=


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RC Flat PlatesRC Flat Plates (19 V(19 V uu values from 9 half values from 9 half --scale models)scale models)

0

50

100

150

200

250

0 50 100 150 200 250

Predicted V u

M e a s u r e d V u

Falamaki & Loo (1992)

AS 3600-1994

45 degree line

(kN)

( k N )


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PostPost --tensioned Flat Platestensioned Flat Plates (4 half (4 half --scale models)scale models)

PUNCHING SHEAR

0

20

40

60

80

100

0 20 40 60 80 100

Predicted V u

M e a s u r e d V u

Loo & Chiang (1996)

AS 3600-1994

ACI 318-1989

BS 8110-1985

45 degree line

(kN)

( k N )

ULTIMATE STRENGTH OF WALLS


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OneOne --way and twoway and two --way actionsway actions

(a) One(a) One --way actionway action AS 3600 (2001) ACI 318 (2002)

(b) Two(b) Two --way actionway action

LimitationsLimitations AS3600-2001Hwe/tw ≤ 30f ’c ≤65 MPae ≥ tw/20one-way actiononly solid walls

ACI 318-2002Hwe/tw ≤ 25 or L/ t w ≤25f ’c ≤ 50 MPae ≤ tw/6one-way actiononly solid walls


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TestTest --rigrigset upset up


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1200x1200x401200x1200x40((f f ’’cc=35 MPa)(one=35 MPa)(one --way)way)

1200x1200x401200x1200x40((f f ’’cc= 37 MPa)(two= 37 MPa)(two --way)way)

1600x1600x401600x1600x40((f f ’’cc= 50 MPa)= 50 MPa)

(two(two --way,way,opening)opening)

Design formula*

)e2e2.1t(f 0.2 N aw7.0'

cu −−φ=φ

)/(2500t)(H w2

we=

0.6

design axial strength / unit length (N/mm)

thickness (mm)

compressive strength (MPa)

eccentricity (mm)

additional eccentricity due tosecondary effect (mm)

*Doh, J.H., Fragomeni, S. & Loo, Y.C.; Doh, H., Fragomeni, S. & Kim, J. 2001


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H/t w

N u

/ f ' c L t w

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

f' c = 30 M Paf' c = 50 M Paf' c = 80 M PaFragomeni (NSC)Fragomeni (HSC)OWNS (Stage 1)OWHS (Stage 2)Doh (HSC)Doh (NSC)

Comparison with test data –one-way action

Comparison with test data –two-way action

H/t w

N u

/ f '

c L t

w

10 20 30 40 50 60

0.3

0.4

0.5

0.6

0.7

0.8 f' c = 30 M Paf' c = 50 M Paf' c = 80 M PaSaheb & Desayi (1990)Fragomeni (NSC)(1995)Fragomeni (HSC)(1995)Doh (NSC)

Doh (HSC)


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u21uo N)k k ( N α−=Formula for wall with openings:

WALL

⎟ ⎠ ⎞

⎜⎝ ⎛ η+=α

LAA o

⎟ ⎠ ⎞

⎜⎝ ⎛ η−=η

2L

⎟⎟

⎠ ⎞

⎜⎜

⎝ ⎛

−η−=η

wow

oow2

w21

tLLt

LtLt

H

t

L/2η~

L

G3G2G1

Elevation

Lo

Ho

G3G2G1

Cross- sectional Plan

oη

η

k 1 = 1.18 (for one-way action)= 1.00 (for two-way action)

k 2 = 1.19 (for one-way action)= 0.93 (for two-way action)

WallPanels

FailureLoad (kN)

N*(kN)

N* Failure load

OW 01 253.10 250.54 0.99

OW 02 441.45 344.64 0.78

OW 11 309.02 290.30 0.94

OW 12 294.30 285.97 0.97

OW 21 185.41 184.38 0.99 O n e - w a y a c

t i o n

OW 22 195.71 200.68 1.03

TW01 735.75 707.70 0.96

TW02 1177.20 1067.90 0.91

TW11 750.47 676.21 0.90

TW12 1030.05 878.52 0.85

TW21 618.03 471.44 0.76 T w o - w a y a c

t i o n

TW22 647.46 612.48 0.95

Average 0.92

Comparison of test results and new proposed method

Degenerate shell elements composed of concreteand smeared steel layers

teSmeared-outsteel layers

12

n sn s-1

x

y

z

Mid reference plane

z c+ 1z czc- 1

z 3z2z1123

n cn c- 1

Concretelayers

Layer number

z 1z 2

z s-1z s

u

vw

θ y

xθ

5 DOFs per node- in-plane displacements,

u and v- transverse

displacement w- two independent

bending rotations aboutx and y axes, y and x


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Cracking

f c'

0.3f c'

Effect of tension stiffening

E0

f t

Effect of bulk mo

Strain-hardening model

Perfect plasticity model

loading-unloading

Crushing

σ

ε

modulus

0.8f y

0.002

Es

01

Es1f y

11

Es2

σ

ε

Smeared crack approach for cracked concrete

Material modelling

• Tri-linear σ-ε for steel

• Tension-stiffening and shear stiffnessdeterioration effects after concrete cracking

• Strain-hardening plasticity procedure forconcrete compressive behaviour

• Tension-stiffening and shear stiffnessdeterioration effects after concrete cracking



Numerical Modelling

teSmeared-outsteel layers

12

n sn s-1

x

y

z

Mid reference plane

zc+1zczc-1

z3z2z1

123

n cn c-1

Concretelayers

Layer number

z1z2

zs-1zs


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LFEM for flat plates*

Punching shear strength

Load-deflection response

Crack patterns

___________________________________________________________________________________________________

*Loo, Y.C. & Guan, H 1997; Guan, H. & Loo, Y.C. 1994, 1997a, 1997b, 2002

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Deflection (mm )

L o a

d d e n s

i t y

( k N / m )

Ex per iment * ( po int 1) Pr op os ed met ho d ( poin t 1)Ex per iment * ( po int 2) Pr op os ed met ho d ( poin t 2)Ex per iment * ( po int 3) Pr op os ed met ho d ( poin t 3)

M2

12 3

Collapse load

32.7

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

Deflection (mm )

L o a

d d e n s

i t y

( k P a

)

Ex per iment* (point 1) Pr opos ed method ( point 1)Ex per iment* (point 2) Pr opos ed method ( point 2)

