To the Graduate School:

The members of the Committee approve the thesis of Cristy L. Guenther presented onJuly 10, 2007.

____________________________________Jennifer E. Tanner, Chair

____________________________________Charles W. Dolan

____________________________________David E. Walrath

APPROVED:

Jay A. Puckett, Head, Department of Civil and Architectural Engineering

Don A. Roth, Dean, The Graduate School

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Guenther, Cristy L., Evaluation of Shear and Diagonal Tension in Plain Concrete. M.S.,Department of Civil and Architectural Engineering, August 2007.

Abstract

Shear strength is an important property in civil engineering materials and structures.Several practical concrete structures result in loading conditions with high shear and lowmoment such as corbels, brackets, composite floor systems and bridge decks. Shear failure inconcrete is undesirable due to the brittle nature of failure. In addition, it remains difficult topredict accurately, despite all the research in the area. Experimental and analytical work hasbeen conducted to investigate a modified Iosipescu test as a means of measuring the direct shearstrength of plain concrete beams. The Iosipescu loading configuration results in shear failure ina predefined plane, and the failure path is completely contained within the region of high shear.While other researchers have argued different failure modes for similar loading configurations, itis concluded from this study that high shear stress along the failure plane causes high principaltension. Finite element analyses show that the failure planes observed in the specimens aredefined by the orientation of principal tensile stress. Combined with the experimental results,these finite element analyses provide a means to predict failure based on the magnitude andorientation of the principal tensile stress.

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Evaluation of Shear and Diagonal Tension in Plain Concrete

byCristy Louise Guenther

A thesis submitted to the Department of Civil andArchitectural Engineering and the Graduate School of The

University of Wyoming in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCEin

CIVIL ENGINEERING

Laramie, WyomingAugust, 2007

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UMI Number: 1446905

14469052007

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To my family for all of their support

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Acknowledgements

I would like to thank my advisor Dr. Jennifer Tanner for encouraging me to go to

graduate school, and for her guidance along the way. Thanks to Tyler Robison for all his

assistance in construction and testing. Thanks to JVI Neoprene for providing neoprene for this

project. I would like to thank fellow current and former students Matthew Olsen, Patrick

Lindblom, Cody Parker, Eric Anderson, Christina Behrens, Emre Insel, Kyle Eyre, Jiangang

Deng, Yuan Li, and Zach Gutierrez for making the office a better place, and John Coombs for

making graduate school fun and always keeping me in line. Thanks to my best friends Katie and

Rachel and my boyfriend Jason for always being there when I needed them. Thanks to the

professors in the department of Civil and Architectural Engineering for making a difference in

my life. Thanks to everyone in the machine shop for all of their assistance. I would like to thank

the members of my committee including Dr. Jennifer Tanner, Dr. Charles Dolan and Dr. David

Walrath. Last but not least, I would like to thank my family for all they have done for me; I

wouldn’t have made it this far without them.

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Table of Contents

1 Introduction and Background ................................................................................................. 1 1.1 Research Significance..................................................................................................... 51.2 Literature Review............................................................................................................ 6

1.2.1 Development of Iosipescu Shear Test..................................................................... 61.2.2 Iosipescu Beam Tests on Concrete ......................................................................... 7

2 Analytical Models................................................................................................................. 132.1 Split Cylinder ................................................................................................................ 14

2.1.1 Model .................................................................................................................... 142.1.2 Results................................................................................................................... 15

2.2 Iosipescu Beam ............................................................................................................. 172.2.1 Model .................................................................................................................... 192.2.2 Results................................................................................................................... 21

2.3 Long Beam.................................................................................................................... 282.3.1 Long Beam Model 1 ............................................................................................. 282.3.2 Model 1 Results .................................................................................................... 302.3.3 Long Beam Model 2 ............................................................................................. 332.3.4 Model 2 Results .................................................................................................... 33

2.4 Theory of Elasticity....................................................................................................... 352.4.1 Model .................................................................................................................... 352.4.2 Results................................................................................................................... 36

3 Experimental Testing ............................................................................................................ 383.1 Testing Program............................................................................................................ 383.2 Test Procedures............................................................................................................. 39

