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INVESTIGATION OF STIFFENER AND SKIN INTERACTIONSFOR PRESSURE LOADED PANELS
by
Douglas C. Loup
Committee Chairman: M. N. Hyer
Engineering Mechanics
(ABSTRACT)
This investigation was aimed at understanding the global and
local strain and deflection responses of stiffened skins. Global
deformations of the stiffened skins, under load, produce high local
’stresses in the interface region between the stiffener and skin. Test
panels were designed to study the stiffener and skin interactions
using parameters typical of stiffened skins for aircraft fuselages. A
total of six panels were tested. Two skin laminates, both 0.04 in.
thick, and three stiffener configurations were studied. The panels,
having clamped edge boundary conditions, were subjected to pressure
loads of up to 14.5-14.8 psi. Out-of-plane deflections and long-
itudinal and transverse strains were measured in several locations.
The deflection responses showed a strongly nonlinear behavior at
pressure loads of less than 5 psi. In addition relatively severe
gradients of both longitudinal and transverse strains were measured in
the interface region of the stiffener and skin. Finite element models
incorporating geometric nonlinearities were made of four of the
panels. Results of these models substantiated the overall findings of
the experimental measurements.
ACKNOWLEDGEMENTS
I am much indebted to Dr. Michael Hyer for his help and guidance
throughout this project and for his excellent teaching. I am also
very grateful to Dr. James Starnes, Jr. for his guidance and
considerable help in both planning and executing this project as well
as his advice in the general field of composite structures during my
stay at NASA-Langley. Many NASA—Langley personnel were of great help
to me during this project. I wish to express my thanks to two people
in particular: , who provided much needed technical advice and
assistance throughout the testing program; and, Mr. Allen W me
through the intricacies of the NASA-Langley system. Finally, I
would like to thank my graduate committee, Dr. Carl Herakovich and
Dr. Eric Johnson, for their suggestions and critique of this
thesis. I am thankful for support from the NASA-Virginia Tech
Composites Program through NASA Grant NAG1-343.
iii
TABLE OF CONTENTS
@92
ABSTRACT............................................................ii
ACKNOHLEDGEMENTS...................................................iii
TABLE OF CONTENTS...................................................iv
LIST OF FIGURES.....................................................vi
LIST OF TABLES.....................................................xix
Chapter 1. INTRODUCTION.............................................1
Chapter 2. DESCRIPTION OF TEST EQUIPMENT AND TESTINGPROCEDURES...............................................6
INTRODUCTION....................................................6
OVERVIEN OF BASIC EXPERIMENTAL DESIGN CONSIDERATIONS............6
DETAILS OF EXPERIMENTAL DESIGN CONSIDERATIONS..................16
VACUUM LOADING....................... ..........................24
DESCRIPTION OF PANELS..........................................29
INSTRUMENTATION................................................32
Strain Measurements.......................................32
Dispiacement Measurements.................................33
TEST PROCEDURE.................................................36
TEST CHECKOUT..................................................40
Preioad/Prestrain Conditions..............................40
Effect of Ciamping........................................43
Symmetry of Response......................................44
Chapter 3. EXPERIMENTAL RESULTS AND DISCUSSION.....................51
OVERVIEN OF.RESULTS AND DISCUSSION.............................51
TEST CONDITIONS DEVIATING FROM IDEAL CASE......................51
iv
TABLE OF CONTENTS (continued)
EQSEPRIMARY PANEL RESPONSES........................................65
OUT-OF-PLANE DEFLECTION RESPONSES..............................65
TRANSVERSE RESPONSES...........................................77
LONGITUDINAL RESPONSES.........................................98
STIFFENER STRAINS.............................................123
Chapter 4. PRELDAD EFFECTS, RESULTS AND DISCUSSION................139
TEST CONDITIDNS DEVIATING FROM IDEAL CASE.....................139
OUT-OF·PLANE DEFLECTION RESPONSES.............................154
TRANSVERSE RESPONSES..........................................158
LONGITUDINAL RESPONSES........................................186
Chapter 5. FINITE ELEMENT RESULTS AND DISCUSSION..................216
Chapter 6. SUMMARY, CONCLUSIONS, AND RECDMMENDATIDNS..............248
GENERAL OVERVIEW OF STUDY.....................................248
CONCLUSIONS...................................................249
RECDMMENDATIDNS...............................................252
REFERENCES.........................................................254
APPENDIX A.........................................................255
VITA ...............................~..........................256
v
LIST 0F FIGURES
Ejsyxs Ess
2.1 Schematic Representation of Vacuum Loading Apparatus.........8
2.2 Multi—Bay Loading Apparatus..................................9
2.3 Unstiffened Panel Mounted in Test Apparatus.................12
2.4 View of Test Apparatus Showing Vacuum Plate.................17
2.5 Dimensional Details of Vacuum Plate.........................18
2.6 View of Test Apparatus and Data Acquisition System..........19
2.7 Clamping Details............................................21
2.8 Details of Clevis and Inplane Preloading System.............23
2.9 Stiffener Geometry and Construction Details.................25
2.10 View of Vacuum System.......................................26
2.11 View of Vacuum System Showing Vacuum Pump...................27
2.12 Three Test Panels...........................................30
2.13 Moveable DCDT and Rail System...............................35
2.14 Locations of DCDT's for Measuring 0ut—0f—PlaneDeflection as a Function of Pressure........................38
2.15 Left Side Inplane Edge Slip vs. Pressure Load forFour Clamping Bolt Torque Levels (Unstiffened Panel,
· Light Preload)..............................................45
2.16 Right Side Inplane Edge Slip vs. Pressure Load forFour Clamping Bolt Torque Levels (Unstiffened Panel,Light Preload)..............................................46
2.17 Unstiffened Panel Center Deflection vs. Pressure forFour Clamping Bolt Torque Levels (Unstiffened Panel,Light Preload)..............................................47
2.18 Symmetry of Strain Responses................................49
3.1 0-Ring Forcing Panel Bowing..“............, ..................53
vi
LIST OF FIGURES (continued)
Figure Page
3.2 Transverse and Longitudinal Pretest Profiles forLight Preload Case, Panel D.................................54
3.3 Transverse and Longitudinal Pretest Profiles forLight Preload Case, Panel A.................................55
3.4 Transverse and Longitudinal Pretest Profiles forLight Preload Case, Panel E.................................56
3.5 Transverse and Longitudinal Pretest Profiles forLight Preload Case, Panel B.................................57
3.6 Transverse and Longitudinal Pretest Profiles forLight Preload Case, Panel C.................................58
3.7 Membrane Strain Reversals at Low Pressure Load for LightPreload Case, Panel D.......................................59
3.8 Initial Top Surface Bending Strains vs. MeasurementLocation................._...................................61
3.9 Deflected Panel Contacting Vacuum Plate InsideClamped Region..............................................63
3.10 Center of Panel Out-Of-Plane Deflections vs.Pressure Load, Light Preload Case...........................66
3.11 Skin Out-Of-Plane Deflections vs. Pressure Load,Light Preload Case..........................................68
3.12 Longitudinal and Transverse Profiles at Zero(Pretest) and Maximum (Loaded) Pressure Loads, LightPreload Case, Panel 0.......................................70
3.13 Longitudinal and Transverse Profiles at Zero(Pretest) and Maximum (Loaded) Pressure Loads, LightPreload Case, Panel C.......................................71
3.14 Longitudinal and Transverse Profiles at Zero(Pretest) and Maximum (Loaded) Pressure Loads, LightPreload Case, Panel A.......................................72
3.15 Longitudinal and Transverse Profiles at Zero(Pretest) and Maximum (Loaded) Pressure Loads, LightPreload Case, Panel E.......................................73
vii
LIST 0F FIGURES (continued)
Figure Page
3.16 Longitudinal and Transverse Profiles at Zero(Pretest) and Maximum (Loaded) Pressure Loads, LightPreload Case, Panel B.......................................74
3.17 Strain Gage Locations for Strain Gages Used toMeasure Primary Panel Responses.............................79
3.18 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Light PreloadCase, Panel A...............................................80
3.19 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Light PreloadCase, Panel E...............................................81
3.20 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Light PreloadCase, Panel B...............................................82
3.21 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Light PreloadCase, Panel C...............................................83
3.22 Transverse Bending and Membrane Strains vs. Y Location,Panel Quarter Point (X=5), Light Preload Case,Panel A.....................................................86
3.23 Transverse Bending and Membrane Strains vs. Y Location,Panel Center (X=0), Light Preload Case, Panel A.............87
3.24 Transverse Bending and Membrane Strains vs. Y Location,Panel Quarter Point (X=5), Light Preload Case,Panel E.....................................................88
3.25 Transverse Bending and Membrane Strains vs. Y Location,Panel Center (X=0), Light Preload Case, Panel E.............89
3.26 Transverse Bending and Membrane Strains vs. Y Location,Panel Quarter Point (X=5), Light Preload Case, Panel B......90
3.27 Transverse Bending and Membrane Strains vs. Y location,Panel Center (X=0), Light Preload Case, Panel B.............91
3.28 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Light Preload Case,Panel C.....................................................92
viii
LIST 0F FIGURES (continued)
Figure‘ Page
3.29 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Light Preload Case, Panel C.............93
3.30 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),Light Preload Case, Panel D................................100
3.31 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Light Preload Case, Panel A................................101
3.32 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Light Preload Case, Panel E................................102
· 3.33 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),Light Preload Case, Panel B................................103
3.34 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),Light Preload Case, Panel C................................104
3.35 Illustration of Deflected Stiffener Showing Changesof Curvature...............................................105
3.36 - Comparison of Measured Longitudinal Stiffenerand Skin Profiles at Maximum Pressure Load.................107
3.37 Longitudinal Membrane and Bending Strains vs.Pressure Load, Light Preload Case, Panel D.................109
3.38 Longitudinal Membrane and Bending Strains vs.Pressure Load, Light Preload Case, Panel E.................110
3.39 Longitudinal Membrane and Bending Strains vs.Pressure Load, Light Preload Case, Panel B.................111
3.40 Longitudinal Membrane and Bending Strains vs.Pressure Load, Light Preload Case, Panel C.................112
3.41 Geometry of Short Web, Thick Flange Stiffener..............115
3.42 Geometry of Tall web, Thick Flange Stiffener...............116
3.43 Geometry of Tall web, Thin Flange Stiffener................117
ix
LIST 0F FIGURES (continued)
Figure Page
3.44 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LightPreload Case, Panel D......................................119
3.45 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, Vs. Y Location, LightPreload Case, Panel E......................................120
3.46 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LightPreload Case, Panel B......................................121
3.47 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LightPreload Case, Panel C......................................122
3.48 Stiffener Heb Strain Gage Locations........................124
3.49 Illustration of Longitudinal and Transverse BendingModes of the Stiffener Neb.................................125
3.50 Stiffener web Membrane and Bending Strains vs. PressureLoad, Light Preload Case, Panel A..........................126
3.51 Stiffener Web Membrane and Bending Strains vs. PressureLoad, Biaxial Preload Case, Panel A........................127
3.52 Stiffener Heb Membrane and Bending Strains vs. PressureLoad, Longitudinal Preload Case, Panel A...................128
3.53 Stiffener Web Membrane and Bending Strains vs. PressureLoad, Light Preload Case, Panel E..........................129
3.54 Stiffener web Membrane and Bending Strains vs. PressureLoad, Biaxial Preload Case, Panel E........................130
3.55 Stiffener web Membrane and Bending Strains vs. PressureLoad, Longitudinal Preload Case, Panel E...................131
3.56 Stiffener web Membrane and Bending Strains vs. PressureLoad, Light Preload Case, Panel B..........................132
3.57 Stiffener web Membrane and Bending Strains vs. PressureLoad, Biaxial Preload Case, Panel B........................133
x
LIST 0F FIGURES (continued)
Figure Page
3.58 Stiffener Heb Membrane and Bending Strains vs. PressureLoad, Longitudinal Preload Case, Panel B...................134
3.59 Stiffener web Membrane and Bending Strains vs. PressureLoad, Light Preload Case, Panel C..........................135
3.60 Stiffener web Membrane and Bending Strains vs. PressureLoad, Biaxial Preload Case, Panel C........................136
3.61 Stiffener web Membrane and Bending Strains vs. PressureLoad, Longitudinal Preload Case, Panel C...................137
4.1 Transverse and Longitudinal Pretest Profiles forBiaxial Preload Case, Panel 0..............................140
4.2 Transverse and Longitudinal Pretest Profiles forBiaxial Preload Case, Panel A..............................141
4.3 Transverse and Longitudinal Pretest Profiles forBiaxial Preload Case, Panel E..............................142
4.4 Transverse and Longitudinal Pretest Profiles forBiaxial Preload Case, Panel B..............................143
4.5 Transverse and Longitudinal Pretest Profiles forBiaxial Preload Case, Panel C..............................144
4.6 Membrane Strains at Low Pressure Loads for BiaxialPreload Case, Panel D......................................145
4.7 Membrane Strains at Low Pressure Loads for LongitudinalPreload Case, Panel D......................................147
4.8 Transverse and Longitudinal Pretest Profiles forLongitudinal Preload Case, Panel D.........................148
4.9 Transverse and Longitudinal Pretest Profiles forLongitudinal Preload Case, Panel A.........................149
4.10 Transverse and Longitudinal Pretest Profiles forLongitudinal Preload Case, Panel E.........................150
4.11 Transverse and Longitudinal Pretest Profiles forLongitudinal Preload Case, Panel B.........................151
xi
LIST OF FIGURES (continued)n
Figure° Page
4.12 Transverse and Longitudinal Pretest Profiles forLongitudinal Preload Case, Panel C.........................152
4.13 Illustration of the Bending of the LongitudinalDoublers Under Uniform Longitudinal Preload................153
4.14 Center of Panel 0ut—0f-Plane Deflections vs.Pressure Load, Biaxial and Longitudinal Preload Cases......155
4.15 Skin Out-0f—Plane Deflections vs. Pressure Load,Biaxial and Longitudinal Preload Cases.....................157
4.16 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Biaxial PreloadCase, Panel A..............................................159
4.17 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Biaxial PreloadCase, Panel E..............................................160
4.18 Transverse Bending and Membrane Strains, MeasuredontheFlange and Skin, vs. Pressure Load, Biaxial PreloadCase, Panel B..............................................161
4.19 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Biaxial PreloadCase, Panel C..............................................162
4.20 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, LongitudinalPreload Case, Panel A......................................163
4.21 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, LongitudinalPreload Case, Panel E......................................164
4.22 Transverse Bending and Membrane Strains, Measured on‘the Flange and Skin, vs. Pressure Load, LongitudinalPreload Case, Panel B......................................165
4.23 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, LongitudinalPreload Case, Panel C......................................166
xii
LIST OF FIGURES (continued)
Figure Page
4.24 Transverse Bending and Membrane Strains vs. Y Location,Panel Quarter Point (X=0), Biaxial Preload Case,Panel A....................................................168
4.25 Transverse Bending and Membrane Strains vs. Y Location,Panel Center (X=0), Biaxial Preload Case, Panel A..........169
4.26 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Biaxial Preload Case,Panel E....................................................170
4.27 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Biaxial Preload Case, Panel E..........171
4.28 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Biaxial Preload Case, Panel 8...172
4.29 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Biaxial Preload Case, Panel B..........173
4.30 Transverse Bending and Membrane Strains, vs. Y Location, "
Panel Quarter Point (X=5), Biaxial Preload Case,Panel C....................................................174
4.31 Transverse Bending and Membrane Strains, vs. Y LocationPanel Center (X=0), Biaxial Preload Case, Panel C..........175
4.32 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Longitudinal Preload Case,Panel A....................................................176
4.33 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=O), Longitudinal Preload Case, Panel A.....177
4.34 · Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Longitudinal Preload Case,Panel E....................................................178
4.35 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=O), Longitudinal Preload Case, Panel E.....179
4.36 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Longitudinal Preload Case,Panel B....................................................180
xiii
LIST 0F FIGURES (continued)
Figure Page
4.37 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Longitudinal Preload Case, Panel B.....181
4.38 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Longitudinal Preload Case,Panel C....................................................182
4.39 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Longitudinal Preload Case, Panel C.....183
4.40 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Biaxial Preload Case, Panel D..............................187
4.41 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Biaxial Preload Case, Panel A..............................188
4.42 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Biaxial Preload Case, Panel E..............................189‘
4.43 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Biaxial Preload Case, Panel B..............................190
4.44 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Biaxial Preload Case, Panel C..............................191
4.45 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Longitudinal Preload Case, Panel D.........................192
4.46 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Longitudinal Preload Case, Panel A.........................193
4.47 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Longitudinal Preload Case, Panel E.........................194
4.48 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Longitudinal Preload Case, Panel B.........................195
xiv
LIST OF FIGURES (continued)
Figure Page
4.49 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Longitudinal Preload Case, Panel C.........................196
4.50 Longitudinal Membrane and Bending Strains vs.Pressure Load, Biaxial Preload Case, Panel 0...............198
4.51 Longitudinal Membrane and Bending Strains vs.Pressure Load, Biaxial Preload Case, Panel E...............199
4.52 Longitudinal Membrane and Bending Strains vs.Pressure Load, Biaxial Preload Case, Panel B...............200
4.53 Longitudinal Membrane and Bending Strains vs.Pressure Load, Biaxial Preload Case, Panel C...............201
4.54 Longitudinal Membrane and Bending Strains vs.Pressure Load, Longitudinal Preload Case, Panel D..........202
4.55 Longitudinal Membrane and Bending Strains vs.Pressure Load, Longitudinal Preload Case, Panel E..........203
4.56 Longitudinal Membrane and Bending Strains vs.Pressure Load, Longitudinal Preload Case, Panel B..........204
4.57 Longitudinal Membrane and Bending Strains vs.Pressure Load, Longitudinal Preload Case, Panel C..........205~
4.58 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, BiaxialPreload Case, Panel 0......................................206
4.59 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, BiaxialPreload Case, Panel E......................................207
4.60 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, BiaxialPreload Case, Panel B......................................208
4.61 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, BiaxialPreload Case, Panel C......................................209
xv
LIST 0F FIGURES (continued)
Figure Page
4.62 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LongitudinalPreload Case, Panel D......................................210
4.63 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LongitudinalPreload Case, Panel E......................................211
4.64 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LongitudinalPreload Case, Panel B......................................212
4.65 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LongitudinalPreload Case, Panel C......................................213
5.1 Finite Element Model Discretization........................217
5.2 Center of Panel 0ut-Of-Plane Deflections vs.Pressure Load: Measured and Finite Element Resultsfor Four Panels............................................219
5.3 Skin Out-0f—Plane Deflections vs. Pressure Load:Measured and Finite Element Results for Three Panels.......220
5.4 Transverse and Longitudinal Deformed Panel CrossSections at Maximum Pressure Load (P=15 psi), FiniteElement Results, Panel D...................................223
5.5 Transverse and Longitudinal Deformed Panel CrossSections at Maximum Pressure Load (P#15 psi), FiniteElement Results, Panel C...................................224
5.6 Transverse and Longitudinal Deformed Panel CrossSections at Maximum Pressure Load (P=15 psi), FiniteElement Results, Panel A...................................225
5.7 Transverse and Longitudinal Deformed Panel CrossSections at Maximum Pressure Load (P=15 psi), FiniteElement Results, Panel B...................................226
5.8 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Finite Element Results,Panel A....................................................230
xvi
LIST 0F FIGURES (continued)
Figure Page
5.9 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Finite Element Results, Panel A........231
5.10 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Finite Element Results,Panel B....................................................232
5.11 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Finite Element Results Panel B.........233
5.12 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Finite Element Results,Panel C....................................................234
5.13 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Finite Element Results, Panel B........235
5.14 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Finite Element Results, Panel D...................... ......238
5.15 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Finite Element Results, Panel A............................239
5.16 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Finite Element Results, Panel B............................240
5.17 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Finite Element Results, Panel C............................241
5.18 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, FiniteElement Results, Panel D...................................244
5.19 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, FiniteElement Results, Panel A...................................245
5.20 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, FiniteElement Results, Panel B...................................246
Ixvii
LIST OF FIGURES (continued)
Figure Page
5.21 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, FiniteElement Results, Panel C...................................247
xviii
VLIST OF TABLES
”Tab1e Page
2.1 Skin/Stiffener Combinations Considered......................14
2.2 Average Prestrains for Each Inplane Preioad Condition.......42
3.1 Summary of Bending Strains on Skin and Flange,Light Preload Condition.....................................96
4.1 Summary of Bending Strains on Skin and Flange,Biaxia1 Pre1oad Condition..................................184
4.2 Summary of Bending Strains on Skin and Fiange,Longitudinal Preload Condition.............................185
xix
Chapter 1.
INTRODUCTION
Stiffening has long been used as a means of improving efficiency
in a variety of structures. In a typical aircraft application, stif-
fened skins are required to carry inplane compressive loads, inplane
shear loads, normal pressure loads, or a combination of these loads.
In addition, the skin may well be in the postbuckled state when it is
bearing high loads. Early approaches to the design of stiffened metal
skins relied heavily on empirical data collected from a large number
of specimens [1]. The design goal was to achieve a particular limit
load with no substantial permanent deformation. Local yielding was
allowed and, for the most part, it was beneficial in that it relieved
the high local stresses.
The advent of advanced composite materials has provided another
opportunity for further improvement in the efficiency of structures,
particularly stiffened skins. The ability to tailor the materials in
both the skin and stiffener is one of the prime advantages of compos-
ites. This advantage provides the designer flexibility but restricts
the application of empirical approaches. Not all design configur-
ations can be tested. The cost would be prohibitive. To take advan-
tage of the design flexibility, more specific analyses must be made of
each design configuration to determine its suitability. However, the
brittle nature of the resin-matrix composite materials requires a
different approach to the analysis, and it requires a design criteria
different than used with metal structures. The brittle nature of
l
2
resin-matrix composites causes failure modes that are different than
those experienced with the metallic designs. There is no yielding
with the brittle materials. with composites, the high local stresses
in the region of the interface between the stiffener and skin, in
combination with the lack of yielding, cause local material fail-
ures. These then lead to catastrophic failure of the structure. Some
of these local failure modes are: delamination of the skin; delam-
ination of the stiffener; stiffener buckling or crippling; and stif-
fener/skin separation [2]. Because of the possibility of these fail-
ures, it is very important to know the stress state in these localized
regions.
To date there has been little experimental data related to the
response of stiffened skins in these localized regions. Some analysis
has been conducted, however, to predict the local stress at the
stiffener/skin interface [3,4,5]. These analyses have indicated that
local and global geometric parameters, and skin and stiffener material
properties may be selected to reduce these interface stresses.
(Herein, local geometric parameters refer to those design details that
have little effect on the overall panel response but affect the
response in the local area of the interface. Global geometric
parameters affect the overall panel response but may also affect local
stiffener/skin interactions. An example of the former would be the
tapering of the stiffener flanges at their edges. An example of the
latter would be a doubling of the cross-sectional area of the
stiffener.)
3
The present investigation was designed to contribute further to
understanding the local and global response of stiffened skins. The
study was primarily experimental. The study was intended to provide
researchers with information regarding the localized response of
stiffened skin. More importantly, however, the study provided a means
to gain additional insight into the localized interaction mechanism by
critically examining the experimental data. Such examination then
can be used to direct further analytical efforts. The principle
objectives of the investigation were to:
- Determine the effects of different stiffener and skin con-figurations on the panel response at both a local and a globallevel. Variations in stiffener cross-sectional geometry andskin material properties were considered.
