AD-A112 725 DAYTON UNIV ON RESEARCH INST F/S l1/4EXPERIMENTAL AND NUMERICAL ANALYSIS OF AXIALLY C014RESSED CIRCU-(ETC(U)OCT Al N R GAULO F33615-79-C-3030

UNCLASSIFIED AFWAL-TR-8-3158 NL

2~~ flffllffllffl ll

III 1.0.0111111.25

", .L jf.l .4. IllLLi

AFWAL-TR-81-3158

EXPERIMENTAL AND NUMERICAL ANALYSIS OF AXIALLY COMPRESSEDt-3 CIRCULAR CYLINDRICAL FIBER-REINFORCED PANELS WITH VARIOUS

BOUNDARY CONDITIONS

i NELSON R. BAULD, JR.

S CLEMSON UNIVERSITYCLEMSON, SC 29631

OCTOBER 1981

TECHNICAL REPORT AFWAL-81-3158Final Report for Period 1 October 1978 - 30 September 1981

Approved for public release; distribution unlimited.

DTCD.

FLIGHT DYNAMICS LABORATORY "_.Uj AIR FORCE WRIGHT AERONAUTICAL LABORATORIES_.-. AIR FORCE SYSTEMS COMMAND_ WRIGHT-PATTERSON AIR FORCE BASE, OHIO 45433

S0 032

NOTICE

When Government drawings, specifications, or other data are used for anypurpose other than in connection with a definitely related Governmentprocurement operation, the United States Government thereby incurs noresponsibility nor any obligation whatsoever; and the fact that thegovernment may have formulated, furnished, or in any way supplied the saiddrawings, specifications, or other data, is not to be regarded by implicationor otherwise as in any manner licensing the holder or any other person orcorporation, or conveying any rights or permission to manufacture use, orsell any patented invention that may in any way be related thereto.

This report has been reviewed by the Office of Public Affairs (ASD/PA) and isreleasable to the National Technical Information Service (NTIS). At NTIS, itwill be available to the general public, including foreign nations.

This technical report has been reviewed and is approved for publication.

NARENDRA S. KHOT FREDERICK A. PICCHIONI, Lt Col, USAFProject Engineer Chief, Analysis & Optimization Branch

FOR THE COMMANDER

RALPH L. KUSTER, JR., Col, USAFChief, Structures & Dynamics Div.

If your address has changed, if you wish to be removed from our mailinglist, or if the addressee is no longer employed by your organization pleasenotify AFWAL/FIBR , W-PAFB, OH 45433 to help us maintain acurrent mailing list

Copies of this report should not be returned unless return is required bysecurity considerations, contractual obligations, or notice on a specificdocument.

AIR FORCE/56780/18 March 1982 - 200

l . . . .. .. . .. . . . . . . . . . , . . . . . .. ,,, .. . . ... _ . . .. . . .. . . . . , .. i

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (When Dala.Entered)

REPORT DOCUMENTATION PAGE READ INSTRUCTIONSBEFORE COMPLETING FORM

I. REPORT NUMBER 2. kOVT ACCESSION NO. 3 RECIPIENT'S CATALOG NUMBER

AFWAL-TR-81-3158 4fl-1~-~ -7. ____________

4. TITLE (and Subtitle) S TYPE OF REPORT & PERIOD COVERED

EXPERIMENTAL AND NUMERICAL ANALYSIS OF AXIALLY Final Report for Period

COMPRESSED CIRCULAR CYLINDRICAL FIBER-REINFORCED I October 1978-30 Sept 1981

PANELS WITH VARIOUS BOUNDARY CONDITIONS 6. PERFORMING O1G. REPORT NUMBER

7. AUTHOR(.) 8. CONTRACT OR GRANT NUMBER(I

Nelson R. Bauld, Jr.F33615-79-C-3030

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

Clemson University AREA & WORK UNIT NUMBERS

Clemson, SC 29631 Proj 2307, Task 2307N5Work Unit 2307N501

It. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

University of Dayton October 1981Research Institute 13. NUMBER OF PAGES

Dayton, OH 45469 15114. MONITORING AGENCY NAME & ADDRESS(f different from Cont oiling Office) I5 SECURITY CLASS. (of this report)

