bott masters thesis etd
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HORIZONTAL STIFFNESS OF WOOD DIAPHRAGMS
by
James Wescott Bott
Thesis submitted to the faculty of
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
in
CIVIL ENGINEERING
APPROVED:
J. Daniel Dolan, Co-Chairman W. Samuel Easterling, Co-Chariman
Joseph R. Loferski
April 18, 2005
Blacksburg, Virginia
Keywords: wood diaphragm, shear stiffness, diaphragm stiffness, diaphragm deflection
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HORIZONTAL STIFFNESS OF WOOD DIAPHRAGMS
by
James Wescott Bott
ABSTRACT
An experimental investigation was conducted to study the stiffness of wood diaphragms.
Currently there is no method to calculate wood diaphragm stiffness that can reliably account for
all of the various framing configurations. Diaphragm stiffness is important in the design of wood
framed structures to calculate the predicted deflection and thereby determine if a diaphragm may
be classified as rigid or flexible. This classification controls the method by which load is
transferred from the diaphragm to the supporting structure below.
Multiple nondestructive experimental tests were performed on six full-scale wood
diaphragms of varying sizes, aspect ratios, and load-orientations. Each test of each specimen
involved a different combination of construction parameters. The construction parameters
investigated were blocking, foam adhesive, presence of designated chord members, corner and
center sheathing openings, and presence of walls on top of the diaphragm.
The experimental results are analyzed and compared in terms of equivalent viscous
damping, global stiffness, shear stiffness, and flexural stiffness in order to evaluate the
characteristics of each construction parameter and combinations thereof. Recommendations are
presented at the end of this study as to the next steps toward development of an empirical method
for calculating wood diaphragm stiffness.
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iv
TABLE OF CONTENTS
ABSTRACT ii
ACKNOWLEDGEMENTS iii
TABLE OF CONTENTS iv
TABLE OF FIGURES vi
TABLE OF TABLES viii
CHAPTER
I. INTRODUCTION 1
1.1 Introduction 11.2 Objectives and Scope of Research 41.3 Literature Review 7
1.3.1 Early Testing 71.3.2 Dynamic Testing 101.3.3 Similar Diaphragms 12
II. EXPERIMENTAL PROCEDURE 15
2.1 Scope of Testing 152.2 Test Apparatus 162.3 Diaphragm Construction 232.4 Test Parameters 272.5 Instrumentation 382.6 Test Protocol 452.7 Test Data Analysis 46
2.7.1 Yielding 472.7.2 Global Deformation 492.7.3 Cyclic Stiffness 512.7.4 Shear Deformation 56
2.7.5 Shear Stiffness 582.7.6 Flexural Deformation 602.7.7 Flexural Stiffness 602.7.8 Hysteretic Energy 612.7.9 Equivalent Viscous Damping 63
III. RESULTS AND DISCUSSION 67
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v
3.1 Introduction 673.2 Test Conditions 673.3 Nail Bending Test Results 693.4 Moisture Content and Density Results 713.5 Construction Parameter Results 73
3.6 Diaphragm Stiffening Methods 78
IV. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 82
4.1 Summary 824.2 Conclusions 83
REFERENCES 86
APPENDIX A 88
APPENDIX B 95
APPENDIX C 119
APPENDIX D 120
APPENDIX E 128
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vi
TABLE OF FIGURES
Figure Page
1.1 Cross-Section of a Typical Wood Framed Floor 2
1.2 Deep Beam Analogy 4
2.1 Load Frame, Actuator Connection, and Load Distribution Channel 17
2.2 Triangular Reaction Frame 18
2.3 Basic Test Apparatus and Configuration 20
2.4 Triangular Reaction Frame Plan View Schematic 21
2.4a Elevation View of Triangular Reaction Frame 21
2.5 Partial Section of Diaphragm Test Apparatus (loading parallel to joists) 22
2.6 Rim-Joist Splice for 10 x 40 ft. Specimens 24
2.7 Basic Specimen Sizes / Orientations (16 x 20 ft. and 20 x 16 ft.) 25
2.7 (Cont.) Basic Specimen Sizes / Orientations (10 x 40 ft.) 26
2.8 Fully Sheathed 10 x 40 ft. Specimen 27
2.9 Corner Sheathing Opening 29
2.10 Center Sheathing Opening 30
2.11 Test Configuration with Chords (and corner opening) 32
2.12 Test Configuration without Chords 32
2.13 Test Configuration with Walls 34
2.14 Wall-Lifting Davits 35
2.15 10 x 40 ft. Specimen with Walls and Wall-Braces 36
2.16 Application of Sprayed Foam Adhesive 37
2.17 Foam Adhesive Shown After Removal of a Sheathing Panel 38
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viii
TABLE OF TABLES
Table Page
3.1 Average Moisture Content and Density Results by Specimen 72
3.2 Average Percent Differences by Construction Parameter 74
A.1 Specimen 1 Test Results 89
A.2 Specimen 2 Test Results 90
A.3 Specimen 3 Test Results 92
A.4 Specimen 4 Test Results 93
A.5 Specimen 5 Test Results 94
A.6 Specimen 6 Test Results 94
B.1 Test Comparisons for the Effects of Blocking 96
B.2 Test Comparisons for the Effects of Foam Adhesive 99
B.3 Test Comparisons for the Effects of Blocking and Foam Adhesive 101
B.4 Test Comparisons for the Effects of Increased Nail Density 102
B.5 Test Comparisons for the Effects of Chords 103
B.6 Test Comparisons for the Effects of Walls 105
B.7 Test Comparisons for the Effects of Center Sheathing Openings 109
B.8 Test Comparisons for the Effects of Corner Sheathing Openings 113
C.1 Instrument Descriptions 119
D.1 Specimen 1 Joists Moisture Content and Density 121
D.2 Specimen 1 Sheathing Moisture Content and Density 122
D.3 Specimen 2 Joists Moisture Content and Density 123
D.4 Specimen 3 Joists Moisture Content and Density 124
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ix
D.5 Specimen 4 Joists Moisture Content and Density 125
D.6 Specimen 5 Joists Moisture Content and Density 126
D.7 Specimen 6 Joists Moisture Content and Density 127
E.1 Specimen 1 Test Descriptions 129
E.2 Specimen 2 Test Descriptions 130
E.3 Specimen 3 Test Descriptions 132
E.4 Specimen 4 Test Descriptions 133
E.5 Specimen 5 Test Descriptions 134
E.6 Specimen 6 Test Descriptions 134
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CHAPTER I: INTRODUCTION 1
CHAPTER I
INTRODUCTION
1.1 INTRODUCTION
Modern structural engineering frequently involves sheathed construction, a load
resistance method exemplified in various structural elements by many combinations of suitable
materials. A common form of sheathed construction, the diaphragm, is a thin, usually planar
system of sheathing and frame members, intended to withstand considerable in-plane forces.
When referring to residential housing, everyday plywood construction typically comes to mind.
Most apparent examples of diaphragms are walls, upper-story floors, and roofs of
everyday structures such as residential houses, office buildings, and warehouses. Though similar
in function, wall diaphragms, called shear walls, require different consideration for design and
analysis, and thus fall outside of the scope of this investigation. Roofs and above-grade floors,
when designed as such, fall into the classification as true diaphragms. Typical combinations of
materials employed are wood sheathing on wood frame, metal sheathing on wood frame, metal
sheathing on metal frame, wood sheathing on metal frame, and variations using concrete,
structural insulation panels, and other construction materials. This research project is limited to
wood-framed and plywood-sheathed floor diaphragms typical in residential housing.
The common floor and roof diaphragm serves dual purposes by supporting vertical forces
(from loads such as furniture, people, snow, uplift, and its own dead load) and by transmitting
horizontal forces (from wind pressure or earthquake accelerations) to the supporting shear walls.
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CHAPTER I: INTRODUCTION 2
Floors and roofs are inherently able to carry gravitational loads due to the typical design by
which appropriately spaced framing members are covered with sheathing and fastened together.
Joists and rafters, the common framing members of floors and roofs, respectively, are oriented to
maximize the moment of inertia for resistance to flexure. Thus, a 2x10 floor joist would be
installed such that the nominal ten-inch side is vertical. The sheathing spans the distance
between and transmits loads to the framing members below. The framing members then
distribute the loads proportionally to supporting walls or posts. Also, when adequately fastened
together, the sheathing and framing can produce a flexurally efficient composite section.
Resistance to vertical forces, though a primary consideration in design and construction of floors
and roofs, is not the subject of this study.
Sheathing
Wood Floor Joists
Figure 1.1 Cross-Section of a Typical Wood Framed Floor
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CHAPTER I: INTRODUCTION 3
Horizontal forces applied to diaphragms are almost exclusively from wind and
earthquakes. Wind pressure on the exterior walls is transmitted proportionately along the edge
of a diaphragm as a uniform load. In the case of wind-loaded floors, connections with the top
plate of the wall below and the bottom plate of the wall above provide paths for load transfer.