— Gain insight into the mechanisms of stiffener and skin inter-actions by measuring and quantifying strains, strain_ gradi-ents, and displacements.
‘
- Determine the effect of a small amount of inplane tensileprestrain on the responses of stiffened skins.
Specifically, clamped-edge panels subjected to a pressure loading
ranging from ambient to just below design levels were considered.
Pressure loading was selected because it is a realistic loading con-
dition. Also, it was a somewhat more tractable means of producing in
the laboratory the deformations which contribute to the high local
stresses. Deformation by buckling by applying either inplane shear or
inplane compressive loading is possible and also realistic. However,
experimental fixtures designed to apply controlled inplane shear or
compressive loads can be quite complex.
The clamped edge condition was chosen because it accurately rep-
resents the boundary conditions experienced by a representative panel
4
on an aircraft fuselage or wing structure. On a wing, for example,
neighboring panels on the four sides will restrain the inplane motions
at the panel's edges. Attachment to the substructure will also pro-
vide an inplane restraint, as well as the out-of—plane restraint.
Pressure levels up to 15 psi were used. This is typical, but
perhaps on the low side of some design requirements for pressurized
fuselages. with these pressure levels and with the clamped edge
conditions, signifjgggt_membrane/strains were generated in the test ·
panels. These were due to geometric nonlinearities. As will be seen,
the nonlinearities strongly influence the response of the panels..The
stiffeners studied were "T"-type stiffeners. The horizontal
portion of the "T", the flange, was bonded to the skin itself. The
vertical part of the "T", the web, was perpendicular to the skin.
Interest was in the strains in the stiffener flange, in the stiffener
web, in the skin very close to the stiffener flanges, and in the skin
near the clamped edges. The deformed and undeformed shapes of the
panels were also of interest. Experiments were conducted on panels
with flanges of various thickness, webs of various heights, and two
skin laminates. One skin had quasi—isotropic elastic properties and
the other skin_had—orthotropic—elastic’properties. Though the studywas mostly empirical, some finite-element analysis was also used.
The approach to and the results of the investigation are dis-
cussed in the following chapters. First the mechanics of the testing
are described and discussed. Attention is given to the apparatus
designed for the testing and attention is given to the selection and
design of the test panels. In the chapter following that‘ the
5
experimental results are presented and discussed. Effects of the skin
and stiffener variations on the interaction mechanisms between the
stiffener and skin are emphasized. The effects of inplane preload on
the responses of each panel are discussed. In the fifth chapter the
results of nonlinear finite element models of four of the panels are
presented. The final chapter summarizes the findings and presents
conclusions of the investigation.
Chapter 2.·
DESCRIPTION OF TEST EQUIPMENT AND TESTING PROCEDURES '
INTRODUCTION
Of major concern in the basic design of the experiment was: 1)
How to apply the pressure load; 2) How to enforce the clamped edge
condition, and; 3) How to apply the inplane preload. In addition, of
major concern in the basic design was determining the minimum number
of tests required to illustrate the effects of the important panel
parameters on panel response. The following paragraphs present an
overview of how these and other considerations were approached in
selecting a final configuration for the test apparatus, and the selec-
tion of the panels to be tested. Details of the apparatus and panels
tested are discussed after the overview is presented.
OVERVIEN OF BASIC EXPERIMENTAL DESIGN CONSIDERATIONS
Pressure testing with compressed air, particularly when failure
is a possibility, normally involves a significant number of safety
precautions. Testing at remote sites located away from populated
_ laboratories is sometimes required. As an alternative, fluids can be
used to apply pressure. Fluids, such as oil, are incompressible and
therefore'are less dangerous when pressure is suddenly released due to
failure. However, fluids pose problems when using electrical devices
such as data acquisition equipment. To circumvent the problems with
fluid, and to allow the testing to be conducted in a normal laboratory
environment without endangering other personnel, loading of the panelsU
6
7
was accomplished by use of a vacuum. This loading method was imple-
mented with an apparatus using the concept shown in Figure 2.l. In
this apparatus the stiffened panel was clamped to a relatively thick
and stiff plate with a central recessed area. This plate will be
referred to as the vacuum plate. A vacuum pump was used to evacuate
the recessed area beneath the stiffened panel and a throttle valve
regulated the level of vacuum pressure. The pressure load indicated
in the figure was determined by the difference of the prevailing at-
mospheric pressure above the panel and the regulated vacuum pressure
beneath the panel. This test apparatus configuration had the advan-
tage of placing the stiffener on the side of the panel with the great-
er pressure. This is exactly as it would be for a pressurized fuse-
lage application. In addition, this test apparatus configuration made
the stiffener accessible for deflection measurements or visual in-
spection during loading.°
The clamping of the panel to the vacuum plate, to enforce the
clamped edge conditions, was an important consideration. The two
important and necessary conditions characterizing a clamped edge are,
enforcement of zero normal slope, and; enforcement of zero inplane
displacement (normal and tangential). Implicit in the clamped edge
condition is the condition of zero out-of-plane deflection at the
clamped edge. In orderto more closely approximate a clamped edge
boundary condition, a multi—bay loading apparatus was considered.
Figure 2.2 illustrates this concept. The principal idea behind the
multibay apparatus is the use of symmetry to enforce the zero slope
condition. In this apparatus a panel is clamped to a vacuum plate
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containing nine recessed areas or bays. A vacuum is applied to all
nine bays. The panel is forced down into each bay. The deformation
forms lines of local symmetry, with regard to out—of-plane deflection,
along the lines AB, BC, CD, and DA indicated in the figure. The zero
slope condition is automatically enforced along these lines, bounding
what becomes the central area of interest. These lines then become
the "edges" of the panel. To enforce the zero inplane displacement
« condition along the panel edges, not a trivial matter, the panel could
be clamped to the vacuum plate along all lines of contact, including
those outside the central area. This would not pose any problems.
However, the physical dimensions and cost of fabrication of both the
apparatus and test specimens for this multibay arrangement were felt
to be beyond the intended scope of this study. Therefore, it was
decided to use the multibay concept on the stiffener ends only. This
enforced the zero slope condition on the stiffener ends, a location
where it was expected to be the most difficult to enforce by
conventional clamping means only. The portion of the multibay concept
selected for the final design is shown in the unshaded portion of
Figure 2.2. The clamping of the plate to prevent inplane motion was
then applied along lines A'ABB', D‘DCC', A'D', AD, BC, and B'C'.
The inplane tensile preload was applied by stretching the stif-
fened panels within a frame, much like the fabric in a trampoline is
stretched. Uniformly spaced bolts, with clevises, attached the panel
to the frame and provided the inplane tensile forces. The clevises
were individually loaded by tightening a nut on the threaded shaft,
the shaft attaching each clevis to the frame. Loading uniformity was
ll
accomplished by monitoring electrical resistance strain gages, mounted
on each clevis, during loading. Figure 2.3 shows the stretching frame
and instrumented clevises attached to doublers at the edge of an un-
stiffened panel. There are many features to the experiment that are
shown in Figure 2.3. They will eventually be discussed.
Determining the range of geometric and material parameters of the
panels to be tested was an important step. It was necessary that any
parameter felt to influence skin/stiffener interactions be varied over
at least a limited range. Also it was important that the dimensions
of the panels be representative of actual fuselage dimensions. Fin-
ally, knowing that each panel would involve many hours of set-up and
test time, it was important to keep the number of panels to be tested
to a reasonable number.
The dimensions of the center test section of the panel were se-
lected to represent a fuselage section with 5 in. stringer or stif-
fener spacing and 20 in. frame spacing. Two panel thicknesses of 8
plies, or approximately 0.040 in., and 16 plies, approximately 0.080
in., were considered as being representative of a fuselage appli-
cation. In addition, such thicknesses would provide acceptable
deflection and strain response to the pressure loading capability of
the vacuum test apparatus. T-type stiffeners were selected because
the geometry of the stiffener could be changed easily to control
stiffener stiffness. Relatively simple and easily-defined changes of
either web height or flange thickness were used to control the
stiffness. The T-type stiffener had the additional advantage of being
relatively easy to fabricate.
T27
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Figure 2.3 Unstiffened Panei Mounted in Test Apparatus
l3
Table 2.1 is a matrix of stiffener geometries and skin material
configurations considered in the process of identifying the panels
finally selected. This matrix represents what was considered as a
minimum number of material and geometric parameter combinations. The
combinations include, within a restricted range, both the extremes and
the nominal conditions of skin thickness, flange thickness, web
height, and skin elastic properties. The elastic properties of the
stiffener were not considered as a variable, although they could have
been.
Skin layups that were considered are listed across the top of the
Table. In the spirit of selecting parameters typical of fuselage
applications, no angle-ply layups were considered. Also typical of
fuselage skins, :45 outer skin plies were specified in each layup.
For each skin listed, the inplane and the bending stiffnesses are
indicated. These stiffnesses represent laminate stiffnesses normal-
ized with respect to the 8-ply quasi-isotropic layup. The longi-
tudinal direction is the direction parallel to the stiffener. It is
also the 0° fiber orientation. The transverse direction is perpen-
dicular to the stiffener. It is the 90° fiber orientation. Bending
stiffnesses are normalized with respect to the transverse bending
stiffness of the 8-ply quasi-isotropic skin.
On the left side of the Table is a column of stiffener descrip-
tions. The layup of the web and flange of each stiffener is listed
with the description of the stiffener cross-section. The stiffeners
are described in order of decreasing bending and axial stiffness. An_
unstiffened skin was also included and only two web heights were con-
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sidered. The two heights represented what was felt to be extremes in
longitudinal bending stiffness for a typical application. Two flange
thicknesses were considered. These represented two distinct trans-
verse flange bending stiffnesses. The 1.5 in. flange width was se-
lected on all configurations because this is the flange width required
for proper bonded joint performance.
The combination of an entry from the skin column and an entry
from the stiffener row forms a particular panel configuration. At the
intersection of the column and row, the particular configuration is
described in qualitative terms. The column of panel configurations
under the thin quasi-isotropic skin (3rd column) formed a baseline
group. within this group the effects of longitudinal and transverse
stiffener stiffness could be compared. The column to the left of that
provided a comparison of these stiffener effects in the presence of a
transversely stiffer skin. The other columns provided additional
comparisons of skin and stiffener combinations, as indicated by the
descriptions of each configuration.
The fabrication cost of the panels limited the number of panels
to those indicated by asterisks. It was felt that these panels would
best highlight the effects of stiffener stiffness, stiffener flange
stiffness, and skin stiffness (with a single skin thickness) on stif-
fener/skin interactions. The unstiffened panel was selected to pro-
vide baseline response information for comparison. Since quasi-iso-
tropic skins have been used often in metal/composite design trade-off
studies, this skin was emphasized. Note the letter designations given
each of the selected panels, Panel A, Panel B, etc. These desig-
l6
nations will be used in the following sections when referring to test
results of particular panels.
DETAILS 0F EXPERIMENTAL DESIGN CONSIDERATIONS
Having determined the basic configurations of the test apparatus
and test panels, their detail designs were then established. The
three bay vacuum plate is shown in Figures 2.4, 2.5, and 2.6. Shown
also in Figures 2.4 and 2.6 is the trampoline—type stretching frame
with the clevises hanging free.
The 41.25 in. long x 11.25 in. wide x 2 in. thick 3-bay vacuum
plate was machined from a single piece of steel. The two end bays
were 8.75 in. wide x 8.75 in. long x 1 in. deep. The center bay was
8.75 in. x 18.75 in. long x 1 in. deep. A 0.25 in. x 0.15 in. deep
groove was machined around the perimeter of each bay to accommodate
the three separate 0-rings used to seal the portion of the panel over
each bay. The three 0-rings are visible in Figures 2.4 and 2.6 as
light colored lines around the lip of each bay area. The patterns at
. the bottom of each recessed area are due to the milling machine used
to make the vacuum plate. A 1/2 inch pipe thread hole was machined in
the center of each bay. The vacuum pump fittings were attached at
these holes. Near one end of the center bay a 5 in. wide x 6 in. long
opening was machined through the plate. This opening allowed the
attachment of a sealed electrical connector through which electrical
resistance strain gage signals were transmitted. Small tubing con-
nectors for a mechanical pressure gage and an electrical pressure
transducer were also located on this connector plate. One-half inch
l7
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Figure 2.4 View of Test Apparatus Showing Vacuum Plate
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diameter holes were spaced around the perimeter of the vacuum plate,
as indicated in Figure 2.5. These holes were for the bolts used to
clamp the test panels to the vacuum plate. Two smaller, 5/16 in.
diameter, holes were located at the center of each of the shorter ends
of the bays. These are also indicated in Figure 2.5. These holes
were used for clamping bolts which passed through the stiffener
flanges.
The panels were clamped to the vacuum plate using bolts and alu-
minum bars. The panels were clamped around the perimeter of all three
bays. This was shown in Figure 2.3. Schematic details of the clamp-
ing are shown in Figure 2.7. The clamping bars were machined from 1
in. diameter aluminum bars. The bars had flat surfaces machined on
the top side at each bolt hole so that the clamping bolt heads had a
uniform contact surface. The panel was contacted and clamped along a
straight narrow area on the bottom side of the round clamping bar. On
the short end of the test bay the clamping bars were in two halves.
This allowed for clearance for the stiffener web. The bars on the
short ends also had notched areas on the clamping surfaces to allow
for the increased thickness of the stiffener flanges. This is indi-
cated in Figure 2.7. Each flange thickness was measured as the panel
was installed and shims of the appropriate thickness were used between
the clamping bar and flange so that the clamping bar was in contact
uniformly along its length on both the skin and the stiffener
flange. A thick shim was used in this notched area when testing the
unstiffened panels.
2lAlumiriumClamping Bar A
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Figure 2.7 Clamping Details
22
The inplane preloading frame and clevises can be seen in Figures
2.3, 2.4, and 2.6. The frame was constructed of four pieces of 1/4
in. thick x 3 in. deep U—shaped channels bolted together at their cor-
ners. The channels opened outward, the channel flanges being hori-
zontal. Holes were drilled through the web of each channel so the
clevises could be attached. Threaded rods passed through the holes
and into the clevises. The clevises, in turn, transmitted the inplane
preload to the panel. Figure 2.8 shows a schematic of a clevis, il-
lustrating how they were attached to the frame and panel edges. The
locations of the strain gages, used to monitor the preload, are also
indicated in the figure. Two 0.25 in. thick x 1 in. wide x 2.75 in.
long parallel pieces of steel were welded to a 1 in. steel cube to
form the U—shaped clevis. A 0.5 in. diameter hole was drilled through
each parallel portion, 0.5 in. from their ends, at the open end of the
U-shape. The clevises transmitted the preload to the panel through a
0.375 in. diameter pin which was passed through these holes and
through a hole in the edge of the test panel. Steel doublers were
bonded to the edges of the test panels to distribute the tensile loads'
along the panel and to provide additional bearing strength to the
panel at the clevis pin contacts. On the opposite end of the U-shape,
a 0.375 in. diameter threaded rod was threaded into the 1 in. cube.
This threaded rod was passed through the holes in the frame described
above. The preload was applied to the panel by tightening a nut on
the threaded rod.
A similar clevis was constructed to allow the application of a
preload to the stiffener. The stiffeners were extended 2 in. beyond
23
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the ends of the panel to allow for the clevis attachment. The load
was applied by means of 0.188 in. diameter pins which passed through
the clevis and the web and flange of the ends of the stiffener. Fig-
ure 2.9 shows the hole locations for these pins. This figure also
shows details of the stiffener construction which will be discussed
further in a section to follow.
The preload uniformity and magnitude were controlled by adjusting
the torque on each clevis loading nut. This was done while monitoring
the signal from the back-to-back strain gages mounted on the clevis.
These gages were connected to opposite legs of a four-leg Nheatstone
bridge circuit such that their signals were added, cancelling the ef-
fects of bending strains and adding the membrane strain responses of
each gage. Each clevis was calibrated using a load cell and a tensile
test frame. The applied load and the voltage required to balance the
bridge circuit was recorded for several load levels. The force per
millivolt slope of the best-fit straight line was determined from this
load-strain gage response data for each clevis. These individual
calibration factors were used for each clevis in the data acquisition
conversion calculations. The average of these clevis calibration
factors was 2560 lb/mv.
VACUUM LOADING
The vacuum system is shown in Figures 2.10 and 2.11. As seen in
Figure 2.10, tubing fittings were attached to the three threaded holes
in the three bays of the vacuum plate. This was described earlier and
was indicated in Figure 2.5. The three tubes were joined to a single
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tube with a tubing cross-fitting. This single tube was connected to a
mechanical vacuum pump by means of a flexible rubber coupling. This
is shown in Figure 2.11. Two valves, indicated as the throttle valve
and main valve in Figure 2.10, were also attached to this tube. The
main valve was mounted inline with the pump and the throttle valve was
mounted on a tee fitting which was open to the ambient pressure when
the valve was opened. Also indicated in Figure 2.10 are a mechanical
pressure gage and an electrical pressure transducer, both of which
measured the absolute pressure in the center bay of the vacuum plate.
The application of the pressure load was accomplished as fol-
lows: The throttle valve was opened all the way. With the main valve
closed, the vacuum pump was turned on. At this point, since the main
valve was closed, isolating the vacuum pump from the vacuum plate, the _
pressure in the area between the panel and vacuum plate was equal to
the ambient pressure. The main valve was then opened. with the~
throttle valve still open, the pump was still pumping ambient air
only, through the throttle valve. Thus, the pressure under the panel
was still equal to the ambient pressure. The throttle valve was then
slowly closed, restricting the flow to the pump, lowering the pressure
in the bays under the panel. The center bay pressure was monitored
with the pressure gages, as the throttle valve was being closed, to
control the rate of pressure loading. Maximum pressure load was
achieved when the throttle valve was completely closed and the vacuum
pump was pumping only from the volume between the test panel and
vacuum plate, and the tubing volume. Since the vacuum pump was cap-
able of pumping vacuum pressures in the millitorr range, the maximum
29
pressure load was essentially equal to the ambient atmospheric pres-
sure. Data were recorded throughout this process as the pressure load
increased from zero to the maximum level, a level of about 15 psi.
DESCRIPTION OF PANELS
As was seen in Table 2.1, a total of five panel configurations
were tested. One of each of the configurations indicted by asterisks
in that table were fabricated. An additional panel of the type des-
ignated as Panel E was fabricated. Since inspection of ‘the first
panel of this type indicated a poor quality bond between the stiffener
and panel, a second panel was fabricated. Both panels were subse-
quently tested and had essentially the same response over the range of
pressure and preloads applied. Only the results from the second panel _
will be presented in the chapter to follow.
Three of the panels are shown in Figure 2.12. The basic config-
uration of all of the panels was the same. They all had overall di-
mensions of 48 in. long x 22 in. wide., They all had an 8 ply AS4/3502
graphite-epoxy skin. 'AS4/3502 material properties, as provided by the
panel fabricator, are given in Appendix A. The skins were autoclave-
cured. Stiffeners were also fabricated from AS4/3502. They were
cured separately and then bonded to the panels at room temperature.
Steel doublers, 2 in. wide x 1/8 in. thick, were bonded to both sur-
faces around the four edges of each panel.
A hole pattern of 0.48 in. and 0.312 in. diameter holes was
drilled in the center area of each panel to match the clamping bolt
hole pattern in the vacuum plate. The 0.48 in. diamter holes aligned
30
HOLES FORSTEELDOUBLERS gLä¥IS LOADING STIFFENERSCLAMPING A
BOLT HOLEPATTERN
L Ut-
es~•
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·VFigure2.12 Three Test Panels
3l
with the 0.50 in. diameter panel clamping bolt holes in the vacuum
plate. The 0.312 in. diameter holes aligned with the 0.3125 in. diam-
eter stiffener clamping bolt holes in the vacuum plate. The clearance
between the edge of the 0-ring groove and the 0.5 in. clamping bolt
holes was very small. Panel misalignment could have caused a bad
seal. Making the panel clamping bolt holes smaller than the vacuum
plate holes allowed for a slight misalignment without imparing the
seal. However, both the panel and vacuum plate holes were oversized
relative to the bolts used. This clearance allowed for panel stretch-
ing under preload. It also allowed the reduction of the tolerance
requirements on the hole locations and subsequent reduction of the
machining costs. All panels had holes for the clevis loading pins
drilled through the doubler plates and skins at locations correspond—_
ing to the clevis spacing.
The T-type stiffeners bonded to the stiffened panels were also.
all of similar construction. Figure 2.9 shows details of their con-
struction. The cross section A-A shows the method of fabrication of
the stiffener. Strips of 8-ply sheets were formed into L-shapes and
then butted together. The outer bend radius of the two L's formed a
small void at their intersection. A small strip of unidirectional
material aligned with the stiffener axis was placed in this void
area. For the thin flanged stiffener the legs of the L‘s formed the
flanges. For the thick flanged stiffeners another 8-ply strip was
placed underneath these L's. Special jigs were used to maintain
”alignment while the stiffeners were cured in an autoclave. At each
end of the stiffener two holes were drilled in the center of each
32
flange and two holes were drilled in the web, as near the neutral axis
of the stiffener as possible. These holes were used for preloading
the stiffener in tension with the special clevis, as described
earlier.
INSTRUMENTATION
Several types of instrumentation were used to record data during
the testing of the panels. Some of these were alluded to in the pre-
vious paragraphs and have been seen in photographs of the apparatus.
The following paragraphs will describe the instrumentation used and
how it was applied in this experimental program.
Strain Measurements _
Electrical resistance strain gages were used extensively to mea-
sure panel response. The strain gages were bonded to the panel at
various locations. These locations were selected to measure the
strain response of interest. Of equal importance, the gages were used
to determine if there were any anomolies in the test fixture, appli-
cation of the load, or in the panel itself. Because the bending re-
sponse of the skin to the pressure loading was not, strictly speaking,
symetric about either the longitudinal or lateral centerline, a per-
fectly symmetric response to the pressure loading was not expected. _
However, strain gages mounted in mirror image symmetric postions
should show very similar responses if the test fixture and the panel
were well behaved. Thus, some gage positions were selected simply to
monitor the degree of symmetry in the response.
33
Gages mounted in areas of anticipated high strain gradients had
active gage lengths of 0.05 in. Gages in areas of anticipated uniform
strain fields had gage lengths of 0.187 to 0.125 in. The sealed
electrical connector shown in Figure 2.4 permitted the use of gages on
the bottom surface of the panel, inside the vacuum bay. This per-
mitted use of back-to-back gage pairs on the top and bottom surfaces
of the panel. Mounted in this manner, the strains measured by the
gages could be analyzed to determine the bending and rnembrane com-
ponents.
Displacement Measurements
Displacement measurements were made using electrical devices
called direct current differential transformers, or DCDT's._ The
DCDT's are, as the name indicates, transformers. They have spring-
loaded moveable cores. The core serves as the displacement measure-
ment probe. The core moves with the moving object while the windings
of the transformer remain stationary. As it moves, the core changes
the inductive coupling of the transformer and thus changes the voltage
output of the transformer. The voltage output can be calibrated as a
function of core displacement. The spring-load provides positive
contact force with the object being measured. The sensitivity and
accuracy of the DCDT's permitted displacement measurement accuracy of
approximately :0.0005 inches. The 0COT's were used to measure both
out-of-plane deflections and possible inplane slippage at the clamped
boundaries of the panels.