Flight Dynamics Laboratory (AFWAL/FIBRA) UNCLASSIFIEDAir Force Wright Aeronautical Laboratories (AFSC) 1.. DECLASSIFICATION 0OWNGRAONG-Wright-Patterson AFB, Ohio 45433 SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release, distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, If different from Report)

I. SUPPLEMENTARY NOTES

It. KEY WORDS (Conllnue on reverse side If necessary ,nd identify by block number)

Buckling LoadComposite StructuresPlates and ShellsJ

Finite Difference Methods

Experiments

20. A STRACT (Continue On reverse side if neceesry and Identify by block nmber)

;OThis report presents comparisons between the experimental and numerical buck-ling behaviors of fiber-reinforced, circular cylindrical panels under pre-

scribed uniform end-displacements. Numerical predictions used in the compari-sons were obtained from the energy-based, finite-difference computer proqramCLAPP. Test specimens were clamped along both curved edges and were eithersimply supported or unsupported along the straight edges.,-

DD , 4JAN 73 EDITION OF INOV SS IS OBSOLETE UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE ('When Dai Fnt-red)

FOREWORD

This report was prepared by Dr Nelson R. Bauld, Jr., Professor,Department of Mechanical Engineering, Clemson University, Clemson,South Carolina, in partial fulfillment of the requirements underContract F33615-79-C-3030. The effort was initiated under ProjectNo. 2307, "Research in Flight Vehicle Structures," Task 2307N501,"Basic Research in Structures and Dynamics." The project monitorfor the effort was Dr Narendra S. Khot of the Structures and DynamicsDivision (AFWAL/FIBRA).

The technical work was performed during the period October 1978through September 1981. Review report was submitted in October 1981and the final report in January 1982.

UAc c e : s - ,: r

] -- I/ I ,.

!L

iii

TABLE OF CONTENTS

Section Page

I INTRODUCTION

II TESTING PROCEDURE 3

1. Test Specimens 3* Program A 4

Program B 52. Test Fixture 53. Testing Machine 94. Imperfection Device 105. Positioning of Head-Plate and Base-Plate 12

6. Specimen Installation 14

IIl EXPERIMENTAL DATA 17

1. Initial Geometric Imperfections 172. Strain Measurements 18

Program A 18* Program B 18

3. End-Shortening 21

4. Buckling Behaviors 21

IV EXPERIMENTAL AND NUMERICAL RESULTS 22

I. Analysis of Results of Testing Program A 22* Specimens with simply-supported 22

straight edgesSpecimens with unsupported straight 25edges

2. Analysis of Results of Testing Program B 35Specimens with simply-supported 35edgesSpecimens with unsupported straight 40

edges

V LONGITUDINAL STIFFENERS 45

I. Introduction 452. Stiffener Strain Energy 46

3. Stiffener Energy in Matrix Form 474. Displacement Continuity 495. Finite-Difference Considerations 526. Incorporation into CLAPP 597. Quasi-Isotropic Fiber-Reinforced Stiffeners 6O

-I-AECEDi PAGJE BLAW-NOT fl1.4ML V

Appendix Page

A Strain, End-shortening, and Imperfection 68Measurements for Test Panels withSimply-Supported Straight Edges andClamped Curved Edges. Testing Program A.

B Strain, End-shortening, and ImperfectionMeasurements for Test Panels with 93Unsupported Straight Edges and ClampedCurved Edges. Testing Program B.