When subjected to earthquake accelerations, its own inertia, or resistance to motion, and that of
attached walls or partitions causes horizontal loading of a diaphragm. Diaphragms are usually
more than capable of withstanding these loadings due to high in-plane shear capacity. Sheathing
material itself exhibits considerable in-plane shear strength. Hence, the reason a sheet of
plywood is much more rigid when loaded along the thin edge (in-plane) as opposed to the large
flat surface (out of plane). Accordingly, a low aspect ratio system of sheathing panels, properly
fastened together end-to-end along the edges, has an effective shear capacity. The fact that it is
usually so thin makes sheathing an efficient and lightweight means of resisting in-plane loads.
Resistance to these in-plane loads through diaphragm action may be compared to the
loading of a deep wide-flange beam, as illustrated in Figure 1.2. The shear walls of a structure
are analogous to the simple supports of the beam and provide the reaction against the forces
transmitted through the diaphragm. The inter-connected sheathing panels behave like the web of
the beam to resist the shear component of in-plane loads. And, the extreme edges of the
sheathing and/or the boundary members running perpendicular to the direction of the loads
simulate the flanges of the beam by carrying the tension and compression from the flexural
reaction to the loads.
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CHAPTER I: INTRODUCTION 4
Flange
Web
Figure 1.2 Deep Beam Analogy
The behavior of floor and roof diaphragms has become an important issue with respect to
lateral stiffness and deflection. It has been noted that there is seldom a problem with the strength
of diaphragms, because failures are predominantly associated with the connections between a
diaphragm and supporting walls. Though the occurrence of actual failures is rare, diaphragms
have sometimes been a controlling factor in the overall failure of structures during seismic events
(Dolan 1999). Poor understanding of wood diaphragm behavior has spurred the interest of
researchers to formulate more accurate methods of analysis and design similar to methods
already employed in the design of cold-formed steel diaphragms.
1.2 OBJECTIVES AND SCOPE OF RESEARCH
The objective of this study is to evaluate the stiffness effects of various diaphragm
construction parameters for use in the development of an accurate method to determine shear
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CHAPTER I: INTRODUCTION 5
stiffness of wood diaphragms based on the formulas currently used in cold-formed steel design.
Such a formula would allow an improved method of predicting diaphragm deflections. The
capability to accurately calculate diaphragm stiffness and deflections will enhance the safety and
economy of wood diaphragms.
The current lack of an accurate method to predict diaphragm stiffness prevents designers
from knowing exactly how much stiffness to expect from any given design. Adequate
diaphragm stiffness is required in order to allow load sharing among the supporting shear walls.
In other words, flexible diaphragms resist loads locally (i.e., they can not transfer loads
horizontally very far). Thus, the loads induced into a flexible diaphragm must be transferred to
local supports (i.e., walls that are the closest to the location of the induced load). A perfectly
rigid diaphragm would be the other end of the spectrum where all of the supporting walls share
in resisting the load according to their relative stiffness. In reality, the diaphragm stiffness falls
somewhere in between these two extremes. However, the higher the diaphragm stiffness, the
better the load sharing capability is of the structural system and therefore, the better the expected
performance.
Currently, diaphragms must be classified as either flexible or rigid in order to select one
of two different design methods for the transfer of load to the supporting structure. Wood
diaphragms have been traditionally assumed as flexible, thereby allowing a load distribution
design based on the tributary area method. This method, however, is not applicable when
diaphragms exhibit torsional irregularities such as asymmetric geometry and openings (e.g.
stairwells) or differences in locations of center of rigidity and center of force. To account for
such torsional irregularities a designer must assume a rigid diaphragm and transfer the load based
on relative stiffness of the supporting walls.
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CHAPTER I: INTRODUCTION 6
According to the NEHRP Recommended Provisions for Seismic Regulations for new
Buildings and Other Structures (1997)and as adopted in the Uniform Building Code (1997)and
the 2000 International Building Codea diaphragms classification changes from rigid to flexible
when diaphragm deflection under load is equal to or greater than twice the deflection of the
supporting walls. Thus, designers are now forced to calculate the stiffness of wood diaphragms,
(and convert the stiffness into a corresponding deflection) in order to even make the distinction
between rigid and flexible.
Predicting diaphragm stiffness (or deflection) is difficult because currently there is no
simple and accurate method that can account for geometrical irregularities as well as all of
todays varying construction practices. The one current method for calculating deflection of
wood diaphragms as developed by APA is complicated and is not able to incorporate many
factors such as sheathing openings, absence of chords, use of sheathing adhesive, and non-
rectangular shapes. Designers need a simple and accurate method to determine wood diaphragm
stiffness if they are expected to even begin to select the proper load distribution method.
The specific objective of this study is to evaluate several basic diaphragm construction
details for their individual and combined effects on diaphragm stiffness. These results will then
be used under another task of the CUREE-Caltech Woodframe Project to develop and calibrate a
finite element model for diaphragm analysis. The overall goal of the experimental diaphragm
testing and finite element modeling is the development of an equation to accurately predict wood
diaphragm stiffness in the form of shear stiffness, G, as already accomplished by the cold-
formed steel industry.
This specific task is accomplished by a series of experimental tests on full-scale
diaphragms followed by careful analysis of the results. The test materials and procedures are
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CHAPTER I: INTRODUCTION 7
discussed in detail in Chapter II. Data collected from the tests is evaluated in Chapter III for
numerical trends indicating the effects of the various specimen configurations on stiffness.
These trends are used to make general observations regarding the stiffening characteristics of
each diaphragm construction parameter. All of the stiffness results for every test of each
specimen are listed for reference in Appendix A.
1.3 LITERATURE REVIEW
The objective of this literature review is to examine the studies in the field of theoretical
and experimental diaphragm research. A study of research performed in this field is important in
order to know what characteristics have already been established and what questions of
diaphragm behavior are still unanswered. Sporadic since the 1950s, most of the testing of wood
diaphragms has occurred at the facilities of the Douglas-fir Plywood Association (DFPA),
American Plywood Association (APA), Oregon State University, Oregon Forest Products
Laboratory, Washington State University, and West Virginia University. The volume of
literature available is small, therefore, rather than place the review in a separate chapter, the
reviewed literature is provided as a section within this chapter.
1.3.1 Early Testing
The DFPA sponsored some early tests in diaphragm behavior. Countryman (1952)
describes lateral tests on plywood-sheathed diaphragms. Four specimens, 12 x 40 ft. and 20 x 40
ft., and six one-quarter scale models, 5 x 10 ft., were tested by monotonic loading at fifth-points.
The specimens had varying parameters such as blocking, openings, staggered panels, gluing,
plywood thickness, nail size, and boundary nailing patterns. Stiffness of the diaphragms was
calculated from measured lateral deflection in the middle of the lower chord and applied load.
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CHAPTER I: INTRODUCTION 8
Shear deformation, and not flexural deformation was determined to be the predominant form of
deflection. Load versus deflection plots show that the actual deflection was consistently higher
than calculated values using existing equations. It was found that diaphragms behave like a
horizontal girder with a shear-resistant web. Due to their location at the extreme edges, chord
members of a diaphragm act like the flanges of a girder by resisting the flexural tension and
compression forces. The sheathing serves as the web of the girder to resist the shear. Strength
and stiffness of the specimens was found to be primarily dependent on the strength of the nailed
plywood-to-frame connections.
Due to over conservative design codes, the DFPA pursued further studies in diaphragm
action. Countryman and Colbenson (1954) report on tests of fifteen full-scale diaphragms,
conducted to better understand the strength effects from:
1. Omission of blocking
2. Panel arrangement
3. Nailing schedules
4. Span-thickness combinations
5. Length-width ratio
6. Seasoning of frame lumber
7. Use of three inch lumber
8. Cut-in blocking for chords
9. Load application perpendicular to joists
10.Screwed cleats in lieu of blocking
All 24 x 24 ft. specimens were monotonically loaded with four equal lateral forces at fifth
points of the span, and deflections were measured from the middle of the unloaded chord.
Plywood thickness and nailing schedule, along with blocking to a lesser degree, were found to be
the predominant factors in determining strength and stiffness. Ultimate applied shears ranged
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CHAPTER I: INTRODUCTION 9
from 733 to 2530 plf, while ultimate deflections occurred from 0.52 to 3.2 in. For blocked
diaphragms, the measured deflections are consistent with a formula produced as a result of the
DFPA Report No. 55 (Countryman 1952) with an average error of 15%.
In conjunction with the research described above, the DFPA also sponsored tests at the
Oregon Forest Products Laboratory. The two 20 x 60 ft. roof diaphragms tested, were
constructed with the lightest framing and plywood thickness permissible at that time for a roof of
this size (Stillinger and Countryman 1953). The 2 x 10 joists were framed at 24 in. o.c. and
sheathed with 3/8-in. thick plywood. One of diaphragms was blocked along the panel edges.
The diaphragms were loaded monotonically by hydraulic jacks at the fifth points. The 3/8-in.
thick plywood was found to be adequate, though not as strong as specimens with thicker
plywood. The lightweight framing system performed adequately. Lastly, it was found that for
unblocked diaphragms, no special boundary nailing detail was required regardless of the reduced
strength.
