SHEAR STRENGTH OF END REGIONS OF PRESTRESSED  
 
SELF-CONSOLIDATING CONCRETE BEAMS 
 
 
 
 
 
Except where reference is made to the work of others, the work described in this 
thesis is my own or was done in collaboration with my advisory committee. This 
thesis does not include proprietary or classified information. 
 
 
 
 
_________________________ 
Mustafa ?spir G?rb?z 
 
 
 
Certificate of Approval: 
 
 
 
_____________________________ 
Anton K. Schindler 
Gottlieb Associate Professor 
Civil Engineering 
 
 
 
_____________________________ 
Mary L. Hughes 
Assistant Professor 
Civil Engineering 
 
_____________________________ 
Robert W. Barnes, Chair 
James J. Mallett Associate Professor 
Civil Engineering 
 
 
 
_____________________________ 
Joe F. Pittman 
Interim Dean 
Graduate School 
 
SHEAR STRENGTH OF END REGIONS OF PRESTRESSED  
 
SELF-CONSOLIDATING CONCRETE BEAMS 
 
 
 
Mustafa ?spir G?rb?z 
 
 
 
A Thesis 
Submitted to 
the Graduate Faculty of 
Auburn University 
in Partial Fulfillment of the 
Requirements for the 
Degree of 
Master of Science 
 
 
 
Auburn, Alabama 
May 10, 2008
 iii 
SHEAR STRENGTH OF END REGIONS OF PRESTRESSED  
 
SELF-CONSOLIDATING CONCRETE BEAMS 
 
 
Mustafa ?spir G?rb?z 
 
Permission is granted to Auburn University to make copies of this thesis at its discretion, 
upon request of individuals or institutions and at their expense. The author reserves all 
publication rights. 
 
 
 
 
 
 
______________________________ 
Signature of Author    
 
 
 
______________________________ 
Date of Graduation    
 iv 
VITA 
Mustafa ?spir G?rb?z, son of Fikret and Nuran G?rb?z, was born July 8, 1984, in 
Ankara, Turkey. He graduated from TED Ankara College Private High School in 2001. 
He attended Middle East Technical University in Ankara, Turkey and graduated as a high 
honor student in June 2005 with a Bachelor of Science degree in Civil Engineering with 
Structural Mechanics as undergraduate specialization. He entered Graduate School at 
Auburn University in January 2006. 
 v 
THESIS ABSTRACT 
SHEAR STRENGTH OF END REGIONS OF PRESTRESSED 
  
SELF-CONSOLIDATING CONCRETE BEAMS 
 
 
Mustafa ?spir G?rb?z 
Master of Science, May 10, 2008 
(B.S., Middle East Technical University, Ankara, Turkey, 2005) 
 
108 Typed Pages 
Directed by Robert W. Barnes 
 
Understanding of the shear and bond performance of self-consolidating concrete 
(SCC) is vital to fully implement SCC usage in structures. State highway structures are a 
potential application for prestressed SCC systems once more knowledge is gained 
regarding this performance. 
In order to investigate the shear and bond performance of end regions of 
prestressed SCC beams, several conventional and SCC prestressed T-beams were tested 
in flexure with unequal shear spans. Displacement and strand end slip were measured as 
the specimens were loaded to failure. These results are provided together with behavioral 
descriptions. Results were analyzed using flexural beam theory and AASHTO LRFD 
design provisions.
 vi 
It was concluded that AASHTO LRFD shear specifications provide overly 
conservative provisions for high strength (SCC) beams not fully utilizing superior bond 
characteristics of SCC systems.
 vii 
ACKNOWLEDGEMENTS 
 
Funding of this research was provided by the Alabama Department of 
Transportation.  
I would like to thank Dr. Robert W. Barnes for his continuous support, 
encouragement and understanding throughout my study in Auburn. I would like to thank 
my committee members Dr. Mary L. Hughes and Dr. Anton K. Schindler for their 
invaluable advice and help. I would also like to thank Billy Wilson for all his help during 
the experiments. 
I would like to thank my Middle East Technical University professors Dr. Cem 
Topkaya for helping me get to Auburn as well as Dr. U?ur Ersoy, to whom I owe my 
love for my profession. 
 viii 
Style manual used 
Chicago Manual of Style      
Computer software used 
Microsoft Word, Microsoft Excel    
 ix 
TABLE OF CONTENTS 
 
LIST OF FIGURES ......................................................................................................... xiii 
LIST OF TABLES........................................................................................................... xvi 
CHAPTER 1. INTRODUCTION ....................................................................................... 1 
1.1. Background.............................................................................................................. 1 
1.2. Research Objectives................................................................................................. 2 
1.3. Research Scope ........................................................................................................ 2 
1.4. Organization of Thesis............................................................................................. 3 
1.5. Notation.................................................................................................................... 4 
CHAPTER 2. BACKGROUND ON THE DESIGN OF REINFORCED CONCRETE 
BRIDGE SYSTEMS TO RESIST SHEAR........................................................................ 5 
2.1. Shear Behavior......................................................................................................... 5 
2.2. Principal Stress Analyses......................................................................................... 6 
2.3. Mohr?s Circle........................................................................................................... 6 
2.4. Diagonal Cracking ................................................................................................... 8 
2.4.1. Flexure-shear cracking...................................................................................... 8 
2.4.2. Web-shear cracking .......................................................................................... 9 
2.5. Behavior After Diagonal Cracking .......................................................................... 9 
2.6. Failure Modes .......................................................................................................... 9
 x 
2.7. Compression Field Theory..................................................................................... 11 
2.8. Modified Compression Field Theory..................................................................... 12 
2.9. AASHTO Shear Provisions ................................................................................... 14 
2.9.1. Sectional design method ................................................................................. 14 
2.9.2. General procedure........................................................................................... 14 
2.9.3. Simplified procedure....................................................................................... 16 
2.9.4. Minimum transverse reinforcement requirement............................................ 16 
2.9.5. Maximum aggregate size ................................................................................ 17 
2.9.6. Longitudinal reinforcement demand............................................................... 18 
2.9.7. Critical section for shear ................................................................................. 19 
2.9.8. Strut-and-Tie Modeling .................................................................................. 19 
2.10. Simplified Modified Compression Field Theory................................................. 20 
2.11. High-Strength Concrete ....................................................................................... 20 
CHAPTER 3. SPECIMEN PROPERTIES AND TESTING............................................ 21 
3.1. Introduction............................................................................................................ 21 
3.2. Specimen Identification ......................................................................................... 22 
3.3. Material Properties................................................................................................. 24 
3.3.1. Prestressing steel............................................................................................. 24 
3.3.2. Mild reinforcing steel...................................................................................... 24 
3.3.3. Concrete .......................................................................................................... 25 
3.4. Prestressing Parameters ......................................................................................... 28 
3.5. Test Setup and Instrumentation ............................................................................. 28 
3.6. Instrumentation ...................................................................................................... 32 
 xi 
3.6.1. Measurement of applied load.......................................................................... 32 
3.6.2. Measurement of displacements....................................................................... 33 
3.6.3. Measurement of strand slip............................................................................. 34 
3.6.4. Measurement of strains at extreme compression fibers.................................. 34 
3.6.5. Data acquisition .............................................................................................. 35 
CHAPTER 4. TEST RESULTS ....................................................................................... 36 
4.1. Introduction............................................................................................................ 36 
4.2. Specimen STD-M-E............................................................................................... 36 
4.3. Specimen STD-M-W ............................................................................................. 42 
4.4. Specimen SCC-MS-E ............................................................................................ 46 
4.5. Specimen SCC-HS-W............................................................................................ 50 
4.6. Specimen SCC-HS-E............................................................................................. 53 
4.7. Summary of Test Results....................................................................................... 57 
CHAPTER 5. ANALYSIS AND DISCUSSION ............................................................. 59 
5.1. Flexural Analysis ................................................................................................... 59 
5.2. AASHTO LRFD Shear Analyses .......................................................................... 66 
5.2.1. Shear cracking................................................................................................. 66 
5.2.2. Shear capacity ................................................................................................. 69 
5.2.3. Post-cracking tension demand ........................................................................ 71 
5.3. Transverse Reinforcement ..................................................................................... 75 
5.3.1. Effect of transverse reinforcement on post-cracking tension demand............ 75 
5.3.2. Transverse reinforcement spacing .................................................................. 78 
CHAPTER 6. CONCLUSION AND RECOMMENDATIONS ...................................... 83 
 xii 
6.1. Summary................................................................................................................ 83 
6.2. Conclusions............................................................................................................ 83 
6.3. Recommendations.................................................................................................. 85 
REFERENCES ................................................................................................................. 86 
APPENDIX A. NOTATION ............................................................................................ 89 
 xiii 
LIST OF FIGURES 
Figure 2-1. Width-averaged shear stress distributions on rectangular and T sections........ 5 
Figure 2-2. Mohr?s Circles for nonprestressed and prestressed beam elements................. 7 
Figure 2-3. Flexure-shear and web-shear cracks (Naaman 2004) ...................................... 8 
Figure 2-4. Major shear failure modes (Naaman 2004).................................................... 10 
Figure 2-5. Stress-strain relationship for cracked concrete in compression ..................... 12 
Figure 2-6. 3-D Representation of compressive stress-strain relationship ....................... 13 
Figure 2-7. Average stress strain relationship for concrete in tension.............................. 13 
Figure 3-1. Specimen cross section detail (Levy 2007).................................................... 22 
Figure 3-2. Specimen identification system of Levy (2007) ............................................ 23 
Figure 3-3. Specimen identification system used in this study......................................... 24 
Figure 3-4. Test setup diagram ......................................................................................... 29 
Figure 3-5 Test setup ........................................................................................................ 29 
Figure 3-6. Neoprene pads, steel supports and concrete blocks ....................................... 31 
Figure 3-7. Hydraulic actuator and force transducer ........................................................ 32 
Figure 3-8. Potentiometers................................................................................................ 33 
Figure 3-9. Strand slip measurement ................................................................................ 34 
Figure 3-10. Data acquisition system................................................................................ 35 
Figure 4-1. Applied load and strand slips vs. load point displacement - STD-M-E......... 37 
Figure 4-2. Initial crack at 32 kips applied load ? STD-M-E ........................................... 38
 xiv 
Figure 4-3. Final state of crack at the end of test? STD-M-E........................................... 39 
Figure 4-4. Shear tension failure showing loss of bond ? STD-M-E ............................... 39 
Figure 4-5. Load point displacement and strand slip versus time ? STD-M-E ................ 40 
Figure 4-6. Applied load and strand slip versus time ? STD-M-E ................................... 41 
Figure 4-7. Applied load and strand slips versus load point displacement - STD-M-W.. 42 
Figure 4-8. STD-M-W: Initial crack at 27.2 kips applied load - STD-M-W.................... 43 
Figure 4-9. STD-M-W: Final state of crack at the end of test - STD-M-W ..................... 44 
Figure 4-10. Load point displacement and strand slip versus time - STD-M-W.............. 45 
Figure 4-11. Applied load and strand slip versus time - STD-M-W ................................ 45 
Figure 4-12. Applied load and strand slips versus load point displacement - SCC-MS-E46 
Figure 4-13. Flexural cracks under load point at 51kips applied load - SCC-MS-E........ 47 
Figure 4-14. Flexural cracks under load point at 56 kips applied load - SCC-MS-E....... 48 
Figure 4-15. Final condition of flexural cracks at the end of test - SCC-MS-E ............... 48 
Figure 4-16. Final condition at the end of test - SCC-MS-E ............................................ 49 
Figure 4-17. Applied load and strand slips versus load point displacement - SCC-HS-W
........................................................................................................................................... 50 
Figure 4-18. Flexural cracks under load point at 48 kips applied load - SCC-HS-W ...... 51 
Figure 4-19. Final condition of flexural cracks at the end of test - SCC-HS-W............... 52 
Figure 4-20. Final condition at the end of test - SCC-HS-W............................................ 52 
Figure 4-21. Applied load and strand slips versus load point displacement - SCC-HS-E 53 
Figure 4-22. Shear crack at 66 kips cracking load - SCC-HS-E....................................... 54 
Figure 4-23. Final state of the shear crack at the end of test - SCC-HS-E ....................... 55 
Figure 4-24. Load point displacement and strand slip versus time - SCC-HS-E ............. 56 
 xv 
Figure 4-25. Applied load and strand slip versus time - SCC-HS-E ................................ 56 
Figure 5-1. Layers for sectional analysis .......................................................................... 60 
Figure 5-2. Concrete fibers affected by tension stiffening ............................................... 61 
Figure 5-3. Flexural analysis result for STD-M-E............................................................ 62 
Figure 5-4. Flexural analysis result for STD-M-W .......................................................... 63 
Figure 5-5. Flexural analysis result for SCC-MS-E.......................................................... 63 
Figure 5-6. Flexural analysis result for SCC-HS-W......................................................... 64 
Figure 5-7. Flexural analysis result for SCC-HS-E .......................................................... 64 
Figure 5-8. Experimental versus valculated Vc values...................................................... 68 
Figure 5-9. Vc as function of ?x for sxe ? 15 in................................................................... 69 
Figure 5-10. Applied load at strand tension capacity for specimen STD-M-E ................ 73 
Figure 5-11. Applied load at strand tension capacity for specimen STD-M-W ............... 74 
Figure 5-12. Applied load at strand tension capacity for specimen SCC-HS-E............... 74 
Figure 5-13. Applied load at strand tension capacity for specimen STD-M-E with and 
without transverse reinforcement...................................................................................... 76 
Figure 5-14. Applied load at strand tension capacity for specimen STD-M-W with and 
without transverse reinforcement...................................................................................... 77 
Figure 5-15. Applied load at strand tension capacity for specimen SCC-HS-E with and 
without transverse reinforcement...................................................................................... 78 
Figure 5-16. Diagonal crack location of specimen STD-M-E.......................................... 80 
Figure 5-17. Diagonal crack location of specimen SCC-HS-E ........................................ 80 
Figure 5-18. Diagonal crack location of specimen SCC-M-W......................................... 81 
Figure 5-19. smax (maximum stirrup spacing) versus of dv (effective shear depth)........... 82
 xvi 
LIST OF TABLES 
Table 3-1. Mixture properties ........................................................................................... 26 
Table 3-2. Fresh properties ............................................................................................... 27 
Table 3-3. Hardened properties......................................................................................... 27 
Table 3-4. Previous testing results.................................................................................... 28 
Table 3-5. Test configuration dimensions and strand release conditions ......................... 30 
Table 4-1. Specimen cracking and ultimate loads and failure modes............................... 57 
Table 4-2. Crack positions of specimens .......................................................................... 58 
Table 5-1. Loads corresponding to flexural cracking and ultimate strength .................... 65 
Table 5-2. Cracking moments corresponding to crack locations...................................... 65 
Table 5-3. Shear capacity calculations based on applied maximum shear....................... 70 
Table 5-4. Shear capacity calculations based on Vn = Vu .................................................. 71 
Table 5-5. Tension demands compared to tension capacities........................................... 72 
Table 5-6. Cracking loads and reserve strengths of specimens ........................................ 79 
 1 
Chapter 1. Introduction 
1.1. Background 
Prestressed concrete is used as an efficient structural system for various applications 
worldwide. Prestressed, especially precast, concrete elements are preferred over 
conventionally reinforced concrete elements in many applications due to the efficiency 
and versatility they provide in construction, as well as their inherent durability. Use of 
high strength concrete has accelerated the widespread use of prestressed concrete 
elements. High-strength, self-consolidating concrete (SCC), however, has not yet been 
fully employed in prestressed concrete bridge structures because of lack of structural 
performance data related to its use.  
SCC, first developed in Japan in 1980?s, can be placed without time-consuming 
and costly vibration procedures, thereby making it economically beneficial. Although 
SCC is favored by the industry due to its efficiency in placing and finishing, some official 
specifications do not yet permit the use of SCC in prestressed concrete applications. 
Approval of the use of SCC in prestressed systems by transportation agencies awaits the 
results of further research. For example, shear and bond performance of prestressed SCC 
is a source of debate among researchers, transportation agencies and the industry. Shear 
and bond performance of SCC is an important issue because of the increased fine 
aggregate content that aids in creating the flowability of SCC.
 2 
1.2. Research Objectives 
The Alabama Department of Transportation (ALDOT) has sponsored an investigation by 
the Auburn University Highway Research Center into the use of SCC in prestressed 
concrete bridge girders. The primary objectives of the investigation are to: 
? Develop SCC mixtures for use in prestressed concrete bridge structures,  
? Evaluate the behavior of SCC mixtures in prestressed concrete girders, including 
fresh properties, early-age behavior, and long-term behavior, and 
? Develop implementation guidelines and recommendations for industry use.  
The study presented in this thesis is a portion of the aforementioned project. The primary 
objective of this study was to evaluate the shear and bond behavior of prestressed 
reinforcement in beams constructed with SCC and to evaluate the long-term performance 
of SCC when used in prestressed concrete girders. 
1.3. Research Scope 
This study consisted of an experimental investigation into the shear behavior of 
prestressed concrete beams. Five specimens, which were portions of beams previously 
tested by Levy (2007), were tested: two were made of conventional moderate-strength 
concrete, one was made with moderate-strength SCC and the remaining two were made 
of high-strength SCC. All of these mixtures were designed for implementation in 
pretensioned concrete bridge girders. Each of the five specimens was tested to failure 
with single-point loading positioned to create unequal shear spans. The behavior of the 
test specimens was compared with flexural analysis results and the provisions of 
American Association of State Highway and Transportation Officials Load and 
 3 
Resistance Factor Design (AASHTO LRFD) Bridge Design Specifications (2007) for 
shear. 
The mixing, fabrication, measurements, and testing of the beams were performed 
in the Structural Engineering Laboratory of the Auburn University Department of Civil 
Engineering. 
1.4. Organization of Thesis 
Chapter 2 provides a literature review including basic principles of shear behavior in 
structural concrete. Several theories developed to understand shear behavior of reinforced 
and prestressed concrete members are presented. AASHTO LRFD Specifications 
(AASHTO LRFD 2007) on shear design and analysis are described, including 
assumptions and rationalizations on which several approaches are founded.  
Chapter 3 provides a description of the design and fabrication of the prestressed 
specimens. The results of fresh and hardened property testing of the concrete mixtures as 
well as other experimental results obtained by Levy (2007) are presented in this chapter. 
The test setup and instrumentation are also presented in this chapter. 
Chapter 4 provides the results of the conducted experiments that were conducted. The 
behavior of each specimen during testing is described in detail. 
Chapter 5 provides flexural and shear analysis results and comparisons with relevant 
test data. Several outcomes of such comparisons and other observed testing behavior are 
also discussed in this chapter. 
Chapter 6 offers conclusions based on the work documented in this thesis. 
Recommendations for further research are also provided within this chapter. 
 4 
1.5. Notation 
The notation used in this document mainly follows the notation outlined in the AASHTO 
LRFD Bridge Design Specifications (2007). A list of the notation used throughout is 
presented in Appendix A. 
 
