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UNIVERSITI PUTRA MALAYSIA
LIMIT CRITERIA OF POST-TENSIONED THIN WEB BEAMS
LEE TEANG SHUI
FK 1989 1
It is hereby certified that we have read this thesis entitled 'Limit Criteria of Post-Tensioned Thin Web Beams' by Lee Teang Shui, and in our opinion it is satisfactory in terms of the scope, quality, and presentation as partial fulfilment of the requirements for the degree of Doctor of Philosophy
. . ....... . . .. . . . . . .
PETER MONTAGUE, Ph.D. Professor
Department of Engineering University of Manchester
(External Examiner)
��j. � • • • • • • • • • • • • • • • • rt • • • •
SHUAIB H. AHMAD, Ph.D. Associate Professor
North Carolina State University (External Examiner)
ZOHADIE BA DAlE, Ph.D. Associate Professor/Dean
Faculty of Engineering Universiti Pertanian Malaysia
(Internal Examiner)
.. . . . . . .. . .. . .. . . .
S. A. SALAM, Ph.D. Associate Professor
Faculty of Engineering Universitl PeTtanian Malaysia
(Internal Examiner/Supervisor)
» #
I certify that the Board of Examiners have met on October 14, 1989 to conduct the final examination of this candidate on his Doctoral thesis in accordance with Universiti Pertanian MalaYSia (Higher Degree) Act 1980 and Universiti Pertanian Malaysia (Higher Degree) Regulations 1981, and recommended that the candidate be awarded the relevant degree •
Date: 2 2 MAR 1990 . . . . . . . . . . . . . . . . . . . �.
AHMAD MAHDZAN AYOB, Ph.D. Professor/Dean of Graduate Studies
(Chairman, Board of Examiners)
This thesis was submitted to the Senate of Universiti Pertanian Malaysia and was accepted as fulfilment of the requirements for the degree of Doctor of Philosophy.
, -
Date: AHMAD MAHDZAN AYOB, Ph.D. Professor/Dean of Graduate Studies
LIMIT CRITERIA OF POST-TENSIONED THIN WEB BEAMS
By
LEE TEANG SHUI
A Thesis Submitted in Partial Ful filment of the Requirements for the Degree of Doctor of Philosophy
in the Faculty of Engineering Universiti Pertanian Malaysia
october 1989
ACKNOWLEDGEMENTS
The a ut hor wi s he s to record hi s apprec i at i o n a nd
grat itude to hi s s upervisor Dr . S . A . S a l a m, Depart me nt
o f civ i l a nd Env i ro nme nt a l Eng i ne e r i ng , Uni ve r s i t i
Pe r t a n i a n Ma l a ys i a (UPM ) fo r hi s s up e rv i s i o n,
e ncourageme nt a nd co mments . Appreciation is also due to
Ir . Aba ng Abdul l a h b i n Aba ng Al i , Profes sor a nd former
Dea n of Fa cul t y of Eng i neering , Univers i t i Perta ni a n
Ma l a ys i a , Dr . Mo hd . Zo hadie Barda i e , t he Dea n o f t he
Faculty of Engi neeri ng, Universiti Perta ni a n Mal a ys ia ,
a nd above a l l , Unive r s i t i Pert a ni a n Ma l a ys i a for t he
s upport prov ided . Recog ni t i o ns of apprec iat i o n are
a l s o d ue to t he Li b r a r y A ut ho r i t i e s i n Uni v e r s i t i
Ma l a ya , Univers i t i Tek no l og i Ma l a ys i a a nd Unive r s i t i
Pertanian Malaysia for provid i ng excel l e nt services and
s o ur c e s wher e mo s t o f t he l i t e r a t ur e rev i e wed a r e
obta i ned. The a ut hor wi s hes t o e xpre s s hi s profo und
grat i t ude t o En . B a harud i n b i n Abd ul Ka r i m fo r t he
val ua ble ass ista nce give n, without which the laboratory
e xp e r i me nt s und e r t a ke n wo ul d no t ha ve b e e n d ul y
compl eted in the scheduled time. Tha nks are also due to
Hj. Gha za l i b i n Said, En. Mesra n bi n Rasan, En. Sul e ima n
b i n Abdul Azi z, En. Jo hn Posko Amalara j, En. Ga nesan a /I
Pat hayappan and En. Sahat bin Daud, all o f who m have i n
o ne wa y o r a no t he r , he lped dur i ng t he c o ur s e o f t he
e xperime nts. The author is grateful to Dr . Douglas C.
