Dynamic response of concrete beams externally reinforced with carbon fiber reinforced plastic

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Dynamic response of concrete beams externally reinforced with carbon fiber reinforced plastic
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Fibrous composites -- Testing   ( lcsh )
Composite-reinforced concrete -- Research   ( lcsh )
Aerospace Engineering, Mechanics, and Engineering Science thesis, Ph. D
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Thesis:
Thesis (Ph. D.)--University of Florida, 1996.
Bibliography:
Includes bibliographical references (leaves 170-173).
Statement of Responsibility:
by David Mark Jerome.
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Typescript.
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Vita.

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DYNAMIC RESPONSE OF CONCRETE BEAMS
EXTERNALLY REINFORCED WITH
CARBON FIBER REINFORCED PLASTIC










By

DAVID MARK JEROME


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA


1996














This work is dedicated to my wife Elisabetta Lidia, and our twin sons Matthew Allen and

Nathan Kelley, who were born on November 1, 1993, during the course of this investigation.














ACKNOWLEDGMENTS

The author would like to acknowledge the advice and counsel given to him by his faculty

supervisory committee: Professors E. K. Walsh, D. M. Belk, J. E. Milton and C. S. Anderson.

Special recognition is reserved for Professor C. A. Ross, supervisory committee chair, without

whose advice, mentorship, encouragement, and friendship, this research would not have been

possible.

The author would like to acknowledge the following individuals at the Wright

Laboratory Air Base Technology Branch at Tyndall Air Force Base, Florida, for their

contributions listed below: Mr. Dale W. Wahlstrom for fabrication of the concrete beams and

Split Hopkinson Pressure Bar (SHPB) samples, and for assistance with the compressive and

splitting tension tests on the Forney load frame; Mr. William C. Naylor for strain gage and

instrumentation assistance; Mr. Dean W. Hitzelberger for assistance with the Material Test

System (MTS ) load frame; Mr. Francis W. Barrett III for high speed camera assistance on the

drop weight impact machine; and Mr. Carl R. Hollopeter for maintenance of the drop weight

impact machine and instrumentation assistance. Use of the Forney and MTS load frames and

drop weight impact machine, all of which are owned and supported by the Wright Laboratory

Air Base Technology Branch, Tyndall Air Force Base, Florida, is also gratefully acknowledged.

The author also wishes to acknowledge the assistance of Ms. Cathy A. Rickard for ably

typing a large portion of the manuscript, and Mr. Danny R. Brubaker and Mr. Bruce C. Patterson

for help in preparing several of the figures.

Finally, the author wishes to acknowledge the help and support of the Wright Laboratory

Armament Directorate at Eglin Air Force Base, Florida, during his educational endeavors.















TABLE OF CONTENTS

page

ACKNOW LEDGM EN TS..................................................................................................... iii

KEY TO ABBREVIATIONS............................................................................................... vi

A B STRA CT............................................................................ .................................................... vii

CHAPTERS

1 IN TRO DU CTION ................................................................................................ 1

O bjective................................................................................... ............... 1
Background..................................................... .......................................... 1
Approach...................................... ..................... ........................................ 10

2 EXPERIMENTAL WORK ....................................................... .................... 13

Fabrication of Concrete Beam Specimens........................................................ 13
Application of the CFRP................................................................... 15
Surface Preparation...................................................................... 16
Characterization of the Concrete............................................................... 22
Static Compression Tests............................................................. 22
Static Splitting Tensile Tests...................................................... 26
Dynamic Compression Tests...................................................... 29
Dynamic Splitting Tensile Tests..................................... ........... 32
Test Results.................................................... .............................. 37
Static Beam Bending Experiments.................................................................. 39
Description of the MTS Load Frame.............................. ........... 39
Instrumentation Used/Measurements Made......................................... 42
Test Results.................................................... .............................. 42
Calculation of Fracture Energies..................................... ........... 54
Dynamic Beam Bending Experiments............................................................. 58
Description of the Wyle Laboratories Drop Weight Impact Machine 59
Instrumentation Used................................................................. 61
Calibration of the Tup.................................................................. 62
M ethod of Test.................................................. ........................... 73
Interpretation of Test Results...................................................... 75
Dam ping Loads................................................ ............................ 91
Results and Discussion................................................................. 93
Comparison of Dynamic and Static Test Results............................. ......... 97









3 ANALYTICAL MODEL.................................................................................... 103

Section A nalysis............................................................................................... 103
Region I A ll Elastic.......................................................................... 105
Region 2 Cracked Tension Concrete, All Other Elastic................. 109
Region 3 Cracked Tension Concrete, Inelastic Compression
Concrete, All Other Elastic.................... ................................... 112
Comparison to MTS Test Data........................................................ 115
Determination of Beam Equivalent Mass...................................................... 121
Single Degree of Freedom Representation of a Beam Subject to a
Half- Sine Pulse Impulsive Load................................................................ 125
Comparison to Drop Weight Impact Test Data.............................................. 130

4 FINITE ELEMENT METHOD CALCULATIONS................................................. 134

Description of the ADINA FEM Computer Code........................................... 134
The Concrete Material Model............................................................. 137
The CFRP Material Model................................................................. 141
Concrete Beam with CFRP Finite Element Model...................................... 141
Dynam ic Loading Calculations........................................................................ 142
Results and Comparison to Test Data............................................................ 144

5 SUMMARY AND DISCUSSION............................................................................ 157

Characterization of the Concrete.......... ............................................................... 158
Static Beam Bending Experiments................................................................... 159
Dynamic Beam Bending Experiments............................................................ 160
Static versus Dynamic Beam Bending Experiments................................... 161
A nalytical M odel............................................................................................... 162
Finite Element Method (FEM) Calculations.................................................... 163
Future Research................................................................................................ 164

6 CON CLU SION S................................................................................................. 167

R E FER EN C E S........................................................................................................................... 170

APPENDICES

A SUMMARY OF CONCRETE UNCONFINED COMPRESSIVE
ST REN G T H S................................................................................................. 174
B MTS LOAD DISPLACEMENT CURVES............................................... 177
C SUMMARY OF STATIC THREE POINT BENDING EXPERIMENTS...... 194
D DYNAMIC BEAM BENDING EXPERIMENTAL DATA TABULAR
SUM M ARY ............................................................................................. 197
E ANALYTICAL MODEL COMPUTER PROGRAM.................................... 202
F ADINA INPUT AND PLOT FILES FOR BEAM LW6-43............................ 222
G ADINA INPUT AND PLOT FILES FOR BEAM LW9-66............................ 229

BIOGRAPHICAL SKETCH................................................................................................ 236














KEY TO ABBREVIATIONS


American Concrete Institute (ACI)

Automatic, Dynamic, Incremental, Nonlinear Analysis (ADINA)

Carbon Fiber Reinforced Plastic (CFRP)

Fiber Reinforced Plastic (FRP)

Finite Element Method (FEM)

Glass Fiber Reinforced Plastic (GFRP)

Linear Voltage Displacement Transducer (LVDT)

Material Test System (MTS)

Methyl Ethyl Ketone (MEK)

Modulus of Rupture (MOR)

Single Degree of Freedom (SDOF)

Split Hopkinson Pressure Bar (SHPB)

Swiss Federal Laboratories for Testing and Research (EMPA)














Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy

DYNAMIC RESPONSE OF CONCRETE BEAMS
EXTERNALLY REINFORCED WITH
CARBON FIBER REINFORCED PLASTIC

By

DAVID MARK JEROME

May 1996

Chair: C. Allen Ross
Cochair: James E. Milton
Major Department: Aerospace Engineering, Mechanics, and Engineering Science

A series of 54 laboratory scale concrete beams 3 x 3 x 30 in (7.62 x 7.62 x 76.2 cm) in

size were impulsively loaded to failure in a drop weight impact machine. An additional 16

beams were quasistatically loaded to failure in a load frame. The beams had no internal steel

reinforcement, but instead were externally reinforced on the bottom or tension side of the beams

with one, two, and three ply unidirectional carbon fiber reinforced plastic (CFRP) panels. In

addition, several of the beams were also reinforced on the sides as well as the bottom with three

ply CFRP. The beams were simply supported and loaded at beam midspan.

The lightweight concrete used in the test specimens was characterized via quasistatic and

dynamic compression and splitting tensile tests. In compression, the concrete behaved the same

as normal weight concrete. In tension, however, its behavior was quite different.

The beams sustained dynamic loads with amplitudes up to 10 kips (44.5 kN) and

durations less than 1 millisecond. Measurements including total load, midspan displacement and

strains, and a high speed framing camera (10,000 frames/sec) gave insight into failure








mechanisms. Failure to account for inertia in the loads will result in incorrect calculation of the

beam's peak bending load.

The quasistatic bending tests were conducted in load control at 2 Ibs/sec (8.9 N/sec).

Both crosshead load and midspan displacement were recorded.

Fracture energies were determined by calculating the areas under the bending load

versus displacement curves. Dynamic fracture energies and peak displacements for the CFRP

reinforced beams were always less than the static values. However, dynamic peak bending loads

were 2 3 times larger than the corresponding static values. This implies that for a given load

rate, a beam has a fixed capacity to absorb energy, dictated by the peak bending load and limited

by displacement, emphasizing the brittle nature of concrete when loaded dynamically.

The beams were analytically idealized as a single degree of freedom (SDOF) system,

subjected to a half sine pulse impulsive load. The SDOF analysis generally overpredicted the

displacement-time behavior of the beams, due to modeling limitations.

Dynamic beam behavior was also studied numerically using the finite element method.

Excellent agreement with experimental evidence was obtained.















CHAPTER 1
INTRODUCTION


Objective

The objective of this investigation was to understand the dynamic behavior of plain

lightweight concrete beams and plain lightweight concrete beams embedded with nylon fibers,

both of which were externally reinforced with carbon fiber reinforced plastic (CFRP) panels.

One, two, and three ply external CFRP strengthening panels were bonded to the bottom or

tension side of laboratory size (3.0 x 3.0 x 30.0 in/7.6 x 7.6 x 76.2 cm) concrete beams. In

addition, three ply CFRP was also applied to the sides as well as the bottom of some of the

beams. A schematic of the externally reinforced beam cross-section is shown in Figure 1. A

total of seventy-two beams were tested statically and dynamically. The experimental and

analytical studies of the static and dynamic response of these beams is the basis for this

dissertation.

Background

Since the mid sixties, existing concrete structures in Europe, South Africa, the US, and

Japan had all been externally post-strengthened by bonding steel plates to the bottom or tension

sides of the beams or slabs. The first actual use of externally applied fibrous composite

materials to enhance the load carrying capability of a concrete structure is attributed to a

researcher in Switzerland in 1989. Kaiser [1] is credited as the first worker to employ carbon

fiber reinforced plastic (CFRP) to post-strengthen concrete beams. Motivation for Kaiser's work

was driven by several factors: difficulties in manipulating the unwieldy steel plates into position















3 in
(7.62 cm)


1


2


^_ 3 in _
(7.62 cm)
I Plain Concrete


Side CFRP


Adhesive


Bottom CFRP


Figure 1. Cross Section of Externally Strengthened Concrete Beam


at the construction site, corrosion at the steel/concrete interface, improper formation of

construction joints, and a limited selection of steel plate sizes. The CFRP material system, with

such desirable material attributes as being lightweight, being very strong (150-320 Ksi/1.034 -

2.206 GPa tensile strength), having outstanding corrosion resistance, and having excellent

fatigue properties, seemed a logical solution to the post-strengthening problem. Kaiser tested

twenty-six beams with a span of 6.56 ft (2 m), and one with a span of 22.96 ft (7 m), both

employing unidirectional CFRP on the bottom or tension side of the beams. He concluded that

the calculation of flexure in reinforced concrete elements post-strengthened with CFRP could be

performed similar to conventionally reinforced concrete structural elements, but that shear

cracking in the concrete could lead to delamination of the CFRP. He also concluded that flexural

cracking did not seem to influence the loading capacity of the beam, and that the addition of the

CFRP on the bottom of the beam led to a finer crack distribution in the beam when compared

with the plain concrete beam. Additionally, he stated that the difference in the thermal








expansion coefficients between concrete and the CFRP resulted in stresses at the CFRP/concrete

interface due to changes in temperature, but that after one hundred frost cycles ranging from -13

to +680 F (-25 to +200 C), no deleterious effects were noted on the load capacity of the beams.

In 1987, Meier and colleagues at the Swiss Federal Laboratories for Materials Testing

and Research (EMPA) conducted feasibility studies on the use of CFRP to rehabilitate the beams

in a bridge; in particular, as cables for cable-stayed and suspension bridges, prestressing tendons,

and other applications where steel repair plates could be replaced with advanced composite

panels [2, 3]. This may have been the genesis of Kaiser's pioneering work. Their more recent

work [4, 5, 6, 7] continues to focus on the large variety of modem materials recently employed

or soon to find application in modem bridge construction, focusing primarily on the use of

fibrous composites. Meier [7] also describes the first use of CFRP to rehabilitate a damaged

bridge in Switzerland in 1991. The Ibach bridge, in the county of Lucerne, was damaged when

construction workers were coring the bottom of a 127.92 ft (39 m) span for a traffic light and

accidentally severed several of the wires in a prestressing tendon in the outer web. The bridge

was successfully repaired with only 13.6 lbs (6.2 kg) of CFRP, compared with the 385 lbs (175

kg) of steel that normally would have been used to repair the bridge.

Triantafillou and Plevris [8] have studied the failure mechanisms of fiber reinforced

plastic (FRP) strengthened concrete beams subjected to a bending load which included: steel

yield-CFRP rupture, steel yield-concrete crushing, compressive failure, and crushing. In

addition to discussing the concept of concrete strengthening with prestressed FRP composite

sheets, they obtained equations describing each failure mechanism and produced diagrams

showing the beam designs for which each failure mechanism is dominant. In collaboration with

colleagues at EMPA in Switzerland, they have also studied hybrid box beams composed of

aluminum and CFRP to meet the requirements of low weight, high strength and stiffness, relative









ease of design and fabrication, and high reliability [9]. They analyzed the problem of a

minimum weight design, CFRP-reinforced, thin-walled rectangular aluminum section subjected

to given strength and stiffness constraints, and showed that at the optimum design, various local

failure mechanisms occur almost simultaneously, while beam stiffness rarely controls.

Triantafillou and Meier [10] studied the basic mechanics of glass fiber-reinforced plastic (GFRP)

box beams, which combine a layer of concrete in the compression zone and a unidirectional

CFRP laminate in the tension zone. A design methodology for the hybrid sections is also

presented, based on a complete set of stiffness, strength, and ductility design requirements. The

method of strengthening and reinforcing concrete beams using thin FRP sheets as externally

bonded reinforcement, described by Triantafillou and Plevris [8], can be extended if the sheets

are prestressed before they are applied to the concrete surface [11]. This prestressing technique

is being considered in the building of new structures, particularly bridges, and the strengthening

of existing ones. An analytical model was developed which predicts the maximum achievable

prestress level, so that the prestressed FRP system does not crack and fail near the two ends upon

release of the prestress force. The flexural behavior of concrete beams prestressed with

externally bonded FRP sheets is discussed, based upon four experiments and their subsequent

analysis. Test results indicate a modest 25 percent improvement in the flexural strength of the

four beams when prestressed FRP panels were used, compared with when the non-prestressed

FRP panels were used.

