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ANALYSIS OF THE AASHTO LRFD HORIZONTAL SHEAR

STRENGTH EQUATION

Maria Lang

Thesis submitted to the faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

IN

CIVIL ENGINEERING

Carin Roberts-Wollmann, Co-Chairperson

Kamal B. Rojiani, Co-Chairperson

Cristopher D. Moen

September 8, 2011

Blacksburg, VA

Keywords: Horizontal Shear, Shear Friction

ANALYSIS OF THE AASHTO LRFD HORIZONTAL SHEAR STRENGTH EQUATION

Maria Lang

ABSTRACT

The composite action of a bridge deck and girder is essential to the optimization of the

superstructure. The transfer of forces in the deck to the girders is done across a shear interface

between the two elements. The transfer occurs through the cohesion of the concrete at the

interface and then through the shear reinforcement across the interface. Adequate shear strength

is essential to the success of the superstructure.

A collection of 537 horizontal shear tests comprised the database for the study of various

concrete types and interface surface treatments. The predicted horizontal shear strength

calculated from the AASHTO LFRD bridge design code was compared to the measured shear

strength. The professional bias was computed for each specimen. The professional biases,

standard deviations, and coefficients of variation for each category were calculated. The material

properties factor along with fabrication factor was researched. The loading factors were

researched and calculated for use in calculating the reliability index. The final step was to

compute the reliability index for each category. The process was repeated to learn the reliability

of the equation proposed by Wallenfelsz. The results showed that the reliability index for the

AASHTO LRFD horizontal shear strength equation wash much lower than the desired target

reliability index of 3.5. The reliability index for the Wallenfelsz equation was higher but still not

close to the target reliability index.

ACKNOWLEDGEMENTS

I would like to thank Dr. Carin Roberts-Wollmann and Dr. Kamal Rojiani for their

guidance and help throughout this research. It was a pleasure to work with them. I found them

truly understanding and willing to assist in my goals for my graduate degree. I would also like to

thank Dr. Moen for his guidance and for serving on my committee.

I would like to express my enormous amount of gratitude towards my family. Their

support was essential to my success throughout my undergraduate and graduate school. Their

calming reassurances and answers to my need for assistance helped me stay grounded and know

that I would make it through and go far. I could never be where I am without them.

I would also like to thank my fellow graduate students who made my graduate school

process more enjoyable. It was a delight sharing classes and an office with you.

iii

TABLE OF CONTENTS

ABSTRACT………………………………………………………………………………………ii

ACKNOWLEDGEMENTS………………………………………………………………………iii

TABLE OF CONTENTS………………………………………………………………………....iv

LIST OF FIGURES………………………………………………………………………………vi

LIST OF TABLES……………………………………………………………………….............vii

CHAPTER 1: INTRODUCTION…………………………………………………………………1

1.1 Horizontal Shear Transfer....…………………………………………………………..1

1.2 Research Objective and Scope………………………………………………………...3

1.3 Thesis Organization…………………………………………………………………...5

CHAPTER 2: LITERATURE REVIEW……………………………………….…………………6

2.1 Horizontal Shear…………………………………………………………...………….6

2.2 Research on Horizontal Shear…………………………………………………………7

2.2.1 Banta…………………………………………………………………………….7

2.2.2 Bass, Carrasquillo, & Jirsa………………………………………………………8

2.2.3 Choi………………………………………………..…………………………….9

2.2.4 Hanson…………………………………………………..………………………9

2.2.5 Hofbeck, Ibrahim, & Mattock………………………………...………………..10

2.2.6 Kahn & Mitchell…………………………………………………...…………..10

2.2.7 Kahn & Slapkus………………………………………………………..………11

2.2.8 Kamel…………………………………………………………………………..12

2.2.9 Loov & Patnaik…………………………………………..…………………….12

2.2.10 Mattock, Johal, & Chow……………………………………………………….13

2.2.11 Mattock, Li, & Wang………………………………………...………………...14

2.2.12 Patnaik………………………………………………………….………………15

2.2.13 Saemann & Washa……………………………………………………………..16

2.2.14 Scott……………………………………………………………………………17

2.2.15 Valluvan, Kreger, & Jirsa………………………………………..…………….17

2.2.16 Walraven & Reinhardt……………………………………………..…………..18

2.3 AASHTO LRFD Bridge Design Specifications……………………………………..19

2.4 Reliability Analysis…………………………………………………………………..21

2.4.1 Reliability Index………………………………………………………………..22

2.4.2 Resistance Statistics...………………………………………………………….23

2.4.3 Load Statistics…………………………………………………………………..24

2.5 Summary of Literature Review…………………………………………..…………..25

iv

CHAPTER 3: DATABASE AND CALCULATION METHODS…………………………..….26

3.1 Selection of Data…………………………………………………………………….26

3.2 Calculation of Predicted Horizontal Shear…………………………………………..27

3.3 Reliability Analysis Procedures……………………………………………………..27

CHAPTER 4: PRESENTATION OF RESULTS AND ANALYSIS…………………………...31

4.1 Typical Results……………………………………………………………………….31

4.1.1 Rough Interface………………………………………………………………...31

4.1.1.1 Normal Weight Concrete………………………………………………...35

4.1.1.2 Lightweight Concrete…………………………………………………….36

4.1.1.3 High Strength Concrete…………………………………………………..36

4.1.2 Smooth Interface……………………………………………………………….37


4.1.2.2 Lightweight Concrete…………………………………………………….42

4.1.2.3 High Strength Concrete………………………………………………..…42

4.1.3 Monolythic Interface…………………………………………………………...42


4.1.3.2 Lightweight Concrete………………………………………….…………46

4.1.3.3 High Strength Concrete…………………………………………..………47

4.2 Reliability Analysis……………………………………………………………..……47

4.2.1 Bias and Coefficient of Variation………………………………………….…..48

4.2.2 Reliability Indices……………...……………………………………………....50

4.2.3 Comparison to Wallenfelsz………………………………………………….....52

CHAPTER 5: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS………………..56

5.1 Summary……………………………………………………………………………..56

5.2 Conclusions……………………………………………………………………….....57

5.3 Design Recommendations…………………………………………………………...58

5.4 Recommendations for Future Research……………………………………………...59

REFERENCES…………………………………………………………………………………..60

APPENDIX A…………………………………………………………………………………...62

APPENDIX B…………………………………………………………………………………...89

APPENDIX C…………………………………………………………………………………..103

APPENDIX D…………………………………………………………………………………..126

v

LIST OF FIGURES

Figure 1.1 Cracking at interface resulting in horizontal shear friction……………………………1

Figure 1.2 Tensile forces in reinforcing steel after cohesion failure……………………………...2

Figure 1.3 Deflected non-composite beam under loading………………………………………...2

Figure 1.4 Deflected composite beam under loading……………………………………………..3

Figure 1.5 Typical push-off test…………………………………………………………………...4

Figure 2.1 Horizontal shear forces in composite section………………………………………….6

Figure 3.1 Rough interface normal variable distributions..……………………………………...29

Figure 3.2 Smooth interface normal variable distributions.……………………………………..29

Figure 3.3 Monolithic interface normal variable distributions..…………………………………30

Figure 4.1 Clamping stress versus actual horizontal shear stress for rough interface and normal

strength concrete …………………………………..………………………………...32

Figure 4.2 Clamping stress versus actual horizontal shear stress for rough interface and

lightweight concrete ……………………………………………………………...….33

Figure 4.3 Clamping stress versus actual horizontal shear stress for rough interface and high

strength concrete ………………………………………………………………...…..34

Figure 4.4 Clamping stress versus actual horizontal shear stress for smooth interface and normal

weight concrete …………………………………………………………………..….38

Figure 4.5 Clamping stress versus actual horizontal shear stress for smooth interface and

lightweight concrete ……………………………………………………...………….39

Figure 4.6 Clamping stress versus actual horizontal shear stress for smooth interface and high

strength concrete……………………………………………………………………..40

Figure 4.7 Clamping stress versus actual horizontal shear stress for monolithic interface and

normal weight concrete………………………………………………………………43

Figure 4.8 Clamping stress versus actual horizontal shear stress for monolithic interface and

lightweight concrete………………………………………………………………….44

Figure 4.9 Clamping stress versus actual horizontal shear stress for monolithic interface and high

strength concrete……………………………………………………………………..45

Figure 4.10 Reliability indices for AASHTO LRFD for normal weight concrete………………50

Figure 4.11 Reliability indices for AASHTO LRFD for lightweight concrete………………….51

Figure 4.12 Reliability indices for AASHTO LRFD for high strength concrete………………..51

Figure 4.13 Reliability indices for D+L load combination for Wallenfelsz equation for normal

weight concrete………………………………………………………………………54

Figure 4.14 : Reliability indices for D+L load combination for Wallenfelsz equation for normal

weight concrete………………………………………………………………………54

Figure 4.15 Reliability indices for D+L load combination for Wallenfelsz equation for normal

weight concrete………………………………………………………………………55

vi

LIST OF TABLES

Table 4.1 Statistics of the Professional Factor…………………………………………………...48

Table 4.2 Statistical Parameters of Resistance…………………………………………………..49

Table 4.3 Statistics of Professional Factor for Wallenfelsz Equation...…………………………53

Table 4.4 Resistance Statistics for Wallenfelsz Equation…………………………….………….53

vii

CHAPTER 1: INTRODUCTION

1.1 Horizontal Shear Transfer

It is common practice for a bridge’s superstructure to be constructed in two phases. The

first phase is the erection of the girders. The second phase is the construction of the bridge deck.

In order for the superstructure to work at optimal load-carrying capacity, it is necessary that there

is an adequate transfer of the horizontal shear force due to the dead and live loads from the deck

to the girders. A part of the shear force is transferred through interface friction resulting from

surface conditions, as illustrated in Figure 1.1. As the cohesion of the concrete fails, a crack

forms and the two surfaces start to slide against one another with resultant friction forces. In

addition to friction, resistance and transfer are provided by the reinforcing steel or shear

connectors across the interface, as shown in Figure 1.2. The reinforcing steel is subject to tensile

stress due to the opposing horizontal shear forces from the deck and girders. The tension in the

steel causes a clamping force on the interface from the opposing concrete members being forced

into compression in order to counteract the tensile stress in the steel.

Figure 1.1: Cracking at interface resulting in horizontal shear friction.

Crack

1

Figure 1.2: Tensile forces in reinforcing steel after cohesion failure.

The prevention of sliding across the interface allows the girders and deck to act

compositely. Figure 1.3 illustrates that a non-composite system’s deck slab would just slide on

the girder, because the members act separately; there is no mechanism for transferring shear

forces across the interface. Figure 1.4 shows that in a composite beam the beam and slab act

together and there is minimal slip, resulting in additional stiffness.

Figure 1.3: Deflected non-composite beam under loading.

2

Figure 1.4: Deflected composite beam under loading.

In a typical composite concrete beam the interface between the beam and deck is either

smooth or intentionally roughened by raking the surface to a minimum height of 0.25 in. If the

deck and girders are to be cast at different times, all interfaces should be clean and free of

laitance, which could reduce the friction force. The members may have different types of

concrete and different concrete strengths. Normal weight, lightweight, and high performance

concretes are the most commonly found concrete types. There are several equations for

calculating the horizontal shear force transferred between composite members. These equations

depend upon the researcher or the appropriate design code. The factors considered in these

equations for predicting the horizontal shear include the amount of reinforcement, reinforcement

strength, spacing of reinforcement, concrete type, concrete strength, applied normal force,

surface treatment, and interface area.

1.2 Research Objective and Scope

The objective of this research is to ascertain the level of reliability of the equation for

predicting the nominal shear resistance of an interface plane in the American Association of

3

State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design

(LRFD) bridge design specifications. The steps needed to accomplish this objective include:

1. Develop a database of experimental test results on horizontal shear strength

2. Determine statistics of horizontal shear strength

3. Evaluate the inherent reliability of the AASHTO horizontal shear equation by

computing the reliability index for horizontal shear strength.

An important objective of the study was to compile a database of experimental test results on

horizontal shear strength available in the literature. The database comprised of a total of 537 test

results from either push-off tests, as illustrated in Figure 1.5, or full beam tests, as illustrated

earlier in Figure 1.4. The specimens had either a rough interface, or a smooth interface, or were

cast monolithically. The database includes specimens made with normal weight, lightweight, or

high strength concrete of varying strength. Some of the experiments had shear reinforcement

across the interface, while others had none at all. The applied clamping stress also fluctuated

depending on the researcher.

Figure 1.5: Typical push-off test.

In order to access the reliability of the AASHTO horizontal shear equation it is necessary

to obtain the statistics of the load and resistance. The factors that affect resistance statistics are

the professional factor, the material factor and the fabrication factor. The professional factor is

4

the ratio of actual to predicted strength. Statistics of the professional factor were determined

from an analysis of the test results. Statistics of the material and fabrication factors and statistics

of loads were determined from available literature. The measure of reliability used in this study

is the reliability index obtained from a first-order second-moment reliability analysis. The third

objective of the study was to determine the reliability index for a range of interface types,

concrete strengths, reinforcement amounts and clamping force. The reliability study will

highlight the need for a review of the current equation.

1.3 Thesis Organization

Chapter 2 reviews the results of experimental studies on horizontal shear strength

available in literature. An overview of the AASHTO LRFD specifications for horizontal shear

strength is also presented. An explanation of how the data was selected and analyzed is discussed

in Chapter 3. Results from the study and a discussion of these results are presented in Chapter 4.

Chapter 5 contains a summary, conclusions, and recommendations from the research.

5

CHAPTER 2: LITERATURE REVIEW

2.1 Horizontal Shear

It is very common for precast girders to be used in combination with a cast-in-place deck.

In order for these two elements to act as one unit and thus gain strength from one another, an

adequate connection between the members is required. This increases the overall stiffness of the

section and enhances the load-carrying capacity of the bridge. The connections allow for the

transfer of forces between the two elements, seen below in Figure 2.1.

Figure 2.1: Horizontal shear forces in composite section

There is considerable variation in the equations for predicting horizontal shear strength in

the literature. The horizontal shear equation used for designing a member depends on the design

code governing the project. The most fundamental of all equations is the horizontal shear stress

equation shown below which stems from elastic beam theory.

�� = ��

where vh = horizontal shear stress, V = vertical shear force at section, Q = first moment of area of

the portion above interface with respect to the neutral axis of section, I = moment of inertia of

the composite cross section, and bv = width of interface. This equation is used to determine the

actual shear stress, while code equations are typically used to determine the shear capacity.

Deck

Girder

Horizontal

Shear

(2-1)

6

2.2 Research on Horizontal Shear

Transfer of the horizontal shear force is critical in a composite section. The researchers

below were all in pursuit of an understanding of how horizontal shear transfer occurs. They

performed experimental tests with different types of concrete, surface treatments, reinforcement

ratios, and loading processes in order to learn how the shear strength of a specimen changes in

accordance with these variables. The researchers evaluated the different horizontal shear strength

equations from various design codes. Some of the researchers proposed different equations for

predicting horizontal shear strength. The following sections discuss details of the different

experimental studies, how the tests were set up and what conclusions were drawn from the

experiments.

2.2.1 Banta

Banta (2005) completed 24 push-off tests on ultra high performance and lightweight

concrete. The ultra high performance Ductal® concrete block acted as the base or beam for the

push-off tests, while the lightweight concrete was the top slab. A concrete block was placed on

top of the specimen in order to produce an imposed normal force. Each Ductal® block was six

inches high and ten inches wide with lengths measuring 12 in., 18 in., or 24 in. Banta studied

four different interface treatments – smooth, keyed, deformed, and chipped. The horizontal shear

reinforcement varied from one to six legs of No. 3 reinforcing bars. The samples were loaded

monolithically while the applied load increased.

As with other push-off tests, the general behavior observed from Banta’s tests was that

the horizontal shear resistance increased until an initial crack formed, after which there was a

drop in strength to zero when no reinforcement was present. When reinforcement was present,

the increase in resistance continued until the steel leg ruptured. Banta found that current design

7

practices were conservative in predicting the horizontal shear with the AASHTO design equation

being the most conservative. He concluded that the best surface treatment was the chipped

surface so long as the chipping process did not cause stress on the beam.

2.2.2 Bass, Carrasquillo, and Jirsa

Bass, Carrasquillo, and Jirsa (1989) studied shear transfer of an interface with new and

old concrete under repeated cyclic loading. They performed 33 full scale push-off tests. The

specimens differed in the surface treatment, amount and embedment depth of the steel, amount

of normal reinforcement within each side of the specimen, and concrete strength of each side.

The base blocks were constructed vertically as if they were a column, which acted as the old

concrete. The base blocks were 24 in. wide and 24 in. deep for a length of 42 in. Almost all of

the new walls were 10 in. wide and cast alongside the columns with a length of 42 in. A “bond

breaker” was in place causing the shear interface length to be only 36 in. The new walls were

cast in an overhead, vertical, or horizontal manner. The various surface treatments used between

the old and new walls were untreated, heavily sandblasted, chipped, shear keys, and epoxy

bonding. The reinforcement crossing the shear interface varied from two to six No. 6

reinforcement dowels spaced between six to twelve inches.

The specimens underwent ten different load cycles. The first six load cycles were to a

specified load level. The next three load cycles aimed for a displacement of 0.1 in., and the last

load induced a displacement of 0.5 in. Bass, Carrasquillo, and Jirsa observed that the shear

capacity was greater when the shear reinforcement is embedded deeper. They also found that the

surface treatment did not have a clear effect on the shear strength when displacements were

greater than 0.2 inch. Deeper embedment and a greater amount of reinforcement both increase

the shear capacity.

8

2.2.3 Choi

Choi (1996) studied the shear strength when powder-driven nails were used across the

interface. Choi completed several different tests to understand the use of powder-driven nails,

including nail pullout strength tests and interface shear tests. Four large slabs measuring 4 m

(157.5 in.) by 1.4 m (55.1 in.) with a depth of 0.2 m (7.9 in.) were used as the base of the test

specimens. The surface of the slab was sandblasted to various degrees for the experiments. Shear

faces varied between 230 and 700 cm2 (35.65 and 108.5 in

2). The top pieces of the specimen had

a depth of 145 mm (5.7 in.). The number of powder-driven nails varied from zero to two nails in

a specimen. Choi found that the different levels of sandblasting did not seem to make a

difference in the horizontal shear strength. Specimens with nails had greater shear resistance than

those without nails.