C Strain, End-shortening, and ImperfectionMeasurements for Test Panels for Testing 118Proqram B

D User's Manual for Computer Program CLAPP 133

vi

LIST OF ILLUSTRATIONS

Figure Page

I Geometry of curved panel specimen. 3

2 Head-plate and base-plate with auxilliary pressureblocks and clamping devices. 5

3 Testing fixture installed in the Tinius-Olsenhydraulic testing machine. 9

4 Imperfection measuring device attached to thebase-plate of the testing fixture. 10

5 Imperfection measuring device in position tomeasure initial geometrical imperfections of aspecimen. 11

6 Device used to establish the relative parallelismof the head-plate and the base-plate of thetesting fixture. 12

7 Test specimen installed in base-plate and bookendsthat supply simply-supported edge conditions. 15

8 Simply-supported edge of a test specimen showingvertical pressure blocks. 16

9 Simply-supported specimen partially installed in

the testing fixture and associated strainmeasuring equipment. 19

10 Numerical and experimental load versus end-shortening curves for a 16 in. x 16 in. panelwith simply-supported straight edges. 26

1l Analytical and numerical load versus end-shortening curves for panels with simply-supportedstraight edges. 27

12 Experimental strains corresponding to prescribedvalues of end-displacement for a panel with simply-supported straight edges and constrained circumfer-ential displacements. 28

13 Analytical nodal loads corresponding to prescribedvalues of end-shortening for a specimen with simply-supported straight edges with constrained circumfer-ential displacements. 29

vii

14 Analytical and experimental load versus end-

shortening curves for the perfect and imperfect

panel with unsupported straight edges. 32

15 Experimental strains corresponding to prescribedvalues of end-shortening for test specimens with

unsupported straight edges. 33

16 Analytical nodal loads corresponding to prescribedbalues of end-shortening for an initial imperfec-

tion of the form W = 0.005 (1+cos 7e/a) for

specimen with unsupported straight edges. 34

17 Theoretical and experimental equilibrium paths

for simply supported test specimens for testingProgram B. 37

18 Analytical load versus deflection curves for theperfect and imperfect panel with simply-supportedstraight edges and unconstrained circumferential

displacements. 38

19 Theoretical and experimental equilibrium paths for

specimens of Program B with unsupported straightedges. 43

20 Equilibrium paths for the axially compressed panelwith unsupported straight edges. 44

21 General thin-wall open cross section. 48

22 Detail of coefficient matrix [PAS2]. 53

23 Typical stiffener elements and the local numberingsystem for the surrounding grid points. 54

24 Interoid stiffener element and its local numberscheme. 56

25 Geometric details of a fiber reinforced laminate. 63

26 Stiffener stress distribution. 63

v

I viii

LIST OF TABLES

Table Page

I Experimental and numerical buckling results

for circular cylindrical panels, testing

program A.

2 Experimental and numerical buckling results

for circular cylindrical panels, testing

program B.

ix

SECTION I

INTRODUCTION

The principal purpose of this investigation is to provide a basis for

assessing the capability of the computer program CLAPP [l] to predict

buckling loads for fiber-reinforced, circular cylindrical panels under

prescribed uniform axial end-displacements.

Two testing programs were undertaken to accomplish this objective.

They are designated as Program A and Program B in this report.

Program A. Experimental buckling loads were determined for 20 specimens

having identical fiber patterns of [0/9012s and 20 specimens having iden-

tical fiber patterns of [0/+45/90] s . The specimens of a particular fiber

pattern were characterized geometrically by five different aspect ratios

and by two different sets of boundary conditions. The aspect ratios were

a/b = 1/2, 3/4, 1, 4/3, and 2, where a and b are the dimensions of the

projection of a panel into its base plane as shown in Figure 1. Boundary

conditions along the straight edges of a specimen corresponded to either

an unsupported edge or a simply-supported edge. For the simply-supported

edge a distinction between unconstrained and constrained circumferential

displacements is also made. Boundary conditions along the curved edges

corresponded to a clamped edge for all specimens.