34
For the inplane slippage measurements, the DCDT's were clamped to
a fixed base. The DCDT's measured the movement of L-shaped angles
bonded to the panel near the clamped edges. The DCDT's and angles can
be seen in Figure 2.3. The deflection measurement made in this manner
may have contained a component of displacement due to the rotation of
the bracket. However, the probe contacted the angle at less than 0.5
in. above the surface of the panel and rotations were minimal at this
panel location. This would minimize the effect of any rotation on the
measurement.’
_
Out-of-plane deflections were measured with 0CDT's mounted ver-
tically above the panel. Out-of—plane deflection profile measurements
were made by means of a DCDT which was moved horizontally and parallel
to the panel, along a rail fixed above the panel. As the_DCDT was
moved horizontally, a rotary transformer was turned, producing a vol-
tage signal calibrated to the horizontal movement. As the DCDT moved
horizontally the DCDT core moved vertically, following the deflected
surface of the panel. The DCDT—measured deflection provided a measure
of the panel deflection profile along the line which the DCDT trans-
versed. Figure 2.13 shows the moveable DCDT and rotary transformer
mounted on the rail above a panel. This rail device was used to mea-
sure both the pretest panel deflection profiles and the panel profiles
under maximum pressure load. The pretest profiles could be used to
determine the pretest shape of the panels.
As mentioned before, the pressure load was measured both with a
mechanical gage and an electrical pressure transducer. The electrical
pressure transducer signal was the only pressure signal recorded. The
35
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mechanical gage was used only for visual test monitoring. The trans-
ducer was a diaphragm—type pressure gage. In this type of transducer
a bridge circuit produces a voltage signal which is proportional to
the strain measured on the diaphragm. This voltage is calibrated to
the applied pressure. The pressure load was measured as the dif-
ference between the initial pressure reading and the instantaneous
readings recorded during the test.
In all of the tests, an automatic data acquisition system was
used to record the voltage signals from the instrumentation. The vol-
tages were converted to digital signals within this system and then4
stored on magnetic tape. These digital signals were then converted to
their respective physical units, e.g., inches, psi, etc., using the
appropriate calibration factors. The data acquisition system recorded
blocks of up to 100 signals simultaneously twice per second during the
testing. This method ensured correlation between the applied pressure
load and measured panel responses.
TEST PROCEDURE
The general procedure used for the testing of each panel was as
follows: The panel, with strain gages installed, was placed on the
vacuum plate with the clamping bolt holes in approximate alignment.
The clevises were attached to the panel and left untightened. Strain
gage wires were then connected to the data acquisition system. All
clevis strain gage and panel strain gage output voltages were then
balanced to zero in this unloaded condition. This condition was the
reference condition for all measurements. The inplane preload was
37
then applied to the panel, using the clevis strain gage voltages to
determine uniformity. with the panel preloaded to the desired level,
it was then clamped to the vacuum plate. The clamping bolts were
torqued to 25 ft-lbs in a symmetric pattern, clamping the panel be-
tween the aluminum clamping bars and the vacuum plate.
The DCDT's used to measure panel slippage were installed and
their voltage outputs balanced to zero. Using the DCDT and rail
system, the pretest shape of the panel was measured and recorded. The
shapes were recorded two ways. First, the out—of-plane deflection of
the top of the stiffener web was recorded as a function of longitu-
dinal position along the panel. Second, the out-of-plane deflection
as function of transverse postion, perpendicular to the stiffener, was
recorded. Ideally a global out-of-plane deflection measure, such as
moire', would have been best. However, with the panel horizontal,
this would have meant a vertical moire' arrangement, suspending the
illumination source and camera from above. The other approach would
be to record deflection profiles at several locations, rather than
just two. However, strain gages and strain gage wires attached to the
panel made this difficult. Therefore, for the scope of this study,
the single deflection profile in each direction was felt to be suf-
ficent.
After measuring the pretest out-of-plane shape in both direc-
tions, and just prior to the start of the pressure loading, one DCDT
was positioned on the top of the web at the panel center. Another
DCDT was placed at the panel center on the skin, midway between the
stiffener and clamped edge. Figure 2.14 illustrates these two DCDT
° 38
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positions. These two OCDT's measured the out-of-plane deflections of
the panel during the pressure loading.
The pressure load was then applied to the panel using the vacuum
system described earlier. The DCDT voltages, the strain gage vol-
tages, and the applied pressure were recorded throughout the loading
process. During the loading process, which was relatively slow, panel
response was carefully observed through visual inspection. There were
two areas of concern during the loading. One concern was separation
of the skin and the stiffener. This obviously was of major interest,
particularly in determining where along the stiffener separation may
have initiated. The second area of concern was stiffener web
buckling. At the centerspan of the web, with the entire panel bowed
downward under the pressure load, a majority of the stiffener web was
in compression. Being of high aspect ratio (thickness to width),
buckling or crippling could have occurred. There were back-to-back
strain gages mounted near the top of the web to quantitatively assess
this. However, a visual inspection would determine, qualitatively,
whether it was occurring. If crippling did occur, the stiffener could
twist, or roll, and trigger an unsymmetric panel response, or even
premature failure.
Once the maximum presure load was reached, the DCDT and rail
system were used to record the loaded panel shape. Both longitudinal‘
and transverse shapes were measured. The pressure load was then re-
leased. The panel was unclamped and the preload was removed. The
procedure was then repeated for the next preload condition.
40
TEST CHECKOUT
Several measurements were made and analyzed to determine if the
testing procedure was satisfactory, and to determine if the test ap-
paratus was operating properly. In the following paragraphs the re-
sults of these measurements are discussed under three topics: Pre-
load/prestrain conditions; effect of clamping bolt torque, and sym-
metry of panel response.
Preload/Prestrain Conditions
The prestrain is distinguished from the preload discussed earlier
in that prestrain represents the panel response to the effects of
clamping and the inplane preload from the clevises. Three inplane
preload conditions were applied to each panel in this investigation.
These preload conditions were: a light preload; a biaxial preload,
and; a longitudinal preload. A light preload was defined as
approximately 20 pounds applied to each clevis. This more or less
just snugged the clevis/frame system. A biaxial preload was defined
as approximately 650 pounds on each clevis. A longitudinal preload
was defined as 650 pounds on each clevis attached to the short ends of
the panel and 20 pounds on each clevis attached to the long edges.
The preloads produced membrane prestrains in the panels which
were somewhat different from those expected, based on calculations of
equivalent inplane loading of laminates. These differences were due
primarily to the stiffening effects of the steel doublers. The doub-
lers had a higher inplane stiffness than the panels. As a result,
they carried a large part of the preload. This reduced the strains
4l
generated at the center portion of the test panels. This effect was
particularly noticeable for the longitudinal strains. There were
several reasons for this. First, since the panels were narrower than
they were long, the doublers on the longitudinal edges were closer
together than the doublers on the two lateral edges. This closer
spacing of the doublers made the panel stiffer longitudinally than it
was laterally. Second, the lateral doublers were split to accommodate
the stiffener flange. This caused the doublers to be less stiff in
the lateral direction. Finally, in the longitudinal direction, the
stiffener controlled the prestrains near the center of the panel.
This was overcome to some degree by prestraining the stiffener also;
In addition to the effects of the doublers, differences in the
stiffener configurations and the two skin stiffnesses produced dif-
ferences in the prestrains under the same preload conditions. How-
ever, these differences were small enough that the panels were still
considered as a group for each preload condition in the results and
discussion chapter to follow.
U
Table 2.2 lists the average longitudinal and transverse membrane
pretrains measured on the skin for each panel at the three preload
conditions. For the light preload case the strains are generally
small, as wanted, and of no consequence. The variation in prestrains
for the light preload condition indicates the range of scatter in the
strain readings. This scatter was due primarily to the zero drift of
the gage readings. For the biaxial preload, the prestrains of the
orthotropic skin panel are noticeably different from those of the
quasi-isotropic panels. The higher transverse membrane stiffness of
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the orthotropic skin reduced the transverse prestrains relative to the
quasi-isotropic case. For the longitudinal preload the prestrains
were relatively uniform among panels. This was due to the stiffening
effect of the steel doublers along the longitudinal edges. The panel
response was limited by the stretching of the doublers and the re-
sponse was essentially independent of the panel stiffness. The neg-
ative transverse prestrains for this preload condition are due to a
Poisson effect. »
Since the preloading effects are peculiar to each particular
panel, the actual prestrains for each panel would be more accurate
representations of the initial conditions for each panel than, for
instance, the strain data from the clevises. However, for conven-
ience, the discussion of the results is organized into the three pre-
load levels. To be complete, in the following sections the initial
strain readings are indicated in each plot of strain responses. Any
effect of variation in prestrain among panels may then be evaluated.
Effect of Clamping
The effectiveness of the clamping restraint on the panel was very
dependent on the clamping force, and hence on the torque applied to
the clamping bolts. The bolts available for use for this investi-
gation had a safe torque capacity of 25 ft—lbs. Since it would
provide the maximum clamping effect for the given clamping
configuration it was decided to use this maximum torque on the
bolts. A series of tests were conducted, however, to measure the
degree to which this maximum allowable bolt torque provided a clamping
44
restraint. Four tests were conducted in which a lightly preloaded un-
stiffened quasi—isotropic panel was clamped to the vacuum plate using
bolt torques of 10, 15, 20, and 25 ft-lbs. Pressure load was applied
to the panel in each case. The center out-of-plane deflection and
panel-edge inplane slippage deflections were recorded. These edge and
center deflections measurements are shown as a function of pressure
load in Figures 2.15, 2.16, and 2.17 respectively. Figure 2.15 shows
the slippage of the longitudinal edge of the panel at the center of
the left edge of Figure 2.3. This slippage was measured by the DCDT
at that location. Figure 2.16 shows the slippage of the longitudinal
edge of the panel at the center of the right edge. This was measured
by a DCDT at that location.
Looking at Figures 2.15 and 2.16, it can be seen that the edge
slippage was reduced considerably with increasing bolt torque. The
out-of-plane center deflection measurements in Figure 2.17 show the
effect this edge slip restriction had on the panel response. As the
clamping bolt torque was increased, the edge slip was restrained and
the center deflection was reduced. It is not expected that the max-
imum clamping capability of the clamping system was reached with a 25
ft-lb torque. However, the relatively small change in maximum centerI
deflection between the 20 and 25 ft-lbs torque levels indicates that
little improvement on the clamping restraint could have been made with
greater bolt torques.
Symmetry of Response
Some strain gages were installed specifically to determine the
45
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. 15 Ft-Lbs f*50.01CUFZ .mLI-Ij//,;;//”//ii:9«’
25 Ft-Lbs0.0
O 5 10 15E ’
P (psi)
Figure 2.15 Left Side Inplane Edge Slip vs. Pressure Load forFour Clamping Bolt Torque Levels (Unstiffened Panel,Light Preload)
46
0.02
Q2 l0 F1;-Lbs·O.EU2 0.01 Ä-LbsY; JQ /
Lu
/// 25 F:-Lbs0.0
0 5 l0 l5P (psi) ·
Figure 2.16 Right Side Inplane Edge Slip vs. Pressure Load for °Four Clamping Bolt Torque Levels (Unstiffened Panel,Light Preload)
47
10 Ft-Lbs0.4 .15 Ft-Lbs
0,3 Ft—LbS25 Ft-Lbs..éTZ_c>.SU
2‘g0.2
¤s..3:cuC.)0.1
0.0
0 5 10 15P (psi)
Figure 2.17 Unstiffened Pane1 Center 0ef1ection vs. Pressure forFpur C1amping Bo1t Torque Leve1s (Unstiffened Pane1,Light Pre1oad)
”
48
symmetry of the strain responses. Some of these gage responses are
illustrated in Figure 2.18. Two top surface transverse and two top
surface longitudinal midpanel gage responses for the unstiffened panel
(Panel D) are shown in the figure. The unstiffened panel was used for
initial test because it was much more sensitive to anamolies in the
fixtures than the stiffened panels. The terminology L1, L2 and T1, T2
denote longitudinal and transverse gage locations, respectively.
As can be seen in this figure, and as will be seen throughout,
none of the strain responses are zero at zero pressure. This is be-
cause the preclamped condition is considered the zero strain con-
dition. The clamping produces a panel response which, in some cases,
could influence responses to applied pressure. Therefore, as said
before, this initial response was recorded and is presented here. The
strain reversals at low pressures measured by the gages T1 and T2 on
the unstiffened panel indicate an initial shell—like bending re-
sponse. This response is caused by panel bowing, either due to de-
viations from initial flatness when manufactured, or due to deviations
from flatness caused by clamping. This response is discussed further
in the chapter to follow. The magnitude of the reversal for the
transversely mounted gages appears large. This is due to the
combination of compressive top surface bending and initial compressive
membrane response at this location.
For comparison, two longitudinal gage responses at midpanel on
the top surface of the skin of the panel with the tall stiffener,
thick flange, and quasi-isotropic skin (Panel A) are also shown.
The responses illustrated in Figure 2.18 are typical of those
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50
measured on the other panels. The strain responses of the symmetri-
cally located gages in each case were very similar. This similarity
in magnitude and overall trend in response was gratifying. It in-
dicated that, on-the—whole, the test apparatus and panels were be-
having within normal expectations.
Chapter 3.l
EXPERIMENTAL RESULTS ANDDISCUSSIONOVERVIEN
OF RESULTS AND DISCUSSION
The test results were examined from two basic and important view-
points. The first viewpoint was to examine the test results to deter-
mine the deviation of the test conditions and panel response from the
ideal case of a perfectly flat, perfectly clamped panel. This
viewpoint is important because in many cases the ideal situation,
often the situation modeled, and the actual situation have subtle
differences due to manufacturing and, in this case, the fixturing and
the test methodology. The second viewpoint was to examine the test
results to determine the primary responses of the panel to the
pressure and inplane loadings. Implicit in the latter was an
examination of the results to determine important differences in skin
and stiffener interactions among the various panels. These two
viewpoints overlapped in that the panel initial conditions and degree
of deviation from the ideal responses also depended on the panel
configuration. Conversely, the panel responses for the various
configurations depended on the deviation from the ideal conditions.
In the following paragraphs the results are presented and discussed
within the context of these two viewpoints and those areas of overlap
are discussed as they occur.
TEST CONDITIONS DEVIATING FROM IDEAL CASE
One prominent deviation from the ideal condition of a flat panel
5l
52
was created by the design of the clamping and vacuum sealing part of
the fixture. This occurred for all tests. As the panel was clamped
between the clamping bars and vacuum plate, the 0-ring contacting the
panel just inside the clamping bar forced the panel to bow upward.
This effect is shown in an exaggerated sense in Figure 3.1. This
upward bowing was due to the fact that the 0-ring, by its design, did
not compress to be perfectly flat. The actual pretest out-of-plane
deflection measurements for the various panels tested reflect this
initial out—of—plane condition. The pretest longitudinal and
transverse profile measurements are shown in Figures 3.2 through 3.6
for the lightly preloaded condition. The data shown in these and
subsequent deflection profile figures are the raw data. Extraneous
data points, recorded as the DCDT was lifted over the stiffener for
the transverse profiles, have been removed. The data points at the
center of both the longitudinal and transverse profiles were set at
zero deflection in the pretest profiles. Also, as seen in Figure
2.13, the rail was supported on the stretching frame as the profiles
were measured. In this arrangement the rail was not parallel to the
plane of the panel. As a result, the profiles appeared to have a
slight slope, typically only 0.0005 (in./in.), which was exagerated by
the scale of the figures. So, for clarity the data was rotated about
the center point to remove the slope component. As seen, in figures
3.2-3.6, the initial bow was on the order of the panel thickness,
roughly 0.050 in. for the unstiffened panel and 0.025 in. for the
stiffened panels. Because of initial upward bending, the panels had
an initial behavior more closely approximating a shallow shell than a
~
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60
flat plate. This is supported by the membrane strain response of the
panels, as measured with back-to—back gages near their edges. As an
example, membrane strain responses from the unstiffened panel are
shown in Figure 3.7. (Such response was also discussed in conjunction
with Figure 2.18.) The membrane strains initially decreased with
increasing pressure, then increased. Such behavior corresponds to the
initial compressive membrane strain response of a shallow shell prior
to buckling, or snap—thru. It should be noted that no audible "oil
canning" or other distinctive snap was heard during the testing.
Another aspect of this panel bowing was the offset of the initial
strains. This is particularly evident when examining the bending
component of the initial strains. As was described earlier, the
strain gages were zeroed prior to the application of any inplane
preload and prior to the clamping. Any deformation due to clamping or
preloading is reflected in initial strain readings. Since the
curvature induced by the bowing was not uniform over the area of the
panel, as indicated by the pretest shapes in Figures 3.2 thru 3.6, the
initial strain readings after clamping were not uniform from point to
point on the panel. The initial bending strains at the top surface of
each of the panels tested and for the lightly preloaded condition are
overlayed in Figure 3.8. In Figure 3.8, a positive longitudinal
strain corresponds to the panel bowing upward in the longitudinal
direction while a positive transverse strain indicates upward bowing
in the transverse direction. These strains indicate, as the pretest
shape measurements do, that the panels were initially bowed. Figure
3.8 shows the strains along four lines extending outward from and
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62
perpendicular to the centerline. Two lines are on one side of the
centerline and two lines are on the other side. On either side,
distance away from the centerline is considered positive.
It should be noted in the pretest shape figures that for the
stiffened panels, the stiffener restrained bowing. The figures
showing pretest out-of-plane deflection versus transverse position
indicate an upside down "N" shape, reflecting the restraining effect
of the stiffener. —
The effect of the bowing on the behavior of the panels was not
investigated any further. However, the magnitude of the bowing, as
measured in the pretest shapes, and the similarity of initial strains,
indicated that the initial conditions of all panels were similar. The
comparisons among panel responses due to pressure loading were made
under the assumption that all panels started from a similar set of
initial conditions. That the initial shape was not flat is considered
very important. Any detailed analytical modeling of the response of
the panel must include the initial effects of the bowing.
The design of the test fixture created another condition which
influenced the behavior of the panels. As pressure was applied, the
panel deflected downward. At a certain deflection the skin contacted
the edge of the recessed area in the vacuum plate. Figure 3.9 illus-
trates this condition. The actual contact was never observed but must
be concluded. Simple calculations involving initial panel shape,
panel deflection due to pressure, and the geometry of the vacuum plate
indicated interference with the edge most certainly occurred.
Restricting the out-of-plane deflection at the edges of the panel
~
64
decreased the effective widthwise and lengthwise dimensions of the“
panel. This resulted in a configuration which may have behaved dif-”
ferently than one with a wider edge spacing. Again, although the
effect of this condition relative to an ideal boundary was not known,
the condition and therefore the effect on each of the panels was be-
lieved to be similar. The responses of each panel were then compared
without further regard to this edge condition.
As was described in the previous section, DCDT's were placed so
as to measure inplane slippage of the panel under pressure load.
Figure 2.3 showed some of the details of this measurement. For the
heavily stiffened panels these DCDT's registered essentially no
displacement for pressures up to approximately 7 to 10 psi. At higher
pressures the panel began to slip and the DCDT's measured an average
of 0.002 in. slippage of each side. The unstiffened and the lightly
stiffened panel had an average of 0.005 in. slippage on each side.
Slippage, detectable within the sensitivity of the DCDT's, began at
approximately 5 psi. This was seen in figure 2.15 with the bilinear
nature of the 25 ft-lb curve. As with the previously mentioned lack
of ideal conditions, this inplane slippage condition was not treated
in a quantitative manner when comparing the results of the various
panels. This was felt to be justified in that the effect of the edge
slippage would be to reduce the stiffness of each panel relative to an
ideal panel with a rigidly clamped edge. This decrease of panel
stiffness is not a significant factor in the comparisons of the six
panel responses made in the·paragraphs to follow.
65
PRIMARY PANEL RESPONSES
Three types of measurements were used to measure the primary
panel responses. These measurements were: out-of-plane deflections;
transverse (perpendicular to the stiffener axis) strains, and; long-
itudinal (parallel to the stiffener axis) strains. Strains on the
skin and on the stiffener were measured. In the following paragraphs
these responses are discussed for the panels with a lightly preloaded
condition. A later section will discuss results for the responses
with the two other preload conditions. Then responses with and with-
out preload will be compared.
OUT-0F-PLANE DEFLECTION RESPONSES
The out-of—plane deflection measurements at the center of the
panel provided a global measure of the effectiveness of the stiffen-
er. Figure 3.10 shows the center (top of web) deflection as a func-
tion of the applied pressure for the four stiffened panel configura-
tions and the center deflection of the unstiffened panel. The panel
designations, i.e. Panel A, B etc., are indicated for each response
curve. The locations of the out-of-plane deflection measurements were
shown in Figure 2.14. These data indicate that, relative to the
unstiffened panel, the stiffened panel with short web had only a
slight decrease in center deflection at any given pressure level.
Compared with the unstiffened panel, the panels with the tall webs had
large decreases in center deflection. All panels with the tall webs
had essentially the same pressure-deflection relation. This indicates
that web height dominated the deflection response of the center of the
66
0.4 ·Panel
D
0.3 ‘ C
EZ_o-E8 0.2G:wcaLBCmL)
BE1 0.1 ^
0.0
0 5·
10 15P (psi)
Figure 3.10 Center of Panel Out-0f—Plane Deflections vs.Pressure Load, Light Preload Case
67
stiffened panels. Flange thickness and skin stiffness provided
negligible effect to the restriction of center deflection.
The skin deflections as a function of applied pressure for the
four stiffened panels are shown in Figure 3.11. Panel designations
are indicated for each curve. The difference in the skin deflections
relations among the panels with the tall webs reflects the effects of
skin stiffnesses on the skin deflection. The panel with the
transversely stiffer orthotropic skin, Panel E, appears to have its
skin ‘deflection restricted the most. The panels with the quasi-
isotropic skins, Panels A and B, had a greater deflection at any given
pressure level. It was felt that differences in skin deflections, at
least at this location, due to differences in flange thicknesses could
not be resolved from the data. Panel C, with the short web, had the
greatest skin deflection of the four stiffened configurations. This
obviously is because the center of this panel deflected considerably.
By comparing Figures 3.10 and 3.11, two important points can be
made. First, it can be seen that the deflections at the center of the
panels with the tall webs were less than the deflections of their
skins. However, for the panel with the short web, the center de-
flection was greater than the skin deflection. As will be seen short-
ly, this translates into significantly different profile of out-of-
plane deflections transverse to the stiffener. Second, and more im-
portantly, it is clear that nonlinear effects are important. Due to
the strong influence of the stiffener, the pressure—deflection re-
sponses at the center of the panels with the tall webs was nearly
linear. However the pressure-deflection responses measured on the
68
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0.3 ‘
Z; Pane1
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Figure 3.11 Skin Out—0f-Plane Defiections vs. Pressure Load,Light Preioad Case
69
skin of these small panels was strongly nonlinear. In fact, the out-
of-plane skin deflection for all stiffened panels and the center
deflections for the unstiffened and lightly stiffened panels appeared
to be nearly bilinear. The initial slope was relatively steep,
indicating large deflections with small increases in pressure load.
This initial deflection was due primarily to bending response. The
slope of the second segment is shallower, indicating less out-of-plane
deflection response for similar pressure load increases. This latter
deflection was a combination of bending and membrane stretching
responses, with the membrane response dominating at the higher
pressure levels.