3.2.1 Compression Cylinders......................................................................................... 393.2.2 Split Cylinders ...................................................................................................... 393.2.3 Iosipescu Beam Test ............................................................................................. 413.2.4 Modulus of Rupture .............................................................................................. 453.2.5 Split Prism............................................................................................................. 46

3.3 Results........................................................................................................................... 484 Discussion of Results............................................................................................................ 595 Conclusions........................................................................................................................... 69

5.1 Finite Element Modeling General................................................................................. 695.2 Iosipescu Finite Element Model ................................................................................... 695.3 Experimental ................................................................................................................. 705.4 Final Conclusions.......................................................................................................... 70

6 References............................................................................................................................. 716.1 Cited References ........................................................................................................... 716.2 Referenced Standards and Codes.................................................................................. 72

Appendix A: Load, Shear, and Moment Calculations ................................................................. 73Appendix B: Notation and Definitions ........................................................................................ 75Appendix C: Iosipescu FEM Dimensions and Loads .................................................................. 76

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List of Figures

Figure 1: Shear span-to-depth ratio................................................................................................ 2Figure 2: Increase in shear strength based on depth to shear span ratio ........................................ 4Figure 3: Small shear span-to-depth conditions............................................................................. 5Figure 4: Specimen geometry and loading for Iosipescu shear test and ASTM D 5379............... 7Figure 5: Loading, notch configuration, and failure path for different researchers..................... 10Figure 6: ASTM C496 ................................................................................................................. 14Figure 7: Different loading conditions used in split cylinder model ........................................... 15Figure 8: Horizontal stress along diameter of split cylinder for different loading conditions..... 16Figure 9: Horizontal stresses along diameter of split cylinder normalized to 2P/πLD................ 17Figure 10: Loading for Iosipescu beam ....................................................................................... 18Figure 11: Centerline and diagonal failure plane to evaluate stresses ......................................... 18Figure 12: Stress components and angle...................................................................................... 19Figure 13: Different loading conditions used in Iosipescu beam model ..................................... 20Figure 14: Horizontal stress along centerline of Iosipescu beam for different loading conditions....................................................................................................................................................... 21Figure 15: Normal stresses along diagonal of Iosipescu beam for different loading conditions. 23Figure 16: Shear stress along diagonal of Iosipescu beam for different loading conditions ....... 24Figure 17: Shear stress along centerline of Iosipescu beam for different loading conditions ..... 25Figure 18: Stresses along diagonal for Iosipescu beam modeled with a unit thickness .............. 26Figure 19: Stresses along diagonal for Iosipescu beam modeled using actual thickness ............ 27Figure 20: Long beam model....................................................................................................... 29Figure 21: Shear stresses in beam section near concentrated load (not to scale) ........................ 31Figure 22: Normal stresses in beam section near concentrated load (not to scale) ..................... 32Figure 23: Shear stresses in beam section near concentrated load (not to scale) ........................ 34Figure 24: Beam geometry and applied loads (Timoshenko and Goodier 1970) ........................ 35Figure 25: Shear stresses along line n-n for different values of b/c............................................. 36Figure 26: Testing apparatus used for splitting tensile strength of 4 in. cylinders ...................... 40Figure 27: Test setup for splitting tensile strength of 6 in. cylinders .......................................... 41Figure 28: Modified Iosipescu test fixture................................................................................... 42Figure 29: Free body diagram of test fixture ............................................................................... 42Figure 30: Loading, shear, and moment diagrams for Iosipescu beam test................................. 43Figure 31: Loading point setup .................................................................................................... 44Figure 32: Neoprene used to compensate for unparallel surfaces ............................................... 44Figure 33: Modified Iosipescu Beam Test................................................................................... 45Figure 34: Modulus of rupture beam ........................................................................................... 46Figure 35: Test setup for splitting tensile strength of a prism ..................................................... 47Figure 36: Failure stress ratio versus compressive strength ........................................................ 48Figure 37: Differences in cracks based on aggregate size ........................................................... 50Figure 38: Test results for pea gravel ........................................................................................... 51Figure 39: Test results for 3/8 in. aggregate ................................................................................. 52Figure 40: Test results for ¾ in. aggregate ................................................................................... 53Figure 41: Specimen size effect in split cylinder test results....................................................... 54Figure 42: Results for 4 in. split cylinders................................................................................... 55Figure 43: Iosipescu beam results................................................................................................ 56