ii
G o o de f rom t h e D ep a r tmen t o f c i v i l E n g i n e er i ng ,
University o f Manchest er, Un i t ed Kingdom, f o r h i s
advice given during his short visit to the Faculty o f
Engineeri ng, Universiti Pertanian Mal aysia, in 1 9 88,
u n der t h e a c a dem i c l i n k f o st er ed b et w een t h e tw o
universities .
Lee, Teang Shui
Universiti Pertanian Malaysia S erdang , 4 3 4 00 Selangor Darul Ehsan Mal aysia
October 1989
iii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF PLATES
LIST OF SYMBOLS
ABSTRACT
ABSTRAK
CHAPTERS
I INTRODUCTION
General
Advantages of Prestressed Concrete Over Reinforced Concrete
Pretens ioned and Posttensioned Prestressed Concrete
Bonded and Unbonded Posttensioned Prestressed Concrete
Partially Prestressed Concrete
Definition
Development of Partial Prestressing
Advantages and Disadvantages
I and T sections
Limit Criteria for Prestressed Concrete
Objectives and Scope of Work
iv
PAGE
i i
x
x i i
xvi
xix
xxi i
xxiv
1
1
5
7
8
1 0
1 0
13
16 18
19
2 4
II FLEXURAL STRENGTHS OF PARTIALLY PRESTRESSED CONCRETE MEMBERS
PAGE
28
Introduction 28
Steel Stresses in Prestressed Concrete Beams 3 2
Determination of the Neutral Axis Depth 38
Code Provisions 41
Flexural Strengths of Partially Prestressed Beams by the strain Compability Method 43
III SHEAR STRENGTHS OF PARTIALLY PRESTRESSED CONCRETE MEMBERS 52
IV
V
Introduction to Shear in Prestressed Concrete
I and T sections
Shear Strength of Partially Prestressed Concrete Beams
Ultimate Shear Prescribed by Code of Practice BS 8 110:198 5
FLEXURAL CRACKS IN PARTIALLY PRESTRESSED CONCRETE
Introduction
Cracking Load
Predicting Maximum Crack width
DEFLECTION OF PARTIALLY PRESTRESSED FLEXURAL MEMBERS
Introduction
Predicting Deflection and Camber
v
5 2
6 1
64
66
72
72
75
77
87
87
89
VI EXPERIMENTAL PROGRAM
General Description of Model Beams
constant and Varying Parameters of the Beams
Concrete : Mix Design for strength
Prestressing steel, Normal Reinforcement and Web Reinforcement
Ducts and Grouting for Prestressing Tendons
End Blocks
Prestressing of Tendons and Measuring of Camber
Beam Testing Procedure
Beam Testing Errors
PAGE
99
99
104
105
106
107
108
108
109
110
VII EXPERIMENTAL RESULTS 112
Presentation of Theoretical Calculations and Experimental Data 112
strain Measurements 113
VIII DISCUSSION 166
Flexure 166
Theoretical Predictions and Observed Ultimate Flexural Failure 166
Effect of Bond on Ultimate Flexural Load 169
Effect of Prestress on Ultimate Flexural Load 170
Effect of Additional Reinforcements on Ultimate Flexural Load 172
vi
PAGE
Prediction of Ultimate Flexural Moment by Code BS 8110 173
Shear 175
Shear Cracking Resistance of Prestressed Concrete 175
Theoretical and Experimental Shear Cracking Strength 176
Effect of Deformed Bars on the First-shear-cracking Load on Concrete in Prestressed Concrete Beams 179
Effect of Shear Reinforcement on First-shear-cracking Load on Concrete in Prestressed Concrete Beams 180
Effect of Prestress on First-shear-cracking Load on Concrete 182
Combined Effect of Prestress, Additional Reinforcements and Shear Reinforcement on First-shear-cracking Load on Concrete 182