Ex per iment* (point 3) Pr opos ed method ( point 3)

W2

12 3

Collapse load

28.91

Load-Deflection

LFEM


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Comparison ofComparison of VVuu (models w ith spandrel beams)(models w ith spandrel beams)Connec- Type * Experiment LFEM AS 3600-1994

tion V u (kN) PredictedV u (kN)

PredictedExperiment

PredictedV u (kN)

PredictedExperiment

W1-A C 50.15 58.58 1.17 119.07 2.37W2-A C 48.08 52.88 1.10 120.94 2.52W3-A C 43.38 46.30 1.07 70.42 1.62W4-A C 47.07 52.14 1.11 96.12 2.04

W1-B E 117.63 116.21 0.99 146.92 1.25W2-B E 120.36 104.79 0.87 150.05 1.25W3-B E 93.57 96.47 1.03 94.99 1.02

W2-C C 45.17 46.70 1.03 113.54 2.51W3-C C 44.33 48.65 1.10 73.38 1.66W4-C C 46.32 50.79 1.10 82.93 1.79

M2-A C 53.90 56.21 1.04 82.90 1.54 M3-A C 25.70 34.10 1.33 127.31 4.95 M4-A C 58.97 65.79 1.12 114.77 1.95

M2-B E 123.22 115.43 0.94 116.24 0.94 M3-B E 76.50 68.37 0.89 214.32 2.80 M4-B E 130.24 149.69 1.15 137.82 1.06

M3-C C 24.30 29.75 1.22 131.89 5.43 M4-C C 60.09 74.50 1.24 102.75 1.71

R90-D E 36.20 † 37.73 1.04 51.71 1.43

Mean : 1.081 2.097 Note: * C - corner column; E-edge column

† This specimen did not fail in punching; the reported result is the maximum value.

Failure load (Failure load ( kPakPa ))Model Type * Experiment Predicted Predicted

Experiment W1 SB 30.63 29.50 0.96W2 SB 28.91 30.00 1.04W3 SB 24.69 23.60 0.96W4 SB 28.95 25.75 0.89

M2 SB 32.70 † 37.50 † 1.15

M3 SB 17.84 15.60 0.87 M4 SB 33.85 37.00 1.09

R90-D SB 21.70 23.00 1.06

Mean : 1.003W5 TS 19.01 18.50 0.97

M5 TS 25.18 30.50 1.21 R3-A TS 23.80 20.50 0.86 R4-A TS 22.50 19.00 0.84

R90-A TS 25.50 23.50 0.92 R90-B FE 23.80 22.50 0.95 R90-C FE 20.00 20.50 1.03

Mean : 0.969

Note: † SB - spandrel beam; ‡ TS - torsion strip; * FE - free edge† Line load in kN/m

LFEM


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Crack patternCrack pattern

ObservedObserved(bottom surface)(bottom surface)

PredictedPredicted(bottom layer)(bottom layer)

PredictedPredicted(top layer)(top layer)

ObservedObserved(top surface)(top surface)

LFEM

Features – Q1 Tower

Instrumentation; Measurements;Prediction method; Comparison


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Level 63 as of 5 October 2004

Current State of ConstructionCurrent State of Construction

Q1 TOWER

Column and WallColumn and WallLocationsLocations

14 columns and 5 walls perfloor

Number of DEMEC point 3to 9 measurements percolumn/wall


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Instrumented Levels and Concrete Compressive

Strengths for Columns at the Specific Level

Level 71, 32 MPa

Level 49, 40 MPa

Level B1 and B2,65 MPa

Level 31, 50 MPa

Dateof

Construction

25/01/200319/02/2003

10/03/2004

02/08/2004

Jan 2005

Demountable MechanicalDemountable MechanicalStrain Gauge (DEMEC)Strain Gauge (DEMEC)

Gauge Length = 200 mm

1 division = 0.002 mm or 10 microstrain


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-100

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 Days

S

t r a

i n

1

0 -

6

TC05TC06

StartedDate

1/2/2003 1/6/2003 31/08/2003 31/11/2003 1/02/2004 1/06/2004

LastReading

23/09/2004

No. of slabsconstructed 0 2 6 13 27 5540

AUTUMN WINTER SPRING AUTUMN WINTER SUMMER

1.35

0.68

1.13

0.90

0.45

0.23

1.56

0

S h o r t e n

i n g

( m m

)

40 days time lag

-100

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 Days

S

t r a

i n

1

0 -

6

TC05

TC06

StartedDate

1/2/2003 1/6/2003 31/08/2003 31/11/2003 1/02/2004 1/06/2004

LastReading

23/09/2004



1.35

0.68

1.13

0.90

0.45

0.23

1.56

0

S h o r t e n

i n g

( m m

)


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-100

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 Days

S

t r a

i n

1

0 -

6

TC10TC12

StartedDate

1/2/2003 1/6/2003 31/08/2003 31/11/2003 1/02/2004 1/06/2004

LastReading

23/09/2004



1.35

0.68

1.13

0.90

0.45

0.23

1.56

0

S h o r t e n

i n g

( m m

)

Differential shortening160 microstrain0.36 mm

Differential shortening estimate (80 storey)

mm22227500010160 6

=

Age Adjusted Modulus Method Age Adjusted Modulus Method((TrostTrost andand BazantBazant , 1972), 1972)

[ ] [ ]1)s,t(C).s,t()s(E)t(

)t()s,t(C1)s(E

)t( 1c

s1c

it −χ

σ∆−ε++σ=ε

Elastic + creep

Shrinkage

ReinforcementRestraint


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Age Adjusted Modulus Method Age Adjusted Modulus Method((TrostTrost andand BazantBazant , 1972), 1972)

A computer program based on this method

COLECS by Allan Beasley (1987)

[ ] [ ]1)s,t(C).s,t()s(E)t(

)t()s,t(C1)s(E

)t( 1c

s1c

it −χ

σ∆−ε++σ=ε

-0.2

0.0

0.2

0.4

0.60.8

1.0

1.2

1.4

1.6

1.8

0 100 200 300 400 500 600 700 Days

COLECS

TC06

No of slabsconstructed 0 2 6 13 27 5540


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-0.2

0.00.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 100 200 300 400 500 600 700 Days