 5 
Chapter 2. Background on the Design of Reinforced Concrete Bridge 
Systems to Resist Shear 
2.1. Shear Behavior 
External forces acting on structures cause shear stresses in addition to axial and flexural 
effects. Unlike normal stresses caused by axial forces, shear stresses are not distributed 
linearly over the depth of flexural members. However, they are fairly constant across the 
cross-sectional dimension perpendicular to the applied load (i.e. width); therefore, the 
width-averaged value is often used for simplicity. Width-averaged shear stress 
distributions across the depth of typical homogeneous, isotropic, and linearly elastic 
rectangular and T-shaped cross sections can be seen in Figure 2-1. 
  
Figure 2-1. Width-averaged shear stress distributions on rectangular and T sections 
ave?
Neutral Axis 
(N. A.) 
(N. A.) 
 6 
Theoretical shear stress distributions assume second-degree polynomial curve 
shapes and reach maximum values at the centroid. Average shear stress (?ave) on a 
horizontal section of a beam can be calculated using: 
 
It
VQ
ave =?   
where V is the shear force, Q is the first moment of the area of the shaded section with 
respect to the neutral axis, I is the moment of inertia of the cross section about the neutral 
axis, and t is the width of the section at the point of interest (Beer and Johnson 1992). 
2.2. Principal Stress Analyses 
The shear strength of concrete is much higher than its tensile strength. Therefore, shear 
stresses are not direct causes of cracking in concrete. Moreover, shear stresses are seldom 
observed by themselves; most of the time they are accompanied by axial stresses. 
Principal stress analysis is required to understand the resulting effects of axial and/or 
shear stresses.  
2.3. Mohr?s Circle  
In order to obtain principal stresses, ?1(minimum) and ?2(maximum), at a point in a 
beam, Mohr?s Circle analysis can be used. Mohr?s Circles of typical concrete elements 
from nonprestressed and prestressed beams are shown in Figure 2-2. Tensile stresses are 
shown as positive. 
 7 
 
Nonprestressed beam element at centroid 
 
Prestressed beam element at centroid 
Figure 2-2. Mohr?s Circles for nonprestressed and prestressed beam elements 
It can be seen that axial compressive stresses caused by prestressing forces 
significantly reduce principal tensile stresses that result from shear stress. The largest 
tensile principal stresses, compared to the tensile strength or modulus of rupture values of 
concrete, can be calculated at specific loadings to predict diagonal cracking loads. 
Diagonal tensions are of concern because they lead to cracking of concrete due to its 
relative low tensile strength (Naaman 2004). Element failures that are called shear 
failures are mostly diagonal tension failures or sometimes diagonal compression failures, 
since true shear failure at the material level is rarely observed (Ferguson et al. 1988). 
Load 
Load 
 8 
2.4. Diagonal Cracking 
When principal tensile stresses existing at various angles with the horizontal reach critical 
values they cause cracking in the concrete. These inclined cracks are called diagonal 
cracks and several researchers classify diagonal cracking into two main types: flexure-
shear cracking and web-shear cracking (Sozen and Hawkins 1962; MacGregor et al. 
1965; Lorentsen 1965). These two main shear cracks are shown in Figure 2-3. 
 