Figures 3.12 thru 3.16 show the transverse and longitudinal pro-
files of the out-of—plane deflections of the panels measured at maxi-
mum pressure load. The transverse and longitudinal pretest profiles
are also shown. These pretest profiles illustrate the effect of the
initial panel bowing on the out-of-plane deflection measurements. The
DCDT's measuring the center and skin deflections were zeroed
initially. As a result they measured the total change in panel
position, from the initial bowed shape to the position at maximum
pressure load. The maximum deflections shown in figures 3.10 and 3.11
are indicataed on each panel profile in their respective locations.
As was the case when measuring the initial transverse profile,
the DCDT and rail system had to be moved across one side of the
stiffener flange, up over the web, and across the other side of the
flange. Because of this, the data were not taken in°a smooth single
sweep and, in fact, the data reflected the thickness of the flange
70
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75
above the surface of the skin. The flange thickness has been
subtracted from the DCDT data in the flange area and data has been
removed from the profiles that reflect lifting the DCDT over the
web. As a result, the data is not as smooth as the longitudinal
profile data. Nevertheless, the important information is there. The
transverse profiles further illustrate the differences between the
skin and center deflections described above. Specifically, the
profiles of the unstiffened and short web panels both had the same“U"
shaped profile, Figure 3.12 and 3.13 respectively. The maximum
deflections occurred at the center of these panels. In contrast, the
profiles of the panels stiffened with the tall web had a "H" shape.
The maximum deflection of the panels with the tall webs occurred on
the skin, approximately midway between the stiffener and clamped edge,
on both sides of the stiffener. These transverse profiles reflect
another feature, perhaps the most important feature, of stiffened
panel response. In all stiffened panels, there is a change in the
slope and curvatures of the out—of—plane deflections, relative to the
Y-direction, near the edge of the flange. The change in the slopes
and curvatures of the profiles indicate the potential severity of the
transverse bending strains in the area of the flange/skin interface.
For the lightly stiffened panel, with the“U"
shape profile, the slope
and curvature appear uniform in this area. In addition, the sign of
the curvature, appears to remain the same. However, for the panels
with the tall stiffeners, there is an abrupt change. In addition, the
curvature of the skin appears to change sign near the edge of the
flange. This combination of conditions would seem to be detrimental
76
to interface stresses.
Transverse profiles of the panel with the quasi-isotropic skin,
tall web, and thick flange (Panel A), and the panel with the same
stiffener· but an orthotropic skin (Panel E) are very similar. Any
effect of the skin stiffness on the deflection response cannot be
discerned from these profiles. However, the profile of the panel with
the quasi-isotropic skin, tall web, but thinner flange (Panel B) in
Figure 3.16 had not as deep a "w" as the other two panels with the
tall webs. This indicates a less severe transverse bending gradient
may have existed for this panel relative to the other two and this
would be due to having a thinner flange.
Symmetry of the profiles indicates that no twisting of the stif-
fener occurred. Due to the presence of D16 and D26 terms in the skin
stiffness matrix, a small amount of twist would be expected under
these loading conditions. However, imperfections in the stiffener or
skin, or an imperfection in the bond between the two would have
resulted in a severe dissymmetry of the profile. The symmetry of the
profiles also indicates the symmetry of the boundary conditions.
The longitudinal loaded profiles of the stiffened panels in
Figures 3.13, 3.15, and 3.16 show distinct inflection points
(reversals of curvature) along the length of the stiffeners. These
profiles were made by moving the DCDT along the rail and measuring the .
deflection at the top of the stiffener web. The stiffener web
extended above the clamping bars on the short end of the panel. This
allowed the measurement of the deflected shape to be made up to and
including the clamped edge. For the stiffened panel in Figure 3.14
77
the data were taken on the flange and so information is lacking near
the ends of the panel where the clamping bars interferred with the
measurement. For the unstiffened panel the inflection points occur
very close to the ends of the panel, out of the range of the
measurement. The inflection points in these longitudinal profiles and
their locations relative to the ends of the panel are felt to be im-
portant indicators of skin/stiffener interactions. This interaction
will be discussed-further in paragraphs to follow.
TRANSVERSE RESPONSES
A second type, or category, of measurement of primary response
was the measurement of the transverse bending strains in the vicinity
_ of the stiffener flange and skin interface. Of major interest were
both the magnitude of the strains and the strain gradients. By the
llatter is meant the change of strain with respect to the transverse
coordinate, Y. The discrete nature of the strain gage measurements
resulted in having to define the gradient as the difference in the
strain readings from the flange strain-gage location to the skin
strain-gage location. The flange strains were measured using back-to-
back strain gages, one mounted on the top surface of the flange, and
one mounted below this, on the bottom surface of the skin. Strictly
speaking, the strains measured were not flange strains. They were the
strains in the flange-skin thickness. The skin strains were measured
by back-to—back gages, one on the top surface of the skin, the other
on the bottom surface of the skin.· These gage pairs did indeed
measure skin response. For measuring transverse strain response, the
78
gage response axes were aligned perpendicular to the stiffener axis.
The back-to—back pairs were located along two lines, each line being
perpendicular to the stiffener axis. One line eminated from the
quarter point along the stiffener length, halfway between the center
of the panel and the end. The other line eminated from the midpoint
of the stiffener, at the center of the panel. At each of these
locations two gage pairs were located on the stiffener flange, near
the flange edge, and two pairs were located near the flange edge, on
the skin. Figure 3.17 shows the locations of the two lines and the
locations of the strain gages. Also shown in the figure are the
location of longitudinal gages. The responses of these gages will be
discussed in the following sections.
In the discussion of gage response, transverse distance away from
the longitudinal centerline of the panel will be denoted as Y (Y = 0
at the center). No distinction will be made as to whether Y is to one
side or the other of the centerline. Likewise, longitudinal distance
away from the transverse centerline of the panel will be denoted as X
(X = 0 at the center).
The bending and membrane strains measured on the flange by the
gage pair nearer the flange edge, and measured on the skin by the gage
pair on the skin nearer the flange edge, are illustrated as a function
of pressure load in Figure 3.18 thru 3.21. A positive strain
corresponds to downward bending. The various figures correspond to
measurements from each of the stiffened panels. The responses
measured at the panel quarter point, X = 5.0, and at the panel center,
X = 0.0, are shown on each figure. The QF and CF designations
LDC\I
E3~·‘= ” 3%
sg ägg c
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2500Bending · QSStrain CS
1250.: A; .5 CFV!
Q . QF.2z: O (
_ 5 ' 10 15P (psi)
-1250
1000
' MembraneStrain QS
500.E CS _fü
E2
_ä OFä 0 el.-
6 10 CF 15P (psi)
-500
Figure 3.18 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Light PreloadCase, Panei A
8]
2500
BendingStrain
QS]250
E cs¤3U)
uEE Q _ . . GF
5 E ]0 ]5P (psi)
-]250
]000
MembraneStrain
500E QS
EE csU')
E.2 OFZ? 0
6 10 OFi6P (psi)
-500
Figure 3.19 Transverse Bending and Membrane Strains, Measured onthe Fiange and Skin, vs. Pressure Load, Light PreloadCase, Panei E
82
2500
BendingStrain
QS
1250 CS
/ orF
CF0 lr5
’ 10 15 ~P (psi)
-1250 °
1000
MembraneStrain ' QS
500CS
CF
5 10 15P (psi)
-500
Figure 3.20 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Light Preload .Case, Panel B
83
2500
Bending1250 StrainEeus-.4-:
ä QS2
5‘
10 OF 15
P (psi)
CF-1250
1000
CFMembraneStrain
S500 Q_:Es.4-: . _8s.
-.*32: O
5'
10 OF 15P (psi)
-500
Figure 3.21 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, Light PrelzadCase, Panel C
84
correspond to the strain measured on the flange at the panel quarter
point and the panel center, respectively. Similarly, the QS and CS
designations correspond to the strains measured on the skin at ·the
panel quarter point and center, respectively. Figure 3.21 is missing
the strain measurements for the skin at the panel center. Problems
with the gages prevented recording of strain data in this location for
this test.
These· transverse strain responses of the panels have several
features in common. At low pressures, the bending strains increased
more rapidly with pressure than at high pressure. This is seen by the
relatively steep initial slope of the pressure-bending strain re-
sponse. This effect is quite evident in the skin bending response.
The bending strain responses appear nearly bilinear, similar to the
out-of-plane deflections described earlier. This two—stage response
indicates the change from a primarily bending response, at low pres-
sure loads, to combination bending-membrane response, at higher
pressure loads. The transition from all-bending to a combination
response is less evident in the membrane strain response. However, it
can be seen that the initial slope of the membrane strains are, on the
whole, nearly horizontal, indicating little membrane response at the
low pressures. At about 1 or 2 psi, the skin membrane strains begin
to increase steadily with pressure. The only difference in the
bending strain responses among panels is the negative flange bending
strain for Panel C, at the panel center. This is due to the panel
deforming into a "U" shape rather than a "w" shape.
Some of the figures indicate a slight initial compressive
85
membrane strain with increasing pressure. This is due to the initial
curvature and resulting shell-like behavior mentioned earlier. The
strain reversal associated with this compressive effect is about 60
microstrain for the skins. Evidence of the initial curvature in the
panels can also be seen by the presence of the initial non-zero
bending strains. Recall that all strains are referenced to the pre-
clamped state.
Another feature of the panel responses shown in these figures is
the difference between the bending strains measured on the flanges and
those measured on the skin. In all cases the flanges experience very
little bending strain while the skin near the flange experienced a
great deal of bending strain. This change in bending strains with
location is the gradient mentioned earlier.
The transverse bending strain gradients are better illustrated by
showing the strains as a function of their location on the panel. The
bending and membrane strains measured by the gage pairs of Figures
3.18 through 3.21 are shown in Figures 3.22 through 3.29. Each pair
of figures, e.g., 3.22 and 3.23, represents the responses of one
panel. The figures show the strains as a function of distance from
the stiffener web, Y, for discrete pressure loads of approximately 0,
5, 10 and maximum (14.5-14.8) psi. Figures 3.22, 3.24, 3.26, and 3.28
show the strain information at the quarter point location and Figures
3.23, 3.25, 3.27, and 3.29 show the information at the center of the
panels.
The bending strain results have been ranked in order of
decreasing maximum bending strain. The results in Figures 3.22 and
. 86
2500® 0. psi +
Bending E]
l250
E2 dä*.36 A 3·— O E?—··1—·T·<y····—·‘***”‘—*T··—<Er—"*·”*—·‘**‘wE 0
0.5 1.0 1.5_ Y (in.)
-l250
1000
MembraneStrain
600 "' C. .§ E +
E _ E13 AE I [h · „L
'° “’ 'il" '1l
0.6 1.0 G 1.6
Ä
Y (in.)
-500
Figure 3.22 Transverse Bending and Membrane Strains vs. Y Location,Panel Quarter Point (X=5), Light Preload Case,Panel A
87
2500C) 0. psiY E ii. ¤¤¤¤i¤¤ E+ HHS Strain
A1250
c"SL
.
A2. GJ
EE 0 ·w ¢*"'*""***—w*———————·—*——————1. O Q
* 0.5 1.0 1.5Y (in.)
-1250
1000
MembraneStrain
500 .C ·+.,5 EI + .js III3 i LL ~L A.8 I raZ Q,. ,_,_,_,__ __, V; , _ä
10.5 1.0 1.5
Y (in.)
-500
Figure 3.23 Transverse Bending and Membrane Strains vs. Y Location,Pane1 Center (X=0), Light Pre1oad Case, Pane1 A
_ 88
Z500 0 0. psiA , .5 Bending
Strain_ ' +
E]1250
AL.5mL+>3L Q-2 0 qy"*""""'1"""*""""'"1
. GD . Q) ..Z
05A
1 0 1 5Y (in.)
-1250
1000
MembraneA
Strain Q
500+· I
_= ,E]
·+
ä ÜA
-2 0A F1 ,,„ Q)
Z ¢:l'T"'*··*"‘l-'"|
0.5 1.0 1.5Y (in.)
-500
Figure 3.24 Transverse Bending and Membrane Strains vs. Y Location,äanei Euarter Point (X=5), Light Pre1oad Case,
ane1
Ä89
2500 C) 0. psiBending
4_ I4'7 Strain
1250 +c ED•; AI:3-§ 0 EI ZI2 0.5 1.0 C) 1.5
C) Y (in.)
-1250
1000 ‘
MembraneStrain
500ac
䫤g äE E
A A-2 Ia ßaz: 0 CT"‘T““‘“Ef""""E§“““'V'—"TÜ°'°_””"'"""""7
0.5 1.0 1.5Y (in .)
-500 _
Figure 3.25 Transverse Bending and Membrane Strains vs. Y Location,Pane1.Center (X=0), Light Preioad Case, Panei E
90
2500G 0. psi.A Bending‘
Strain+ 14.8
EE1250 IA
EE+· Ü]S A_: 0 0:£ 0 ·r·—·······—···1
0.5 1.0 1.5
Y (in.)
-1250
1000MembraneStrain
~+E1 1-
600 E].E .AE E Ag ‘“ E1 cu;; 0 @E...,.„.£L........„.._„...„0>..3._.„..-..g
0.6 1.0 1.5” E
Y (in.)
-600
Figure 3.26 Transverse Bending and Membrane Strains vs. Y Location,Pane1 Quarter Point (X=5), Light Pre1oad Casa, Pane1 B
_ 91 _
2500 A.‘ G1 0. psi
Bending_ + 14'8 Strain
1250.2. A
E1; üQ A A A.2
0Üz Ü . O ¤ Ö
0.5 1.0 1.5Y (in.)
-1250 .
1000 ' A
MembraneStrain
500 +: + III
E Ü A AO__ _
A(DfüZ
I I 1
0.5 1.0 1.5Y (in.)
-500
Figure 3.27 Transverse Bending and°Membrane Strains vs. Y 1ocation,A
Pane1 Center (X=0), Light Pre10ad Case, Pane1 B
92
2500
gi O. psi
E $6 Bending+_ ]4°5 Strain
1250_:S52 QZ O ‘ O Öl-—-ii.
0.5 1.0 1.5Y (in.)
-1250
1000MembraneStrain
5001
Ei.5 +- .AE E]4-* ' ~”
A. -g 0 0 Q'F"
° Q ~ 0“ G
1-I0.5 6 1.0 1.5
Y (in.)
-500
Figure 3.28 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Light Preload Case,Panel C
93
2500
C) 0. psi
Bending4_ 14:5 Strain
12501:'Ss.-1-»V)
E..9z 0.
(D
0.5 A_ 1.0 ' 1.5 I
E] E1Y (in.)
-1250 + +
1000 MembraneStrain
++·_+ E]
600 E EE A Afü
fsen AE.2 0 OZ 0C)
0.5 1.0 1.5Y (in.)
-500 .
Figure 3.29 Transverse Bending and Membrane Strains, vz. Y Location,Panei Center (X=O), Light Pre1oad Case, ßanei C
94
3.23 are for the panel with the tall web, thick flange, and quasi-
isotropic skin (Panel A). This panel exhibited both the highest
bending strain and largest bending strain gradient. The results in
Figures 3.24 and 3.25, for the panel with the tall web, thick flange,
and orthotropic skin (Panel E) show some decrease in the maximum
bending strains and the bending gradient relative to the panel in
Figures 3.22 and 3.23. This decrease may be attributed to the
orthotropic skin. The orthotropic skin is somewhat stiffer in
transverse bending than the quasi-isotropic skin and produces a
smaller change in bending stiffness from the flange to the skin, and
therefore smaller maximum bending strain magnitudes. Figures 3.26 and
3.27 show results for the panel with the tall stiffener, thin flange,
and quasi-isotropic skin (Panel B). The maximum bending strains for
this panel as shown in the figures were approximately equal to those
for the orthotropic panel (Figures 3.24 and 3.25). The gradient of
bending strains between the flange and skin was reduced relative to
the orthotropic panel, however. 'The jump in bending strain was re-
duced because of the increase in bending strain in the less stiff
flange.
Comparing the results in Figures 3.26 and 3.27 with Figures 3.22
and 3.23 provides an even more striking indication of the effect of
the flange thickness on the magnitude and distribution of the
transverse bending strains. By reducing the flange thickness by half,
from 0.08 to 0.04 in., with all other parameters being the same, the
maximum bending strain measured on the skin was reduced from 2250 to
1400 microstrain. The gradient between the stiffener flange and skin
95 _
was reduced from 2150 to 1140 microstrain.
The results for the panel with the short web, thick flange, and
quasi-isotropic skin (Panel C) are shown in Figures 3.28 and 3.29.
These bending strain distributions indicate a completely different be-
havior than shown in the previous figures. The bending strains at the
stiffener quarter point, Figure 3.28, were relatively uniform, with
the flange having a moderate compressive bending strain (150
microstrain) in its top surface. The bending strains at the stiffener
midpoint, Figure 3.29, show the flange had a relatively strong
compressive bending strain in its top surface. Problems with the
gages on the skin next to the flange prevented strain measurements in
this location. As a result, observations on the bending gradient
could not be made. The bending strains which were recorded indicate
that at the center of the panel the entire transverse out-of-plane
deflection profile of the panel was concave upward. At the quarter
point the profile was in a transition between the all concave "U-
shape" to the "N-shape" exhibited along the entire length of the other
panels stiffened with the tall webs.
Thei bending strains on the flange edge and the skin near the
flange, at the panel quarter point and panel center, are sumarized in
Table 3.1 for all of the panels. Both the strains at the maximum
pressure loads and the initial, or zero pressure condition strains,
are listed in the Table. The difference between the flange and skin
strain readings at maximum pressure for each of the panels is shown in
the Table as A Max. To account for the nonzero strains at zero
pressure load, the difference between the change in strain readings,
96
Q
S-!N
Q 1.0 O LO 1.0 Q111 M N Q Q N 1.0 1
cn Q M Q M M Q 1.0 Q 11.1.1 C N 1-1 1-1 N 1-1 1-1
ä 2¢ 1.1.1 Q2 5 <=·1-1 1.1.°'° L|.¢NE
•--1 Q Q Q 10 1.0 Q QQN- 10 Q Q N 1.0 1.0 18 >< 1-1 1-1 M Q Q Q 1N 1-1 1-1 1-1 -1*0eu <0
*171 11.1gz Q Q: Q LD O Q Q Q1U Q N LD Q Q Q
·*·° .: ·1—1 1-1 M 1-1 1-1 N M 1-1·¤ Q 1Q•!'.1
1.1.1'° Q 0 Q O Q 10 O 1.0 10
N z L Q 1.0 1.0 N 1.0 N NU1 GJ 1-1 1-1 1-1¤ N 1 1 1 1 1 1 1 11** LL|'“
1.'3 1.0gg >< Q Q Q L0 10 Q 10 N
10 Q 1.0 Q N N 1.0 N 1-1
C Z 1-1 N 1 1-1 1-1 N 1-11x
-1.n¤ 1.1.1O cw Q LD Q Q LD Q
1: N N Q 1-1 N 10 1W 111 Q Q 1D Q N N M 11: .: N N 1-1 N 1-1 1-1"' Q15L-1-1
cnz 0 Q 1-0 O Q Q 1.0 LD
O1 1- L N N so M .-1 N N 1O x cu N Q N 1-1 N 10 1-1 1
°•" 1/1 N 1 1 1 1 1 1 1*0ccuQ
Q Q Q Q Q Q 1.0‘*·>< LO LD Q Q O Q N 1
O 1U N 1D Q M Q N .-1 1 111Z N 1-1 1-1 N 1-1 1-1 U1
>~ 1:‘- 1UE 1.E 1- mm3 111 QQ
1/1 c <1: 1.1.1 Q Q <: 1.1.1 Q Q cc?E ***2*1 1.1.Q
><Q, Z/N • c"'
•—•C L • C 1·1-·¤ 1.1§·1- 111 c L ·1- .14‘¤
v1 eu .1-1 -1- 111 cm1* ¤:1—L L .1-1 Q -1-111
1.1.110.1-1 •¤ 1.0 : II .21:0> en :1 II ev >< mcmuc Q1 >< Q ><1¤zzL eu.:<•—•1.1 r- +-1 1* IQZ2? G) C G)1-zz C 11- c AN;
LIJ‘¤’ ¢¤ O 1U •—•¤·IQ ¤. 1:. 1:1. vv
97
from zero to maximum pressure, on the flange and the change in straine
readings, from zero to maximum pressure, on the skin is shown in the
Table as the A Change. Both of these measures of the gradient in
bending strain from flange to skin rank the panels in the same order
of decreasing gradient, only the magnitudes of the gradients are
affected. It is not evident which of the measures of gradient is more
representative of the panel response. To determine this, a further
- investigation of the effect of the initial conditions would be
required.
The measured deflection profiles of the four stiffened and one
unstiffened panel, which were shown in Figures 3.12 through 3.16,
support in a qualitative sense the quantitative observations made with
respect to the bending strain magnitudes and gradients. The deflec-
tion profile of the panel with the tall web, thick flange, and the
quasi—isotropic skin (Panel A) indicates the steep strain gradient due
to the relatively large change in curvature at the flange/skin
intersection. The relatively low resolution of the profile shape
measurements prevented the ranking of the three stiffened panels with
tall webs with respect to their local bending strain magnitudes and
gradients. However, the behavior of these panels relative to that of
the panel with the short web is very obvious in these profiles. The
bending stiffness of the panel with the short web was insufficient to
restrain the skin deflections locally. As a result, the panel
deformed in the concave "U-shape" mentioned above, similar to that of
the unstiffened panel. This results in the bending strain
distribution shown in Figure 3.29.
98
The membrane strain components associated with the transverse
strains shown in Figures 3.22 thru 3.29 indicated a sudden increase in
the membrane strain from the flange to the skin. This response can be
explained by the step-decrease in the thickness from the flange to the
skin. The change in thickness causes a step decrease in the inplane
stiffness and resulting sharp increase in membrane strain. The jump
in strain is apparent in all of the panels with tall webs, Figures
3.22 thru 3.27. This is also seen in Figure 3.28 at the quarter point
of the panel with the short web. The strain magnitude and jump in
strain from flange to skin in each of these figures are similar enough
to make relative comparison difficult. The most apparent difference
in response occurred for the panel with the short web and shown in
3.29. As mentioned earlier, a problem with the gages on the skin near
the flange in this test prevented data acquisition at this center
location. As a result, conclusions about the gradient cannot be
made. However, the membrane strains in the flange and skin at the
center location were much greater than they were for the other pan-
els. This was related to the much greater center deflection of this
panel, relative to the more heavily stiffened panels. The increased
deflection resulted in the increased membrane strain in the panel.
LONGITUDINAL RESPONSES _
The third category of primary response measurements was the
measurements, particularly strain measurements, associated with longi-
tudinal strain gradients imposed by the stiffener. The principle
effect of the stiffener on the skin along the length of the stiffener
99
can be illustrated by looking at the longitudinal strains on the bot-
tom surface of the panel along the centerline. Figures 3.30 through
3.34 show these strains at discrete pressure loads of approximately 0,
5, 10, and maximum (14.5-14.8) psi. The strains are indicated with
respect to the locations at which they were measured. (Recall from
Figure 3.17 that X=0 is the center of the panel and X=8.5 in. is near
the end.) The unstiffened panel (Panel D) response shown in Figure
3.30 indicates that the bottom surface strain was a tensile strain at
the center and it increased to a maximum value near the end of the
panel. This tensile strain on the bottom surface of the panel was a
combination of the positive bending strain at this surface and the
tensile membrane strain due to the stretching on the panel between the
clamped ends. This latter component of strain was due strictly to
nonlinear effects.