In China, Shijie and Ruixian [12] have analyzed the adhesive bond characteristics of

GFRPs used to externally reinforce concrete beams. Static loading and fatigue tests were carried

out on GFRP reinforced beams with spans of 13.12 ft (4 m). They concluded that the fatigue life

of a GFRP strengthened beam is approximately three times that of the unreinforced beam.

Applications for repairing two highway bridges were also discussed.








At the University of Arizona, Saadatmanesh and Ehsani [13] conducted four tests on 5 ft

(1.52 m) long concrete beams that had been externally reinforced with GFRP plates which were

bonded to the tension side of the beams. One beam was unreinforced, and designated as the

control beam. One #3 steel tensile reinforcement rod was also cast into the beams. The beams

were simply supported and subjected to two concentrated loads symmetrically placed 3 in (7.62

cm) on either side of the midspan. Deflection at the midspan, as well as strains on the surface of

the GFRP plates, were measured as the beams were loaded to failure. Load versus strain and

load versus deflection plots were obtained on all five tests. They concluded that strengthening

concrete beams with epoxy bonded GFRP plates is a feasible way of increasing the load carrying

capacity of existing beams and bridges, and that selection of a suitable epoxy for bonding the

GFRP panels onto the beams is necessary to improve the ultimate capacity of the beam. They

noted that the epoxy adhesive should have sufficient stiffness and strength to transfer the shear

force between the composite plate and the concrete.

Sharif et al. [14] and Ziraba et al. [15], in the Department of Civil Engineering at King

Fahd University of Petroleum and Minerals in Saudi Arabia, experimentally investigated the

repair of initially-loaded reinforced concrete beams with epoxy-bonded fiberglass reinforced

plastic (FRP) plates. The reinforced concrete beams were initially loaded to 85 percent of their

ultimate flexural capacity and subsequently repaired with the epoxy-bonded FRP plates and then

re-loaded to failure. Different repair and plate anchoring schemes were investigated to try and

eliminate premature failure of the FRP plate/bond due to the high concentration of shear stress,

and to promote ductile behavior of the beam. Load-deflection curves for the FRP repaired beams

are presented, and the different failure modes for each beam are discussed. Their results,

consistent with those obtained by other researchers, indicated that the flexural strength of the








FRP repaired beams is greater than that of the control beams, and that the ductile behavior of the

FRP repaired beams is inversely proportional to FRP plate thickness.

University of Nevada researchers Gordaninejad et al. [16] focused on the behavior of

composite bridge girders constructed from CFRP sections and concrete slabs. Their study

examined four-point bending of three beams; one plain graphite/epoxy I-beam, and two beams

constructed from concrete slab and graphite/epoxy sections which were adhesively bonded

together. All three beams were one-eighth scale models of bridge girders. Theoretical and

experimental studies were performed on the plain I-beam sections to develop a basic

understanding of the beams flexural behavior. The tests and analyses were then extended to the

composite girders. They concluded that slip at the interface between the concrete slab and the

graphite/epoxy beam had a minor effect on the failure load, but produced a significant reduction

in stiffness of the composite section.

Chajes et al. [17,18] at the University of Delaware tested a series of reinforced concrete

beams in four-point bending to determine the ability of several different types of externally

bonded composite fabric materials to improve the beam's flexural capacity. The different fabric

materials were chosen to allow a variety of fabric stiffnesses and strengths to be studied. The

fabrics used were made of aramid, E-glass, and graphite fibers, and were bonded to the beams

using Sikadur 32, a two-component, high modulus, high strength, construction epoxy. A series

of pull-off tests were run to investigate the bond strength of the adhesive, and it was determined

that a single layer of aramid, a triple layer of E-glass, and a double layer of graphite fabric can be

expected to develop full tensile capacity in approximately 2.0 in (50.8 mm) for both the E-glass

and graphite fabric, and in approximately 3.0 in (76.2 mm) for the aramid fabric. Test results

indicated that the external fabric reinforced beams yielded an increase of approximately 50

percent in both flexural capacity and stiffness. For the beams reinforced with graphite fiber and








E-glass fabrics, failures were attributed to fabric tensile failure in the beam's constant moment

section, whereas the beams reinforced with aramid fabric failed due to crushing of the concrete

in compression. An analytical model based on the stress-strain relationships of the concrete,

steel, and composite fabrics was also developed, and comparisons were made with the

experimental results.

Recently, the Japanese have also investigated the use of carbon fiber reinforced plastic to

retrofit several large scale structures in the field [19]. The Japanese work is different from the

European, Saudi, and U.S. approaches in that it makes use of dry fiber CFRP sheets rather than

the pre-preg plates or strips. Two petrochemical industries, the Tonen Corporation and

Mitsubishi Chemical, have aggressively pursued this technology, and have developed proprietary

processes to impregnate the dry CFRP sheets with various epoxy resins. This technique

effectively eliminates the requirement for mechanical or vacuum fixturing when applying the

CFRP sheets to the structure. Unfortunately, the available literature describing their processes

are proprietary and are unavailable through normal journal articles or library access. The only

other work cited were Japanese symposia proceedings, which were also unavailable through

normal library channels.

The U.S. military has also recognized the potential of advanced composite materials to

strengthen and rehabilitate existing concrete structures. In the past, massive concrete protective

structures were constructed to shelter military personnel and equipment from conventional

weapon attacks. Now, as the US military moves into an era in which "mobility" is becoming

more and more important, new materials must be sought out that can be easily transported and

used for rapid construction while still maintaining adequate levels of protection for personnel

and equipment. Composite materials, typically used by the military solely in aerospace

applications, are now being investigated to potentially solve the burgeoning demand for








lightweight, durable construction materials. To investigate CFRP's potential for Air Force

applications, Hughes and Strickland [20] at Tyndall Air Force Base in Florida, in conjunction

with faculty members from the University of Florida, Ohio State, and Auburn, have conducted a

series of tests on small concrete beams reinforced with uniaxial CFRP strips on the tension side

of the beams. Initial tests were performed on 1.0 x 1.0 x 12.0 in (2.54 x 2.54 x 30.48 cm) and 2.0

x 2.0 x 12.0 in (5.08 x 5.08 x 30.48 cm) concrete beams in both three and four-point bending

tests. The number of plies in the CFRP reinforcing strip was varied from one to three, and three

different cementitious mixes were used for the beam material. Additionally, CFRP strips were

also applied along the sides of some of the beams. Test results indicated that the failure load was

increased by 4.4 to 9.0 times the baseline failure load when the CFRP strips were applied to the

beams, when compared to plain concrete beams without such strips.

The most recent work to date on concrete beams externally reinforced with CFRP has

been conducted by Chajes et al. [18], Sierakowski et al. [21], and Ross et al. [22]. Sierakowski

et al. [21] used a strength of materials approach to develop an analytical model which evaluates

the shift in the neutral axis that occurs in statically loaded concrete beams that have been

externally reinforced with CFRP strips. The shift in the neutral axis of the beam occurs when the

tensile stress in the concrete at the bottom of the beam exceeds the fracture stress of the concrete,

which is roughly 10 percent of the concrete's compressive strength. It is this cracking that causes

a shift in the neutral axis of the beam, and a subsequent change in the beam's planar moment of

inertia. In this analysis, two particular cases were studied. In the first case, the externally

bonded CFRP strips were placed on the bottom or tension side of the beams only, and in the

second case, the strips were placed on the bottom as well as the sides of the beams. The

analytical model is compared to experimental test data gathered on some small scale beams, 3.0

x 3.0 x 30.0 in (7.62 x 7.62 x 76.2 cm ) in size, and some large scale beams, 0.67 x 0.67 x 9.0 ft








(0.20 x 0.20 x 2.74 m) in size, both of which were tested in third-point loading in the structures

laboratory owned by the Wright Laboratory Air Base Technology Branch at Tyndall Air Force

Base, Florida. Reasonable agreement between experiment and analysis was obtained. Ross et al.

[22] performed a complete review and analysis of twenty-two experiments that were conducted

in the summer of 1994 also at the Tyndall Air Force Base, Florida, structures laboratory. The

concrete beams were again 0.67 x 0.67 x 9.0 ft (0.20 x 0.20 x 2.74 m), had three ply

unidirectional CFRP on the bottom or tension side of the beams, and were all tested to failure

using a third point loading test frame. The tension steel varied in size from number 3s to number

8s in the beams. Complete section analysis was conducted on the beam cross sections and load-

displacement curves were calculated and compared with the test beams both with and without

CFRP. In an effort to quantify the strengthening effects of the CFRP, an enhancement ratio,

defined as the peak load on a beam with a given steel percentage and CFRP, divided by the peak

load of the same beam with steel only, was obtained and is shown in Figure 2. Results show

considerable enhancement for the beams with the lower tensile steel ratios, and little to no

enhancement for beams with high tensile steel ratios. Ross et al. [22] also concluded that for the

experiments in which concrete beams reinforced with CFRP were tested, the weakest link

appears to be in the shear strength of the adhesive/CFRP interface. When delamination occurs

between the CFRP and adhesive, the tensile strength of the CFRP is not used to its fullest

potential, and the authors recommend further work on improving the bond between the CFRP

and the concrete. The principal conclusion of the study was that a quantifiable strength

enhancement was obtained by the addition of a very thin (0.0175 in/0.4445 mm) strip of CFRP

added to the bottom side of the beams, especially for those beams with tensile steel ratios of one

percent or less.











ER,ENHANCEMENT RATIO

ZERO PERCENT DATA NOT SHOWN
2.5 -



0
1.5 -----0 -



POWER REGRESSION, ER = a*PS b
0.5 ---------------------------------

0
0 1 2 3 4
PS, PERCENT TENSION STEEL

0 3 4 5 6 7 8
STEEL BAR SIZE


Figure 2. CFRP Enhancement Ratio [22]


Approach

After a thorough and careful review of this literature, it became evident that the approach

for this investigation should consider:

1. A systematic experimental study of the effect of varying the number of plies of

CFRP on the static load carrying capacity of concrete beams.

2. An experimental study of the dynamic behavior of concrete beams both with and

without external CFRP reinforcing panels.

3. Development of a comprehensive analytical model which attempts to predict not

only the static load-displacement behavior of the beams, but the dynamic

displacement-time behavior as well.








4. Finite element method (FEM) calculations of the dynamic response of beams

both with and without external CFRP reinforcing panels.

In order to carry out a systematic experimental study of the effect of varying the number

of plies of the CFRP on both the static and dynamic load carrying capacity of the beams, the

approach was to test laboratory scale concrete beams with none, one, two, and three plies of

unidirectional CFRP to failure both statically, using a MTS load frame, and dynamically, using

a drop weight test machine. All tests were conducted in center-point loading mode, as shown in

Figure 3. Eighteen static and fifty-four dynamic beam bending experiments were attempted,

based on the test matrix shown in Table 1 below.




P, P(t)
L/2 L/2 "
A _q*_______

Strain Gage
Locations


Plain Concrete
P/2 Adhesive
P/2 CFRP P/2
Section A-A Adhesive





Figure 3. Center or Three Point Bending Mode Used in Static and Dynamic Tests


It has already been well-established that concrete, although brittle, is a rate sensitive

material both in tension and compression. In order to thoroughly characterize the concrete used

in the beam test samples, the approach was to conduct a series of static and dynamic









Table 1. Test Matrix for Static and Dynamic Beam Bending Experiments


Dynamic Tests

Beam* Drop Height #1 Drop Height #2 Drop Height #3

BO X X X
BI X X X
B2 X X X
B3 X X X
B4 X X X
B5 X X X


Static Number of Number of
Tests Iterations Beams


X 3
X 3
X 3
X 3
X 3
X 3

Total Number Beams


Key*

BO Plain Concrete Beam
B Concrete Beam with 1 ply CFRP on Bottom of Beam
B2 Concrete Beam with 2 ply CFRP on Bottom of Beam
B3 Concrete Beam with 3 ply CFRP on Bottom of Beam
B4 Concrete Beam with 3 ply CFRP on Bottom and Sides of Beam
B5 Fibrous Concrete Beam with 3 ply CFRP on Bottom of Beam


compression and splitting tension tests. Standard compression tests on concrete cylinders were

also required to ensure that the static unconfined compressive strength fe was known for each

beam. This attribute is very important, since other material parameters which were required for

subsequent analyses and modeling are typically derived from it, such as the secant modulus and

modulus of rupture. This was the approach taken for the research.














CHAPTER 2
EXPERIMENTAL WORK


Fabrication Of Concrete Beam Specimens

A total of 72 lightweight concrete beams were prepared for the experimental portion of

the research. The beam size chosen was 3.0 x 3.0 x 30.0 in ( 7.62 x 7.62 x 76.2 cm), and the

aggregate used was a lightweight aggregate with the trade name Solite which reduced the

overall density of the concrete by about 20 percent. The aggregate used in these beams was

sieved to pass a 0.375 in ( 0.925 cm) sieve, but was retained on a 0.25 in (0.635 cm) sieve. No

tension steel reinforcement was used in any of the beams, due to their small size. Each batch of

concrete beams were cast in lots of eight, with four 4.0 in (10.16 cm) diameter by 8.0 in (20.32

cm) long cylinders cast at the same time as the beams for subsequent material property testing.

The mix proportions in Table 2 were used for each lot of eight beams and four cylinders cast.



Table 2. Lightweight Concrete Mix Proportions



Type 1 Portland Cement 35.25 lbs (16.02 kg)

Concrete Sand 85.63 lbs (38.92 kg)

Lightweight Aggregate 69.38 lbs (31.54 kg)

Water 19.00 lbs (8.64 kg)








A 5.6 percent moisture content in the aggregate was chosen as the standard. The

aggregate was soaked in water for one day and then allowed to drain off overnight prior to

combining it with the other mix constituents to facilitate the mixing process. If the moisture

content of the mix turned out to be too high, the amounts of aggregate and water were then

adjusted to account for the difference. This made a workable mix that flowed well on the

vibrator, with no measurable slump. The unit weight for all of the beams cast was 118 lbs/ft3

(1892.7 kg/m3). Table 3 lists the beam designators and the dates on which those lots of beams

were cast.


Table 3. Beam Designator and Cast Schedule


BEAM DESIGNATOR DATE CAST


LW1-1 through LW1-8

LW2-9 through LW2-16

LW3-17 through LW3-24

LW4-25 through LW4-32

LW5-33 through LW5-40

LW6-41 through LW6-48

LW7-49 through LW7-56

LW8-57 through LW8-64

LW9-65 through LW9-72

LW10-73 through LW10-80

LW11-81 through LW1 1-88


16 November 1994

29 November 1994

6 December 1994

14 December 1994

17 January 1995

18 January 1995

23 February 1995

28 February 1995

2 March 1995

7 March 1995

9 March 1995








Additionally, another half batch of concrete was cast into one 12.0 x 12.0 x 6.0 in (30.48

x 30.48 x 15.24 cm) box to make samples for Split Hopkinson Pressure Bar (SHPB) testing

along with two additional 4.0 in (10.16 cm) diameter by 8.0 in (20.32 cm) long cylinders, and

one additional 6.0 in (15.24 cm) diameter by 12.0 in (30.48 cm) long cylinder for subsequent

concrete characterization testing. These samples were cast on 29 November 1994. For the last

two sets of beams, labeled LWF10 and LWF 11, three pounds of nylon fibers per cubic yard (1.78

kg/m ) were added to the mix to make two sets of fibrous concrete beams.