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Figure 44: Modulus of rupture test results ................................................................................... 56Figure 45: Split prism test results ................................................................................................ 57Figure 46: Comparison of Iosipescu beam results ........................................................................ 58Figure 47: Iosipescu beam specimen from Mix 1 shown before testing and at failure ............... 60Figure 48: Iosipescu beam specimen from Mix 6 shown before testing and at failure ............... 60Figure 49: Loading, failure path, principal tensile stress surface plot, and direction of principaltensile stresses (psi)....................................................................................................................... 61Figure 50: Comparison of shear stresses in beam without notches ............................................. 62Figure 51: Shear stress along centerline for different notch depths............................................. 63Figure 52: Shear stress along centerline for Bazant and Pfeiffer (1986) and Ingraffia andPanthaki (1985)............................................................................................................................. 64Figure 53: Loading configuration, failure path, and principal tensile stress surface plot (Ingraffiaand Panthaki 1985) ....................................................................................................................... 66Figure 54: Loading configuration, failure path, and principal tensile stress surface plots (Bazantand Pfeiffer 1986) ......................................................................................................................... 68Figure 55: Free body diagram of Iosipescu test brackets and concrete specimen (UW)............. 73Figure 56: Loading, shear, and moment diagrams for Iosipescu beam test................................. 74Figure 57: Specimen and loading of Iosipescu beam test............................................................ 76Figure 58: Applied loads for Iosipescu beam FEM model .......................................................... 77Figure 59: Loading configuration and dimensions used for Bazant and Pfeiffer FEM............... 78Figure 60: Loading configuration and dimensions used for Ingraffia and Panthaki FEM .......... 79

List of TablesTable 1: Comparison of maximum shear and bending stresses in long beam............................. 31Table 2: Comparison of maximum shear and bending stresses in long beam............................. 34Table 3: Experimental test results................................................................................................ 49

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1 Introduction and Background

Shear strength is an important property in civil engineering materials and structures.

Shear failure in plain concrete is the formation of a crack that forms when principal tensile

stresses exceed the tensile strength, otherwise known as diagonal tension failure. In reinforced

concrete design shear reinforcement begins to work after cracking. Shear failures are considered

undesirable because they reduce the ductility of structural elements and may cause catastrophic

failure if the concrete and shear reinforcement are not sufficient to carry the load. Shear failure

remains difficult to predict accurately, despite all the research in the area.

Shear failure in unreinforced concrete is a brittle failure and occurs suddenly with no

advanced warning. With increasing load, tensile cracks form where the tensile stresses exceed

tensile strength and will cause immediate failure of the element. A typical concrete element is a

beam, which is generally reinforced with steel to stop the progression of cracks. Beams subject

to bending stresses have longitudinal reinforcement effective in resisting tension near the tension

face of the beam. Shear stresses increase in proportion to increasing loads, and significant

diagonal tensile stresses are created in regions of high shear forces and low moment, especially

close to supports. Consequently, concrete beams are provided with shear reinforcement to

increase the probability of a ductile failure controlled by yielding of flexural reinforcement rather

than a brittle shear failure. Adequate designs must account for tensile stresses resulting from

shear alone or those resulting from combined shear and bending. For this reason it is important to

have a model to predict the loads at which these cracks will form.

There are two types of shear cracks in traditional simply supported reinforced concrete

beams subject to gravity loads. 1) Vertical flexural cracks form first and are distributed in the

center of the beam. Cracks in zones of moderate shear may propagate diagonally forming

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flexure-shear cracks. 2) Cracks form perpendicular to diagonal tensile stresses at locations of

high shear and low moment. Near the ends of a simply supported beam subject to gravity loads

these cracks are oriented at 45˚. For beams with small shear span–to-depth ratios (Figure 1), the

shear stresses are very high while the flexural stresses are very low. At a location of high shear,

V, and small bending moment, M, there will be little to no flexural cracking before the formation

of shear cracks and a direct shear failure can occur. Generally, beams with smaller shear span-

to-depth ratios have greater shear strength than beams with large shear span–to-depth ratios. For

beams subjected to concentrated loads, the major variable affecting the mode of failure is the

distance from the load to the support, and the depth of the member.