2.2.4 Hanson

Hanson (1960) studied the horizontal shear strength between precast girders and cast-in-

place slabs. Hanson performed 62 push-off tests. He also conducted full beam tests on ten T-

shaped girders. He varied the use of adhesive bond agents, keys, stirrups, and surface roughness.

The precast base of the specimen was eight inches wide with a depth of twelve inches. The cast-

in-place top piece was 24 in. wide by 7 in. deep. The length of surface interface was 6, 12, or 24

inches. The surface treatments used were smooth, rough, bonded, unbonded, keyed, bare smooth

aggregate, and bare rough aggregate.

The push-off tests were performed vertically with the applied load acting parallel to the

interface. Hanson found that there was a base shear strength value depending on the interface

treatment. Reinforcement steel across the interface added strength to the base shear strength.

Keys did not add to or increase the strength of the shear resistance. Hanson suggested that

9

connections that are “a combination of a rough, bonded contact surface and stirrups extending

from the precast girders into the situ-cast deck slab” are of greatest concern for future research.

2.2.5 Hofbeck, Ibrahim and Mattock

Hofbeck, Ibrahim, and Mattock (1969) also studied the shear transfer across an interface.

They performed 38 push-off tests in order to understand the shear transfer behavior in interfaces

where a crack exists before shear transfer. The effects of shear reinforcement and concrete

strength on shear resistance were also studied. The typical specimens had a shear interface of 50

square inches with an overall depth of 10 inches. The amount of steel reinforcement varied from

zero to six stirrups with sizes varying from 1/8 in. diameter to No. 5. reinforcing bars. Concrete

strengths ranged from 2385 psi to 4510 psi.

The push-off specimens were axially loaded in the vertical position. Some of the

specimens were initially cracked and others were initially uncracked. The testing of the shear

specimens occurred with incremental loads. As the specimens were being tested, diagonal cracks

formed across the interface for both cracked and uncracked specimens. Hofbeck, Ibrahim, and

Mattock found that the precracked specimens produced lower ultimate shear strength. They also

reported that concrete strength had no effect on the shear strength, and that the shear strength

was a function of the reinforcement ratio. The shear-friction theory gave conservative answers,

so the researchers suggested imposing limits on the theory.

2.2.6 Kahn and Mitchell

Kahn and Mitchell (2002) performed fifty push-off tests in order to determine if the

American Concrete Institute (ACI) building code shear friction equation was adequate for high-

strength concrete. The specimens varied between a pre-cracked, uncracked, and cold joint. The

10

cold joints were treated as smooth or roughened. Concrete strengths ranged between 6,800 psi

and 17,900 psi, and reinforcement ranged between zero and four two-leg stirrups of No. 3 bars.

The shear interface was five inches by twelve inches long.

The specimens were tested four months after being cast. The specimens were placed

vertically while being axially loaded. Kahn and Mitchell found that the ACI code provided a

conservative estimate of the shear strength for high strength concrete. The researchers proposed

using the following equation for the horizontal shear stress capacity:

� = 0.05 �� + 1.4�� ≤ 0.2 ��[��] where vu = ultimate experimental shear stress capacity, f’c = concrete compressive strength, ρv =

shear friction reinforcement ratio (area of reinforcing steel to the product of interface width and

reinforcement spacing), and fy = yield stress of reinforcement. The equation is limited to

reinforcing steel having a yield strength fy of less than 60 ksi.

2.2.7 Kahn and Slapkus

Kahn and Slapkus (2004) studied shear transfer in high strength composite T-beams.

They tested six T-beams with precast webs and cast-in-place flanges. The concrete strength of

the webs was 12,000 psi, while the flanges were either 11,000 psi or 7,000 psi. The interface had

aggregate exposed to a height of 0.25 in. or greater. The test beams had five, seven, or nine No. 3

U-shape reinforcement across the surface.

The beams with 7,000 psi concrete flanges all failed in shear, while the beams with the

11,000 psi concrete flanges failed in flexure. Monolithic loading was applied at two points both

4.5 inches from the center of the beam. The shear interface area was 6 in. wide and 39.5 in. long.

Kahn and Slapkus found that the current AASHTO equation could be upwards of six times over

(2-2)

11

conservative for interface shear. They surmised that the equation proposed by Loov and Patnaik

(1994) was the best predictor of horizontal shear.

2.2.8 Kamel

Kamel (1996) conducted a study on composite bridge systems. A part of his research was

focused on the transfer of forces across an interface. He looked at 63 push-off tests to understand

the significance of shear interface type and connector type. The interface types considered in this

study included a debonded key, rough bonded, rough unbonded, smooth debonded, and smooth

bonded surfaces. The connectors were high strength threaded rods, reinforcement stirrups, or no

connectors. Several series of tests were conducted with various types of specimens. The shear

interface areas varied depending on the series, along with the type and amount of connectors and

number of interfaces.

The specimens were loaded in different ways according to the type of test. The double

shear specimens were placed vertically in the testing machine and the center slab was loaded.

Single shear tests were laid horizontally and a varying horizontal load was applied in addition to

a possible constant vertical load. Kamel found that the debonding sealant provided some extra

adhesion between the interfaces. He also found that extended reinforcement bars were more

effective than high strength threaded rods.

2.2.9 Loov and Patnaik

Loov and Patnaik (1994) completed sixteen beam tests in order to determine if the current

ACI horizontal shear stress equations could be simplified. The researchers varied two parameters

in their tests – the clamping stress and concrete strength. Clamping stresses ranged between 58

and 1120 psi when the concrete strength was 5000 psi. The concrete strength was also varied

12

between 6400 psi and 7000 psi with a constant clamping stress of 120 psi. Two groups of full

beam samples were tested: one with the flange running the entire length of the beam and the

other with flanges stopping short of the ends. The overall web length was 10 feet 6 inches. The

beam with short flanges stopped 3 feet 11 inches from the center on each side. The amount of

steel in addition to the web width was adjusted in order to gain a certain amount of clamping

stress. The beams were designed to mimic a precast beam with a cast-in-place deck. Almost all

of the beams were considered to have a rough interface.

The beams were loaded at a single point in the center of the beam. The beams were

supported three inches in from the end of each beam. Beams that had the full length flanges had

diagonal, flexure cracking before gaining horizontal cracking, thus the need for the shorter flange

span specimens. Some beams did end up failing in flexure, but most failed in horizontal shear.

Loov and Patnaik recommended using the following equation for predicting shear capacity:

�� = � !"15 + �� # �� ≤ 0.25 ��(��)

where vn = the nominal shear strength, k = a constant, λ = a constant used to account for the

effect of concrete density, ρvfy = the clamping stress, and f’c = the concrete strength. The

researchers noticed that there is minimal slip and stress before horizontal shear stress starts to

act.

2.2.10 Mattock, Johal and Chow

Mattock, Johal, and Chow (1975) performed 27 push-off tests in order to understand the

effects of moment on a shear plane, placement of reinforcement across the shear interface, and

tension across the shear plane. Six groups of specimens were tested, including four groups of

corbel type push-off tests and two groups of standard push-off tests. The corbel tests had a shear

(2-3)

13

interface measuring ten inches by six inches with each side ten inches deep. The standard push-

off tests had a shear interface of twelve inches by seven inches with an overall depth of fourteen

inches.

Eccentric loads were applied in the corbel push-off tests to study the effect of a moment

across a shear plane. The corbel specimens were incrementally loaded. For the standard push-off

tests, a tensile force was applied concentrically across the shear face. After analyzing the data

collected, Mattock, Johal, and Chow found that an applied moment does not affect the transfer of

shear force. It was essential for reinforcement to be in the tension region in order to ensure shear

transfer. The researchers believed that the equations below by Birkeland (1968) and Mattock

(1974), respectively, most accurately predicted the shear transfer, and that both equations should

be limited to 0.3f’c.

�� = 33.5'� �

�� = 400 + 0.8� �

2.2.11 Mattock, Li and Wang

Mattock, Li, and Wang (1976) studied the use of lightweight concrete and the effects it

has on horizontal shear. They performed 66 push-off tests in which they varied the type of

aggregate used in the lightweight concrete. The four types of aggregate used were naturally

occurring sand and gravel, rounded lightweight aggregate, angular lightweight aggregate, and

“sanded lightweight” aggregate. Concrete strength, the amount of shear reinforcement, and

precracking of an interface were three other variables studied. All of the push-off specimens had

an interface of ten inches by five inches with each side having a depth of six inches.

The specimens were loaded vertically on the testing machine. Uncracked specimens did

not display cracking until after tension cracks appeared at the shear interface. Mattock, Li, and

(2-5)

(2-4)

14

Wang discovered that the shear capacity for lightweight concretes is less than the shear capacity

for normal weight concretes. They found that the type of lightweight aggregate does not have a

significant effect on shear strength. Most current equations for shear friction needed to be

adjusted for lightweight concrete. The researchers suggested using the following equations for

sanded lightweight and all-lightweight respectively with both having � � at a minimum of 200

psi.

� = 0.8� � + 250�� ≤ 0.2 ��)*1000�� = 0.8� � + 200�� ≤ 0.2 ��)*800��

2.2.12 Patnaik

Patnaik (2001) performed 24 test beam tests in order to study the adequacy of the ACI

building code provisions for horizontal shear with a smooth interface. Two types of beams were

considered in the study – rectangular shaped sections and T-shaped sections. All of the T-beams

had flanges that were shorter than the length of the beams. The width of the interface varied for

the rectangular beams, while the T-beams had a set interface width of six inches. The concrete

strength ranged from 2500 psi to 5225 psi, while the clamping stress from the reinforcement

varied between 45 psi and 525 psi. The beams were all designed to fail in horizontal shear before

flexure or diagonal shear.

All of the beams were loaded in the center of the beam in increments. All beams

displayed horizontal shear slipping. Patnaik did not see a clear correlation between concrete

strength and horizontal shear strength, but he did realize that the clamping stress did have an

impact on the shear strength. All of the ACI design equations considered provided very

conservative predictions of horizontal shear. Patnaik recommended the use of the following

equations.

(2-7)

(2-6)

15

� = 0.6 + ��, �, ≤ 0.2 ��-./5.501-[798��] � = 0 )*��, �, < 0.3501-[50��]

where vu = the horizontal shear strength, ρvfy = the clamping stress in MPa, and f’c = the concrete

strength in MPa.

2.2.13 Saemann and Washa

Saemann and Washa (1964) tested 42 beams in order to better understand the influence of

the connections between precast and cast-in-place concrete. They were trying to gain a better

understanding of the effects of the level of roughness, position of joint in relation to the neutral

axis, length of the beam, reinforcement ratio across the interface, shear keys, and concrete

strength. The neutral axis was designed to be two inches above or below the shear interface. The

reinforcement ratio varied between 0 and 1.07 percent. The actual compressive strength of the

webs varied between 2530 psi and 3800 psi, while the compressive strength of the slabs ranged

from 2680 psi to 3870 psi.

The beams were statically loaded at two points each one foot from the center of the beam.

The beams were all designed to fail in shear before failing in flexure. Saemann and Washa

observed three types of failure: tension, tension-shear, and shear. Tension failures tended to

occur with the long beam specimens. The intermediate and short length beams tended towards

shear failures unless they had a reinforcement ratio greater than 1.0 percent. For a reinforcement

ratio greater than 1.0%, the intermediate and short beams experienced the tension-shear failure.

The shear strength went up for the short and intermediate beams with increased roughness and

increased reinforcement. The long beams did not seem as influenced by roughness or

reinforcement. Keys had about equal effectiveness to that of intermediate roughness. Increased

(2-9)

(2-8)

16

concrete strength did not have a significant effect on the strength. The joints with interfaces

below the neutral axis had greater strength than those above the neutral axis.

2.2.14 Scott

Scott (2010) performed 36 push-off tests in order to determine if there is significance in

having two different types of concrete at the shear interface. The shear interface of the specimens

was 24 in. by 16 in. with an overall depth of 18 in. The test specimens had three different

combinations of concrete type at the interface: lightweight-lightweight, lightweight-normal

weight, and normal weight-normal weight. The reinforcement ratio also varied between 0 and 1.2

percent. All of the specimens were raked to create a rough interface. The precast section that

acted as the girder was designed to have a strength of 8000 psi regardless of the type of concrete.

The deck cast-in-place section was designed for 4000 psi.

During testing, the push-off specimens were placed horizontally with a normal weight of

2.5 kips applied. The loading was applied to be concentric with the shear plane. Scott learned

from the experiments that the AASHTO LRFD horizontal shear equation was conservative,

especially for lightweight elements. Lightweight-normal weight specimens acted very similar to

the lightweight-lightweight sections. Normal weight-normal weight specimens provided greater

shear strength in comparison to those with lightweight concrete. There was greater variation in

shear strength for the lightweight concrete specimens than the normal weight specimens.

2.2.15 Valluvan, Kreger and Jirsa

Valluvan, Kreger, and Jirsa (1999) assessed the validity of the horizontal shear equation

in ACI 318-95 for concretes placed at different times. They performed 16 push-off tests, where

the effect of amount of reinforcing across the interface, amount of permanent compressive stress

17

on the interface, strength of the concrete, and construction procedure was considered. The

specimens were designed to have a shear interface of 4 in. by 32 in. The interface surfaces were

sandblasted in order to achieve a roughened interface. The existing concrete side had a concrete

strength of 3500 psi or 1750 psi. The new concrete section’s strength was either 6000 psi or 5100

psi.

The specimens were placed horizontally and a concentric load was applied along the

shear interface. The loads were either applied monotonically or in reversed cycles. Valluvan,

Kreger, and Jirsa found that the ACI code provided very conservative results, so they proposed

the following equations.

5� = "6�, � + 7#8 ≤ 0.25 ��6�)*8006� 9:;ℎ=.7 ≤ 8006�

5� = 78 ≤ 0.6 ��6� )*21006� 9:;ℎ=.7 > 8006�

where Vn = nominal shear capacity of the shear plane in lb, Avf = area of shear-friction

reinforcement across the shear plane in in.2, fy = yield strength of shear-friction reinforcement in

psi, N = permanent net compression across the shear plane in lb, μ = coefficient of friction, and

Ac = area of concrete section resisting shear transfer in square inches. The researchers claimed

that the ACI code equations were extremely conservative when there was a sustained

compression force.

2.2.16 Walraven and Reinhardt

Walraven and Reinhardt (1981) conducted a series of experimental tests to gain a better

understanding of horizontal shear transfer in order to create a more complete finite element

model. The objective of the study was to determine the effect of reinforcement ratio, bar size,

concrete strength, roughness of the interface, angle of the reinforcement, and dowel action on

horizontal shear strength. The reinforcement ratio varied between 0.14 and 3.35 percent with bar

(2-11)

(2-10)

18

sizes between 4 mm (0.16 in.) and 16 mm (0.63 in.). The concrete strengths were 20 N/mm2

(2900 psi), 30/35 N/mm2

(4350/5075 psi) and 56 N/mm2 (8120 psi). The specimens had an

interface length of 300 mm (11.8 in.) with a width of 120 mm (4.7 in.) and overall depth of 400

mm (15.7 in.). The researchers also performed tests with external reinforcement. All of the

specimens were pre-cracked before testing.

The specimens were placed vertically for loading across the shear plane. Walraven and

Reinhardt did not find any significance in the size of the bar used; it seemed that the most

influential factor was reinforcement ratio. The angle of the shear reinforcement was not

significant unless inclined to 135 degrees. The quality of concrete had an effect on the pattern of

cracking. Hysteresis was observed when the specimens were unloaded and reloaded.

2.3 AASHTO LRFD Bridge Design Specifications

The purpose of this study is to evaluate the AASHTO LRFD (2010) horizontal shear

strength equations. The equation for horizontal shear strength as given in the AASHTO

specifications is:

5?@ = A5�@ 5?@ ≥ 5@

where Vri = factored interface shear resistance (kip), φ = resistance factor for shear (0.90 for

normal weight concrete and 0.70 for lightweight concrete), Vni = nominal interface shear

interface (kip), and Vui = factored interface shear force due to total load based on the applicable

strength and extreme event load combinations (kip). The nominal shear resistance of the

interface plane shall be taken as:

5�@ = C6�� + 8"6�, � + 1�# ≤ D�. EFG ��6��FH6��

(2-13)

(2-12)

(2-14)

19

where c = cohesion factor, Acv = area of concrete considered to be engaged in interface shear

transfer (in2), μ = friction factor, Avf = area of interface shear reinforcement crossing the shear

plane within the area Acv (in2), fy = yield stress of reinforcement (not to exceed 60 ksi), Pc =

permanent net compressive force normal to the shear plane; if the force is tensile then Pc=0.0

(kip), K1 = fraction of concrete strength available to resist interface shear, f’c = specified 28-day

compressive strength of the weaker concrete on either side of the interface (ksi), and K2 =

limiting interface shear resistance (ksi). The values for c, μ, K1, and K2 depend on the type of

concrete and the condition of the interface surface. These values are listed below:

For normal-weight concrete placed monolithically:

c = 0.40 ksi

μ = 1.4

K1 = 0.25

K2 = 1.5 ksi

For lightweight concrete placed monolithically, or nonmonolithically, against a clean

concrete surface, free of laitance with surface intentionally roughened to amplitude of

0.25 in.:

c = 0.24 ksi

μ = 1.0

K1 = 0.25

K2 = 1.0 ksi

For normal-weight concrete placed against a clean concrete surface, free of laitance, with

surface intentionally roughened to amplitude of 0.25 in.:

c = 0.24 ksi

μ = 1.0

20

K1 = 0.25

K2 = 1.5 ksi

For concrete placed against a clean concrete surface, free of laitance, but not intentionally

roughened:

c = 0.075

μ = 0.6

K1 = 0.2

K2 = 0.8 ksi

These equations were determined from data obtained from tests on horizontal shear

conducted by various researchers. The normal weight, non-monolithic concrete strength data

ranged between 2.5 ksi and 16.5 ksi. The normal weight, monolithic concrete data varied from

3.5 ksi to 28.0 ksi. Sand-lightweight concrete strengths were between 2.0 ksi and 6.0 ksi, while

all-lightweight concrete strength data was between 4.0 ksi and 5.2 ksi.