After casting, each beam was initially cured underwater for 28 days, and then cured in

air until it was subsequently tested. The minimum recommended time for concrete test

specimens between fabrication and conducting any type of dynamic testing is 60 days; for these

beams the minimum time turned out to be 90 days. This is to allow time for the concrete to

achieve sufficient strength, since its strength increases with time.

Application of the CFRP

Once the concrete beams had sufficiently dried after the 28 day water cure, the process

of bonding the CFRP to the beams could begin. The one, two, and three ply CFRP panels were

supplied by the Wright Laboratory Materials Directorate, Wright Patterson Air Force Base,

Ohio. The panels were all of the same material, an AS4C/1919 graphite epoxy. The C

designation denotes a commercial grade of AS4 graphite epoxy, and the 1919 denotes a 2500 F

(121.10C) cure. Table 4 contains the relevant material properties of AS4C/1919 CFRP.

All of the CFRP panels came as pre-cut panels 3.0 x 30.0 in ( 7.62 x 76.2 cm) in size.

The cured ply thicknesses of the one, two, and three ply panels were individually measured with

a micrometer; the other material properties were provided by the Wright Laboratory Materials

Directorate.









Table 4. Pre-Preg CFRP Material Properties


0 Tensile Strength 320 ksi (2206.9 MPa)
o 6
0 Tensile Modulus 20 x 10 psi (137.9 GPa)

Fiber Volume 60 percent

Cured Ply Thickness

one ply 0.0085 in (0.2159 mm)

two ply 0.0140 in (0.3556 mm)

three ply 0.0195 in (0.4953 mm)




The adhesive used to bond the CFRP panels to the concrete beams was a thixotropic,

modified, two part epoxy engineering adhesive manufactured by the Dexter Corporation in

Seabrook, New Hampshire with the trade name Hysol. This adhesive was recommended for its

toughness, flexibility, and efficacy in bonding dissimilar materials. The adhesive has excellent

peel and lap shear strengths, and has a pot-life of 40 50 minutes at 77 F (28.9 C) for 0.55 lbs

(250 gms) of mixed adhesive. The two part epoxy was mixed in equal parts (by either weight or

volume since the densities of the two parts were the same) and mixed thoroughly until the off-

white Part A and black Part B were a uniform gray in color. Some heat buildup or exotherm was

noticed during the mixing process, but since less than 1 cup of Part A and Part B were ever

mixed at one time, no excessive exotherm or heat buildup ever developed.

Surface Preparation

As with any bonding or adhesive process, proper surface preparation of the bonded

materials is a necessity. The bonding surfaces should be clean, dry, and properly prepared. The










bonded parts should be held in intimate contact until the adhesive is set. It was not necessary to


maintain fixturing for the entire adhesive cure schedule (3 days @ 770F) but only until handling


strength is achieved. The manufacturer considers handling strength to be the same as tensile lap


shear strength. Handling strength of 750 psi (5.2 MPa) is achieved in 6 8 hours @ 77F


(28.9 C). Figure 4 is the manufacturer's graph of tensile lap shear strength versus time at room


temperature 77 F.


Figure 4. Tensile Lap Shear Strength (psi) versus Time (days) for Dexter Hysol Adhesive



To properly prepare the concrete and CFRP surfaces to be bonded, all grease, oil, and

foreign particles had to be removed from each surface. As with most high performance

engineering adhesives, this step is critical, since for good wetting, the surface to be bonded


should have a higher surface tension than the adhesive. Therefore, the adhesive manufacturer's


*r 4000-
a.

h
r~
I 3000-
0
z
w
I-
S2000-



1000-
-I
C,
z


1 2 3
TIME AT ROOM TEMPERATURE, DAYS








recommendations were closely followed to ensure proper surface preparation of the concrete and

CFRP. For the CFRP, the following surface preparation steps were taken:

1. Use peel ply side of CFRP for bonding surface.

2. Degrease surface with methyl ethyl ketone (MEK).

3. Lightly abrade surface with medium grit emery paper. Take extreme care to

avoid exposing the carbon reinforcing fibers. (This is particularly important for

the one ply CFRP panels since they are only 0.0085 in (0.2159 mm) thick).

4. Repeat step 2; degrease surface with methyl ethyl ketone (MEK).

Since the concrete beams were new, recently cast test specimens, it was extremely

important to make sure that the de molding release agent, which was either 10W-30 motor oil

or WD-40 lubricant, was completely removed from the bottoms and sides of the beams. The

following procedure was used to prepare the surfaces of the concrete beams:

1. Degrease the surface to be bonded with acetone.

2. Repeat step 1, if excessive de-molding oil is noted on the exterior surface.

3. Mechanically scarify (abrade) the surface with a grinding wheel.

4. Repeat step 1, degrease the surface with acetone.

5. Remove dust and concrete particulates with a stiff bristle whisk broom.

The cleaned concrete and CFRP surfaces should be bonded as soon as possible after the surface

preparation procedures have been accomplished, and the bonding procedure itself should be

performed in a room separate from the room or area in which the cleaning and surface

preparation procedures are accomplished.

After the above surface preparation steps were completed, the CFRP strengthening

panels were ready to be bonded. Six beams and six CFRP panels could be reasonably handled

and bonded at one time. One third of a cup of Part A and one third of a cup of Part B Hysol








adhesive was sufficient to produce a 0.030 in (0.762 cm) bondline between the CFRP and the

beam for six specimens. After the Hysol was spread on the surface with a wide-bladed putty

knife as shown in Figure 5(a), a square tooth trowel was used to produce a series of 0.0625 in

(1.6 mm) high by 0.0625 in (1.6 mm) wide adhesive beads along the length of the beam, as

shown in Figure 5(b). This also served to remove any excess Hysol from the beam's surface,

and produced a uniform volume of adhesive on the beam as well.

Next, the CFRP panel was placed on top of the Hysol beads, shown in Figure 6, and

pressed into the adhesive while being concurrently smoothed with a paper towel. This served to

seat the panel on the beam as well as eliminating any excess air bubbles between the CFRP panel

and the beam.

After all six of the beams were prepared in this manner and keeping mind of the time so

as not to exceed the fifty minute pot life of the adhesive, the beams were then placed in a large

vacuum bag with 0.25 in (6.35 mm) foam spacers in between each beam. The perimeter of the

bag was sealed with a caulk compound. The vacuum bag itself was made of ordinary 0.006 in

(0.152 mm) thick polyethylene film. A vacuum pump was connected to the polyethylene bag via

a vacuum hose and a short length of 0.5 in (12.7 mm) galvanized pipe, which was then inserted

into the bag and also sealed with a caulk compound. A gage had been placed in line with the

length of galvanized pipe to measure the amount of vacuum pressure. Once the entire bag with

the six concrete beams inside was sealed, the pump was turned on. The pump was a Welch

Duoseal (Welch Vacuum Technology, Incorporated, Skokie, Illinois) two stage vacuum pump

which was driven by a 0.5 horsepower electric motor, with a clutch, pulley, and V-belt attached.

The performance specifications of the vacuum pump are shown in Table 5. Once any minor leaks

in the bag had been found and sealed, the vacuum pump quickly pulled the bag down to 28.5 in



















































(b)

Figure 5. Epoxy Adhesive Being Placed on Surface of Beams








































Figure 6. CFRP Panel Being Placed on Beams


Table 5. Vacuum Pump Specifications (New Pump)


Free Air Displacement

Pump Rotational Speed

Guaranteed Partial Pressure


5.6 ft3/min

525 RPM

29.5 in Hg (14.5 psi)


Hg (14.0 psi), since the initial volume of air trapped inside the bag was relatively small. The

pressure differential created by the vacuum placed the beams into uniform hydrostatic








compression, placing a uniformly distributed force of 1260 lbs (5.62 kN) on each of the six 90.0

in2(580.6 cm2) surfaces of each of the six beams. This fixturing force held the six CFRP panels

firmly in place on top of the beams until the Hysol reached its handling strength of 750 psi

(5.17 MPa) tensile lap shear strength in 6 8 hours at 770 F (28.90 C). The vacuum pump

typically ran for seven hours at a time for each batch of six beams to meet this curing schedule.

Afterward, the beams were then removed from the bag and allowed to cure for the remainder of

the three day cure schedule.

This process was used to bond 12 one ply panels, 12 two ply panels, and 24 three ply

panels to the bottom or tension side of these 48 concrete beam samples. The remaining 12

beams had three ply panels bonded to both the sides as well as the bottoms. For these beams,

each of the three sides were bonded separately following the procedures above. Chajes et al.

[18] also used a vacuum fixturing process to bond some composite strengthening panels to some

beams, but their process was unknown to the author at the time of this work. A patent is

currently under review for the vacuum fixturing process used in this investigation.

Characterization of the Concrete

In order to determine the material properties of the concrete used to fabricate the beam

test specimens, a series of quasistatic and dynamic loading experiments were conducted on the

samples of concrete which were cast at the same time as the beam samples were cast.

Static Compression Tests

The first tests conducted were static compression tests on 4.0 in (10.16 cm) diameter by

8.0 in (20.32 cm) long cylinders. Four cylinders from each batch of concrete were tested in

compression in a Forney System 2000 (Forney Incorporated, Wampum, Pennsylvania)

loadframe which has a 400,000 lb (1,779 kN) capacity. The four failure loads were averaged,

2 2
and then divided by the area of the test cylinder's cross section, which was 12.57 in (81.07 cm )








to yield the so-called unconfined compressive strength of the concrete, fe. Appendix A

summarizes the results of these static compression tests.

The unconfined compressive strength may be associated with the hypothetical,

statistically derived compressive stress-strain curve in Figure 7 shown below, where the peak

compressive stress is the value of fc found in the tests.


Figure 7. Hypothetical Compressive Stress-Strain Curve


Certain properties of the stress-strain curve are necessarily described. The tangent to the

curve at the origin is called the initial tangent modulus of elasticity, Eci. A line drawn from the

origin to a point on the curve at which fc = 0.45 fc is called the secant modulus of elasticity, Ecs.

For low strength concrete, Ei and Ecs differ widely. For high strength concrete, there is

practically no difference between the two values. For lightweight concrete the initial slope is


Strain, 6, in/in (mm/mm) &c








somewhat less than for normal weight concrete, and the maximum stress fc occurs for larger

strain values. Ec is the compressive strain associated with fc. It is commonly accepted that the

post-peak or strain softening portion of the stress-strain curve is terminated at a stress level of

0.85fc which is referred to as the concrete's ultimate strength. The strain associated with 0.85fc

is therefore the ultimate strain, denoted by su.

Figure 8 is an actual stress-strain curve for lightweight concrete, generated at the Tyndall

Air Force Base structures laboratory in 1994. Unfortunately, the curve stops at fe which is about

6 ksi (41.4 MPa), and doesn't show the strain softening part of the curve due to strain gage

failure. However, an important feature is present in this curve which differentiates lightweight

concrete from its normal weight counterpart; the strain at f c. Typical values for c the strain at

fc, for normal weight concrete, are 0.002 in/in (cm/cm). Here we note that for the lightweight

concrete, the strain value Ec at f, is larger, about 0.003 in/in (cm/cm). If we assume that the

strain softening part of the stress-strain curve is symmetric, we may extrapolate the value at Eu,

the ultimate strain at rupture, which is associated with a stress of 0.85f'c in the strain softening

region. This value is found to be about 0.004 in/in (cm/cm), which is also larger than that of the

typical value of 0.003 in/in (cm/cm) for eu for normal weight concrete. Not only does the

maximum stress occur at a larger strain, but also the rupture stress has a larger strain value

associated with it as well.

Knowing the values of fc from quasistatic testing allows us to directly calculate the

tangent and secant moduli from standard empirical equations developed by the American

Concrete Institute (ACI). In general practice, the secant modulus of elasticity is used whenever

an elastic modulus value is needed, and is simply referred to as Ec. The ACI equation for the

secant modulus is defined as











7000




6000 -... *




5000


,1

4000

3000 ---- ---- ---.'l --- -------- ----




2000






1000





0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035
Strain












E, Secant Modulus (psi)

w Unit Weight (lbs/ft3)

fe Unconfined Compressive Strength (psi)
1000 ,"----- ----------------
,, i
,,,"

000 0.00 .05 002 0.05 003 003
Stai

Figre8.Stes -Stai Crv fr igtwigt onree CortsyofL.. usynki 194

E=3 32(r~l 1

where-- / ------------------
EcSean Mduus(pi
w Uni Weigt (lb/ft*
f'cUncnfiedComresiveStengh (si








In addition to the 4.0 in (10.16 cm) diameter by 8.0 in (20.32 cm) long samples, six

2.0 in (5.08 cm) diameter by approximately 2.0 in (5.08 cm) long specimens were also tested in

direct compression, in order to provide a direct sample size comparison to the Hopkinson bar

samples. A load rate of approximately 2000 lbs/min (8.9 kN/min) was used for the first three

samples, and then a load rate of approximately 20,000 lbs/min (89.0 kN/min) was used for the

last three samples. It should be noted that the strain rate was calculated by dividing the stress

rate by a secant modulus which was calculated from an average unconfined compressive failure

stress of 6,708 psi (46.3 MPa). In addition, the dynamic increase factor is the ratio of the

dynamic failure stress to the average static failure stress. The dynamic increase factor is

subsequently plotted as a function of the log of the strain rate. For these quasistatic strain rates,

there is clearly no increase in the compressive strength of the concrete, as expected. Table 6

summarizes the results of these direct compression tests on the 2.0 in (5.08 cm) diameter

specimens.

Static Splitting Tensile Tests

It has been well established that concrete is about an order of magnitude weaker in

tension than in compression. See for example, Neville [23] or Winter and Nilson [24]. The

tensile or fracture strength of concrete is an important material property, since tensile failure is

the dominant failure mode in concrete. In order to determine the tensile strength of the concrete

test specimens used in this investigation, a series of splitting tensile or Brazilian tests were

conducted in the Forney System 2000 compression load frame. The method of conducting

splitting tensile tests has also been well established. See, for example, Neville [23]. This

indirect method of applying tension in the form of splitting was first suggested by a Brazilian

named Fernando Carneiro, hence the name Brazilian test, although the method was also

developed independently in Japan. In this test, the cylindrical sample is placed with its








Table 6. Quasistatic Direct Compression Tests on 2.0 in (5.08 cm) Diameter
by 2.0 in (5.08 cm) Long Lightweight Concrete Specimens


Specimen Specimen Load at Time to Load Stress Stress Strain* Dynamic
Number Length Failure Failure Ibs/min psi psi/sec Rate Increase
in (cm) lbs (kN) min (sec) (kN/min) (MPa) (kPa/sec) I/sec Factor
1 2.006 21,760 11 1979 6926 10.5 3.03 x 1.03
(5.095) (96.8) (660) (8.8) (43.4) (72.4) 10
2 2.01 20,050 9.98 2055 6525 10.9 3.15 x 0.97
(5.105) (89.2) (599) (9.1) (45.0) (75.2) 106
3 2.012 20,960 10 2092 6672 11.1 3.20 x 0.99
(5.11) (93.2) (600) (9.3) (46.0) (76.6) 10
4 2.012 22,140 1.15 19,246 7047 102.1 2.95 x 1.06
(5.11) (98.5) (69) (85.6) (48.6) (704.1) 105
5 2.013 17,760 1 17,810 5653 94.2 2.72 x 0.85
(5.113) (79.) (60) (79.2) (39.0) (649.7) 10"
6 2.012 22,760 1.1 20,696 7245 109.8 3.17x 1.09
(5.11) (101.2) (66) (92.1) (50.0) (757.2) 105

Based on a Secant Modulus Calculated From an Average Compressive Failure
Stress of 6708 psi (46.3 MPa); Ec = 3.46 x 106 psi (23.89 GPa)


longitudinal axis between and parallel the platens of the load frame as shown in Figure 9. The

load is increased at a constant load rate until failure by splitting along the vertical diameter takes

place. These so-called splitting tensile tests were conducted in lieu of the more difficult direct

tensile test so as not in incur the difficulties of holding the specimens to achieve axial tension,

and the uncertainties of secondary stresses induced by the holding devices. Again, the samples

tested were from the same batches of concrete from which the beams were cast. Sample sizes

were approximately 2.0 in (5.08 cm) in diameter and 2.0 in ( 5.08 cm) long.