Program B. Experimental buckling loads were determined for 6 specimens

with the same fiber pattern ([0/901 2s), the same aspect ratio (a/b = 1.247,

a = 16 in. and b = 12.83 in.), and the same boundary conditions (unsupported

straight edges and clamped curved edges). Similarly, experimental buckling

loads were obtained for 5 specimens with the fiber pattern [0/+45/90] s ,

aspect ratio a/b = 4/3 (a = 16 in. and b = 12 in.), and boundary conditions

consisting of simply-supported straight edges and clamped curved edges.

A second purpose of this investigation is to modify the computer pro-

gram CLAPP so as to minimize the effort required to input necessary data.

This phase of this investigation is contained as a USER'S MANUAL in

Appendix D.

Finally, a third purpose is to modify CLAPP so that it can be used to

predict the buckling behavior of fiber-reinforced, circular cylindrical

panels and flat plates that are augmented by longitudinal stiffeners. This

is accomplished for isotropic stiffeners with a variety of cross sections

and for a quasi-isotropic stiffener with a hat shaped cross section.

2

SECTION II

TESTING PROCEDURE

(Il-i). TEST SPECIMENS. Each of the circular cylindrical specimens of

Program A and Program B was laminated from graphite-epoxy, and each speci-

men was cured in a mold for which the external radius was )2 inches.(I)

The external radius of a specimen tended to be slightly less than 12 inches

upon removal from the mold. The thickness of a test specimen was taken as

an average of the thicknesses at 32 locations along a perimeter located

uniformly 1-1/2 inches from the exterior perimeter of the specimen. The

average thickness for each specimen of Program A is shown in column 2 of

Table 1. The average thickness for each specimen of Program B is shown

in column 2 of Table 2. Figure 1

indicates pertinent geometrical

parameters of a typical specimen.

TThe radius, R = 12.0 in., is the

aradius of a perfectly circular

panel installed in the testing

fixture, and the thickness shown ___

is the average thickness of a 0.038 in.

typical panel.

Laminate stiffness properties R=2. in.

were calculated by lamination .Figure 1. GEOMETRY OF CURVED

theory [2] using the following PANEL SPECIMEN

lamina properties:

(1) All specimens were fabricated and cut by the Air Force Flight DynamicsLaboratory, Air Force Wright Aeronautical Laboratories, Air Force SystemsCommand, Wright-Patterson Air Force Base, Ohio.

3

E = 20,524 ksi, E = 1,333 ksi, G2 = 752 ksi, =12 0.335, and ) 2 =

0.022. E and E22 are Young's moduli of elasticity parallel and perpen-

dicular to the fiber direction, G12 is tht shearing modulus associated

with these two directions, and ,12 and -21 are Poisson ratios.

Program A. The specimens of Program A were distinguished by aspect ratio

(a/b), laminate fiber pattern, and boundary conditions.

Specimens having five different aspect ratios (a/b = 1/2, 3/4, 1, 4/3,

and 2) were tested. It is convenient to perceive of specimens that are

associated with a specific aspect ratio to form a group. Thus, five

separate groups of specimens are identifiable.

Each group of specimens consisted of two sub-groups: one sub-group

being associated with simply-supported straight edges, and one sub-group

being associated with unsupported straight edges. Boundary conditions

along the curved edges were clamped for all specimens in each group.

Two laminate fiber-patterns ([0/9012 and s

for each sub-group. Moreover, each member of each group was duplicated to

provide a means to assess repeatibility of experimental results.

From the foregoing discussion it will be observed that each group con-

tained eight specimens: four with simply-supported straight edges and

four with unsupported straight edges. Of the four specimens in a sub-

group (either simply-supported or unsupported straight edges) two were

characterized by a fiber-pattern of [0/90 1 2s and two were characterized

by a fiber-pattern of [0/+45/90] . The complete experimental effort

amounted to forty specimens. Table I has been organized to ref'ect the

foregoing classification of specimens.

4

I

The physical dimensions of the base-planes (projected area of a specimen)

of the specimens associated with the five aspect ratios were 8 x 16, 12 x 16,

16 x 16, 16 x 12, and 16 x 3 (all dimensions are in inches). These dimen-

sions correspond to the inside dimensions of the specimens after installation

in the testing fixture.