Predicted Ultimate Shear Strength and Experimental Ultimate Shear Strength of Concrete in Prestressed Concrete Beams 184
Effect of Shear Reinforcements on the Ultimate Shear Strength of Prestressed Concrete Beams 185
Combined Effect of Deformed Bars and Shear Reinforcements on the Ultimate Shear Strength of Prestressed Concrete Beams 187
Effect of Bond on Shear strengths of the Partially Prestressed Beams 187
Serviceability of Beams not Reinforced in Shear 188
Cracking Load, Number of Cracks, Crack Width and Crack Spacing 189
General 189
Cracking Load 191
vii
IX
PAGE
Number of Cracks 194
Crack width 2 09
Crack Spacing 2 2 2
Effect of Bond on Cracking Load , Number of Cracks and Crack width 2 2 4
Factors controll ing Serviceabi l ity 2 2 7
Deflection 2 2 9
Effect of Shear Reinforcements on Deflection 2 2 9
Effect of Deformed Bars on Deflection 2 3 4
Predicting Defl ection of the Prestressed Beams 2 3 5
Effect of Bond on Deflection 2 36
CONCLUSIONS AND RECOMMENDATIONS
Conclusions
Ultimate Load
Shear Strength
Flexural Cracking
Deflection
Recommendations
REFERENCES
APPENDICES
A End Block in Posttensioned Beams
B Design of Normal Concrete Mixes by DOE Method
v i i i
2 3 9
2 3 9
2 3 9
2 4 0
241
2 4 3
243
2 4 5
2 56
2 56
2 5 7
C HP4 1C Program for Determining Neutral Axis and Calculat ing Ultimate Moment
D HP4 1C Program for Determining Serv ice Stresses and cracking Load
E HP4 1C Program for Determining centroi d of T Beams
F HP4 1 C Program for Calculating Deflection by Naaman's Method
G HP4 1 C Program for Calculating De flection (after Goode )
H HP4 1 C Program for Crack width
I HP4 1 C Program for Students' T stati stical Test for Pa ir Observations
J Analysis of Partially Prestressed Concrete Beams for Testing
K Ca lculation of Crack widths
VITA
L Theoretical Calculations, Experimental Data and Observations of Model Beams
ix
PAGE
2 58
2 63
2 65
2 67
2 70
2 72
2 7 6
2 7 8
2 85
2 88
3 06
LIST OF TABLES
TABLE
1 criteria for Serviceability Limits
PAGE
in Prestressed concrete Beams 22
2 Limit States for Prestressed Concrete (BS 8 1 10 : 198 5) 23
3 Comparison of Experimental Ultimate Flexural Load to Theoretical Ultimate Flexural Load for Beams Designed to Fail in Flexure 167
4 Comparison of Experimental Ultimate Flexural Load to Theoretical Ultimate Flexural Load for Beams Designed to Fail in Shear 168
5 Increase in Ultimate Load (experimental) Capacity of Prestressed Beams Due to Prestress or Nonprestress Reinforcements 171
6 Experimental and Code-calculated Ultimate Moment of Prestressed Beams 174
7 Shear Strengths of Experimental Partially Prestressed Concrete Beams 178
8 Combined Effect of Prestress, Additional Reinforcements and Shear Reinforcements on Concrete Shear Cracking Resistance (Loads at Shear Cracking, KN) 183
9 Combined Effect of Additional Deformed Bars and Shear Reinforcements on Experimental Shear Strength of Prestressed Concrete 183
10 serviceability of Beams Not Reinforced in Shear 190
1 1 Comparisons of Cracking Loads 193
12 Cracking Load of Beams with 76 mm Web and Various Levels of Prestress and Deformed Bars . (Beam Number in Circle) 195
13 Cracking Load of Beams with 56 mm Web and Various Levels of Prestress and Deformed Bars. (Beam Number in Circle) 196