Calculation of the horizontal tensile strength follows the derivation of Boussinesq (1892)

as given by Malvern [25] and Timoshenko [26]. An element on the vertical diameter of the

cylinder is subjected to a compression stress of
























Figure 9. Diagram of the Splitting Tensile or Brazilian Test


c= 2P D2
7rLD r(D r)


and a horizontal tensile stress of


f 2P
7nLD


where


Compressive Stress, psi
Compressive Load, lbs
Length of Specimen, in
Diameter of Specimen, in
Distance of the Element from the Upper Load, in
Distance of the Element from the Lower Load, in


P
Wood


111i1


D=2 in
(5.08 cm)

A


T tttt ttt
p-- L=2 in
(5.08 cm)









f, Tensile Stress, psi

Similar to the direct compression tests, a series of six quasistatic splitting tensile tests

were also conducted at two different load rates, one load rate being approximately 2,000 lbs/min

(8.9 kN/min) and the other about 10,000 lbs/min (44.5 kN/min). Knowing the load and time to

failure allows calculation of the stress and stress rate, respectively, using Equation (3). Once the

stress rate is known, the strain rate may be calculated by dividing by the secant modulus,

determined previously as 3.46 x 106 psi (23.89 GPa). Table 7 summarizes the results of these

splitting tensile tests on the 2.0 in (5.08 cm) diameter by approximately 2.0 (5.08 cm) long

specimens. Similar to the quasistatic direct compression tests, the dynamic increase factor is

calculated from the ratio of the splitting tensile stress for the three tests at a given load rate.

Obviously, there is no increase in strength at these low strain rates; hence the dynamic increase

factors are all ~ 1.0.


Dynamic Compression Tests

Strain rate effects on concrete strength have been examined experimentally by many

investigators [27 38]. However, in order to quantify the strain rate sensitivity of this particular

lightweight concrete in both tension and compression, a series of Split-Hopkinson Pressure Bar

(SHPB) tests were conducted on a 2.0 inch (5.08 cm) diameter SHPB located at Tyndall Air

Force Base, Florida. This particular SHPB has been described in full detail by Ross [38]. In

particular, compression tests on concrete from strain rates of 1/sec to 500/sec have been

conducted using this system. A schematic of the SHPB system is shown in Figure 10.

The striker bar impacts the incident bar which induces an elastic wave whose magnitude

and pulse length are proportional to the striker bar velocity and length, respectively. This elastic

wave is propagated down the length of the incident bar and impinges upon the cylindrical

concrete specimen, where part of the elastic wave is transmitted into the transmitter bar, and part

of the wave is reflected back into the incident bar. Ross [38] shows that for a specimen whose









Table 7. Quasistatic Indirect Splitting Tensile Tests on 2.0 in ( 5.08 cm) Diameter
by 2.0 in (5.08 cm) Long Lightweight Concrete Specimens


Specimen Specimen Specimen Load at Time to Load Rate Stress Stress Rate, Strain* Rate, Dynamic
Number Diameter Length Failure Failure lbs/min psi/sec Increase
in (cm) in (cm) lbs (kN) min (sec) (kN/min) psi (MPa) (kPa/sec) 1/sec Factor
1 1.99 2.012 4888 2.44 2003 776 5.3 1.53 x 10 1.23
(5.06) (5.111) (21.7) (146.4) (8.9) (5.4) (36.6)
2 1.99 2.012 3840 1.92 2000 611 5.3 1.53 x 10 0.97
(5.06) (5.111) (17.1) (115.2) (8.9) (4.2) (36.6)
3 1.99 2.012 3160 1.58 2000 502 5.3 1.53 x 10 0.8
(5.06) (5.111) (14.1) (94.8) (8.9) (3.5) (36.6)
4 2.00 2.008 4520 0.67 6780 717 17.9 5.17 x 10- 1.01
(5.08) (5.28) (20.1) (40.0) (30.2) (4.9) (123.5)
5 2.00 2.008 4180 0.44 9464 663 25.00 7.22 x 106 0.94
(5.08) (5.28) (18.6) (26.5) (42.1) (4.6) (172.4)
6 2.00 2.008 4680 0.43 10,800 740 28.5 8.22 x 10- 1.05
(5.08) (5.28) (20.8) (26.0) (48.0) (5.1) (196.6)


* Based on a Secant Modulus Calculated From an Average Compressive
Failure Stress of 6708 psi (46.3 MPa); Ec = 3.46 x 106 psi (23.89 GPa)





31



Sample

Striker Bar Incident Bar Transmitter Bar




Bridge Bridge


Strain Gage Strain Gage
Conditioner Conditioner


Recorder

Digital
Oscilloscope



Figure 10. Schematic of the Compressive Split-Hopkinson Pressure Bar


length is small compared to the length of the elastic wave, the integral of the reflected pulse is

proportional to the strain in the specimen. The incident and reflected pulses are recorded by a

strain gage located on the incident bar, and the transmitted pulse is recorded by a strain gage

located on the transmitter bar. The strains associated with each of these three pulses are

monitored by a full bridge of strain gages, which is then amplified and conditioned using a strain

gage conditioning amplifier, Model 2311 (Measurements Group, Raleigh, North Carolina). The

signals are then recorded on a Nicolet 4094 digital oscilloscope (Nicolet Instrument

Corporation, Madison, Wisconsin). The traces are subsequently stored for further processing

and analysis on a disk recorder. Following these procedures, a series of seventeen direct

compression tests were run on the SHPB, using a 26.0 in (66.04 cm) striker bar, and gun

chamber pressures of 20 200 psi (0.138 1.379 MPa). For these direct compression tests, the

specimens were lightly lubricated using a molybdenum disulfide grease, and pressed between the








incident and transmitter bars. They were held in place by friction between the two bars. Ross

[38] developed the following conversion factors, specific to this SHPB, to determine the incident

and transmitted stresses, and the strain rate from the strain gage data.

6
Co= volts/gain x (2.058 x 10 ) (4)

6
S= volts/gain x (1.4 x 10 ) (5)

where

o( Transmitted Compressive Stress, psi

e Strain Rate, 1/sec

Once the strain rate and compressive failure stress has been calculated, the dynamic increase

factor may be calculated by dividing the failure stress by the average of the three quasistatic

failure stresses, which was previously found to be 6708 psi (46.3 MPa). Table 8 shows the data

for the seventeen SHPB direct compression tests using the 26.0 in (66.04 cm) striker bar.

Dynamic Splitting Tensile Tests

To understand the potential dynamic strength enhancement due to strain rate effects of

lightweight concrete in tension, a series of thirteen splitting tensile SHPB experiments were also

conducted. The splitting tensile test was chosen over the more difficult to conduct direct tensile

test so as not to incur the difficulty of clamping or holding the specimen to achieve axial tension,

and the uncertainty of developing secondary stresses in the specimen induced by the holding

fixtures.

With regard to the specimen, it is rotated ninety degrees with respect to the incident and

transmitter bars. Two small pieces of steel stock, 0.25 x 0.25 x 2.0 in (6.35 x 6.35 x 50.8 mm) in

size, each with one side radiused to fit the contour of the concrete specimen, are affixed to the

outside of the specimen along a diameter line, parallel to each other, to help distribute the load as

shown in Figure 11. Figure 12 shows the orientation of the specimen in the SHPB. For the









Table 8. Direct Compression Tests on 2.0 in (5.08 cm) Diameter By
2.0 in (5.08 cm) Long Lightweight Concrete Specimens


Specimen Gun Amplifier Transmitted Strain Dynamic
Number Pressure Gain Stress, Rate Increase
psi (kPa) IA/IB v/psi/MPa v/l/sec Factor (DIF)
DCLW- 1 20
(137.9) 100/1000 4.22/8799/62.7 0.448/62.7 1.31
DCLW 2 30
(206.9) 100/1000 4.83/9940/68.6 0.770/107.8 1.48
DCLW- 3 50
(344.8) 100/100 0.535/11,010/75.9 1.098/153.7 1.64
DCLW 4 100
(689.7) 100/100 0.705/14,509/100.1 1.678/234.9 2.16
DCLW 5 20
(137.9) 100/1000 4.365/8986/62.0 0.474/66.4 1.34
DCLW 6 30
(206.9) 100/1000 4.81/9899/68.3 0.720/100.8 1.48
DCLW 7 50
(344.8) 100/100 0.494/10,167/70.1 1.026/143.6 1.52
DCLW 8 100
(689.7) 100/1000 6.77/13,936/96.1 1.524/213.4 2.08
DCLW 9 100
(689.7) 100/1000 6.705/13,799/95.2 1.540/215.6 2.06
DCLW- 10 50
(344.8) 100/1000 5.23/10,763/74.2 0.984/137.8 1.60
DCLW- 11 30
(206.9) 100/1000 4.39/9035/62.3 0.720/100.8 1.35
DCLW- 12 20
(137.9) 100/1000 4.57/9405/64.9 0.536/75.0 1.40
DCLW- 13 150
(1034.5) 100/1000 7.48/15,394/106.2 1.940/271.6 2.30
DCLW- 14 150
(1034.5) 100/100 0.67/13,789/95.1 1.870/261.8 2.06
DCLW-15 150
(1034.5) 100/100 0.734/15,106/104.2 1.920/269.0 2.25
DCLW- 16 200
(1379.3) 100/100 0.754/15,517/107.0 2.250/315.0 2.31
DCLW 17 200
(1379.3) 100/100 0.66/13,583/93.7 2.340/328.0 2.03



























Figure 11. Schematic of Test Specimen Preparation for SHPB Splitting Tensile Test


, STEEL STOCK


SIDE VIEW


INCIDENT
BAR


TOP VIEW


TRANSMITTER
BAR


Figure 12. Side and Top Views of Test Specimen Orientation for SHPB Splitting Tensile Test


I| 0.25in
VTVTij.635 mm)

I--

2.0 in
(5.08 cm)




i p
2.0 in
(5.08 cm)








splitting tensile test, the incident and transmitted signals are both compressive, and the reflected

signal is tensile. For analysis purposes, the peak of the transmitted compressive signal is

converted to a load which is then assumed to be the peak load applied to the specimen, similar to

the quasistatic loading case shown in Figure 9. The static tensile stress ft normal to the load

direction is given by Equation (3). Equation (4) is the conversion from volts to transmitted

compressive stress, and must be modified in order to calculate the splitting tensile stress. It is

easily shown that all that is necessary to modify Equation (4) to account for splitting tensile

stress is to divide by the specimen length, or simply

6
crT = volts/gain x (1/L) x (2.058 x 10 ) (6)

where

(T, Transmitted Splitting Tensile Stress, psi

L Specimen Length, in

To calculate the strain rate, pick two points on the ascending or pre-peak portion of the

transmitted compressive signal, and calculate the slope. Then, using Equation (6), we can

calculate the splitting tensile stress rate. Finally, dividing by the quasistatic secant modulus,

which was calculated from an average compressive failure stress of 6,708 psi (46.3 MPa), allows

us to compute the strain rate. One may question whether a statically determined value of the

secant modulus is a valid parameter to use to calculate strain rate from stress rate. However,

Ross [38] states that the dynamic modulus data obtained from SHPB tests are not valid since

elastic deformation occurs in the rise time of the load pulse, and during that time the specimen is

not uniformly loaded along its length. Nonuniformly loaded specimens have nonuniform strain

distributions which may yield false modulus data. Additionally, John and Shah [39] assume the

modulus to be rate independent, which has also been observed by Gopalaratnam and Shah [40],

and Tinic and Bruhwiler [41].








Once the strain rate and splitting tensile failure stresses have been calculated, the

dynamic increase factor may again be calculated, by dividing the failure stress by the average of

the three quasistatic splitting tensile failure stresses, found previously to be 630 psi (4.3 MPa).

Table 9 shows the data for the thirteen SHPB indirect splitting tensile tests. The first nine tests


Table 9. SHPB Indirect Splitting Tensile Tests on 2.0 in (5.08 cm) Diameter
By 2.0 in (5.08 cm) Long Lightweight Concrete Specimens


Specimen Specimen Gun Amplifier Transmitted Strain Dynamic
Number Length Pressure Gain Stress, ao Rate, a Increase Factor
IA/1B mV 1
in (cm) psi (kPa) v/psi/MPa us sec (DIF)
SCLW 1 2.008 8 1000/1000 0.968/992/6.8 20.2/5.98 1.58
(5.100) (55.2)
SCLW 2 2.012 8 1000/1000 0.950/972/6.7 16.2/4.77 1.54
(5.111) (55.2)
SCLW 3 2.013 8 1000/1000 1.164/1190/8.2 25.1/7.45 1.89
(5.113) (55.2)
SCLW-4 2.012 30 100/1000 1.650/1688/11.6 120.2/17.25 2.68
(5.111) (206.9)
SCLW- 5 2.009 30 100/1000 1.434/1469/10.1 93.5/13.44 2.33
(5.103) (206.9)
SCLW 6 2.015 30 100/1000 1.732/1769/12.2 133.6/19.16 2.81
(5.118) (206.9)
SCLW 7 2.013 50 100/1000 1.288/1317/9.1 50.0/14.74 2.09
(5.113) (344.8)
SCLW 8 2.012 50 100/1000 0.808/2849/12.8 66.5/19.60 2.94
(5.111) (344.8)
SCLW 9 2.013 50 100/1000 1.728/1767/12.2 66.8/19.70 2.80
(5.113) (344.8)
SCLW- 10 2.011 15 1000/1000 1.012/1036/7.1 3.7/1.03 1.64
(5.108) (103.5)
SCLW 11 2.015 15 1000/1000 0.878/897/6.2 5.1/1.50 1.42
(5.118) (103.5)
SCLW- 12 2.011 20 1000/1000 0.690/706/4.9 5.0/1.48 1.12
(5.108) (137.9)
SCLW- 13 2.013 20 1000/1000 1.050/1073/7.4 6.9/2.04 1.70
(5.113) (137.9)

Based on a Secant Modulus Calculated From an Average Compressive Failure
Stress of 6708 psi (46.3 MPa); Ec = 3.46 x 106 psi (23.89 GPa)








were conducted with a 26.0 in (66.04 cm) striker bar; the last four tests were conducted with a

50.0 in (127 cm) striker bar. The longer striker bar allowed the samples to be loaded at a lower

strain rate while maintaining gun chamber pressures in the 15 20 psi (10.35 137.9 kPa) range.