The presence of a stiffener along the centerline of the panel can
significantly change this strain response. This is shown in Figure
3.31 for the panel with tall web, thick flange, and quasi-isotropic
skin (Panel A). At the center of the panel the bottom surface strains
are tensile. At the end of the panel, instead of being tensile, as
they were for the unstiffened panel, the strains on the bottom surface
were compressive. The strains change sign at approximately the
quarter point of the panel. This strain distribution also resulted
from a combination of bending and membrane strains. However, along
the centerline beneath the stiffener these strains are strongly
influenced by the deflection behavior of the stiffener. This can be
seen by referring to Figure 3.35. In this figure the deflected Shape
. ]00
2000”
_
0 0. psi +A 5.
·E] l0.+ l4.7
‘ [B
· *+
l000
E1
A
A_:Es.+-»U)os.-22 O
2. 4. . .6 8 G) TO.X (in.)
—]00O
Figure 3.30 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0), ALight Preload Case, Panel O
101
2000
ID 0. psiA 5.ID 10.+ 14.6
1000 ·
.2 + ‘·g Iä ID.2
A‘A. iäE: .A0 .
2. 4. 6. Q 6. A 10._ E]
X (in.) 4_
-1000
Figure 3.31 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),Light Preload Case, Panel A
102
2000G1 0. psi
5.El 10.4- 14.7
1000 „:
.3w {Il0s.A
Z
0 O OA
2. 4. 6. Q 8.4 10.E]
X (in.) _?
-1000-]
Figure 3.32 Longitudina1 Strains on the Bottom Pane1 Surface,vs. X Location, A1ong the Pane1 Centeriine (Y=O),Light Pre1oad Case, Pane1 E
103
’ 2000
CJ O. psiA 5.E1 10.+ 14.8
1000
E +U
«¤5g ESIs.
-.9 AZ
O0 A
2. 4. 6. 6. A io.X (in.) _ III
U
+
-1000 -
Figure 3.33 Longitudinal Strains on the Bottom Panel Surface,. vs. X Location, Along the Panel Centerline (Y=0),
Light Preload Case, Panel B _
104
2000·
0 0. psiA 5.‘ E] 10.+ 14.5
1000 +. El
.= A +ZGP mU)o
E 0 O
2. 4. 6. 8. 10.
X (in.)
A
E1+
-1000
Figure 3.34 Longitudinal Strains on the Bottom Panel Surface, .vs. X Location, Along the Panel Centerline (Y=0),Light Preload Case, Panel C ·
105
zanUUr:E
<QV
:°!'
3O.:ms.tv „c3w-P
ß .‘¤U4-•U2u-3u-O:0.:OL·•··3
<.> uuU6s.>us-mz::<.>IV•—U-•—•O
anV M
‘ Mevs.
CQ ä· E
l06
of a stiffener is shown. Attached to the flange is a thickness of
skin. The neutral bending axis of this combination of stiffener and
skin is shown. Over the length AB, the stiffener is curved
downward. This forces the flange and the skin attached to it into
compression. Over the length BC, the stiffener is curved upward.
This forces the skin into tension. Oepending on the stiffness of the
stiffener, the inflection point, B, may be closer or further from end
A than illustrated. 'This only determines where under the stiffener
the skin changes from compression to tension. This effect of the'
stiffener forcing the response of the skin is felt to be important.
It indicates that shearing stresses between the stiffener flange and
skin are important. Many studies have been conducted with the
assumption that it is the tensile stresses between the skin and flange
that are responsible for local failures. The data of Figures 3.30-
3.34, and the illustration of Figure 3.35 indicate shear stresses
probably aggrevate the effect of tensile stresses.
Another indication of the effect of the stiffener can be seen if
the skin deformations away from the stiffener are examined. The
difference in stiffener and skin deformations is shown in Figure
3.36. This figure shows the longitudinal deflection profile of the
stiffener and the longitudinal deflection profile of the unstiffened
skin along a line approximately 2.5 in. from the stiffener web, about
half way between the longitudinal clamped edge and the stiffener.
These profiles were measured on the panel with the tall web, thick
flange, and quasi-isotropic skin. The profile of the skin shows it to
have had a concave upward shape along the entire length. The
TO7
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transition to the concave downward curvature shape, or the inflection
point, occurred close to the clamped end, out of the range of the
measurement. The stiffener profile, however, shows the transition of
the curvature to have occurred at approximately the quarter point of
the length, as illustrated in Figure 3.35. The fact that the stif-
fener changes curvature at a different longitudinal location than the
skin changes curvature is important. The difference in the location
of the inflection points leads to transverse gradients in the
longitudinal strains.
To measure this transverse gradient of longitudinal strain, back-
to-back gages were mounted with their active axes aligned parallel to
the stiffener axis. These gage pairs were spaced along two lines
extending perpendicular to the stiffener axis, one at 1 1/2 inches
from the clamped end and one at the center of the panel. The location
of these longitudinal gages is shown in Figure 3.17. The panel with
the tall web, thick_flange, quasi-isotropic skin was not instrumented
in these locations. Gradient studies were initiated after this panel
had been tested. Transverse gradients of the longitudinal strains
were therefore not recorded for this panel. The unstiffened panel had
gages in slightly different locations than shown in Figure 3.17. The
locations were Y = 0.0, Y = 1.5, and Y = 3.5 in.
The membrane and top surface bending components of the strain b
measured by these gages are shown as a function of pressure in Figures
3.37 through 3.40 for the unstiffened panel and three of the stiffened
panels. The designations, 1E, 2E, 3E, 1C, 2C, 3C, refer to locations
of the strain measurements. E and C designate the X-location, near
109
l1E1000 ZE
MembraneStrain
1C
soo 2C
.2 3C¤·:
:4y/E:3EUT2 ¤ 5
-.9Z: 5 10 15
P (psi)
-500
700. Bending
Strain 2C
··* 3C(U
_; 10 P (psi) 15E . 5 TE2E
-700 3E
-1400
V Figure 3.37 Longitudina1 Membrane and Bending Strains vs.Pressure Load, Light Preioad Case, Pane1 D
110e
1000
Membrane 2C500 Strain IC
.E 3CI5
fsU)E 3E.2Z O :x¤·*·'
" 5 _ 10 15P (psi)
ZE
500E
1E
7003C
Bending.E Strain 2CE1;
O ____ L___9-— —e .-
.2Z:5 10 15
P (psi)1C
-700 - ZE
1E
I3E
-1400
Figure 3.38 Lengitudinal Membrane and Bending Strains vs.Pressure Lead, Light PreIead Case, PaneI E
l]]] '
]00OMembraneStrain ~
]CZC „
500
3C. P/···· 3E
fs,90.2
5 10 i5Z P (psi)
ZE
-500 ]E
700 gc' Bending ig
Strain igZC
EEig 0oL.2 5 ]0 ]5E p (psi) 2E
-700 E 3E
-]400 ·
Figure 3.39 Longitudinal Membrane and Bending Strains vs.Pressure Load, Light Preioad Case, Panei B
112
1000
MembraneStrain gc500 _ 1C
3C.E ,5 3EE
.E: 5‘
10 15P (psi)
ZE
-500
1E700 BendingStrain
ZE.E 3C
EE10 Z6 15E?
5 P (psi). 1C
-7003E
-1400
Figure 3.40 Longitudinal Membrane and Bending Strains vs.Pressure Load, Light Preload Case, Pane1 C
113
the End of the pane1, X = 8.5 in., and at the Center of the pane1, X =
0.0. For the stiffened pane1s, the numbers 1, 2, 3, refer to the Y-
Tocation of the strain measurements: 1 = on the f1ange, Y = 0.625in.;
2 = on the skin, Y = 1.125in.; and 3 = on the skin, Y = 2.5 in. For
the unstiffened pane1 the corresponding Y—1ocations are: 1 = at the
center, Y = 0.0; 2 = away from center, Y = 1.5 in.; and 3 = near the
edge, Y = 3.5 in.
Looking at Figure 3.37 it can be seen that the membrane strain in
the unstiffened pane1 was tensi1e and increased with increasing
pressure 1oad in each of the Tocations monitored. It can a1so be seen
that the greatest membrane strain was measured at the center1ine of
the pane1 near the pane1 end (1E). The membrane strain decreased away
from the center1ine, toward the c1amped 1ongitudina1 edge (3E). There
was a sma11 amount of strain reversa1 due to initia1 bowing of the
pane1. Comparing these measurements with those from the stiffened
pane1s in Figures 3.38 through 3.40, the effect of the stiffener on
the 1ongitudina1 response of the pane1s can be seen. The membrane
strains near the pane1 end in the stiffener f1ange and in the skin ·
near the stiffener f1ange (1E and 2E) were increasing compressive
strains with increasing pressure 1oad. Away from the stiffener at Y =
2.5 in. (3E), the skin can be seen to have had an increasing tensi1e
membrane strain with increasing pressure 1oad, as was the case for the
unstiffened pane1 response. At the center of the pane1 (1C, 2C, 3C)
the membrane strain can be seen to be uniform1y increasing with
pressure, simi1ar to the unstiffened pane1 response. The magnitude of
the strains in the center of the stiffened pane1s are somewhat reduced
due to the stiffener restraint of membrane stretching.
114
The 1ongitudina1 membrane and bending strain distinctions are not
precise in describing the strain components in the stiffener f1ange.
The cross-sectiona1 areas of the stiffeners and skin under the f1anges
for each of the three stiffener configurations tested in the investi-
gation are shown in Figures 3.41, 3.42, and 3.43. The neutra1 axis
and f1ange/skin centroid are indicated for each cross—section. The
greater the distance the upper f1ange surface and 1ower skin surface
are from the cross-section centroid, the greater the inf1uence of
stiffener bending on the surface strains. Neglecting the effects of
geometry changes due to transverse bending of the f1anges and skin, it
can be seen that for the short web stiffener in Figure 3.41, the top
surface of the f1ange is above the neutra1 axis. The top surfaces of
the f1anges for the two stiffeners with ta11 webs were both be1ow the
neutra1 axis. As a resu1t, a 1ongitudina1 concave downward curvature
in the stiffener wou1d produce a tensi1e bending strain in the top
surface of the f1ange of the short web stiffener. In contrast, the
same concave downward curvature wou1d produce a compressive bending
strain for the top surface of the f1ange of a stiffener with a ta11
web. This effect is seen in the p1ots of bending strains shown in
Figures 3.38 through 3.40. The bending strains were compressive in
the f1anges of the stiffeners with ta11 webs, IC and IE of Figures
3.38 and 3.39. In Figures 3.40, near the end of the pane1 (IE) with
the short web stiffener, the bending strain was tensi1e on the top of
the f1ange.
To better i11ustrate the transverse gradients of 1ongitudina1
strain, the strain data is shown as a function of the gage's trans-
115
-n1-In-.08· Centroid Of F1ange/Skin
Cross Section.08 50· .1025F1ange °04
:¤:::::¤¤=|=:: .„;;;;;;;s==;======- _
sk1n-/I I I I1.50 06Tota1 Cross Section‘Neutra1 Axis
(A11 Dimensions In Inches)
Figure 3.41 Geometry of Short web, Thick F1ange Stiffener
116
—I—-I-¤— .08
1.50
Total Cross Section
08 Neutral Axis
Flange —\·04 .358
I 06Centroid Of Flange/SkinCross Section
(All Dimensions In Inches)
Figure 3.42 Geometry of Tall web, Thick Flange Stiffener
· 117
-•T-T*——.08
1.60
Tota1 Cross SectionNeutra1 Axis
.04 IF1angeX04 .420
skin/I 1.60 l.O4Centroid Of F1ange/SkinCross Section
g (A11 Dimensions In Inches)
Figure 3.43 Geometry of Ta11 web, Thin F1ange Stiffener
118
verse Tocations. The strain data from the gages on the bottom surface
of the skin are i11ustrated. Figures 3.44 through 3.47 show these
bottom surface strains measured at 0, 5, 10, and maximum (14.5-14.8)
psi pressure 1oads and i11ustrated with respect to the gage 1ocation
a1ong the transverse 1ines shown in Figure 3.17.
The character of the bottom surface strains at the center of the
pane1 is very simi1ar for a11 pane1s. The strains are tensi1e and
increase with increasing pressure. The magnitude of the tensi1e
strains decreases moving from the center1ine (Y=0) toward the
1ongitudina1 edge (Y=3.5). The pane1 with the short web shows a
s1ight1y higher tensi1e strain under the stiffener.
The character of the bottom surface strains at the end of the
pane1 ref1ect the stiffener forcing the skin into compression near the
center1ine. Moving away from the stiffener the skin strains become
tensile, ref1ecting decreasing inf1uence of the stiffener. The
magnitudes of the strains at the end increased with increasing
pressure. The magnitudes of the strains for Pane1 E were s1ight1y
higher than for the other two stiffened pane1s. 0bvious1y, the
unstiffened pane1, Pane1 D, did not show these compressive strains.
The presence of this transverse gradient of the 1ongitudina1 strains,
and the fact that it increased with increasing pressure 1oad, suggests
this may be a significant prob1em area of stiffener' and skin
interaction.
119
2000° ¤® 0. psi
+ A 5. Panel EndEJ 10. (x=8.5 in.)+ 14.71000 E
.2 +E A El4-*
Q AA·U
0 I
GJ . G)1.0 2.0 3.0 4.0 5.0
Y (in.)
-1000
2000
Panel Center(X=0.0 in.)
1000EQ +4-* E] I-A 0 ..2 m fiz 0 ‘ •’°“"”‘—'“*"V“”"‘*“‘°"“«‘“*‘*"·=/""‘1"""—“‘“*‘“*‘”";
1.0 2.0 3.0 4.0 5.0Y (in.)-1000 ·
Figure 3.44 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LightPreload Case, Panel D
- 120
· 2000 0 0. psi
Pane1 Endin.)
+1000 A· + 4
s. A E15 Eä A AE 01 ä -**--1-·—* -1
1.0 2.0 3.0 4.0 5.0Y (in.)-1000 · ‘
2000 .
Pane1 Center(X=0.0 in.) A1000 ‘
E ‘·¤ +AE ~ + +E A A A E ._E oA[§———A-*·"‘· ,—-—-—@——-—,—————e»-———-—,—-—-Ej--—--—„ -- ,
1.0 2.0 3.0 4.0 5.0
]
Y (in.)
-1000
Figure 3.45 Longitudina1 Strains on the Bottom Pane1 Surfaceat the Center and End, Vs. Y Location, LightPre1oad Case, Pane1 E
121
2000LD O. psiA 5. Pane1 EndLD 10. _ .+ 14.8 (X—8.5 in.)
1000 +.E E1E + +A
A A°”0 · a
ll Q! 1.0 2.0 3.0 4.0 5.0Y (in.)
-1000 « „
2000Pane1 Center(X=0.0 in.)
1000E
_ E + + · ,Ü m E1 E4
+ ·O -!—L A A A E Ü]U Q L;}
E 0 Q Q (0 F1 ...|A_ {L1 __ ___!
1.0 2.0 3.0 4.0 5.0Y (in.)
-1000
Figure 3.46 Longitudina1 Strains on the Bottom Pane1 Surfaceat the Center and End, vs. Y Location, LightPre1oad Case, Pane1 B
122
2000 0 0. psiA 5. Pane1 End[J 10. _ .+ 14.5 (X-8.5 in.)1000 +
C.E E] ,+S *' A. IE·§ 0 El .A2: _ CD C) *
A E$1 1.0 2.0 3.0 4.0 5.0
Y (in.)-1000
2000 ·Pane1 Center(X=0.0 in.)
1000 +E 1:1 E +E5 A E1S ^· A. +s. I] _,_.2 A1 51Z Ü ’l·‘·r——·€:·“»·*—;······—···@···———·;————··~:Ö··— ·*··—1l······—·—·————g
1.0 2.0 3.0 4.0 5.0
Y (in.)-1000 _Figure 3.47 Longitudina1 Strains on the Bottom Pane1 Surface
at the Center and End, vs. Y Location, LightPre1oad Case, Pane1 C .
l23
STIFFENER STRAINS
Back-to-back gage pairs were attached to the stiffener webs of
each panel. These gages measured the state of strain in the stif-
feners during the pressure loading and provided a means of determining
if buckling of the web was imminent or had occurred. The gage
patterns for the stiffener web are shown in Figure 3.48. Note the
numbering of the location, i.e., 1, 2, ..., 6. The longitudinal gage
pairs indicated any out-of-plane bending associated with any
longitudinal buckling. The transverse or vertically oriented gages
indicated any bending associated with local buckling or web crippl-
ing. These two bending modes are illustrated in Figure 3.49.
The membrane and bending strain components for each panel at the
three preload levels are shown in Figures 3.50 through 3.61. The"M“
_
or "B" following the strain gage location number indicates whether a
membrane or bending strain was being measured. The absence of any~
significant bending strain in any of the tests indicates that no
stiffener buckling occurred.
The mode of stiffener deformation may be inferred from these
strain responses. The longitudinal membrane strain responses of the
tall webs in Figures 3.50 through 3.58 were all nearly linear. This
indicates that the mode of deformation was primarily bending. The
membrane responses of the short web stiffener in Figures 3.59 through
3.61, were distinctly nonlinear. Also, as shown in these figures for
the short web stiffener, the tensile longitudinal membrane strains
measured near the ends of the stiffener continued to increase with
increasing pressure. The compressive membrane strains dt thé Center
124 ·
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125
LONG ITUD I NAL BEND I NG
TRANSVERSE BEND I NG
Figure 3.49_ Iiiustration of Longitudinai and Transverse BendingModes of the Stiffener web
126
5000
2500 . lM. __?
4
,///
. ,/
E2B,6B 4M
m
äGM
,,_ „
5.z0 15
P <¤Si> 6M1B,4B,5B
3M
-3000 .
Figure 3.50 Stiffener web Membrane and Bending Strains vs. PressureLoad, Light Preload Case, Panel A
127
5000 .
· 1M2500 ZM
eg 2B v
lg M6B 4M
th
g 6M
5 P(ps1) 10 16,46,6B 51415— 3B
M 3M
-3000
Figure 3.51 Stiffener Web Membrane and Bending Strains vs. PressureLoad, Biaxial Preload Case, Panei A
128
5000
1M
2500 ‘ ZM
E¢U 6ä B 4MoÖ ’ 6ME 0
_
4B,5B
3M
-3000
Figure 3.52 Stiffener Web Membrane and Bending Strains vs. PressureLoad, Longitudinal Preload Case, Panel A
129 -
5000
2500 ‘1M2M
EE ,.4* 4***.2U __,,..
3B°" 0 1¤¤1r-··-··—'”'
_“—q_
5 48 10 1B,2B 15
P (psi)
3M
-3000
Figure 3.53 Stiffener web Membrane and Bending Strains vs. PressureLoad, Light Pre1oad Case, Pane1 E
130
5000U
Z500‘
1MZM
E4-*ll'!
E / ""2 g P 2B,3B,4B 1B.v2: -pn-—
{5 10 15
P (psi) _
3M
-3000
Figure 3.54 Stiffener web Membrane and Bending Strains vs. PressureLoad, Biaxial Preload Case, Panel E
‘I3°l
5000
Z500‘
]MZM
E4->U!
4M
E 0 2B,4B lBz5
l0 3B l5 ·P (psi)
3M
-3000
Figure 3.55 Stiffener web Membrane and Bending Strains vs. PressureLoad, Longitudinal Preload Case, Panel E
132
5000
2600‘F
’7//03
Eb 4MU'!ofg 4B 2B
0 ··5
10 15P (psi) 1B 3B
3Mi
-3000
Figure 3.56 Stiffener web Membrane and Bending Strains vs. PressureLoad, Light Preload Case, Panel B
133
5000
2500“ ' 3
1M,2M
EE«•-> 4M8 IB 2B,4BE 0 — AL- ·-——- —-—·—- ——-———-——-,
5 10 3B 15P (psi)
3M
-3000
Figure 3.57 Stiffener web Membrane and Bending Strains vs. PressureLoad, Biaxial Preload Case, Panel B ·
134
5000 _
2500 ”1MZM
EE-•-> 4MCh
E 4B ZB 1B,2L.Z
0 "5 P (psi) 10 gg 15
'3M
-3000
Figure 3.58 Stiffener web Membrane and Bending Strains vs. PressureLoad, Longitudinai Preload Case, Panei B
135
50002M1M
.& 1Eg 4MO.
3 18,46O 1
,_,__
5 10 15P (psi) 3B
ZB
3M
-3000 C
Figure 3.59 Stiffener web Membrane and Bending Strains vs. PressureLcad, Light Preioad Case, Panei C
136
5000
2M1M
2500 _‘_:
Es.*: amE /,_,j,E
0 >’ ——~?_—.——;———..,, -266* ·——‘*
5 10 15P (pw §§3M
-3000”
Figure 3.60 Stiffener Heb Membrane and Bending Strains vs. Pressure ·Load, Biaxial Preload Case, Panel C
137
5000 _
1M,2MI
2500
•C.
E 4M1 B ,4B
E 0 —·a$7——i ""”“"‘"—"—
5 10 3B 15P (PS1) ZB
3M
73000
Figure 3.61 Stiffener web Membrane and Bending Strains vs. PressureLoad, Longitudina1 Preioad Case, Pane1 C
138
of the stiffener had 1itt1e change in magnitude at the higher pres-
sures. This indicates that the mode of deformation made a transition
from primari1y bending to a combination of bending and membrane stret-
ching.
0
Chapter 4.
PRELOAD EFFECTS, RESULTS AND DISCUSSION
Having described the responses of the lightly preloaded panels to
pressure loading, the effects of the two additional conditions of
preload will now be discussed. As with the light preload, the results
of the preloaded tests were considered from the two viewpoints, namely
the deviation of the panel and test from ideal conditions, and the
primary responses of the panel.
TEST CONDITIONS DEVIATING FROM IDEAL CASE
The preloads applied to the panels had a strong effect on their
initial shapes. Figures 4.1 through 4.5 show the pretest shapes of_
the panels for the biaxial preload condition. Comparison of these
with the pretest shapes of the lightly preloaded panels, Figures 3.2k
through 3.6, shows one of the significant effects of the biaxial
preload. The bowing of the panels was nearly eliminated by this
inplane preloading. Reduction of the initial bowing allowed the
panels to respond more like the response expected for a flat plate.
In particular, the membrane strain reversals at low pressures were
considerably reduced or eliminated. Figure 4.6 shows the membrane
strains measured near the edges of the unstiffened panel with the
biaxial preload. Figure 3.7 showed the strains measured in the same
locations for the lightly preloaded panel. The reduction of strain
reversal with the biaxial preload is readily apparent from these
figures.
139
140
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Figure 4.7 shows the membrane strains from the same locations for
the longitudinal preload condition. Although the reversals were re-
duced as compared with the light preload, they were not eliminated.
The source of these reversals is seen in the pretest shapes of each of
the panels for the longitudinal preload condition, Figures 4.8 through
4.12. From these figures it is clear the longitudinal preload pro-
duced an equal if not greater bowing of the panel than that which
occurred for the light preload due strictly to the clamping alone.