Figure 2-3. Flexure-shear and web-shear cracks (Naaman 2004) 
Diagonal cracks are not fully restrained by longitudinal reinforcement and usually 
transverse reinforcement is required to avoid brittle failures (Nawy 2006). Because crack 
locations are discrete and the material is no longer isotropic, diagonal cracks make 
average constitutive (stress-strain) relationships complex (Collins 1978). 
2.4.1. Flexure-shear cracking  
Flexure-shear cracks are observed to start at, or in the vicinity of, flexural cracks and they 
quickly propagate in an inclined path (Bresler and MacGregor 1967). The propagation 
path is along the (diagonal) plane of principal tension (Naaman 2004). After flexural 
cracking, significant stress redistributions occur; this makes it difficult to accurately 
 9 
predict (1) the load that causes a flexure crack to transform into a flexure-shear crack and 
(2) the shear that can be resisted by the concrete after the formation of a flexure-shear 
crack in a reinforced beam (Bresler and MacGregor 1967; Collins and Mitchell 1997). 
2.4.2. Web-shear cracking  
Web-shear cracking is observed before flexural cracking, especially in beams with 
narrow webs. In regions where shear force is high relative to bending moment, a diagonal 
tension crack often occurs before a flexural crack because diagonally aligned principal 
tensile stresses near the centroid are relatively higher than flexural stresses near the 
tension face (Naaman 2004). Usually prestressing forces delay the formation of flexural 
cracks, which can result in web-shear cracks appearing first in high-shear regions of 
prestressed beams (MacGregor and Hanson 1969). Since web-shear cracking happens 
before any flexural cracking, principal stresses leading to cracking can be calculated 
more accurately (Bresler and MacGregor 1967). 
2.5. Behavior After Diagonal Cracking 
After diagonal cracks form, concrete contribution to shear stress transmission is greatly 
reduced. Adequate transverse and longitudinal reinforcement is required to balance these 
stresses (Collins and Mitchell 1997). Although diagonal cracking is not a failure mode of 
reinforced members by itself, it is a major contributor to the final failure of members. 
2.6. Failure Modes 
Flexure-shear cracking or web-shear cracking may lead to several shear failure modes.  
Shear span to depth ratio (a/d) is used as a classification parameter for failure modes. 
 10 
Major types that can be observed in slender (a/d > 2.5) to short (1 < a/d < 2.5), 
rectangular and I-beams are: diagonal tension failure, web crushing failure, shear tension 
failure and shear compression failure as shown in Figure 2-4 (Bresler and MacGregor 
1967; ASCE-ACI 1973). 
  
a) Diagonal Tension Failure b) Web crushing failure 
  
c) Shear tension failure d) Shear compression failure 
Figure 2-4. Major shear failure modes (Naaman 2004) 
Diagonal tension failure is usually observed in moderately slender beams. In this 
case, a web-shear or flexural-shear crack propagates throughout the depth of the beam 
causing a failure. Web crushing failure is observed typically in I-beams with narrow 
webs. Web crushing is caused after web-shear cracking by excessive compressive 
stresses on the diagonal compression elements. Shear tension failure is observed in short 
beams when a secondary crack forms branching off a shear crack at the level of 
longitudinal reinforcement and propagates towards the beam end. This secondary crack 
 11 
causes a loss of bond resulting in an anchorage failure of the longitudinal reinforcement. 
(Bresler and MacGregor 1967; ASCE-ACI 1973). In addition, the diagonal nature of 
shear cracking can result in a tension demand on the flexural reinforcement that is larger 
than what would be computed by only considering bending moment at a section 
(Ferguson et al. 1988). When an anchorage failure does not occur, the concrete at the 
compression (upper) end of the crack may fail in crushing. This type of failure is called 
shear compression failure (Naaman 2004). 
2.7. Compression Field Theory  
Compression Field Theory was presented by Michael P. Collins in 1978. It is based on 
the assumptions that concrete carries no tension after it is cracked and it carries 
compression in forms similar to truss models. The diagonal compression field in concrete 
transmits the shear stresses (Collins 1978). 
In this method of analysis, an implicit relationship is used between strain values 
and the angle of principal compression (?). Having necessary equilibrium and 
compatibility equations determined, transverse, longitudinal and principal compression 
strains can be calculated using an assumed value of ?. Using these three strains, another 
estimate of the angle of principal compression is obtained, and an iterative trial-error 
solution is reached.  
As an upper limit to the ultimate shear capacity (vu) of a member after the 
transverse reinforcement yields, Compression Field Theory assumes that the longitudinal 
steel yields or the concrete compressive stress reaches its limiting value. This approach is 
expressed in the following equation (Collins 1978): 
 12 
???
?
???
? ++?
jdb
Nfffv
w
pyplyltytu ??? )(  or 
2)(
tyttytduu fffv ?? ??  
where ? stands for the reinforcement ratio, fy for yield strength, N for axial force, bw, web 
width, jd for effective depth of shear and fdu for the limiting value of the average principal 
compressive stress in concrete. Additional subscripts t, l and p stand for transverse and 
longitudinal mild reinforcement and prestressing steel, respectively (Collins 1978). It can 
also be added that the prestressing or mild reinforcing steel anchorage capacity also limits 
the ultimate capacity of the member when the section considered is within the transfer or 
development length regions. 
2.8. Modified Compression Field Theory  
Modified Compression Field Theory (MCFT) was presented by Frank J. Vecchio and 
Michael P. Collins in 1986 as a further development of the 1978 Compression Field 
Theory by Collins. After an experimental program involving tests of square reinforced 
concrete elements under well defined axial and shear loads, average stress versus average 
strain relationships, as shown in Figure 2-5 and Figure 2-6, were obtained for cracked, 
reinforced concrete under normal and shear stresses. 
 Figure 2-5. Stress-strain relationship for cracked concrete in compression  
(Vecchio and Collins 1986) 
 13 
 
Figure 2-6. 3-D Representation of compressive stress-strain relationship  
(Vecchio and Collins 1986) 
In contrast to the original Compression Field Theory (Collins 1978), MCFT takes 
into account tensile stresses developed in the concrete between the cracks (tension 
stiffening). Tensile behavior of concrete is modeled as shown in Figure 2-7. 
 
Figure 2-7. Average stress strain relationship for concrete in tension  
(Vecchio and Collins 1986) 
At crack points, steel may be assumed to have yielded, but between cracks steel 
may not have yielded because concrete carries some of the tensile stresses in that region 
(Vecchio and Collins 1986). 
 14 
2.9. AASHTO Shear Provisions 
AASHTO LRFD Bridge Design Specifications (AASHTO LRFD 2007) address shear and 
torsion in concrete structures in Section 5.8. Both Article 5.8.3 (Sectional Design Model) 
and Article 5.6.3 (Strut-and-Tie Model) can be applied to flexural regions where plane 
sections remain plane. For components in which the distance from the point of zero shear 
to the face of the support is less than twice the depth of the member, use of Article 5.6.3 
is left to the engineer?s discretion (AASHTO LRFD 2007). 
2.9.1. Sectional design method 
The Sectional Design Method is used to compare factored shear forces and factored shear 
resistances at sections along the span. The governing equations used to calculate 
resistance are Equations 5.8.3.3-1 to 5.8.3.3-4, which are used to calculate nominal shear 
resistance (Vn), nominal shear resistance provided by concrete (Vc) and nominal shear 
resistance provided by shear reinforcement (Vs). The component of effective prestressing 
force in the direction of the applied shear (Vp) is also used as a variable in the calculation 
of Vn. 
For prestressed members, Vc can be calculated using either the General Procedure 
(Article 5.8.3.4.2) or the Simplified Procedure for Prestressed and Nonprestressed 
Sections (Article 5.8.3.4.3). 
2.9.2. General procedure 
The General Procedure (Article 5.8.3.4.2) is essentially an application of the Modified 
Compression Field Theory by Vecchio and Collins (1986), although this theory is not 
directly in the provisions. It is an iterative process that follows different paths depending 
 15 
on the amount of transverse reinforcement supplied. Sections are divided into two 
categories having (1) at least equal to or (2) less than the minimum transverse 
reinforcement specified in Article 5.8.2.5. An iterative process, in both cases, is used to 
determine ?x, the longitudinal strain in on the flexural tension side of the member. ?x is 
then used to find ? (factor relating ?x to Vc, indicating the ability of diagonally cracked 
concrete to transmit tension and shear) and ? (angle of inclination of diagonal 
compressive stresses in degrees). For increased ? values, although Vc is decreased, Vs is 
increased due to the fact that principal tension orientation more closely aligns with the 
vertical orientation of transverse reinforcement. 
 For members having at least the minimum transverse reinforcement, shear-stress-
to-f?c ratio is used as the governing parameter for the tables used for the iterations of ?  
and ?  values. However, for members having less than the required minimum transverse 
reinforcement sxe, a spacing parameter, is used. The spacing parameter is calculated as 
follows: 
8063.038.1 ?+=
g
xxe ass in. 
where: 
sx = the lesser of either dv (effective shear depth) or maximum distance between layers of 
longitudinal crack control reinforcement (in.)  
ag = maximum aggregate size (in.)  
 16 
2.9.3. Simplified procedure 
For concrete beams having at least minimum transverse steel reinforcement and not 
subject to significant axial tension, a simplified procedure is suggested to calculate Vc. 
This method, in which Vc is taken as lesser of Vci (nominal shear resistance provided by 
concrete when inclined cracking results from combined shear and moment) and Vcw 
(nominal shear resistance provided by concrete when inclined cracking results from 
excessive principal tensions in web), is similar to the ACI 318 (2005) approach and is 
based on recommendations by the NCHRP Report 549 (Hawkins et al. 2005). 
2.9.4. Minimum transverse reinforcement requirement 
In Article 5.8.2.5, AASHTO LRFD requires a minimum amount of transverse steel to 
control the diagonal cracks and increase ductility, as well as to provide post-cracking 
reserve strength. This minimum amount is required when the factored shear force is more 
than the half of the nominal shear resistance of the concrete added to the component of 
prestressing force in the direction of the shear force. Post-cracking reserve strength refers 
to the shear capacity of the member after diagonal cracking. The minimum transverse 
reinforcement requirement is defined by: 
y
v
cv f
sbfA '0316.0?  
where: 
Av = area of a transverse reinforcement within distance s (in.2) 
bv = width of web (in.) 
s = spacing of transverse reinforcement (in.) 
fy = yield strength of transverse reinforcement (ksi) 
 17 
 When the minimum transverse reinforcement requirement is substituted into the 
Vs and Vc equations as described in Article 5.8.3.3, the following equation is obtained: 
?
?cotc
s
VV ?  
This minimum transverse reinforcement requirement was analyzed by Ozcebe et 
al. (1999), Angelakos et al. (2001) and Rahal and Al-Shaleh (2004), and it was reported 
to be adequate. However, it was also reported that further testing was necessary to justify 
the validity of this requirement for high-strength concrete (fc? ? 10 ksi).  
2.9.5. Maximum aggregate size 
In the case of members with less than the minimum transverse reinforcement, concrete 
contribution to shear resistance is critical. Therefore, for a more accurate prediction of 
shear resistance, concrete-aggregate interlocking and other shear-friction factors need to 
be taken into greater account (Sherwood et al. 2007). When cracks widths increase, it has 
been seen that stresses that can be transmitted across cracks gradually decrease, 
indicating a certain transfer mechanism of interlocking grains (Moe 1962). It has been 
observed that close to sixty percent of the shear resistance is provided by the aggregate 
interlocking mechanism (Fenwick and Paulay 1968). In the application of the Modified 
Compression Field Theory, maximum aggregate size is used as a parameter in the 
determination of shear resistance due to aggregate interlock (Vecchio and Collins 1986).  
When high-strength concrete (fc? ? 10 ksi) is used, the maximum aggregate size is 
recommended to be taken as zero (Bentz et al. 2006). This argument is considered valid 
because with high-strength concrete, aggregate interlocking does not play an important 
 18 
role in transferring shear forces. This is due to the fact that aggregates are cut through in 
case of a diagonal crack in high-strength concrete. 
2.9.6. Longitudinal reinforcement demand 
Shear causes an axial tension demand in the longitudinal steel reinforcement?both in 
prestressing strands and in mild reinforcement. This demand, which is beyond the 
demand due to bending moment and axial force alone, has to be satisfied by the axial 
tension capacity of the longitudinal reinforcement. AASHTO LRFD (2007) specifications 
evaluate this capacity by assuming the mild steel reinforcement yields and the 
prestressing strands develop resistance in a linear or bi-linear fashion over the transfer 
and development lengths. AASHTO LRFD (2007) Article 5.8.3.5 requires the 
longitudinal reinforcement capacity to be larger than the longitudinal strength demand 
satisfying the following equations: 
???? cot5.05.0 ??
?
?
???
? ??++?+
sp
v
u
c
u
fv
u
yspsps VV
VN
d
MfAfA  
or 
?? cot5.0 ??
?
?
???
? ???+
sp
v
u
yspsps VV
VfAfA  (for the span between the face of the support 
and the critical section) 
where: 
Aps = prestressing strand area (in.2) 
fps = effective prestressing stress (ksi) 
As = longitudinal mild reinforcement area (in.2) 
fy = yield strength of longitudinal mild reinforcement (ksi) 
 19 
Mu = factored moment (kip-in.) 
dv = effective shear depth (in.) 
Nu = factored axial force (kip) 
Vu = factored shear force (kip) 
Vp = component of effective prestressing force in the direction of the applied shear (kip) 
Vs = nominal shear resistance provided by shear reinforcement (kip) 
 ? = angle of inclination of diagonal compressive stresses (o) 
?f, ?v, ?c = flexural, shear and compressive resistance factors, respectively  
2.9.7. Critical section for shear 
AASHTO LRFD (2007) Article 5.8.3.2 specifies the critical section for shear to be a 
distance of dv (effective shear depth, as described in Article 5.8.2.9) from the internal 
face of the support. For the design of the portion of the span between the support face and 
the critical section, this section is used for all shear capacity calculations, as well as for 
tension demand calculations of longitudinal reinforcement. The basic assumption for this 
approach is that loads inside the span up to the critical section are directly transferred 
(without beam action) to the support (Naaman 1994). 
2.9.8. Strut-and-Tie Modeling 
In Article 5.8.1.1 of the AASHTO LRFD Bridge Design Specifications (2007), it is stated 
that if the point of zero shear is closer than two times the member depth to the face of the 
support it may be considered as a deep member. However, the AASHTO specifications 
are not clear about the requirement on the design or analysis method. It is stated in the 
commentary that the strut and tie model yields less conservative results for regions near 
 20 
discontinuities. Therefore, it is understood that the strut and tie model can be used at the 
engineer?s discretion in order to achieve more efficient designs. 
2.10. Simplified Modified Compression Field Theory 
In 2006, Bentz et al. introduced a simplified method based on the Modified Compression 
Field Theory. This new method, called Simplified Modified Compression Field Theory 
(SMCFT), is aimed at predicting shear strengths of members without the iterative 
procedures necessary with the MCFT. SMCFT presents closed-form equations, instead of 
the current AASHTO LRFD tables for the calculation of ?x, ? and ? values (Bentz et al. 
2006). 
SMCFT is also employed in the 2004 Canadian Standards Association (CSA) 
A23.3 shear provisions for reinforced concrete (Bentz and Collins 2006). 
2.11. High-Strength Concrete 
AASHTO LRFD specifications, in Article 5.4.2.1, imply that properties that might be 
related to concrete compressive strength are derived using compressive strengths of 10.0 
ksi or less. It is advised to use concrete compressive strengths of 10.0 ksi or more only if 
relationships between such properties and concrete strengths are established by physical 
tests.
 21 
Chapter 3.  Specimen Properties and Testing 
3.1. Introduction 
Test specimens used in this study were 5 portions of pretensioned T-beam specimens 
previously tested in the Auburn University Civil Engineering Department Structures 
Laboratory by Kelly Levy in 2006?2007 (Levy 2007). The original beams were 23?-0? 
long when cast and pretensioned. Each specimen tested in this study was one end of a 
beam that had been tested to failure in flexure. The resulting beam segments ranged in 
length from 129 in. to 148 in., and each had one undamaged end region that was a 
prestress transfer zone in the original beam. The cross section for all specimens is shown 
in Figure 3-1.
 22 
(4) #3 bars
(2) 12" ? strands
6"
9"
24"
13
"
3"
1'-
3"
118" 12
"
6"
3 4"
2"2"2"
3 4"
11 4"
#3 U-stirrups
3"
#3 bars @ 9" 
     or 10" c/c
1"
3"
 