2.4 Reliability Analysis

The assurance of structural safety and reliability is one of the key objectives in

engineering design. Such designs are normally formulated under inherent conditions of

uncertainty. These uncertainties result from the random nature of loading and the structural

resistance, as well as imperfections in the load and resistance models. Through the applications

of reliability theory it is possible to quantify some of the uncertainties involved in design, and to

incorporate consideration of these uncertainties in design codes.

Reliability is a measure of the likelihood of a failure. In structural reliability analysis

failure is defined within the context of a limit state. A limit state is the boundary between desired

and undesired performance. The two types of limit states in structural design are strength limit

21

states and serviceability limit states. In the fundamental reliability model, the load, Q, and the

resistance, R, are considered to be random variables which can be described by their respective

probability density functions. The quantitative measure of safety or reliability is the probability

of survival, ps, which is given by

ps = P(R > Q)

or its complement measure, the probability of failure pf

pf = P(R < Q)

In general the probability density functions for the resistance fR(r) and the load effect fQ(q) are

required to evaluate the probability of failure. In practice, the density functions of the load and

resistance are seldom available. Thus, for practical application, approximate methods of

reliability evaluation are necessary. Most of these methods are based on characterizing the load

and resistance by their first two moments, that is, their means and standard deviations and the

measure of reliability is the reliability index.

2.4.1 Reliability Index

Various formats for calculating the reliability index β have been developed. These are

described in Nowak and Collins (2000). In general, reliability can be expressed through the use

of a limit state function g() such as

g(R,Q) = R – Q

where R – Q represents the safety margin. Failure occurs when R – Q < 0 or when g() < 0. The

probability of failure pf can be expressed as

pf = P(R-Q) < 0 = P(g() <0)

If R and Q are normally distributed random variables the reliability index can be

calculated from the following equation:

22

I = JKLJMNOKPQOMPR

S.T

where mR = mean value of resistance, mQ = mean value of the total load effect, σR = standard

deviation of resistance, and σQ = standard deviation of the total load effect. The reliability index

is directly related to the probability of failure, pf, by

I = ALG(�,) where φ

-1() is the inverse standard normal distribution function.

2.4.2 Resistance Statistics

The resistance structure can be represented as the product of the nominal resistance and

three factors:

U = U� ×0 × W × 1

where Rn = nominal resistance, M = material factor (reflecting variations in material properties

such as concrete strength, yield strength of reinforcing steel and modulus of elasticity), F=

fabrication factor (representing variations in member dimensions, moment of inertia and

placement of reinforcement), and P = professional factor (reflecting the accuracy of the

analytical model for predicting the resistance). The mean value of the resistance is given by:

DX = U� Y Z [

where λM = mean value (or bias factor) of M, λF = mean value (or bias factor) of F, and λP =

mean value (or bias factor) for P. The coefficient of variation of the resistance, R, is:

5X = (5YH + 5ZH + 5[H)G/H

where VR = coefficient of variation for nominal resistance, VM = coefficient of variation of M,

VF = coefficient of variation of F, and VP = coefficient of variation of P.

(2-19)

(2-17)

(2-15)

(2-18)

(2-16)

23

For the purposes of the study, the bias and coefficient of variation of the material and

fabrication factors were taken from previous research. Nowak and Szerszen (2001) listed

statistics of the fabrication factor for dimensions of concrete components, steel reinforcing bars

and prestressing strands. For example, it was suggested that for the width of a beam that is cast-

in-place the mean value of the fabrication factor is 1.01and the coefficient of variation is 0.04.

Nowak and Szerszen (2001) computed statistics of concrete strength from test data

obtained from industry. The test data included normal strength concrete in the range of 3,000 psi

to 6,500 psi, high strength concrete with strengths varying between 7,000 psi and 12,000 psi, and

lightweight concrete with strengths ranging between 3,000 psi and 5,000 psi. They determined

that the bias factor depends on the concrete strength. There is variation in the bias value if the

concrete strength is below about 5,000 psi. The bias at 3,000 psi is 1.4 and the bias curves down

to 1.15 at 5,000 psi. If the concrete strength is greater than 5,000 psi, the bias levels out to 1.15.

According to Nowak and Szerszen (2001) the coefficient of variation of concrete strength is 0.10

due to the uniformity of the data.

2.4.3 Load Statistics

For short and medium span girder bridges the most important load combination is a dead

load and live load. Thus, the loads considered in this study were limited to dead load and live

load. The statistical parameters for the dead and live load were obtained from previous research.

According to Nowak (1999) bias factor (ratio of mean to nominal) for cast-in-place concrete is

1.05 with a coefficient of variation of 0.10. For precast concrete the bias factor is 1.03 and the

coefficient of variation is 0.08. The variation in dead load comes from the weight of materials,

the dimensions, and the idealization in analytical models. For live loads Nowak (1999)

24

determined that the bias factor for a 75 year live load is 1.28 with a coefficient of variation of

0.18.

For the dead and live load combination the AASHTO LRFD standard specifies a dead

load factor of 1.25 for structural and attached nonstructural components and live load factor of

1.75 for vehicular load.

The mean and standard deviation of the combined load are obtained from the mean and

standard deviations of the individual loading components. The mean load is given by

D� = ] ^_ + ` __

where mQ = mean load, D = dead load, λDL = dead load bias factor, L = live load, and λLL = live

load bias factor. The standard deviation of the load is calculated from the following equation:

a� = '(] ^_5̂ _)H + (` __5__)H

where σQ = standard deviation of the combined load, D = dead load, λDL = dead load bias factor,

VDL = coefficient of variation of the dead load, L = live load, λLL = live load bias factor, and VLL

= coefficient of variation of the live load.

2.5 Summary of Literature Review

This literature review has shown that there is a considerable variability in the prediction

of horizontal shear strength based on the test results from the various studies. Research results

indicated that the reinforcement ratio, treatment of the interface, and the type of concrete are the

most important factors in predicting horizontal shear strength. The strength of the concrete did

not seem to play a significant role. The study of horizontal shear strength equation in the 5th

edition of the AASHTO LRFD bridge design will utilize the data obtained from the literature

review in order to assess the reliability of the AASHTO horizontal shear equation.

(2-20)

(2-21)

25

CHAPTER 3: DATABASE AND CALCULATION METHODS

3.1 Selection of Data

When considering the results of the researchers discussed in the literature review, not all

data was applicable to the current study. The primary types of data desired were data from tests

on interface types of smooth, rough, or monolithic where a failure had occurred in shear. Data

from Loov and Patnaik (1994); Kahn and Slapkus (2004); and Mattock, Johal, and Chow (1975)

was excluded for the cases where the specimens failed in flexure. Two of the specimens from

Valluvan, Kreger, and Jirsa (1999) were not included in the database because of failure in the

grout. Several of the specimens from Saemann and Washa (1964) failed in tension and tension-

shear and so they were excluded from the study. Data from Banta (2005) was not considered

because the interface consisted of deformed (a wavy deformation of 0.5 in. on 2 in. intervals),

keyed, and chipped (the jackhammered surface exposed steel fibers which added to the strength)

surfaces. Some of the specimens from Saemann and Washa (1964) and Hanson (1960) were also

excluded because the specimens had a keyed interface. Some specimens from Bass, Carrasquillo,

and Jirsa (1989) were excluded because of shear keys or because the specimens were cast

overhead. Several specimen groups from Kamel (1996) were excluded because of the double

shear interface and shear keys. Walraven and Reinhardt’s (1981) specimens with external

reinforcement were also excluded in this study.

Most of the tests for horizontal shear consisted of either a standard push-off test or a full

beam test. The interface area for the full beam tests was taken as the interface width multiplied

by the standard spacing of one unit of shear reinforcement. One exception to this was for Kahn

and Slapkus (2004), since they specified an interface area in their article. The interface area for

the push-off tests was taken as the product of the given width and contact length.

26

3.2 Calculation of Predicted Horizontal Shear

The AASHTO LRFD Bridge Design horizontal shear strength equation (2-14) was the

primary equation under consideration for this study. The information collected from the

experimental test results for the database consisted of the surface type, the concrete type, the

shear interface area, the amount of reinforcement across the interface, the yield strength of the

reinforcement, the applied normal force, the strength of the concrete, and the actual measured

shear strength. The surface was considered smooth if the intentional amplitude of an interface

surface did not reach 0.25 inch. For specimens made with two different types of concrete, the

concrete type that produced the most conservative results, which was lightweight, was taken as

the type of concrete. If the test was a full beam test where the interface area was taken as the

width of the interface multiplied by the spacing of the reinforcement, the area of the

reinforcement was taken as one unit of reinforcement whether that was one or two legs. The

yield strength of the reinforcing steel was taken as whatever was supplied by the researcher; no

limitations were used in the equation. If the concrete members were not cast monolithically, the

lesser concrete strength was used in the equation. The values of the applied shear were divided

by two to satisfy equilibrium for full beams tests for the cases where the load was applied at one

point in the center of the beam. The horizontal shear predicted by the AASHTO horizontal shear

equation using all of the measured properties from the experimental tests were then compared to

the actual measured horizontal shear values.

3.3 Reliability Analysis Procedures

Once the predicted horizontal shear values using measured parameters were calculated,

an analysis of the reliability of the AASHTO LRFD equation was performed. In order to

determine the reliability index, β, it is necessary to determine the statistics of the load and

27

resistance. The resistance as given in Equation (2-17) is the product of the nominal resistance

and the professional, material, and fabrication factors. The professional factor, P, is the ratio of

the measured shear strength to the shear strength predicted by the AASHTO LRFD horizontal

shear equation. Statistics of the professional factors such as the bias (or mean), standard

deviation and coefficient of variation for each category of concrete type (normal, lightweight,

high performance) and interface type (rough, smooth, monolithic) were computed using the

information collected in the database. The nominal resistance was obtained from the AASHTO

horizontal shear equation (Equation 2-14) using actual measured values for all of the variables in

the equation. The standard normal variable, Z, was calculated and plotted in order to determine if

P was normally distributed. The equation for the standard normal variable is:

� = ��

��

where Vtest = the measured strength of the specimen, Vcalc = the predicted strength, Vmean = the

average measured strength of the all the specimens in category, and σ = the standard deviation

for the category. If the data set is normally distributed, the standard normal variables should form

an approximate straight line when plotted. Figures 3.1, 3.2, and 3.3 show the plotted distributions

of the standard normal variables. Since the charts showed a straight line in each category, this

indicates that P is normally distributed.

(3-1)

28

Figure 3.1: Rough interface normal variable distributions

Figure 3.2: Smooth interface normal variable distributions

-2

-1

0

1

2

3

4

0 1 2 3 4 5

Sta

nd

ard

No

rm

al

Va

ria

ble

Professional Bias

HIGH PERFORMANCE

LIGHTWEIGHT CONCRETE

NORMAL WEIGHT CONCRETE

-2

-1

0

1

2

3

4

0 2 4 6 8

Sta

nd

ard

No

rm

al

Va

ria

ble

Professional Bias

HIGH PERFORMANCE CONCRETE



29

Figure 3.3: Monolithic interface normal variable distributions

The resistance statistics (mean and standard deviation) for the load and resistance were

then calculated. The mean resistance was computed by multiplying the nominal resistance by the

professional, material and fabrication bias factors as given in Equation (2-18) and the coefficient

of variation of R was computed from the Equation (2-19) using the coefficients of variation of P,

M, and F presented in Section 2.4.2. The mean value and standard deviation of the load were

determined from Equations (2-20) and (2-21) using load statistics given by Novak (1999). The

reliability index was calculated from Equation (2-15) for a wide range of D/(D+L) (dead to total

load) ratios.

-3

-2

-1

0

1

2

3

4

0 0.5 1 1.5 2 2.5 3

Sta

nd

ard

No

rm

al

Va

ria

ble

Professional Bias

HIGH PERFORMANCE CONCRETE



30

CHAPTER 4: PRESENTATION OF RESULTS AND ANALYSIS

4.1 Typical Results

When considering the data presented, the necessity of separating the data for more

accurate results was apparent. The data was separated into three interface categories, namely,

rough, smooth, and monolithic. Within these three categories the data was further subdivided by

concrete type into normal weight, lightweight, and high strength concrete. In general the values

for horizontal shear obtained from the experimental studies were significantly higher than those

predicted by the AASHTO horizontal shear equation indicating that the AASHTO equation is

overly conservative. The average value of the professional factor, which is the ratio of the

measured strength to the calculated horizontal shear strength, for the different categories ranged

from 0.65 to 3.18. Also, the coefficients of variation of the professional factor tended to be quite

high indicating that there is considerable variability in the data. The higher coefficients of

variation were typically obtained for the studies in which there were a large number of

specimens. Since most of the research had been done with normal weight concrete of a rough or

smooth interface, the greatest variation between samples was found in this category.

4.1.1 Rough Interface

Figures 4.1, 4.2, and 4.3 show the variation of horizontal shear stress with clamping

stress for specimens with a rough interface for normal weight, lightweight, and high strength

concrete, respectively. Also shown in these figures is the horizontal shear strength as predicted

by the AASHTO equation. As can be seen from the figures, there is a considerable amount of

scatter in the test results even for a particular researcher such as, for example, the test results

from Valluvan, Kreger, and Jirsa (1999). This scatter will be reflected in a high coefficient of

variation.

31

Figure 4.1: Clamping stress versus actual horizontal shear stress for rough interface and normal strength concrete.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)

Clamping Stress (AvFy+Pn)/Acv (ksi)

Loov & Patnaik (NW)

Scott (NW)

Hanson (NW)

Valluvan, Kreger & Jirsa (NW)

Bass, Carrasquillo & Jirsa (NW)

Kamel (NW)

AASHTO Normal

32

Figure 4.2: Clamping stress versus actual horizontal shear stress for rough interface and lightweight concrete.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)


Scott (LW)

AASHTO Lightweight

33

Figure 4.3: Clamping stress versus actual horizontal shear stress for rough interface and high strength concrete.

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)


Kahn & Mitchell (HS)

Kahn & Slapkus (HS)

AASHTO Normal

34

4.1.1.1 Normal Weight Concrete

There were 77 tests from six different research groups on rough interfaces with normal

weight concrete. Again, there was a great deal of variation in the test results. The majority of the

data obtained from Hanson (1960) did not predict the shear strength well. All of the specimens

with a rough interface had measured strength that were higher than the predicted strength. The

measured shear strength for the specimens with bonded rough surfaces was higher and the ratio

of measured to predicted strength was closer to 1.0.

There was a great deal of variability in the ratio of measured to predicted strength for the

data obtained from Loov and Patnaik (1994). Bias values for this data set ranged between 0.37

and 2.52. As the spacing between units of reinforcement increased, the bias value also increased.

The measured values for the specimens tested by Scott (2010) were reasonably close to the

values predicted by the AASHTO equation. Bias values for the test data from Valluvan, Kreger,

and Jirsa (1999) ranged from 1.01 to 3.80. The actual shear force increased with the increase in

the clamping force.

The measured horizontal shear strength for the three specimens tested by Bass,

Carrasquillo, and Jirsa (1989) was higher than the strength predicted by the AASHTO equation.

The professional bias for the tests done by Kamel (1996) ranged from 0.37 to 1.36. The bias

values were higher for the specimens that had threaded rods made from higher strength (100 ksi).

For the other six specimens, there was no clear reason as to why there was so much variability in

the results.

The measured shear stress for a given clamping stress is plotted in Figure 4.1. The shear

stress predicted by the AASHTO equation is also shown in the figure. It can be seen that the data

is predicted well by the current equation, since most of the measured values are close to the

values predicted by the AASHTO equation.

35

4.1.1.2 Lightweight Concrete

Figure 4.2 shows clamping force versus measured horizontal shear force for rough

interface and lightweight concrete. All of the data was obtained from Scott (2010). As can be

seen from the figure the data for this category is quite uniform. Most of the test specimens gave

horizontal shear values that were higher than those predicted by the AASHTO equation. The

professional bias varied between 0.89 and 2.08. There were only two specimens for which the

bias was less than 1.0. All of the measured values were below the upper limit specified in the

AASHTO equation.

4.1.1.3 High Strength Concrete

For the case of rough interface and high strength concrete, the measured horizontal shear

values were much higher than the values predicted by the AASHTO equation. For example, for

the data obtained from Kahn and Mitchell (2002), the average professional bias was 2.83.

Although no clear trends were observed it did appear that for concrete strength higher than

12,000 psi the bias was over 3.0. The measured horizontal shear values for the data from Kahn

and Slapkus (2004) were less than those predicted by the AASHTO equation. The same pattern

was observed for the test results on normal weight concrete. There does not appear to be any

clear reason that their measured values were lower than those predicted by the AASHTO

equation.

Figure 4.3 shows that there is a need for a different equation since the test results show a

much higher increase in shear strength with increasing clamping force than that predicted by the

AASHTO equation.

36

4.1.2 Smooth Interface

There were 220 test specimens that had a smooth interface. In general the measured shear

strength of the smooth interface specimens was higher than that predicted by the AASHTO

equation. There was only one set of test results (Hanson, 1960) for which the measured shear

strength values were less than those predicted by the AASHTO equation. Figures 4.4, 4.5, and

4.6 show the variation of measured shear stress with clamping stress. Also shown in the figures

is the shear strength predicted by the AASHTO equation.