COLECS

TC10


-0.2

0.0

0.2

0.4

0.60.8

1.0

1.2

1.4

1.6

1.8

0 100 200 300 400 500 600 700 Days

COLECS

TC12


Q1 TOWER


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SUMMARYSUMMARY

On-Going work – HSC structures – Column and wall shortening – Deep beams and walls with openings

CrackingDampingDeflection

Flat plates, walls

Serviceability

Strength

Simplified solutions: explicit formulasRigorous solution: LFEM

Complicated problems

THANK YOU THANK YOU


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Section 2: Cracking and CrackWidth Formulas


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1

CRACKING AND CRACK WIDTHFORMULAS

PROFESSOR YEW-CHAYE LOO


Griffith UniversityQueensland , Australia

SHORT COURSE ON

ADVANCED TOPICS IN ANALYSIS AND DESIGN OF CONCRETE STRUCTURESS

Kuala Lumpur, Malaysia 5-6 September 2005

OVERVIEWINTRODUCTIONCRACKING – TYPES, CAUSES & FORMULASTEST PROGRAMPROPOSED CRACK WIDTH FORMULAS FORNSC BEAMSCOMPARISON WITH TEST DATACOMPARISON WITH CODE FORMULASCOMPARISON WITH OTHER FORMULASVERIFICATION FOR HSC BEAM DATACONCLUSIONS

SHORT COURSE ON ADVANCED TOPICS IN ANALYSIS AND DESIGN OF CONCRETE STRUCTURE



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2

INTRODUCTIONServiceability is one of the major considerations inthe design of structuresCracking and crack control in concrete structuresare major serviceability issuesCracking is more pronounced for high strengthconcrete (HSC) structures because of their relativebrittleness compared to normal strength concrete(NSC)

All major codes for design and construction withconcrete are applicable only to and based on NSC

SHORT COURSE ON ADVANCED TOPICS IN ANALYSIS AND DESIGN OF CONCRETE STRUCTURES


CRACKING – TYPES, CAUSES & FORMULASTypes of Cracks:

Cracking in reinforced concrete buildings orstructural elements is usually classified accordingto the cause of cracking

There are five major types of cracks:flexural cracks in reinforced (and prestressed)concrete beams, frames, and slabs;diagonal tension (shear cracks);splitting cracks along the reinforcement in beamsand in the anchorage zones of prestressedelements;cracking in concrete shear walls; andtemperature and shrinkage cracks




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3

There are many factors causing cracks in concreteCracks caused by load are the main ones consideredin designThe others are usually eliminated or reduced byselecting suitable material and improving the qualityof constructionFlexural crack width depends on geometrical f actorsand on loadingThe width of crack is restricted at the transverse barsin reinforced concrete members and it widens towardthe surface of the member The Concrete Cover and the Spacing of the barsare of primary importance



Loading affects crack width several waysThe crack width is proportional to f s n ,where f s is the steel stress and n is about1.4. However, n can be taken as unitywithout significant error The distribution and width of cracks alsodepend on the variation of momentsalong the member The loading history is also important




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4

Prediction of crack widths has been studiedby many researchersMost of the available crack width formulasare based on research conducted onstructural members made of NSCThe authors also developed two NSC beamformulas

for average crack widthsfor maximum crack widths



8 full-scale HSC beams were tested tofailure to investigate the crackingbehaviour of HSC beams

A comparison is made with the authors’proposed NSC beam formulas to verifytheir applicability to HSC beams

The NSC beam formulas are found to begenerally applicable to HSC beams




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5

TEST PROGRAMTotal 30 NSC RC & PPC beamsand 8 HSC RC beams

Beam length, L

l

Applied load

Loading beam

100 mm 100 mm



as void

60 180 60

2 5

1 0 0

Typical RC box beam

2 8

300 mm

3 0 0 m m

mm m m



Overall cross-section 300 mm x 300mm

180 mm x 180 mm void

3 different L – 5.5 m, 6.7 m & 8.0 m

5 different ρ values

f ′c varied from 25.4 to 37.7 MPa

11 RC simply-supported box beams




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6

12 PPC simply-supported box beams

3 different L- 5.5 m, 6.8m & 8.0 m4 different degrees of prestressingf’c varied from 25.9 to 46.4 MPa4 different ρ values

Typical PPC beam


asvoid

180 60

2 5

1 0 0

300 mm

3 0 0 m m

mm

1 7 5

m m 60



4 RC simply-supported solid beams

35 40

36 78 36

3 6 2 0

Typical RC solid beam

3540

2 1 0

4 0 2 0

Cross-section - 150 mm x 250mm All 2.5 m longf’c varied from 34.1 to 37.1 MPa3 different ρ values




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7

3 RC two-equal-span continuous beams


as void

36 76 76 36

60 180 60

1 0

1 3 0

4 6

6 0

Section at mid-span

1 4 3 6


as void

36 228 36

36 57 36

1 0

4 6

3 2

Section over thesupport

1 4

1 8 0

3 6

5757 57

2 8

76

12 m long - two spans 6 m eachf’c varied from 30.6 to 34.2 MPa3 different positive ρ values3 different negative ρ values



8 HSC RC simply-supported beams

3 beams of cross-section 300 mm x 300 mm, 3 of250 mm x 250 mm and 2 of 150 mm x 200 mm6 different L – 2.4 m, 3.0 m, 4.0 m, 4.5 m, 5.0 m& 6.0 m5 different ρ valuesf ′c varied from 58.3 to 65.9 MPa

25

150

2525 100

200

300

25 250 25

25 -35

300 x 300 mm beam section 150 x 200 mm beam section

250

25 200 25

30 -35

250 x 250 mm beam section




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8

Test ProcedureBeams subjected to two-pointstatic loading

Crack widths at each load levelmeasured using a crack detectionmicroscope

Crack spacings measured at 60 to70% of ultimate load



PROPOSED NSC BEAMCRACK WIDTH FORMULAS

Crack formation and developmentis a complex phenomenoninvolving many parameters

Crack spacing, lcr related to:(i) the Φ/ρ ratio; Φ = avg. bar dia(ii) the concrete cover, c(iii) the average spacing between

reinforcing bars, s




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9

The regression equation takes theform:

lcr = C 1 c + C 2 s + C 3 (Φ/ρ)

4 RC and 4 PPC beam data usedin the regression analysis

These are from the earlier tested30 NSC beams



Table 1. Parameters used in development of averagecrack spacing formula

Beam

number

Average bar

diameter,

Φ (mm)