Program B. As was stated in the introduction, the specimens of Program B

can be categorized into two groups: one group with fiber pattern [0/9012s'

aspect ratio 16/12.83 = 1.247, and unsupported straight edges; and one

group with fiber pattern [0/+45/90] s aspect ratio 16/12 = 4/3, and simply-

suported straight edges. The results of buckling tests on these specimen

are tabulated in Table 2.

(11-2). TEST FIXTURE. The testing fixture used in both testing programs

was a modification of a test fixture used by Wilkins [3]. Modifications

of the Wilkins' testing fixture were necessary to accommodate specimens of

different aspect ratios. Figure 2 _. I .

shows the head-plate and the base-

plate (with their auxilliary

pressure blocks and clamping

plates) through which an axial

compressive load was applied to

a specimen. All surfaces of the

head-plate, and of the base-

plate, were carefully machined

so that they were within 0.001 in.

of being parallel.FIGURE 2. Head-plate and base-plate with

auxiliary pressure blocks andclamping plates.

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8

(1-3). TESTING MACHINE. An axial compr(,ssive load was appli ed to a ,pcci-

men through a 120,000 lb Tinius-Olsen hydraulic te.-,ting machine. Most experi-

mental buckling loads were of such a magni tudt that the intermediate ranqe

(12,000 lb range) of the testinq machine could be ned effectively. The

finest division for this range is 50 lb. The low range (3000 lb ranqe) wau

used to test several specimens with unsupported straight edges. The finest

division for this raniye is 5 lb.

The surfaces of the platten and the cross-head of the testing machine

were dressed so that they were nearly plane.

The head-plate and the base-plate of the testing fixture are shown

installed in the Tinius-Olsen testing machine in Figure 3.

Early in testing

Program A it became

apparent that the

cross-head would

tilt as the reactive

force of the speci-

men on the cross-head

tended to lift it off

the threads of the

vertical columns. To

eliminate the tilting

action two large

aluminum nuts were

machined and placed FIGURE 3. Test i ng Ii xt ure inta, it i n the Tin i,,-h 1 sen hyd raul I i c ttI i rM mal i ne.

on the vertical screws

9

beneath the cross-head. At an appropriate point during the installation

of a specimen these nuts were tightened against the lower surfaces of the

cross-head causing it to lock in place. These aluminum locking nuts are

shown in Figure 3.

(11-4). IMPERFECTION DEVICE. Figure 4 shows the mechanical device that

was used to measure deviations of a specimen from a perfect cylindrical

form; that is, to measure the initial geometric imperfections of a speci-

men.

Components of this device were constructed so that the vertical sides

of the circular groove in the platform of the device were concentric with

the vertical sides of the circular groove in the base-plate of the testing

fixture. The imperfection device

was secured to the base-plate of

the testing fixture so that its

slotted vertical platform-

supports were perpendicular

to the base-plate. This en-

sured concentricity of the

platform groove with the groove

in the base-plate for any

platform level.

To position the imperfec-

tion device relative to the

base-plate of the testing

fixture, the dial indicator

mechanism shown in Figure h FIGURE 4. Imperfection measurinq device

attached to the'base-plate ofthe testing fixture.

10

was designed so that it could be moved smoothly and snugly in the circular

groove of the platform of the imperfection measuring device. With the tip

of the dial indicator extension resting against the vertical side of the

circular groove in the base-plate, the mechanism was moved along the plat-

form groove. By trial the imperfection measuring device was adjusted rela-

tive to the base-plate so that the pointer of the dial indicator was undis-

turbed for a complete cycle along the platform qroove. Once the proper

position was located the imperfection measuring device was secured to the

base-plate of the testing fixture by machine bolts. Positioning pins were

installed so that the correct position could be duplicated. This procedure

resulted in a variation of less than 0.001 in. for a conplce trav'erse oi

the platform groove.