x
TABLE
14
1 5
16
17
18
19
20
21
Summary of Calculations of Crack width by Various Methods
Observed and Calculated Average Crack Spacing
Loads at 12 mm and 20 mm Deflection of 76 mm Web Prestressed Beams With Shear Reinforcements
Loads at 12 mm and 20 rom Deflection of 76 mm Web Prestressed Beams without Shear Reinforcements
Loads at 12 mm and 20 mm Deflection of 56 mm web Prestressed Beams With Shear Reinforcements
Loads at 12 mm and 20 mm Deflection of 56 mm Web Prestressed Beams without Shear Reinforcements
Effect of Shear Reinforcement on Deflection of 76 mm Web and 56 mm Web Prestressed Beams. (Ratio of Loads of Prestressed Beams with and without Shear Reinforcements at Respective Deflections)
Calculated and Experimental Total Deflections of Prestressed Beams
xi
PAGE
2 11
2 23
231
231
232
232
233
237
FIGURE
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
LIST OF FIGURES
Classification of Prestressed Concrete (Flexural Members)
stress s train Conditions At Ultimate Load Condition
Crack Patterns and Idealiz ed Zone structures (After Moayer and Reagan, 1 9 7 4)
Types of Cross sections of Experimental Beams
strain Distribution Along Depth At Mid Span of Beam 4 at Various Loadings
strain Distribution Along Depth At Midspan of Beam 9 at Various Loadings
strain Distribution Along Depth At Midspan of Beam 14 at Various Loadings
strain Distribution Along Depth At Midspan of Beam 2 5 at Various Loadings
strain Distribution Along Depth At Midspan of Beam 27 at Various Loadings
strain Distribution Along Depth At Midspan of Beam 3 2 at Various Loadings
strain Distribution Along Depth At Midspan of Beam 3 7 at Various Loadings
Load vs Deflection Graphs for Beams 1, 3, 5, 7 and 9 .
1 3 Load v s Deflection Graphs for Beams 2 , 4 , 6, 8 and 10.
14
15
16
Load vs Deflection Graphs for Beams 1 1 , 1 2 , 13, 14 and 15.
Load vs De flection Graphs for Beams 16, 1 8 , 2 0 , 2 2 and 2 4.
Load vs Deflection Graphs for Beams 17, 19, 2 1, 2 3 and 2 5 .
xii
PAGE
4
46
56
1 0 0
1 2 6
1 2 7
1 2 8
1 2 9
1 3 0
1 3 1
1 3 2
1 3 3
134
135
1 3 6
1 3 7
FIGURE
17
18
19
2 0
2 1
2 2
2 3
2 4
2 5
26
2 7
28
2 9
3 0
3 1
Load vs Deflection Graphs for Beams 2 6 , 2 8 , 3 0 and 3 2.
Load vs Deflection Graphs for Beams 2 7 , 2 9 , 3 1 and 3 3.
Load vs Deflection Graphs for Beams 3 4 , 3 5 , 3 6 and 3 7 .
Load vs Deflection Graphs for Beams 38, 4 0 , 4 2 and 4 4.
Load vs Deflection Graphs for Beams 3 9 , 4 1 , 4 3 and 4 5.
Comparisons of Load Deflection Behavior for Beams with 76 mm Thick Web and 2 Prestressing Tendons
Comparisons of Load Deflection Behavior for Beams with 76 rom Thick Web and 4 Prestressing Tendons
Comparisons of Load Deflection Behavior for Beams With 76 mm Thick Web and 6 Prestressing Tendons
Comparisons of Load Deflection Behaviour for Beams With 76 mm Thick Web and 8 Prestress ing Tendons
Comparisons of Load Deflection Behaviour for Beams with 56 rom Thick Web and 2 Prestressing Tendons
Comparisons of Load Deflection Behaviour for Beams with 56 mm Thick Web and 4 Prestressing Tendons
comparisons of Load Deflection Behaviour for Beams with 56 mm Thick Web and 6 Prestress ing Tendons
Load vs Total Number of Cracks Graphs for Beams 1 , 3 , 5 , 7 & 9 .
