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UNIVERSITI PUTRA MALAYSIA
STRUCTURAL BEHAVIOUR OF PRESTRESSED CONCRETE HOLLOW BEAMS
ROSLI MOHAHAD ZIN
FK 1993 1
STRUCTURAL BEHAVIOUR OF PRESTRESSED CONCRETE HOLLOW BEAMS
By
ROSLI MOHAHAD ZIN
Thes i s Submitted in Par t i a l Fulfilment of the Requireme n t for the Degree of Master of S c i ence in the Fa culty o f Engi neering,
Universiti Pertanian Ma laysia
April 1993
ACKNOWLEDGEMENTS
The a u t hor wi shes to expre ss h i s many t hanks to Dr . S.A
Salam, formarly the cha irman of supervi sory comm i t t e e of t h i s
projec t , t h e newly appointed mai n s upervi sor Enc i k Mohd. Salleh
Jaafar, and co-supervi sors Pro fessor Abang Abdullah Aban g Ali
and Encik Zakaria Che Muda for their con t i nuous support.
g uidan ce , encouragement and help t o make this s t udy possible.
Thanks are also due to En c i k Mohd. Ha l i m Othman , En c i k
Baharuddin, a n d Tuan Haji Ghazali for their help 111 la bora tory
works , Puan Rogayah and Puan Za i n e for thei r help i n typing the
manuscri pt, and those whose names a re not men t i oned here who
he lped i n the prepara t ion of the manuscript .
Last but not t he least , my s i n c ere gra titude is due to
Un ivers i t i Pert anian Ma lays i a , Serdang , for t he perm i s s ion to
undertake M.S programme at the Faculty of Engineeri n g and t o
unde r t ake this research.
ii
ACKNOWLEDGEMENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF PLATES
LIST OF NOTATIONS
ABSTRACT
ABSTRAK
CHAPTER
1. INTRODUCTION
TABLE OF CONTENTS
Prestressed Concrete
ii
vii
viii
x
xi
xiv
xvi
1
General Principle of Prestressed Concrete 2
Advantaees of Prestressed Concrete Hollow Beams . 4
Scope and Objective
2. LITERATURE REVIEW
Selection of the Best Shapes for Prestressed Concrete Under Flexure
Prestressed Concrete Hollow Beams
5
7
9
Design of Prestressed Concrete Hollow Beams 1 1
Arrangement of Steel of Prestressed Hollow Beams . 12
Summary of Literature Survey 14
iii
3. THEORETICAL CONSIDERATION
Beam Subjected to Third Point Loading 15
Prediction of Cracking Load and Hending Moment 16
Prediction of Ultimate Load and Bending Moment 17
Location of Neutral Axis
Ultimate Moment Carrying Capacity
Ultimate Load
Prediction of Service Load
Calculation of Deflection
4. MATERIALS
Concrete
Cement,Sand and Aggregates
Prestressing Wires
Stirrup Reinforcement
Plastic Tubing, Grease etc.
5. TEST PROGRAMME
Beam Specimen Preparation
The Beam Mould
Casting and Curing of Concrete
Test Cubes
Removal of Rectangular Hollow Section and
18
23
24
24
25
27
27
29
29
30
32
32
33
34
Plastic Tubing . . . . . . . . . . . . . . . . . . . • . . . . . . . . 35
Prestressing 36
Grouting 37
iv
The Test
Testing Ma chine
Setting of the Beam
Beam Testing
Testing the Cubes
Details of Beam Tested
6. RESULTS AND DISCUSSIONS OF BEAM TESTS
Beam Test Results
Beam SOl
Beam U 0 1
Beam U02
Beam U#l
Beam U#2
Beam Ul3
Beam U00 1
Beam U00 2
Beam B01
Beam B02
Discussion
Ultimate Load
Cracking Load
Crack Width and Crack Propagation
Strain Gauge Results
Service Loa d
v
36
36
37
37
3 8
39
46
46
47
4 8
50
51
52
54
55
56
57
58
59
63
64
65
66
Deflection
7. CONCLUSIONS AND RECOMMENDATIONS
Con c l usi ons
Ultimate load
Cracking
De f l ection
Recommendations for Further Research
BIBLIOGRAPHY
APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D
CURRICULUM VITAE
vi
67
97
97
98
qg
100
111
113
117
149
161
172
LIST OF TABLES