The APA became interested in lateral shear testing of diaphragms not composed of
Douglas-fir plywood. Tissell (1966) validated the DFPA tests from 1955 as well as going on to
test diaphragms of other various species of wood that were becoming popular in construction.
Nineteen full-scale 16 x 48 ft. diaphragms were tested. Plywood characteristics, sheathing-to-
framing connections, nail types, and framing member types were varied in the tests. Monotonic
loading from 16 hydraulic jacks at 3 ft. on center was used to approximate a uniform lateral load.
Lateral deflections were measured with dial gages at mid span of the tension chord. The design
shear values were found to be very conservative, with the average ultimate load being 1545 plf
and the average allowable design load being only 420 plf (includes factors of safety). Sheathing
of different species of wood was found to have a small but accountable change in shear strength
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CHAPTER I: INTRODUCTION 10
and stiffness. However, effects from plywood grade and quality were found to be negligible.
Tissell concluded that shear strength equivalent to that of blocked diaphragms is possible by
stapling tongue-and-groove 2-4-1 plywood. Further, shorter ring-shank nails are permissible as
long as a minimum penetration is attained. Open-web steel joist-framed diaphragms were
slightly stronger than the lumber framed diaphragms. The DFPA design values determined from
the tests previously discussed (Countryman and Colbenson 1954) were found to adequately
conservative.
1.3.2 Dynamic Testing
GangaRao and Luttrell (1980) explain the efforts at West Virginia University to quantify
shear response of diaphragms with the ultimate goal being the preparation of accurate analysis
models for future design purposes. Since diaphragms had been mainly studied under static
loading conditions, they propose that stiffness characteristics are an equally critical issue in a
correct estimation of behavior under real-life dynamic loading. Preliminary dynamic results
from tests at West Virginia University were used to derive joint slip and shear deformation
response equations based on dynamic loading. They predicted that damping characteristics with
respect to joint slip are the critical factors needed to appropriately describe diaphragm behavior
under dynamic loads.
At the time, Polensek (1979) was the only researcher making attempts at quantifying
damping characteristics for horizontal dynamic loading. His tests of plywood sheathed
diaphragms with six or ten inch joists yielded average equivalent viscous damping ratios
between 0.07 and 0.11. However, he considered that the data accumulated had been too varied
for an accurate estimation of the damping ratio. It was apparent, however, that an increase in the
damping effect is directly proportional to floor span.
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CHAPTER I: INTRODUCTION 11
At West Virginia University, Jewell (1981) performed experimental tests on partial
(cantilever) diaphragms in order to analyze a range of different parameters such as nail spacing,
boundary conditions, connection details, load type, and damping capacity. Three 16 x 24 ft.
diaphragms and six 16 x 16 ft. diaphragms were tested under monotonic, cyclic, and impact
loads in the directions perpendicular and parallel to the joists. Replica diaphragms were also
modeled in the same configurations as flexible composite members in a finite element analysis to
determine any inaccuracy in this theoretical approach. Based on a comparison of the theoretical
and experimental test results, Jewell was able to analyze relationships of plywood behavior, nail
slip, effect of loading, effect of joist hangers, and damping to the stiffness of diaphragms. In
most cases, the finite element approach yielded slightly less conservative results for stiffness
(i.e., predicted deflections were lower than actual), based on the parameters listed above.
Corda (1982) and Roberts (1983) performed additional cantilever diaphragms tests at
West Virginia University in another codependent study involving laboratory testing and finite
element modeling. Corda tested six 16 x 24 ft. specimens cyclically and statically to failure in
order to study local and global in-plane shear stiffness response to variations of blocking,
openings, plywood thickness, corner stiffeners, and framing nail sizes. It is noteworthy that nail
softening after loads up to 9 kips on some specimens caused a large decrease in stiffness.
Increased plywood thickness (without using longer nails) and corner openings reduced strength
but had little effect on stiffness. Roberts theoretical analysis of equivalent models of the
diaphragms tested by Corda, showed some evident discrepancies. Problems with the finite
element analysis program included the limitation to monotonic loading, inaccurate predictions of
panel slip, and the iterative processes of calculation of diaphragm deflection with respect to nail
slip, a bilinear relationship, demanding the modification of results to a nonlinear solution using
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CHAPTER I: INTRODUCTION 12
the tangent stiffness method. Based on the problems encountered, Roberts suggested that the
limitations imposed on the program user in modeling plywood diaphragms need to be eliminated
by further experimental research into stiffness characteristics of panel slip, plywood layout and
connection, diaphragm openings, and nail slip under cyclic loading.
A recent APA report by Tissell and Elliott (1997) describes diaphragm testing for high
load conditions equivalent to earthquakes accelerations. The primary intent was to formulate
design and construction approaches for these high-load diaphragms, which may incorporate
use of two layers of plywood, thicker plywood, or stronger fastener conditions. Ten of the
diaphragms tested were 16 x 48 ft., and the dimensions of an eleventh specimen were changed to
10 x 50 ft. Hydraulic jacks at a spacing of 24 in. o.c. were used to apply a cyclic uniform load
along the long side of the diaphragms. Results show that it is possible to increase shear strength
by increasing the number of fasteners or adding another layer of sheathing in areas of high shear.
This report also notes that plywood panel shear capacity must be checked for high-load
diaphragms. Staples were found to be adequate fasteners in lieu of nailed sheathing-to-framing
connections. Along the same lines, field glued joints and a reduced number of nails are adequate
for these diaphragms.
1.3.3 Similar Diaphragms
The abundant studies of floors comprised of materials other than wood are important in
order to understand general behavior of diaphragms. It is possible that wood diaphragm design
methods may be simplified and accurately rationalized in terms of methods already in use for
other materials. A theoretical study of the behavior of composite steel beam and concrete deck
diaphragms was made by Widjaja (1993) at Virginia Polytechnic Institute and State University.
Similar to many efforts currently in progress for wood diaphragms, the purpose of this study was
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CHAPTER I: INTRODUCTION 13
to develop an accurate finite element analysis model that predicts diaphragm behavior,
incorporates possible variations of design parameters, and derives design strength equations.
Similarly, experimental cantilever tests on cold-formed steel diaphragms are important in the
design of many steel-frame building roofs and composite floors (during construction, before
concrete). Post-frame diaphragm testing (wood frame and metal sheathing) is also significant in
terms of the more agricultural or shed type buildings.
With sponsorship from NUCOR Research and Development, Hankins et al. (1992)
performed eighteen cantilever diaphragm tests at Virginia Polytechnic Institute and State
University to determine strength and stiffness of cold-formed steel sheathing, 20 and 22 gage
thickness (Vulcraft 1.5B1 deck), welded or bolted to a steel frame. The 16 x 16 ft. specimens
were subjected to monotonic loads. Thirteen diaphragms utilized an 8 ft. span, requiring only
one filler beam. The other five specimens had a filler beam spacing of 4 ft., requiring three filler
beams. Bolt and puddle weld arrangement, used to secure the sheathing, was varied to determine
its effects on diaphragm behavior. Results from the tests indicate that specimens with thicker
gage sheathing have more strength and stiffness. However, even though specimens with smaller
filler beam spacing (three filler beams as opposed to one) had more strength, the diaphragm
stiffness was less in some cases.
Hausmann and Esmay (1977) report the results of tests on twenty-six full size post-frame,
metal-clad diaphragm panels. All specimens were 8 x 16 ft. with rafters at 4 ft. o.c. along the 16
ft. side and purlins at 2 ft. o.c. along the 8 ft. side. Loaded monotonically at the ends of the three
interior rafters, the panels were analyzed for strength and stiffness based on varying parameters
such as framing arrangement, type, number, and metal of fasteners, aluminum or steel sheathing,
and with or without insulation. It was determined that purlins laid flat to the rafters was the more
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CHAPTER I: INTRODUCTION 14
suitable method of framing. Screw fasteners in the panel valleys increased diaphragm stiffness
and strength, especially for the steel clad specimens. Aluminum panels were more suitable with
nailing, due to a larger cover width for each sheet. Placing insulation between wood-framing
and metal cladding not only reduces diaphragm strength, but also seriously affects stiffness.
Fastener configurations have important and measurable effects on diaphragm behavior.
Anderson and Bundy (1990) performed additional post-frame diaphragm tests to outline
the effects of openings in the sheathing. Fifteen cantilever specimens, 7-2/3 x 12 ft. with two
interior rafters and seven purlins were tested monotonically with varying amounts of sheathing
missing. Diaphragms were constructed with SPF lumber, screw fasteners, and steel sheathing.
Fastener configurations were found to be extremely important for diaphragm stiffness.
Openings in the sheathing at normal intervals caused the specimens to be ineffective as
diaphragms. It was also found that spacing of purlins has little impact on strength or stiffness of
the diaphragms.