It was difficult to lower the chamber pressure below 8 psi (55.2 kPa) with the 26.0 in (66.04 cm)

striker bar.

Test Results

Failure of the static direct compression samples was by crushing, and the six samples are

almost identical in appearance. These tests were used as a basis for comparison with the other

data, since the unconfined compressive stress is the major property used in almost all discussion

of concrete data. The SHPB direct compression results show that as the load rate, hence the

strain rate increases, the number of fracture surfaces increases, hence the amount of

pulverization of the sample increases.

Failure of both the static and dynamic splitting tensile cylinders are almost identical,

breaking along a diameter plane. For the SHPB splitting tensile tests, with increasing load rate,

the split cylinder halves have increasing velocity and additional fractures occur during impacts

with the side walls of the debris catcher on the SHPB. However, Ross [38] states that during

splitting tensile tests in which high speed photography was used, the halves appear to be intact

after splitting. In fact, the films show that the fracture begins to occur first near the center of the

test specimen, which is also borne out by numerical simulations, which show that the tensile

stresses are larger in the center of the specimen than near the edges.

Figure 13 is a graph of the results for all of the quasistatic and SHPB direct compression

tests. The dynamic increase factor (DIF) is plotted as a function of the logarithm of the strain

rate for five different strength normal weight concrete mixes, as well as for the lightweight

concrete under investigation. One may conclude from this data that in compression the













CONCRETE STRAIN RATE EFFECTS
COMPRESSIVE STRENGTH
7



24
I -T__-____
|: 5.-- .---_--- --- -- --- --- --- ----_


0_______ ____ "___ I




-7 -6 -5 -4 -3 -2 -1 0 1 2 3
LOG STRAIN RATE, / SECONDS

SE Mix, fc = 7900 psi F Mix, fc = 8250 psi G Mix, fc = 5700 psi 0 H Mix, c = 5600ps
o J Mix, fc = 4060 psi 4 LW Mix, fc = 5775 psi



Figure 13. Concrete Strain Rate Effects Compressive Strength


lightweight concrete behaves identically, at least within the scatter of the data, to its normal

weight counterpart, whether quasistatically or dynamically. The lightweight concrete shows

moderate strain rate sensitivity, similar to its normal weight counterpart, with increases in

strength up to 2.3 times the static value at strain rates from 100 to 300/sec.

Figure 14 shows the analogous splitting tensile data. In tension, the lightweight concrete

does not appear to fall within the data scatter for the five different strength normal weight

concrete mixes. In fact, the data show that the lightweight concrete is less strain rate sensitive

than its normal weight counterparts, being shifted about a half-decade in strain rate for a constant

dynamic increase factor. Conversely, this means that the lightweight concrete must be loaded

approximately three times faster in order to have the same dynamic strength as normal weight

concrete. In either case, the normal and lightweight concrete have a higher strain rate sensitivity











CONCRETE STRAIN RATE EFFECTS
TENSILE STRENGTH
7 -
6--
5
4{ 4

3-
o 2



-7 -6 -5 -4 -3 -2 -1 0 1 2 3
LOG STRAIN RATE, 1 / SECONDS

SE Mix, fc = 7900 psi F Mix, fc = 8250 psi A G Mix, fc = 5700 psi H Mix,c = 5600psi
o J Mix, fc = 4060 psi t LW Mix, fc = 5775 psi



Figure 14. Concrete Strain Rate Effects Tensile Strength


in tension than in compression, which is consistent with the results of other researchers [31, 35,

36, 38, 39, 41] work on normal weight concrete. The author is unaware of any previous strain

rate sensitivity studies on lightweight concrete.

Static Beam Bending Experiments

The next step towards understanding the potential benefits of external application of

CFRP panels to concrete beams is a careful study of the static bending behavior of the beams

when subject to a quasistatic center point loading condition, simply supported, as shown in

Figure 15. Plain concrete beams, as well as beams with one, two, and three ply CFRP panels

bonded to the bottom or tension side of the beams were tested. Additionally, two more beams in

which three ply CFRP was bonded to the sides as well as the bottom, were tested.

Description of the MTS~ Load Frame

The three point bending tests were conducted on the MTS 880 load frame, (MTS

Systems Corporation, Minneapolis, Minnesota). The load frame may be run in either a load












P

SL/2 = 13.5 in
(34.29 cm)


CONCRETE
; BEAM

CFRP
PANEL


^______,___L = 27.0 in _
(68.58 cm)


Figure 15. Schematic of Quasistatic 3 Point Bending Tests



control or a displacement control mode, and is capable of loading material specimens up to

50,000 lbs (222.95 kN) in both uniaxial tension or compression. However, special tension

platens are required for cementing the concrete tensile specimens when conducting tension

experiments. Figure 16 shows a photograph of the MTS load frame with a concrete beam test

specimen.


The supporting platform on the machine was modified to accommodate the supported

span length of 27.0 in (68.58 cm) by placing roller supports in a notched plate which was then

bolted to the support platform by a series of Allen head bolts as shown in Figure 17. Since the

beams were 30.0 in (76.2 cm) long, and the supported span length was 27.0 in (68.68 cm) there

was a 1.5 in (3.81 cm) overhang on each end of the beam. The load cell was fitted with a special

half-cylinder platen to load the entire width of the beam uniformly at its center.































Figure 16. MTS Load Frame located at Wright Laboratory, Tyndall Air Force Base, Florida


Figure 17. MTS Support Platform Arrangement








Instrumentation Used/Measurements Made

The beams were loaded using the load control mode of operation on the MTS, at a load

rate of 2 lbs/sec. The crosshead load, time, and deflection were recorded every two seconds by

the data acquisition software resident in the MTS controller. Beam midpoint displacement was

also recorded using a small linear voltage displacement transducer (LVDT), which was mounted

separately on the MTS supporting platform. A small, flat circular tab was glued to the bottom

center of each beam to facilitate attachment of the LVDT to the beam's midpoint. Midspan

deflection was also recorded by the MTS data acquisition system every two seconds. Load to

failure versus deflection curves could then be generated for each beam tested; therefore, the

static fracture energy could be computed by calculating the area under the load to failure versus

deflection curve.

Test Results

A total of 16 beams were tested to failure on the MTS load frame in three point

bending. Since plain concrete is a brittle material, failure occurs abruptly and catastrophically.

Beams with some tension steel reinforcement in them fail somewhat more "gracefully", due to

the ductile nature of steel. Reinforcing steel used in concrete structural elements generally follow

an elastic plastic with strain hardening stress strain curve, as shown in Figure 18, with yield

points typically in the 40 60 ksi (276 414 MPa) range. Typical elastic moduli are in the 29

Msi (200 GPa) range, with strain hardening moduli in the 1.2 Msi (8.3 GPa) range. As

mentioned previously, due to the small cross section of these beams, no tension steel was used

in them.

A typical load displacement curve for the plain concrete beam is shown in Figure 19.

Since these beams have neither steel nor CFRP tension reinforcement in them, they remain

elastic until failure, at which time the lower "fibers" of the beam reach a stress level which










































Figure 18. Typical Stress-Strain Curve For Reinforcing Steel Used In Concrete Structures


LOAD vs DISPLACEMENT
BEAM LW5-38, PLAIN CONCRETE

700

600

500

400

300 -

200

100

0 .. .
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
DISPLACEMENT, INCHES




Figure 19. Load Displacement Curve for Beam LW5-38, Plain Concrete Beam


1.2 Msi
(8.3 GPa)


29 Msi
(200 GPa)








exceeds the modulus of rupture value for lightweight concrete. A crack merely forms at the

bottom of the beam, and runs to the upper surface, simply breaking the beam into two pieces.

Since the modulus of rupture for concrete is on the order of 10 12 percent of the

unconfined compressive strength f', the loads at failure for these beams are quite low, typically

about 640 lbs (2898 N). The corresponding displacement is also quite small; therefore the

fracture strengths are also quite small for the plain concrete beams. Appendix B contains the

load displacement curves for the three plain concrete beams tested.

Next, beams reinforced with one ply CFRP on the bottom were tested. Figure 20 shows

the load displacement curve from beam LW2-16. Immediately, one notices a significant

difference in the appearance of the load displacement curve in that there are two distinct

regions; an initial all elastic region with a much higher slope or stiffness than the second

region, which continues until failure occurs at approximately 1150 lbs (5116 N). The

displacement at failure is 0.160 in (4.07 mm). The failure load for the beam with one ply CFRP

is 1.8 times higher than for the plain concrete beam. The stiffness in Region 1 is 55,700 lbs/in

(97.5 kN/cm), and the stiffness in region 2 is 2960 lbs/in (5.18 kN/cm). The beam also fails by a

different mechanism. No longer does a flexural crack merely split the beam in two. With the

addition of the CFRP, the flexural crack(s) still occur in the center cross section of the beam, but

the beam now fails by a combination of flexure and shear at a distance of about L/4 on either

side of the beam centerline. As soon as the combination of bending and shear stress combine to

produce a maximum principal stress higher than the tensile fracture stress, the beam fails. This

crack starts on the bottom of the beam and runs upward at a 45 angle until it reaches the neutral

axis of the beam, which itself has shifted upward when the initial flexural crack(s) first appeared,

as the concrete reached its modulus of rupture. Figure 21 is a photograph of beam LW2 16











LOAD vs DISPLACEMENT
BEAM LW2-16, 1 PLY CFRP BOTTOM ONLY



3000

2500

S2000

1500

1000

500

0
0 0.05 0.1 0.15 0.2 0.25
DISPLACEMENT, INCHES




Figure 20. Load Displacement Curve for Beam LW2-16, Plain Concrete Beam with One Ply
CFRP


Figure 21. Typical Failure of Concrete Beam Reinforced with One Ply CFRP








with one ply CFRP, loaded to failure. This shift in the neutral axis has been previously studied

by Sierakowski et al. [21], and Ross et al. [22], and is the basis of the section analyses which are

derived and discussed in detail in Chapter 3. Furthermore, as the outer portion of the now failed

beam rotates upward, the peel strength of the Hysol epoxy adhesive, 30 lbs/linear inch (52.5

N/linear cm) is exceeded, and the CFRP delaminates from the bottom of the beam. This

delamination consistently originated at the point where the crack started at the bottom of the

beam and ran to the end of the beam, as shown in Figure 21 above.

Next, three beams were tested with two ply CFRP on the bottom or tension side of the

beams. The failure loads increased to about 2300 lbs (10.22 kN), with corresponding

displacements of about 0.241 in (6.13 mm). The shape of the load-displacement curve was very

similar to that of the beams reinforced with one ply CFRP, with two distinct regions; one all-

elastic region with a high stiffness 60,000 lbs/in (105.26 kN/cm), and then an abrupt change in

slope as the flexural cracking occurs, with a concomitant reduction in stiffness to about 6570

Ibs/in (11.51 kN/cm). The failure is quite abrupt, and occurs when the combination of moment

and shear produce stresses which exceed the tensile strength of the concrete, usually

symmetrically distributed about the beams' centerline, at about the quarter span location. Figure

22 shows a photograph of beam LW4-27, a plain concrete beam with two ply CFRP, loaded to

failure. As the failure occurred and the outer portion of the failed beam rotated upward, the

CFRP was peeled off the bottom of the beam, starting at 7.5 in (19.05 cm) from the beam's

center, and continuing outward to the end of the beam, as shown in Figure 23.

Two concrete beams with three ply CFRP were tested next, and the load displacement

curve for beam LW9-67 is shown in Figure 24. The load-displacement curve is similar to those

shown for the one and two ply beams, with two distinct regions; the first all elastic region has a

stiffness of about 59,100 Ibs/in (103.50 kN/cm) and the second region has a stiffness of

































Figure 22. Typical Failure of Concrete Beam Reinforced with Two Ply CFRP


(12.7 cm)
DELAMINATED '
CFRP 7.5 in
(19.05 cm)


SMALL FLEXURAL
CRACKS


Figure 23. Damage Assessment of Beam LW4-27 with Two Ply CFRP










LOAD vs DISPLACEMENT
BEAM LW9-67, 3 PLY CFRP BOTTOM ONLY

3000

2500

i 2000 --"

S1500oo

1000 -

500

o _--_-_______________ ___
0 0.05 0.1 0.15 0.2 0.25
DISPLACEMENT, INCHES




Figure 24. Load Displacement Curve for Beam LW9-67, Plain Concrete Beam with Three Ply
CFRP



9797 lbs/in (17.16 kN/cm). The initial elastic stiffness for the two ply beam is slightly greater

than the three ply beam because its unconfined compressive strength f, is larger, hence, its

modulus of rupture value is larger, which translates to a slightly higher elastic stiffness. After

failure occurs, one notices that the CFRP does not delaminate from the initial crack location on

the bottom of the beam and continue along the bottom of the beam to the end, as in the one and

two ply beams. Instead, the CFRP appears to have been pulled out of the concrete for only a

small portion along the bottom, and then is still securely bonded to the remainder of the beam on

out to end, as shown in the Figure 25.

Interestingly enough, the 2448 pounds (10.89 kN) average total load and the associated

displacements at failure are both not significantly different for these three ply beams than the

values for the two ply beams. In fact, the total displacements at failure are less. This may be due

to the fact that the stiffness of the three ply beam at failure is about 3500 lbs/in (6.13 kN/cm),































Figure 25. Damage Assessment of Beam LW9-67 with Three Ply CFRP


which is 49 percent greater than the stiffness of the two ply beam, which translates to higher

bending and shear stresses for a given amount of displacement.

Three more beams were tested in the MTS machine with three ply CFRP on the bottom

or tension side of the beams, except that for these beams the concrete mix was modified with

0.75 in (1.905 cm) long nylon fibers, at three pounds (1.36 kg) per cubic yard. Figure 26 shows

the load displacement curve for beam LWF 10-76, which shows the two characteristic regions.

The first all elastic region has an initial stiffness of 54,900 lbs/in (96.15 kN/cm), and the second

region has a slope or stiffness of about 10,390 lbs/in (18.20 kN/cm). The failure loads averaged

2349 lbs (10.45 kN), and the failure displacements averaged 0.175 in (4.45 mm). Figure 27

shows a diagram of the post-test damage on beam LWF10-76, which shows damage quite similar

to the plain concrete beams with three ply CFRP. In fact, it is impossible to discern any

qualitative or quantitative difference, within the scatter of the data, between the beams with

nylon fibers and three ply CFRP, and beams without nylon fibers and three ply CFRP. Figure 28


2.5 in 9.
(6.35 cm)


GOOD BOND


5.5 in
(13.97 cm) !
CFRP PULLED --- 12 in -
OUT OF CONCRETE (30.48 cm)






































Figure 26. Load-Displacement Curve for Beam LWF10-76, Nylon Fiber
Concrete Beam with Three Ply CFRP


,GOOD BOND


5
(12.7
4


in '
7cm)
11 in CFRP PULLED
(27.94 cm) OUT OF CONCRETE


Figure 27. Damage Assessment of Beam LWF10-76 with Three Ply CFRP


LOAD vs DISPLACEMENT
BEAM LWF10-76, FIBROUS CONCRETE, 3 PLY CFRP BOTTOM ONLY

3500

3000

2500

S2000

1500

1000

500

0
0 0.05 0.1 0.15 0.2 0.25
DISPLACEMENT, INCHES








shows a photograph of the post-test damage inflicted on beam LWF10-76. The nylon fibers did

not appear to influence the failure mechanism either.


