Figure 1: Shear span-to-depth ratio

Chapter 11 of ACI 318 defines building code requirements for shear and torsion. Unless

designs use strut and tie models, the cross sections subject to shear are designed based on

Equation (1), where Vu is the factored shear force at the section, Vn is the nominal shear strength,

and φ is the strength reduction factor.

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un VV ≥φEquation (1)

The nominal shear strength is computed by Equation (2), where Vc is the nominal shear provided

by concrete and Vs is the nominal shear strength provided by shear reinforcement.

scn VVV +=Equation (2)

Section 11.3 of ACI 318 covers the shear strength provided by concrete for nonprestressed

members. For members subject to shear and flexure only Vc can be calculated according to

Equation (3), where f’c is the concrete compressive strength, bw is the width of the web, and d is

the distance from the compression face of the beam to the centroid of the tensile steel.

dbfV wcc '2=Equation (3)

Engineers may calculate Vc using the more detailed calculation of Equation (4), where ρw is the

reinforcement ratio, Vu is the factored shear at the section, and Mu is the factored moment at the

section.

cwu

uwcc fdb

M

dVfV '5.3)2500'9.1( ≤+= ρ Equation (4)

The value of Vud/Mu is equivalent to the depth to shear span ratio. Figure 2 shows with an

increasing depth to shear span ratio there is an increase in shear strength when calculating Vc

using Equation (4).

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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 1 2 3 4 5 6 7 8

Depth to shear span ratio

Sh

ear

stre

ng

th/√

f’c

(psi

)

Equation 4

2√f'c

3.5√f'c

Figure 2: Increase in shear strength based on depth to shear span ratio

There are conditions where small shear span–to-depth ratios occur in reinforced concrete

members such as squat shear walls. Other common situations occur in precast concrete

structures particularly in regions near connections. Shear forces must be transferred across the

interface between a beam and a composite slab or at the supports of precast elements such as

corbels or brackets loaded near the column (Figure 3).

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P

b.) Corbel loaded near column

P

a.) Beam and composite slab

P

b.) Corbel loaded near column

P

a.) Beam and composite slab

Figure 3: Small shear span-to-depth conditions

Although many researchers have created testing programs to predict the shear strength of

plain concrete beams, one of the major problems in shear strength studies is determining the

concrete shear strength at a location of high shear and low moment (direct shear strength) as

opposed to the shear strength determined by combined flexure and shear (flexure-shear strength).

This study modified the Iosipescu test (Iosipescu 1967) to develop a method for measuring the

shear strength of plain concrete in confined locations such as shown in Figure 3. The Iosipescu

loading scheme induces a high shear stress at the center of the specimen. The high shear region

occurs where the moment approaches zero and results in direct shear failure of test samples.

1.1 Research Significance

Experimental and analytical work has been conducted to investigate a modified Iosipescu

test fixture proposed by Ross (2000) as a means of measuring the shear strength of plain concrete

beams. A final test procedure proposed by Ross (2000) has been further investigated as a

standard test for determining shear resistance of plain concrete over a wide range of concrete

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mixtures. Iosipescu beam test results were compared to results from ASTM standardized tests

for the tensile and compressive strength of concrete to confirm the need for a new standard.

Finite element results are compared to experimental results to evaluate shear strength. The

Iosipescu test provides a simple and effective method to experimentally confirm the confined

shear capacity of plain concrete.

1.2 Literature Review

Literature was reviewed regarding the origin of the Iosipescu shear test for metals, along

with similar shear tests for plain concrete beams. The information is summarized and discussed

in the following sections.

1.2.1 Development of Iosipescu Shear Test

A test procedure was developed by Nicolae Iosipescu (1967) that produces failure of test

specimens under pure shear stresses. A pure shear load is generated using a simple device that

generates a shear force in a straight beam in the area of zero moment and results in failure of the

specimen. Prior to this test, shear testing procedures existed, but none that produced failure of

the material under shear stress alone. The solution of the problem of pure shear testing was

established by Iosipescu on the basis of principles of strength of materials and the theory of

elasticity. Iosipescu found it was necessary to weaken the specimen in the desired failure section

by means of angular notches. Two 90˚ notches were cut to ¼ of the beam depth on both the top

and bottom surfaces (Figure 4). A photoelastic study on Plexiglas was used to experimentally

confirm the model. Iosipescu believed this study indicated that using notches ensured maximum

shear stresses remained constant through the cross section. First used for studies of shear

strength in railway weldments, this test has subsequently been applied to other rolled metals and

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cast metals. Iosipescu shear tests are now applied to non-metal materials. The V-notched beam

test, ASTM D5379, established a standardized procedure for testing the shear properties of

composite materials. Composite materials are limited to fiber reinforced polymer laminated

composites.