In addition to the physical testing, there has been a great deal of computer modeling of post-
frame diaphragms for scientific purposes in order to aid designers and validate experimental
results. For example, Wright and Manbeck (1993), among many others, conducted finite
element analyses of post-framed diaphragm panels. Following procedures provided by Woeste
and Townsend (1991), they modeled full size 8 x 12 ft. diaphragms with 2x4 in. purlins at 2 ft.
o.c., 2x6 in. rafters at 3 ft. o.c., and steel cladding secured with 16d nails. The finite element
model was compared to three identical experimental diaphragm tests. The finite element model
closely predicted diaphragm shear strength, but under-estimated shear stiffness by 28%. Results
show that discrepancies arise due to difficulties in modeling nonlinear behavior of fasteners and
intricate load paths between the wood frame and steel sheathing.
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CHAPTER II: EXPERIMENTAL PROCEDURE 15
CHAPTER II
EXPERIMENTAL PROCEDURE
2.1 SCOPE OF TESTING
Multiple stiffness tests and one test to failure were performed on each of six full-scale
diaphragms at the Thomas M. Brooks Forest Products Center of the Virginia Polytechnic
Institute and State University located in Blacksburg, Virginia. Consortium of Universities for
Research in Earthquake Engineering (CUREE) sponsored the research under its Wood Frame
Project, Task 1.4.2 Diaphragm Studies.
Diaphragm dimensions for four specimens were 20 x 16 ft. with varying orientations,
while two high-aspect ratio specimens were 10 x 40 ft. Multiple tests on each specimen were
possible due to the non-damaging deflections being imposed, allowing an economical means of
incorporating multiple test parameters. Test parameters investigated for effects on diaphragms
stiffness were: 1) corner opening, 2) center opening, 3) fully sheathed, 4) 6-12 nail pattern, 5) 3-
12 nail pattern, 6) with/without chords, 7) with/without walls, 8) with/without blocking, and 9)
with/without foam adhesive. Specimens were subjected to non-destructive, low-amplitude
dynamic-cyclic loading by a computer-controlled hydraulic actuator, while load and deflection
values were being recorded by a computer data acquisition system. The final test on each
specimen, though not a primary focus of this study, was an attempt to cause diaphragm failure.
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CHAPTER II: EXPERIMENTAL PROCEDURE 16
2.2 TEST APPARATUS
Diaphragm testing was conducted on a 22 X 50 ft. concrete pad with 42 in. wide by 27 in.
tall concrete back-walls along two adjacent sides. The heavily reinforced back-walls have two
7/8 in. diameter anchor bolts embedded in the concrete at 2 ft. on center with a 400,000 lb point-
load capacity at a minimum spacing of 6 feet.
A computer controlled hydraulic actuator was mounted horizontally at the midpoint of
the 50 ft. back-wall. The actuator had a 55 kip capacity with a 6 in. stroke, and included a 50
kip Interface load cell, screwed onto the end of the hydraulic cylinder. Load was transferred
from a ball joint at the end of the actuator, through a pin-connected gusset to a 20 ft. long
C6x10.5 steel channel. The channel, as shown in Figure 2.1, was fastened along the entire width
in the center of the specimen span with 5/8 in. diameter lag screws. In cases where a joist did not
fall in the center of the diaphragm, 4x4 blocks are placed under the sheathing to provide a
backing for the lag screws used to attach the steel load distribution channel.
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CHAPTER II: EXPERIMENTAL PROCEDURE 17
Figure 2.1 Load Frame, Actuator Connection, and Load Distribution Channel
Offset equal distances (based on dimensions of diaphragm specimens) from the centerline
of the actuator were triangular reaction frames, as shown in the photograph of Figure 2.2. The
frames were constructed of 4 X 6 in. steel tubes welded together. Each reaction frame was
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CHAPTER II: EXPERIMENTAL PROCEDURE 18
connected to the concrete back-wall with four 7/8 in. diameter anchor bolts. A one-inch thick
end plate was welded to the end of the steel tube of the reaction frame and was drilled and tapped
for a 1 in. threaded rod. A two-foot piece of threaded rod was screwed through the plate into
the steel tube leaving the desired length exposed. A shop-fabricated, full-bridge load cell made
of 2 in. diameter steel rod and strain gauges screwed onto the opposite end of the threaded rod.
The load cell had a large hex-nut welded to one end to connect to the threaded rod protruding
from the triangular reaction frame. Gusset plates welded to the opposite end of the load cell
provided a pinned connection to the diaphragm support frame.
Figure 2.2 Triangular Reaction Frame
Each end of the diaphragm was attached to a 20 ft.-L2x2x steel angle, which was
welded intermittently to the side of a 20 ft.-3 X 5 in. steel tube using lag screws. One end of
each steel tube was pin-connected to the gusset plates of the reaction load cells. This support
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CHAPTER II: EXPERIMENTAL PROCEDURE 19
frame served the same purpose as shear walls by transmitting loads out of the diaphragm at each
end. The reaction frame load cells then measured these loads. The support frame served a
secondary purpose, to hold the diaphragm at the proper elevation for concentric loading from the
actuator. Several one-inch diameter PVC pipes were also placed on the concrete under the
specimen to help hold the interior of the specimen at the proper elevation, and to act as
frictionless rollers under the joists as load was applied. The schematic drawings of Figures
2.3, 2.4, and 2.5 illustrate all of the elements of the test apparatus including the specimen support
frame, the triangular reaction frame, and the load distribution channel.
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CHAPTER II: EXPERIMENTAL PROCEDURE 20
Figure 2.3 Basic Test Apparatus and Configuration
Steel Channel(C6 x 10.5)
Lag Screws
Concrete Back Wall
See Figure 2.4
for Detail
Fig.2.5
Load Cell
Actuator
Diaphragm Sizeand SheathingLayout Varies
Support Frame3" x 5" Steel Tube
Triangular ReactionFrame
Load Cell
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CHAPTER II: EXPERIMENTAL PROCEDURE 21
Load Cell
Steel TubeFrame
Fig.2.4a
Figure 2.4 Triangular Reaction Frame Plan View Schematic
Pinned Connection
ConcreteBackwall
Diaphragm Support Frame
Figure 2.4a Elevation View of Triangular Reaction Frame
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CHAPTER II: EXPERIMENTAL PROCEDURE 22
Figure 2.5 Partial Section of Diaphragm Test Apparatus(for specimens loaded parallel to the joists)
Steel Angle:-Welded to Steel Tube-Lag Screwed to End Joist
2 x 12 Joists @ 16"
(Douglas Fir)
2332" T&G Plywood
Sheathing
PVC Pipe Rollers
114"
Steel Channel (C6X10.5) - LagScrewed to non-structural blocks
Steel PipeRoller
3" x 5" x 3 8" Steel Tube
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CHAPTER II: EXPERIMENTAL PROCEDURE 23
2.3 DIAPHRAGM CONSTRUCTION
Of the six, full-scale diaphragm specimens, two were 16 x 20 ft. in dimension and were
loaded parallel to the direction of the joists on the 20 ft. side. Two specimens were 20 x 16 ft. in
dimension, loaded perpendicular to the joists on the 16 ft. side. The last two specimens were 10
x 40 ft. in dimension, loaded parallel to the joists on the 40 ft. side. Resembling the size and
shape of one side of a roof of a typical residential home, these 10 x 40 ft. specimens were
intended to test the envelope of diaphragm performance with respect to aspect ratio.
The diaphragm specimens were framed with Douglas-fir 2 x 12 joists spaced at 16 in. o.c.
and nailed with three 16d nails at each end to a 2 x 12 Douglas-fir rim joist. In the case of
specimens loaded parallel to the direction of the joists, the bottom of each end joist was attached
to the diaphragm support frame using lag screws as shown in Figure 2.5. Conversely, when
loading was applied perpendicular to the joists, the rim-joists were connected to the support
frames. Since the lumber used was 20 ft. in length, the rim joists of the 40 ft. long specimens
had to be spliced in the center with steel plates and bolts as shown in Figure 2.6 (while such a
splice may not be feasible in real-life construction due to interference with finish materials,
effective transfer of compression and tension forces in the chords was essential for valid test
results). The three main specimen configurations, including loading and reaction locations, are
schematically illustrated in Figures 2.7a-c. A photograph of a 10 x 40 ft diaphragm specimen is
presented in Figure 2.8.
A wood sample was taken from each joist of every specimen for moisture content and
density analysis. This information was recorded for possible use when evaluating test results,
since moisture content changes in lumber affects fastener performance.