1. Properties of Concrete Beam Specimens
2. Details of Beams Tested
PAGE
3 1
4 3
3 . Experimental Against Ca l c ulated Ultimate Load 7 0
4. Experimenta l Against Ca lculated Cra cking Load 7 1
5 . Ultimate Strength of Prestressed ijo l l ow Beams compared to Solid Beam Under Identical Circ umstances . . . . . . 7 2
6. Cal cu lation of Deflection at Service Loa d
7 . Experimenta l Against Theoretic a l Maximum deflection
7 3
at Service Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4
8. Experimenta l Aeainst Theoretical Maximum Deflection at Actual Cracking Loa d . . . . . . . . . . . . . . . . . . . . . . . . . . 75
9. Experimenta l Aeainst Cal c u l ated Cracking Load and Ultimate Loa d for Unhonded Beams With Variable Weight Reduction . . . . . . . .. . . .. .. . . . . . . . . . . . . . . . .. . 76
10. Experimental Agains t Ca l cul ated Cra cking Load and Ultimate Load for Bonded Beam With Variable Weight Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
vii
LIST OF FIGURES
1 . Pres tressed Con c r e t e
2 . Beam Subjected t o Th ird Po i n t Loading
3 . S t ress-s t ra i n Rel a t i onsh ip a t U l t ima t e (Neutr a l axis w i t h i n t h e flange)
4. Stress-s t r a i n Diagram for Prest ressing S t eel
5. St ress-stra i n Re lat ionship at U l t imate (Neutral axis wit h i n the web)
6 . Grad i n g Curve for Coarse , Fine and Combined Aggregat e Mc Intosh and En t roy Type Gra d i ng
7. Det a i l s of Beam Tes t ed
8 . Load Aga inst De f l e c t i on Beams UO l,U02,SO l
9. Load Against Def l e c t i on Beams Ull , UI2 , UI3
1 0 . Load Aga inst Def l e c t i on Beams U001 , U002
1 1 . Load Aga i nst Def l e c t i on Beams UOl , Ull , UOOI
1 2. Load Aga inst De f l e c t i on Beams U02 , UI2 , U002
1 3. Load Agai n s t Deflect ion Beams B0 1,B02
1 4. Load Aga i n s t Max . Crack Width Beams UO l , U0 2 , 801
1 5 . Load Against Max . Crack Width Beams Ull , UI2 , UI3
1 6 . Load Again s t Max . Crack Wid th Beams U001 , U002
17 . Load Aga i n s t Max . Crack Width Beams B0 1 , B0 2 , S0 1
1 8 . Beam Depth Against S t ra in, Beam UOI
19. Beam Depth Against S t arin , Beam U0 2
20. Beam Depth Against S t r a i n , Beam Ull
2 1 . Beam Depth Against Stra i n , Beam UI2
vi i i
PAGE
3
1 5
1 9
21
22
28
44
77
78
79
8 0
8 1
8 2
8 3
84
85
86
87
88
89
90
22 . Hearn Depth Agains t
23 . Beam Depth Against
24 . Beam Dep th Agains t
25 . Beam Depth Against
26. Beam Depth Against
27. Beam Depth Against
28. Beam Detai ls U01
29 . Beam Det a i l s UI1
30 . Beam De tails BOI
Stra in, Beam
S t r a in , Beam
S t ra in, Beam
S t rain , Beam
S t ra in, Beam
S t r a in , Beam
U#3
U00 1
U002
B0 1
BOI
S02
.. . . . . " . " . " " . " .
" . . " " " . . ,, . . . .
" " " . " . . " . " . ,, .
. . " " " " . . . ,, . ,, " "
" . . " " . . " " . . . . .
" " . " . " . . . . . . " .
. . " . " . .. . . " . .. . . . " . . " . . . . . . .. " .. " " . .. .
. . " " " " " " " .. . " . . " " " " " " .. " .. .. .. .. .. " .. .. .. .. ..
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
ix
PAGE
9 1
92
9 3
94
95
96
1 27
1 3 7
148
1 .
2 .
3.
4.
5.
6 .
7 .
8 .
LIST OF PLATES
The Cast ing Mou l d
Cas t i n g o f Beam
Beam Ready for St ress ing
Crack Measur ing Mic roscope and Demec Gauge
Grou t i n g Pump
Prestressing i n Progress
The Beam Tes t i n g Frame and Test Set up . . . . . . . . . . .
Crack i n g Pa t t ern of Beam U0 1 . .. . . . . . . . . . . . . . . . . . .