Figure 3-1. Specimen cross section detail (Levy 2007) 
3.2. Specimen Identification 
For ease of future reference, the specimen identification system is consistent with the 
system used by Levy (2007). Figure 3-2 shows the specimen identification scheme used 
by Levy. 
 23 
 
Figure 3-2. Specimen identification system of Levy (2007) 
The modified identification system used for this study is shown in Figure 3-3. Not 
all the beams tested previously were available and appropriate for retesting. All of the 
beam portions came from the Length A beams of the previous study. The E or W 
descriptor represents whether the beam portion was the east or west end of the original 
flexural specimen. The beam portions that were used as specimens in this study were 
tested with a point load placed so that the undamaged prestress transfer end of the 
original beam was the short shear span. The S or L descriptor is used to differentiate 
between the two ends of the specimen as tested in this study. 
SCC  
STD  
M (Moderate) 
H (High) 
SCC-MA-BE 
E (East End) 
W (West End) Specimen End  A(Fly Ash) 
S(GGBF Slag) 
SCM 
Concrete Mixture 
Concrete Strength Specimen Length A (23?-0?) 
B (16?-4?) 
C (13?-0?) 
D (9?-8?) 
SCM = Supplementary Cementitious Materials 
 24 
 
Figure 3-3. Specimen identification system used in this study 
3.3. Material Properties  
3.3.1. Prestressing steel 
The prestressing steel used in this study was low-relaxation ?? in.?special? Grade 270 
seven-wire prestressing strand. The cross-sectional area and modulus of elasticity of the 
strand given by the manufacturer are 0.164 in2 and 28,900 ksi, respectively. The 
measured diameter of this strand was 0.515 in. The strand used in all of the beams came 
from one roll that was manufactured by the American Spring Wire Corporation. 
3.3.2. Mild reinforcing steel 
The mild reinforcing steel used in this study was ASTM A615 Grade 60 reinforcing bar. 
0.375-in. nominal diameter No. 3 bars were used for flange reinforcement and transverse 
(shear) reinforcement. Transverse reinforcement was placed with 10 in. spacing. For 
analysis purposes, the modulus of elasticity and yield stress of the bars were assumed to 
be 29,000 ksi and 60 ksi, respectively. 
S (Short Shear Span) 
L (Long Shear Span) 
M (Moderate) 
H (High) 
SCC-MS-ES 
 Testing End 
SCC  
STD  
Concrete Mixture 
Concrete Strength 
E (East) 
W (West)   As-Cast Portion 
S(GGBF Slag) SCM 
 25 
3.3.3. Concrete 
Three types of concrete mixtures were used in this study. One was a conventionally 
consolidated (?standard?) moderate-strength concrete mixture. The remaining two 
mixtures were self-consolidating concrete (SCC), one having high strength and one 
having moderate strength. The standard mixture was designed to resemble a mixture 
commonly used by the Alabama Department of Transportation (ALDOT) for prestressing 
applications.  
The standard mixture is called STD-M (moderate-strength). The SCC mixtures 
used for this study were SCC-13 (high-strength) and SCC-15 (moderate-strength) using 
the notation of previous phases of this ALDOT project (Roberts 2005; Swords 2005). 
This study follows the Levy (2007) nomenclature, and the two SCC mixtures are called 
SCC-HS (high strength with GGBF slag), and SCC-MS (moderate strength with GGBF 
slag) respectively. The moderate-strength SCC mixture had a 50% Grade 100 GGBF slag 
replacement. The high-strength SCC mixture had a 30% Grade 100 GGBF slag 
replacement. All concrete mixtures had a maximum aggregate size of ??. Mixture 
constituents, as well as fresh and hardened properties of the three concrete types, are 
given in Table 3-1, Table 3-2 and Table 3-3 as reported by Levy (2007): 
 26 
Table 3-1. Mixture properties 
Mixtures Mixture 
Constituents STD-M SCC-MS SCC-HS 
Water (pcy) 270 270 260 
Cement (pcy) 640 375 650 
Fly Ash (pcy) 0 0 0 
GGBF Slag (pcy) 0 375 279 
Coarse agg. (pcy) 1964 1613 1544 
Fine agg. (pcy) 1114 1323 1265 
AEA (oz/cwt) 0.33 0.00 0.00 
WRA (oz/cwt) 4.0 6.0 6.0 
HRWRA (oz/cwt) 3.5 4.5 5.0 
VMA (oz/cwt) 0.0 2.0 2.0 
 
where: 
GGBF = Ground Granulated Blast Furnace, 
AEA = Air-Entraining Admixture, 
WRA = Water-Reducing Admixture. 
HRWRA = High-Range Water-Reducing Admixture, and 
VMA = Viscosity-Modifying Admixture. 
 
 27 
Table 3-2. Fresh properties 
MIXTURE 
PROPERTY 
STD-M SCC-MS SCC-HS 
Slump Flow (in.) 9.5 28.5 26 
Unit Weight (lb/ft3) 142.2 148.4 155.2 
Air Content (%) 11.0 5.0 3.0 
VSI - 1.0 1.0 
T-50 (sec.) - 1.54 3.75 
J-Ring Difference (in.) - 2 2.5 
L-Box (H2/H1) - 0.92 0.63 
Temperature (?F) 82 89 95 
 
Table 3-3. Hardened properties 
MIXTURE 
PROPERTY 
STD-M SCC-MS SCC-HS 
f'ci (psi) 5000 5300 9990 
Ec i(ksi) 4900 4950 6050 
f'c,28(ASTM )(psi) 5990 9640 13150 
f'c,28(AC) (psi) 6320 9170 13380 
Ec,28(AC) (ksi) 5150 6950 7050 
fct,28(AC) (psi) 560 840 830 
ASTM = Cured according to ASTM C192 specifications 
AC = Air-cured 
 28 
3.4. Prestressing Parameters 
Several properties of the specimens related to prestressing steel were previously 
determined by Levy (2007). Transfer and development lengths (lt,exp and ld,AASHTO, 
respectively), fpj, fpe and fps values for all five specimens are given in Table 3-4.  
Table 3-4. Previous testing results 
Specimen lt,exp (in.) ld, AASHTO  (in.) fpj (ksi) fpe (ksi) fps (ksi) 
STD-M-E 22 75 209 178 264 
STD-M-W 32 75 209 178 264 
SCC-MS-E 20.5 72 211 188 265 
SCC-HS-E 18 71 210 192 266 
SCC-HS-W 20.5 71 210 192 266 
where: 
fpj = stress in prestressing steel at jacking, 
fpe = effective stress in prestressing steel after losses, and 
fps = average stress in prestressing steel at the time for which the nominal resistance of the 
member is required. 
The transfer length, jacking stress, and effective stress values were determined 
based on measurements of concrete strains in the specimens. The development length and 
fps were determined using AASHTO LRFD design provisions. 
3.5. Test Setup and Instrumentation 
The test setup consisted of a simply supported beam loaded by a single concentrated load 
closer to the original prestress transfer end of the beam. The reason why unequal shear 
 29 
spans were chosen was that shear failures were expected and longer embedment lengths 
were already tested by Levy (2007). Use of a nonsymmetric loading promoted failure at 
the undamaged, original prestress transfer end of the specimen. The test setup is 
illustrated in Figure 3-4, and a representative photograph is given in Figure 3-5. 
 
Figure 3-4. Test setup diagram 
 
Figure 3-5 Test setup 
 Overhang 
Shear Span 
Support Span (114 in.) 
Load 
 30 
For the Levy (2007) study, prestressing force was transferred by flame-cutting of 
the strands. Due to the physical orientation of the beams on the prestressing bed, each 
original beam had one flame-cut end and one dead end where strands were cut after the 
transfer. Table 3-5 indicates the physical differences of the test configuration for each 
specimen. 
Table 3-5. Test configuration dimensions and strand release conditions 
Specimen Shear Span 
(in.) 
Overhang 
(in.) 
Strand Release 
Condition at End 
Total Length 
(in.) 
STD-M-E 30 4 Dead 129 
STD-M-W 30 2 Flame Cut 148 
SCC-MS-E 30 2 Dead 138 
SCC-HS-W 30 2 Flame Cut 129 
SCC-HS-E 16 2 Dead 147 
Steel rocker supports were located at support positions and rested on reinforced 
concrete pedestals to elevate and support the specimens during testing. Between the steel 
supports and the specimen, lubricated and unreinforced neoprene pads were used to 
minimize horizontal force transfer. These supports can be seen in Figure 3-6. 
 31 
 
Figure 3-6. Neoprene pads, steel supports and concrete blocks 
Loading was applied by piston displacement of a hydraulic actuator attached to a 
reaction frame. Between the hydraulic piston and the beam there was a steel beam 
positioned to transmit the force to the load plate attached to the beam surface with a high 
strength gypsum-cement mixture. The hydraulic actuator may be seen in Figure 3-7. 
 32 
 
Figure 3-7. Hydraulic actuator and force transducer 
3.6. Instrumentation 
Applied load, displacements, top fiber compressive strains, and strand end slips were the 
main responses monitored during testing of specimens. Instruments used during the time 
of testing are presented in this section. 
3.6.1.  Measurement of applied load 
The applied load was measured by a built-in force transducer between the hydraulic 
actuator and the steel beam. The force transducer and the steel beam can be seen in 
Figure 3-7.  
Hydraulic actuator 
Load transducer 
Steel beam 
Load Plate 
 33 
3.6.2. Measurement of displacements 
All displacements were measured using linear potentiometers. One potentiometer was 
placed under the beam directly below the load point. Potentiometers were also placed 
under the flange at each end on each face at the location of the support to measure any 
support deflection throughout each test. These potentiometers were also used as a safety 
measure to monitor any possible unexpected behavior of the beam under applied load. 
The actual displacement of the beam relative to the supports was calculated using the 
output from these potentiometers. Glass microscope slides were glued to the surface of 
the beam at the point of contact for each potentiometer in order to compensate for surface 
imperfections. Figure 3-8 show the positions of potentiometers used, and a close-up of 
two potentiometers can be seen in Figure 3.6. 
 