Load vs Total Number of Cracks Graphs for Beams 11 , 12 , 13 , 14 & 15 .
Load vs Total Number of Cracks Graphs for Beams 16 , 18 , 2 0 , 2 2 & 2 4.
xiii
PAGE
1 3 8
1 3 9
1 4 0
1 4 1
1 4 2
1 4 3
1 4 4
145
146
147
148
149
150
151
152
FIGURE
32
3 3
3 4
3 5
36
3 7
38
39
4 0
4 1
42
4 3
4 4
4 5
46
47
48
Load vs Total Number of Cracks Graphs for Beams 17 , 19, 21 , 23 & 25 .
Load vs Total Number of Cracks Graphs for Beams 26 , 28 , 3 0 and 3 2.
Load vs Total Number of Cracks Graphs for Beams 3 4 , 3 5 , 36 & 37 .
Load vs Total Number o f Cracks Graphs for Beams 3 8 , 4 0 , 42 & 4 4 .
Load vs Maximum Crack Width Graphs for Beams 1 , 3 , 5 , 7 & 9 .
Load vs Maximum Crack width Graphs for Beams 2 , 4 , 6 , 8 & 1 0 .
Load vs Maximum Crack width Graphs for Beams 11, 12 , 13 , 14 & 15 .
Load vs Maximum Crack width Graphs for Beams 16, 18 , 20 , 22 & 24 .
Load vs Maximum Crack Width Graphs for Beams 26 , 28 , 3 0 & 3 2.
Load vs Maximum Crack width Graphs for Beams 27 , 29 , 3 1 & 3 3 .
Load vs Maximum Crack width Graphs for Beams 3 8 , 4 0 , 42 & 4 4
Load vs Maximum Crack width Graphs for Beams 3 4 , 3 5 , 36 & 3 7 .
Load vs Maximum Crack Width Graphs for Beams 17 , 19 , 21, 23 & 25 .
Load vs Maximum Crack width Graphs for Beams 39 , 4 1 , 4 3 & 4 5 .
Flexural cracking Pattern of 76 mm Web Beams with Shear Reinforcements and 0 Deformed Bars.
Flexural Cracking Pattern of 76 rom Web Beams without Shear Reinforcements and with 0 Deformed Bars.
Flexural Cracking Pattern of 76 mm Web Beams with Shear Reinforcements and 2 Deformed Bars .
xiv
PAGE
1 5 3
1 5 4
155
1 56
1 57
158
159
160
161
162
163
164
165
165
198
199
200
FIGURE PAGE
49 Flexural Cracking Pattern of 7 6 mm Web Beams with Shear Reinforcements and 4 Deformed Bars . 20 1
5 0 Flexural Cracking Pattern o f 7 6 mm Web Beams Without Shear Reinforcements and With 4 Deformed Bars . 2 0 2
5 1 Flexural Cracking Pattern of 56 mm Web Beams with Shear Reinforcements and 0 Deformed Bars. 2 0 3
5 2 Flexural Cracking Pattern o f 56 mm Web Beams Without Shear Reinforcements and 0 Deformed Bars . 2 04
5 3 Flexural Cracking Pattern of 56 mm Web Beams With Shear Reinforcements and 2 Deformed Bars. 2 05
54 Flexural Cracking Pattern of 56 mm Web Beams With Shear Reinforcements and 4 Deformed Bars . 2 0 6
5 5 Fl exural Cracking Pattern o f 5 6 mm Web Beams without Shear Reinforcements and with 4 Deformed Bars . 2 0 7
xv
PLATE
1
2
3
4
5
6
7
8
9
10
1 1
12
LIST OF PLATES
Beam 1 ( 76 mm Web ) with Wide Flexural Cracks and No Shear Cracks . Good Recovery on Unloading .
Diagonal Tension Shear Failure of Lightly Prestressed Beam 2 .
Few and Widely Spaced Cracks With Wide Opening of Lightly Prestressed Beam 3 .
Beam 4 ( 76 rom Web ) Unreinforced in Shear , Failed in Flange compression in Flexural Span .