Figure 4: Specimen geometry and loading for Iosipescu shear test and ASTM D 5379

1.2.2 Iosipescu Beam Tests on Concrete

Iosipescu and Alexandrescu (1965) proposed a similar device to test concrete in pure

shear. They believed that it was necessary to weaken the specimen using notches to ensure that

the specimen fractured in pure shear. Two 90 degree notches cut to a depth a quarter of the

height were made in each specimen. By weakening the test pieces, the authors believed that a

pure shear state occurred and maximum shear stresses were uniformly distributed throughout the

section. The specimens usually fractured along the centerline between notch tips (Figure 4).

Specimens failed in pure shear, and because of the notches the failure plane was vertical along

the centerline. Iosipescu concluded that this test method could be used for the pure shear testing

of concrete.

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A research program was conducted by Bazant and Pfeiffer (1986)1 at Northwestern

University to investigate the shear fracture of concrete. In the terminology of fracture mechanics

shear fracture is referred to as Mode II failure. Similar to Iosipescu, notched beams were loaded

in a manner that produced concentrated shear forces and failure. The test specimens used were

beams with rectangular cross section and a constant length-to-depth ratio of 8:3. Specimens of

various depths (1.5, 3, 6, and 12 inches) were tested while maintaining a constant thickness of

1.5 inches. All beams were cast from the same batch of concrete and symmetric notches (0.1 in.

wide) were cut to a depth of one sixth the beam depth on the top and bottom surfaces at the

center of each specimen. When loaded, cracks propagated between the two notch tips resulting

in failure of the specimen (Figure 5a). The authors concluded that shear fracture exists. Tests

were also repeated using wider shear spans and in these cases the cracks propagated from the

notch tip in a direction normal to the maximum principal tensile stress. Maximum loads

measured from the specimens with a small shear span were found to be greater than the

specimens with a wide shear span.

Bazant and Pfeiffer (1986) believed that their test method was a good way to measure

pure Mode II fracture. This conclusion was further supported by linear elastic finite element

results. They believed that the cracks initiated from the notch tips and propagated continuously

toward the center, representing shear cracks.

The behavior in the tests described by Bazant and Pfeiffer (1986) conflict with those

observed in similar specimens tested at Cornell University (Ingraffia and Panthaki 1985)2.

Again, tests were performed with similar loading, but with only a single notch in the bottom

1 This journal article is based on conference proceedings from 2nd Symposium on the Interaction of Non-NuclearMunitions on Structures, Panama City Beach, FL, April 15-19, 1985.2 Results discussed in this article were originally published in 1981. Arrea, M., and Ingraffia, A.R., 1981, “MixedMode Crack Propagation in Mortar and Concrete”, Department of Structural Engineering Report 81-13, CornellUniversity

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center of the beam. However, the principal loads were applied further from the notch tips. In all

the tests performed, fractures initiated at the notch tip in a direction normal to the principal

tensile stress (Figure 5b). Similar tests were performed on limestone and granite specimens with

comparable behavior patterns. One of the important conclusions of these tests was that shear

fracture did not occur in the specimens. Ingraffia and Panthaki conducted a linear elastic finite

element analysis on the specimen geometry of Bazant and Pfeiffer (1986) to validate the

findings. Finite element analysis showed the principal stresses in the region between notch tips

were tensile, and the direction of the stresses was horizontal. The diagonal region between the

two center supports had uniform tensile stresses. The shear stress distribution shows that the

minimum shear stress is in the center of the beam and maximum near the notch tips. To validate

the finite element model the authors used theory of elasticity, arguing that by moving the center

loads closer together the intensity of shear stresses were decreased rather than increased. It was

concluded that the failure was similar to a splitting tensile strength test, and the failure mode was

actually cracking due to principal tensile stresses rather than shear fracture.

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