Holes for positioning pins were drilled at one-inch intervals along ,he

slotted vertical platform supports. This ensured that the position of the

imperfection measuring

device relative to the

base-plate of the testing

fixture could be duplicated

at appropriate levels.

Once the platform was lo-

cated at a specified level

by the posit ioninq pins,

it was locked in that

position by cap screws.

Figure 5 shows the

imperfection measuring FIGURE 5. Imperfection measurinq device inposition to measure initial qeometric

imperfections of a specimen.

II

device installed on the testing fixture. Deviation of a specimen from per-

fect circularity were measured by movinu the dial indicator mechanism along

the platform qroove.

(11-5). POSITIONING OF HEAD-PLATE AND BASE-PLATE. Two requirements were

essential for proper alignment of the head-plate relative to the base-

plate of the testing fixture. First, the circular arc associated with an

edge of the circular groove in the head-plate and the correspondino cir-

cular arc of the circular groove in the base-plate must lie in parallel

planes. This requirement is realize -.": the head-plate (when attached

to the cross-head ot the testir., r , and the base-plate (when attached

to the platten of the testinq r c ire parallel. Secondly, these two

arcs must lie in a conmmon clrc 1 ndrical surface that is perpendi-

cular to the base-plate (and, hencie, p.,erpendicular to the head-plate).

Parallelism of the heaJ-

plate and the base-plate was

assessed using the device

shown in Figure 6. This

device cons;ists of a rigid

base that was machined to

fit snugly in the circular

groove of the base-plate,

and that could be moved

smoothly along the groove.

A dial indicator was

attach'd to a 'tiff -t, FIGURE 6. DeviCe ued to etabli,,h the relative

rod which was, Cilr. 1 ( lt i sm of tit, head-plate atnd thewo n c w a, a fixeu tst-plate o-f tit, tet i in t iX IJre

I2

the moveable base. With the plunger of the dial indicator resting against

the surface of the circular groove in the head-plate, the device was moved

along the circular groove in the base-plate. Using the centerline of the

circular groove as a reference, it was observed that the variation in the

distance between the surfaces of the grooves in the head-plate and the

base-plate did not exceed 0.0035 in. on either side of the centerline for

the maximum arc of 18.5 in. (circumferential arc length of the widest speci-

men). This variation was accordingly smaller for narrower specimens. Once

the head-plate and the base-plate had been assessed to be as parallel as

reasonable efforts would allow, they were securely clamped to the cross-

head and to the platten of the Tinius-Olsen testing machine by specially

designed clamps. These clamps can be seen in Figure 5.

The imperfection device was used to bring corresponding circular arcs

in the head-plate and in the base-plate into concentricity. To accomplish

this alignment the platform of the imperfection measuring device was posi-

tioned at an appropriate level and the tip of the dial indicator extension

shown in Figure 4e was allowed to rest against the vertical side of the

circular groove in the head-plate. Since the groove in the platform of the

imperfection measuring device is concentric with the vertical edge of the

circular groove in the base-plate, the corresponding edge of the circular

groove in the head-plate will be concentric with its counterpart in the

base-plate when the pointer of the dial indicator is undisturbed as the

indicator mechanism is moved smoothly along the platform groove. Thus,

appropriate alignment of the head-plate and the base-plate of the testing

fixture was accomplished.

13

(11-6). SPECIMEN INSTALLATION. The procedure used to install specimens in

the testing fixture was similar for specimens with unsupported straight

edges and for specimens with simply-supported straight edges. It is con-

venient to describe the installation procedure for the specimens with

unsupported straight edges first, and, subsequently, describe the additional

installation features associated with the specimens for which the straight

edges were simply-supported. In either case the curved edges of all speci-

mens were clamped.