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CHAPTER II: EXPERIMENTAL PROCEDURE 24
Figure 2.6 Rim-Joist Splice for 10 x 40 ft. Specimens (typical both sides)
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CHAPTER II: EXPERIMENTAL PROCEDURE 25
(a) 16 x 20 ft. Specimen
(b) 20 x 16 ft. Specimen
Figure 2.7 Basic Specimen Sizes / Orientations
20'
Load Applied4'x8'x23 32" T&G
Plywood Sheathing
16'
Cut-out showsframing layout below
2 x 12 Joists @ 16"(Douglas Fir)
2 x 4 Blocking(on flat)
2 x 12 Rim-Joist(Douglas Fir)
20'
Load Applied
16'
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Load Applied4'x8'x2332" T&G P
Sheathing
40'
(c) 10 x 40 ft. Specimen
Figure 2.7 (Continued) Basic Specimen Sizes / Orientations
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CHAPTER II: EXPERIMENTAL PROCEDURE 27
Figure 2.8 Fully Sheathed 10 x 40 ft. Specimen
The specimens were sheathed with nominal 4 x 8 ft. sheets of 23/32 in. tongue-and-
groove plywood in a staggered panel configuration. Sheathing was cut as required to complete
the desired panel configuration. Sheets were attached to the framing with 10d nails in a 6/12 nail
pattern, meaning nails are spaced at 6 in. around the perimeter and at 12 in. on the interior
supports of each sheathing panel. Typical sub-flooring construction adhesive was not used
between the joists and plywood sheathing; however some tests involved the use of sprayed foam
adhesive.
2.4 TEST PARAMETERS
Specimens were subjected to a number of different construction variations, including the
multiple combinations thereof. The variations tested were:
1. Sheathing openings fully sheathed, corner opening, center opening
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CHAPTER II: EXPERIMENTAL PROCEDURE 28
2. Chord members with / without rim joist
3. Blocking with / without 2 x 4 blocking
4. Walls with / without 4 ft. tall stud-framed walls
5. Sprayed foam adhesive & nails versus nailed only
6. Sheathing nail density 6/12 versus 3/12 nail pattern
Variations to the basic specimen listed above, are individually discussed in detail in the
following paragraphs.
Openings in the plywood sheathing were intended to simulate common openings in floors
of residential homes for stairways, atriums, and vaulted ceilings. These openings weaken and/or
cause torsional irregularities that can dramatically affect the stiffness of diaphragms. Duplex
(double-headed) 10d nails were used to fasten the sheathing panels that were to be removed from
the specimens in order to simulate openings. The corner opening in all sizes and orientations of
specimens was easily achieved by removing one full 4 x 8 ft sheet of plywood from a corner.
However, the center opening presented more challenges due to the staggered sheathing
configuration and tongue-and-groove plywood. For both orientations of the 16 x 20 ft.
specimens, an 8 x 12 ft. rectangular opening was made by prying the unfastened sheets up in the
center along the tongue-and-groove seam like an army tent and lifting them out. Some sheets
had to be cut in half to achieve a rectangular opening. Due to the high aspect ratio of the 10 x 40
ft. specimens, a proportional rectangular opening in the center was not reasonable, since typical
roof and floor diaphragms would not have such an opening. A schematic drawing and
accompanying photograph of the two opening types used in the tests are presented in Figures 2.9
and 2.10.
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CHAPTER II: EXPERIMENTAL PROCEDURE 29
Figure 2.9 Corner Sheathing Opening
Load Applied
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CHAPTER II: EXPERIMENTAL PROCEDURE 30
Figure 2.10 Center Sheathing Opening
Load Applied
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CHAPTER II: EXPERIMENTAL PROCEDURE 31
The chords of a diaphragm are the exterior framing members that are oriented
perpendicular to the direction of loading. They serve to resist bending moment induced in a
diaphragm while also supporting the extreme edges of the sheathing. In the case of floor
diaphragms, the chords may either be the rim joist or simply the last joist at each end of the floor,
depending on the orientation and direction of loading. Residential roof diaphragms typically do
not have a true rim joist, either at the lower edge along the fascia or at the ridge (unless the fascia
board or ridge beam is considered to be effective). The absence of an effective chord is
especially prevalent for roof systems utilizing metal plate connected trusses.
Though all testing was performed on floor diaphragm specimens, chord effects should be
similar for roof-like specimens. The effectiveness of chords was quantified by running tests with
and without the designated chord members (rim joists) in place. Only those specimens having
rim joists as the chords (specimens loaded parallel to the direction of the joists) could be tested in
this manner. The rim joists were nailed to the diaphragm at each joist with three 16d duplex
nails. Plywood edges were nailed to the rim joist with 10d duplex nails at 6 in. o.c. Duplex nails
were used for easy removal of the rim joists between different test specimen configurations. One
of the diaphragm specimens is shown in both configurations of having the rim joist acting as the
chord in place and removed in Figures 2.11 and 2.12 respectively.
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CHAPTER II: EXPERIMENTAL PROCEDURE 32
Figure 2.11 Test Configuration with Chords (and corner opening)
Figure 2.12 Test Configuration without Chords
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CHAPTER II: EXPERIMENTAL PROCEDURE 33
Blocking is the term used for the short framing members that span between joists and
serve to interlock the unsupported joints between sheathing panels. They can have the same
cross-sectional dimensions as the joists (full-depth blocking improves noise and vibration
dampening), or blocks can simply be smaller lumber laid on flat. In this investigation, specimen
configurations with blocking used 2 x 4s laid on flat installed between joists where each line of
unsupported sheathing panel joints would fall prior to installing the sheathing. The blocks were
fastened to the joists on each side with two 16d common toe nails. Plywood panel edges that fell
over the blocks were nailed every 6 in. with 10d duplex nails for easy removal to simulate
blocked and unblocked conditions. To reconfigure the specimen without blocking, the sheathing
nails were extracted, the diaphragm was tilted on-end with a forklift, and blocks were removed.
Likewise, replacing blocking involved tilting the diaphragm up to install new 2 x 4 blocks from
below, and then re-nailing the sheathing to the blocking.
A potentially significant unknown in diaphragm design is the effect of walls on the
horizontal stiffness. Walls of a structure transfer wind loads to the floors to which they are
connected. Also, the mass of the walls themselves present added lateral loads to diaphragms
during earthquakes. These walls, especially the flexural stiffness of their own bottom plate, may
also benefit a floor diaphragm by helping to resist these same lateral loads.
For testing purposes, four-foot high walls were installed along the two chord edges of
specimens. As shown in Figure 2.13 these walls were constructed of 2 x 4 studs at 16 in. o.c.
and 7/16 in. OSB sheathing on the outside. The 2 x 4 bottom plate of the walls was fastened
through the plywood sheathing to the floor joists below with 3 x in. self-tapping Simpson
screws for a strong connection yet easy removal. For the 16 x 20 ft. specimens, regardless of
orientation, the walls were set in place and removed with a long, cable-supported, boom attached
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CHAPTER II: EXPERIMENTAL PROCEDURE 34
to a large forklift. Starting with the second specimen, lever-action davits, as shown by the
photographs of Figure 2.14, were welded to the side support frames at each end of the walls to
more quickly and safely facilitate raising and lowering for configurations with and without walls.
As shown in Figure 2.15 for the 40 ft. long specimens, the walls on each side were built in 20 ft.
sections, set in place with the boom, and connected in the center. From then on, the davits at
each end of the walls accompanied by braces in the center allowed for repeated installation and
removal of walls. Braces were required to laterally stabilize the wall segments for the 10 x 40 ft.
diaphragm specimens.
Figure 2.13 Test Configuration with Walls
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CHAPTER II: EXPERIMENTAL PROCEDURE 35
(a) Walls Lowered and Attached (b) Walls Unfastened and Raised
Figure 2.14 Wall-Lifting Davits
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CHAPTER II: EXPERIMENTAL PROCEDURE 36
Figure 2.15 10 x 40 ft. Specimen with Walls and Wall-Braces
Current trends in construction involve the use of adhesives for an ever-widening range of
applications. In this case the method of fastening sheathing panels to framing members was
varied between nailed only and nailed plus sprayed adhesive. The adhesive material used was a
sprayed, two-part, self-expanding, poly-isocyanurate foam adhesive manufactured by ITW
Foamseal. The foam adhesive was tested using coupon tests to quantify its stiffness as a
connection. The connection stiffness was determined to be equivalent to that obtained by using
elastomeric adhesives typically used in wood floor construction. While elastomeric adhesive
would have been more representative of traditional construction, it would have prevented the
possibility of removing sheathing without damage once fastened down, thereby making it costly
and difficult to alter specimen sheathing configurations. Sheathing fastened down with the foam
adhesive could be removed with minimal damage by cutting the adhesive at the joints with a
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CHAPTER II: EXPERIMENTAL PROCEDURE 37
knife. Also, testing of the foam adhesive will provide useful information for its effectiveness in
roof retrofit applications. After having tested all of the nailed-only configurations, the foam
adhesive was applied to the underside of fully-constructed specimens that could be safely tilted
on-end (i.e. the two 16 x 20 ft. and the two 20 x 16 ft. specimens). Specifically, the adhesive was
sprayed along each side of every joist at the interface with the sheathing. Adhesives were not
used on the 10 x 40 ft. specimens due to the specimens flexibility, which made tilting the
specimens without damage impossible. A photograph of the foam adhesive being applied is
shown in Figure 2.16, and a photograph of a sheathing panel removed is shown in figure 2.17.