37

Figure 4.4: Clamping stress versus actual horizontal shear stress for smooth interface and normal weight concrete.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)


Saemann & Washa (NW)


Patnaik (NW)

Choi (NW)

Hanson (NW)

Kamel (NW)

AASHTO

38

Figure 4.5: Clamping stress versus actual horizontal shear stress for smooth interface and lightweight concrete.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)


Banta (LW)

AASHTO

39

Figure 4.6: Clamping stress versus actual horizontal shear stress for smooth interface and high strength concrete.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)



AASHTO

40


There were a total of two hundred tests performed on specimens with smooth interfaces

made from normal weight concrete. The ratio of measured to predicted shear strength ranged

from 1.1 to 5.17 for the tests conducted by Saemann and Washa (1964). This ratio was higher for

specimens with intermediate roughness, that is, specimens that did not meet the roughness

amplitude of 0.25 in. It also appeared that specimens with similar conditions but had smaller

interface areas had higher measured to predicted strength ratios. The test data obtained from

Bass, Carrasquillo, and Jirsa (1989) also gave ratios of measured to predicted horizontal shear

strength greater than 1.0. For this set of tests the ratio ranged from 1.14 to 2.40. The lowest ratio

of 1.14 was obtained for the only specimen that was smooth, while the other specimens were

sandblasted but not to the required roughness amplitude. There did not seem to be a clear

difference beyond the level of roughness as to why some specimens had higher or lower

measured to predicted strength ratios. The professional bias for the tests by Patnaik (2001) was

1.80. The ratios of test to predicted shear strength varied from 0.71 to 4.41.

The highest actual to predicted ratios were found for test specimens that had the greatest

amount of reinforcement in the smallest amount of interface area. Choi (1996) performed 103

push-off tests. The overall professional bias factor for this set of tests was 2.16 and the values

ranged from 0.43 to 6.83. There was a clear increase in the bias when there was no reinforcement

across the shear interface in the push-off specimens. Other than the lack of reinforcement, there

were no other factors that could account for the variation in the bias values. For the specimens

tested by Hanson (1960), there was no effort made to prevent bonding to the precast girder.

These tests produced a mean actual to calculated shear strength ratio of 0.69. The measured to

predicted ratios varied between 0.45 and 1.15. There was no clear reasoning for the variation.

The mean value of test to predicted shear strength ratios for the specimens tested by Kamel

41

(1996) was 2.32 with individual values of the ratio ranging from 1.05 to 4.37. There were two

specimens that were bonded, and these two specimens gave ratios greater than four. All of the

other specimens were smooth, unbonded that all had ratios of test to predicted shear strength

below 2.75. Figure 4.4 shows that the current AASHTO equation is quite conservative, since

most of the measured shear strength values lie above the line.


Banta (2005) was the only researcher in this database that considered a smooth interface

for lightweight concrete. The ratio of actual shear strength to predicted shear strength varied

between 0.66 and 2.99. When no reinforcement steel was present, the ratio was higher. The bias

was lower when there was less steel area relative to the interface area. There were only three

push-off tests out of a total of eighteen for which the bias was less than 1.0. Figure 4.5 illustrates

that the current AASHTO equation is a good fit for the results presented by Banta.


There were only two specimens which had a smooth interface and were made with high

strength concrete. These two specimens were tested by Kahn and Mitchell (2002). The

professional bias values for the two specimens were 3.18 and 3.19. Since there were only two

specimens, no conclusions can be made with any confidence as seen in Figure 4.6.

4.1.3 Monolithic Interface

The monolithic data set of 207 specimens showed that the shear strength for the

monolithic data was predicted fairly well by the AASHTO LRFD equation. Figures 4.7, 4.8, and

4.9 illustrate how well the monolithic specimens’ shear stresses are predicted by the equation.

42

Figure 4.7: Clamping stress versus actual horizontal shear stress for monolithic interface and normal weight concrete.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)


Hofbeck, Ibrahim & Mattock (NW)

Mattock, Johal & Chow (NW)

Mattock, Li, & Wang (NW)

Walraven & Reinhardt (NW)

AASHTO - Norm. Wt.

43

Figure 4.8: Clamping stress versus actual horizontal shear stress for monolithic interface and lightweight concrete.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)


Mattock, Li, & Wang (LW)

Walraven & Reinhardt (LW)

AASHTO - Lightweight

44

Figure 4.9: Clamping stress versus actual horizontal shear stress for monolithic interface and high strength concrete.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)



AASHTO - Norm. Wt.

45


The data for monolithically cast specimens made from normal weight concrete was

obtained from tests performed by four research groups. The bias values for the tests by Hofbeck,

Ibrahim, and Mattock (1969) ranged from 0.55 to 1.57 with a mean of 1.20. The AASHTO

equation under predicted the strength of all the uncracked specimens. There was a slight trend

that if there was a very low amount of reinforcement across the interface, the shear equation did

not do an adequate job of predicting the horizontal shear strength. The ratio of actual to

calculated horizontal shear strength for the results from Mattock, Johal, and Chow (1975) were

less than or equal to 1.0. The professional bias was 0.92 and the ratio of measured to predicted

strength ranged from 0.63 to 1.36. A general trend that was observed was that for a constant

interface shear area, the ratio of actual to measured strength decreased as the shear reinforcement

decreased. Test results from Mattock, Li, and Wang (1976) in comparison to the AASHTO

equation produced a mean professional factor of 1.09 with values of the ratio of measured to

predicted shear strength being between 0.64 and 1.48. The highest ratio of 1.48 was found when

there was no shear reinforcement across the interface. Walraven and Reinhardt (1981) data was

predicted well by the current equation through the mean professional factor of 1.21 with a

minimum ratio of 0.89 and maximum ratio of 1.79. There was a higher ratio when the concrete

mix did not include quartz powder in the concrete mix. Figure 4.7 shows that the current

equation has an even variation around the predicted value, which means the current equation

works well for normal weight monolithic concrete.


Mattock, Li, and Wang (1976) also performed shear tests for lightweight concrete in

monolithic placements. The average professional factor was 1.13 in a range of 0.76 to 2.33.

46

When there was no reinforcement across the interface, the bias was above 2.0, while all other

ratios were below. Walraven and Reinhardt (1981) performed a series of shear strength test on a

set of lightweight concrete. The data presented confidence in the AASHTO equation with a mean

actual to predicted ratio of 1.81 within the range of 1.40 to 2.30. It seemed that as the clamping

stress increased, the actual to predicted horizontal shear ratio came closer to 1.0. Figure 4.8

illustrates that there may be a need to change the inclination of the clamping stress.


The only tests on horizontal shear strength of high strength concrete specimens formed

monolithically were done by Kahn and Mitchell (2002). The results of the 38 push-off tests when

compared with the AASHTO equation resulted in mean actual shear strength to predicted shear

strength ratio of 1.61. The range of ratios was 0.68 to 2.72. It was apparent that uncracked

specimens were under predicted as seen through a higher ratio of actual to theoretical where the

minimum ratio is 1.53. Values of the professional factor for the cracked specimens ranged

between 0.68 and 1.39. This clearly indicates that the importance of whether or not a surface has

been precracked. There is a high amount of variation as illustrated in Figure 4.9, and the data is

mostly conservative.

4.2 Reliability Analysis

After all of the ratios of actual to predicted horizontal shear strengths were calculated, the

distribution of the data was confirmed to have a normal distribution as shown in Figures 3.1, 3.2,

and 3.3. All of the data categories within each group were normally distributed, since the

standard normal variables were in a straight line. Since there is insufficient data on cohesion and

friction factors to perform a Monte Carlo simulation, a simple reliability analysis was performed

47

where the overall equation was considered instead of an advanced reliability analysis considering

all of the individual variables in the shear equation.

4.2.1 Bias and Coefficient of Variation

The professional factor, which is the ratio of actual horizontal shear strength to calculated

horizontal shear strength, was calculated for each specimen. The mean professional factor for

each category was calculated along with the standard deviation and coefficient of variation. A

summary of the bias, standard deviation, and coefficient of variation is presented in Table 4.1. It

is seen that for the categories where there were a large number of test results there is a great deal

of variability as indicated by the high values of the coefficient of variation. For the cases where

the test results were obtained from only one research study, the information must be taken with

some hesitation, since there are no other results to compare against. Since construction

procedures are not always consistent it is important to compare and verify tests data from one

study with that obtained from other similar studies.

Table 4.1 Statistics of the Professional Factor

Concrete

Weight

Interface

Surface

Number

of

Specimens

Number of

Research

Groups

Mean Standard

Deviation

Coefficient

of

Variation

Normal

Rough 77 6 1.192 0.757 0.634

Smooth 200 6 2.081 1.315 0.632

Monolithic 106 4 1.133 0.238 0.210

Lightweight

Rough 18 1 1.439 0.360 0.250

Smooth 18 1 1.520 0.646 0.425

Monolithic 63 2 1.241 0.419 0.338

High

Strength

Rough 13 2 2.364 0.986 0.417

Monolithic 38 1 1.615 0.677 0.419

48

Statistical parameters of the resistance (mean and coefficient of variation) were then

computed using the statistics of the professional factor listed in Table 4.1 and the statistics of the

material and fabrication factors obtained from previous research as described in Section 2.4.2.

The statistical parameters of the horizontal shear resistance are summarized below in Table 4.2.

Table 4.2 Statistical Parameters of Resistance

Concrete

Weight

Interface

Surface

Bias

Factor

Coefficient

of Variation

Normal

Rough 1.482 0.643

Smooth 2.690 0.641

Monolithic 1.396 0.236

Lightweight

Rough 1.686 0.272

Smooth 1.765 0.438


High

Strength

Rough 2.746 0.431


49

4.2.2 Reliability Indices

Reliability indices were calculated for the dead plus live (D+L) load combination for the

different categories of interface and concrete type using Equations (2-20) and (2-21). Reliability

indices for a range of dead to dead plus live load (D/(D+L)) ratios are shown in Figures 4.10,

4.11, and 4.12.

Figure 4.10: Reliability indices for AASHTO LRFD for normal weight concrete

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW- Rough

NW - Mono

50

Figure 4.11: Reliability indices for AASHTO LRFD for lightweight concrete

Figure 4.12: Reliability indices for AASHTO LRFD for high strength concrete

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

51

Since there were only two test specimens with high strength concrete and smooth

interface, the reliability analysis was not performed for this category because of a lack of data.

The specimens with normal weight concrete monolithically placed had the highest reliability

indices followed by specimens with lightweight concrete and a rough interface. It is important to

remember that the results for categories for which the test data was obtained from one research

group should be considered with reservation since the variation in results due to different

construction methods and concrete mixes cannot be observed.

4.2.3 Comparison to Wallenfelsz

Wallenfelsz (2006) studied the horizontal shear strength of precast on precast sections. At

the conclusion of this research, Wallenfelsz proposed the following equation for predicting the

horizontal shear strength:

�� = �� + �� Cohesion is considered separately from the clamping stress under the belief that the cohesive

bond fails before the clamping of the reinforcement occurs. The cohesion factor and friction

factors were taken to be the same as those in the current AASHTO LRFD equation. In order to

compare the horizontal shear strength predicted by AASHTO LRFD equation and the

Wallenfelsz equation, the reliability analysis was repeated using the nominal resistance as

predicted by the Wallenfelsz equation. A summary of the statistical parameters of the

professional factor for the Wallenfelsz equation is given in Table 4.2. The mean value of the

professional factor was higher than expected, since the two elements of the AASHTO equation

are considered separately in the Wallenfelsz equation. Also, the coefficient of variation for most

of the categories was lower.

(4-1)

52

Table 4.3 Statistics of Professional Factor for Wallenfelsz Equation

Concrete

Weight

Interface

Surface

Number

of

Specimens

Number of

Research

Groups

Mean Standard

Deviation

Coefficient

of

Variation

Normal

Rough 77 6 1.406 0.513 0.365

Smooth 200 6 2.976 1.580 0.531

Monolithic 106 4 1.555 0.509 0.328

Lightweight

Rough 18 1 1.894 0.300 0.159

Smooth 18 1 1.987 0.557 0.280

Monolithic 63 2 1.590 0.851 0.535

High

Strength

Rough 13 2 3.736 1.541 0.412

Monolithic 38 1 2.655 1.189 0.448

Resistance statistics were then computed from Equations (2-18) and (2-19) using the statistics of

the professional factor from Table (4.3). Resistance statistics for the various categories are

shown in Table 4.4. Figure 4.11 shows reliability indices calculated for the dead plus live load

(D+L) combination for the Wallenfelsz equation are higher than those obtained using AASHTO

LRFD equation.

Table 4.4 Resistance Statistics for Wallenfelsz Equation

Concrete

Weight

Interface

Surface

Bias

Factor

Coefficient

of Variation

Normal

Rough 1.747 0.381

Smooth 3.847 0.542


Lightweight

Rough 2.219 0.192

Smooth 2.308 0.300


High

Strength

Rough 4.339 0.426


53

Figure 4.13: Reliability indices for D+L load combination for Wallenfelsz equation for normal

weight concrete


weight concrete

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW -

Rough

NW -

Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW -

Rough

LW - Mono

54


weight concrete

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

55

CHAPTER 5: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

5.1 Summary

Composite action of a bridge’s deck and girder system is essential in producing an

efficient superstructure. The combination of the deck and girder increases the moment of inertia

so a stiffer cross section is produced to resist the moment. Applied forces on the deck are

transferred through to the girders by the cohesive action between the interface of the deck and

the girder, in addition to the tensile forces in the reinforcement crossing the interface. The

transfer of forces allows for the girder and deck to act as one to resist the applied load.

The objective of this research was to study the reliability of the provisions for horizontal

shear strength in the AASHTO LRFD bridge design specifications. A database of applicable

horizontal shear tests was created from previous research done in this area. The database

contains the essential equation variables for each specimen. The horizontal shear strength

predicted by the AASHTO equation was computed using the actual measured values of all of the

variables in the equation. The professional factor is the ratio of the measured horizontal shear

strength from the tests to the shear strength predicted by the AASHTO equation. Statistics of the

professional factor namely the professional bias which is the mean value of this ratio and the

coefficient of variation of the professional factor were determined for various categories based

on the interface surface and concrete type.

In order to determine the level of reliability, the statistics of the material properties factor

and the fabrication factor were also needed. The statistics of these factors were determined by

Nowak (1999) from the results of his research and were used for the purposes of this study. The

mean and coefficient of variation of the resistance were then determined using the statistics of

the professional factor, P, the material factor, M, and the fabrication factor, F. The mean and

56

coefficient of variation of the load effect were computed for a range of dead to total (dead plus

live) load ratios. The reliability index for the AASHTO LRFD horizontal shear equation was

then computed using the means and coefficients of variation of the resistance and loading. The

process was repeated for the equation proposed by Wallenfelsz (2006) to determine if that

equation was a better predictor of horizontal shear strength.

5.2 Conclusions

In most of the experimental cases considered, the AASHTO LRFD horizontal shear

equation provided a conservative prediction of the horizontal shear strength provided by the

specimen. This was evident by the fact that the professional bias factors were above 1.0. The

professional bias factor was influenced by the shear reinforcement ratio for some of the

experimental studies. However, there were other studies in which the reinforcement ratio did not

have an influence on the professional bias.

The reliability of the AASHTO horizontal shear equation was found to be well below the

target value of 3.5 due to the fact that there was considerable variability in the test data as

evidenced by the high coefficients of variation for the professional factor. Reliability indices for

normal strength concrete were low for the rough (0.95) and smooth (1.20) interface conditions.

The monolithic interface fared better with an average reliability index of 2.45. The variation in

the reliability index due to interface type was greater for lightweight concrete, with values of

reliability index ranging from 2.40 for rough interface, 1.50 for smooth interface and 1.75 for

monolithic respectively. The average reliability index for high strength concrete was 1.75.

Wallenfelsz’s equation resulted in the reliability indices that were closer to the target

value of 3.5. The resistance bias factors for Wallenfelsz’s equation were higher than those for the

AASHTO equation while the loading factors remained the same. For normal weight concrete the

57

average reliability index was 1.55 for smooth surfaces, 1.75 for rough surfaces, and 2.00 for

monolithic. For lightweight concrete the average reliability index was 2.50 for smooth surfaces,

3.30 for rough surfaces, and 1.30 for monolithic. The reliability index for high strength concrete

was 2.05 for rough surfaces and 1.75 for monolithic.

The reliability indices for both equations were not close to the target reliability index of

3.5 which clearly shows that a better equation is needed for predicting horizontal shear stress.

5.3 Design Recommendations

The reliability of the current AASHTO LRFD horizontal shear equation is suboptimum,

which is a cause for concern. It is recommended that a lower resistance factor (φ) should be used

in order to increase the reliability. With the current equation, all of the φ factors for horizontal

shear strength should be made equal to the minimum 0.60. Even with the low φ factor, there is

still a level of concern over the low reliability indices.

Based on these findings, there is a need for a new equation for predicting horizontal

shear. As recommended below, the factors that influence horizontal shear capacity need to be

fully understood in order to develop a better horizontal shear equation. Since the reliability of

Wallenfelsz’s equation is higher than that of the current AASTHO LRFD equation, utilization of

Wallenfelsz’s equation is recommended until a better equation has been developed. The current

AASHTO cohesion and friction factors may be used in conjunction with the Wallenfelsz’s

equation as shown below:

�� = �� + �� where c = cohesion factor, Acv = area of concrete considered to be engaged in interface shear

transfer (in2), μ = friction factor, Avf = area of interface shear reinforcement crossing the shear

58

plane within the area Acv (in2), fy = yield stress of reinforcement (ksi), and Pn = permanent net

compressive force normal to the shear plane. If this equation is implemented, the recommended

φ factors would be 0.7 for the lightweight concrete and 0.6 for normal weight and high strength

concrete. However, it is important to remember that test data for each of the different categories

of surface interface for high strength and lightweight concrete was quite limited as compared

with normal weight concrete and so the recommendations for high strength and lightweight

concrete should be reevaluated when additional test data becomes available.

5.4 Recommendations for Future Research

Based on the on the results of this study some suggestions for future research are as

follows:

• Additional experimental tests of horizontal shear strength of lightweight and high strength

concrete specimens of various interface types should be conducted.

• Research with a focus on identifying the most important factors influencing horizontal shear

strength must be completed in order to develop an equation that more accurately predicts the

shear strength.