Steel ratioρ

TheratioΦ/ρ

(mm)

Averagespacing

between

bars, s(mm)

Concretecover, c

(mm)

Averagecrack

spacing, lcr

(mm)

2 20 0.01154 1733 120 12 131.66 20 0.02309 866 48 12 43.7

10 24 0.03348 717 48 12 48.711 20 0.01154 1733 120 12 120.021 6.6 0.00511 1292 40 27 126.523 10.8 0.00737 1465 62 38 126.924 8.1 0.00730 1110 38.5 27 118.230 5.6 0.00460 1217 40 40 142.0




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10

The resulting equation for averagecrack spacing:

lcr = 0.6(c - s) + 0.1 ( Φ /ρ )



Crack Width Formulas for NSCBeams

The proposed formula for averagecrack widths, w

cr ,is developed as:

wcr = (f s /E s) [0.6(c - s) + 0.1 ( Φ /ρ)] (1)

The proposed formula for themaximum crack widths is:wmax = 1.5 (f s /E s ) [0.6(c - s) + 0.1 ( Φ /ρ)] (2)




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11

COMPARISON WITH TEST DATA Authors’ Test Beams (30 NSC)

wcr, calculated in mm

0.40.30.20.10.0

w c r ,

m e a s u r e

d i n m m

0.4

0.3

0.2

0.1

0.0

- 30% line

+ 30% linePartially prestressed concrete beamsReinforced concretecontinuous beamsReinforced concretesolid beamsReinforced concrete

box beams



Other Beams

26 Clark’s (1956) RC beams

16 Chi & Kirstein”s (1958) RCbeams

8 Hognestad’s (1962) RC beams

9 Kaar & Mattock’s (1963) RCbeams




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12

Other Beams (Continued)

34 Nawy”s (1986) beams

• 20 pre-tensioned – 6 fully prestressed T-beams – 12 PPC T-beams – 2 PPC I-beams

• 14 post-tensioned PPC T-beams

Crack widths comparedboth at tension face and steel levelboth average and maximum



Investigator Reinforcementstress levels,ksi

No. ofspecimens

No. of observations

Averagecrack width

Maximumcrack width

Clark (1956) 15, 20, 25,30, 35, 40, 45 26 161

Chi &Kirstein ( 1958 )

15, 20, 25,30, 35, 40

16 76

Hognestad (1962)

20, 30, 40, 50 8 32

Kaar &Mattock ( 1963 )

40 9 9

Nawy (1986) 30, 40, 60 34 102

(1 ksi = 6.895 Mpa)

Table 2. Crack width test data




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13

Equation 1 or 2 in mm

.9.8.7.6.5.4.3.2.10.0

M e a s u r e d c r a c

k w

i d t h s

i n m m

.9

.8

.7

.6

.5

.4

.3

.2

.1

0.0

Legend

+ 30% line

- 30% line

Kaar & Mattock's bea

Hognestad's beams

Nawy 's beams

(14 post-tensioned)

Nawy 's beams(20 pre-tensioned)

Chi & Kirstein's bea

Clark's beams

93 Other Beams (All NSC)



COMPARISON WITH CODE FORMULASCode Formulas Compared

ACI formula (ACI, 1995)wmax at tension face for RC beams

BS formula (BS, 1985; BS, 1987)wmax at tension face for RC beams

Eurocode formula (EC2, 1991).wcr at tension face for RC beams




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14

Comparison with Eurocode formulaThe measured crack widths are divided bythe calculated widths to evaluate theaccuracy of the calculation methodsThe test data included 199 data points fromauthors’ 18 RC beams and those from Clark(1956)’s and Chi & Kirstein (1958)’s beamsThe results are presented in figure on nextslide

It can be seen that both the formulas providereasonable results, with no one methodproviding more accurate results than theother



Eurocode versus Proposed Formula – Authors, Clark’s and Chi & Kirstein’sbeams

Measured/calculated crack width (Eurocode formula)

2.462.191.921.651.381.12.85.58.31.04

N u m

b e r o

f o b s e r v a

t i o n s

100

80

60

40

20

0

Measured/calculated crack width (Equation 1)

2.362.071.781.491.20.91.63.34.05

N u m

b e r o

f o b s e r v a

t i o n s

100

80

60

40

20

0




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15

Comparison with the ACI and the BS formulasThe measured crack widths are divided by the calculatedwidths to evaluate the accuracy of the calculationmethodsThe test data included data points from Clark (1956)’sand Chi & Kirstein (1958)’s beamsFor Chi & Kirstein’s beams the calculated crack widthswere multiplied by the strain gradient factor βThe results are presented in figure on next slide

It is found that while both the proposed and the ACI formulas reasonably deter-mine the crackwidths, the BS formula grossly underestimatesthe values



Measured/calculated crack width (Equation 2)

5.704.904.103.302.501.70.90.10

N u m

b e r o f o b s e r v a t

i o n s

100

80

60

40

20

0

Measured/calculated crack width (ACI formula)

5.704.904.103.302.501.70.90.10

N u m

b e r o f o b s e r v a t

i o n s

100

80

60

40

20

0

Measured/calculated crack width (BS formula)

5.704.904.103.302.501.70.90.10

N u m

b e r o

f o b s e r v a

t i o n s

100

80

60

40

20

0

Comparison of formulas - Clark’s and Chi &Kirstein’s beams




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17

Calculated maximum crack w idths in mm

1.21.0.8.6.4.20.0

M e a s u r e

d m a x

i m u m c r a c

k w

i d t h s

i n m m

1.2

1.0

.8

.6

.4

.2

0.0

Legend

- 30% line

+ 30% line

Suri and Dilger

Batchelor-El Shahawi

Modified Gergely-

Lutz formula

Equation 2

Comparison of formulas – Authors’ 7 PPCbeams



VERIFICATION FOR HSC BEAMDATA

For each beam, at different steel

stress levels both average andmaximum crack widths calculated

Measured and calculated crackwidths are compared




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18

Comparison for Average Crack Widths

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.1 0.2 0.3 0.4 0.5

Predicted average crack widths in mm

M e a s u r e d a v e r a g e c r a c

k w

i d t h s

i n m m

Beam HSB 1

Beam HSB 2

Beam HSB 3

Beam HSB 4

Beam HSB 5Beam HSB 6

Beam HSB 7

Beam HSB 8

+ 30% line

- 30% Line



Comparison for Maximum Crack Widths

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Predicted maximum crack widths in mm