Figure 3-8. Potentiometers 
Potentiometers at supports 
Potentiometer at load point 
 34 
3.6.3. Measurement of strand slip 
Strand slip was measured with linear potentiometers at the end closest to the load point. 
This end, which was subjected to the larger shear force, was a prestress transfer location 
in the original beam. All strand movement was measured relative to the end of the beam. 
The potentiometers were mounted onto brackets which were then attached to the strands. 
Potentimeters used to measure strand slip can be seen in Figure 3-9. 
 
Figure 3-9. Strand slip measurement 
3.6.4. Measurement of strains at extreme compression fibers 
Compressive strains at the top surface of the beam were monitored during flexural testing 
using an Electrical Resistance Strain Gauge (ERSG) with a 2.36-in. (60-mm) gauge 
length. For all specimens except SCC-HS-E, strain gauges were positioned 6 in. from the 
load point on the shorter shear span. For specimen SCC-HS-E, two strain gauges were 
 35 
attached at the same distance but with 1 in. offsets from the centerline due to the presence 
of a recess for lifting hardware. 
3.6.5. Data acquisition 
All instrumentation signals were acquired by an Optim MEGADAC Data Acquisition/ 
Signal Conditioning Unit and then transferred to a laptop computer where all data was 
recorded and stored. Data was acquired and stored every 1/10th of a second from each 
instrument. The data acquisition system used for testing is shown in Figure 3-10. 
 
Figure 3-10. Data acquisition system
 36 
Chapter 4. Test Results 
4.1. Introduction 
This chapter includes a detailed description of each of the five tests in the experimental 
program. Key performance characteristics of all five tests are summarized at the end of 
the chapter. 
4.2. Specimen STD-M-E 
The applied load and strand slip versus load point displacement graph for specimen STD-
M-E, constructed of a conventional moderate strength concrete mixture, is given in 
Figure 4-1. 
After a range of approximately linear elastic behavior, a web-shear crack between 
the support and the load point was observed in specimen STD-M-E when the applied load 
reached 32.1 kips and the load point displacement was 0.05 in. The inclined shear crack 
that formed at this load is shown in Figure 4-2. Immediately after cracking, the width of 
the shear crack was about 0.5 mm (0.020 in.) at the prestressing strand level and 0.2 mm 
(0.008 in.) at the centroid of the cross section. The corresponding shear force when the 
crack opened was 23.6 kips. The cracking load was not attained again by the beam as 
more displacement was applied. After cracking, the specimen exhibited excessive strand 
slip which could also be heard at the time of experiment.  
 37 
0
5
10
15
20
25
30
35
40
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Load Point Displacement (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Str
an
d S
lip
 (in
.)
Load Strand Slips
 
Figure 4-1. Applied load and strand slips vs. load point displacement - STD-M-E 
A gradual failure of the specimen followed as the load point displacement was 
increased and the resistance of the beam decreased to a value of approximately 16 kips. 
The test was stopped at a displacement of 0.65 in. At this point, the crack width was 11 
mm (0.43 in.) at the strand level and 4 mm (0.15 in.) at the centroid. Figure 4-3 and 
Figure 4-4 show the final state of the crack at the end of the test. The observed failure 
behavior was consistent with a ?shear tension? failure, which (as related in Chapter 2) 
entails a loss of reinforcement development between the inclined crack and the beam end 
that is precipitated by the influence of a shear crack. 
 38 
 
Figure 4-2. Initial crack at 32 kips applied load ? STD-M-E 
The shear crack was diagonally positioned 19 in. from the beam end at strand 
level, extending to 28 in. from beam end at the centroid. 
 39 
 
Figure 4-3. Final state of crack at the end of test? STD-M-E 
 
Figure 4-4. Shear tension failure showing loss of bond ? STD-M-E 
 40 
In order to have a better understanding of the behavior at the time of shear crack 
opening, a load point displacement and strand slip versus time graph, and an applied load 
and strand slip versus time graph are given in Figure 4-5 and Figure 4-6, respectively. 
Both graphs indicate that the shear crack and strand slip took place at the same 0.1-
second data acquisition interval. 
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
1396.0 1396.5 1397.0 1397.5Time (sec.)
Lo
ad
 Po
int
 D
isp
lac
em
en
t (
in.
)
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Str
an
d S
lip
 (in
.)
Load Point Displacement
Strand Slips
 
Figure 4-5. Load point displacement and strand slip versus time ? STD-M-E 
 41 
0
5
10
15
20
25
30
35
1396.0 1396.5 1397.0 1397.5
Time (sec.)
Ap
pli
ed
 L
oa
d (
kip
s)
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Str
an
d S
lip
 (in
.)
Load Strand Slips
 
Figure 4-6. Applied load and strand slip versus time ? STD-M-E 
 42 
4.3. Specimen STD-M-W 
The applied load and strand slip versus load point displacement graph of the specimen 
STD-M-W is given in Figure 4-7. 
0
5
10
15
20
25
30
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Load Point Displacement (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Str
an
d S
lip
 (in
.)
Load Strand Slips 
 
Figure 4-7. Applied load and strand slips versus load point displacement - STD-M-W 
Behavior of STD-M-W was very similar to that of STD-M-E. Since they were 
portions of the same original beam, this was as expected. After a short range of linear 
elastic behavior, a web-shear crack between the support and the load point was observed 
at a 0.03 in. displacement, when the applied load reached 27.2 kips, lower than the 
cracking load of STD-M-E. This difference may be attributed to the longer transfer length 
in the short shear span of this specimen. The width of the shear crack was 0.6 mm (0.024 
in.) at the prestressing strand level and 0.2 mm (0.008 in.) at the centroid. When the crack 
 43 
opened, the corresponding shear force was 20.0 kips. This shear crack is shown in Figure 
4-8. The cracking load could not be reached again, and the specimen exhibited excessive 
strand slip after this point. Again, a shear tension failure of the specimen followed as the 
displacement was increased. Finally, the crack width reached 8 mm (0.32 in.) at the 
strand level and 6 mm (0.24 in.) at the centroid. The test was stopped after 1.8 in. of 
displacement and 0.9 in. of strand slip. At this point, the load resisted by the beam was 
approximately 20 kips, and had remained fairly constant over the final 0.25 in. of 
displacement and 0.1 in. of strand slip. The final state of the specimen is shown in Figure 
4-9. 
 
Figure 4-8. STD-M-W: Initial crack at 27.2 kips applied load - STD-M-W 
The shear crack was diagonally positioned 18 in. from the beam end at strand 
level, extending to 25 in. from the beam end at the centroid. 
 
 44 
 
Figure 4-9. STD-M-W: Final state of crack at the end of test - STD-M-W 
Load point displacement and strand slip versus time as well as applied load and 
strand slip versus time graphs of specimen STD-M-W are shown in Figure 4-10 and 
Figure 4-11. The behavior observed from these graphs is similar to that of STD-M-E, 
showing the same simultaneous behavior of shear crack opening and strand slip. 
 
 45 
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
911.0 911.5 912.0
Time (sec.)
Lo
ad
 Po
int
 D
isp
lac
em
en
t (
in.
)
0.000
0.004
0.008
0.012
0.016
0.020
0.024
0.028
0.032
Str
an
d S
lip
s (
in.
)
Load Point Displacement
Strand Slips
 Figure 4-10. 
Load point displacement and strand slip versus time - STD-M-W 
0
5
10
15
20
25
30
911.0 911.5 912.0
Time (sec.)
Ap
pli
ed
 L
oa
d (
kip
s)
0.000
0.005
0.010
0.015
0.020
0.025
0.030
Str
an
d S
lip
 (in
.)
Applied Load Strand Slips
 
Figure 4-11. Applied load and strand slip versus time - STD-M-W 
 46 
4.4. Specimen SCC-MS-E 
The applied load and strand slip versus load point displacement graph of specimen SCC-
MS-E is given in Figure 4-12. 
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Load Point Displacement (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Str
an
d S
lip
 (in
.)
Load Strand Slips 
 
Figure 4-12. Applied load and strand slips versus load point displacement - SCC-MS-E 
Specimen SCC-MS-E exhibited a different behavior when compared to the 
standard concrete specimens. This specimen did not have a shear crack but it had flexural 
cracks under the load point, which can be seen in Figure 4-13 and Figure 4-14. The 
applied load at first cracking was 46.1 kips, and the specimen failed in a flexural failure 
mode after opening of several flexural cracks reaching a maximum load of 63.1 kips. 
Figure 4-15 and Figure 4-16 show the state of the flexural cracks and the beam at the end 
of testing. Strand slips initiated when the flexural crack started to get wider at 51.7 kips 
of applied load. Although strand slip gradually increased with increasing load, strand 
 47 
anchorage was sufficient to allow the strands to rupture in tension at a load of 63.1 kips. 
The width of the main crack at strand level was recorded as 1.5 mm (0.060 in.) at 56 kips 
and 11 mm (0.43 in.) at the end of the test. 
 
Figure 4-13. Flexural cracks under load point at 51kips applied load - SCC-MS-E 
Load point  
 48 
 
Figure 4-14. Flexural cracks under load point at 56 kips applied load - SCC-MS-E 
 
Figure 4-15. Final condition of flexural cracks at the end of test - SCC-MS-E 
Load point  
Load point  
 49 
 
Figure 4-16. Final condition at the end of test - SCC-MS-E 
 50 
4.5. Specimen SCC-HS-W 
The applied load and strand slip versus load point displacement graph for specimen SCC-
HS-W is given in Figure 4-17. 
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load Point Displacement (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Str
an
d S
lip
 (in
)
Load Strand Slips 
 
Figure 4-17. Applied load and strand slips versus load point displacement - SCC-HS-W 
Specimen SCC-HS-W had behavior similar to the moderate-strength SCC 
specimen SCC-MS-E. Again, this specimen did not have a shear crack, but it had flexural 
cracks under the load point. The initial crack is shown in Figure 4-18. Cracking initiated 
at an applied load of 46.6 kips, and the specimen failed in a flexural failure mode after 
opening of several flexural cracks, reaching a maximum load of 64.5 kips when the 
strands ruptured. Strand slips initiated at 56.7 kips of applied load. However, strand slips 
in this specimen were not as large as in the previous tests. The width of the main crack at 
 51 
strand level was recorded as 1.0 mm (0.040 in.) at 56 kips and 8 mm (0.32 in.) at the end 
of the test, just before the strands ruptured. The final state of flexural cracks and the beam 
are shown in Figure 4-19 and Figure 4-20. 
 