9 . Cracking Pat t ern of Beam U02
10 . Cracking Pat t ern o f Beam U#l
1 1 . Cracking Pat t ern o f Beam UI2
1 2 . Cracking Pa t t ern of Beam UI3
13. Cra cking pa t t ern of Beam U00 1
14. Cracking Pa t t ern of Beam U002
1 5 . Cracking Pat t ern of Beam BOl
1 6 . Cra c k i n g Pat tern o f Beam BO�
1 7 . Cracking Pat t ern of Beam SOl
x
PAGE
1 0 1
102
1 0 2
1 0 3
104
104
105
105
106
106
107
1 07
1 08
108
1 09
1 0 9
1 10
a
A
b
C
d
e
LIST OF NOTATIONS
Distance from top flange to centre of top steel
Area of cross-section
Area of prestressing
Area of prestressing steel in the tension zone
Cross-sectional area of the two legs of a links
Width or effective width of the section or flange in the compression zone
Width of flange
Width of web
Total compression force
Compressive force in concrete block (flange)
Compressive force in concrete block (web)
Compressive force of top prestressing steel
Effective width to the centroid of steel area
Eccentricity of prestressing force
Young's modulus of elasticity of concrete
Young's modulus of elasticity for prestressing steel
Overall flexural tensile stress in concrete
Characteristic strength of concrete
Design compressive stress at the centroidal axis due to prestress
Design tensile stress in the tendon
Characteristic strength of prestressing wires
xi
h
L
Mo
p. 1
T
x
Maximum des i gn pri n c i p l e tens i l e stress
Depth of cross-sect ion
Depth of top fl ange
Secon d moment of area of the sec t i on
Effe c t i ve span
Cracking moment
S e l f wei ght moment
Girder moment
Moment necessary to pr oduc e zero st r ess in the concrete at the ext reme fibre
Tota l moment
U l t ima t e moment
Cracking load
Effect ive prest ressi n g force
I n i t i a l prestressing force
Spa c i n g of the links
Tensi l e force
Desi gn ult ima te shear resis tance o f the con c rete
Des i gn u l t ima t e shear resistance of a s ec t i on cracked i n f l exure
Desi gn ultimate shear resistance of a section un cracked in f l exure
Locati on of n eutra l axis from top flange
Lever arm to Cl
Lever arm t o C2
Lever arm to st op steel
First moment of area (below neut r a l axis)
xii
First moment of area (above neutral axis)
Strain in compression steel
Strain of top steel due to bending
Total strain
Deflection at mid span of the beam due to two
point loading
Deflection due to self weight U.D.L at mid span
Deflection due to effective prestress (bottom steel)
Deflection due to effective prestress (top steel)
Total deflection
xiii
An abstract o f the thesi s presented to the Senate o f Uni vers i ti Pertanian Malaysia i n partial fulfilment o f the requi rements for the degree of Master of Sci ence .
STRUCTURAL BEHAVIOUR OF PRESTRESSED CONCRETE HOLLOW BEAMS
BY
ROSLI MOHAMAD ZIN
APRIL 1993
Chairman Dr. S . A . Salam {December 19 8 8 - July 1992}
Mr . Mohd . Salleh Jaa f ar (July 1992 - April 1 99 3 )
Faculty Engi neering
Thi s thes i s is concerned with the primary objective of
studying the structural behavi our o f prestressed concrete
hollow beams . Ten simply supported recta ngular hollow beams and
one rectangular solid beam were tested on an effectjve span of
2 . 80 m subjected to two third point loadi ngs. The variables i n
th e study were th e percentage of self weight reduced and the
amount of prestress i ng w ires. Eight beams were testpd unbonded
while the other two beams were f ully bonded.
xiv
Ultimate loads, cracking loads, crack widths and
deflections were recorded at various loadings and crack
propagations were observed. The results obtained were compared
with theoretical values.
It was observed that due to the absence of material in
the hollow portion, compared to a solid beam with similar
outside dimensions, the ultimate moment carrying capacity of
prestressed hollow beam is reduced if neutral axis of the beam
at failure is located below the top flange. However, if the
neutral axis of the beams at failure is located within the top
flange, then the ultimate moment carrying capacity is at least
equivalent to that of a solid beam. It was also observed that
the theory on the ultimate moment carrying capacity presented
in this thesis gives a fairly good prediction. However, the
theory used to predict cracking load as well as deflection was
found not suitable for unbonded beams as it greatly
underestimates the deflection and overestimates the cracking
load. It was also observed that bonding has a great influence
on crack widths and deflections. Bonded beams show more uniform
crack distribution with reduced maximum crack width and
increased ultimate load capacity. From test results, it is
recommended that prestressed hollow beams should be made bonded
in order to achieve at least the predicted cracking load.
xv
Sebuah abstrak tesis yang dikemukakan kepada Senat Universiti Pertanian Malaysia bagi memenuhi sebahagian daripada kelayakan Ijazah Master Sains.