Beam 5 ( 76 mm Web ) Unbonded Failed in Flexure with Wide Cracks. Excel lent Recovery Upon Unloading As Shown .
Beam 6 ( 76 mm Web ) Unbonded with No Shear Reinforcements , Fai led in Flange compress ion .
Flexural-shear Failure of Highly Prestressed Beam 7 After Exceeding Theoretical Loads .
Shear-compression Failure of Very Highly Prestressed Beam 8 without Shear Reinforcement .
Beam 9 (76 mm web , On Release of Load ) Failed With Flange Compress ion
Shear compress ion Failure o f Beam 10 With Very High Prestress, without Shear Reinforcement and At Equal Theoretical Flexural Load .
Beam 1 1 ( 76 mm web , With Load Released) Failed in Shear Compression on Left Load Point .
Flange Comrpess ion Flexural Failure of Beam 12 At Equal To Theoretical Flexural Load .
xvi
PAGE
1 1 5
1 15
1 1 5
1 16
1 16
1 16
1 16
1 17
1 17
1 17
1 17
1 17
PLATE
1 3
1 4
1 5
16
17
18
19
20
2 1
2 2
2 3
2 4
2 5
26
PAGE
Violent Flexural Failure of Unbonded Beam 1 3 ( 76 mm Web ) . 1 18
Flexural Shear Failure After Exceeding Theoretical Loads of Highly Prestressed Beam 14 . 1 18
Shear Compression State After Recovery of Very Highly Prestressed Beam 15 With 8 Tendons and 2 Deformed Bars . 1 18
Flexural Failure of Beam 16 With 2 Prestressing Tendons and 4 Deformed Bars . Flange Compression and Flexural Web Disturbance . 1 19
Recovered Diagonal Tension Shear Failure of a Lightly Prestressed Beam with the Aid of 4 Deformed Bars . 1 19
Medium Prestress Beam 18 Just After Exceeding Theoretical Ultimate Flexural Capacity . 1 19
Diagonal Tension and Bar Tension Failure of Beam 19 . 1 19
Flange crushing Flexural Failure of Unbonded Beam 2 0. 1 19
Wel l-recovered Shear Failure with the Aid of 4 Deformed Bars , of Beam 2 1.
Flange Compression Failure o f Beam
1 2 0
2 2 ( 76 mm Web , with Load Rel eased) . 1 2 0
Recovery o f Beam 2 3 with High Prestress and Deformed Bars, After Failing in Shear . 120
Violent Shear Compression Failure of Highly Prestressed Beam 2 4 (76 mm Web) . 12 1
Very Highly Prestressed Beam 2 5 , Failing in Shear in Tensioned bars , and At Ful l Recovery . 1 2 1
Typical Wide Crack of Low Prestressed Beam Failing in Flexure ( Beam 26 with 56 mm Web ) . 1 2 1
xvii
PLATE
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
PAGE
Fewer Cracks of Beam 27 (56 mm Web) without Shear Reinforcements . 122
Very Thin Beam 28 After Shear Failure . 122
Large and Few Cracks of Bonded Beam 29 . 122
Explosive Web Cum Flange Crushing of High Prestress 56 rom Web Beam 32 . 122
Flexural Failure of Beam 33 . 123
Flange Heaving Failure of Beam 34 (56 mm Web) 123
Flexural Failure of Beam 35 With 4 Tendons and 2 Deformed Bars (133 kN) 123
Shear Compression Failure of Beam 37 (56 mm Web) . 123
Flexural Failure of Beam 38 with 2 Tendons and 4 Deformed Bars (121 kN) 123
Diagonal Shear and Tensioned Bar Failure of Lightly Prestressed Thin Beam 39 . 124
Flexural Flange Crushing of Bonded Beam 40 After Exceeding Theoretical Ultimate Flexural Load . 124
Laterally Explosive Web Crushing Failure With Secondary Failure in Separation of Deformed Bars in Beam 41 (56 mm Web) . 124
Violent Laterally Explosive Web Crushing of Thin Web (56 mm) Beam 43 with 4 Prestressing Tendons and 4 Deformed Bars. 124
Flange Compression Failure of Beam 44 with 56 rom Web, 6 Prestressing Tendons and 4 Deformed Bars . 125
Tensioned Bar Shear Failure of Beam 45 with 6 Tendons and 4 Deformed Bars and without Stirrups . 125
xviii
f ci
f cu
G k
Q k
V TSR
v s
LIST OF SYMBOLS
concrete strength at transfer
concrete cube compressive strength, N/mm2
Dead load
Appl ied l oad
Material partial safety factor
Total shear resistance of a section
Shear resistance of a 4 5° strut inclination truss anal ogy
v Ultimate shear cracking resistance of a c sect ion of the concrete
V Web shear cracking capacity of a section-co uncracked in fl exure
V cr
b w
h
f t
f cp
Fl exural shear cracking capacity of a section cracked in flexure
Web width of T beam
Total depth of T beam
Maximum principal tensile stress
compressive stress at the centroidal axis due to prestress, taken as positive
f Effect ive prestress in the tendons after all pe losses have occurred .