• For a more advanced reliability analysis, further research into the statistical parameters of the

cohesion and friction factors must be done in order to perform Monte Carlo simulation for

the horizontal shear equation.

59

REFERENCES

Banta, T. E. (2005). Horizontal Shear Transfer Between Ultra High Performance Concrete and

Lightweight Concrete. Via Department of Civil & Environmental Engineering. Blacksburg, VA,

Virginia Polytechnic Institute & State University. Masters of Science: 138.

Bass, R. A., R. L. Carrasquillo, et al. (1989). "Shear Transfer across New and Existing Concrete

Interfaces." ACI Structural Journal 86(4): 383-393.

Choi, D. (1996). An Experimental Investigation of Interface Bond Strength of Concrete Using

Large Powder-Driven Nails. Department of Civil Engineering. Austin, TX, The University of

Texas at Austin. Doctor of Philosophy: 340.

Hanson, N. W. (1960). "Precast-Prestressed Concrete Bridges 2. Horizontal Shear Connections."

Journal of the PCA Research and Development Laboratories 2(2): 38-60.

Hofbeck, J. A., I. O. Ibrahim, et al. (1969). "Shear Transfer in Reinforced Concrete." Journal of

the American Concrete Institute 66(1): 119-128.

Kahn, L. F. and A. D. Mitchell (2002). "Shear Friction Tests with High-Strength Concrete." ACI

Structural Journal 99(1): 98-103.

Kahn, L. F. and A. Slapkus (2004). "Interface Shear in High Strength Composite T-Beams." PCI

Journal 49(4): 102-110.

Kamel, M. R. (1996). Innovative Precast Concrete Composite Bridge Systems. Civil

Engineering. Lincoln, Nebraska, University of Nebraska. Doctor of Philosophy: 246.

Loov, R. E. and A. K. Patnaik (1994). "Horizontal Shear Strength of Composite Concrete Beams

With a Rough Interface." PCI Journal 39(1): 48-69.

Mattock, A. H., L. Johal, et al. (1975). "Shear transfer in reinforced concrete with moment or

tension acting across the shear plane." PCI Journal 20(4): 76-93.

Mattock, A. H., W. K. Li, et al. (1976). "Shear transfer in lightweight reinforced concrete." PCI

Journal 21(1): 20-39.

Nowak, A. S. (1999). Calibration of LRFD Bridge Design Code. Washington, D.C., National

Cooperative Highway Research Program: 37.

Nowak, A. S. and M. M. Szerszen (2003). "Calibration of Design Code for Buildings (ACI 318):

Part 1 - Statistical Models for Resistance." ACI Structural Journal 100(3): 6.

Nowak, A. S. and K. R. Collins (2000). Reliability of Structures. Boston, McGraw-Hill.

Nowak, A. S. and M. M. Szerszen (2001). Reliability-Based Calibration for Structural Concrete,

Portland Cement Association: 188.

60

Officials, A. A. o. S. H. a. T. (2010). AASHTO LRFD bridge design specifications. Interface

Shear Transfer - Shear Friction. Washington, D.C.: 7.

Patnaik, A. K. (2001). "Behavior of Composite Concrete Beams with Smooth Interface." Journal

of Structural Engineering 127(4): 359-366.

Saemann, J. C. and G. W. Washa (1964). "Horizontal Shear Connections Between Precast

Beams and Cast-in-Place Slabs." Journal of the American Concrete Institute 61(11): 1383-1408.

Scott, J. (2010). Interface Shear Strength in Lightweight Concrete Bridge Girders. Via

Department of Civil & Environmental Engineering. Blacksburg, VA, Virginia Polytechnic

Institute and State University. Masters of Science: 147.

Valluvan, R., M. E. Kreger, et al. (1999). "Evaluation of ACI 318-95 Shear-Friction Provisions."

ACI Structural Journal 96(4): 473-481.

Wallenfelsz, J. A. (2006). Horizontal Shear Transfer for Full-Depth Precast Concrete Bridge

Deck Panels. Via Department of Civil & Environmental Engineering. Blacksburg, VA, Virginia

Polytechnic Institute & State University. Masters of Science: 118.

Walraven, J. C. and H. W. Reinhardt (1981). "Theory and Experiments on the Mechincal

Behaviour of Cracks in Plain and Reinforced Concrete Subjected to Shear Loading." Heron

26(1a): 68.

61

APPENDIX A

Database Values

62

Appendix A

Appendix A is a collection of the information collected from previous research that was used for this study.

Banta Data

Table A.1 Banta data (lightweight concrete)

Beam ID Surface Type Acv (in2) Avf (in

2) fy (ksi) Pc (kip) f'c (ksi) Actual V (kip)

12S-0L-0-A Smooth 100 0 72 0.16 5.862 10.66

12S-0L-0-B Smooth 100 0 72 0.16 5.862 19.03

12S-2L-2-A Smooth 100 0.44 72 0.16 5.862 41.59

12S-2L-2-B Smooth 100 0.44 72 0.16 5.862 40.95

18S-1L-1-A Smooth 160 0.11 72 0.256 5.862 13.61

18S-1L-1-B Smooth 160 0.11 72 0.256 5.862 13.86

18S-2L-1-A Smooth 160 0.22 72 0.256 5.862 23.36

18S-2L-1-B Smooth 160 0.22 72 0.256 5.862 23.03

18S-2L-2-A Smooth 160 0.44 72 0.256 5.862 46.97

18S-2L-2-B Smooth 160 0.44 72 0.256 5.862 41.78

18S-2L-3-A Smooth 160 0.66 72 0.256 5.862 64.42

18S-2L-3-B Smooth 160 0.66 72 0.256 5.862 56.33

18S-0L-0-A Smooth 160 0 72 0.256 5.862 21.32

18S-0L-0-B Smooth 160 0 72 0.256 5.862 16.38

24S-0L-0-A Smooth 220 0 72 0.352 5.862 46.39

24S-0L-0-B Smooth 220 0 72 0.352 5.862 50.04

24S-2L-2-A Smooth 220 0.44 72 0.352 5.862 43.55

24S-2L-2-B Smooth 220 0.44 72 0.352 5.862 23.89

Banta, T. E. (2005). Horizontal Shear Transfer Between Ultra High Performance Concrete and Lightweight Concrete. Via Department

of Civil & Environmental Engineering. Blacksburg, VA, Virginia Polytechnic Institute & State University. Masters of Science: 138.

63

Bass, Carrasquillo, & Jirsa Data

Table A.2 Bass, Carrasquillo, and Jirsa data (normal weight concrete)



12A 1/4" chip 420 1.32 60 0 2.75 118

18A 1/4" chip 420 1.32 60 0 2.75 118

21A 1/4" chip 420 1.32 60 0 3.7 115

14A Smooth 420 1.32 60 0 2.75 90

1A Sandblasted 420 1.32 60 0 3.1 145

2A Sandblasted 420 1.32 60 0 3.1 153

3A Sandblasted 420 1.32 60 0 3.1 152

4A Sandblasted 420 1.32 60 0 3.1 165

5A Sandblasted 420 1.32 60 0 3.1 150

6A Sandblasted 420 1.32 60 0 3.1 165

7A Sandblasted 420 0.88 60 0 3.1 132

8A Sandblasted 420 2.64 60 0 3.1 210

9A Sandblasted 420 1.32 60 0 3.1 190

10A Sandblasted 420 1.32 60 0 3.1 130

11A Sandblasted, cast vert. 420 1.32 60 0 2.7 104

17A Sandblasted 420 1.32 60 0 2.7 125

20A Sandblasted 420 1.32 60 0 2.87 134

23A Sandblasted 420 1.32 60 0 3.95 135

24A Sandblasted 420 1.32 60 0 3.95 160

1B Sandblasted 420 1.32 60 0 3.21 102

2B Sandblasted 420 1.32 60 0 3.21 150

3B Sandblasted 420 1.32 60 0 3.21 162

4B Sandblasted 420 0.88 60 0 3.21 137

5B Sandblasted 420 1.32 60 0 3.21 166

6B Sandblasted 420 1.32 60 0 3.21 172

17B Sandblasted 420 1.32 60 0 2.87 151

21B Sandblasted 420 1.32 60 0 3.57 132

Bass, R. A., R. L. Carrasquillo, et al. (1989). "Shear Transfer across New and Existing Concrete Interfaces." ACI Structural Journal

86(4): 383-393.

64

Choi Data

Table A.3 Choi data (normal weight concrete)



1-H-1.1 Smooth 36 0.1368 87 0 4.641 15.3

1-H-1.2 Smooth 36 0.1368 87 0 4.641 18.225

1-M-1.1 Smooth 36 0.1368 87 0 4.641 23.625

1-M-1.2 Smooth 36 0.1368 87 0 4.641 9.9

1-L-1.1 Smooth 36 0.1368 87 0 4.641 15.75

1-L-1.2 Smooth 36 0.1368 87 0 4.641 17.55

1-H-2.1 Smooth 72 0.2736 87 0 4.641 26.775

1-H-2.2 Smooth 72 0.2736 87 0 4.641 33.075

1-L-2.1 Smooth 72 0.2736 87 0 4.641 35.775

1-L-2.2 Smooth 72 0.2736 87 0 4.641 30.6

1-H-0.1 Smooth 72 0 87 0 4.641 22.5

1-H-0.2 Smooth 72 0 87 0 4.641 27.675

1-M-0.1 Smooth 72 0 87 0 4.641 26.1

1-M-0.2 Smooth 72 0 87 0 4.641 32.625

1-L-0.1 Smooth 72 0 87 0 4.641 29.025

1-L-0.2 Smooth 72 0 87 0 4.641 25.2

2-1-36.1 Smooth 36 0.1368 87 0 2.755 16.65

2-1-36.2 Smooth 36 0.1368 87 0 2.755 16.2

2-0-36.1 Smooth 36 0 87 0 2.755 15.525

2-0-36.2 Smooth 36 0 87 0 2.755 18.45

2-1-72.1 Smooth 72 0.1368 87 0 2.755 28.35

2-1-72.2 Smooth 72 0.1368 87 0 2.755 26.1

2-2-72.1 Smooth 72 0.2736 87 0 2.755 30.825

2-0-72.1 Smooth 72 0 87 0 2.755 26.1

2-0-72.2 Smooth 72 0 87 0 2.755 29.475

2-1-108.1 Smooth 108 0.1404 87 0 2.755 34.65

2-1-108.2 Smooth 108 0.1404 87 0 2.755 26.1

2-2-108.1 Smooth 108 0.27 87 0 2.755 31.275

65



2-2-108.2 Smooth 108 0.27 87 0 2.755 32.85

2-0-108.1 Smooth 108 0 87 0 2.755 34.2

2-0-108.2 Smooth 108 0 87 0 2.755 33.975

1-H-1U.1 Smooth 72 0.1368 87 0 4.641 13.05

1-H-1U.2 Smooth 72 0.1368 87 0 4.641 11.475

1-H-2U.1 Smooth 72 0.2736 87 0 4.641 17.55

1-H-2U.2 Smooth 72 0.2736 87 0 4.641 18.45

1-N-1U.1 Smooth 72 0.1368 87 0 4.641 6.3

1-N-1U.2 Smooth 72 0.1368 87 0 4.641 6.975

3-H-1U.1 Smooth 72 0.1368 87 0 4.061 12.15

3-H-1U.2 Smooth 72 0.1368 87 0 4.061 11.025

3-H-2U.1 Smooth 72 0.2736 87 0 4.061 18.9

3-H-2U.2 Smooth 72 0.2736 87 0 4.061 21.375

3-N-1U.1 Smooth 72 0.1368 87 0 4.061 7.2

3-N-1U.2 Smooth 72 0.1368 87 0 4.061 5.4

1M1NC.1 Smooth 36 0.1368 87 0 4.2 19.35

1M1SC.1 Smooth 36 0.1368 87 0 4.2 20.025

1M1CR.1 Smooth 36 0.1368 87 0 4.2 15.975

1N1NC.1 Smooth 36 0.1368 87 0 4.2 14.4

1M2NC.1 Smooth 72 0.2736 87 0 4.2 34.425

1M2NC.2 Smooth 72 0.2736 87 0 4.2 34.65

1M2SC.1 Smooth 72 0.2736 87 0 4.2 32.625

1M0NC.1 Smooth 72 0 87 0 4.2 30.15

2M1NC.1 Smooth 36 0.1368 87 0 2.755 15.75

2M1NC.2 Smooth 36 0.1368 87 0 2.755 16.2

2M1CR.1 Smooth 36 0.1368 87 0 2.755 18.225

2N1NC.1 Smooth 36 0.1368 87 0 2.755 9.225

2M2NC.1 Smooth 72 0.2736 87 0 2.755 28.35

2M2SC.1 Smooth 72 0.2736 87 0 2.755 27.45

2M2CR.1 Smooth 72 0.2736 87 0 2.755 28.125

2M0NC.1 Smooth 72 0 87 0 2.755 21.825

66



3M1NC.1 Smooth 36 0.1368 87 0 4.061 15.075

3M1SC.1 Smooth 36 0.1368 87 0 4.061 10.8

3M1CR.1 Smooth 36 0.1368 87 0 4.061 14.4

3M2NC.1 Smooth 72 0.2736 87 0 4.061 24.975

3M2CR.1 Smooth 72 0.2736 87 0 4.061 23.625

4M1NC.1 Smooth 36 0.1368 87 0 4.2 12.6

4M1NC.2 Smooth 36 0.1368 87 0 4.2 11.925

4M1CR.1 Smooth 36 0.1368 87 0 4.2 10.35

4M2NC.1 Smooth 72 0.2736 87 0 4.2 27.45

4M2NC.2 Smooth 72 0.2736 87 0 4.2 24.975

4M2CR.1 Smooth 72 0.2736 87 0 4.2 17.55

4M0NC.1 Smooth 72 0 87 0 4.2 31.725

4-1-1D Smooth 72 0.1368 87 0 1.450 13.95

4-1-1DH Smooth 72 0.1368 87 0 1.885 14.4

4-1-2D Smooth 72 0.1368 87 0 2.320 14.625

4-1-3D Smooth 72 0.1368 87 0 2.610 23.4

4-1-4D Smooth 72 0.1368 87 0 3.045 18.225

4-1-7D Smooth 72 0.1368 87 0 3.480 14.4

4-1-14D Smooth 72 0.1368 87 0 3.916 20.925

4-1-28D Smooth 72 0.1368 87 0 4.206 13.725

4-0-1D Smooth 72 0 87 0 1.450 14.85

4-0-1DH Smooth 72 0 87 0 1.885 11.7

4-0-2D Smooth 72 0 87 0 2.320 17.775

4-0-3D Smooth 72 0 87 0 2.610 21.375

4-0-4D Smooth 72 0 87 0 3.045 16.425

4-0-7D Smooth 72 0 87 0 3.480 18.9

4-0-14D Smooth 72 0 87 0 3.916 22.725

4-0-28D Smooth 72 0 87 0 4.206 16.2

3-WT-HD Smooth 72 0.1368 87 0 0.870 6.075

3-WT-1D Smooth 72 0.1368 87 0 1.450 16.875

3-WT-2D Smooth 72 0.1368 87 0 2.175 26.775

67



3-WT-3D Smooth 72 0.1368 87 0 2.610 29.925

3-WT-4D Smooth 72 0.1368 87 0 2.755 26.325

3-WT-7D Smooth 72 0.1368 87 0 3.190 30.375

3-WT-14D Smooth 72 0.1368 87 0 3.335 30.375

3-WT-35D Smooth 72 0.1368 87 0 3.625 35.1

3-DY-HD Smooth 72 0.1368 87 0 0.870 6.975

3-DY-1D Smooth 72 0.1368 87 0 1.450 19.125

3-DY-2D Smooth 72 0.1368 87 0 2.175 22.725

3-DY-3D Smooth 72 0.1368 87 0 2.610 21.6

3-DY-4D Smooth 72 0.1368 87 0 2.755 28.35

3-DY-7D Smooth 72 0.1368 87 0 3.190 27

3-DY-14D Smooth 72 0.1368 87 0 3.335 27.9

3-DY-35D Smooth 72 0.1368 87 0 3.625 22.5

Choi, D. (1996). An Experimental Investigation of Interface Bond Strength of Concrete Using Large Powder-Driven Nails.

Department of Civil Engineering. Austin, TX, The University of Texas at Austin. Doctor of Philosophy: 340.