KELAKUAN STRUKTUR RASUK KONKRIT PRA-TEGASAN BERONGGA
OLEH
ROSLI MOHAMAD ZIN
APRIL 1993
Pengerusi Dr . S.A. Salam (Disember 1988 - Julai 1992)
En. Mohd. Salleh Jaafar {Julai 1992 - April 1993}
Fakulti Kejuruteraan
Tesis ini bertujuan menjalankan kajian mengenai kelakuan
rasuk-rasuk konkrit pra-tegasan berongga . Sepuluh buah rasuk
berongga dan sebuah rasuk padu tersokong secara mudah diuji di
atas jarak berkesan Z.80m dengan dua beban titik ketiga.
Pemboleh ubah terdiri dari peratus pengurangan beban diri serta
jumlah dawai pra-tegasan. Kesan ikatan relah juga dikaji . Lapan
buah rasuk telah diuji tanpa ikatan sementara dua buah lagi
terikat penuh melalui turapan tekanan.
xvi
Beban muktamad , beban retak , l ebar retak dan l en t uran
dir ekodkan pada t ahap beban ber lai nan dan pemben t ukan retak
diperh a t ikan . Keput usan yang diperolehi di bandi n gkan dengan
ni l a i-ni l a i teor i .
Ada l a h diperha t ikan , den gan kehadiran r uang berongga , j i ka
d i bandingkan dengan rasuk padu yang mempunyai s a iz kera tan
rentas yang serupa , kemampuan mena n ggung beban mukt amad bagi
rasuk berongga akan berkurangan j i ka paks i nutral pada keadaan
muktamad t er l e t a k di bawah beb i b i r a t a s . Walaubaga imanapun ,
j i ka paksi nut r a l t e r l e t ak di beb i b i r a t as ,
menanggung beban muktamat bagi rasuk berongga
kemampuan
sekurang-
kurangnya akan sarna dengan kemampuan menanggung beban muktamad
bagi rasuk padu. Dapat j u ga diperhat ikan teori beban mukt amad
yang d i g unakan d a l a m t es i s ini memberikan s a t u ramalan yang
agak b a i k . Namun begi t u teori -teori yang d i gunakan bagi meramal
beban retak beg i t u j uga lenturan bagi ra suk t i dak terikat
di dapa t i t i dak sesuai memandangkan rama l a n yang diberikan
adalah j auh dari yang s ebena rnya . Adalah diperha t i kan j uga ,
ikatan memberi kesan ke at as lebar retak dan lenturan. Rasuk
yang teri kat mampu mengagi hkan r etak dengan
seterusnya dapa t mengurangkan l ebar retak
beban muktamad . Berdasarkan keputusan
lebih berkesan
dan menin gkat kan
u j i a n , a d a l ah
disyorkan supaya rasuk-rasuk berongga d i bua t secara t erikat
untuk mencapai sekurang-kuran gnya set aka t ketahap beban retak
yang d i r amalkan.
xvi i
CHAPTER 1
INTRODUCTION
Pres t ressed Concrete
Prestressed concrete is a very important construction
material and its use will continue to grow in the next century.
In 1939 Freyssinet introduced an economical way of producing
prestressed concrete. Since then, more and mOTe research was
done for developing a better understanding of prestressed
concrete.
As mentioned by Bate and Bennett (1980), prestressing
can be defined as a technique whereby the performance of a
structure is improved by the introduction of permanent stress
(prestress) so as to cancel some of the st ress produced by the
dead and imposed load. Mosley and Buneey (1987) defines
prestressing as the artificial �reation of stresses in a
structllre before loading, so that the stresses which then exist
under load aTe more favourable than would otherwise be the
case.
The principle of prestressing when applied to �on�rete
will result in what we called prestressed �oncrete. Perhaps one
of the best definitions of prestressed concrete is given by
1
2
the ACI Committee on prestressed concrete. This de finition is
"Prestressed concrete : concrete in which there have been
introduced internal stresses of which magnitude and
distribution that the stresses resulting from given external
loading are counteracted to a desired degree" .
British Standard BS 8110 Part 1: 1985 , Clause 4 . 1.3
classifies prestressed concrete structures i nto three
categories which are as follow:
a. Class 1
b. Class 2
c. Class 3
no flexural tensile stress
flexural tensile stress but no visible cracking
flexural tensile stresses but surface width of cracks not exceeding O. lmm for members in very severe environments and not exceeding 0. 2mm for all other members.