Figure 4-18. Flexural cracks under load point at 48 kips applied load - SCC-HS-W 
 
Load point  
 52 
 
Figure 4-19. Final condition of flexural cracks at the end of test - SCC-HS-W 
 
Figure 4-20. Final condition at the end of test - SCC-HS-W 
  Load point  
 53 
4.6. Specimen SCC-HS-E 
The applied load and strand slip versus load point displacement graph for specimen SCC-
HS-E is given in Figure 4-21. This specimen came from the same original beam as 
specimen SCC-HS-W; however, the shear span was reduced to 16 in. (See Table 3-5 for 
test configuration dimensions.) 
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load Point Displacement (in.)
Ap
pli
ed
 L
oa
d (
kip
s) 
 
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Str
an
d S
lip
 (in
.)
Load Strand Slips 
 
Figure 4-21. Applied load and strand slips versus load point displacement - SCC-HS-E 
Specimen SCC-HS-E exhibited a similar behavior as the moderate-strength 
concrete specimens with longer shear spans (and longer effective strand embedment 
lengths). After a range of elastic behavior, a web-shear crack between the support and the 
load point was observed in the specimen when the applied load reached 66.1 kips. This 
shear crack can be observed in Figure 4-22. At this load, the width of the shear crack was 
0.8 mm (0.032 in.) at prestressing strand level and 0.3 mm (0.012 in.) at the centroid of 
 54 
the cross section. The shear force when the crack opened was 56.8 kips. This shear is a 
higher percentage of the applied load (86%) than in the rest of the test specimens (74%) 
because of the shorter shear span for this test. 
 
Figure 4-22. Shear crack at 66 kips cracking load - SCC-HS-E 
After cracking, the specimen exhibited excessive strand slip, and the cracking 
load could not be reached again as a shear tension failure of the specimen was evident as 
the load point displacement was increased. Finally, the test was stopped at a displacement 
of 1.2 in. and an applied load of 30 kips. At this point, the crack width had reached 35 
mm (1.38 in.) at strand level and 11 mm (0.43 in.) at the centroid. Strand slips had 
increased to approximately 1.0 in. at the cessation of the test. Figure 4-23 shows the final 
state of the shear crack at the end of test. 
 55 
 
Figure 4-23. Final state of the shear crack at the end of test - SCC-HS-E 
The shear crack was diagonally positioned 11 in. from beam end at strand level 
extending to 18 in. from the beam end (directly below the load point) at the centroid. 
Load point displacement and strand slip versus time and applied load and strand 
slip versus time graphs of specimen SCC-HS-E are shown in Figure 4-24 and Figure 
4-25. Behavior observed from these graphs is similar to those of moderate-strength, 
conventionally consolidated concrete specimens STD-M-E and STD-M-W, showing the 
same simultaneous behavior of shear crack opening and strand slip. 
 56 
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
2600.5 2601.0 2601.5 2602.0
Time (sec.)
Lo
ad
 Po
int
 D
isp
lac
em
en
t (
in.
)
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
Str
an
d S
lip
 (in
.)
Load Point Displacement
Strand Slips
 Figure 4-24. 
Load point displacement and strand slip versus time - SCC-HS-E 
0
10
20
30
40
50
60
70
2600.5 2601.0 2601.5 2602.0
Time (sec.)
Ap
pli
ed
 L
oa
d (
kip
s)
0.000
0.004
0.008
0.012
0.016
0.020
0.024
0.028
Str
an
d S
lip
 (in
.)
Applied Load Strand Slips
 
Figure 4-25. Applied load and strand slip versus time - SCC-HS-E 
 57 
4.7. Summary of Test Results 
Table 4-1 is provided to show a summary of cracking loads, ultimate loads, types of 
cracks and failure modes. Further analyses, comparisons and related discussions follow in 
Chapter 5. 
Table 4-1. Specimen cracking and ultimate loads and failure modes 
Specimen Shear 
span (in.) 
Cracking 
load (kips) 
Ultimate 
load (kips) 
Type of 
crack 
Failure mode 
STD-M-E 30 32.1 (23.6) 32.1 (23.6) Web-shear Shear-tension 
STD-M-W 30 27.2 (20.0) 27.2 (20.0) Web-shear Shear-tension 
SCC-MS-E 30 48.1 (35.4) 63.1 (46.5) Flexural Flexural/Strand slip 
SCC-HS-W 30 48.0 (35.4) 64.5 (47.5) Flexural Flexural/Strand slip 
SCC-HS-E 16 66.1 (56.8) 66.1 (56.8) Web-shear Shear-tension 
Corresponding shear forces are given in parentheses 
 
Table 4-2 shows the initial crack positions of the specimens with respect to beam ends 
and support points. Crack position is given at strand level and at centroid. 
 
 58 
Table 4-2. Crack positions of specimens 
Specimen At strand level (in.) At centroid (in,)  Type of crack 
STD-M-E 19 28 Web-shear 
STD-M-W 18 25 Web-shear 
SCC-MS-E 32 32 Flexural 
SCC-HS-W 39 38 Flexural 
SCC-HS-E 11 18 Web-shear 
 
 
 59 
Chapter 5. Analysis and Discussion 
5.1. Flexural Analysis 
It can be seen from the test results that three test specimens (STD-M-E, STD-M-W and 
SCC-HS-E) failed with shear-tension modes of failure, and the remaining two (SCC-MS-
E and SCC-HS-W) beams exhibited flexural modes of failure.  
A layer-by-layer flexural analysis, as described by Collins and Mitchell (1997), 
was performed for each of the specimens in order to evaluate their idealized flexural 
response, ignoring the effects of shear deformations. The beam cross section was divided 
into several thin layers with unequal thicknesses which were analyzed as individual 
members being subjected to axial loading. The relative deformations of these layers were 
constrained so that plane sections remained plane. A total of forty-one layers were 
implemented, with thinner layers in the flange of the beam?where inelastic compressive 
behavior was expected?and thicker layers in the web region. The rows of mild steel 
reinforcement and prestressing strand were represented by two additional layers. The 
subdivision of each cross section into layers is shown in Figure 5-1. An elastic uncracked 
analysis was used to estimate initial stresses and strains for each layer.
 60 
 
Figure 5-1. Layers for sectional analysis 
For each value of top fiber compressive strain, the corresponding neutral axis 
depth and curvature were calculated based on an initial guess, followed by iteration 
aimed to zero the sum of axial forces of all of the layers. After the neutral axis location 
and curvature were determined, the corresponding value of moment was calculated. This 
procedure was repeated for a range of top fiber strains from a dead-weight only condition 
to ultimate flexural capacity. 
For prediction of load-displacement response, tension stiffening was considered 
based upon the procedure described by Collins and Mitchell (1997). After cracking, 
concrete fibers located within 7.5 diameters of reinforcement were assigned average 
tensile stresses according to the relationship described by Collins and Mitchell (1997). 
28th day air-cured compressive and tensile strengths of concrete are used as given in 
Table 3-3. Figure 5-2 shows the zones of concrete fibers affected by tension stiffening. 
 61 
  
Figure 5-2. Concrete fibers affected by tension stiffening 
Mild reinforcing steel was assumed linear elastic up to a yield point of 61 ksi with 
Es = 29,000 ksi (determined according to previous material testing). Beyond the yield 
point a perfectly plastic behavior (constant stress) was assumed. 
 For the prestressing strands the following relationship was used based on previous 
material testing: 
??
?
?
?
??
?
?
?
+
+
12112
p ))(114(1
2794148.959 = f
p
p ??  
where,  
fp = stress in prestressing steel, and 
?p = strain in prestressing steel. 
 62 
Applied load versus load-point deflection graphs for all five specimens are given 
in Figure 5-3 through Figure 5-7, showing comparisons of calculated idealized flexural 
response with the actual experimental response. Calculated and measured flexural 
cracking and ultimate loads for each specimen are given in Table 5-1. The applied load 
that corresponds to the AASHTO nominal moment capacity is also reported in this table. 
This load is less than the value computed from the layer-by-layer approach because 
AASHTO limits the stress in the strands to a value less than the nominal strength of 270 
ksi.  
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load-Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
Applied Load
Idealized Flexural Response
Onset of Slip
 
Figure 5-3. Flexural analysis result for STD-M-E 
 63 
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load-Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s) 
 
Applied Load
Idealized Flexural Response
Onset of Slip
 Figure 5-4. 
Flexural analysis result for STD-M-W 
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load-Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
Applied Load
Idealized Flexural Response
 
Figure 5-5. Flexural analysis result for SCC-MS-E 
 64 
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load-Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
Applied Load
Idealized Flexural Response
 
Figure 5-6. Flexural analysis result for SCC-HS-W 
0
20
40
60
80
100
120
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load-Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
Applied Load
Idealized Flexural Response
Onset of Slip
 
Figure 5-7. Flexural analysis result for SCC-HS-E 
 65 
Table 5-1. Loads corresponding to flexural cracking and ultimate strength 
 Analysis Results Experimental Results 
Specimen 
Flexural 
cracking 
load 
(kips) 
Ultimate 
load 
(kips) 
P at 
AASHTO 
Mn (kips) 
Flexural 
(F) or 
shear (S) 
cracking 
load (kips) 
Ultimate 
capacity 
(kips) 
STD-M-E 36.2 52.6 50.2 32.1 (S) 32.1 
STD-M-W 36.2 52.6 50.2 27.2 (S) 27.2 
SCC-MS-E 37.8 56.2 52.5 48.1 (F) 63.1 
SCC-HS-W 39.9 60.3 53.5 48.0 (F) 64.5 
SCC-HS-E 65.4 97.4 86.1 66.1 (S) 66.1 
 
In Table 5-2, analytically computed flexural cracking moments are compared with 
the actual moments at the locations where cracks were observed.  
Table 5-2. Cracking moments corresponding to crack locations 
 Analysis results Experimental results 
Specimen 
Flexural cracking 
moment (kip-ft) 
Applied moment (kip-ft) at the time and 
location of flexural (F) or shear (S) crack 
STD-M-E 66.7 29.6 (S) 
STD-M-W 66.7 21.7 (S) 
SCC-MS-E 69.6 88.6 (F) 
SCC-HS-W 73.5 88.4 (F) 
SCC-HS-E 75.0 41.7 (S) 
 
 66 
Specimens SCC-MS-E and SCC-HS-W, both having failed flexurally, show good 
agreement with flexural analysis results, while having slightly more ultimate capacity 
than predicted. This difference of ultimate capacity is attributed to the relative 
movements of support locations which caused slight changes in total span length, as well 
as uncertainties in material properties such as strength and modulus of elasticity and other 
random experimental errors. 
Specimens STD-M-E, STD-M-W and SCC-HS-E each failed in a shear-tension 
mode of failure. Comparison with analysis results show that they reached neither flexural 
cracking moments nor their flexural capacities at their times of failure.  
5.2. AASHTO LRFD Shear Analyses 
5.2.1. Shear cracking 
AASHTO LRFD (2007) provisions lack a prediction value for initial shear 
cracking. In this study, Vc is used as a parameter for cracking shear load. Normally, Vc is 
considered the concrete contribution to the shear resistance of a cracked section. If 
transverse reinforcement is provided, Vc is the concrete contribution to the ultimate shear 
capacity, not simply the shear that causes initial shear cracking. However, it is reasonable 
to assume that the AASHTO LRFD expression for Vc in members without transverse 
reinforcement provides a more accurate estimate of the shear corresponding to first 
cracking because transverse reinforcement is not engaged until after the crack forms. 
Therefore, all of the specimens were analyzed as if they did not have any transverse 
reinforcement.  
 67 
Figure 5-8 shows a plot of Vc values, calculated using the AASHTO LRFD shear 
provisions in Section 5.8.3.3 at the critical section versus experimental ultimate loads. 
The critical section, a distance of dv away from the support, is used as the section for 
analysis because the AASHTO LRFD specifications indicate this location is to be used 
for design of all sections located between the critical section and the support. The critical 
section was found to be the weakest among the sections between the critical section and 
the load point because it was within the transfer length of prestressing strands. Effective 
prestressing force was not fully transferred for most of the specimens at this cross 
section; therefore, in the calculation process, the prestressing force was adjusted for 
according to the bi-linear stress-distance relationship, as described by AASHTO LRFD 
Commentary C5.11.4.2 (2007), using experimentally determined transfer lengths and 
AASHTO predicted development lengths. 
Three more specimens described by Levy (2007), STD-M-D, SCC-MS-D and 
SCC-HS-D, are also included in these results. These three additional specimens had the 
same cross section and were constructed with the same concrete as those described in this 
thesis. Specimens that did not experience shear cracks are denoted with a ?+? marker as 
these specimens would not have experienced shear cracks until greater loads than were 
achieved prior to flexural failure. 
 68 
SCC-HS-E
STD-M-ESTD-M-W
STD-M-D
SCC-MS-E SCC-HS-W
SCC-MS-DSCC-HS-D
0
10
20
30
40
50
60
0 10 20 30 40 50 60
Calculated Vc (kips)
Ex
pe
rim
en
tal
 V
u 
(ki
ps
)
Specimens having flexural modes of failure
Specimens having shear-tension modes of failure
 