68

Hanson Data

Table A.4 Hanson data (normal weight concrete)



RS6-1 Rough 48 0.4 50 0 3.5 12

RS6-2 Rough 48 0.4 51 0 3.7 15.744

RS12-1 Rough 96 0.4 48.5 0 4.13 29.472

RS12-2 Rough 96 0.4 47 0 3.58 21.312

RS24-1 Rough 192 0.4 49 0 3.54 44.544

RS24-1 Rough 192 0.4 52 0 3.43 37.824

RS24-3 Rough 192 0.4 50 0 3.42 48.96

RS24-4 Rough 192 0.4 49 0 3.51 61.44

BRS6-1 Rough & Bond 48 0.4 50 0 3.5 32.64

BRS6-2 Rough & Bond 48 0.4 50 0 3.24 18.96

BRS6-3 Rough & Bond 48 0.4 51 0 3.7 30.72

BRS12-1 Rough & Bond 96 0.4 48.5 0 4.13 47.04

BRS12-2 Rough & Bond 96 0.4 47 0 3.58 43.68

BRS12-3 Rough & Bond 96 0.4 51 0 3.31 33.6

BRS12-4 Rough & Bond 96 0.4 51 0 3.31 34.08

BRS12-5 Rough & Bond 96 0.4 51 0 3.31 29.76

BRS12-6 Rough & Bond 96 0.4 50 0 3.96 35.04

BRS12-7 Rough & Bond 96 0.4 50 0 3.96 41.28

BRS12-8 Rough & Bond 96 0.4 50 0 3.96 42.24

BR12-1 Rough & Bond 96 0.4 50 0 3.04 39.936

BR12-2 Rough & Bond 96 0.4 50 0 3.98 53.28

BR12-3 Rough & Bond 96 0.4 50 0 4.15 43.68

BR12-4 Rough & Bond 96 0.4 50 0 4.08 33.6

BR12-5 Rough & Bond 96 0.4 50 0 4.08 34.752

BR12-6 Rough & Bond 96 0.4 50 0 3.72 39.36

BR12-7 Rough & Bond 96 0.4 50 0 3.72 39.168

BR12-8 Rough & Bond 96 0.4 50 0 3.72 38.88

BRS24-1 Rough & Bond 192 0.4 49 0 3.54 89.664

69



BRS24-2 Rough & Bond 192 0.4 52 0 3.43 66.24

BRS24-3 Rough & Bond 192 0.4 50 0 3.42 76.8

BRS24-4 Rough & Bond 192 0.4 50 0 3.51 85.44

BS6-1 Bond only 48 0.4 50 0 3.24 7.536

BS6-2 Bond only 48 0.4 50 0 3.24 10.8

BS6-3 Bond only 48 0.4 50 0 3.7 11.04

BS6-4 Bond only 48 0.4 50 0 3.7 10.32

BS6-5 Bond only 48 0.4 50 0 3.7 11.52

BS12-1 Bond only 96 0.4 50.15 0 4.05 15.84

BS12-2 Bond only 96 0.4 50.15 0 3.66 10.56

B12-1 Bond only 96 0.4 50 0 4.05 12

B12-2 Bond only 96 0.4 50 0 3.66 22.08

B12-3 Bond only 96 0.4 50 0 3.98 12.48

B12-4 Bond only 96 0.4 50 0 4.15 8.64

B12-5 Bond only 96 0.4 50 0 4.08 11.52

B24-1 Bond only 192 0.4 50 0 4.22 20.928

B24-2 Bond only 192 0.4 50 0 4.22 18.048

B24-3 Bond only 192 0.4 50 0 4.22 19.2

Hanson, N. W. (1960). "Precast-Prestressed Concrete Bridges 2. Horizontal Shear Connections." Journal of the PCA Research and

Development Laboratories 2(2): 38-60.

70

Hofbeck, Ibrahim, and Mattock Data

Table A.5 Hofbeck, Ibrahim, and Mattock data (normal weight concrete)



1.0 Mono 50 0 0 0 4.04 24

1.1A Mono 50 0.11 50.7 0 3.92 37.5

1.1B Mono 50 0.11 48 0 4.34 42.2

1.2A Mono 50 0.22 50.7 0 3.84 50

1.2B Mono 50 0.22 48 0 4.18 49

1.3A Mono 50 0.33 50.7 0 3.84 55

1.3B Mono 50 0.33 48 0 3.92 53.5

1.4A Mono 50 0.44 50.7 0 4.51 68

1.4B Mono 50 0.44 48 0 3.855 64

1.5A Mono 50 0.55 50.7 0 4.51 70

1.5B Mono 50 0.55 48 0 4.065 69.2

1.6A Mono 50 0.66 50.7 0 4.31 71.6

1.6B Mono 50 0.66 48 0 4.05 71

2.1 Mono 50 0.11 50.7 0 3.1 29.5

2.2 Mono 50 0.22 50.7 0 3.1 34

2.3 Mono 50 0.33 50.7 0 3.9 42

2.4 Mono 50 0.44 50.7 0 3.9 50

2.5 Mono 50 0.55 50.7 0 4.18 65

2.6 Mono 50 0.66 50.7 0 4.18 69.25

3.1 Mono 50 0.025 50.1 0 4.04 12

3.2 Mono 50 0.099 56.8 0 4.01 26

3.3 Mono 50 0.22 50.7 0 3.1 34

3.4 Mono 50 0.4 47.2 0 4.04 51.4

3.5 Mono 50 0.62 42.4 0 4.04 57.6

4.1 Mono 50 0.11 66.1 0 4.07 35.2

4.2 Mono 50 0.22 66.1 0 4.07 49

4.3 Mono 50 0.33 66.1 0 4.34 59

4.4 Mono 50 0.44 66.1 0 4.34 70

71



4.5 Mono 50 0.55 66.1 0 3.39 66

5.1 Mono 50 0.11 50.7 0 2.45 25.5

5.2 Mono 50 0.22 50.7 0 2.62 35

5.3 Mono 50 0.33 50.7 0 2.385 40.5

5.4 Mono 50 0.44 50.7 0 2.58 39.75

5.5 Mono 50 0.55 50.7 0 2.62 50.5

6.1 Mono 50 0.11 48 0 3.96 40

6.2 Mono 50 0.55 48 0 3.93 62

6.3 Mono 50 0.11 48 0 3.96 16

6.4 Mono 50 0.55 48 0 3.93 46.15

Hofbeck, J. A., I. O. Ibrahim, et al. (1969). "Shear Transfer in Reinforced Concrete." Journal of the American Concrete Institute 66(1):

119-128.

72

Kahn and Mitchell Data

Table A.6 Kahn and Mitchell data (high performance concrete)



SF-7-1-CJ Rough, 1/4 in 60 0.11 83 0 9.347 54

SF-7-2-CJ Rough, 1/4 in 60 0.22 83 0 9.347 82.08

SF-7-3-CJ Rough, 1/4 in 60 0.33 83 0 10.259 110.28

SF-7-4-CJ Rough, 1/4 in 60 0.44 83 0 10.259 132.66

SF-10-3-CJ Rough, 1/4 in 60 0.33 83 0 9.485 113.94

SF-10-4-CJ Rough, 1/4 in 60 0.44 83 0 9.485 126.06

SF-14-1-CJ Rough, 1/4 in 60 0.11 83 0 12.764 90.9

SF-14-2-CJ Rough, 1/4 in 60 0.22 83 0 12.764 99.18

SF-14-3-CJ Rough, 1/4 in 60 0.33 83 0 12.506 134.7

SF-14-4-CJ Rough, 1/4 in 60 0.44 83 0 12.506 153.12

SF-10-1-CJ Smooth 60 0.11 83 0 11.117 31.74

SF-10-2-CJ Smooth 60 0.22 83 0 9.515 49.32

SF-4-1-C Cracked 60 0.11 69.5 0 5.361 34.98

SF-4-1-U Uncracked 60 0.11 69.5 0 5.361 57.9

SF-4-2-C Cracked 60 0.22 69.5 0 5.361 55.68

SF-4-2-U Uncracked 60 0.22 69.5 0 5.361 80.1

SF-4-3-C Cracked 60 0.33 69.5 0 5.361 71.16

SF-4-3-U Uncracked 60 0.33 69.5 0 5.361 85.86

SF-7-1-C Cracked 60 0.11 83 0 9.347 41.7

SF-7-1-U Uncracked 60 0.11 83 0 9.347 87.54

SF-7-2-C Cracked 60 0.22 83 0 9.957 51.72

SF-7-2-U Uncracked 60 0.22 83 0 9.957 118.14

SF-7-3-C Cracked 60 0.33 83 0 10.692 71.52

SF-7-3-U Uncracked 60 0.33 83 0 10.692 138.42

SF-7-4-C Cracked 60 0.44 83 0 10.259 62.76

SF-7-4-U Uncracked 60 0.44 83 0 10.259 149.1

SF-10-1-C-a Cracked 60 0.11 83 0 9.515 25.8

SF-10-1-C-b Cracked 60 0.11 83 0 11.117 30

73



SF-10-1-U-a Uncracked 60 0.11 83 0 9.515 100.08

SF-10-1-U-b Uncracked 60 0.11 83 0 11.117 91.86

SF-10-2-C-a Cracked 60 0.22 83 0 12.158 50.76

SF-10-2-C-b Cracked 60 0.22 83 0 11.775 48.12

SF-10-2-U-a Uncracked 60 0.22 83 0 12.158 130.68

SF-10-2-U-b Uncracked 60 0.22 83 0 11.775 124.08

SF-10-3-C-a Cracked 60 0.33 83 0 12.71 64.68

SF-10-3-C-b Cracked 60 0.33 83 0 11.333 63.36

SF-10-3-U-a Uncracked 60 0.33 83 0 12.71 144.84

SF-10-3-U-b Uncracked 60 0.33 83 0 11.333 147.9

SF-10-4-C-a Cracked 60 0.44 83 0 12.429 74.16

SF-10-4-C-b Cracked 60 0.44 83 0 12.256 76.26

SF-10-4-U-a Uncracked 60 0.44 83 0 12.429 156.06

SF-10-4-U-b Uncracked 60 0.44 83 0 12.256 160.02

SF-14-1-C Cracked 60 0.11 83 0 14.095 24.9

SF-14-1-U Uncracked 60 0.11 83 0 14.948 94.98

SF-14-2-C Cracked 60 0.22 83 0 13.408 40.2

SF-14-2-U Uncracked 60 0.22 83 0 13.735 108.48

SF-14-3-C Cracked 60 0.33 83 0 12.91 55.5

SF-14-3-U Uncracked 60 0.33 83 0 13.185 146.22

SF-14-4-C Cracked 60 0.44 83 0 13.881 73.26

SF-14-4-U Uncracked 60 0.44 83 0 13.767 156

Kahn, L. F. and A. D. Mitchell (2002). "Shear Friction Tests with High-Strength Concrete." ACI Structural Journal 99(1): 98-103.

74

Kahn and Slapkus Data

Table A.7 Kahn and Slapkus data (high performance concrete)



7-5 Rough 237 0.44 80.68 0 7.28 72.84

7-7 Rough 237 0.66 80.68 0 7.28 89.56

7-9 Rough 237 0.88 80.68 0 7.28 95.31

Kahn, L. F. and A. Slapkus (2004). "Interface Shear in High Strength Composite T-Beams." PCI Journal 49(4): 102-110.

75

Kamel Data

Table A.8 Kamel data (normal weight concrete)



48 Rough, bond 1920 0.78 100 76.8 7.9 227.52

49 Rough, bond 1920 0.4 100 38.4 7.9 222.72

54 Rough, bond 960 0.66 60 39.36 4.491 340.8

55 Rough, bond 960 0.66 60 39.36 4.491 269.76

56 Rough, bond 960 0.66 60 39.36 4.491 353.28

57 Rough, bond 960 0.66 60 39.36 4.491 422.4

60 Rough, bond 960 0.66 60 39.36 4.491 165.12

61 Rough, bond 960 0.66 60 39.36 4.491 119.04

14 Smooth, debond 480 0 0 0 5.117 53.28

15 Smooth, debond 480 0 0 24 5.117 125.28

16 Smooth, debond 480 0 0 48 5.117 175.68

17 Smooth, debond 480 0 0 60 5.117 143.04

18 Smooth, debond 480 0 0 72 5.117 101.76

19 Smooth, debond 480 0 0 84 5.117 105.6

20 Smooth, debond 480 0 0 96 5.117 169.92

21 Smooth, debond 480 0 0 120 5.117 113.76

62 Smooth, bond 480 0 0 0 5.949 157.44

63 Smooth, bond 480 0 0 48 5.949 312

Kamel, M. R. (1996). Innovative Precast Concrete Composite Bridge Systems. Civil Engineering. Lincoln, Nebraska, University of

Nebraska. Doctor of Philosophy: 246.

76

Loov and Patnaik Data

Table A.9 Loov and Patnaik data (normal weight concrete)



1 Rough 22.125 0.22 63.51 0 5.423 32.85

2 Rough 58.115 0.22 63.51 0 5.0605 18.225

3 Rough 34.81 0.22 62.64 0 4.4225 28.2375

5 Rough 58.115 0.22 62.35 0 5.046 23.7375

6 Rough 58.115 0.22 62.06 0 5.3795 22.6125

7 Rough 15.635 0.22 62.64 0 5.191 37.2375

8 Rough 116.23 0.22 59.015 0 5.162 26.775

9 Rough 58.115 0.22 62.06 0 5.3795 19.2375

10 Rough 116.23 0.22 59.305 0 5.452 28.8

12 Rough 11.623 0.22 59.16 0 5.017 36.675

13 Rough 116.23 0.22 62.495 0 2.784 23.7375

14 Rough 116.23 0.22 62.495 0 2.842 15.4125

Loov, R. E. and A. K. Patnaik (1994). "Horizontal Shear Strength of Composite Concrete Beams With a Rough Interface." PCI

Journal 39(1): 48-69.

77

Mattock, Johal, and Chow Data

Table A.10 Mattock, Johal and Chow data (normal weight concrete)



A1 Mono 60 0.66 53 0 3.975 60

A2 Mono 60 0.66 53 0 4.13 60

B1 Mono 60 0.66 53 0 3.89 52

C1 Mono 60 0.66 53 0 3.98 50.5

C2 Mono 60 0.66 53 0 3.915 53

C3 Mono 60 0.66 53 0 3.805 51

D1 Mono 60 0.4 53 0 3.92 39

E1C Mono 84 0.88 51.8 0 3.855 74

E2C Mono 84 0.88 52.1 -8.4 4.22 78.04

E3C Mono 84 0.88 52.7 -13.692 3.96 59.98

E4C Mono 84 0.88 50.5 -16.8 3.82 56.53

E5C Mono 84 0.88 52.3 -25.2 4.02 44.27

E6C Mono 84 0.88 50.9 -33.6 3.985 31

E1U Mono 84 0.88 52.7 0 4.06 91.48

E4U Mono 84 0.88 49.1 -16.8 3.86 79.46

E6U Mono 84 0.88 50.8 -33.6 4.12 50.99

F1C Mono 84 1.32 50.1 0 4.22 82.99

F4C Mono 84 1.32 51.3 -16.8 3.89 70.48

F6C Mono 84 1.32 51.7 -33.6 4.15 67.54

F1U Mono 84 1.32 52.2 0 4.035 115

F4U Mono 84 1.32 53.2 -16.8 4.175 96.01

F6U Mono 84 1.32 51 -33.6 4.245 89.54

Mattock, A. H., L. Johal, et al. (1975). "Shear transfer in reinforced concrete with moment or tension acting across the shear plane."

PCI Journal 20(4): 76-93.

78

Mattock, Li, and Wang Data

Table A.11 Mattock, Li, and Wang data (normal weight concrete)



M0 Mono 50 0 0 0 3.935 29.5

M1 Mono 50 0.22 50.9 0 4.18 38

M2 Mono 50 0.44 52.7 0 3.9 49

M3 Mono 50 0.66 52.3 0 3.995 55.5

M4 Mono 50 0.88 50.9 0 4.15 57

M5 Mono 50 1.1 52.7 0 3.935 64

M6 Mono 50 1.32 52.7 0 4.12 66

N1 Mono 50 0.22 50.9 0 4.18 23

N2 Mono 50 0.44 52.7 0 3.9 39

N3 Mono 50 0.66 52.3 0 3.995 48

N4 Mono 50 0.88 50.9 0 4.15 57.5

N5 Mono 50 1.1 50.9 0 3.935 58.75

N6 Mono 50 1.32 50 0 4.12 59.5

Table A.12 Mattock, Li, and Wang data (lightweight concrete)



A0 Mono 50 0 0 0 4.23 25

A1 Mono 50 0.22 47.7 0 3.74 37.9

A2 Mono 50 0.44 53.6 0 4.095 45.7

A3 Mono 50 0.66 53.2 0 3.91 51

A4 Mono 50 0.88 50.9 0 4.1 55

A5 Mono 50 1.1 50.9 0 3.96 59.5

A6 Mono 50 1.32 51.8 0 4.25 67.2

B1 Mono 50 0.22 49.6 0 3.74 22.5

B2 Mono 50 0.44 50.9 0 3.36 32.6

B3 Mono 50 0.66 50.9 0 3.91 42

B4 Mono 50 0.88 49.1 0 4.1 47

79



B5 Mono 50 1.1 50.5 0 3.96 50

B6 Mono 50 1.32 51.8 0 4.25 57.7

C1 Mono 50 0.22 49.6 0 2.33 18.2

C2 Mono 50 0.44 53.6 0 2.33 25.7

C3 Mono 50 0.66 50.9 0 2 26.3

C4 Mono 50 0.88 52.3 0 2.05 28

C5 Mono 50 1.1 53.6 0 2.33 32

C6 Mono 50 1.32 49.6 0 2.33 37

D1 Mono 50 0.22 51.8 0 5.995 18.5

D2 Mono 50 0.44 52.3 0 5.995 33.4

D3 Mono 50 0.66 52.3 0 5.71 38.6

D4 Mono 50 0.88 52.3 0 5.71 51.1

D5 Mono 50 1.1 52.3 0 5.6 54.1

D6 Mono 50 1.32 51.8 0 5.6 61

E0 Mono 50 0 0 0 3.96 28

E1 Mono 50 0.22 52.3 0 4.15 39

E2 Mono 50 0.44 52.3 0 4.03 43.6

E3 Mono 50 0.66 52.3 0 4.065 48

E4 Mono 50 0.88 53.2 0 4.04 57.5

E5 Mono 50 1.1 50.5 0 4.115 60

E6 Mono 50 1.32 52.3 0 4.05 62.5

F1 Mono 50 0.22 53.2 0 4.15 22.5

F2 Mono 50 0.44 52.3 0 4.03 26.5

F2A Mono 50 0.44 50.9 0 3.97 31

F3 Mono 50 0.66 52.3 0 4.065 36.7

F3A Mono 50 0.66 51.4 0 3.97 35.1

F4 Mono 50 0.88 50.9 0 4.04 43.5

F5 Mono 50 1.1 51.8 0 4.115 46

F6 Mono 50 1.32 53.2 0 4.05 49.1

G0 Mono 50 0 0 0 4.03 26.5

G1 Mono 50 0.22 52.3 0 4.145 41

80



G2 Mono 50 0.44 50.5 0 3.88 42.3

G3 Mono 50 0.66 51.8 0 4.1 53

G4 Mono 50 0.88 53.2 0 4.42 57.5

G5 Mono 50 1.1 51.8 0 4.005 57

G6 Mono 50 1.32 51.8 0 4.005 59.5

H1 Mono 50 0.22 49.8 0 4.145 20

H2 Mono 50 0.44 51.8 0 3.88 31

H3 Mono 50 0.66 51.8 0 4.1 43.3

H4 Mono 50 0.88 51.8 0 4.42 47

H5 Mono 50 1.1 50.5 0 3.95 49.5

H6 Mono 50 1.32 49.8 0 4.08 52.1

Mattock, A. H., W. K. Li, et al. (1976). "Shear transfer in lightweight reinforced concrete." PCI Journal 21(1): 20-39.