Figure 2.16 Application of Sprayed Foam Adhesive
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CHAPTER II: EXPERIMENTAL PROCEDURE 38
Figure 2.17 Foam Adhesive Shown After Removal of a Sheathing Panel
Sheathing nail density was varied for a few tests on the third and fourth specimens, both
of which were 20 x 16 ft. loaded perpendicular to the joists. The nail pattern was changed from
6/12 to 3/12 on the fully sheathed and nailed only configurations. In other words, nail spacing
around the perimeter of each sheathing panel (where supported by joists or blocking) was
decreased from 6 in. to 3 in. o.c. using easily removable 10d duplex nails. The 3-12 nail pattern
was tested while the walls and blocking parameters remain variable.
2.5 INSTRUMENTATION
Movements, deflections, and loads were measured at multiple locations on the diaphragm
specimens using electronic sensors of various types in conjunction with a computer controlled
Data Acquisition system (DAQ). The DAQ used for this project LABTECH, a Windows PC-
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CHAPTER II: EXPERIMENTAL PROCEDURE 39
based program. Prior to testing, all instruments used in this research project were carefully
calibrated for accurate results. Before any series of tests in a day, all instruments were checked
to make sure they were correctly mounted, functioning properly, and zeroed. Due to the exposed
conditions of the outside testing facility, all instruments were demounted and taken inside or
covered with plastic daily to protect from inclement weather, dew, and frost.
An internal Linear Variable Displacement Transducer (LVDT) measured the deflections
caused by the hydraulic actuator. Signals from this highly sensitive device were transmitted to
the computer controller, which in turn used the information as the feedback channel to control
the actuator. Loads measured by the 50 kip Interface load cell were recorded by the DAQ and
had no effect on the displacement-controlled actuator.
The custom-built load cells at each end of the diaphragm measured the reaction loads,
both in tension and compression due to the cyclic loads from the actuator. These reactions
simulated the shear loads that supporting walls of an actual structure must withstand. Prior to
use, these load cells, as described in Section 2.2, were separately calibrated in tension only on a
universal testing machine with an excitation of 10 Volts (compression was not feasible due to a
pinned-pinned condition when using special calibration fixtures). Both were loaded
incrementally to 40 kips tension, and in each case the linear calibration plot proved that no
yielding within the load cell occurred. The slopes of these lines were used in the DAQ as
multipliers to convert the output voltage signals from the load cells into equivalent values of
load.
Horizontal movement of the plywood sheathing relative to the framing members below
was measured at two locations with external LVDTs. An aluminum bracket mounted to the
end-joist at each rear corner held the barrels of a pair of LVDTs in place horizontally. The
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CHAPTER II: EXPERIMENTAL PROCEDURE 40
plungers of these instruments react against metal tabs, which were screwed and glued to the
plywood at the rear corners of the diaphragm. The LVDTs of each pair pointed in orthogonal
directions to account for biaxial sheathing movement. A photogragh of the LVDT mounting
setup is shown in Figure 2.18.
Figure 2.18 LVDTs and Mounting Bracket
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CHAPTER II: EXPERIMENTAL PROCEDURE 41
String Potentiometers (abbreviated, string-pot) were used at multiple locations to
determine diaphragm movement, deformation, and slippage relative to the test frame. Seven
string-pots were set along the front face of the specimens to measure the global deflection. A
string-pot was attached to each steel side support frame to determine the slip in the side load cell
connections and between the steel frame and the diaphragm itself. Likewise, a string-pot was
mounted to the steel load channel in the center to determine any slip its lag screw connection to
the specimen. Two string-pots were mounted diagonally on each side of the diaphragm
centerline to record the deformation caused by shear deflection during testing. Schematics
illustrating the positions of each displacement sensor for each specimen configuration are
presented in Figures 2.19 through 2.21. A list describing each instrument is presented in
Appendix C.
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CHAPTER II: EXPERIMENTAL PROCEDURE 42
GR1
Concrete Back Wall
LVDTL-NS
LVDTL-EW
GL1SlipL
DL1
SlipC
DL2 DR1
GL2 GL3 GC
LVDT
R-NS
LVDTR-EW
DR2
3" x 5"Steel Tube
GR2 SlipRGR3
Figure 2.19 Instrumentation Plan for 16 x 20 ft. Specimen
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CHAPTER II: EXPERIMENTAL PROCEDURE 43
Concrete Back Wall
GC GR1 GR2 GR3 SlipRGL1 GL2 GL3SlipL
SlipC
DL1 DL2 DR1 DR2
LVDTL-NS
LVDTL-EW
LVDTR-EW
LVDTR-NS
Figure 2.20 Instrumentation Plan for 20 x 16 ft. Specimen
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Concrete Back Wall
GC GR1 GR2GL1 GL2 GL3SlipL
SlipC
DL1 DL2 DR1
LVDT
L-NS
LVDT
L-EW
Figure 2.21 Instrumentation Plan for 10 x 40 ft. Specimen
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CHAPTER II: EXPERIMENTAL PROCEDURE 45
2.6 TEST PROTOCOL
In most cases of experimental research, how a specimen is stressed and to what extent, is
equally as important as the specimens characteristics. In this project great care was taken to
NOT apply deflections so large that specimens reached or exceeded their yield point and were
damaged. On the other hand, it is critical to apply sufficient deflection to obtain valid test data.
This limit was found for each specimen size and orientation by loading monotonically in small
increasing increments until signs of diaphragm damage are seen or heard, or until the slope of the
load/deflection curve, shown in real-time on the DAQ computer screen, appeared to be
decreasing. The deflection amount used for all tests was slightly lower than the largest
monotonic deflection. Additionally, deflections for this project followed a cyclic pattern that
somewhat simulates the cyclic loading of earthquakes, only not nearly as rapid, since this
apparatus is not intended or equipped to perform shake-table testing.
The load protocol for all tests, except those to failure, was five sinusoidal cycles at the
predetermined deflection, 0.25 for specimens one and two (20 ft. wide), 0.20 for specimens
three and four (16 ft. wide), and 0.80 for specimens five and six (40 ft. wide). The frequency
of these cycles was set in the actuator controller at 0.0833 Hz for test durations of 60 seconds.
Five cycles, or even possibly less, are adequate since this project does not incorporate the effects
of load fatigue.
While not a primary focus of this project, the last test of each specimen was an attempt to
cause failure. The CUREE protocol (Krawinkler et al. 2000) used for these tests is a deflection-
controlled quasi-static cyclic load history. This protocol is based on a finite series of cycles with
plateaus and peaks of increasing amplitude. Yield deflection, , was estimated for each
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CHAPTER II: EXPERIMENTAL PROCEDURE 46
specimen and used as the reference deflection from which amplitudes of other cycles were
determined. If failure did not occur by the end of the series, the CUREE protocol allows for
additional cycles at higher amplitudes until the specimen fails.
2.7 TEST DATA ANALYSIS
As with any physical experiment, manipulation of raw test data (in this case, load and
deflection values) is required for a logical comparison of the different specimen configurations.
In this study, several specific variables are calculated in order to weigh the benefits and
detriments caused by changing test parameters as described in Section 2.4. These variables and
the methods used for their calculation are presented in the following sections.
Test data from each deflection and load measuring instrument was recorded by the DAQ
computer and entered into a spreadsheet format. Each column of data in the spreadsheet
corresponds to one of the twenty-four channels (instruments) being used, and is ordered
chronologically with time from the start of each test. A table listing each of these instruments,
its model and serial number, and calibration coefficient is in Appendix C.
These text-format spreadsheet files were later imported individually into a Microsoft
Excel calculation template. This template was programmed with the calculations necessary for
automatic computation of stiffness results and other important variables. The template also
provided instant load-deformation graphs for the data.
The first step of the calculations was to take the raw deflection data and convert it into
tared values by subtracting out the initial reading. For example, a string potentiometer with a
range of 10 in. is drawn out 5.25 in. and attached to the specimen. The first data entry for this
channel will indicate a deflection of 5.25 in. Therefore each of the data points in that column
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CHAPTER II: EXPERIMENTAL PROCEDURE 47
must be tared by either subtracting or adding 5.25 in. depending on the direction of deflection in
order to attain the actual change in deflection.
Because the DAQ system had to be manually started and stopped in conjunction with the
independently controlled actuator, a section of data from the beginning and end of each test was
invalid. Therefore, the template was also programmed to shorten the data columns to include
only the meaningful data acquired during testing.
2.7.1 Yielding
While not a desired outcome of small-deformation stiffness testing, yielding is an
important concept to understand in terms of elastic versus plastic behavior. A material subjected
to a static load will undoubtedly undergo some deformation, though potentially immeasurably
small depending on its physical properties. If once unloaded, the material returns to its original
state, it is considered to have behaved elastically. However, if the material is loaded beyond its
elastic range causing permanent deformation even after being unloaded, then it has experienced
yielding. The force, fy, required to cause yielding is referred to as the yield point. Further
yielding caused by continued loading past this point, but before failure, is called plastic
deformation. Idealized elastoplastic response of a material subjected to force, f, causing
deformation, , is illustrated in Figure 2.22.