M e a s u r e

d m a x

i m u m

c r a c

k w

i d t h s

i n m m

Beam HSB 1


Beam HSB 4

Beam HSB 5


Beam HSB 8

+ 30% Line

- 30% Line




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19

CONCLUSIONS8 full-size HSC beams tested to investigate thecracking characteristics of HSC beams

Average and maximum crack spacings andcrack widths measured at each level of loadingfor each beam

The authors’ earlier developed NSC beamcrack width formulas verified for theirapplicability to HSC beamsThe initial findings are very encouraging asmost of the data points lay within + 30% limits



TUTORIAL EXERCISESFor a simply supported beam of the following cross-section and aspan of 2.4 m, calculate the average crack widths (use Chowdhury& Loo formula) at 3, 5, 7, 9, 11, 13 and 15 kN loads applied at thecentre of the beam. The stirrups used are10 mm diameter plainbars. The beam cross-section is 150 mm x 250 mm.



35 40

36 78 36

3 6 2 0

Typical beam cross-section

3540

2 1 0

4 0 2 0

2-N 12 bars3-N 20 bars


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Section 3: Damping Characteristicsand Analysis


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THE APPROACH• In total, 26 beams tested• Free-decay method was used for the

determination of damping• Damping values ( δ) predicted from the residual

crack widths and span lengths of beams• Residual crack widths are related to the

instantaneous crack widths

• 4 RC and 4 PPC beam data used forformulation

• Comparisons were made with test results fromall 26 NSC beams and 8 HSC beams

DAMPING - DEFINITION ANDMODEL

• Nature of Damping – There are mainly three ways in which energy

is dissipated:• (i) Material Damping• (ii) System Damping• (iii) Radiation Damping

– These together constitute the structuraldamping

• Damping Model – Viscous Damping


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DAMPING MODELS• Friction or Coulomb Damping due to

microcracking - Rubbing of cracked surfaces• Viscous Damping due to the moisture movement

within the pores• Solid damping due to the sliding friction within

the gel structure

• Total energy dissipation due to inelasticdeformations and energy dissipation at crackedsurfaces


• The logarithmic decrement , δ , is obtainedas:

δ = (1/n) log e

Time t

Amplitude A

A 1A n+1

n periods

1n

1

A1),(ncycleatamplitudeA1,cycleatamplitude

++


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• The damping coefficient C, or alternativelythe damping ratio ξ , where ξ = C/C c, inwhich C c is the critical damping constant,is related to δ as

δ = =

where m and ωd respectively are the massand the damped natural frequency of freevibration

ξ−

πξ21

2

ω

π

dmC


EXPERIMENTAL PROGRAM

• 11 reinforced concrete simply supported beams• Full-size box beams - overall cross-section 300

mm x 300 mm (for all beams)• 180 mm x 180 mm void in each beam -

embedded polystyrene prism• 3 different L – 5.5 m, 6.7 m and 8.0 m• 5 different ρ values – 0.01154, 0.01163,

0.02309, 0.02326 and 0.03348• f ′c varied from 25.4 to 37.7 MPa


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EXPERIMENTAL PROGRAM,CONT.

Beam length, L

l

Applied load

Loading beam

100 mm 100 mm


EmbeddedPolystyrene

as void

60 180 60

2 5

1 0 0

Typical RC box beam

2 8

300 mm

3 0 0 m m

mm m m


• 12 partially prestressed concrete simplysupported beams

• 3 different L – 5.5 m, 6.8 m and 8.0 m• f ′c varied from 25.9 to 46.4 MPa• 4 different degrees of prestressing - 0.25,

0.50, 0.75 and 1.00• 4 different ρ values – 0.00460, 0.00511,

0.00730 and 0.00737


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• 3 two-equal-span continuous beams• Each beam 12 m long - 2 spans 6 m each• f ′c varied from 30.6 to 34.2 MPa• 3 different positive ρ values – 0.01163,

0.02283 and 0.02361• 3 different negative ρ values – 0.01519,0.02714 and 0.02854

TEST PROCEDURE

• Beams were tested in two stages understatic loading

• Residual crack widths measured at zero

load after each load application• Free vibration with hammer excitation

used for damping measurement• Accelerometer at the center of the beam to

receive the vibration signals


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TEST PROCEDURE, CONT.

Stages in a vibration measurement system

DEVELOPMENT OF DAMPINGPREDICTION FORMULAS

• Variables influencing logarithmicdecrement , δ – beam span lengths, L – compressive strengths of concrete, f ′c – degrees of prestressing, η – steel ratios, ρ – residual crack widths, w r

• The main factors affecting the dampingvalues were found to be w r and L


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REINFORCED CONCRETEBEAMS

• Data from the following 4 beams were used in theregression analysis

• The resulting damping prediction formula isδ = 0.048 w r + 0.011 L

1 25.9 20 3 5.5

6 25.4 20 6 5.5

8 31.0 20 3 8.0

BEAMNUMBER

f c(MPa)

Bardiameter

Numberof bars

BeamLength (m)

11 27.6 20 3 6.7

PARTIALLY PRESTRESSEDCONCRETE BEAMS

• Data from the following 4 beams used in theregression analysis

• The resulting damping prediction formula is:δ = 0.054 w r + 0.0104 L

Beamnumber

f c

(MPa)Prestres-sing steel

Reinforcingsteel

Beamlength

Degree of prestressing

15 25.9 2φ5 2Y16+1Y12 5.5 0.2518 31.0 10φ5 1Y12 5.5 1.0022 31.3 7φ5 2Y12 6.8 0.7524 39.1 5φ5 4Y12 8.0 0.50


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RESIDUAL CRACK WIDTHPREDICTIONS

• Residual crack width is obtained from instantaneousaverage crack width, w i using

w r = 0.312 w i• A unified formula for the prediction of w i is given as

w i = (f s /E s ) [0.6 (c – s) + 0.1 ( ρ )]where

– f s is the average steel stress – E s is the modulus of elasticity for steel – c is the concrete cover – s is the average spacing between the reinforcing bars – Φ is the average bar diameter – ρ is the steel ratio