f pu
v c
d e
Strength of a prestressing tendon
concrete shear stress
Effect ive depth of steel reinforcements
xix
M 0
M u
V
A ps
A nps
A sv
S v
f y
f yv
d t
v u
b we
f ps
€ ps
x
m
E s
E c
h f
Moment necessary to produce zero stress in the concrete at the extreme tension fibre .
Bending moment value at the section due to the particular ultimate load condition
Shear force value at the section due to the particular ultimate load condition
Total area of prestress ing tendon section
Total area of nonprestressed steel section
Cross-sectional area of two l egs of a l ink/strirrup
Link/stirrup spacing
strength of a nonprestressed steel bar
Strength of the shear reinforcement
Depth to the bottom most longitudinal reinforcement
Maximum shear stress of concrete
Effective web width of T beam
Stress in prestressed tendon
Strain inprestressed tendon
Depth to neutral axis
Modular ratio
Elastic modulus of steel
Elastic moudlus of concrete
Flange depth
xx
f 6 i nc h dia meter x 12 i nc h cyl i nder c' co mpress ive stre ngt h at 28 da ys
f Des ign tens ile stress in t he tendons p b
d n
Dept h to t he ce ntro id of t he compressio n zone or O . 45 x if fla nge t hickness e qual or more t ha n O . 9 x
€ Co ncrete strai n at e xtre me compressio n fi bre cu
a stress
xxi
ABSTRACT
Abstract of thesis sub mitted to t he S enate of Univers iti Pe rt a n i a n Ma l a ys i a , i n p a r t i a l ful fi l me n t o f t he re quirements for the degree of Doctor of Philosophy.
LIMIT CRITERIA OF POST-TENSIONED THIN WEB BEAMS
s upervisor Faculty
By
LEE TEANG SaUl
October, 1 9 8 9
Dr. S . A. Salam Engineering
A total of 45 partiall y prestressed post-tensioned
t hi n web T-b e a ms we re t e s t e d t o i n ve s t i ga t e t he i r
ul t i ma t e s he a r a n d fl e xur a l s t r e n g t hs a n d t he
s e rviceab i l it y l i mits o f defl ect i on and crack width.
The varying para meters inc l uded in t he s t udy are t he
a mo un t o f p r e s t r e s s , a mo un t o f s up p l e me n t a r y
nonprestressed reinforc e ment s , prestre s s ing tendons
being bonded or unbonded , absence or presence o f s hear
r e i n fo r c e me n t s a n d w i d t h o f t he we b . A s t r a i n
co mpatibil ity met hod with the associated bond factors i s
presented for the ult i mate fle xural strength analys i s of
t he b e a ms . Fo r p r e d i c t i o n o f t he o r e t i c a l l o a d s ,
mat e r i a l c haract e r i s t i c s are t a ken a t t he i r ul t i mate
wit h no materials safety factor associated. Equil ibrium
o f forces and a tril inear stress stra in relations hip for
xxi i