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CHAPTER II: EXPERIMENTAL PROCEDURE 48
Figure 2.22 Idealized Elastoplastic Force-Deformation Curve
force (f)
deformation ()
fy
y
failure
plastic behaviorelastic behavior
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CHAPTER II: EXPERIMENTAL PROCEDURE 49
2.7.2 Global Deformation
Maximums and minimums were established from deflection or load readings of each
instrument. The rigid body motion determined from string potentiometers measuring slip in test
frame connections was subtracted from maximum positive and negative global deformations.
The resulting adjusted maximum global deformations were plotted against instrument location
distances along the length of the specimen. This curve represents a diaphragms shape at
maximum deformation, and also aids in visualizing effects of torsional irregularity. The sign
convention used for the purposes of this study is illustrated in Figure 2.23. Outward deformation
caused when the hydraulic actuator pushes out is considered positive. An actual diaphragm
deformation curve from Specimen 2, Test 8 (16 x 20 ft., no chords, with walls, corner opening,
blocked, nailed only) is presented in Figure 2.24. Note, the lop-sidedness (towards the right)
caused by a torsional irregularity due to the corner sheathing opening on that side.
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CHAPTER II: EXPERIMENTAL PROCEDURE 50
Figure 2.23 Simplified Diaphragm Deformation Curve with Sign Convention
Figure 2.24 Diaphragm Deformation Curve - Specimen 2, Test 8
-
+
-
g
+
g
Distance AlongDiaphragm Edge
GlobalDeformation
(g)
0.230.19
-0.12
-0.16
-0.21-0.20
-0.15
0.13
0.19
0.24
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 2 4 6 8 10 12 14 16 18 20
Distance, L to R (ft)
GlobalDeformation,
RBMS
ubtracted
(in)
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CHAPTER II: EXPERIMENTAL PROCEDURE 51
2.7.3 Cyclic Stiffness
Stiffness is the most basic and yet also the most useful of all the variables determined for
this study. In lay terms stiffness is simply a measurement of a structures capacity for resisting
deformation. Although stiffness can be expressed in several different forms, in general it is the
amount of force required to cause a known unit of elastic deformation. Thus, if a system is
linearly elastic, then its stiffness, k, can be described as the slope of the force-deformation curve
as illustrated in Figure 2.25.
Figure 2.25 Stiffness of a Linearly Elastic System
Cyclic loading requires a different approach to calculating stiffness. Cyclic loads change
the force-deformation plot from a straight line to an elliptical loop known as a hysteresis as
shown in Figure 2.26. Because the slope changes along the hysteresis, cyclic stiffness must be
approximated. A visual comparison of two common methods of determining cyclic stiffness
and their associated equations is presented in Figure 2.26. The peak-to-peak method shown in
Figure 2.26a approximates stiffness as the slope of an imaginary line between the points of
maximum positive and maximum negative deflection. Figure 2.26b shows the origin-to-peak
f
1
k
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CHAPTER II: EXPERIMENTAL PROCEDURE 52
method where stiffness is an average of slopes of imaginary lines from the origin out to the
points of maximum positive and negative deflection.
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CHAPTER II: EXPERIMENTAL PROCEDURE 53
(a) Peak-to-Peak Method
(b) Origin-to-Peak Method
Figure 2.26 Cyclic Stiffness Calculation Methods
f
max
+
max-
k+
+
+
+
=maxmax
maxmax ff
k
f
max
+
max-
k+
k-
2
+ +=
kkk
fmax+
fmax-
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CHAPTER II: EXPERIMENTAL PROCEDURE 54
The spreadsheet program determined cyclic stiffness values using both the origin-to-
peak method and the peak-to-peak method. The first value calculated was cyclic stiffness
based on the force required from the actuator to cause a unit amount of deformation (excluding
rigid body motion) at the center of the diaphragm specimen. For tests in which the load-
deformation hysteresis is not centered on the origin due to uneven loading of the specimen, the
origin-to-peak method may not seem appropriate. While the peak-to-peak method may
seem better suited for such cases of uneven loading, a comparison of the two methods shows that
the cyclic stiffness results never varied by more than 3% in all 132 tests. Therefore, both
methods are assumed to be valid for test data exhibiting uneven loading. Due to the similar
results under either method and for brevity, this study will focus on analysis using the peak-to-
peak method from this point forward. (Note: the cause of uneven loading is assumed to be
residual stresses stored in the specimen from the previous test due to friction.)
As shown by Figure 2.27, either method produces similar results for a load hysteresis that
is well centered on the origin. Likewise, for hysteresis loops that are not centered on the origin
as shown by Figure 2.28, the two methods still yield similar results.
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CHAPTER II: EXPERIMENTAL PROCEDURE 55
-20
0
20
-0.25 0 0.25
Deformation (in)
Load(kips)
Figure 2.27 Cyclic Load-Deformation Hysteresis, Specimen 3, Test 3(Loops symmetric about the origin.)
-20
0
20
-0.25 0 0.25
Deformation (in)
Load(kips)
Figure 2.28 Cyclic Load-Deformation Hysteresis, Specimen 3, Test 24
(Loops not symmetric about the origin due to uneven loading.)
-9.45 kips
9.46 kips
-0.17 in
0.18 in
-15.18 kips
9.01 kips
0.15 in
-0.20 in
Origin-to-Peak:
kip/ft54.12
0.17-
9.45-
0.18
9.46
kcyclic =
+
=
Peak-to-Peak:
kip/ft0.5417.00.18
45.99.46k
cyclic=
+
+=
0.2% Difference of 0.1 kip/ft.
Origin-to-Peak:
kip/ft68.02
20.0
15.18-
15.0
01.9
kcyclic
=+
=
Peak-to-Peak:
kip/ft1.6920.00.15
18.159.01k
cyclic=
+
+=
1.6% Difference of 1.1 kip/ft.
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CHAPTER II: EXPERIMENTAL PROCEDURE 56
2.7.4 Shear Deformation
Global deformation is the sum of diaphragm shear deformation and flexural deformation
as illustrated in Figure 2.29. Since the load is applied at the center of diaphragm specimens, then
theoretically the shear deformation for each half of the diaphragm is equal. Diaphragm shear
deformation, visually detailed in Figure 2.30, can be determined from a geometric manipulation
of deflection results from the diagonal string potentiometers.
FLEXURAL
DEFORMATION
GLOBAL DEFORMATION
(Neglecting Rigid Body Motion)
SHEAR
DEFORMATION
(g)
(f) (s)
Figure 2.29 Diaphragm Deformation Theory
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CHAPTER II: EXPERIMENTAL PROCEDURE 57
F
F2
F2
bb
d
s
L2
L2
Diagonal String Pot.
(at zero deflection)
Diagonal String Pot.
(at deflection L)
Figure 2.30 Diaphragm Shear Deformation
First, the maximum diagonal deformation values in each direction for each half of the
diaphragm are determined, then averaged together, giving an average diagonal deformation, L,
for each half of the diaphragm, and for both positive and negative deformation. Using small
angle assumptions, shear deformation, s, can be expressed as:
2
Ls = (2.7.1)
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CHAPTER II: EXPERIMENTAL PROCEDURE 58
where is shear strain of the diaphragm and is calculated from the diagonal string potentiometer
deflections and geometric diaphragm properties by:
bd
dbL
22 +
= (2.7.2)
The data spreadsheet program calculated a s value for both halves of the specimen as
well as for maximum positive and negative diaphragm deformation. In some cases, shear
deformation for the left side of the diaphragm did not equal that of the right side and the positive
maximum did not equal the negative maximum. Though uneven loading can be attributed to
differences in positive versus negative shear deformation results, the differences in left side
versus right side shear deformation are due to different shear stiffness of each side.
2.7.5 Shear Stiffness
Shear stiffness is equal to shear force divided by shear deformation. Using the shear
deformations just determined, the spreadsheet program calculates shear stiffness for both sides of
the diaphragm using:
+
+
+
+=
SS
shear
VVk (2.7.3)
where V- and V+ are the maximum positive and negative shear forces applied to a side of the
diaphragm.
Under symmetric loading conditions and torsionally regular construction, the shear force
resisted by either side of the diaphragm is theoretically half of the load applied at the center by
the actuator. Thus, theoretically for torsionally regular test configurations, Vequals the reaction
force F/2 as shown by Figure 2.30, and can be verified by the load readings from the reaction
load cells at each side. However, asymmetric configurations such as a corner sheathing opening
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CHAPTER II: EXPERIMENTAL PROCEDURE 59
may cause the diaphragm to resist more of the actuator-applied load on the stiff side of the
diaphragm and less on the soft side. In such instances, Vshould be determined independently
for the left and right sides using the maximum readings from the left and right side load cells,
respectively. Accordingly, for torsionally irregular configurations (corner opening being the
only case for this study) the left and right side shear stiffness values must be kept separate.