This increased bowing was caused by the inward bending of the doublers
under the application of the longitudinal clevis loads. Figure 4.13
illustrates the doubler bending condition in an exaggerated sense. As
can be seen, the bending resulted from the lack of a solid doubler
along the end of the panel. The inward bending caused the panel to
bow, transversely. This bowing was increased further after clamping
due to the effect of the 0-rings.1
As mentioned earlier the effect these pretest bowed shapes had on
the primary panel responses was not thoroughly investigated. Since
the panels had different pretest bowed shapes for each preload con-
dition, the effect of the preload prestrain and the preload bowing
were interrelated. In the discussion to follow, the effects of the
prestrain and the effects of the bowing were distinguished when
comparing the responses for the different preload levels.
The other aspects of deviations from the ideal conditions were
the same as the light preload case. Contact of the panel with edges
of the recessed area was strictly a function of the vacuum plate de-
sign. Preload did not change this condition. The two factors in-
147
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- 153
Longitudina1Pre1oad
Figure 4.13 I11ustration of the Bending of the LongitudinaiDoub1ers Under Uniform Longitudinai Pre1oad _
l54
fluencing inplane slippage were clamping bolt torque, which was the
same for all tests, and the frame stiffness, Since the lightly pre-
loaded panels "snugged-up" the system, any inplane slippage was re-
acted by the full frame stiffness. There was no dead-zone in which
the panel slipped without restraint from the frame. Additional pre-
load had no effect on the frame stiffness, and again there was no
dead-zone. Hence, the inplane slippage was unaffected by preload.
OUT-0F—PLANE DEFLECTION RESPONSES
The out-of-plane deflections at the center of each of the panels
as a function of pressure are illustrated in Figure 4.14 for the
biaxial and longitudinal preload conditions. The center out-of-plane
deflections for the light preload condition was shown in Figure
3.10. As in Figure 3.10, the panel designations, A, B, C, etc., are
used to identify the curves. The preload condition is indicatediby B
or L for biaxial or longitudinal preload, respectively. Relative to
the other preload conditions, the biaxial preload reduced the center
deflections of the unstiffened panel and the stiffened panel with the
short web. Center deflections of the panels with the tall webs were
also reduced, but only slightly. The deflection responses of the
unstiffened and short webbed panels had the bilinear nature described
earlier. _For these panels, the initial slope for the biaxial preload
tests was shallower than for the other preload conditions. This
shallower slope indicates a stiffer response due, in part, to a
greater membrane contribution from the skin at relatively low pres-
sures. At higher pressures the slopes of the unstiffened and lightly
155
Pane1
0.4 _ _ DL,, L„ Long1tud1na1- Pre1oad
„ B„ Biaxia1— Pre1oad
0.3 ‘CL
B
,_CB
S:.9 0.2 ·.1.:uzu
ZZzuQs.3 .
BL•:
8 ELAL0.1
in
;i"(/5EB
0.0
0 5 10 15P (psi) L .
Figure 4.14 Center of Pane1 Out-0f—P1ane Def1ections vs.Pressure Load, Biaxia1 and Longitudina1 Pre1oad Cases
l56
stiffened panel deflections for the three preload conditions are simi-
lar. The response at high pressure was dominated by membrane stretch-
ing. Since the inplane stiffness of the unstiffened and lightly
stiffened panels were the same, the high pressure responses were simi-
lar.
The center deflection of the unstiffened panel for the longi-
tudinal preload had the largest magnitude of any of the three test
conditions. The greater panel bowing for this preload condition
caused this increase in deflection. The initial slopes of the deflec-
tion response of the unstiffened panel, for both the light preload and
longitudinal preload conditions, were very steep. As discussed ear-
lier, this steep slope was because the response was primarily a
bending response at the low pressure level. During these two tests
the panel had to deflect sufficiently to change from an all concave
downward to an all concave upward shape before the membrane stretching
of the skin became a factor in the response. This was not the case
for the initial response of the biaxial preload case, when the panel
was flatter initially. Any stiffening effect of the longitudinal
preload similar to the stiffening effect of the biaxial preload was
negated by this greater pretest bowing.
The relation between skin deflection and pressure for each of the
stiffened panels for the biaxial and longitudinal preload conditions
is shown in Figure 4.15. The skin deflections measured for the light
preload condition are shown in Figure 3.11. Observation and comments
on these responses parallel those made above for the center deflec-
tions. The skin deflections of the panels for the biaxial preload
157 ‘
0.4
„ LH Longitudina1— Pre1oad
n Bu BiaXia1— Preioad0.3 —
. Pane1
S CLä 0.2E CB‘; ALQ BLEjä EL
0.1 (
_ . BB////’EB
0.005 10 15
P (psi)
Figure 4.15 Skin Out-Of-P1ane 0ef1ections vs. Pressure Load,Biaxia1 and Longitudina1 Pre1oad Cases
l58
were less than for either of the other two preload conditions. The
initial slopes for the biaxial preload cases were shallower than the
other two preload cases, indicating the greater initial membrane ef-
fect seen for the center deflections of the unstiffened and short
webbed panels. The slopes at the higher pressures are similar for all
of the preload conditions.
TRANSVERSE RESPONSES —
Preload also had an effect of the second type of primary response
considered, that is, the transverse bending gradients near the stif-
fener. Figures 4.16 through 4.19, and 4.20 through 4.23 for the
biaxial and longitudinal preloads respectively, show the relations of
the flange and skin membrane and bending strains as a _function of
pressure load. As for the light preload responses, Figures 3.18
through 3.21, these relations indicate several features which the
panel responses had in common.
In almost all cases the bending strains responses in the skin
were somewhat bilinear. This change in slope indicated the change in
mode of response, froni primarily bending to a combination bending-
membrane stretching response. Comparing the skin membrane response of
the biaxial preload with the other two preload conditions, it is clear
the bilinear nature is not as distinct. This is because the response
of the panel with biaxial preload had a larger component of membrane
response at low pressure levels than did the other two preload
cases. Also evident' by comparing strain response among the three
· preload levels is the fact that the biaxial preload stiffened the
159
2500
Bending _Strain QS
CS
1250EEE+5; CFcb OF
EE 0 _ .5 10 15
P (psi)
-1250
1000Membrane _Strain QS
CS500
OC
Q:Fä O
_¤ CFif 0
5 10 15P (psi)
-500
Figure 4.16 Transverse Bending and Membrane Strains, Measured enthe Fiange and Skin, vs. Pressure Lead, Biaxiai PreieadCase, Panei A
160 -
2500‘
BendingStrain
S1250 Qc .E . CSL4-:W
Q ~ CF-22: 0 _
5 ’ 10 15P (psi) QF
-1250 ·
1000
MembraneStrain QS
soo CS_«:ELY? cr2 L2. L2-
/—.2 ° ““‘"’ ” 'P ' OF2* 0
5 10 15P (psi) I
-500
Figure 4.17 Transverse Bending and Membrane Strains, Measured onthe F1ange and Skin, vs. Pressure Load, Biaxia1 Pre1oadCase, Pane1 E
161
2500
BendingStrain
1250 OS:'Q CSL+>8L-22: 0 _
5 10 15P (psi) QF
CF-1250
1000”
SMembrane QStrain
CS
500.5
FE O‘j ' CFL.22: 0
5 10 152 P (psi)
-500
Figure 4.18 Transverse Bending and Membrane Strains, Measured onthe F1ange and Skin, vs. Pressure Load, Biaxia1 PreioadCase, Pane1 B
162
2500
1250 Bending_: StrainEI:U')
u
- · ' CS5 ‘ 10 QF 15
P (psi)
-1250 CF
1000 Membrane CSStrain QS
CF
500_:EI:U')2 PF-25; 0
5 10 15
P (psi)
-500 .
Figure 4.19 Transverse Bending and Membrane Strains, Measured onthe Fiange and Skin, vs. Pressure Load, Biaxiai Pre1oadCase, Panei C .
163 „
2500 Bending QSStrain
i CS
1250 ‘
E ·,‘Q .th
E croE g OF
51
10 15P (psi)
-1250
l1000 ·
Membrane. Strain
500.= QSQ cs«•->U7os..E QFE: 0
5 10 15
CFP (psi)
-500
Figure 4.20 Transverse Bending and Membrane Strains, Measured onthe Flange and Skin, vs. Pressure Load, LonqitudinalPreload Case, Panel A
164
2500BendingStrain
QS
1250 CS_:Eis
‘
g CF OFE 0 — ‘llyl
5 10 15P<pSi>
C-1250
1000
MembraneStrain
500 . QSEE csUi ' -oL.9 O OF
· Ilz? 5 10 CF 15P (psi)
-500
Figure 4.21 Transverse Bendinq and Membrane Strains, Measured onthe F1ange and Skin, vs. Pressure Load, LongitddinaiPreicad Case, Panei E
165
2500
BendingStrain QS
1250
.6CS
E4-*
8 QFS / 5 "E Ü V' CF
5 10 15P (psi)
-1250
1000
MembraneStrain QS500
C
ECS
tig
QF .
E 0 CF
5 10 15
· P (psi)
-500
Figure 4.22 Transverse Bending and Membrane Strains, Measured onthe F1ange and Skin, vs. Pressure Load, Longitudina1
· . Pre10ad Case, Pane1 B
166
2500 _
Bending]250 Strain
.=E5U1o QSI: QF;§ 0
5 ‘ 10 15P (psi)
CF-1250
1000
MembraneStrain
CF
500 QS_:EI:U1 .oS-u
§§ O5 10 15
QF
P (psi)
-500
Figure 4.23 Transverse Bending and Membrane Strains, Measured on_ _
the Fiange and Skin, vs. Pressure Load, Longitudina?Preicad Case, Panei C
l67
initial response. This was also indicated by the out-of-plane deflec-
tions. The longitudinal preload had little effect on the transverse
bending or membrane response. The principle effect of the long-
itudinal preload on the strains was the offset of the membrane
strains, in compression, due to Poisson contraction of the skin.
Also, the membrane strain reversal, due to increased bowing, was
greater for the longitudinal preload case. At higher pressure loads
the slopes of the membrane responses were very similar for all preload -
levels. This indicated that the high pressure membrane response of
the panels was independent of preload and initial bowing,
Figures 4.24 through 4.31 show the bending and membrane strains
at approximately 0, 5, 10, and maximum (14.5-14.8) psi pressure loads
as a function of gage location for the biaxial preload conditions.
Figures 4.32 through 4.39 show the bending and membrane strains in the
same manner for the longitudinal preload condition. Comparing these
results with the light preload condition in Figures 3.22 through 3.29
the effects of the preload on the transverse bending gradient can be
assessed. As can be seen, the ranking of the panel response from
strongest to weakest bending gradient was unchanged by the preload
conditions., The actual gradient or jump for each panel is tabulated
for the three preload conditions in Tables 4.1 and 4.2 for the biaxial
and longitudinal preload respectively. Table 3.1 showed this data for‘
the light preload case. Comparing the relative change for each
preload condition, it is clear the biaxial preload reduced skin
bending. As a result the bending gradient was reduced. The
longitudinal preload had little effect on the gradient. These
168
2500*]C3 0. psi
Bending ++
74'6 Strain E1250
AE«¤is3 @S-
.2 O fh O OZ
'O0.5 1.0 1.5Y (in.)
-1250
10001
MembraneStrain
+[Il
500 Ac A"' OE 0Ü Ü ,_E <=~ E .
0- nyx
0.5 1.0 7.5Y (in.)
-500
Figure 4.24 Transverse Bending and Membrane Strains vs. Y Location,Panel Quarter Point (X=0), Biaxial Preload Case,Panel A
169
2500C¤ O. psiA 5. .BendingEI Strain +
EU1250
.= AEL*3U2 C) $3
EE 0·· ······—*·*@}“**1***'jgr**"———·—*"*Tv****LL*'·*‘**”·*·“'—wC) ‘ C)
0.5 1.0 1.5Y (in.)
-1250 ·
1000 *Membrane
~ Strain
E + AE]500 .
.= A A*8 .
0"“‘*——”“—‘"‘—l""’¤‘“°"A"‘ "‘ "‘ {5**- ‘——“’ ;
0.5 1.0 1.5
Y (in.)
-500 .
Figure 4.25 Transverse Bending and Membrane Strains vs. Y Location,Panel Center (X=0), Biaxial Preload Case, Panel A
170
2500C) 0. psi ·C63 $6 Bending+_ 14:7 Strain
1250 4-
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0 —_-~_‘—&l_l——_—•~—T'”_- W g"""“'°"’ "" ’ ’ ‘ ,
0-5 1.0 1.5Y (in.)
-500
Figure 4.26 Transverse Bending and Membrane Strains, vs. Y Location,Panel Ouarter Point (X=5), Biaxial Preload Case,Panel E
T7T
2500Ci O. psié- 5. .BendingI] TO. .+_ 14.7 Strain —
T250E2 äi+>g A.2.2 ...z 0 ¤r—¤—·m·—*—i‘—"r——‘——**‘—" 1
C) ‘ C) Q)0.5 T.0 T.5
Y (in.)
—T25O
TOOO’
MembraneStrain
600 +c E]“Z
.42ig - 0 .o_: ES äE 0 ‘ "" "‘°“°“"“"“""_"“""i°‘“"'””"“"°“'—’“°“““°"i'T° " “— " '
·IO.5 T.O T.5
Y (in.)
-500-
Figure 4.27 Transverse Bending and Membrane Strains, vs. Y Location,· Panei Center (X=0), Biaxial Preload Case, Pgnel E
172
2500G1 0. psi
Q $6 Bending+ ]4_6 Strain
1250Ü
E AFUL
4-*3 6fs; 0 AE O' · __ ¤u*"""""—‘T""";;——·*—·‘“·1O0 0.6 1.0 1.5
Y (in.) .
-1250
1000 MembraneStrain + +E II!
600 A AC
E O O1; A, Üc @9L
.2 .Z ONN W- __—_——' INN - ” ”N— _'-” N 'I
0.5 1.0 1_.5Y (in.)
-500 .
Figure 4.28 Transverse Bending and Membrane Strains, 16. Y Location,Panei Quarter Point (X=5), Biaxiai Pre10ad Case, Pane1 B
173
Z500 _ _ .‘ @5 O. psi
36 Bending4_ ]4•6 Strain
1250
..9 Q¢UL.¤3-§ 0""”"""""'EQ*"”V***15····———·—gl—·—1————A1--~—————w———
• _ :‘;'
EC) G)
° 0.5 1.0 1.5Y (in.)
-1250
1000 ‘
MembraneStrain _+
+ m500
E]
.= A AE 0 OisgE.9Z O °'
x0.51.0 1.5Y (in.)
-500
Figure 4.29 Transverse Bending and Membrane Strains, vs. Y Locatibn, .Panel Center (X=0), Biaxial Preload Case, Panel B
174
2500(Ü 0. psi
is“ 5* BendingE m' Strain-F 14.61250
ICFSS-4-*
33 E!
·•— O " ·~~-·-——-6-—-~2é 0.6 1.0 1.5Y (in.)
-1250
1000 ·Membrane
‘
Strain *
A.
500 + O.5 E1 EE .A+3
g -.6 5 5Z 0”——“"'”—'“—l”“"””'7'—'—”'"’“’ '“°—°“"""'°"1 " "_' e ‘4
g0.5 1.0 1.5Y (in.)
-500
Figure 4.30 Transverse Bending and Membrane Strains, vs. Y Location,Panei Quarter Point (X=5), Biaxia1 Pre1oad Case,Pane1 C
175
2500O 0. psi
Bending_1_ 14:6 Strain1250 ‘
·CEÖU1
§ 0E 0- A0‘ O 59 _I
fb0.5 A 1.0 1.51 A v (in.)
E1 Ü+-1250 +1000 I +
Membrane .1.Strain Ü
+ m
600 E A.s A A OE 0+-•8 .Ö O OE O “'“""T""°‘°°""‘“""""°“‘“‘*‘7"-—‘*"*‘“""*’— "*"“ *1
0.5 1.0 1.5_ Y (in.)
-500
Figure 4.31 Transverse Bending and Membrane Strains, vs. Y LocationPanel Center (X=O), Biaxial Preload Case, Panel C
176
2500 gn¤® 0. psi
Bending E
+ 14.6 Stm". A1250
U
EE6 _ 4-16 A „E00.6 0 1.0 O 1.5
Y (in.)
-1250 ° .
1000MembraneStrain
0 .6 0 +.= + E’ · IIIE AE AU
-‘--
·~ E7 „„ rnZ Q- - —--—-—; -—— ._: —-~—-U -- -—-i-—- Y- - .1 I
0.6 1.0 1.5Y (in.)
-600J
Figure 4.32 Transverse Bending and Membrane Strains, vs. Y Location,Pane1 Quarter Point (X=5), Longitudina1 Pre1oad Case,Pane1 A -
177
25000. psi +
E; Bending EJ_1_
14:6 Strain A1250
·CE*"· Aan
ä ä“°
Z“""—'|“"?' n "'""*'1
0 (D0.5 1.0 1.5
Y (in.)
-1250V
1000
- MembraneU
Strain500
E_1_
. ¢¤ +IS Ü :31I/7
E A .Q_ £‘.~.
·¤· 0 .... .___,___ _____ v______| |
G 0 6*0.5 Q1 1.0 1.5
Y (in.)
-500 J 1
Figure 4.33 Transverse Bending and Membrane Strains, vs. Y Lccation,Pane1 Center (X=0), Longitudina1 Pre1oad Case, °ane1 A ·
178 .
2500 -Ü 0. psi=¤ 5. .E 10 Bend1ng +,1, 14'6 Strain E1
1250C
'SE3 EB‘—ig
0 *“""'—**—··‘<3•*'*v'i·‘er"*——*‘—·”———'T*—**—**‘“““”**""”*1
0.5 C) 1.0 «® 1.5Y (in.)
-1250
1000I
MembraneStrain
5001 +
[I1 +.*6 El3 A
Z tik I u 1(D . C1
0.6 Ü 1.0 1.6
-500 ‘
Figure 4.34 Transverse Bending and Membrane Strains, vs. Y Ldcation,Panel Quarter Point (X=5), Longitudinal Preload nase,Panel E
179
2500 qI
°
Gl O. psi
. äh Bending+_ 14:6 Strain
1260 +E]
.E Af¤L4-*
3Ü 0 - Ej—g.....;‘...................--..;.l‘15.........- ...
EE u; 1_ ul 1 ¤ 1
0.5 . .C) 1 0 C) 1 5Y (in.)
-1250r
1000 *Membrane .Strain
500EE 1 0
A .ä"'"“"”I"'”'——‘T1 -7 C- ‘--€%—---7- iiihl-|@0
_ 0.6 Ü 1.0 1.5Y (in.)
-500
Figure 4.35 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Longitudinal Preload Case, Panel E
180 °
2500 - .C) 0. psi
ä Bending' Strain4- 14.6 dj1250 A.E ·I5
= Q3 gg ·Al'V\
"""'*""""'*""""°"””QE 0 ‘ 1 _ LJ ¤C)
‘
0. 6 0 1.0 1.5Y (in.)
-1250 °1000 ÜMembraneStrain +
4-500 ElE]CE
E + A 4ä E Ei 1E 0 ·
”‘ V“‘”Ü""’"" ‘“’'°""” ”} ‘ Ü ‘0 O w0_5 g_Q 1.5
. Y (in.)
-500
Figure 4.36 Transverse Bending and Membrane Strains, vs. Y Lccaticn,Panel Quarter Point (X=5), Longitudinal Prelaad Case,Panel B
181
2500iii 0. psiA 5 .' BendingE1 10. .1_ 14.6 Strain
1250.5
E? EU)
3 @11; 0 ‘*********CT··*r***üT*******:5***1************·“———n
0.5 1.0 1.5Y (in.)
-1250
1000· Membrane
Strain
500I
.5 +E . E]
4-*
2ö E1 ,11 A
EE 0* ä§-“—-V“—“‘駓“*—”'““?EF——”“V“i—_“”‘""“ *“ i“·“i0.5 1.0 1.5
Y (lin.)
-500
Figure 4.37 Transverse Bending and Membrane Strains, vs. Y Location,Panei Center (X=0), Longitudina1 Pre1oad Case, Pane1 B
182
2500(D 0. psi
$(5 Bending5_ 54:6 Strain
1250EE{2eÖU5 0 ,.—T.„..........._.._.F?ä.........„.„Q, _
0 01 0
""'10.5 1.0 1.5
Y (in.)
-1250U
1000 ·MembraneStrain
500 +.2 El
. E +5 ¤ A2 Q A
0—‘ —--·—--—-—-——--——;„„-.| ...- -..;.--...,_,_„_.;- . ._
(
0.5 1.0 1.5(D O
Y (in.)
-500 .
Figure 4.38 Transverse Bending and Membrane Strains, vs. Y Location,Panel Quarter Point (X=5), Longitudinal Preload Case, ·Panel C —
_ 183l
2500C) 0. psi ·
Bending+_ ]4'6 Strain ~
1250'CQ .EV7OL
P 0..E • _0
I I
A 0.5 A 1.0 1.5
Ü E} Y (in.)
+ +-1250
1000MembraneStrain
. E +500 E
Q E
Ä; A AL
4-*
IS AE @ OZ "‘ ‘i ’s
0.5 1.0 1.5(D Y (in.)
·500
Figure 4.39 Transverse Bending and Membrane Strains, vs. Y Location,Pane1 Center (X=0), Longitudina1 Preload Case, Panel C
184
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186
conclusions were also supported by the effect of preload on deflection
as a function of pressure.
LONGITUDINAL RESPONSES
Following the approach used to examine the longitudinal strain
response of the lightly preloaded panels, the effect of the two other
preload conditions on this response can be determined. Figures 4.40
through 4.44 and 4.45 through 4.49 show the bottom surface strain at
the center of the panels for the biaxial preload and longitudinal
preload, respectively. The same strain information was shown for the
light preload condition in Figures 3.30 through 3.34.
Comparing the results in these figures, several observations can
be made. The general shape of the gradient for each panel was un-
changed by the preloads. This would indicate that the longitudinal
stiffener/skin interaction mechanisms were essentially unchanged by
the presence of any preload. The biaxial preload had some effect on
the response however. Compared to the light preload, the initial
strains at zero-pressure were slightly increased. As with the trans-
verse gradients, the overall change in strains from zero-pressure to
maximum pressure was reduced by the biaxial preload. Also, the
differences between strains in the different spatial locations were
slightly reduced. This resulted in a slight decrease in the
longitudinal gradient along the centerline for all of the panels. The
longitudinal preload produced a slightly larger increase in the
initial strains than the biaxial preload. The difference in the
strains at the different spatial locations, however, was not
perceptibly changed compared with the light preload.
187
2000
0 0. psiA 5.m 10. ++ 14.7
—E]
1000 +
A
s: Al
'Ss.4.) .th
E.¤ OZ 0
02. 4. 6. 8. 10.
X(in.)-1000
Figure 4.40 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Biaxial Preload Case, Panel D
188
2000
Ü 0. psi&~ 5.
_ El 10.4- 14.6
10004
4-: 4*.„ g]_§ IE
6 Q 0g O (D 0 (D 0A ° _
2. 4. 6. 8. E] 10.X (in.) +
-1000
Figure 4.41 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),Biaxial Preload Case, Panel A
189I
2000
Cl 0. psi&~ 5.E1 10.+- 14.7
1000
.:2 +g 0S A_ä: 0 0E O A
0E12. 4. 6. 8. ·+ 10.X (in.)