In preparation for buckling tests of specimens with unsupported straight

edges, a specimen was centered in the circular groove of the base-plate of

the testing fixture and the pressure blocks were adjusted by finger tightening

appropriate screws. The platten of the testing machine was then raised to

allow the upper curved edge of the specimen to enter the circular groove of

the head-plate to approximately three-quarters of the groove depth. Pressure

blocks in the head-plate were then adjusted by finger tightening appropriate

screws in the head-plate. Generators at several locations along the circum-

ference of a specimen were aligned vertically with a precision square. The

platten of the testing machine was then raised until the specimen experienced

a compressive force of 25 lb. Pressure blocks in the base-plate and in the

head-plate were adjusted to their final positions by applying a 40 in-lb

torque to appropriate screws while the 25 lb pre-load was maintained.

Preparation for buckling tests of specimens with a simply-supported

straight edges was similar to that for specimens with unsupported straight

edges. A specimen was centered in the circular groove of the base-plate

and its straight edges were inserted in the slots of the vertical edge

supports (hence forth referred to as book-ends) as shown in Figure 7.

14

Pressure blocks in the base-plate and at each book-end were adjusted to

the finger tight position. The platten of the testing machine was then

raised to allow the upper curved edge of the specimen to enter the circular

groove of the head-plate to approximately three-quarters of the groove

depth. Pressure blocks in the head-plate were then adjusted to the finger

tight position. Generators

at several locations along

the circumference of the

specimen were aligned

vertically with a preci-

sion square. The platten

of the testing machine

was then raised until the

specimen experienced a

compressive force of 50 lb.

Pressure blocks in the

base-plate and in the head- FIGURE 7. Test specimen installed in the base-

plate and book-ends that supplyplate were adjusted to the simply-supported edge conditions.

40 in-lb position, and the

vertical pressure blocks in the book-ends (see Figure 8) were adjusted to

the finger tight position for specimens of Program A.

For Program B the pressure exerted on the specimen by the vertical

pressure blocks was adjusted to different amounts.

15

FIGURE 8. Simply-supported edge of a test specimen

showing vertical pressure blocks.

16

SECTION III

EXPERIMENTAL DATA

(Ill-l). INITIAL GEOMETRICAL IMPERFECTIONS. Initial deviations of a

specimen from a perfect cylindrical surface are referred to in this

report as initial geometric imperfections. Imperfection measurements

were obtained at the nodes of a rectangular grid drawn on the inner sur-

face of a specimen. Details of the imperfection grids for specimens

with different aspect ratios are listed in Appendices A and B for speci-

mens with simply-supported straight edges and unsupported straight edges,

respectively. This data corresponds to testing Program A. Details of

the imperfection grids used in testing Program B are listed in Appendix C.

For testing Program A, the reference point for imperfection measure-

ments lies on the specimen centerline two inches below the upper clamped

edge. Measurements were made at equal intervals on either side of the

specimen centerline, and at equal intervals along the generators of a

specimen. Measurements for specimens with unsupported edges were obtained

along these edges, while measurements for specimens with simply-supported

edges were obtained as close to the straight edges as the imperfection

measurinn device would permit. These observations are ref~ected in the

imperfection data contained in Appendices A and E. Actual spacing dimen-

sions for the imperfection grid associated wit'i each panel aspect ratio

are shown in these appendices also.

For testing Program B a specially constructed device, with two circu-

lar members that were concentric with the groove in base-plate, was used

to establish the reference point for imperfection measurements. Measure-

ments for imperfections were made at the locations described for Program A.

17

Actual spacing dimensions for imperfection grids associated with panels

with unsupported straight edges and simply-supported straight edges are

indicated in Appendix C. The imperfection measurements for Program B are

also presented in Appendix C.

(111-2). STRAIN MEASUREMENTS. It was of interest to determine if the

axial compressive end-load was applied uniformly along the curved edges

of a specimen.

Program A. For testing Program A, axial strains were measured along an

arc lying one inch below the upper clamped edge on the specimen centerline

and at two other equally spaced points on both sides of the centerline.

Electrical resistance strain gages were bonded at identical locations on

both sides of a specimen so that, by means of an appropriate four-arm

bridge, only axial strains were sensed. Locations of the strain gages on

the surface nearest the center of curvature of a specimen can be observed

in Figure 7. Appendices A and B contain details for strain gage locations

for Program A.