As a caveat to this approach, a recurring problem during testing of Specimens 3, 4, and 5
was electrical malfunction of the side load cells, especially on the left side. An alternate method
by statics had to be used for tests in which there was reaction load cell malfunction. As
previously indicated, for a torsionally regular and symmetrically loaded specimen, each reaction
force equals half of the actuator-applied force. Similarly, for torsionally irregular specimens (i.e.
corner opening) the reaction forces combined, though not necessarily equal, should add up to the
actuator-applied force, F. If for example, the left side load cell malfunctions, its load can be
approximated by:
RL RFR = (2.7.4)
With the experimental shear stiffness, kshear, calculated for both the left and right sides of
the diaphragm specimen, the spreadsheet program uses elastic beam theory where:
s
sAG
LV
2
= (2.7.5)
where GAsis a more commonly accepted form of shear stiffness. Using the relationship:
s
shear
Vk
= (2.7.6)
Equation 2.7.5 may be solved for GAsin terms of kshearto give:
2
LkAG shears = (2.7.7)
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CHAPTER II: EXPERIMENTAL PROCEDURE 60
A shear stiffness value, GAs, is calculated for both the left and right sides of the
diaphragm. The left and right side values are averaged together for torsionally regular
specimens, but kept separate for torsionally irregular specimens in order to allow proper
comparison of results. For such cases it is possible that the shear stiffness on one side may be
considerably higher than the other.
2.7.6 Flexural Deformation
As shown visually by Figure 2.29, flexural deformation can be determined by:
sgf = (2.7.8)
The spreadsheet program averaged the maximum svalues for each half of the specimen for both
positive and negative deflection. These average shear deformation values were then subtracted
from the corresponding maximum positive and negative global deformations to give a maximum
positive and a maximum negative flexural deformation.
2.7.7 Flexural Stiffness
Experimental flexural stiffness, kf, may be expressed as:
+
+
+
+=
ff
f
FFk (2.7.9)
The spreadsheet uses the above peak-to-peak equation in order to arrive at one flexural stiffness
value.
Elastic beam theory offers an approach to a more common form of flexural stiffness.
Theoretical flexural deformation of a beam with a concentrated load applied at the center is:
EI
FLf
48
3
= (2.7.10)
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CHAPTER II: EXPERIMENTAL PROCEDURE 61
where EI is the flexural stiffness of the beam, or, as in this case, the diaphragm. Solving
Equation 2.7.10 forEIin terms of kf (recalling that kf = F / f) gives:
48
3LkEI
f= (2.7.11)
The spreadsheet program calculated flexural stiffness in the above form for each diaphragm test.
2.7.8 Hysteretic Energy
Hysteretic energy is the energy dissipated during one cyclic loading of a structure and
may be quantified as the area inside a load-deformation hysteresis for one cycle. The area within
a hysteresis from an experimental test can be approximated by numerical integration. Numerical
integration involves averaging the load values of two consecutive points along the curve.
Multiplying this average load by the difference between deformation values of the same two
consecutive data points gives the area under the curve between those two data points.
Geometrically, the calculation equates to determining the area of very narrow trapezoid. This
process must be repeated for every pair of consecutive data points all the way around the loop.
Depending on the location along the curve with respect to the deformation axis, the area is
considered either positive or negative. The net total of these incremental areas is the hysteretic
energy as represented algebraically in Equation 2.7.12:
( ) ++
+
+=
n
n
nnnnd
ffE
1
11
2 (2.7.12)
where the integer nrepresents the individual data points around the entire loop. The spreadsheet
program follows the same process described above to arrive at a value for hysteretic energy for
each diaphragm test. However, for greater accuracy, the program calculates a total area for three
consecutive loops around the hysteresis (using data points only from the middle three loops) and
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CHAPTER II: EXPERIMENTAL PROCEDURE 62
then divides the total by three, yielding an average area inside only one loop. See Figure 2.31 for
a visual description of numerical integration of a hysteresis.
Figure 2.31 Numerical Integration of a Load-Deformation Hysteresis
f
a
Area under curve between points
aandbto be considered positivefa
b
fb
+
a
b
f
c
fc
d
fdd
c
-
Area under curve between points
canddto be considered negative
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CHAPTER II: EXPERIMENTAL PROCEDURE 63
2.7.9 Equivalent Viscous Damping
Damping is the mechanism that causes gradual reduction of vibration in a system and
thereby a loss of energy. In structures, damping and the resulting energy loss is caused by a
variety of conditions such as internal friction of materials subjected to repeated deformations,
friction from movements at connections, opening and closing of cracks, and friction with
external or nonstructural systems with which the structure is in contact. Since the systems that
can cause damping are seemingly limitless and difficult to identify, a mathematical model
capable of predicting actual damping is nearly impossible.
Thus, a concept called equivalent viscous damping is used to represent all of the damping
mechanisms for a simplified approach under the assumption that the structure behaves as a
Kelvin solid viscoelastic element (Fischer and Filiatrault 2000). Equivalent viscous damping is
defined by equating the energy loss during a vibration cycle (i.e. the hysteretic energy as defined
in Section 2.7.8 and graphically as shown in Figure 2.32) in an actual structure to that of an
equivalent viscous system.
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CHAPTER II: EXPERIMENTAL PROCEDURE 64
Figure 2.32 Damping relationship to an equivalent viscous system
Using Figure 2.32 and setting the hysteretic energy, Ed, from one experimental cycle
equal to that of the equivalent viscous system gives:
22 oo
neqd XkE
= (2.7.13)
where eqis the equivalent viscous damping ratio, is the experimental test frequency, nis the
natural frequency of the test structure. Strain energy,ESo, is equal to the area of triangle OAB
(or triangle OCD) from Figure 2.32 and can be calculated from experimental stiffness, ko at
maximum deformationXo:
2
2
oo
OABSo
XkAE == (2.7.14)
Substituting Equation 2.7.14 into Equation 2.7.13 gives:
OABn
eqd AE 4= (2.7.15)
f
Xo
+
Xo-
ko+
ko-
B
A
OD
CEd = Hysteretic Energy(Area enclosed by hysteresis loop)
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CHAPTER II: EXPERIMENTAL PROCEDURE 65
Although for this experiment does not actually equal n, for simplicity the assumption as such
does allow for an acceptable approximation of eq (Chopra 1995). Assuming = n and
solving for the equivalent viscous damping ratio gives:
OAB
deq
A
E
4= (2.7.16)
As shown in Figure 2.32, the maximum deformations in both the positive and negative directions
are not necessarily equal. Therefore, the equivalent viscous damping ratios should be calculated
for triangle OAB using ko+ and triangle OCD using ko
- and then averaged. Thus, equivalent
viscous damping ratio, eq, is commonly expressed as:
So
deq
E
E
4= (2.7.17)
whereESois strain energy (equal to the area of triangle OAB or OCD).
For the purposes of this study, the spreadsheet program calculates the areas on both the positive
and negative sides of the curve using cyclic stiffness values determined by the origin-to-peak
method. The spreadsheet takes an average of the two strain energy values and the hysteretic
energy previously calculated, and uses a formula based on Equation 2.7.17 to determine the
equivalent viscous damping ratio for each diaphragm test.
Although equivalent viscous damping is not technically correct for the tests in this study
due to some non-linearity in the load-deformation response, the maximum specimen deflections
were kept low to minimize error. The viscous damping term is a measure of all of the damping
in the system (hysteretic and material) and is used for modeling the more complex system as a
simplified mass-spring-dash pot system. The equivalent viscous damping is the value for the
dash pot. While the design community views the concept of equivalent viscous damping as very
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CHAPTER II: EXPERIMENTAL PROCEDURE 66
inaccurate for calculating damping in an actual structure, it is used in research simply as a means
of comparing damping capability.
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CHAPTER III: RESULTS AND DISCUSSION 67
CHAPTER III
RESULTS AND DISCUSSION
3.1 INTRODUCTION
The objective of this diaphragm study was to test the stiffness of wood diaphragm
specimens under varying configurations in order to develop a method for determining shear
stiffness similar to that already used by the cold formed steel industry. Combined, 132 non-
destructive stiffness tests were performed on 6 different specimens. Due to the high volume of
data produced, a test-by-test analysis and comparison of results would be monotonous and not in
the best interest of the reader. Therefore, the calculations applied to each set of test data will be
thoroughly explained step-by-step in general terms. The remainder of this chapter will be
devoted to discussion of trends in test results and relating those trends back to the various
construction parameters. The individual test results are presented in Appendix A.
3.2 TEST CONDITIONS
As a foreword to discussion of results, the reader needs to be aware of the ever-changing
conditions encountered during testing, namely weather. Testing of diaphragm specimens began
on January 12, 2001 and continued until July 6, 2001. Throughout those six months the weather
played a substantial role in the test schedule, specimen moisture content, and periodic
malfunction of instruments and equipment.
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CHAPTER III: RESULTS AND DISCUSSION 68
As indicated in Chapter 2, the diaphragm testing facility is an outside concrete slab with
no protection from the weather. A large tarp was always used to cover speci