Figure 28. Typical Failure of Nylon Fiber Concrete Beam Reinforced with Three Ply CFRP



The last type of beams tested were plain concrete beams externally reinforced with three

ply CFRP on the bottom as well as both sides of the beam, shown in Figure 29. Two beams were

tested in this configuration, and the load displacement curve for beam LW7-53 is shown in

Figure 30. Unfortunately, the two beams tested yielded a large difference in experimental

results; beam LW9-70 failed at 4060 lbs (18.06 kN), and beam LW7-53 failed at 5297 lbs (23.56

kN), with displacements at failure of 0.205 in (5.21 mm) and 0.284 (7.21 mm) respectively. The

displacements were not significantly greater than those of the two ply beams. However, the

loads at failure were a factor of two higher than for those beams with either two or three ply

CFRP on the bottom only.

















Three Ply
Side CFRP


Three Ply
Side CFRP








Three Ply
Bottom CFRP


Figure 29. Concrete Beam with Three Ply CFRP on Bottom and Sides


Figure 30. Load Displacement Curve for Beam LW7-53, Plain Concrete Beam
Reinforced with Three Ply CFRP on Bottom and Sides


LOAD vs DISPLACEMENT
BEAM LW7-53, 3 x 3 PLY CFRP


4000

3000

2000


1000

0 -
0


0.1 0.15
DISPLACEMENT, INCHES


0.2 0.25


0.3








The load displacement curves are of the same two region form, with an initial elastic

stiffness of about 63,200 lbs/in (110.68 kN/cm), an abrupt change of slope at the concrete's

modulus of rupture point, with a resulting reduced stiffness of about 16,709 Ibs/in (29.26 kN/cm)

until failure occurs. The initial elastic stiffness is roughly the same as that of the other beams,

with a slight increase which may be attributed to the side CFRP. However, after the modulus of

rupture is reached within the concrete and the slope abruptly changes, the beams remain

substantially stiffer than the other four types of beams reinforced with bottom CFRP. Table 10

below is a summary of the average initial elastic stiffnesses, and the average post-flexural


Table 10. Summary of Beam Stiffnesses from MTS Static Three-Point Bending Experiments


Number of Plies of CFRP Elastic Stiffness Post-MOR Stiffness
lbs/in (kN/cm) lbs/in (kN/cm)
45,714
0 (80.06)
55,700 2,960
1 (97.55) (5.18)
60,100 6,570
2 (105.26) (11.51)
59,100 9,797
3 (103.50) (17.16)
54,900 10,390
3* (96.15) (18.20)
63,200 16,709
3** (110.68) (29.26)

Fibrous Concrete Beams with 3 lbs (1.36 kg) Nylon Fibers/Cubic Yard
** Three ply CFRP Both Sides and Bottom



cracking or post-modulus of rupture (MOR) stiffnesses for all six types of beams tested. Note

that the beams with three ply CFRP on all three sides are approximately 60 70 percent stiffer

than the other two types of beams reinforced with three ply CFRP on the bottom only. Figure 31

below shows the post test damage of beams LW9-70 and LW7-53. Note that the side CFRP is

split and buckled along the major shear failure crack in the concrete, which is at 45 degrees from
































Figure 31. Typical Failure of Concrete Beam Reinforced on Bottom
and Both Sides with Three Ply CFRP


the vertical as shown in Figure 32. It is theorized that the side CFRP prevents the concrete from

rotating or lifting upward upon failure, thereby preventing the peeling or delamination failures

seen in the one and two ply test specimens earlier. The side CFRP also holds all the pieces of the

failed beam together as one unit. In fact, the beams still maintain a limited capacity to carry a

load, although this fact was not quantified during the course of this investigation.

Calculation of Fracture Energies

Failure may be defined in many ways for a structure or structural element. In this case,

it is the abrupt termination in the ability of the beam to take any more load increments, which for

these beam bending experiments run in load control, was two lbs/sec. Once the maximum

principal stress at some location in the beam exceeded the concrete's tensile strength, the

concrete fails, hence the beam fails.












SIDE CFRP
BUCKLED






4 in
GOOD BOND (10.16 cm)
8 in --
CFRP PULLED (20.32 cm)
OUT OF CONCRETE
12 in
(30.48 cm)





Figure 32. Damage Assessment of Beam LW7-53 with Three Ply CFRP Bottom and Sides


Fracture energies were calculated for all of the beams in an attempt to quantify the

capability of the beams to absorb energy. Fracture energy was then defined as the area under the

load displacement curve until failure occurred; the area under the load displacement curve

was found by numerical integration using the Trapezoid Rule.

Assuming that a straight line approximation between each set of load displacement

points is reasonable, the area of each trapezoidal segment is calculated and summed, and the

areas or fracture energies of all sixteen experimental load displacement curves were so

determined. Appendix C is a tabular summary of all of the relevant data from the static MTS

three point bending experiments. Also displayed in the table are load increase, displacement

increase, and fracture energy increase ratios. The load increase ratio is defined as the peak load

divided by the average peak load of the three plain concrete beams, which was 637.3 lbs (2.83

kN). The displacement increase ratio is defined as the maximum displacement divided by the








maximum displacement recorded on plain concrete beam LW5-38. The reason all three

displacements were not averaged and used as the baseline as in the case of the load increase ratio

was because the LVDT did not work very well on beams LW5-33 and LW5-36, as can be seen

by their respective load displacement curves in Appendix B, where the LVDT did not begin

recording displacement immediately after loading began but instead abruptly jumped up to some

value before it worked properly. Finally, the fracture energy increase ratio is defined as the

fracture energy divided by the fracture energy calculated from plain concrete beam LW5-38.

Table 11 shows the average load, displacement, and fracture energy increases computed

from the results of the table presented in Appendix C. Several conclusions may be drawn after


Table 11. Average Load, Displacement, and Fracture Energy Increase
Ratios Compared to Plain Concrete


Average
Average Average Fracture
No. of Load Displacement Energy
Plies of Increase Increase Increase
CFRP Ratio Ratio Ratio
1 1.80 11.45 29.83
2 3.60 17.24 77.76
3 3.85 12.86 59.94
3* 3.68 12.53 58.38
3** 7.34 17.47 145.84

Fibrous Concrete Beams with 3 lbs (1.36 kg) Nylon Fibers/Cubic Yard
** Three Ply CFRP Both Sides and Bottom



careful review of Table 11. Beams with three ply CFRP on the bottom and sides are clearly able

to take the most load before failure, with an average load increase ratio of 7.34. Somewhat

surprising is that the beams with nylon fibers in them and reinforced with three ply CFRP appear

to offer little advantage in either load or displacement to failure over the plain lightweight








concrete beams with three ply CFRP on the bottom only. One might theorize that the fibers

should provide some additional energy absorption capability in the form of crack attenuation

capability, but the average fracture energy increase ratio is 58.38, which is slightly less than the

plain lightweight concrete mix with three ply CFRP with a 59.94 fracture energy increase ratio.

In fact, the three ply fibrous concrete, three ply regular lightweight concrete, and two ply regular

lightweight concrete all have similar total load to failure capabilities, with the one ply CFRP

beams having a factor of two less load carrying capacity. Most surprising are the relative

ductilities of the beams; the two ply beams are the most ductile of the bottom or tension side

only reinforced beams. The three sided beams are roughly equivalent in ductility. Therefore, the

fracture energy increase ratio is the highest for the two ply beams when compared to its tension

reinforced only counterparts, which is solely attributed to this increased ductility. Since the two

ply and three sided three ply beams have roughly the same ductility, the factor of two increase in

fracture energy of the three sided three ply beams is directly proportional to its load increase

ratio.

In summary, it has been experimentally demonstrated that beams with three ply CFRP

on the bottom and sides have the highest load, displacement, and fracture energy increase ratios.

Beams with two ply CFRP on the bottom only have the next highest fracture energy increase

ratio, due to their high ductility and relatively high load increase ratio. Conversely, the

experimental evidence indicates little to no benefit is realized using nylon fibers in the concrete

mix as a potential technique to increase the static load, displacement, or fracture energy capacity,

when compared to similarly reinforced beams without the nylon fibers added to the mix. There

are still tremendous gains over the plain concrete beams in load and displacement capacity even

with the bottom only one, two, and three ply CFRP reinforced beams. Increases of two to four in

load and 11 to 17 in displacement are quite easily achieved with the addition of the CFRP.








Consequently, increases in fracture energy from 30 to 78 are also achieved, when compared to

the baseline plain concrete beams.

Dynamic Beam Bending Experiments

In order to determine the dynamic response and behavior of beams externally reinforced

with CFRP panels, a series of 54 drop weight tests were conducted in which the six beam types

were subjected to impulsive center point loading, shown in Figure 33. Mindess and Banthia


P(t)


I 1.5 in
-- --(3.81 cm) I


CONCRETE
BEAM

CFRP
PANEL


___ L = 27.0 in _
(68.58 cm)


Figure 33. Simply Supported Beam With Dynamic Center Point Load


[27 33] have conducted drop weight impact tests on plain and conventional steel reinforced

concrete beam specimens with dimensions (length x width x height) 55.12 x 3.94 x 4.92 inches

(140.0 x 10.0 x 12.5 cm) and a simply supported span length of 37.80 in (96.0 cm). However,

their applied loads were not impulsive. Here, we define the term impulsive load as a load pulse

with a temporal duration less than 25 percent of the fundamental period of the structure








undergoing loading; in this case the structural element is a simply supported beam. None of the

previously cited CFRP reinforced concrete beam work [References 1 22] involved dynamic

loading, and for those conventionally reinforced beams dynamically tested by Mindess and

Banthia, the loading was not impulsive. Unfortunately, short duration impulsive loads greatly

complicate the process of analyzing the test results, and will be discussed in detail later.

Description Of The Wyle Laboratories Drop Weight Impact Machine

The test apparatus used in this investigation was a Wyle Laboratories SKM01 drop

weight impact machine (Wyle Laboratories, El Segundo, California). Figure 34 is an overall

view of the test apparatus.

The overall height of the apparatus is about 15 feet (4.6 m) above the floor. To provide

as rigid a platform as possible, the bottom frame of the impact machine is bolted to an 8 in

(20.32 cm) thick reinforced concrete floor slab, with four 0.75 in (1.905 cm) diameter by 10

threads per inch bolts with corresponding nuts and lock washers. The impact machine uses a tup

carriage to deliver the weight and instrumented tup to the test sample. The tup carriage relies on

two bearings to guide it along two Rockwell C60 hardened steel shafts to the impact location on

the test sample.

The tup carriage is machined out of aircraft quality 7075-T6 aluminum, and various

weights (steel plates) may be added in equal increments to each side of the tup carriage up to 100

Ibs (45.5 kg) total. The additional weights) also structurally reinforces the tup carriage. The

weights are attached to the tup carriage via two load pins and a bottom weight plate. Four 0.625

in (1.59 cm) diameter by eighteen threads per inch socket head cap screws attach the additional

weights to the bottom plate, and two 1.0 in (2.54 cm) diameter by eight threads per inch nuts

fasten the weights to the load pins. The tup is attached to the tup carriage by four 0.125 in

(0.3175 cm) diameter by eighteen threads per inch socket head cap screws. The tup is machined








































Figure 34. Overall View Of The Instrumented Drop Weight Impact Machine


from a Rockwell C40 hardened piece of 4340 steel, and the 4.0 in (10.16 cm) wide impacting

edge conforms to the Charpy impact requirements of ASTM D256-90b, paragraph 11.3

(formerly D256-56 10(d)). The tup itself weighs 1.5 lbs (0.68 kg). The total mass of the tup

assembly and weights used in this investigation was carefully weighed and found to be 96.14 Ibs

(43.7 kg). The Wyle drop weight impact machine has the capability to provide a 10 ft (3.05 m)

free fall height; however, the highest drop height in this study was 2 ft (0.61 m).











Instrumentation Used

Some of the instrumentation used in the dynamic testing was attached to the drop weight

machine itself, some was attached to the beam test specimens, and yet another was external to

both the test machine and specimens. In order to measure the average acceleration and velocity

of the impact hammer as it drops and impacts the beam specimens, a photocell was mounted on

one of the two steel guide rails of the machine. The photocell's position could be adjusted up or

down so that the velocity of the tup could be measured just prior to impact. The photocell had a

slot in which a strip of aluminum that was attached to the impact hammer could pass through,

and break the continuity of the light source in the photocell. This strip of aluminum was

measured to be 1.2355 in (3.1382 cm) in width. An electronic counter was connected to the

photocell, and it recorded the amount of time that the light source was broken or off during the

passage of the aluminum strip through the slot in the photocell. The width of the aluminum strip

divided by the time recorded by the counter gave the impact velocity of the tup.

From conservation of energy considerations, a weight will fall under the influence of

gravity g and impact with a velocity of

v=2h (7)

when dropped from a height h above some datum, as shown in Figure 35. Unfortunately, the

acceleration of the impact hammer and tup assembly is not the acceleration of gravity g, due to

unavoidable friction between the hammer bearings and the steel guide rails. However, by using

the photocell to measure the impact velocity on a series of drop tests, and from Equation (7), the

acceleration of the hammer and tup assembly was consistently found to be about 0.9g. As a

result, careful attention was paid to the guide rails to minimize this friction effect; frequent

































Figure 35. Sketch Of Mass m Dropped At Rest From Height h


cleaning of the steel guide rails with acetone between tests seemed to reduce the variability in the

machine's acceleration constant.

Calibration Of The Tup

The total load or resistance that the tup develops as it impacts the specimen was

measured by using the average of two sets of four electrical resistance strain gages, each set of

four strain gages being mounted on either side of the tup, as shown in Figure 36. The strain

gages were from Micro Measurements (Micro Measurements Division, Measurements

Group Incorporated, Raleigh, North Carolina). Two of the gages in each circuit measure

compressive strain directly, and the other two measure the transverse strain. Each circuit forms a

full four-gage bridge which is inherently temperature compensated, and gives increased

sensitivity from the Poisson effect in the transverse gages. An additional benefit to providing a


vi= 0




h

vf=1^






























Figure 36. The Tup And Its Circuit


full bridge of strain gages on either side of the tup is to eliminate any bending effects in the tup

which may occur during a test; when the two output voltage signals are averaged, the effects of

bending are neutralized. The gages are connected to an Ectron Model 563H transducer

conditioning amplifier (Ectron Corporation, San Diego, California). Excitation voltage, output

gain, and bridge balancing are all manually set on the transducer conditioning amplifier.

Excitation voltage was nominally 5 Vdc, and the output gain was set at 100. Connections from

the transducer conditioning amplifier to the digital oscilloscope are direct and straightforward as

shown in Figure 37. The oscilloscope used was a Nicolet Model 4094B (Nicolet Instrument

Corporation, Madison, Wisconsin) four channel digital device with dual disk recording

capability. Normal operation used one disk for recording up to four channels of data in

conjunction with the second math pack disk being used for titles, delays, etc.