COMPARISON WITH TESTDATA

• For the 14 RC beams

Measured versus predicted damping values

Predicted δ - Equation 3

.16.12.08.040.00

M e a s u r e

d δ

.16

.12

.08

.04

0.00

+ 30% limits

- 30% limits

Continuous beams

Simply-supported

beams


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• A good correlation exists between the calculatedand the measured damping values

• The majority of the 191 correlation points lie wellwithin the + 30% limits

• All but one of the correlation points for the 3 two-equal-span continuous beams lie well within the+ 30% limits

• This indicates that the damping formula which isdeveloped based on simply-supported beamdata is also applicable to the individual spans ofcontinuous beams


• For the 12 PPC beams

Measured versus predicted damping values

Predicted d - Equation 4

.16.12.08.040.00

M e a s u r e

d d

.16

.12

.08

.04

0.00

- 30% limits

+ 30% limits


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• The overall correlation is acceptable as amajority of the 81 correlation points liewithin + 30% limits

• It should be pointed out that, for partiallyprestressed beams with low or no

residual crack widths, the measureddamping values varied widely for thedifferent test beams

• This may be due to the inaccuracy of thecrack measurements

COMPARISON WITH HSC BEAMS

• Eight full-size simply-supported reinforced HSC beams

• Cracking characteristics in terms of crack spacing andwidth

• Damping behaviour in terms of logarithmic decrementsin free vibration

• Beams subjected to two-point loading for crackdevelopment in a constant moment region


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DETAILS OF TEST BEMS

4.5058.34 – N20250 x 250HSB 86.0058.34 – N24300 x 300HSB 75.0065.93 – N20250 x 250HSB 64.0065.93 – N20250 x 250HSB 52.4063.43 – N16150 x 200HSB 42.4061.53 – N16150 x 200HSB 35.0062.33 – N28300 x 300HSB 23.0060.93 – N24300 x 300HSB 1

SpanL (m)

f ′ c(MPa)

A stb x D(mm x mm)

BeamDesignation

Cross Sectional Details of Test Beams

25 for HSB 130 for HSB 2

25

150

2510025

R6 stirrups @100 mm c/cfor HSB 3

250

2520025R10 stirrups@ 75 mm c/cfor HSB 4

250

300

25 250 25

R10 stirrups @110 mm c/c for HSB 1

R6 stirrups @110 mm c/cfor HSB 2

30 for HSB 535 for HSB 6

300

25 250 25

300

35

175

250

25 200 25

250

R6 stirrups @120 mm c/c

30

Beams HSB 1 and HSB 2 Beam HSB 7

Beams HSB 3 and HSB 4 Beams HSB 5 and HSB 6

Beam HSB 8

Beam length, L

l

Applied load

Loading beam

200 mm 200 mm

l = 867 mm for beam HSB 1, l = 1534 mm for beam HSB 2,l = 667 mm for beam HSB 3, l = 734 mm for beam HSB 4,

l = 1200 mm for beam HSB 5, l = 1534 mm for beam HSB 6,l = 1867 mm for beam HSB 7 and l = 1367 mm for beam HSB 8

Loading Arrangementsfor Test Beams


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COMPARISON OF DAMPINGVALUES

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Predicted δ

M e a s u r e

d

Beam HSB 1

Beam HSB 2

Beam HSB 5

Beam HSB 6

Beam HSB 7

Beam HSB 8

+ 30% Line

- 30% Line

CONCLUSIONS

• Two damping prediction formulasdeveloped – one for RC and one for PPCbeams

• Comparison with the test data of all the 26NSC and 8 HSC beams shows that theaccuracy of the proposed formulas is good

• The formula for RC beams is alsoapplicable to continuous beams


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Section 4: Deflection


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DEFLECTION

PROFESSOR YEW-CHAYE LOO


Griffith UniversityQueensland , Australia

SHORT COURSE ON

ADVANCED TOPICS IN ANALYSIS AND DESIGN OF CONCRETE STRUCTURESSKuala Lumpur, Malaysia 5-6 September 2005

DEFLECTION


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• Deflection

– static loading

– repeated loading

– impact

● A new method for incorporatingtension stiffening effects

● Curvature values at sectionsbetween adjacent cracks

● Short-term deflections for 35flexural members compared

_____________________________________________________________ *Piyasena, R., Loo, Y.C. & Fragomeni, S. 2002


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• Procedure for intensive creepdeflection of R.C. box beams*

• The intensive creep factor is

k = k 1 + R log 10 T where T is the number of loading cycles,

k1 = 1.18 + (0.029/r) {(M t – Md)/(My – Mcr )} andR = (0.0015/r) {(M t – Md)/(My – Mcr )}

____________________________________________ *Loo, Y.C. & Wong, Y.W. 1983, 1984, 1986; Wong, Y.W. & Loo, Y.C. 1985


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Deflection of RC beams under repeated loading

k versus T for M t/M v = 0.7


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k versus steel ratio for M t/M v = 0.7

• Maximum deflection of RC and PPCbeams* – deflection under repeated mid-span

impact of below yield intensity

– Deflections compared – Comparisons with other formulas – Design charts produced ___________________________________________ *Loo, Y.C. & Santos, A.P. 1985; Loo, Y.C. 1991


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Correlation of measured and computed total deflections – proposed formula

Correlation of measured and computedtotal deflections – Balaguru & Shah(1982) formula

Correlation of measured and computedtotal deflections – Lovegrove & El Din(1982) formula


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y´max = y max / [(2/m bω12) (1.25 m s v02 k 2/3)3/5]

α = (m b/m s)β = 1.47 ( ω1/π) (5m s/4kv 01/2)2/5

ω1 = (π2/L2) √(EI/ ρA)

IMPACT AND ENERGY ABSORPTION


84/205

• Impact deflection analysis ofbeams• Precast beam-column

connections – under repeated load – under cyclic loading

• An analytical solution for instantaneousdeflection of beams under mid-spanimpact*

• An integral equation incorporatingHertz’s contact law

• Equivalent moment of inertia forrepeated loading• RC and PC beams• Comparisons with published results

___________________________________________________ *Loo, Y.C. & Santos, A.P. 1986


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Correlation of measured and computed deflections – Hussain’s (1982)and Wijewardene’s (1984) beams

Correlation of measured and computed deflections – Bate’s (1961) beams


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Correlation of measured and computed deflections – Hughesand Speir’s (1982) beams