General Principle of Prestressed Concrete
The basic concept of prestressed concrete is i lustrated in
Figure 1. A very high stren gth steel tendon has been placed in
the duct. After concrete has achieved required strength, the
tendon will be stressed prior to external l oading. Resulting
from the prestressing of tendon (Figure 1. a), the stress in the
beam varies from a maximum compression in the bottom fibre to a
small tension in the top fibre and causes the beam to deflect
upward . When external loads are applied, the stress
distribution will be as shown in Figure l(b). Combined with the
stress due to prestress produce a state of stress as in Figure
3
l(c). where maximum compression or a small tension in the
bottom fibre.
COMPRESSIon
(a) STRESS DUE TO PRESTRESS
w
TENSION
( b I STRESS DUE TO MOMElfT
w
ctJMPRESSION
( c ) COMBINED STRESSES
Figure.l- General Principle of Prestressed Concrete.
4
Advantages of Prestressed Concrete Hol low Beams
The advantages of considering prestressed concrete hollow beams
in concrete design are :
i ) The reduced weight of the member will help in economi zi ng
the section; the smalle r dead load and depth of members
will res ult in saving materi als f rom other secti ons o f
structure, e.g foundation. I n pr ecast members , a reducti on
o f weight saves handling and transportation costs.
ii) Excellent torsional s trength , and rigidity combine with
good flexural strength as prestress ed hollow beams a r e
closed section.
i i i } Low maintenance cost mainly due to i ts durabili ty,
Fati gue test on hollow beams indi cate that million of
cycles of load applications i n excess o f desi gn load does
not result in any sign of distress (Bender and Kriesel,
1969).
It is also known that when the ratio of dead to li ve load
is large, the use of structural hollow s ection become
signi ficant s i nce the saving in weight i s substantial. For
prestressed hollow beams the amount of weight that can be
reduced depending on width/wall thickness ratio and percentage
of wei eht reduction. It has been known tha t works on the effect
of width/wall thickness ratio on the behaviour of prestressed
6
beams are fully prestressed where two of them will be grouted
with cement grout to make it bonded . Deflection and crack width
will be measured at various load levels . Results will be
compared with the predicted values . Some conclusions will be
drawn, as to what extent the reduction in weight is feasible so
far as the increase of deflection and cracking is concerned .
CHAPTER 2
LITERATURE REVIEW
Parr and Maggard (1972) mentions that a survey of
b r i d ges b u i lt or proposed in the last few years in the United
States revea ls a growing awareness of at l east two items :-
i) The uti l ization of mate r i a ls and cross-section wh ich
may be more e f f icient and econom ica l than those used
in the past.
i i ) a mor e ser ious consi deration of aesthetic
requi rements.
For that reason the use of thi n webbed or hol low
structur a l secti ons has increased si g n i f i cantly throughout the
l ast d ecade .
Selection of the Best Shapes for Prestressed Concrete Under
Flexure
The simplest form of shape is rectangu l a r and is the most
economical as far as formwork is concerned . Lin and Burns
(1982) expla ins that rectangu lar section has sma l l kern
dist ance and the a va i l ab l e l ever arm for s t eel is l i mi t ed.
Rectangu l a r section is not as e fficient in the use of concrete
as nonr ectangular section such as the I-shaped sect i on . Hence
7
8
other shapes whi ch are frequently used for prestressed
concrete are :
i ) The symmetrical and unsymmetrical
I-section
i i ) The T-sect ion
i i i ) The inverted T-secti on
i v ) Box secti on.
Lin and Burns ( 1982) added that the suitability o f the
above shapes depend on certain requ irements . The I-sec t ion has
its concrete conc entrated near the extreme fibre so that it can
most ef fectively furnish the c ompression force. The more the
concrete is concentrated near the extreme f i bre , the greater
will be the lever arm f urnished for the internal resisting
couple . If the ratio of moment d ue to self wei ght to total
moment M 1M is suf fi c iently large , there is li ttle danger o f G T
o verstressing the flanges at transfer , and concrete in the
bottom flange can be accordingly d iminished . It may not be
economi c ally used, however where M 1M rat io is small , because G T
the center o f pressure at transfer may l i e below the bottom
kern po int . Then tensile stress may result in the top fl ange
and h i gh compressive stresses in the bottom flange.
The box secti on has th e same properti es as the I-section
in resisting moment . For ec onomy in steel and concrete it is
best to put the c oncrete near the extreme f i bres of the