I- -I
R, R2 R3R










Nicolet) 4094 Nicolet) 4094
Recorder Recorder


Ectron
Model 563H
Signal
Conditioning
Amplifier


CONCRETE
BEAM
TEST
SPECIMEN


Displ Gage


TSupply/Conditioning
Hi-Speed
Camera


Figure 37. Schematic of the Instrumentation Used In The Dynamic Beam Bending Experiments










Calibration of the tup was done statically, by loading it in compression in the Forney

load frame. The method is similar with one used by Bentur et al. [27] to calibrate the tup in a

drop weight machine at the University of British Columbia. In the present work, the tup was

disconnected from the drop weight machine and bolted to a steel plate, such that the blade of the

tup was perpendicular to the steel plate. The steel plate was then placed on the bottom platen of

the Forney load frame, with the tup facing upward. The crosshead was then lowered until it just

touched the edge of the tup. The two full strain gage bridges were balanced on the transducer

conditioning amplifier, and their output was connected to the Forney's data acquisition system.

The tup was then loaded to 50 kips (222.4 kN) at a load rate of 75 lbs/sec. A load of 50 kips

(222.4 kN) is about 45 percent of the compressive yield load for the 4340 steel from which the

tup is machined. It was not anticipated that the tup would be loaded much beyond 10 kips (44.5

kN) during actual dynamic testing, so 50 kips (222.4 kN) was deemed sufficient for calibration

purposes.

Results for the first tup calibration test are shown in Figure 38. Plotted is the output

voltage (amplified 100 times) versus the tup load. Each strain gage bridge is plotted separately



STATIC TUP CALIBRATION #1
FORNEY LOAD FRAME
1.8
1,6
1.4
TWO CALIBRATION CURVES,
1.2 ONE FOR EACH BRIDGE
z 1


0.6
0.4
0.2

0 10000 20000 30000 40000 50000 60000
LOAD, POUNDS


Figure 38. Strain Gage Output Voltage Versus Load








versus the tup load, so there are two lines on the plot. Since the tup is responding elastically, the

strains and therefore the voltage are linear, as one would expect. After the first calibration test

was completed, a second test was conducted to ensure repeatability. The same linear response

was almost identically duplicated.

To establish an overall calibration factor for the tup, the slopes of all four voltage versus

load curves (lines) from both tup calibration tests were calculated and averaged together. This

value was found to be 30,277.3 lbs/volt (134.7 kN/volt). Assuming the frequency response of

the tup is much greater than the frequency response of the specimen, one may then use this

calibration, which is quite specific to tup geometry, strain gage excitation voltage, and transducer

conditioning amplifier gain, to convert a voltage versus time signal to a load versus time signal

in the dynamic tests.

After the tup was calibrated, it was installed back onto the impact hammer to begin

dynamic testing. Both bridge outputs from the Ectron" signal conditioning amplifier were re-

connected to the oscilloscopes, as shown in Figure 37. Since the tup load signal was used as the

internal trigger for all of the instrumentation, each bridge output was connected to a separate

oscilloscope. An internal trigger uses a rise in the load signal above a preset threshold value to

trigger data collection. A general rule of thumb when using an internal or load trigger for the

rest of the instrumentation is that the trigger level be set at roughly ten percent of the expected

maximum load to ensure that the trigger level is well above any background noise. A typical

value used for the trigger voltage was 20 mV, which equates to 605.5 lbs (2.69 kN) of load as

sensed by the tup. Additionally, an adequate number of data points collected prior to the trigger

signal must also be saved, in order to capture the initial rise in the tup load. Typically, 500 gpsec

of pre trigger data points was sufficient to record the initial portion of the tup's load time

signal.








Instrumentation attached to the beam test specimens consisted of a series of electrical

resistance strain gages, which were applied to one side on the center cross-section of each beam,

as shown in Figure 39. These strain gages were also from Micro-Measurements.


Figure 39. Sketch of Strain Gage Locations on the Beam


The strain gage located on the top of the beam was chosen as gage number one. It was

located at a distance of 2.75 in (6.99 cm) from the bottom of each beam. Unfortunately, the gage

could not be located on the top of the beam, due to the fact that it would be in the same location

that the tup would be striking and loading the beam. Gage number one was usually 1.9 in (4.8

cm) in length, in order to measure the representative strain over at least five aggregate diameters

in the concrete. However, when the sides of the beam were reinforced with CFRP, gage number

one was reduced in length to 0.25 in (0.64 cm), since strain in the CFRP is more uniform.


1.9 in
--0 (4.826 cm) -








Strain gage number two was located on the geometric center of the beam and the initial

neutral axis location, as shown in Figure 39. Similar to the case with strain gage number one,

when the gage was mounted on concrete, it was 1.9 in (4.8 cm) in length, but when the beams

had side CFRP, the smaller 0.25 in (0.64 cm) gage length was used.

The bottom strain gage was chosen as gage number three. Usually, the shorter 0.25 in

(0.64 cm) gage length was used, except for the case of the unreinforced concrete beams, when

the 1.9 in (4.8 cm) gage length was used. Not all of the beams had three gages at the center cross

section; this three gage configuration was only used on every third beam tested. The remainder

of the beams had gages on the top or position one, and the bottom of the beam or position three.

The gages were mounted on the concrete beams in accordance with the manufacturer's

recommendations for surface cleaning and preparation, which were very similar to the

procedures followed for application of the Hysol adhesive and CFRP. In addition to surface

cleaning of the concrete, a bed of epoxy was initially applied to the area in which the 1.9 in (4.8

cm) concrete gage was to be affixed, in order to fill in any voids in the surface. After the epoxy

cured, it was block sanded back to the original surface height. The gages are usually fixtured in

place while the M-Bond AE-10 (Micro-Measurements Division, Measurements Group

Incorporated, Raleigh, North Carolina) two part epoxy cures, with a clamping device which

applies 5 20 psi (34.5 137.9 kPa) of pressure. However, since the vacuum bag technique

worked so well for fixturing the CFRP while the Hysol epoxy cured and produced 14 psi (96.55

kPa) of uniform hydrostatic pressure, this technique was also used to fixture all of the strain

gages while the M-Bond AE-10 epoxy cured as well. Typically, it took six hours for the epoxy

to cure at 750F (23.90C); all 54 beams were each left in the vacuum bag for this period of time.

Three completion bridges consisting of three 120 ohm resistors were made, and bridge

output was connected directly to the signal conditioning amplifier, where the gages could be








manually balanced. Excitation voltage for the bridges was nominally 5 Vdc, and the

amplification or gain was set at 10. In order to convert the strain gage output voltage versus time

to strain versus time requires elementary analysis of the Wheatstone Bridge circuit shown in

Figure 40, where one of the "resistors" in the circuit is the strain gage. When the gage is applied


Figure 40. Strain Gage Bridge Circuit

to the beam and subjected to a strain, say tensile, the magnitude of the resistance in the gage

would be increased, causing the bridge to become unbalanced. The magnitude of this imbalance

is measured as output of the bridge, and is proportional to the strain at that location in the beam.

The output of the bridge is measured as a change in voltage which is given by


AV- Ve ARg AR3 AR, AR4
(1 + f)2 R R3 R2 R4


AnVgs


Vexcitation








where

AV Change in Output Voltage, volts

Ve Excitation Voltage, volts

Rg Nominal Gage Resistance, ohms

ARg Change in Gage Resistance, ohms

R1, R2, R3 Bridge Completion Resistor Resistances, ohms

AR1, AR2, AR3 Bridge Completion Resistor Change in Resistance, ohms

The strain gage and the bridge completion resistors all have the same resistance so that

R2 R41
Rgage R3

and Equation (8) becomes

V e AR
4 .R (9)
4R


Each strain gage has a gage factor commonly denoted by GF. The gage factor is defined as the

ratio of the unit change in resistance to the unit change in length, which is given by

AR/R
GF= A (10)
AL/L

where

A R Total Change in Gage Resistance, ohms

AL Total Change in Gage Length, in

R Gage Resistance, ohms

L Gage Length, in

The gage factor is also an index of the strain sensitivity of a gage and is a constant for the small

range of resistance changes and strains normally encountered. Equation (10) may be rewritten as









AR
S=s(GF) (11)

which when substituted into Equation (9) yields


e AV (12)


Using the appropriate gage factors, excitation voltage, and amplifier gain in Equation (12) yields

the following calibration factors for the strain gages

e = 0.0381AV (13)

for the 0.25 in (0.635 cm) strain gages which were used on the CFRP and

= 0.0377AV (14)

for the 1.9 in (4.826 cm) strain gages, which were used directly on the concrete. These factors

may then be used to convert voltage versus time to strain versus time.

Piezoresistive accelerometers were also mounted on the beams in an attempt to measure

the distribution of acceleration along the length of the beam. Endevco model 7270A (Endevco

Corporation, San Juan Capistrano, California) piezoresistive accelerometers with a range of

20,000 g's were mounted side by side 4.5 in (11.43 cm) from beam midpoint. The

accelerometers have a frequency response of 50 kHz, and are very low mass, being etched from a

single piece of silicon, which includes the inertial mass and an active full Wheatstone Bridge

circuit, complete with an on chip zero balance network. The accelerometers were then

connected to the Ectron signal conditioning amplifier, and subsequently to the Nicolet

recording oscilloscopes, as shown in Figure 37. Nominal excitation voltage was 5 Vdc, and the

gain was set at 5. Each accelerometer had its own calibration factor, given by the manufacturer,

which converted voltage versus time to g's versus time.

Displacement versus time at beam midpoint was measured directly using a noncontact,

linear proximity measuring system. A Kaman Instruments Model KD2300 multipurpose,








variable impedance transducer (Kaman Instrumentation Corporation, Colorado Springs,

Colorado) with a 0.5 in (1.27 cm) measuring range was used. Since the beam static failure

displacements were on the order of 0.3 in (0.762 cm), this measuring range was deemed adequate

for dynamic testing. The sensor head was mounted underneath the beams, flush with the support

platform of the drop weight machine. A piece of non-magnetic aluminum tape was affixed to the

bottom midpoint of each beam, which was used as a target for the sensor head. The system had

its own signal conditioning electronics package, where zero, gain and linearity adjustments could

be made, so its output was hooked directly to the recording oscilloscope. The output voltage of

the system is proportional to the distance between the face of the sensor and the metallic target

located on the beam, so merely inverting the signal gave displacement versus time directly. The

frequency response of the system was 50 kHz.

The last piece of external instrumentation used in the dynamic beam bending

experiments was a 0.63 in (16 mm) high speed framing camera. The type of camera used was a

Photec Model 0061-0132A high speed rotating prism camera system (Photographic Analysis

Incorporated, Wayne, New Jersey), and was operated at a framing rate of 10,000 frames per

second. The camera was mounted to the side of the test specimens such that the lens of the

camera viewed the side of the beams, and was at the same height as the bottom of the beam. At

10,000 frames per second, additional lighting was required to illuminate the beam test specimens

during the impact event. The aperture setting on the camera was such that approximately 8 in

(20.32 cm) on either side of the beam's midpoint was visible during the impact event. Due to the

high costs associated with developing high speed films, the framing camera was only used on

every third drop weight impact test. This coincided with those beams which had the full

complement of three strain gages mounted on the center cross section; these tests were denoted

the highly instrumented tests. Eighteen of these so-called highly instrumented impact tests were








conducted out of a total of fifty-four dynamic beam bending experiments. The high speed film

records also helped to determine the timing of the beam failure, the crack patterns, and verified

the midpoint deflection versus time data from the displacement gage, since each frame yielded

information in 100 psec increments. The eighteen high speed film records were also recorded on

0.5 in (1.27 cm) videotape for further study. However, detailed analysis of the high speed films

required the use of a Photo-Optical Data Analyzer, Model 224A (L-W International, Woodland

Hills, California) to view the individual events recorded on the films. The data analyzer allowed

stop motion, frame by frame, and 24 frame per second operation.

Method of Test

Prior to any actual impact experiments in which data was recorded, several dozen

preliminary drop tests were conducted in order to verify that all of the instrumentation was

working properly. Since the beam's dynamic failure or fracture energies were initially unknown,

and the impact hammer weight was held constant at several iterations on the correct starting drop

height were required for each one of the six beam types in order to find incipient failure. Once

incipient failure was found the drop height could then be increased which not only increased the

incident energy, but also increased the load rate and hence the strain rate in the beam test

specimens. Additionally, once the tup load pulse amplitudes and durations were known, trigger

levels and delay times could be set on the recording oscilloscopes; typically 20 mV for the

trigger level and 500 psec for the delay or amount of pre trigger information saved.

It was originally desired that all six beam types be tested at the same three drop heights.

However, due to the large difference in beam stiffnesses and fracture energies, this became

impractical if not essentially impossible to do. In addition, the inertial forces turned out to be the

dominant forces during the loading process, since the beams were so massive and brittle. The

drop height for incipient failure on the stiffest, most energy resistant beam, which were those








beams reinforced on all three sides with three ply CFRP, would have produced an overwhelming

inertial force on the least stiff beams, which were the plain concrete beams, and preclude

recovery of the dynamic bending load for these types of beams. However, as much overlap in

drop height between the six different stiffness categories of beams as practical was kept, in order

to allow direct comparison between consecutive beam stiffness classes.

In order to conduct a drop weight test, several preliminary procedures needed to be

accomplished. First, the wire leads for the strain gages had to be attached, the accelerometers

had to be glued to the beams using a special adhesive and adhesive accelerator, and the

aluminum tape was affixed to the bottom of the beam for use as a target for the displacement

gage. The beam was then placed on its supports in the drop weight machine, the leads for the

strain gages were attached to the completion bridges, and the accelerometer leads were

connected to the Ectron signal conditioning amplifier. The excitation voltages for all gages and

accelerometers were checked prior to each test, and the strain gage Wheatstone bridges on the

beam and on the tup were balanced. The tup was then raised to the selected drop height and

measured with a scale, making any fine adjustments in height to within 0.031 in (0.8 mm). The

impact hammer guide rails were wiped with acetone, to minimize frictional effects. The

displacement gage was zeroed at 0.5 volts, and the photocell timer was reset to zero. If the high

speed camera was being used, it was loaded with 450 ft (137.2 m) of film, and the floodlights

were turned on and adjusted to properly illuminate the test specimen. One final check of all the

channels on the Nicolet recording oscilloscope was made, and an intentional trigger was

introduced into the tup strain gage bridges to make sure all the channels would record data.

When all the instrumentation was ready, a countdown would be given allowing enough time for

the high speed framing camera to spin up, when finally the impact hammer would be released,

causing the tup to strike the beam at its midpoint, and subsequently induce failure. The eight








channels of data are then transferred from the oscilloscopes to the disk recorders where the data

were written on 5.25 in (13.34 cm) floppy disks. Twenty records, four channels on each record,

were written on each floppy disk. In total, ten floppy disks worth of preliminary and final data

were collected during the course of this investigation. The data was then manipulated using a

scientific and engineering data processing program called VU-POINT Version 2.0, written by

Maxwell Laboratories, Incorporated, La Jolla, California. The VU-POINT* software analyzes,

modifies and plots time series data recorded by waveform digitizes such as the Nicolet 4094

digital oscilloscope.

Fifty-four drop weight tests were conducted on the six different beam types in this

manner, and data were recorded on 51 of the 54 tests conducted. Data was lost on one plain

concrete beam, one two ply CFRP beam, and one beam with three ply CFRP on all three sides,

due to either to spurious or late triggers in the instrumentation system.