-1000
Figure 4.42 Longitudina1 Strains on the Bottom Pane1 Surface,vs. X Location, A1ong the Pane1 Center1ine (Y=0),Biaxia1 Pre1oad Case, Pane1 E
190
2000 —G7 O. psiä> 5.F] 10. ‘ '4- 14.6
1000 ·
4·E mwig A3 IDL.2 (D CJ2: 0
2. 4. 6. 6. E1 10.X (in.) 4-
-1000 ‘
Figure 4.43 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=0),Biaxial Preload Case, Panel B
191
2000
O 0. psi¢· 5.E] 10.4- 14.6
1000
·+
E]
EE A +Q E1äq-
A2: Q O0 C)
2. 4. 6. 8. 10.X (in.)
A
E]4-
-1000
Figure 4.44 Longitudinal Strains on the Bottom Panel Surface.vs. X Location, Along the Panel Centerline (Y=0), ·Biaxial Preload Case, Panel C
1922000 ~ +G? 0. psiA 5.Ü 10. E]
14.6++
E]1000 _ AA
·CE*9 08 0s.
-.9Z 0
2. 4. 6. 8. 10.X (in.)
-1000 ‘
Figure 4.45 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),Longitudinal Preload Case, Panel D
193
2000 .
CJ 0. psicl 5.E1 10.——:— 14 .6
1000
-
+ .
.s E E,§ A +tn A III2 A· °.2 0 O O E OE OA
[B2. 4. 6. 8. 4_ 10.
X (in.) -
-1000Figure
4.46 Longitudina1 Strains on the Bottom Pane1 Surface,vs. X Location, A1ong the Pane1 Center1ine (Y=0),Longitudina1 Pre1oad Case, Pane1 A
194
2000
G) 0. psi¤~ 5.EJ 104- 14.6
1000
+·_::Q Ü
'um2 A 0u2 ® 0
AA
O ._ E]
2. 4. 6. .8 +_ 10.
h° X (in.)
-1000
Figure 4.47 Longitudina1 Strains on the Bottom Pane1 Surface,vs. X Location, A1ong the Pane1 Centerline (Y=0),Longitudina1 Pre1oad Case, Pane1 E
195 V
2000
C) 0. psiß· 5.E] 10.4- 14.6
1000
4-Eg EI+9
8 ASE 0 0 0
A
0 AI IE
2. 4. 6, 8. 10.X (in.)
I+
-1000-
Figure 4.48 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),Longitudinal Preload Case, Panel B
196
2000. ·
(IJ 0. psiA 5,E1 10.
~
1000Ü .
A +
.2 EE Aiz O 0Q 0.2 _Z 0
2. 4. 6. 8. Al 10.X (in.)
E]+·
-1000 .
Figure 4.49 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),Longitudinal Preload Case, Panel C
197
The transverse gradient of the longitudinal strains can be seenl
somewhat in the plots of membrane and bending strains as functions of”
pressure. Figures 4.50 through 4.53 and 4.54 through 4.57 show the
strains for the biaxial and longitudinal preload conditions,
respectively. These results compare with the same strain responses
for the light preload shown in Figures 3.37 through 3.40. The most
noticeable effect of both the biaxial and longitudinal preload
conditions was the shift of the zero-pressure membrane strains. Also
noticeable is the elimination of initial strain reversals at low
pressures when the biaxial preload is used. The biaxial preload
responses show a slight decrease in the spread between the maximum and
minimum membrane and bending strains from the end to the center of thepanel. _Transverse gradients of the longitudinal strains can be further
studied by looking at the bottom surface strains at discrete pressure
levels as a function of gage locations. Figures 3.44 through 3.47
show these relations for the lightly preloaded conditions. Figures
4.58 through 4.61 and 4.62 through 4.65 show these relations for the
biaxial and longitudinal preloads respectively.
The unstiffened panel responses are shown in Figures 3.44, 4.58,
and 4.62, for the three preload conditions. As was seen in the mem-
brane strain vs. pressure relations, the initial bottom surface
strains for both the longitudinal and biaxial preload cases were
increased over that for the light preload case.
For the unstiffened panel, the biaxial preload reduced the
overall increase in strain at each strain gage location. The relative
T98 ·
TE
T000Membrane ·Strain ZE
T500
C” 2C
: BCg ___„; P e 3Ew 0o .Ö .
EE 5 TO T5P (psi)
-500 V
700
BEYTÖTHQ 2C__5 Strain icE ac+>g 0L.2Z 5 T0 P (psi) T5
·700‘
E152E3E
—T40O
Figure 4.50 Longitudinai Membrane and Bending Strains vs.Pressure Load, Biaxiai Preioad Case, Panei D
199
1000
MembraneStrain
2C1C500 3C
.:,;•¤"””"’f:
E ·‘=E:s—___ 3E~ _w 0
2: 5 10ZE
15P (psi) 1E
-500
700Bending 3C
strain 1E·; 1C_; 03_ä 5 10 15Z: - P (psi)
-700V 3E
-1400
Figure 4.51 Longitudinai Membrane and Bending Strains vs.Pressure Load, Biaxiai Preioad Case, Pane1 E
200
T000
MembraneStrain
600 T9.93C
E<g 3E
E *9--U
‘ I
QQ . 5 TO P (psi) T5
2E
TE-500
700BendingStrain 3C; TE
'E TC,2C
j OcLQ) .
Q 5 TO 2E T5P (psi)
-700 3E
-T400
Figure 4.52 Longitudinai Membrane and Bending Strains vs.Pressure Load, Biaxiai Preioad Case, Panei B
201i
1000
MembraneE
StrainZC
500 3C1C
-§ 3Eig 1EQ 0uIE 5 ‘ 10 P (psi) 15
ZE
-500
700 .Bending 1EStrain
'Q 3C4%0ä '“!‘llllIlln-.._ gg
.2 __-......II.:·-.-ll¤—.__ 10 P (psi) 15Z.
1C3E
-700
-1400
Figure 4.53 Longitudinai Membrane and Bending Strains vs.Pressure Load, Biaxia1 Preload Case, Pane1 C
202
IE
2E
1000 Membrane ICStrain2C
500 3Cg,
“3E
.= ääallllnunun-·""'E
-
ä 0uEf 5 · I0 I5
P (psi)
-500
700
Bending ICStrain
· ac
s.u · .
¢E 5 IO P (psi)IE]0
2E-700 3E
-I400 _
Figure 4.54 LongitudinaI Membrane and Bending Strains vs.Pressure Load, L0ngitudinaI PreIoad Case, PaneI D
—203
1000
Membrane ägStrain
500 Ef EEEE/ 3C·‘i 3E.‘ "
Ü Eum
.2 O ’*
5P(psi)
E2E
-500 1E
700
BendingStrain gg
EMIlllnJS 0 __,C_„_.E._.„_ E „ _1---..
s. ·—--.—3 5 10 _ 15Z P (psi) 1E
ZE 1_700 1C 1
E 3E-1400
E
Figure 4.55 Longitudina1 Membrane and Bending Strains vs.Pressure Load, Longitudina1 Pre1oad Case, Pane1 E
E204
1000 .
Membrane lCStrain 2C
500 3g
E 3E
E
_
‘E 2EE , 5 10 15
P (psi) 1E
-500
700Bending 3CStrain 15,35
F 1EE§ 0E
.,‘:.’ 5 10 15 .2 P (psi) ZE
-700 3E
-1400
Figure 4.56 Longitudinal Membrane and Bending Strains vs. ~Pressure Load, Longitudinal Preload Case, Panel B _
205
10002C
Membrane 3CStrain 1C
3
5001E
E .
Q 2E-3 0 r ....._____________„.,;§ .
5 10 15P (psi)
-500
1E700BendingStrain
.E 2E,3Cfs 0 !L}.......... „__V1 ""'ä 10 217 15E L P (psi)
1C-700 . 3E
-1400
Figure 4.57 Longitudina1 Membrane and Bending Strains vs.Pressure Load, Longitudina1 Pre1oad Case, Pane1 C
206
2000
0 0. psi+
A 5. Panel EndÜ ”I0. (X=8.5 in.)+ T4.7
Z l000 III
+.6 A El3 A· s._c>E
0”I.0 2.0 3.0 4.0 5.0. Y (in.)
Y —]000
2000 ‘
Panel Center(X=0.0 in.)
~ ]000E¢¤s.ij +
ä iiiE es Zl.0 2.0 3.0 4.0 5.0
Z Y (in.)
-‘l000
Figure 4.58 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, BiaxialPreload Case, Panel D
207 '
2000 4_¥‘0. psi . °
‘-· 5.. Pane1 End1000 +.E E1:2 . E
-1-A
A¤ IHÖ 2 S2 Ü O 0gg 0 "—';g*··—tpW·——······———r—···—···—·—1·*—······*“·w*—·—····—·”·11.0 2.0 3.0 4.0 5.0
Y (in.)
-1000 .
2000Pane1 Center
g (X=0.0 in.)
1000 _Eg 1" +· 4- .
4-> E1 Ü [I] +8 A A A
01
’1
1.0 2.0 3.0 4.0 5.0Y (in.)
-1000-
Figure 4.59 Longitudina1 Strains on the Bottom Pane1 Surfaceat the Center and End, vs. Y Location, Biaxia1 .Pre1oad Case, Pane1 E
208
2000 _GJ O. psi.a 5-
‘ Pane1 EndLQ 10. _ .1_ 14.6 (X—8.5 in.)
1000.5 +fü5 E11; . 1. EOg %1 A. .A
Q3 1.0 2.0 3.0 4.0 5.0. Y (in.)-1000 l
2000Pane1 Center(X=0.0 in.)
1000-EE + .1.Y? 1 111 -1 1Q LA A A E.] 1;;.5 (T; ,3} Q) (1.Z 0’°‘°”‘— ‘°"" ‘— ‘1 "‘1 1
1.0 2.0 3.0 4.0 5.0Y (in.)
-1000J
Figure 4.60 Longitudina1 Strains on the Bottom Pane1 Surfaceat the Center and End, vs. Y Location, Eiaxia1Pre1oad Case, Pane1 B
209
20000 O. psiA 5. Panel EndE1 10. (x=8.6 in.)2 2+ 14.6
1000.2 +V5 E1 · 4-§ IIIE 0
A AUg 0 ———*·*@·r—·+—+1———*®·'——*+*L‘)·—"*i‘r——·—·”——·1
2 6 ä«· 1.0 2.0 3.0 4.0 6.0
. Y (in.)
-1000
2000 ·. Panel Center
(X=0.0 in.)
1000
A El3 * A A
A$-‘ u
.2 „„ @‘- 2 fü
Z 0·——————————w—-—-i*——“·1--— @=--·.— -~“~~· . · .1.0 2.0 3.0 4.0 6.0
Y (in.) ‘
-1000
Pigure 4.61 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, BiaxialPreload Case, Panel C l
210
2000 (_ü' 0. °+_ A2 5.
PS1E1 10 Panel End
El _1 14:6 (X=8.5 in.)
1000 +E A III
”
EEg .AE.2 ® 0** 0 *"—*·—V——··————··w
1.0 2.0 3.0 4.0 5.0Y (in.)
-1000
2000Panel Center
. (X=0.0 in.)
1000.2 A
E]E 6‘é’ A A.2 Q @ .E 0 ‘“°—°T"—¤*°“‘°*"°—"n‘”"‘"“°“? T‘_” ““‘°“°""—‘¤ "“°‘ ‘l
1.0 2.0 b 3.0 4.0 5.0Y (in.)-1000 _
Figure 4.62 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LcngitudinalPreload Case, Panel D
211
2000- 0 0. psi .?Ö_ Panel End
+ wö (x=8.51n.) +II!
l000+E A m2 E
3 A 4Q .0 ,3 GZ 0 ***56*-** 'r*"‘“‘”;"V—***·—·"¤"”‘*“—·—‘
·‘··1.02.0 3.0 4.0 5.0Y (in.)
-1000
2000Panel Center
. (X=0.0 in.)
1000.,2 +2 A ä ä +3 A . Elo A AA A ä_; 0 O 0 0 0Z O' ~”—‘—~_‘—_|—T—_—”—_I—_”——"—”“””I;—"”—°'—‘—lI”"l””—”—_I
1.0 2.0 3.0 4.0 5.0- Y (in.)
-1000 _Figure 4.63 Longitudinal Strains. on the Bottom Panel Surface
at the Center and End, vs. Y Location, LongitudinalPreload Case, Panel E
212 _
2000C; 0. psi ·L 5. Panel End
in.)I •+1000 [1]
: + +·'S E1 A Ü
E A A2 G) (5_g O-....é§....§lT...........1.....iD.....1.....i2..„„.T„.„- ,„„„,_1Z .
1.0 2.0 3.0 4.0 5.0Y (in.)
-1000
2000-
. Panel Center(X=0.0 in.)
1000
+ + +·‘= P P¤¤2A A A ui3 C1 Cl C3 C1 Q,
0 T-—---I--U-U—---U---——-I-—----- -U--U U- | -U-U----—- - -6 ---- U -|
1.0 2.0 3.0 4.0 5.0Y (in.)
l -1000
Figure 4.64 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, LongitudinalPreload Case, Panel B
213
2000O 0. psi
5. Pane1 EndE1 10. (x=8.5 in.)-1 14.6 1-1000 EE +·¤ +·E E1A°
GJE 0 Ö ® 0Z 0
A1g1l‘———j—1—————·—·1‘——·“———·*w****—"·1
E13 · 1.0 2.0 3.0 4.0 6.0Y (in.)
-1000
2000Pane1 Center(X=0.0 in.)
+E 2 ¤ .. 2
4% A E1 .,."’A [1]0 @ 0 0
0
I1.02.0 3.0 4.0 6.0Y (in.)
-1000
Figure 4.65 Longitudina1 Strains on the Bottom Pane1 Surfaceat the Center and End, vs. Y Location, Longitudina1Preload Case, Pane1 C
2l4
difference between the gage locations was also reduced by the biaxial
preload. The stiffening effect of the biaxial preload seen in the
deflection response is believed to have caused this reduction. This
decrease is more apparent near the end of the panel than at the
center. This difference in the effect of the preload from the panel
end to panel center may have been due in part to the pretest shapes of
the panels. The panels had relatively less pretest curvature at their
centers for both of these preload conditions, hence the difference
between the two conditions due to initial bending response would be
reduced at their centers.
The responses in the presence of longitudinal preload were very
similar to the lightly preloaded response. The responses were simply
shifted upward uniformily by the initial prestrain. In this case the
effects of the greater pretest curvature of the longitudinal preload
condition may have masked any stiffening effect the preload may have
had.
Judging from the unstiffened panel responses, the effects of
preload on the stiffened panels could be anticipated. The effects can
be seen in Figures 4.59 through 4.61, for the biaxial preload
condition, and in Figures 4.63 through 4.65, for the longitudinal
preload condition. Neither of the preload conditions had a
significant effect on the overall response or stiffener/skin
interaction mechanisms described earlier. The principle effects of
the biaxial preload were the increase in the initial strain level, and
the slight decrease in rate of change in strain with increasing
pressure. This latter effect consequently caused a smaller strain
2l5
gradient from skin to stiffener. This reduction of the strain
gradient was due to the stiffening and flattening effect of the
biaxial preload described earlier.
The longitudinal preload merely shifted the initial strains up-
ward. The subsequent responses were essentially unchanged from the
light preload responses. As was mentioned for the unstiffened panel
response, any stiffening effect of the longitudinal preload may have
been masked by the increased pretest curvature. -
Chapter 5.
FINITE ELEMENT RESULTS AND DISCUSSION
Four of the panels were analyzed using nonlinear finite element
models based on a program called STAGS (Structural Analysis of General
Shells) (6). This program was developed jointly by NASA and the Lock-
heed Corporation. The program contains capabilities for analyses with
both material and geometric nonlinearities. The geometric nonlinear-
ities are limited to moderately large rotations (less than 0.3 rad-
ians). For the present study only geometric nonlinearities were con-
sidered.
An example of the element discretization is shown in Figure
5.1. As indicated, only the center 10 x 20 in. section of the test
panels was modeled. Neither the portions of the panel outside the
test region nor any of the fixturing were modeled. All elements were
plate elements. In the analyses the panels were perfectly clamped on
all four edges. Transverse pressure load was applied incrementally to
a maximum of 15 psi. The pressure increments were controlled within
the program, based on a criterion of convergence of strain energy. No
symmetry assumptions were made in the analyses so as to avoid any
improper restraint on the response.
The four panels modeled were: the unstiffened quasi-isotropic
panel (Panel D); the panel with the quasi-isotropic skin stiffened
with a tall web and a thick flange (Panel A); the panel with the
quasi-isotropic skin stiffened with a tall web and a thin flange
(Panel B); the panel with a quasi-isotropic skin stiffened with a
216
217
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GJGJI 1.1.3 3I
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2l8
short web and thick flange (Panel C). No attempt was made to model
the actual test conditions described in the preceeding sections as
deviations from the ideal case. Only the light preload case was
considered. In the model the panels were assumed to be perfectly flat
and rigidly clamped. No considerations were made for the initial
bowing, inplane slippage, or panel contact at the edge of the recessed
area of the vacuum plate.
The purpose of these analyses was to provide an analytical com-
parison for· some of ·the experimental results. Specific comparisons
addressed, and discussed in the following paragraphs, were results
indicating the effects of deviations of the experiment from the ideal
conditions, and results indicating agreement (or disagreement) with
regard to the mechanisms of stiffener and skin interaction and the
effects of geometric parameter variations. It was recognized that it
would have been necessary to model. the actual test conditions to
obtain results comparable in magnitude to the experimental results.
Consequently the comparisons are made in a general sense.
The out-of—plane deflections measured at the center of the panel
and on the skin are shown as a function of pressure in Figures 5.2 and
5.3, respectively. These deflections were given in Figures 3.10 and
3.11. The corresponding out—of-plane deflections calculated by the
finite element models of these particular panels are also shown in the
Figures. The panel designations for the finite element results are in
parentheses, i.e., (D), (C), etc. They also have symbols at pressures
which indicate the incrementally calculated deflections. The strong
nonlinearity of the response required very small pressure increments
219
0.4
Finite Element ResultsIndicated By ParenthesesD
0.3 ‘ C(D)
„__ _ °‘ 1(C)
.;é .’
E ".2 -*5 0.2 ··*1* -.C8 ·· /L ._
.
-»€¤.» „“’
,'· // B0.1 " A
0.00_ 5 10 15
P (psi)
Figure 5.2 Center of Panel 0ut—0f-Plane Deflections vs.Pressure Load: Measured and Finite Element Resultsfor Four Panels
° 220
0.4 .
Finite Element ResultsIndicated By Parentheses
0.3 _
’TPanel.5 · ·—«
CC
.5 -0.2g; 5(C)8
B.= A.§
0.l.„«*"’
-A
l 1
0.00 5 l0 T5
P (psi)
Figure 5.3 Skin 0ut—0f—Plane Deflections vs. Pressure Load:° Measured and Finite Element Results For Three Panels
22l
to achieve proper solution convergence. Only a few of these
increments are indicated in these figures. In each case the
calculated displacements are less than the experimental
measurements. Due to the deviations of the test conditions from the
ideal conditions modeled by finite elements, this was not unexpected.
Looking at the differences between the calculated and measured
center deflection of the unstiffened panel, effects of two of the
deviations from the ideal can be seen. First, the initial slope of
the experimental response is greater than the slope for the calculated
response. This was due to the initial upward bowing of the panel.
Greater upward bowing required a greater deflection, due primarily to
a bending response, before the stiffer membrane stretching response
became effective. The second deviation can be seen in the difference
in slopes between the calculated and measured deflections at higher
pressure loads. The finite element models had rigidly clamped edges
so the slope reflects the inplane stiffness of the skin. The steeper
slope of the experimentally measured deflections indicates the effect
of the inplane slippage. The steeper slope of the measured center
deflections of the tall web stiffened panels indicates the combination
of stiffener end rotation and inplane slippage. Since the stiffener
response is primarily a bending deformation, any rotation of the ends
of the stiffener would soften the response relative to the perfect
case.
Similar conclusions can be drawn from comparisons of the calcu-
lated and measured skin deflections. Panel bowing in the actual panel
produced greater deflections at the lower pressure loads. Imperfect
222
clamping in the actual panel permitted greater deflections at higher
pressure loads.
The effects of the stiffeners are the same for both the measured
and calculated deflection responses. The short web stiffener reduced
the center deflection only slightly. The panels with the tall web
thick flange stiffener and the tall web thin flange stiffener had
essentially the same center deflection. The skin deflection of the
panel with short web stiffener was less than the center deflection,
indicating a "U" shaped transverse profile. The skin deflections of
the panels with the tall web stiffeners were greater than the center
deflections, indicating a "w" shaped transverse profile. The primary
deviation between the calculated and measured responses occur between
the unstiffened panel and the panel with the short web stiffener. At
15 psi, the center deflection of the lightly stiffened panel was
measured to be 17% less than the center deflection of the unstiffened
panel. The finite element calculations show the difference to be only
2%. The difference between predicted and measured stiffening effect
is no doubt due to the fact that the two actual panels were starting
from the different initial conditions. In addition there was
slippage. In the finite element computations, both the unstiffened
and lightly stiffened panels were flat and there was no slippage.
These finite element results show that the short web stiffener was
even less effective than the measurements indicated.
Figures 5.4 through 5.7 show the deformed geometry of each of the
models at 15 psi pressure load. The deformations are as viewed look-
ing along the length of the stiffener axis (transverse profile) and as
223 «
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227
viewed looking perpendicular to the stiffener axis (longitudinal pro-
file). The figures show the deformed boundaries of the elements.
Figures 3.12 through 3.16 and Figure 3.26 showed the line profiles
measured in the experimental study. Bold lines are used in Figures
5.4 through 5.7 to indicate the deformed element boundaries in the
locations corresponding to the locations of the measured line
profiles. The experimentally measured profiles are very similar to
the finite element calculations. This similarity provides an
indication that the models represented the important components of the
panel responses.
The resolution provided by the profiles produced from the finite
element model provides insight to the interactions of the stiffeners
and skins. As mentioned previously, the lines shown in the deformed
geometry figures represent the element boundaries. The element
boundaries were defined along the panel coordinates as shown in Figure
5.1. Each line in Figures 5.4 through 5.7, then, shows a cross-
section view of the panel deformation along that line.
The unstiffened panel model in Figure 5.4 shows a uniform
deformation over the entire panel. In the transverse profile all
lines representing element boundaries are "U" shaped. Similarly, in
the longitudinal profile all lines representing element boundaries are
"U" shaped. The change in curvature, the inflection point, of both
the transverse and longitudinal deflections can be seen to be very
near the edges of the panel. Comparing this with Figure 5.5 for the
panel with the short web and thick flange, the effect of the stiffener
on the panel can be seen. Looking near the top of the transverse
228
profile, the cross sections have a shallow "w" shape. These "w"
shaped cross sections are due to the local restraint of out-of-plane
deformation by the stiffener. The cross section in the area of the
stiffener flange is nearly flat, indicating little flange bending.
The skin adjacent to the flange is curved downward sharply, indicating
a large bending gradient from flange to skin. Moving downward on the
profile (which is equivalent to moving longitudinally away from the
panel end) the "w's" become deeper initially, then shallower again, as
the cross section makes a transition to a "U" shape. At the bottom of
the transverse profile (the longitudinal center of the panel) the
cross section is an all concave upward "U" shape. The flange cross
section is also concave upward and the curvature appears uniform from
the flange to the adjacent skin. This indicates a relatively small
bending gradient and no change in sign of bending strain from the
flange to the skin.