Figure 5-8. Experimental versus valculated Vc values 
It can be observed that AASHTO LRFD provision for Vc is quite accurate for the 
moderate-strength conventionally consolidated concrete mixtures. However, for the high-
strength and moderate-strength SCC, it is observed that AASHTO provisions are quite 
conservative. This statement is further supported by evaluating Figure 5-9, where Vc is 
plotted against ?x for sxe ? 15 in. ?x is the longitudinal strain in the flexural tension side of 
the member and sxe is the crack spacing parameter. For all the tested specimens, sxe was 
calculated to be less than the dividing value of 15 in as maximum aggregate size (ag) was 
taken as ? in. Figure 5-9 illustrates all possible values of Vc for the allowed range of ?x. It 
can be observed that at no ?x value is Vc anywhere close to experimental results for 
concrete strengths other than for the 6.32-ksi conventionally consolidated concrete 
(STD). For those specimens that did not exhibit any diagonal cracks (SCC-MS-E, SCC-
 69 
HS-W, SCC-MS-D and SCC HS-D), ultimate loads achieved (limited by flexural failure) 
are substituted as a form of lower bound. 
STD
-M-
E
STD
-M-
W
STD
-M-
D
SCC
-MS
-E
SCC
-HS
-ES
CC
-HS
-WSC
C-M
S-D
SCC
-HS
-D
0
10
20
30
40
50
60
70
-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00
?x(x1000)
Vc
 (k
ips
)
f'c= 6.32 ksi (STD-M)
f'c= 9.17 ksi (SCC-MS)
f'c= 13.38 ksi (SCC-HS)
 
Figure 5-9. Vc as function of ?x for sxe ? 15 in. 
5.2.2. Shear capacity 
AASHTO LRFD Bridge Design Specifications (2007) were used to calculate predicted 
nominal shear capacities (Vn) of the test specimens. Article 5.8.3.3 was followed as a 
guideline and the General Procedure in Article 5.8.3.4.2 was used for Vc calculations. As 
these are ultimate (i.e. post-cracking) capacity calculations, transverse reinforcement was 
taken into consideration for these Vc calculation procedures.  
In the General Procedure, as described in Article 5.8.3.4.2, when the member has 
at least the minimum required transverse reinforcement, shear ratio (vu/f?c) is used a 
 70 
criterion for the iteration procedure of ? and ? values. Shear ratio is simply the shear 
stress (shear force Vu divided by bvdv) divided by concrete compressive strength. All of 
the tested specimens fall into the lower-bound category of vu/f?c ? 0.075. 
Table 5-3 shows calculated Vc, Vs and Vn values for the specimens as well as the 
maximum applied shear, Vu. These values were calculated at the critical section using the 
maximum applied shear during testing taken as Vu. Again, prestressing force was adjusted 
for using experimentally determined transfer lengths and AASHTO predicted transfer 
lengths. 
Table 5-3. Shear capacity calculations based on applied maximum shear 
Specimen Vc (kips) Vs (kips) Vn (kips) Vu (kips) Failure mode 
STD-M-E 20.4 35.8 56.2 23.6 Shear-tension 
STD-M-W 15.5 27.8 43.3 20.0 Shear-tension 
SCC-MS-E 15.0 19.7 34.7 46.5 Flexural/Strand slip 
SCC-HS-W 18.2 19.7 37.9 47.5 Flexural/Strand slip 
SCC-HS-E 18.2 19.7 37.9 55.7 Shear-tension 
Table 5-4 shows calculated Vc, Vs and Vn values when Vn was taken equal to the 
applied maximum shear, which was taken as Vu for the computation process. This 
approach is closer to an actual shear design process when the capacity of a member is 
calculated according to the anticipated design load. 
 71 
 
Table 5-4. Shear capacity calculations based on Vn = Vu 
Specimen Vc (kips) Vs (kips) Vn (kips) Vmax, exp (kips) Failure mode 
STD-M-E 12.9 23.1 36.0 23.6 Shear-tension 
STD-M-W 12.5 19.7 32.7 20.0 Shear-tension 
SCC-MS-E 15.4 21.5 36.9 46.5 Flexural/Strand slip 
SCC-HS-W 18.3 20.4 38.7 47.5 Flexural/Strand slip 
SCC-HS-E 18.7 21.7 40.7 55.7 Shear-tension 
It can be observed that AASHTO-predicted nominal shear strengths are higher 
than the actual shear forces resisted by the specimens with conventional concrete 
mixtures. The main reason is that the AASHTO Vn provisions assume a diagonal tension 
failure mode. In order to also address the shear-tension failure mode, AASHTO 
specifications include a longitudinal reinforcement check introduced in Article 5.8.3.5.  
On the other hand, AASHTO-predicted nominal shear strengths are lower than the 
resisted shear forces in the specimens with SCC mixtures. The reason attributed to this 
difference is the conservatism of AASHTO LRFD specifications in case of high-strength, 
SCC concrete mixtures.  
5.2.3. Post-cracking tension demand 
Shear-tension failures observed in the experiments were typically initiated by a 
web-shear crack, followed by excessive prestressing strand slip and degradation of bond. 
AASHTO LRFD provisions provide a check for excessive demand on longitudinal 
reinforcement in Article 5.8.3.5. Tension demands based on shear loads and moments on 
 72 
the tested specimens were compared with tension capacities calculated using AASHTO 
LRFD specifications per Section 5.11. Experimental values of transfer lengths were used 
in these calculations, instead of AASHTO-predicted transfer lengths, in order to more 
realistically represent tested specimens.  
Three specimens with shear-tension failure modes were analyzed for tension 
demand and capacity of prestressing tendons at the critical section (as defined by 
AASHTO) at the experimental cracking load (as reported in Chapter 4). Levy (2007) 
specimen STD-M-D was also added because of the similarity in test geometry. Table 5-5 
shows the results of these calculations. 
Table 5-5. Tension demands compared to tension capacities 
Specimen Tension Demand (ksi) Tension Capacity (ksi) 
STD-M-E 156 128 
STD-M-W 117 77 
STD-M-D 144 106 
SCC-HS-E 357 147 
Tension demand exceeding the tension capacity is essentially the cause of 
excessive strand slips, as well as the sudden drop in capacity of the member after a single 
diagonal crack. 
The remaining two specimens, SCC-MS-E and SCC-HS-W, were not analyzed 
for tension capacity of tendons because the AASHTO LRFD approach was derived based 
on equilibrium conditions after inclined cracking at the relevant cross section. These 
specimens did not experience shear-influenced cracking.  
 73 
Shear capacities of the three specimens STD-M-E, STD-M-W and SCC-HS-E 
were calculated assuming that the tension demand on the prestressing strands at the 
AASHTO critical section controls the maximum allowable load. Figure 5-10 thru Figure 
5-12 show the applied loads that cause the strands to equal their capacity at the critical 
section, calculated per AASHTO LRFD specifications Article 5.8.3.5.  
Applied Load at 
Strand Tension 
Capacity
0
5
10
15
20
25
30
35
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Load Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
 Figure 5-10. 
Applied load at strand tension capacity for specimen STD-M-E 
 74 
Applied Load at 
Strand Tension 
Capacity
0
5
10
15
20
25
30
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Load Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
 Figure 5-11. 
Applied load at strand tension capacity for specimen STD-M-W 
Applied Load at 
Strand Tension 
Capacity
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
 
Figure 5-12. Applied load at strand tension capacity for specimen SCC-HS-E 
 75 
Figure 5-14 demonstrates an increasing trend of the load after diagonal cracking 
as opposed to a decreasing trend as can be seen on other specimens with diagonal cracks. 
This behavior is attributed to the centered position of the stirrup seizing the diagonal 
crack and engaging more effectively in shear load resistance.  
5.3. Transverse Reinforcement 
5.3.1. Effect of transverse reinforcement on post-cracking tension demand 
Because the stirrups did not intercept the diagonal cracks in some of the specimens, th 
previous analysis for post-cracking tension demand on prestressing strands was repeated 
for the case when the specimens were assumed not to have any transverse reinforcement. 
Shear capacities of the three specimens STD-M-E, STD-M-W and SCC-HS-E 
were calculated assuming that the tension demand on the prestressing strands at the 
AASHTO critical section controls the maximum allowable load. Figure 5-13 thru Figure 
5-15 show the applied loads that cause the strands to equal their capacity at the critical 
section, calculated per AASHTO LRFD specifications Article 5.8.3.5 for both with and 
without transverse reinforcement. 
 76 
0
5
10
15
20
25
30
35
40
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Load-Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
Applied load at strand tension capacity with transverse reinforcement
Applied load at strand tension capacity without transverse reinforcement
 
Figure 5-13. Applied load at strand tension capacity for specimen STD-M-E with and 
without transverse reinforcement 
 77 
0
5
10
15
20
25
30
35
40
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Load-Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
Applied load at strand tension capacity with transverse reinforcement
Applied load at strand tension capacity without transverse reinforcement
 
Figure 5-14. Applied load at strand tension capacity for specimen STD-M-W with and 
without transverse reinforcement 
 78 
0
10
20
30
40
50
60
70
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Load-Point Deflection (in.)
Ap
pli
ed
 L
oa
d (
kip
s)
Applied load at strand tension capacity with transverse reinforcemet
Applied load at strand tension capacity without transverse reinforcement
 
Figure 5-15. Applied load at strand tension capacity for specimen SCC-HS-E with and 
without transverse reinforcement 
 It can be observed from the graphs that the AASHTO LRFD specifications yield 
lower tension demands for the same specimens without transverse reinforcements. 
Analysis results show that AASHTO LRFD shear provisions are not conservative for 
members having none or less than minimum transverse reinforcement. Therefore, it is 
more safe to use transverse reinforcement if AASHTO LRFD specifications are to be 
used for design. 
5.3.2. Transverse reinforcement spacing 
Post-cracking reserve strengths, which refer to the capacity of the member after diagonal 
cracking, of the members STD-M-E, STD-M-W and SCC-HS-E are shown in Table 5-6 
 79 
together with cracking loads and reserve strength as a percentage of cracking strength. 
Reserve strength refers to the capacity of the member after diagonal cracking. 
Table 5-6. Cracking loads and reserve strengths of specimens 
Specimen Cracking Load 
(kips) 
Reserve Load 
(kips) 
Reserve Load as Percentage of 
Cracking Load 
STD-M-E 32.1 24.1 75% 
STD-M-W 27.2 23.0 84% 
STD-HS-E 66.1 49.7 75% 
It can be observed that specimen STD-M-W has significantly higher reserve 
strength when compared to the other specimens with diagonal cracks, as well as an 
increasing load resistance trend after the initial shear crack as can be seen in Figure 4-7. 
The difference is due to the position of the stirrups relative to the diagonal crack. Both 
STD-M-E and SCC-HS-E exhibited diagonal cracks that passed between two stirrup 
locations as can be seen in Figure 5-16 and Figure 5-17. On the other hand, STD-M-W 
had a stirrup in the middle of the diagonal crack as can be seen in Figure 5-18. This 
position of the diagonal crack enables the stirrup to seize the crack before it is too wide 
and to increase the reserve capacity of the specimen. 
 80 
 