Interpretation of Test Results

To illustrate the procedure which was developed to analyze and interpret the data for all

of the drop weight tests, the data from one specific beam, LW3-20, is analyzed in detail. This

procedure was followed on all subsequent tests. This particular beam was reinforced with one

ply CFRP, the hammer weight was 96.14 lbs (43.7 kg), and the drop height was 8.0 in (20.32

cm). Figure 41(a) shows the beam in the drop weight machine ready to be tested, and Figure

41(b) shows the post-test results. Figure 42(a) shows a side view of beams LW3-20, LW2-12,

and LW2-13, all tested at the same condition. The post test damage from the dynamic tests

shown in Figure 42(a) is remarkably similar to the same beam type tested under quasistatic

loading conditions shown in Figure 42(b). This implies that the failure mechanisms) is the same

for both static and dynamic loading conditions. Results and discussion of all the dynamic tests

are presented later in this chapter.



































(a) Pre Test


(b) Post Test

Figure 41. Pre and Post Test Results for Drop Weight Test on Beam LW3-20
























































Figure 42. Post Test Results for (a) Drop Weight and (b) Quasistatic
Bending Tests on One Ply CFRP Beams








As the tup strikes the beam test specimen, it records the stressing or bending load in the

beam, the beam's inertia, as well as any damping forces which may also be present. However, it

will be shown later that due to the nature of the load pulses, the damping forces can be assumed

negligible in the analysis of the tup load constituents. Figures 43 and 44 show a typical set of

tup loads which were recorded on beam LW3-20. This load pulse is quite typical in shape, but

not in amplitude nor duration, to the other tup loads recorded on other beam types. Generally

speaking, larger drop heights produced larger amplitude and shorter duration tup loads. Figure

43(a) shows the tup load as recorded by strain gage bridge A, and 43(b) shows the tup load

recorded by strain gage bridge B. Figure 44(a) shows the average of the two signals. It should

be pointed out here that the actual load pulse is the first pulse, with an amplitude of 6160 lbs

(27.40 kN). The later two smaller amplitude pulses are merely rebounds of the tup, recorded

after the beam has already failed, shown here for completeness. The reason the load pulse

actually starts at about -150 psec and not zero is because the tup signal has not been time shifted

to account for the 50 mV trigger voltage (t = 0) and its corresponding 500 Lsec of saved pre -

trigger information. In fact, none of the signals in this study have been time shifted in an attempt

to keep the temporal nature of the different measurements as unbiased as possible. Quite simply,

it is the relative times in which the different events occur, as measured by the instrumentation,

which is of greatest interest and relevance. Looking closely at the end of the load pulse in

Figures 43(a) and (b), one notices that the tup has undergone a small amount of bending, as

evidenced by the small positive load measured by bridge A at the end of the load pulse, Figure

43(a), and the negative load sensed by bridge B in Figure 43(b). But when the two signals are

averaged together in Figure 44(a), the bending effect is nullified.

Figure 44(b) shows the average load pulse which has been digitally filtered using the 5

kHz low pass filter shown in Figure 45. The low pass filter resident in the VU-POINT software






























































































Figure 43. Tup A and Tup B Load Versus Time Curves for Beam LW3-20


5888.8






c= 2588.8
..
C


1. ems


TIME


8.8s


2. ms


3. One




























































































Figure 44. Tup A and Tup B Average Load Versus Time Curves for Beam LW3-20


68BS.8


5880.8


a 488a.6

-3
S32888.




a
i, 19e.B.


TIME


6888.8 TUP A/B AUG LOAD vs TIME
BEAM LW3-28
96.14 LBS 8 8 IN
5888.8 1 PLY CFRP BOTTOM ONLY
28 JUNE 1995
5XHz LOW PASS FILTER




1P cn3900.8 -
S2888.8










0.8s 1.8 Z. m 3. 8m
TIME









allows specification of the cutoff frequency (50 percent transmission), in this case 5 kHz, the

sharpness or width of the cutoff, in this case 1.25 kHz, and the gain beyond the cutoff, in this

case 0.01. The number of "filter terms" in Figure 45 is the number of data points that are

smoothed.


Sunnary of LOH-PASS Filter Response
Transition-Freq(s)=5.8khz & Transition-Nidth-1.25khz
Max. Response outside of pass-band=8.81
1787 Filter Terns

APPROX. FILTER TRANSMISSION vs. FREQ.


8.5




8.0


0 hz


5.0khz


Figure 45. 5 kHz Low Pass Filter


A 5 kHz cutoff frequency was consistently used throughout this study on all signals

which required low pass filtering. This is reasonable, since the fundamental frequencies for

these beam types varies from 170 to 300 Hz, an order of magnitude below the chosen cutoff








frequency. Therefore, there is little danger of filtering out any high frequency components

which are important to the dynamic mechanical behavior of this system.

The raw displacement versus time data from the noncontact, linear proximity measuring

system is shown in Figure 46(a). Note that the load pulse actually starts at -205 uisec and ends at

540 psec, but that the beam does not begin to displace until about 100 psec. After beam failure

occurs there is a decrease in the slope of the displacement versus time curve, at which point the

slope becomes constant as the beam merely falls down and comes to rest on the support platform

of the drop weight machine. Figure 46(b) is the smoothed displacement versus time curve after

passage through the 5 kHz low pass filter. The smoothed displacement versus time curve is

differentiated with respect to time, and the resulting velocity versus time is shown in Figure

47(a). Notice that the peak velocity of 102 in/sec (259.08 cm/sec) occurs at about 500 utsec, then

rapidly drops off after the failure occurs, and then continues to oscillate at about 60 in/sec (152.4

cm/sec). At a drop height of 8 in (20.32 cm) the tup strikes the beam at 75 in/sec (189.5 cm/sec),

and transfers its momentum to the beam. Since the mass of the tup is greater than the mass of

the beam, the beam achieves a higher velocity than the tup striking velocity. The velocity versus

time curve is then differentiated with respect to time to yield acceleration versus time, the results

of which are shown in Figure 47 (b). The acceleration of the beam peaks at about 200 psec, with

an amplitude of 750 g's. The time of peak acceleration is consistent with an abrupt change of

slope in the strain versus time data, as the failure process in the beam initiates. Peak strain rates

occur at this time as well, and will be discussed in detail later in this chapter.

Consider, for a moment, the beam as a single degree of freedom system, with the

acceleration versus time known at beam midpoint. In order to estimate the inertial force or

resistance to motion that the beam offers when it is set into motion, the beam's equivalent mass




































TIME


Figure 46. Displacement versus Time Curves for Beam LW3-20


TIME




















































logo.@ I I I
ACCELERATION us TIME
BEAM LW3-28
96.14 LBS 9 B IN
1 PLY CFRP BOTTOM ONLY
28 JUNE 1995
58.8@ 5 NHz LOW PASS FILTER



8.8




-58B.B -



8.8s 1.iams 2.9ns
TIME


Figure 47. Velocity and Acceleration versus Time Curves for Beam LW3-20








must be calculated. Once the equivalent mass is known, the acceleration versus time curve may

be multiplied by the equivalent mass to calculate the beam's inertial load versus time curve. At

the outset of this investigation, it was thought that the beam would initially assume a deflected

shape consistent with the fundamental mode of vibration as shown in Figure 48(a), but this was


Figure 48. General versus Localized Bending


not the case. Since the loading may be considered impulsive, the beam as a whole does not have

time to react to the sudden blow imparted by the tup to the center of the beam. The initial

deflection is therefore localized about the beam's midpoint, as shown in Figure 48(b), and the

original span length of the beam has little significance in calculating the beam's equivalent mass.

In time, the deflection assumes a fully developed plastic state. A method for determining the

beam's average equivalent mass during the time of the load pulse was developed based on the

assumption of a rigid, perfectly plastic beam, utilizing the concept of a traveling plastic hinge


P(t)


(a)








and is discussed in detail in Chapter 3. Once the equivalent mass is known, the beams inertial

load versus time behavior is therefore determined. Figure 49(a) shows the tup or total load and

inertial load versus time curves plotted together. Note that the majority of the load measured by

the tup is represented by the inertial load. At the end of the load pulse, they are coincident.

Taking liberty at the present time to assume no damping forces present, the difference in

amplitude between the tup or total load and the inertial load represents the bending load. Figure

49(b) show the bending load versus time curve. The bending load has a peak amplitude of 2600

lbs (11.57 kN) at 275 psec, and returns to zero at 420 usec. Since the peak load of the tup is

4300 lbs (19.13 kN), failure to account for the inertial load will lead to misleading conclusions

being drawn about the bending load, and hence, the fracture energy. This observation has also

been noted by other researchers [32, 35, 42].

In order to calculate the amount of energy consumed by the beam up until failure occurs,

bending load versus time was plotted against displacement versus time, creating a dynamic

bending load versus displacement curve. This curve is shown in Figure 50(a). Recall that the

bending load versus time curve showed that the bending load dropped to zero at about 420 psec,

which in load displacement space, translates to a displacement of 0.022 in (0.564 mm) at

failure. At the point of failure, the beam stops receiving energy from the impact hammer, and

the tup load falls to zero. The energy consumed by the beam up until failure occurs is sometimes

called the toughness or simply the fracture energy. The area under the dynamic bending load

versus displacement curve therefore represents the fracture energy or the amount of energy

required to create two new fracture surfaces. In the case of plain concrete beams, the beams

break into two halves and the two broken halves swing about their supports away from the tup.

Although these beam halves may retain considerable kinetic energy, they have no bending or

strain energy left in them.






























































































Figure 49. Tup, Inertial, and Bending Load versus Time Curves for Beam LW3-20


S 1 I I 1 f 1 _
/ \ TUP/INERTIAL LOAD vs TIME -
UW UIEM I.U-72a


/ <--TUP A/B AG LOAD 96.14 LBS B 8 IN
8 ii '( A A1 I PLY CFRP BOTTOM ONLY
i 28 JUNE 1995
<----INERTIAL LOAD 5KHz LOW PASS FILTER (BOTH)
2588.8 -
..B .............. ..


c 211



-2508.8 -




8.8s 1.Bms 2.8ma
TIME


3889.8 I 1 I I ] I 6 '
BENDING LOAD vs TIME
BEAM LW3-2Z
96.14 LBS 8 8 IN
PLY CFRP BOTTOM ONLY
288. 28 JUNE 1995 -


a
o 188.8


- o







-258.8us 8.8s 258.8us S88.8us
TIME


-























2008.8


(b)




Figure 50. Bending Load versus Displacement and Fracture Energy versus Time Curves for

Beam LW3-20


: 19.BBB. B
C
-o

z z
Sa.





-1088.8


8.82 8.83
DISPLACEMENT. INCHES


SI I I I I -2
FRACTURE ENERGY zI TIME


4.6 96.14 LBS 8 IN
1 PLY CFRP BOTTOM O0
28 JUNE 1995

5 3.8


h4
C
t ~2.6



1.8
TIME-



s **I /

258.8us 8.Os 258.8uu 588.8us
TIME








The area under the bending load versus displacement curve was found by numerical

integration in VU-POINTa using Simpson's Rule. The resulting dynamic fracture energy versus

time curve is shown plotted in Figure 50(b). The fracture energy at the beam failure time of 420

jisec was 3.6 ft-lbs (4.9 N-m).

Data from the strain gages mounted on the center cross section was useful not only for

determining the strains, strain rates, and stresses, but also for verifying the initial onset of failure

in the beams as well. Figure 51(a) shows the strain versus time traces for strain gages number

one and three. Recall that Figure 39 showed the location of all of the strain gages. Strain gage

number three indicating tensile strain, shows an abrupt change of slope at 200 Psec indicating

that the concrete has begun to fail in tension, and a crack is in the process of propagating from

the bottom of the beam to the top surface. Meanwhile, strain gage number one, located on the

concrete near the top surface, goes into compression and remains in that state until failure

occurs. The third strain gage, strain gage number two, located midway on the beam's center

cross section, was not used on this particular test.

Differentiating the strains with respect to time yielded the strain rates. Its interesting to

note that the peak tensile strain rate recorded in gage number three shown in Figure 51(b) occurs

at almost the same time as the peak inertial load; about 200 lsec, with a magnitude of 18.5/sec.

The shape of gage number three's strain rate versus time pulse is also curiously similar to that of

the inertial load versus time pulse as well. Strain gage number one's compressive strain rate

only reaches about 2/sec during the loading event. Both gages indicate that the strain rates return

to and oscillate about zero after 800 psec.

Figure 51(c) shows the stress versus time curves for gages one and three. The curves

were obtained by multiplying the strain versus time curves by their respective elastic moduli;






























c ^

-I2.E























1













I .


















M16

t .
S.
PC (
\,


Figure 51. Strain, Strain Rate, and Stress versus Time for Beam LW3-20








20 x 106 psi (137.93 GPa) for the CFRP, gage number three, and 3.53 x 106 psi (24.35 GPa) for

the concrete, gage number one. The tensile stress in the CFRP is about 60 times higher than the

concrete compressive stress.

Damping Loads

All dynamic structural systems contain damping to some degree. However, the effect is

not significant if the loading is impulsive and only the maximum response is being investigated.

Damping in structures may arise due to different physical phenomena. In some cases, it may be

due to resistance provided by the medium surrounding the structure such as water, air, or soil. It

is also due to the loss of energy associated with slippage of structural connections either between

members or between the structure and the supports. It may also involve internal molecular

friction of the material itself. In any case, the effect is one of a force opposing the motion.

The analyses conducted during the course of this investigation assumed negligible

damping forces, primarily due to the impulsive nature of the loading. Furthermore, the beams

fail prior to any continuing state of vibration; a state in which damping generally is included. To

further illustrate the validity of the assumption, a calculation was carried out to determine the

relative magnitude of the damping force, and compare it to the other forces present. For the

purposes of this analysis, the damping was assumed to be of the viscous type (as opposed to

Coulomb, or constant damping) where the damping force is proportional to but opposite in

direction of the velocity. Viscous damping is the most commonly assumed for structural

analysis. The amount of damping which removes all vibration is referred to as critical damping,

which is a convenient reference point, since most structures typically have between five and ten

percent of critical damping.

Figure 52(a) shows beam midpoint velocity versus time for beam LW2-11. This is a

typical velocity profile for this beam type (one ply CFRP) and tup drop height (12 in/30.48 cm).























VELOCITY vs TIME
BEAM LW2-11
U s 96.14 LBS 9 12 IN
o PLY CFRP BOTTOM ONLY
20 JUNE 1995

25.8



I I ,II, I i -
8.8s 1.i.s 2.8os 3.Bms
TIME




380.8




288.8-
S I DAMPING LOAD us TIME
S/ \ R BEAM LW2-11
0 z 96.14 LBS 0 12 IN
1 PLY CFRP BOTTOM ONLY (b)
S. 28 JUNE 1995
i 18.8 5XHz LOW PASS FILTER
S- DAMPING FACTOR = 0.85





8.Os 1.Bns 2.Bus 3. ms
TIME



7588.80 a
LOADS vs TIME
BEAM LW2-11
: "<-TUP A/B AUG LOAD 96.14 LBS 8 12 IN
5000.8 1 PLY CFRP BOTTOM ONLY
S--INERTIAL LOAD 20 JUNE 1995
5 Hz LOW PASS FILTER (ALL)
DAMPING FACTOR = 8.85

2588.8 -


1 / \ DAMPING (C)
8.- .LOAD(



-250088. -


I I I i, I ,
Os 1. Bs 2.8us
TIME





Figure 52. Velocity versus Time, and Damping, Tup, and Inertial Loads versus Time for
Beam LW2-11




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