The longitudinal profile also shows a shape transition. Near the
ends of the longitudinal profile the skin is below the bottom of the
stiffener. At approximately at the quarter points of the panel
length, the bottom of the stiffener becomes the lowest point of the
cross section. It remains that way to the center. Also apparent in
the longitudinal profile is the difference in location of inflection
points for the skin and for the stiffener.
Looking at the transverse profile of the model of the panel with
the tall web and thick flange, Figure 5.6, the profile can be seen to
have the "W" shape along the entire length of the panel. This '
illustrates the influence of the stiffener. Also, it can be seen that
229
the flange cross section is nearly flat at all locations, indicating
little flange bending. The change in curvature from flange to skin is
relatively sharp. This indicates a high transverse bending gradient
from flange to skin along the entire panel length. The longitudinal
profile provides little additional information except to indicate the
difference in the location of the inflection points of the stiffener
and the skin. This compares with the skin and stiffener profiles
measured on this panel and shown in Figure 3.36. It is clear from
both the measured and calculated profile, the skin deflected more than
the stiffener.
The transverse profile of the panel with the tall web and thin
flange in Figure 5.7, is very similar to the panel just discussed.
The profile is a "H" shape throughout. However, the flange cross
section is bent. The curvature of the flange reduces the change in
curvature from flange to skin, indicating a reduction in the bending
strain gradient relative to the previous panel with the thick
flange. The longitudinal profile is also very similar to the previous
model. The change in flange thickness had little effect on the
longitudinal response when compared to the thicker flange case.
Figures 5.8 through 5.13 show the transverse membrane and top
surface bending components of strain on the flange and skin. These
strains were calculated at 5, 10, and 15 psi for each of the three
stiffened panel models. They are plotted as a function of location,
as, was done for the experimental results shown previously in Figures
3.22, 3.23, 3.26, 3.27, 3.28, and 3.29.
230
3000 + IEäopsi Bending E1
”_1 15 Strain
A_g 1500eus.+.>8;.2 ä $z
0‘ 0.5 ‘ 1.0 1.5 .
' Y (in.)
-1500
2000
MembraneStrain
_:E 10004-) 1 *U
E ¤¤ EA A
§ ä0
0 0.5 ' 1.0 1.5Y (in.)
Figure 5.8 Transverse Bending and Membrane Strains, vs. Y Location,.Pane1 Quarter Point (X=5), Finite E1ement Resu1ts,Pane1 A
_ 231
3000
Bending ++ 15 Strain E1
A_g 1500«¤s.+->U)o’°
§E @00.5 ‘ 1.0 1.5
Y (in.)
-1500
2000 ·MembraneStrain
10003 + '*'E.8 m E2
A. ¢· .
0
0 0.5 1.0 1.5Y (in.)
Figure 5.9 Transverse Bending and Membrane Strains, vs. Y Location,Pane1 Center (X=0), Finite E1ement Resu1ts,Pane1 A
232
3000· ;_ 5 ”S1 _
_] 15 Strain
EQ +
·~ 1500E m ^+»U'!
E A..9Z E
0”
0.5’
1.0 1.5
Y (in.)
-1500 ”
2000
· MembraneStrain
EI5
1000*E + +cL.2 m E12:
+‘*‘ A
. E1 Q]‘A
A, .A
00 0.5 1.0 1.5
1 Y (in.)
Figure 5.10 Transverse Bending and Membrane Strains, vs. Y Location, .Panel Quarter Point (X=5), Finite Element Results.Panel B
_ 233_
3000 _
- E“1?0pS‘ Bending1_
15 Strain
15ÜÜeuA_: E]
U') „
Q .ABZ E A
00.5 — 1.0 1.5
Y (in.)
-1500
2000 'MembraneStrain
E 1000(U .
Ö + +8 .IB . m [I]E
·+ A. A- _E EJA A
00 0.5 1.0 1.5
Y (in.)
° Figure 5.11 Transverse Bending and Membrane Strains, vs. Y Location,Pane1 Center (X=0), Finite E1ement Resu1ts Pane1 B
234
3000
Bending_+15 Strain
_: 1500Ebth
E.2 W2:
0 ***1.AQ] @1+·
0.5 1.0 1.5
-1500 Y (in.)
2000
MembraneStrain
E° ·+35 1000 +w .E E1 ~v .
EE E1
A A
00 0.5 1.0 1.5
Y (in.)Figure 5.12 Transverse Bending and Membrane Strains, vs. Y Location,
· Panel Quarter Point (X=5), Finite Element Results,Panel C
235U
3000
Bending_1_15 Strain
E 1500euisU')os..2 .Z
0· 0.5 . 1.0 1.5
A A Q $
III III+ Y (in.)-1600 + _
2000 MembraneStrain + +
EJ MU
.,*5U
g 1000U)
E A A.2Z + +
El E]A A
0
0 0.5 1.0 1.5U
Y (in.)
Figure 5.13 Transverse Bending and Membrane Strains, vs. Y Location,Panel Center (X=0), Finite Element Results, Panel B
236
The top surface bending strains reflect the observations made
from the transverse profiles. The strains for the panel with the tall
web and thick flange are shown in Figures 5.8 and 5.9 at the panel
quarter point and center, respectively. At both locations the panel
has very low bending strains on the flange and high bending strains on
the skin adjacent to the flange. The bending strain on the skin and
the gradient from flange to skin is slightly higher at the panel
quarter point than at the center. These observations are the same as
for the measured strains for this panel, shown previously in Figures
3.22 and 3.23.
The transverse profile of the panel with the tall web and thin
flange indicated flange bending. This is seen in transverse bending
strains shown in Figures 5.10 and 5.11 for the panel quarter point and
center, respectively. The bending strains on the thin flange are
higher than for the previously discussed thick flange case. Also the
bending strains on the skin adjacent to the thin flange are reduced
relative to the thick flange result. Consequently, the gradient
between the flange and skin was also reduced. This was seen in the
actual strain measurements made on this panel (Figures 3.26 and 3.27).
The model of the panel with the short web also had results
similar to the measured responses. At the center of the panel, Figure
5.13, the transverse bending strains at the top surface were all
compressive. This corresponds to the "U" shape profile at the center
of the panel. At the quarter point of the panel, Figure 5.12, the top
surface of the flange had compressive bending strains and the skin
adjacent to the flange had tensile bending strains. This corresponds
237
to the transition area of the transverse profile, in which the panel
has a very shallow "w" shape. Both of these bending strain gradients
were seen in the measured strains for the panel with the short web and
previously discussed in Figures 3.28 and 3.29.
The transverse membrane strains shown in Figures 5.8 through 5.13
indicate the change in stiffness from flange to skin due to change in
thickness. The increased thickness in the flange reduced the membrane
strain response. The membrane strain in the skin was highest at the
center of the panel with the short web stiffener. This greater
membrane strain was related to the greater deflection and subsequently
greater skin stretching. These transverse membrane strain
observations were also borne out in the measured strains for these
panels. _
The longitudinal strain gradients measured in the experimental
investigation were also observed in the finite element results.
Figures 5.14 through 5.17 show the bottom surface longitudinal strains
along the centerline of the panel, calculated by the finite element
models. These strains are plotted as a function of location along the
length for pressure loads of 5, 10, and 15 psi. The corresponding
experimentally measured strains were shown in Figures 3.30, 3.31,
3.33, and 3.34.
The unstiffened panel response in both Figure 5.14 and Figure
3.30 shows an increasing tensile strain as one moves from the center
of the panel toward the end. The finite element model provided strain
information nearer the end of the panel than did the strain
measurements on the actual panel. However, in the model the strains
A 238l2000 +
Ä 5 psi +lll 10 .+ 15
1000+ III
AA E
_ A+ El+ A
+ + [5m Ä
m Ü A A.: A A A
EE3 0
_b 2 4 6 6 io= x (an.) +
ElA-1000-2000 IFigure 5.14 Longitudinal Strains on the Bottom Panel Surface, „
vs. X Location, Along the Panel Centerline (Y=0), _Finite Element Results, Panel D
239
‘ 2000
A 5 psiEl10
. 4- 15
1000I I
1+ +- 4-E] g] E] ·+
EI 4-.5 A A A A mE .A
45,) 0
A g 2 4 6 fü A io45 x (16.) E A
AA+ ¤1
+-E]
I4-
-10004-
-2000
Figure 5.15 Longitudinal Strains on the Bottom Panel Surface,.vs. X Location, Along the Panel Centerline (Y=O),Finite Element Results, Panel A
240
2000
A.5 psiE] 104- 151000
+,+· 4_
4E1 gi E] 4-Ü +
02 4 6 Q! ,A 104
X (in.) ElA·‘A .A"’ m E1‘*’ m-1000 +
. ·+
-2000 0 _
Figure 5.16 Longitudina1 Strains on the Bottom Pane1 Surface,vs. X Location, A1ong the Pane1 Center1ine (Y=0),Finite E1ement Resu1ts, Pane1 B
241
2000 ·
_ AA 5 psiE] 10 _+ 15 .
1000 + ++ +
Ü
A
e A +g 0
E]I/I
E.2 2 4 6 8 10Z .X (in.) gg
A
1000El
+ A
E1
+
-2000
Figure 5.17 Longitudinal Strains on the Bottom Panel Surface,vs. X Location, Along the Panel Centerline (Y=O),
° Finite Element Results, Panel C
242
decrease sharply and become compressive right at the end of the
panel. This indicates a change in curvature very near the end of the
panel due to the clamped edge condition. Comparing this with the
stiffened panel responses in Figures 5.15 through 5.17 from the finite
element model, and 3.31, 3.33, and 3.34 for the experimentally
measured responses, the effect of the stiffener in the longitudinal
direction can be seen. The principle effect is to change the location
of the change in curvature. This is seen as the location of change in
sign of the strain. For each panel this location is nearly the same
in the measured responses as in the finite element calculated
responses.
The transverse gradient of longitudinal strains, calculated with
the finite element models, is shown in Figures 5.18 through 5.21. The
bottom surface strains were computed for discrete pressure loads of 5,
10, and15T
psi in the same manner as they were done for the
experimentally measured strains. The corresponding experimentally
measured strains are shown in Figures 3.44, 3.46, and 3.47. As was
mentioned previously, Panel A with the tall web, and thick flange was
not instrumented with strain gages in these locations. These
longitudinal strain gradients therefore were not recorded for this
panel. However, the finite element results for this panel are shown
in Figure 5.19. The measured strain responses and the calculated
strains for the three other panels are very similar. Comparing the
calculated and measured results it can be seen that for both types of
results, the unstiffened panel has uniformily increasing strains from
the clamped edge toward the center. Also, for both results it can be
243
seen that near the ends of the stiffened panels the presence of the
stiffener changes the strain distribution, putting the skin into
compression and producing a strong gradient in the longitudinal
strain. In the finite element results the effects on the strain
distributions of the stiffeners are seen to be nearly the same.
However, the short web stiffener produced a somewhat lower strain
underneath the flange.
At the panels' centers, compared with the unstiffened panel re-
sponse, the presence of the stiffener has little effect on the longti-
tudinal strain distribution. The finite element model results in
Figures 5.18 through 5.21 and the experimental results in Figures
3.44, 3.46, and 3.47 are very similar at this location.
From these strain and deflection computations, it is clear the
basic mechanisms in the problem are being modeled. Qualitative
comparisouns between theory and experiment are good. Recommendations
for modifications of the modeling to more closely match the
quantitative experimental results will be made in the final chapter.
244
2ÜÜÜ + + + + A•
+ E Panel EndE E E] EIQ
+1000 A A A A A E
E A +E A IIIÜ A . 44 4U
E O1.0 2.0 3.0 4.0 5.0
Y (in.)
-1000
2000
Panel Center(X=0.0 in.)
1000·CEU') · _4 4 4 4 44 ·=— 4 E 4 4E 0
1-.0 2.0 3.0 4.0 5.0Y (in.)
-1000Ü
Figure 5.18 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, FiniteElement Results, Panel D
245 .2000Panel End
+15 (X=8.751n.)
1000 + +ED_e E1 El
ä E A A A QQ .A.2 0E A A A 2.0 3.0 4.0 6.01:1 Ü .El+ + v (in.)4-
-1000
2000Panel Center(X=0.0 in.)
1000.Eä ¤ ::1 Q Q QQ A. A. .A A, AA äl Q;U
E O1.0 2.0 3.0 4.0 6.0
_ Y (in.)
-1000
Figure 5.19· Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, Finite ‘Element Results, Panel A
' 246
2000 ._ .. Z} Panel End
in.)
1000 + "'„ ¤ P +
+ A P-1; El A AgA.2O ggZ A A ä ’2.0 3.0 4.0 6.0
E Q 11111.)+
-1000
2000
Panel Center(X=0.0 in.)
1000C
•p-
++
+E Q G El E] +o A AAS-.2 0Z 1.0 2.0 3.0 4.0 6.0
Y(in.)
-1000
EFigure 5.20 Longitudinal Strains on the Bottom Panel Surface
I
' at the Center and End, vs. Y Location, FiniteElement Results, Panel B
247
2000· é- 5 psi
Ei l0 Panel Endg +— l5 (X=8.75 in.)1000 4- ·+
.2 ß mgE + A,,, E1 A amE.202: .
saß1.0 2.0 3.0 4.0 6.0
Y (in.)-1000
2000
Panel Center(X=0.0 in.)
1000.E.2 äaa2.§m2:
0 .1.0 2.0 3.0 4.0 6.0
Y (in.)
-1000
Figure 5.21 Longitudinal Strains on the Bottom Panel Surfaceat the Center and End, vs. Y Location, FiniteElement Results, Panel C
Chapter 6.
SUMMARY, CONCLUSIDNS, AND RECOMMENDATIONS
GENERAL OVERVIEN OF STUDY
The investigation discussed in the proceeding chapters was de-
signed to contribute further to the understanding of the local and
global responses of stiffened skins. The primary objective was to
look at different stiffener and skin configurations and determine the
effect of the configurations on the strain and displacement
response. A second objective was to gain insight into the mechanisms
of stiffener and skin interactions to help direct analytical ‘
efforts. A third objective was to determine the effect of inplane
tensile prestrain on the stiffened skin responses.
Pressure loading was selected as a loading condition represen-
tative of' actual stiffened skin applications, aircraft fuselage ap-
plications in particular. In addition, the pressure loading was safe
to use in a normal laboratory environment and it produced the type of
deformations which permitted the study of the~ responses under
conditions representative of design conditions. Clamped boundary
conditions were also selected as representative of actual fuselage
applications.
A testing apparatus and test panels were designed and the basic
considerations in the design were discussed. Considerations were made
for the application of both the pressure and the inplane tensile
preload, and for the enforcement of the clamped edge condition.
Instrumentation was selected to monitor strain and deflection
responses of the panels, and to monitor the loading.
248
249
The primary responses measured were: out—of-plane deflections;
transverse gradients of transverse bending strains; and transverse
gradients of longitudinal strains. Five different panel configur-
ations were studied. The panels selected had overall dimensions and
stiffnesses representative of aircraft fuselage panels. Variations of
detailed dimensions and stiffnesses were made to determine the in-
fluence geometric and material properties could be expected to have on
panel response. The results presented in the chapters described the
effects these parameters had on the panel responses.
CONCLUSIONS4
The deflection response could be used to draw conclusions regard-
ing overall panel behavior. The conclusions are:
1) The deflection responses were strongly nonlinear, beginning at_ relatively low pressures (less than 5 psi). This nonlinearity
was due to geometric effects and was quite pronounced at highpressures.
2) The stiffener with the short web was essentially ineffectivein restraining the out-of-plane deflection response at thecenter of the panel. The deflection response of the panelwith this stiffener was much like the response of theunstiffened panel. _
3) All of the panels with the tall web stiffeners had essentiallythe same deflection response at the center of the panel. Thetwo flange thicknesses and two skin stiffnesses studied inthis investigation had little effect on the center deflection.
4) The design of the test apparatus produced an upward bowing ofthe panels. This influenced the initial deflection responsesand caused an increase in the deflections at maximum pressure.
Profiles of the deflected panels, measured transverse to the
stiffener axis, provided insight into transverse bending interaction
between the stiffener and skin. Transverse strain responses measured
250
on the stiffener flange and on the skin near the flange also provided
a measure of this interaction. Conclusions based on these measure-
ments are:
1) Transverse strain gradients exist in the area of the stiffenerflange and skin intersection. The gradient was slightly high-er at the quarter point than at the center of the panel.
2) Increasing the transverse bending stiffness of the skin re-duced the gradient. Reducing the flange thickness reduced thegradient to an even greater degree. Neither of these changesof panel configuration had any noticeable effect on the ove-rall deflection response.
3) The short web stiffener had a deflected profile which producedcompressive strains in the top surface of the stiffener flangeand in the skin adjacent to the flange at the center of thepanel. In contrast, the tall web stiffeners caused a topsurface tensile strain on the flange. At the quarter point ofthe short web stiffener the strains were nearly uniform on theflange and skin. The gradient of transverse strains was notsignificant for this panel.
Longitudinal profiles of the deflected panels showed that the
_skin responded differently than the stiffener. In the immediate area
of the stiffener the skin response followed that of the stiffener. At
transverse distances beyond the influence of the stiffener, the skin
response to the pressure load was similar to the response of the
unstiffened skin. The response of the skin in this area was primarily
a membrane response. This was indicated by the nonlinear pressure-
deflection relation. The differences between this response of the
skin in an area unaffected by the stiffener and the response near the
stiffener was resolved over a distance of stiffener influence. The
difference in the sign of the curvature from the skin to stiffener,
and the nonlinear (membrane) response of the skin, produced a
transverse gradient of longitudinal strains. These longitudinal
25l
responses indicate the effect of an inplane shear interaction between
the skin and stiffener. Because this shear interaction could
participate in local failure, observations of the longitudinal
responses are important. The conclusions based on observations of
these longitudinal responses are:
1) The transverse gradient of longitudinal strains was strongestnear the end of the panels. This is the location where thedifference in the curvature of the stiffener and skin was thegreatest. The fact that the strength of the gradient in-creased with increasing pressure suggests that this may be asignificant problem area of stiffener and skin interaction.
2) Stiffener and skin parameters studied in this investigationhad little effect on this gradient near the end of the panel.
3) At the center of the panels the sign of curvature of the stif-fener and skin were the same. The gradient was not an issue.
The effect of inplane tensile preload was also investigated.
Each panel was tested under three preload conditions. These were: a
_ light preload; a biaxial preload, and; a longitudinal preload. The
conclusions with regard to the effects of the biaxial and longitudinal
preloads relative to the light preload are as follows:
1) The biaxial preload reduced the out—of-plane deflections byproducing a stiffer response at the low pressure loads. Thiswas due in part to a flattening effect of the biaxial preloadon the initial panel shape.
2) The longitudinal preload produced larger out-of-plane deflec-tions. This was due primarily to increased panel bowing as aresult of an interaction of the preload and the test appa-ratus. _
3) The biaxial preload reduced the strain gradients measured inthe investigation. The effect of the longitudinal preload onthe strain gradients was inconclusive due to the greater panelbowing.
\
252
RECOMMENDATIONS
Recommendations for further work in this area would be directed
mainly toward improvement of the test apparatus. Specifically, the
clamping arrangement could be improved to eliminate the bowing due to
panel contact with the 0-rings inside the clamp spacing. The contact
of the panel with the inside edge of the bay of the vacuum plate could
also be eliminated with a modified clamping arrangement.
Modification of the apparatus to produce loading conditions which
could produce failures of the panels would be very useful. Some pos-
sible modifications include the attachment of a loading frame which
could apply a vertical tensile load to the stiffener web in the pres-
ence of the pressure load. This loading would simulate the force
induced by a circumferential frame member of a fuselage to a long-
itudinal stringer. Another possibility would be the application of
higher pressure loads. This could be implemented by means of a pres-
surized box mounted over the panel, sandwiching the panel between the
box and the vacuum plate. By pressurizing the box, the differential
pressure load on the panel could be increased. The positive pressures
could be kept at acceptable levels for safety considerations and an
additional 15 psi loading capacity over direct pressure loading would
be attained by taking advantage of the vacuum capability of the pre-
sent fixture.
In addition to these apparatus modifications, modifications to
the test panels could be made to eliminate the undesirable effects of
the steel doublers. The longitudinal stiffening effect and the bend— _
ing of the doublers under the action of the longitudinal preload could
253
be reduced or eliminated by splitting the doublers into small sec—
tions. The small sections would act independently and so would have
less effect on the panel response to the preloads. The disadvantage
of using small sections would be to provide less load distribution
(smoothing) from the localized clevis loads to the interior test por-
tion of the panels.
Modifications to the finite element modeling of the test panels
could improve the quantitative correlation with the measured
results. The pretest panel bowing was a significant factor in the
subsequent panel response to pressure loading. Including this bowing
in the finite element models may produce a considerable improvement in
the correlation with the experimental results. The inplane slip and
edge rotations were also seen to have had an effect on the panel
responses. Modelling these factors by defining a finite stiffness of
the edge restraints would be difficult. However, this too may be
expected to be significant to producing good correlation.
REFERENCES
1. Lundquist, E. E., "Comparison of Three Methods for Calculatingthe Compressive Strength of Flat and Slightly Curved Sheet andStiffener Combinations," NACA, TN—455, 1933.
2. Agarwal, B. L., "Postbuckling Behavior of Composite Shear webs,"AIAA Journal, Vol. 19, No. 7, 1981, pg. 933.
3. Nang, J. T. S., and Biggers, S. B., "Skin/Stiffener InterfaceStresses in Composite Stiffened Panels,“ NASA Contractor Report172261, Contract No. NAS1-15949, 1983.
4. Dickson, J. N., Cole, R. T., and Nang, J. T. S., "Design ofStiffened Composite Panels in the Post-Buckling Range," FibrousComposites in Structural Design, ed. E. M. Lenoe, et. al., PlenumPress, 1980, pg. 313.
5. Agarwal, B. L., "Design Methodology and Life Analysis ofPostbuckled Metal and Composite Panels,“ Technical OperatingReport Analytical Methods Selection, Contract No. F33615—81—C-3208, 1981.
6. Almroth, B. 0., Brogan, F. A., and Stanley, G. M., "User's Manualfor STAGS," NASA Contractor Report 165670, Contract NAS1-10843,1978.
254“
APPENDIX A
AS4/3502 MATERIAL PRDPERTIES
(Source of Information - Lockheed-Georgia, February 8, 1982)
PROPERTY R.T. DRY —67°F NET 160° Net
E11 (psi) 20.5 x 106 20.8 x 106 20.5 x 106
Egg (psi) 1.67 x 106 1.7 x 106 1.35 x 106
61g (psi) .87 X 106 .90 X 106 .60 X 106
012 .30 .35 .30
Egg (psi) · 18.5 X 106 19.5 X 106 19.5 X 106
Egg (ps1) 1.64 X 106 1.7 X 106 1.40 X 106
al (in/in—¤F) .25 x 10°6 .24 x 10'6 .24 x 10'6
ag (in/in—¤F) 16.2 X 10'6 16.0 X 10'6 16.2 X 10'6
p (lb/in3) .057
Resin Volume Fraction 36 1 3%
· 6T(O°·Limit*) .00653 .00580 .00620
EC(0°-Limit*) .00670 .00630 .00620
ET (906-Ultimate) .00500 .00480 .00380
sc (906-Ultimate) .01000 .00900 .01000
;xy(Limit*) .01330 .01330 .01330
*Limit determined at 2/3 ultimate stress, modulus values are secant alsoat 2/3 ultimate stress, initial modulus somewhat higher.
255