Figure 5-16. Diagonal crack location of specimen STD-M-E 
 
Figure 5-17. Diagonal crack location of specimen SCC-HS-E 
Sti
rru
p 
Sti
rru
p 
Sti
rru
p 
Sti
rru
p 
 81 
 
Figure 5-18. Diagonal crack location of specimen SCC-M-W 
AASHTO LRFD specifications have provisions related to transverse 
reinforcement spacing in Article 5.8.3.3. Required stirrup spacing for three specimens, 
STD-M-E, STD-M-W and SCC-HS-E were calculated, and it was found that the 
maximum stirrup spacing calculated per Article 5.8.2.7 controls the design. smax (0.8dv) is 
found to be 9.36 in.?a little less than the supplied spacing of 10 in.  
From the behavior of specimens STD-M-E and SCC-HS-E, it is clear that the 
AASHTO LRFD maximum transverse reinforcement spacing requirement of 0.8dv is not 
always effective in providing each diagonal crack with at least one intercepting stirrup. 
Based on the AASHTO LRFD specifications, the following relationship is derived 
providing a conservative requirement for smax (maximum stirrup spacing) using sxe 
(spacing parameter calculated per Article 5.8.3.4.2) and dv (effective shear depth): 
Sti
rru
p 
 82 
v
xe
dss 6.1max =  
where, both smax and sxe are in inches. This equation is implicitly making use of 
conservative diagonal compressive stress inclinations. Figure 5-19 show variation of smax 
with respect to dv at several ag (maximum aggregate size) values. 
a g  = 0''
a g  = 3/8''
a g  = 3/4''
a g  = 1''
0
2
4
6
8
10
12
14
16
0 10 20 30 40 50 60 70
d v  (in.)
s m
ax
 (in
.)
 
Figure 5-19. smax (maximum stirrup spacing) versus of dv (effective shear depth) 
 
 83 
Chapter 6. Conclusion and Recommendations 
6.1. Summary 
Prestressed self-consolidating concrete (SCC) is not fully understood in terms of shear 
and bond behavior. Therefore, more research was required in this field before full 
employment of SCC in prestressed concrete systems. 
In order to investigate the shear and bond performance of end regions of 
prestressed SCC beams, five prestressed concrete beams were tested in this study with 
single-point loading positioned to create unequal shear spans. There were both 
conventionally consolidated concrete and SCC mixtures. Both shear-tension and flexural 
failure modes were observed. 
Experimental results were compared to computed flexural analysis results and 
AASHTO LRFD shear design provisions. Because current AASHTO LRFD design 
provisions for maximum stirrup spacing proved inadequate for some of the test 
specimens, a simple relationship for determining maximum stirrup spacing is proposed. 
6.2. Conclusions 
The following conclusions can be drawn as a result of this study: 
1. SCC performed better under shear than a similar-strength, conventionally 
consolidated concrete mixture in prestressed concrete beams.
 84 
2. SCC prestressed end regions performed at least as well under external load 
as the performance predicted by AASHTO LRFD design provisions for flexure, shear, 
and development of tension reinforcement.  
3. Concrete contribution to shear resistance (Vc) when the members are 
assumed not to have any transverse reinforcement can be used to estimate shear cracking 
strengths of members. 
4. AASHTO LRFD provisions can be used to accurately estimate shear 
cracking strength of prestressed concrete beams having conventionally consolidated 
concrete mixtures. 
5. AASHTO LRFD provisions are overly conservative in estimating shear 
cracking strength of prestressed concrete beams having conventionally consolidated 
concrete mixtures. 
6. AASHTO LRFD specifications are not conservative in estimating tension 
demands on longitudinal reinforcement when no transverse reinforcement is used. 
7. Use of transverse reinforcement is an effective means of increasing post-
cracking capacities of members that experience shear-tension failures. 
8. Maximum transverse reinforcement spacing provided by AASHTO LRFD 
specifications is not conservative because diagonal cracks can occur that are not crossed 
by at least one stirrup. 
 
 
 85 
6.3. Recommendations  
The following recommendations are suggested: 
1. SCC mixtures with a wider variety of strengths should be tested for shear 
performance and compared to conventional concrete mixtures. 
2. Further SCC research regarding shear behavior is necessary. 
3. High-strength concrete should be more adequately addressed by AASHTO 
LRFD specifications enabling engineers to take advantage of more efficient mixture 
designs. 
4. The general procedure in AASHTO LRFD shear provisions should be 
extended to cover a wider range of concrete strengths. 
5. The following equation is recommended for the determination of 
maximum stirrup spacing: 
v
xe
dss 6.1max =  
 
 86 
References 
AASHTO. 2007. AASHTO LRFD Bridge Design Specifications. 4th Edition. Washington 
D.C. American Association of State Highway Transportation Officials. 
 
ACI Committee 318. 2005. Building Code Requirements for Structural Concrete and 
Commentary. Farmington Hills: American Concrete Institute. 
 
Angelakos, D., E. C. Bentz, and M. P. Collins. 2001. Effect of Concrete Strength and 
Minimum Stirrups on Shear Strength of Large Members. ACI Structural Journal 98: 290-
300. 
 
ASCE-ACI Joint Task Committee 426. 1973. The Shear Strength of Reinforced Concrete 
Members. Journal of the Structural Division: ASCE 99: 1091-1187. 
 
Beer, F. P., E. R. Johnston, Jr. 1992. Mechanics of Materials. 2nd Edition in SI Units. 
England. McGraw-Hill. 
 
Bentz, E. C., F. J. Vecchio, and V. Collins. 2006. Simplified Modified Compression Field 
Theory for Calculating Shear Strength of Reinforced Concrete Elements. ACI Structural 
Journal 103: 614-624. 
 
Bentz, E. C., and V. Collins. 2006. Development of Canadian Standards Association 
(CSA) A23.3 Shear Provisions for Reinforced Concrete. Canadian Journal of Civil 
Engineering 33: 521-534. 
 
Bresler, B., and J. G. MacGregor. 1967. Review of Concrete Beams Failing in Shear. 
Journal of the Structural Division: ASCE 93: 343-372. 
 
Collins, M. P. 1978. Towards a Rational Theory for RC Members in Shear. Journal of 
The Structural Division: ASCE 104: 649-666. 
 
Collins, M. P., and D. Mitchell. 1997. Prestressed Concrete Structures. Toronto. 
Response Publications. 
 
Cook, W. D., and D. Mitchell. 1988. Studies of Disturbed Regions Near Discontinuities 
in Reinforced Concrete Members. ACI Structural Journal 85: 206-216. 
 
Fenwick, R. C., T. Paulay. 1968. Mechanism of Shear Resistance of Concrete Beams. 
Journal of the Structural Division: ASCE 94: 2325-2350.
 87 
Ferguson, P. M., J. E. Breen, and J. O. Jirsa. 1988. Reinforced Concrete Fundamentals. 
5th Edition. New York. Wiley. 
 
Hawkins, N. M., D. A. Kuchma, R. F. Mast, M. L. Marsh, and K. Reineck. 2005. NCHRP 
Report 549: Simplified Shear Design of Structural Concrete Members. Washington. D.C. 
Transportation Research Board. 
 
Lorensten, M. 1965. Theory for the Combined Action of Bending Moment and Shear in 
Reinforced and Prestressed Concrete Beams. Journal of the American Concrete Institute 
62: 403-420. 
 
Levy, K. R. 2007. Bond Behavior of Prestressed Reinforcement in Beams Constructed 
with Self-Consolidating Concrete. M.S. Thesis. Auburn University 
 
Nawy, E. G. 2006. Prestressed Concrete: A Fundamental Approach. 5th Edition. New 
Jersey. Pearson Prentice Hall. 
 
MacGregor, J. G., and J. M. Hanson. 1969. Proposed Changes in Shear Provisions for 
Reinforced and Prestressed Concrete Beams. ACI Journal 66: 276-288. 
 
MacGregor, J. G., M. A. Sozen, and C. P. Siess. 1965. Strength of Prestressed Concrete 
Beams with Web Reinforcement. Journal of the American Concrete Institute: 
Proceedings 62: 1503-1519. 
 
Moe, J. 1962. Discussion of: Shear and Diagonal Tension. ACI Journal: Proceedings 59: 
1334-1339. 
 
Naaman, A. E. 2004. Prestressed Concrete Analysis and Design: Fundamentals. 2nd 
Edition. Ann Arbor. Techno Press 3000. 
 
Ozcebe, G., U. Ersoy, and T. Tankut. 1999 Evaluation of Minimum Shear Reinforcement 
Requirements for Higher Strength Concrete. ACI Structural Journal 96: 361-369.  
 
Rahal, K. N., and K. S. Al-Shaleh. 2004. Minimum Transverse Reinforcement in 5 MPa 
Concrete Beams. ACI Structural Journal 101: 872-878. 
 
Roberts, J. 2005. Evaluation of Self-Consolidating Concrete for Use in Prestressed Girder 
Applications. M.S. Thesis. Auburn University. 
 
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Beam-Shear Strength of Thick Slabs. ACI Structural Journal 104: 180-190. 
 
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ACI Journal, Proceedings 59: 1341-1347. 
 
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Thesis., Auburn University. 
 
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 89 
Appendix A. Notation 
a shear span  
ag maximum aggregate size  
Aps area of prestressing steel  
As area of mild tension reinforcement  
Av area of transverse reinforcement within distance s  
? factor relating effect of longitudinal strain to the shear capacity of concrete 
bv, bw width of web  
d depth of tension reinforcement  
dv effective shear depth  
Ec modulus of elasticity of concrete  
Ep modulus of elasticity of prestressing reinforcement  
Es modulus of elasticity of mild steel reinforcement  
?1 strain in direction of principal tension  
?2 strain in direction of principal compression 
?p strain in prestressing reinforcement 
 90 
?x longitudinal strain on the flexural tension side of the member 
f1 stress in direction of principal tension 
f2 stress in direction of principal conmpression 
f'c specified compressive strength of concrete  
f'c,28 specified compressive strength of concrete at 28 days  
fcr cracking stress of concrete 
fdu limiting value of the average principal compressive stress in concrete 
fly yield strength of longitudinal mild reinforcement 
fp stress in prestressing reinforcement 
fpe effective stress in prestressed reinforcement after losses 
fpj stress in prestressing steel after jacking 
fps 
stress in prestressed reinforcement at the estimated nominal strength estimated 
by AASHTO prior to flexural testing 
fpy yield strength of prestressing reinforcement 
fr modulus of rupture 
ft splitting tensile strength 
fty yield strength of transverse reinforcement 
fy yield stress of mild steel reinforcement 
I moment of inertia 
 91 
jd effective depth for shear 
lt,exp. experimentally determined transfer length 
ld,AASHTO development length estimated by AASHTO with calculated properties 
Mn 
predicted nominal moment capacity according to AASHTO LRFD 
specifications 
Mn factored moment at section 
N axial force 
Q first moment of area about the neutral axis 
?l longitudinal mild reinforcement ratio 
?p prestressing reinforcement ratio 
?t transverse reinforcement ratio 
s transverse reinforcement spacing 
smax maximum permitted transverse reinforcement spacing 
sx, sxe crack spacing parameters 
? axial stress 
t thickness 
? shear stress 
?ave width-averaged shear stress 
? angle of inclination of diagonal compressive stresses 
 92 
V shear stress 
Vc nominal shear resistance provided by tensile stresses in concrete 
Vn nominal shear resistance of the section considered 
Vp component in the direction of applied shear of the prestressing force 
Vs shear resistance provided by shear reinforcement 
vu average factored shear stress on the concrete 
Vu factored shear force at section