81

Patnaik Data

Table A.13 Patnaik data (normal weight concrete)



SR1.1 Smooth 46.492 0.038809 102.1065 0 2.465 7.875

SR1.2 Smooth 46.492 0.038809 102.1065 0 2.465 7.2

SR2.1 Smooth 69.738 0.048123 92.96917 0 5.046 8.325

SR2.2 Smooth 69.738 0.048123 92.96917 0 3.8715 6.4125

SR3.1 Smooth 38.7696 0.048123 92.96917 0 5.046 7.0875

SR3.2 Smooth 38.7696 0.048123 92.96917 0 3.8715 7.0875

SR4.1 Smooth 54.372 0.096246 92.96917 0 5.046 14.0625

SR4.2 Smooth 54.372 0.096246 92.96917 0 3.8715 9.1125

SR4.3 Smooth 38.7696 0.096246 92.96917 0 5.046 6.8625

SR4.4 Smooth 54.372 0.096246 92.96917 0 3.8715 10.575

SR4.5 Smooth 31.0078 0.096246 92.96917 0 5.046 14.0625

SR4.6 Smooth 31.0078 0.096246 92.96917 0 3.8715 13.05

SR5.1 Smooth 23.246 0.096246 92.96917 0 5.046 20.7

SR5.2 Smooth 23.246 0.096246 92.96917 0 3.8715 18.675

SR5.3 Smooth 46.433 0.243721 49.31282 0 4.988 20.7

SR5.4 Smooth 46.433 0.243721 49.31282 0 4.698 23.625

SR5.5 Smooth 34.81 0.243721 49.31282 0 4.9155 29.025

SR5.6 Smooth 34.81 0.243721 49.31282 0 4.582 31.5

ST1.1 Smooth 23.246 0.243721 49.31282 0 3.9005 36.7875

ST1.2 Smooth 23.246 0.243721 49.31282 0 4.3935 39.4875

ST2.1 Smooth 46.492 0.038809 102.1065 0 2.465 7.875

ST2.2 Smooth 46.492 0.038809 102.1065 0 2.465 7.2

ST3.1 Smooth 69.738 0.048123 92.96917 0 5.046 8.325

ST3.2 Smooth 69.738 0.048123 92.96917 0 3.8715 6.4125

Patnaik, A. K. (2001). "Behavior of Composite Concrete Beams with Smooth Interface." Journal of Structural Engineering 127(4):

359-366.

82

Saemann and Washa Data

Table A.14 Saemann and Washa data (normal weight concrete)



1C Smooth 35 0.2 42.6 0 2.95 12.8

6C Smooth 70 0.2 42.6 0 2.87 11.5

2C Smooth 35 0.2 42.6 0 2.97 20.55

7C Smooth 70 0.2 42.6 0 2.81 19

3D Smooth 70 0.11 53.7 0 3.59 17.65

1A Smooth 17.5 0.2 42.6 0 2.71 38.2

4C Smooth 35 0.2 42.6 0 3.17 30

9C Smooth 70 0.2 42.6 0 3.09 24

7D Smooth 70 0.11 53.7 0 3.75 25.6

3C Intermediate 35 0.2 42.6 0 3.07 25.5

8C Intermediate 70 0.2 42.6 0 2.79 23.5

11C Intermediate 70 0.11 53.7 0 2.87 17

2D Intermediate 70 0.11 53.7 0 3.55 23.5

13C Intermediate 140 0.11 53.7 0 3.42 18

15C Intermediate 86 0 0 0 3.03 18

5C Intermediate 35 0.2 42.6 0 3.02 40

10C Intermediate 70 0.2 42.6 0 3.12 28.9

5D Intermediate 70 0.2 42.6 0 3.39 38.2

6D Intermediate 70 0.2 42.6 0 3.68 38

12C Intermediate 70 0.11 53.7 0 2.98 34.5

8D Intermediate 70 0.11 53.7 0 4.61 38

9D Intermediate 70 0.11 53.7 0 4.9 39

14C Intermediate 140 0.11 53.7 0 2.87 31

16C Intermediate 86 0 0 0 3.03 26

Saemann, J. C. and G. W. Washa (1964). "Horizontal Shear Connections Between Precast Beams and Cast-in-Place Slabs." Journal of

the American Concrete Institute 61(11): 1383-1408.

83

Scott Data

Table A.15 Scott data (normal weight concrete)



NN-0-A Rough 384 0 60 2.54 6.15 153

NN-0-B Rough 384 0 60 2.54 6.15 160

NN-0-C Rough 384 0 60 2.54 6.15 156

NN-1-A Rough 384 0.4 60 2.54 6.15 123

NN-1-B Rough 384 0.4 60 2.54 6.15 141

NN-1-C Rough 384 0.4 60 2.54 6.15 173

NN-3-A Rough 384 1.84 60 2.54 6.15 195

NN-3-B Rough 384 1.84 60 2.54 6.15 218

NN-3-C Rough 384 1.84 60 2.54 6.15 229

Table A.16 Scott data (lightweight concrete)



LL-0-A Rough 384 0 60 2.54 6.25 132

LL-0-B Rough 384 0 60 2.54 6.25 140

LL-0-C Rough 384 0 60 2.54 6.25 178

NL-0-A Rough 384 0 60 2.54 6.25 186

NL-0-B Rough 384 0 60 2.54 6.25 131

NL-0-C Rough 384 0 60 2.54 6.25 197

LL-1-A Rough 384 0.4 60 2.54 6.25 242

LL-1-B Rough 384 0.4 60 2.54 6.25 147

LL-1-C Rough 384 0.4 60 2.54 6.25 188

NL-1-A Rough 384 0.4 60 2.54 6.25 169

NL-1-B Rough 384 0.4 60 2.54 6.25 175

NL-1-C Rough 384 0.4 60 2.54 6.25 183

LL-3-A Rough 384 1.84 60 2.54 5.73 201

LL-3-B Rough 384 1.84 60 2.54 5.73 223

LL-3-C Rough 384 1.84 60 2.54 5.73 230

84



NL-3-A Rough 384 1.84 60 2.54 5.73 242

NL-3-B Rough 384 1.84 60 2.54 5.73 238

NL-3-C Rough 384 1.84 60 2.54 5.73 183

Scott, J. (2010). Interface Shear Strength in Lightweight Concrete Bridge Girders. Via Department of Civil & Environmental

Engineering. Blacksburg, VA, Virginia Polytechnic Institute and State University. Masters of Science: 147.

85

Valluvan, Kreger, and Jirsa Data

Table A.17 Valluvan, Kreger, and Jirsa data (normal weight concrete)



A1 Rough 128 1.32 69 0 1.75 76

A2 Rough 128 1.32 69 0 1.75 76

A3 Rough 128 2.64 69 0 1.75 90

A4 Rough 128 0 69 128 1.75 204

A5 Rough 128 1.32 69 128 1.75 182

A6 Rough 128 2.64 69 128 1.75 213

A7 Rough 128 0 69 128 1.75 201

B1 Rough 128 1.32 69 0 3.5 113

B2 Rough 128 2.64 69 0 3.5 130

B3 Rough 128 0 69 128 3.5 254

B4 Rough 128 0 69 192 3.5 291

B5 Rough 128 1.32 69 128 3.5 264

B6 Rough 128 2.64 69 128 3.5 274

B9 Rough 128 1.32 69 44.8 3.5 167

Valluvan, R., M. E. Kreger, et al. (1999). "Evaluation of ACI 318-95 Shear-Friction Provisions." ACI Structural Journal 96(4): 473-

481.

86

Walraven and Reinhardt Data

Table A. 18 Walraven and Reinhardt data (normal weight concrete)



110208t Mono 55.8 0.1559 60.9 0 4.2775 41.102

110208 Mono 55.8 0.1559 60.9 0 4.2775 44.500

110208g Mono 55.8 0.155 60.9 0 4.2775 41.102

110408 Mono 55.8 0.3118 60.9 0 4.2775 52.106

110608 Mono 55.8 0.4677 60.9 0 4.2775 59.792

110808t Mono 55.8 0.6237 60.9 0 4.2775 62.948

110808 Mono 55.8 0.6237 60.9 0 4.2775 57.284

110808h Mono 55.8 0.6237 60.9 0 4.2775 67.883

110808hg Mono 55.8 0.6237 60.9 0 4.2775 69.420

110706 Mono 55.8 0.3070 60.9 0 4.2775 58.174

210204 Mono 55.8 0.0390 60.9 0 4.2775 26.053

210608 Mono 55.8 0.4677 60.9 0 4.2775 78.644

210216 Mono 55.8 0.6231 60.9 0 4.2775 74.841

210316 Mono 55.8 0.9346 60.9 0 4.2775 81.800

210808h Mono 55.8 0.6237 60.9 0 4.2775 64.485

120208 Mono 55.8 0.1559 60.9 0 4.2775 43.367

120408 Mono 55.8 0.3118 60.9 0 4.2775 52.834

120608 Mono 55.8 0.4677 60.9 0 4.2775 54.857

120808 Mono 55.8 0.6237 60.9 0 4.2775 59.145

120706 Mono 55.8 0.3070 60.9 0 4.2775 55.989

120216 Mono 55.8 0.6231 60.9 0 4.2775 52.834

230208 Mono 55.8 0.1559 60.9 0 8.1345 54.371

230408 Mono 55.8 0.3118 60.9 0 8.1345 87.625

230608 Mono 55.8 0.4677 60.9 0 8.1345 101.623

230808 Mono 55.8 0.6237 60.9 0 8.1345 114.811

240208 Mono 55.8 0.1559 60.9 0 2.8855 37.623

240408 Mono 55.8 0.3118 60.9 0 2.8855 48.869

240608 Mono 55.8 0.4677 60.9 0 2.8855 52.996

87



240808 Mono 55.8 0.6237 60.9 0 2.8855 50.892

250208 Mono 55.8 0.1559 60.9 0 5.539 55.261

250408 Mono 55.8 0.3118 60.9 0 5.539 70.310

250608 Mono 55.8 0.4677 60.9 0 5.539 78.078

250808 Mono 55.8 0.6237 60.9 0 5.539 80.424

Table A. 19 Walraven and Reinhardt data (lightweight concrete)



260208 Mono 55.8 0.1559 60.9 0 5.5245 52.753

260408 Mono 55.8 0.3118 60.9 0 5.5245 69.744

260608 Mono 55.8 0.4677 60.9 0 5.5245 79.211

260808 Mono 55.8 0.6237 60.9 0 5.5245 83.822

260208h Mono 55.8 0.1559 60.9 0 5.5245 33.092

260808h Mono 55.8 0.6237 60.9 0 5.5245 71.767

310208 Mono 55.8 0.1559 60.9 0 4.2775 48.141

310408 Mono 55.8 0.3118 60.9 0 4.2775 65.941

310608 Mono 55.8 0.4677 60.9 0 4.2775 71.281

310808 Mono 55.8 0.6237 60.9 0 4.2775 72.333

Walraven, J. C. and H. W. Reinhardt (1981). "Theory and Experiments on the Mechincal Behaviour of Cracks in Plain and Reinforced

Concrete Subjected to Shear Loading." Heron 26(1a): 68.

88

APPENDIX B

Professional Factors

89

Appendix B

Appendix B presents the calculated biases of the professional factor for each test result. The biases were calculated for both the

AASHTO LRFD horizontal shear equation and the proposed horizontal shear equation by Wallenfelsz.

Banta

Table B.1 Professional factors for Banta data (lightweight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

12S-0L-0-A 1.403 1.421 18S-2L-1-A 1.079 1.947 18S-0L-0-A 1.754 1.777

12S-0L-0-B 2.505 2.537 18S-2L-1-B 1.063 1.919 18S-0L-0-B 1.348 1.365

12S-2L-2-A 1.563 2.177 18S-2L-2-A 1.507 2.451 24S-0L-0-A 2.776 2.812

12S-2L-2-B 1.539 2.144 18S-2L-2-B 1.341 2.180 24S-0L-0-B 2.994 3.033

18S-1L-1-A 0.805 1.134 18S-2L-3-A 1.584 2.247 24S-2L-2-A 1.219 2.266

18S-1L-1-B 0.820 1.155 18S-2L-3-B 1.385 1.965 24S-2L-2-B 0.669 1.243

90

Bass, Carrasquillo, & Jirsa

Table B.2 Professional factors for Bass, Carrasquillo, and Jirsa data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

12A 0.656 1.171 6A 2.088 3.472 24A 2.025 3.367

18A 0.656 1.171 7A 2.089 4.167 1B 1.291 2.146

21A 0.639 1.141 8A 1.660 2.210 2B 1.898 3.157

14A 1.139 1.894 9A 2.404 3.998 3B 2.050 3.409

1A 1.835 3.051 10A 1.645 2.736 4B 2.168 4.324

2A 1.936 3.220 11A 1.316 2.189 5B 2.101 3.493

3A 1.924 3.199 17A 1.582 2.630 6B 2.177 3.620

4A 2.088 3.472 20A 1.696 2.820 17B 1.911 3.178

5A 1.898 3.157 23A 1.708 2.841 21B 1.670 2.778

91

Choi

Table B.3 Professional factors for Choi dat (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

1-H-1.1 1.555 2.143 1-N-1U.1 0.502 0.882 4M2CR.1 0.892 1.229

1-H-1.2 1.852 2.552 1-N-1U.2 0.556 0.977 4M0NC.1 5.875 5.875

1-M-1.1 2.40 3.308 3-H-1U.1 0.969 1.701 4-1-1D 1.112 1.954

1-M-1.2 1.006 1.386 3-H-1U.2 0.879 1.544 4-1-1DH 1.148 2.017

1-L-1.1 1.600 2.206 3-H-2U.1 0.960 1.323 4-1-2D 1.166 2.048

1-L-1.2 1.783 2.458 3-H-2U.2 1.086 1.497 4-1-3D 1.866 3.277

1-H-2.1 1.360 1.875 3-N-1U.1 0.574 1.008 4-1-4D 1.453 2.552

1-H-2.2 1.680 2.316 3-N-1U.2 0.431 0.756 4-1-7D 1.148 2.017

1-L-2.1 1.818 2.505 1M1NC.1 1.966 2.710 4-1-14D 1.669 2.930

1-L-2.2 1.555 2.143 1M1SC.1 2.035 2.804 4-1-28D 1.094 1.922

1-H-0.1 4.167 4.167 1M1CR.1 1.623 2.237 4-0-1D 2.750 2.750

1-H-0.2 5.125 5.125 1N1NC.1 1.463 2.017 4-0-1DH 2.167 2.167

1-M-0.1 4.833 4.833 1M2NC.1 1.749 2.410 4-0-2D 3.292 3.292

1-M-0.2 6.042 6.042 1M2NC.2 1.760 2.426 4-0-3D 3.958 3.958

1-L-0.1 5.375 5.375 1M2SC.1 1.658 2.284 4-0-4D 3.042 3.042

1-L-0.2 4.667 4.667 1M0NC.1 5.583 5.583 4-0-7D 3.500 3.500

2-1-36.1 1.692 2.332 2M1NC.1 1.600 2.206 4-0-14D 4.208 4.208

2-1-36.2 1.646 2.269 2M1NC.2 1.646 2.269 4-0-28D 3.000 3.000

2-0-36.1 5.750 5.750 2M1CR.1 1.852 2.552 3-WT-HD 0.485 0.851

2-0-36.2 6.833 6.833 2N1NC.1 0.937 1.292 3-WT-1D 1.346 2.363

2-1-72.1 2.261 3.970 2M2NC.1 1.440 1.985 3-WT-2D 2.135 3.749

2-1-72.2 2.081 3.655 2M2SC.1 1.395 1.922 3-WT-3D 2.386 4.191

2-2-72.1 1.566 2.158 2M2CR.1 1.429 1.969 3-WT-4D 2.099 3.686

2-0-72.1 4.833 4.833 2M0NC.1 4.042 4.042 3-WT-7D 2.422 4.254

2-0-72.2 5.458 5.458 3M1NC.1 1.532 2.111 3-WT-14D 2.422 4.254

2-1-108.1 2.246 4.278 3M1SC.1 1.097 1.512 3-WT-35D 2.799 4.915

92

2-1-108.2 1.692 3.222 3M1CR.1 0.502 2.017 3-DY-HD 0.892 0.977

2-2-108.1 1.409 2.219 3M2NC.1 0.556 1.749 3-DY-1D 5.875 2.678

2-2-108.2 1.480 2.331 3M2CR.1 0.969 1.654 3-DY-2D 1.112 3.182

2-0-108.1 4.222 4.222 4M1NC.1 0.879 1.764 3-DY-3D 1.148 3.025

2-0-108.2 4.194 4.194 4M1NC.2 0.960 1.670 3-DY-4D 1.166 3.970

1-H-1U.1 1.041 1.827 4M1CR.1 1.086 1.449 3-DY-7D 1.866 3.781

1-H-1U.2 0.915 1.607 4M2NC.1 0.574 1.922 3-DY-14D 1.453 3.907

1-H-2U.1 0.892 1.229 4M2NC.2 0.431 1.749 3-DY-35D 1.148 3.151

1-H-2U.2 0.937 1.292

93

Hanson

Table B.4 Professional factors for Hanson data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