• 18 half-scale interior connection modelstested*

• Under static and repeated loading• Two types of precast RC beam-column

connections• The precast connections were superior to

their monolithic counterparts ___________________________________________________ *Yao, B.Z. & Loo, Y.C. 1993; Loo, Y.C., Yao, B.Z. & Han, Q. 1994; Loo, Y.C. &Yao, B.Z. 1995


87/205

Precast connection Type A Precast connection Type B

Test setup Typical load history


88/205

Load-deflection curves under static loading

Load-deflection curves under repeated loading

• 12 half-scale interior connectionmodels tested*

• Under repeated and cyclic loading• Two types of precast RC beam-

column connections• Precast connections possessed

larger energy absorbing capacitiesthan the monolithic models ___________________________________________________ *Loo, Y.C., Yao, B.Z. & Takheklambam, S. 1996


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Load history for cyclic tests

Load-deflection curve under cyclic loading


90/205

THANK YOU THANK YOU ALL ALL


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Section 5: Punching Shear StrengthAnalysis of Concrete FlatPlates


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1

PUNCHING SHEAR DESIGN OF REINFORCED ANDPOST-TESIONED CONCRETE FLAT PLATES: ARE THE MAJOR DESIGN CODE METHODS

ADEQUATE?

Professor Yew-Chaye Loo

Faculty of Engineering and InformationTechnology

Griffith University


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Section 6: Ultimate StrengthAnalysis of Walls (Solidand with Openings)


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Ultimate Strength Analysis ofConcrete Walls (Solid and with

Openings)

AimAimTo investigate the failure behaviour of reinforcedTo investigate the failure behaviour of reinforcedconcrete walls with and without openingsconcrete walls with and without openings

simply supports top and bottom

onlysimply supports on all sidesSolid/ Opening panelsvarying slenderness(H/t w)

New design formula for wallwith/without openings


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(a) In-plane vertical load

(b) Transverse horizontal load (c) In-plane horizontal load

One and TwoOne and Two --way actionway action

Typical example of Concrete core wallsB) Two-way actionA) One-way actionAS 3600(2001)ACI 318(2005)


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Code MethodsCode MethodsAS3600-01 – Section 11 (Design of walls -simplified formula) – Section 10 (Design of columns for

strength and serviceability

ACI318-05

– Chapter 14

BS8110-97 – Section 3.9.4 (Identical to AS3600)

'cawu )0.6f 2e1.2e(t N −−=

AS3600AS3600--01 Wall Design Method01 Wall Design Method

⎟⎟

⎠

⎞⎜⎜

⎝

⎛ ⎥⎦

⎤⎢⎣

⎡=2

ww

'cu t32

kH-1tf 55.0 N

ACI318ACI318--02 Wall Design Method02 Wall Design Method

Ultimate strength per unit length of wall (N/mm)

Thickness of the wall

Eccentricity of load

Additional eccentricity=Hwe2/2500t w

Concrete strength


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LimitationsLimitations

AS3600-01Hwe/tw ≤30

f ’c ≤ 65 MPae ≥ 0.05t w(=tw/20)

Only one-way actionOnly solid walls

ACI318-05/BS8110H/t w ≤25 or L/ t w ≤25

f ’c ≤ 50 MPae ≤ tw/6Only one-way actionOnly solid walls

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50

H/t

N u

/ ( f ' c A g

)

AS3600

ACI318

Pillai(1977)

Saheb/Desayi(1989)

Fragomeni(1995)(NSC)

Fragomeni(1995)(HSC)

Butler(1998)

Previous experimental results o f One-way action


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0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50H/t

N u

/ ( f '

c A

g )

Saheb & Dasey (1991)

Fragomeni(1995) (NSC)

Fragomeni(1995) (HSC)

Previous experimental results of Two-way action

Test specimens and test set upTest specimens and test set up((eccecc =t/6,=t/6, ρρvv== ρρhh = 0.0031= 0.0031))

H (mm) L (mm) t w (mm) f'c(MPa) H/t w AS3600

OWNS2 1200 1200 40 35.7 30.00

OWNS3 1400 1400 40 52.0 35.00

OWNS4 1600 1600 40 51.0 40.00

OWHS2 1200 1200 40 78.2 30.00

OWHS3 1400 1400 40 63.0 35.00

OWHS4 1600 1600 40 75.9 40.00

TWNS1 1000 1000 40 45.4 25.00

TWNS2 1200 1200 40 37.0 30.00

TWNS3 1400 1400 40 51.0 35.00

TWNS4 1600 1600 40 45.8 40.00

TWHS1 1000 1000 40 68.7 25.00

TWHS2 1200 1200 40 64.8 30.00

TWHS3 1400 1400 40 60.1 35.00

TWHS4 1600 1600 40 70.2 40.00

68.544 kN68.544 kN

N/AN/AN/AN/A

N/AN/AN/AN/AN/AN/AN/AN/A

N/AN/AN/AN/AN/AN/AN/AN/A

N/AN/AN/AN/AN/AN/A


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H (mm) L (mm) tw (mm) f'c(MPa) H/t w H/LTAHS1 1600 1400 40 77.8 40.0 1.1TAHS2 1400 1000 40 73.8 35.0 1.4TAHS3 1600 1000 40 77.8 40.0 1.6

Test specimens and test set upTest specimens and test set up((eccecc =t/6)=t/6)

TestTest --rigrig

set upset up

(2400(2400 kNkNcapacity)capacity)


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Eccentricity t/6

∅23 roller

150 ×50 plate20 ×20 EA

40mm thickness test panel

Support ConditionSupport Condition(one(one --way)way)

Side Support ConditionSide Support Condition(two(two --way)way)

150 PFC

40 ×40 ×5 SHS


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1600x1600x40 (f 1600x1600x40 (f ’’c=50MPa)(onec=50MPa)(one --way)way)

1600x1600x40(f 1600x1600x40(f ’’c=76MPa)(onec=76MPa)(one --way)way)


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1600x1600x40(f 1600x1600x40(f ’’c=70MPa)(Twoc=70MPa)(Two --way)way)

1600x1000x40(f 1600x1000x40(f ’’c=78MPa)(Twoc=78MPa)(Two --way)way)


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Experimental results of OneOne --way actionway action

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50

H/t

N u

/ ( f '

c A

g )

AS3600

ACI318

Pillai(1977)

Saheb/Desayi(1989)