RS6-1 0.381 0.600 BRS12-6 0.814 1.521 BS6-1 0.483 0.628

RS6-2 0.493 0.772 BRS12-7 0.959 1.792 BS6-2 0.692 0.900

RS12-1 0.694 1.279 BRS12-8 0.981 1.833 BS6-3 0.708 0.920

RS12-2 0.509 0.925 BR12-1 0.928 1.733 BS6-4 0.662 0.860

RS24-1 0.678 0.967 BR12-2 1.238 2.313 BS6-5 0.738 0.960

RS24-1 0.566 0.821 BR12-3 1.015 1.896 BS12-1 0.823 1.316

RS24-3 0.741 1.063 BR12-4 0.781 1.458 BS12-2 0.549 0.877

RS24-4 0.935 1.333 BR12-5 0.807 1.508 B12-1 0.625 1.000

BRS6-1 1.036 1.632 BR12-6 0.914 1.708 B12-2 1.150 1.840

BRS6-2 0.602 0.948 BR12-7 0.910 1.700 B12-3 0.650 1.040

BRS6-3 0.962 1.506 BR12-8 0.903 1.688 B12-4 0.450 0.720

BRS12-1 1.108 2.042 BRS24-1 1.365 1.946 B12-5 0.600 0.960

BRS12-2 1.044 1.896 BRS24-2 0.990 1.438 B24-1 0.793 1.453

BRS12-3 0.773 1.458 BRS24-3 1.162 1.667 B24-2 0.684 1.253

BRS12-4 0.785 1.479 BRS24-4 1.293 1.854 B24-3 0.727 1.333

BRS12-5 0.685 1.292

94

Hofbeck, Ibrahim, and Mattock

Table B.5 Professional factors for Hofbeck, Ibrahim, and Mattock data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

1.0 1.200 1.200 2.1 1.061 1.475 4.3 1.167 1.932

1.1A 1.349 1.875 2.2 0.955 1.700 4.4 1.290 1.719

1.1B 1.541 2.110 2.3 0.967 1.793 4.5 1.558 1.297

1.2A 1.404 2.500 2.4 1.026 1.601 5.1 0.917 1.275

1.2B 1.409 2.450 2.5 1.244 1.665 5.2 1.069 1.750

1.3A 1.267 2.348 2.6 1.325 1.478 5.3 1.358 1.729

1.3B 1.268 2.413 3.1 0.552 0.600 5.4 1.233 1.273

1.4A 1.327 2.177 3.2 0.933 1.300 5.5 1.542 1.294

1.4B 1.328 2.165 3.3 0.955 1.700 6.1 1.460 2.000

1.5A 1.242 1.793 3.4 1.107 1.945 6.2 1.262 1.677

1.5B 1.362 1.872 3.5 1.141 1.565 6.3 0.584 0.800

1.6A 1.329 1.528 4.1 1.166 1.760 6.4 0.939 1.249

1.6B 1.402 1.601 4.2 1.214 2.407

95

Kahn and Mitchell

Table B.6 Professional factors for Kahn and Mitchell data (high strength concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

SF-7-1-CJ 2.295 3.750 SF-4-3-U 1.530 2.674 SF-10-3-C-a 1.037 1.687

SF-7-2-CJ 2.513 4.495 SF-7-1-C 1.134 1.738 SF-10-3-C-b 1.016 1.652

SF-7-3-CJ 2.639 4.026 SF-7-1-U 2.380 3.648 SF-10-3-U-a 2.323 3.777

SF-7-4-CJ 2.605 3.633 SF-7-2-C 1.043 2.023 SF-10-3-U-b 2.372 3.857

SF-10-3-CJ 2.726 4.160 SF-7-2-U 2.384 4.621 SF-10-4-C-a 0.987 1.450

SF-10-4-CJ 2.476 3.452 SF-7-3-C 1.147 1.865 SF-10-4-C-b 1.015 1.492

SF-14-1-CJ 3.863 6.313 SF-7-3-U 2.220 3.610 SF-10-4-U-a 2.077 3.052

SF-14-2-CJ 3.037 5.432 SF-7-4-C 0.835 1.228 SF-10-4-U-b 2.130 3.130

SF-14-3-CJ 3.223 4.918 SF-7-4-U 1.985 2.916 SF-14-1-C 0.677 1.038

SF-14-4-CJ 3.007 4.193 SF-10-1-C-a 0.701 1.075 SF-14-1-U 2.582 3.958

SF-10-1-CJ 3.181 5.794 SF-10-1-C-b 0.816 1.250 SF-14-2-C 0.811 1.573

SF-10-2-CJ 3.191 4.502 SF-10-1-U-a 2.721 4.170 SF-14-2-U 2.189 4.243

SF-4-1-C 1.393 1.458 SF-10-1-U-b 2.497 3.828 SF-14-3-C 0.890 1.447

SF-4-1-U 1.668 2.413 SF-10-2-C-a 1.024 1.986 SF-14-3-U 2.345 3.813

SF-4-2-C 1.226 2.320 SF-10-2-C-b 0.971 1.882 SF-14-4-C 0.975 1.433

SF-4-2-U 1.764 3.338 SF-10-2-U-a 2.637 5.112 SF-14-4-U 2.076 3.051

SF-4-3-C 1.268 2.216 SF-10-2-U-b 2.503 4.854

96

Kahn and Slapkus

Table B.7 Professional factors for Kahn and Slapkus data (high strength concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP

7-5 0.788 1.280

7-7 0.813 1.574

7-9 0.745 1.342

Kamel

Table B.8 Professional factors for Kamel data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

48 0.370 0.494 60 0.534 0.717 18 1.285 2.356

49 0.413 0.483 61 0.385 0.517 19 1.222 2.095

54 1.102 1.479 14 1.480 1.480 20 1.815 2.950

55 0.872 1.171 15 2.486 3.480 21 1.053 1.580

56 1.142 1.533 16 2.711 4.880 62 4.373 4.373

57 1.365 1.833 17 1.987 3.973 63 4.815 8.667

97

Loov and Patnaik

Table B.9 Professional factors for Loov and Patnaik data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

1 1.703644 2.351097 6 0.81927 1.621247 10 0.703429 1.032436

2 0.652763 1.304376 7 2.123828 2.702129 12 2.515752 2.817859

3 1.275683 2.049046 8 0.65499 0.959843 13 0.570009 0.850953

5 0.858046 1.701906 9 0.696991 1.37927 14 0.3701 0.552514

Mattock, Johal, and Chow

Table B.10 Professional factors for Mattock, Johal, and Chow data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

A1 1.006 1.225 E2C 0.907 1.489 E6U 1.038 1.518

A2 0.969 1.225 E3C 0.756 1.311 F1C 0.936 0.896

B1 0.891 1.062 E4C 0.782 1.461 F4C 0.863 0.989

C1 0.846 1.031 E5C 0.705 1.318 F6C 0.823 1.393

C2 0.903 1.082 E6C 0.629 0.923 F1U 1.357 1.192

C3 0.894 1.041 E1U 1.073 1.409 F4U 1.095 1.284

D1 0.727 1.314 E4U 1.126 2.149 F6U 1.108 1.897

E1C 0.914 1.160

98

Mattock, Li, and Wang

Table B.11 Professional factors for Mattock, Li, and Wang data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

M0 1.475 1.475 M5 1.301 0.789 N3 0.961 0.993

M1 1.065 1.900 M6 1.282 0.678 N4 1.108 0.917

M2 1.005 1.509 N1 0.645 1.150 N5 1.194 0.749

M3 1.111 1.148 N2 0.800 1.201 N6 1.155 0.644

M4 1.099 0.909

Table B.12 Professional factors for Mattock, Li, and Wang data (lightweight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

A0 2.083 2.083 C6 1.270 0.565 F3A 0.764 1.035

A1 1.685 3.158 D1 0.791 1.542 F4 0.870 0.971

A2 1.284 1.938 D2 0.954 1.451 F5 0.920 0.807

A3 1.083 1.452 D3 0.830 1.118 F6 0.982 0.699

A4 1.100 1.228 D4 1.022 1.110 G0 2.208 2.208

A5 1.202 1.063 D5 1.082 0.940 G1 1.744 3.417

A6 1.344 0.983 D6 1.220 0.892 G2 1.236 1.904

B1 0.982 1.875 E0 2.333 2.333 G3 1.147 1.550

B2 0.948 1.456 E1 1.659 3.250 G4 1.150 1.228

B3 0.921 1.250 E2 1.245 1.895 G5 1.140 1.000

B4 0.940 1.088 E3 1.032 1.391 G6 1.190 0.870

B5 1.010 0.900 E4 1.150 1.228 H1 0.871 1.667

B6 1.154 0.844 E5 1.200 1.080 H2 0.891 1.360

C1 0.794 1.517 E6 1.250 0.905 H3 0.937 1.267

C2 0.882 1.090 F1 0.949 1.875 H4 0.940 1.031

C3 1.052 0.783 F2 0.757 1.152 H5 1.003 0.891

C4 1.093 0.608 F2A 0.901 1.384 H6 1.042 0.793

C5 1.099 0.543 F3 0.789 1.063

99

Patnaik

Table B.13 Professional factors for Patnaik data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

SR1.1 1.042767 1.403817 SR4.3 1.267412 2.437477 SR5.5 2.910486 3.855636

SR1.2 1.375429 1.85166 SR4.4 1.267412 2.437477 SR5.6 2.625765 3.478454

SR2.1 0.84567 1.527144 SR4.5 1.488621 2.619318 ST1.1 1.935737 2.870564

SR2.2 0.714651 1.290545 SR4.6 0.964626 1.697318 ST1.2 2.209265 3.276187

SR3.1 1.342827 2.258453 SR5.1 0.829156 1.278227 ST2.1 2.955138 4.025029

SR3.2 1.227728 2.064871 SR5.2 1.119443 1.969727 ST2.2 3.207126 4.368249

SR4.1 1.051836 1.591672 SR5.3 1.82764 2.619318 ST3.1 4.108234 5.101491

SR4.2 0.810198 1.226017 SR5.4 1.69605 2.430727 ST3.2 4.409756 5.475912

Saemann and Washa

Table B.14 Professional factors for Saemann and Washa data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

1C 1.654 2.504 7D 2.911 4.876 10C 2.789 5.505

6C 1.110 2.190 3C 3.296 4.988 5D 3.687 7.276

2C 2.656 4.020 8C 2.268 4.476 6D 3.667 7.238

7C 1.834 3.619 11C 1.933 3.238 12C 3.923 6.571

3D 2.007 3.362 2D 2.672 4.476 8D 4.321 7.238

1A 5.946 7.473 13C 1.282 1.714 9D 4.435 7.429

4C 3.877 5.869 15C 2.791 2.791 14C 2.207 2.952

9C 2.316 4.571 5C 5.170 7.825 16C 4.031 4.031

100

Scott

Table B.15 Professional factors for Scott data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

NN-0-A 1.615628 1.660156 NN-1-A 1.036226 1.334635 NN-3-A 0.950756 1.72658

NN-0-B 1.689546 1.736111 NN-1-B 1.187869 1.529948 NN-3-B 1.062896 1.930228

NN-0-C 1.647307 1.692708 NN-1-C 1.457456 1.87717 NN-3-C 1.116529 2.027625

Table B.16 Professional factors for Scott data (lightweight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

LL-0-A 1.393875 1.432292 LL-1-A 2.038753 2.625868 LL-3-A 0.98001 1.779706

LL-0-B 1.478353 1.519097 LL-1-B 1.238416 1.595052 LL-3-B 1.087275 1.9745

LL-0-C 1.87962 1.931424 LL-1-C 1.583825 2.039931 LL-3-C 1.121404 2.03648

NL-0-A 1.964097 2.018229 NL-1-A 1.423757 1.833767 NL-3-A 1.179912 2.142731

NL-0-B 1.383316 1.421441 NL-1-B 1.474305 1.898872 NL-3-B 1.16041 2.107314

NL-0-C 2.080253 2.137587 NL-1-C 1.541702 1.985677 NL-3-C 0.892248 1.620329

Valluvan, Kreger, and Jirsa

Table B.17 Professional factors for Valluvan, Kreger, and Jirsa data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

A1 1.357 0.834 A6 3.804 0.687 B4 2.598 1.516

A2 1.357 0.834 A7 3.589 1.570 B5 2.357 1.205

A3 1.607 0.494 B1 1.009 1.241 B6 2.446 0.883

A4 3.643 1.594 B2 1.161 0.714 B9 1.491 1.229

A5 3.250 0.831 B3 2.268 1.984

101

Walraven and Reinhardt

Table B.18 Professional factors for Walraven and Reinhardt data (normal weight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

110208t 1.154 1.842 210608 1.318 1.972 230408 1.792 3.296

110208 1.250 1.994 210216 1.254 1.409 230608 1.634 2.548

110208g 1.154 1.842 210316 1.371 1.027 230808 1.521 2.159

110408 1.065 1.960 210808h 1.081 1.213 240208 1.056 1.686

110608 1.002 1.499 120208 1.218 1.943 240408 1.214 1.838

110808t 1.055 1.184 120408 1.080 1.987 240608 1.317 1.329

110808 0.960 1.077 120608 0.919 1.375 240808 1.264 0.957

110808h 1.138 1.277 120808 0.991 1.112 250208 1.552 2.476

110808hg 1.163 1.305 120706 1.154 2.139 250408 1.438 2.644

110706 1.199 2.222 120216 0.885 0.995 250608 1.255 1.958

210204 1.016 1.167 230208 1.527 2.436 250808 1.065 1.512

Table B.19 Professional factors for Walraven and Reinhardt data (lightweight concrete)

Beam ID AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP Beam ID

AASHTO

λP

Wallenfelsz

λP

260208 2.305 3.939 260208h 1.446 2.471 310408 2.036 3.472

260408 2.154 3.672 260808h 1.397 1.889 310608 1.702 2.502

260608 1.891 2.780 310208 2.103 3.595 310808 1.408 1.904

260808 1.632 2.207

102

APPENDIX C

Reliability Indices

103

Appendix C

Appendix C displays the variation of reliability indices for a range of dead to total load ratios

with different resistance factors.

Resistance Factor of 0.6

Figure C.1 Reliability indices for the AASHTO horizontal shear equation for normal weight

concrete for a resistance factor (φ) of 0.60.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

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x

D/(D+L)

NW -

Smooth

NW- Rough

NW - Mono

104

Figure C.2 Reliability indices for the AASHTO horizontal shear equation for lightweight


Figure C.3 Reliability indices for the AASHTO horizontal shear equation for high strength


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

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In

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x

D/(D+L)

HS - Rough

HS - Mono

105

Figure C.4 Reliability indices for the horizontal shear equation proposed by Wallenfelsz for

normal weight concrete for a resistance factor (φ) of 0.60.


lightweight concrete for a resistance factor (φ) of 0.60.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW - Rough

NW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

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ity

In

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x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

106

Figure C.6 Reliability indices for the horizontal shear equation proposed by Wallenfelsz for high

strength concrete for a resistance factor (φ) of 0.60.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

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x

D/(D+L)

HS - Rough

HS - Mono

107






0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW- Rough

NW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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In

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x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

108





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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In

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x

D/(D+L)

NW -

Smooth

NW - Rough

NW - Mono

109




high strength concrete for a resistance factor (φ) of 0.65.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

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x

D/(D+L)

HS - Rough

HS - Mono

110






0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW- Rough

NW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

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ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

111





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

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ity

In

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x

D/(D+L)

NW -

Smooth

NW - Rough

NW - Mono

112





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

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x

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HS - Rough

HS - Mono

113






0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW- Rough

NW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

114





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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x

D/(D+L)

NW -

Smooth

NW - Rough

NW - Mono

115





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

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x

D/(D+L)

HS - Rough

HS - Mono

116






0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW- Rough

NW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

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117


concrete at for a resistance factor (φ) of 0.80.



0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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ity

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x

D/(D+L)

NW -

Smooth

NW - Rough

NW - Mono

118





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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x

D/(D+L)

HS - Rough

HS - Mono

119






0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW- Rough

NW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

120





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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In

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x

D/(D+L)

NW -

Smooth

NW - Rough

NW - Mono

121





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

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x

D/(D+L)

HS - Rough

HS - Mono

122






0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW- Rough

NW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

123





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

NW -

Smooth

NW - Rough

NW - Mono

124





0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

LW -

Smooth

LW - Rough

LW - Mono

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Re

lia

bil

ity

In

de

x

D/(D+L)

HS - Rough

HS - Mono

125

APPENDIX D

Actual Shear Stress vs. Concrete Strength

126

Appendix D

Appendix D presents a collection of charts that compare the actual shear stress to the concrete strength in order to determine if there is

a connection between the two.

Figure D.1 Actual shear stress versus concrete strength for normal weight concrete with a rough interface.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7 8

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)

f'c (ksi)

Loov & Patnaik (NW)

Scott (NW)

Hanson (NW)

Valluvan, Kreger & Jirsa (NW)


Kamel (NW)

127

Figure D.2 Actual shear stress versus concrete strength for lightweight concrete with a rough interface.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7

Act

. V

n/A

cv (

ksi

)

f'c (ksi)

Scott (LW)

128

Figure D.3 Actual shear stress versus concrete strength for high strength concrete with a rough interface.

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)

f'c (ksi)


Kahn & Slapkus (HS)

129

Figure D.4 Actual shear stress versus concrete strength for normal weight concrete with a smooth interface.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)

f'c (ksi)

Saemann & Washa (NW)


Patnaik (NW)

Choi (NW)

Hanson (NW)

Kamel (NW)

130

Figure D.5 Actual shear stress versus concrete strength for lightweight concrete with a smooth interface.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7

Act

. V

n/A

cv (

ksi

)

f'c (ksi)

Banta (LW)

131

Figure D.6 Actual shear stress versus concrete strength for high strength concrete with a smooth interface.

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10 12

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)

f'c (ksi)


132

Figure D.7 Actual shear stress versus concrete strength for normal weight concrete with a monolithic interface.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7 8 9

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)

f'c (ksi)

Hofbeck, Ibrahim & Mattock (NW)

Mattock, Johal & Chow (NW)

Mattock, Li, & Wang (NW)

Walraven & Reinhardt (NW)

133

Figure D.8 Actual shear stress versus concrete strength for lightweight concrete with a monolithic interface.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)

f'c (ksi)

Mattock, Li, & Wang (LW)

Walraven & Reinhardt (LW)

134

Figure D.9 Actual shear stress versus concrete strength for high strength concrete with a monolithic interface.

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10 12 14 16

Act

ua

l S

he

ar

Str

ess

Vn

/Acv

(k

si)

f'c (ksi)


135

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