Butler(1998)

Doh(2002)(NSC)

Doh(2002)(HSC)

Experimental results of TwoTwo --way actionway action

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50H/t

N u

/ ( f ' c A

g )

AS3600

ACI318

Saheb/Desayi(1990)



Doh (2002)(NSC)

Doh (2002)(HSC)

Doh (2002)(HSC)


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0200400600800

10001200140016001800

0 5 10

Deflecti on (mm)

L o a

d ( k N )

TWNS4(top)TWNS4(middle)TWNS4(bottom)TWNS4(side)TWHS4(top)TWHS4(middle)TWHS4(bottom)

TWHS4(side)

LoadLoad vsvs Deflection for TWNS4 and TWHS4Deflection for TWNS4 and TWHS4

Laboratory tests (half-scale of 17 NSCand HSC wall panels)H/t w ↑ with N u/(f’cLt) ↓

Nu/(f’cLt) HSC < N u/(f’cLt) NSC

H/L ↑ with N u/(f’cLt) ↑

Summary of test resultSummary of test result


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Limitations of code methods – f’c


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for simply supported top and bottomonly

for H ≤ L when all four all sides arerestrained

for H > L when all four all sides arerestrained

2

LH

1

1

⎟ ⎠ ⎞

⎜⎝ ⎛ +

α=β

H2Lα=β

α=β

where α is eccentricity parameter and is equal to:

wte

1

1

−=α 88.0

ww t

H

18

te

1

1

⎟⎟

⎠ ⎞

⎜⎜

⎝ ⎛

×−

=α

for H/t w < 30 for H/t w ≥30

H we = H

WallPanels

Failure Load(kN)

Proposed Eq(kN)

Proposed EqFailure load

OWNS2 253.10 250.54 0.99

OWNS3 426.73 340.86 0.80OWNS4 441.45 344.69 0.78OWHS2 482.65 433.76 0.90OWHS3 441.45 389.93 0.88OWHS4 455.84 455.29 1.00

MeanStandard Deviation

0.890.09


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WallPanels

Failure load(kN)

Proposed Eq(kN)

Proposed EqFailure load

TWNS1 765.2 716.43 0.94TWNS2 735.8 707.66 0.96TWNS3 1177.2 1 1020.16 0.87TWNS4 1177.2 1 1067.91 0.91TWHS1 1147.8 957.77 0.83TWHS2 1177.2 1 1047.60 0.89TWHS3 1250.8 1144.67 0.88TWHS4 1648.1 1440.23 0.86TAHS1 1618.7 1486.51 0.92TAHS2 1118.3 1381.09 1.23TAHS3 1265.5 1137.18 0.90TAHS4 1442.1 1228.22 0.85

Mean 0.92Standard Deviation 0.11

Notes: 1 Hydraulic jacks measured 40 tonnes for these specimens (40 ×3×9.81kN).The accuracy of jack was ± 1 tonne ( = 9.81 kN).

2 Load eccentricity = tw/6

Comparison with test data –one-way action

H/t w

N u

/ f '

c L t w

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

f' c = 30 M Paf' c = 50 M Paf' c = 80 M PaFragomeni (NSC)Fragomeni (HSC)OWNS (Stage 1)OWHS (Stage 2)Doh (HSC)Doh (NSC)


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Comparison with test data – two-way action

H/t w

N u

/ f '

c L t w

10 20 30 40 50 60

0.3

0.4

0.5

0.6

0.7

0.8 f' c = 30 M Paf' c = 50 M Paf' c = 80 M PaSaheb & Desayi (1990)Fragomeni (NSC)(1995)Fragomeni (HSC)(1995)Doh (NSC)Doh (HSC)

H/L

N u

/ f ' c L t w

0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

f' c = 30 M Paf' c = 50 M Paf' c = 80 M PaTA H S ( H /t w = 4 0)TA H S ( H /t w = 3 5)L F EM r es u lt s ( f' c = 30 M P a)L F EM r es u lt s ( f' c = 50 M P a)WASTAB resu lt s ( f' c = 30 M P a)WASTAB resu lt s ( f' c = 50 M P a)

Comparison with test data – two-way action


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Test specimensTest specimens --opening panelsopening panels

and test set upand test set up((eccecc =t/6,=t/6, ρρvv== ρρhh = 0.0031= 0.0031))WallPanel

Height(H: mm)

Length(L: mm)

Thickness(tw: mm)

Opening size(mm × mm)

Concretestrength

(f’c: MPa)H/t w

OW01 1200 1200 40 None 35.7 30

OW02 1600 1600 40 None 51.0 40

OW11 1200 1200 40 300 ×300 53.0 30OW12 1600 1600 40 400 ×400 47.0 40OW21 1200 1200 40 300 ×300 50.0 30OW22 1600 1600 40 400 ×400 51.1 40

TW01 1200 1200 40 None 37.0 30TW02 1600 1600 40 None 45.8 40

TW11 1200 1200 40 300 ×300 50.3 30TW12 1600 1600 40 400 ×400 50.3 40TW21 1200 1200 40 300 ×300 50.3 30TW22 1600 1600 40 400 ×400 50.3 40

Numberof

openings

One-wayaction

Two-wayaction

T

Typical example of concrete panel dimensions

(a) OWN11/TW11 (b)OW12/TW12


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Reinforcement layout

Shrinkagecontrol


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OW11OW11 1200x1200x401200x1200x40((f f ’’

cc= 53 MPa)= 53 MPa)

OW21OW21 1600x1600x401600x1600x40

((f f ’’cc= 50 MPa)= 50 MPa)

TW11TW11 1200x1200x401200x1200x40((f f ’’cc= 50.3MPa)= 50.3MPa)

TW12TW12 1600x1600x401600x1600x40((f f ’’cc= 50.3MPa)= 50.3MPa)


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TW21TW21 1200x1200x401200x1200x40((f f ’’

cc= 50.3MPa)= 50.3MPa)

TW22TW22 1600x1600x401600x1600x40

((f f ’’cc= 50.3MPa)= 50.3MPa)

LoadLoad vsvs Deflection for TW21Deflection for TW21

0

100

200

300

400

500

600

700

0 2 4 6 8 10

Lateral Deflection (mm)

L o a

d ( k N )

top

middle

bottom

side

advanced topics in analysis and design of normal and high strength concrete structures volume 2...

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