Program B. For testing Program B, axial strains were measured atry' five

locations described in Program A for specimens with unsupported edges.

Axial strains were measured at only three locations for soecimens with

simply-supported edges: on the centerline and at two points symmetrically

located relative to the centerline. Appendix C contains details for strain

gage locations for Program B.

Strain gage readings were obtained using a Vishay/Ellis-20 digital

strain indicator and a Vishay-Ellis-21 ten channel switching and balancing

unit. This equipment is shown in Figure 9. Strain data associated with

18

''l h i ' -" ' i I I il i ... ... j

r -•

testing Program A are 3 a a

presented in Appendix A

for specimens with simply-

supported straight edges,

and in Appendix B for

specimens with unsupported

straight edges. Strain

data associated with

testing Program B are

presented in Appendix C.

The strain data indi-

cates that the distribution FIGURE 9. Simply-supported specimen partiallyinstalled in the testinq fixture and

of force on the curved edge associated strain measuring equipment.

of a specimen is essentially

uniform in the very early

stages of the loading pro-

cess, but quickly becomes nonuniform. These observations remain valid for

all specimens in each testing program.

Consider specimens with unsupported straight edges. As was stated pre-

viously, specimens were not perfectly circular cylindrical as they emerged

from the mold. Consequently, installation in the testing fixture caused

regions near the ends to assume a circular cylindrical shape of radius 12

inches, while cross sections away from the ends assumed noncircular shapes

with the unsupported edges "dishing" toward the center of curvature. Gen-

erally, the centerline and generators in the regions on either side of the

centerline were straighter than generators near the edges. Since the axial

stiffness of a small strip of specimen parallel to a generator depends on

19

.. . . Ii ll . . . . . . . m.. .. ... . "" " n .. . l l I I I/ i n I I . . . .. . II, -j

its flexural stiffness as well as its in-plane stiffness, the strains asso-

ciated with strips located at various sites on a specimen should be expected

to be different. Indeed, the non-uniformity of the strain distribution

should be expected to be intensified as the loading process proceeds. It is

noted, from the strain data for specimens with unsupported straight edges in

Appendix B, that the strains near the straight edges actually changed from

compression to tension during the early stages of loading. This reversal of

strain near the straight edges is associated with the bifurcation load for

the specimen under an essentially uniform end-load (as opposed to uniform

end-displacement). A more detailed discussion of this behavior is presented

in a later section.

Now consider specimens with simply-supported straight edges. These

specimens experienced the same "dishing" effects as specimens with unsupported

straight edges; however, the book-ends forced the edges to become straight

with the consequent configuration change on the interior of a specimen.

Accordingly, since these initial installed configurations occur in an essen-

tially random manner, nonuniform strain distributions should be expected

during the loading process.

Another possible reason for the nonuniform strain distributions exhibited

by specimens with simply-supported edges is the asymmetry in the axial dis-

placements that can be introduced at the book-ends. The strain distribution

on the interior of a specimen will deviate from uniformity if the axial dis-

placement distributions along the two simply-supported edges differ.

The further observation should be made that not only do the initial imper-

fections influence the buckling resistance of a specimen, but a certain unknown

initial stress distribution is associated with the installed initial configura-

tion that also influences the buckling resistance. The influence of the

20

initial stress distribution on the buckling resistance is rather capricious.

The initial geometric imperfections that are incorporated in CLAPP assume

that the imperfect configuration is stress free.

(111-3). END-SHORTENING. The end-shortening of each specimen in testing

Programs A and B was measured with a dial indicator that was positioned so

as to determine the relative displacement between the platten and the

cross-head of the Tinius-Olsen testing machine. The axial compressive load

applied to the specimen was read directly from the testing machine. Load

and corresponding end-shortening data are listed in Appendices A and B for

specimens of testing Program A and in Appendix C for specimens of testing

Program B.

(111-4). BUCKLING BEHAVIORS. Experimental buckling loads for the 40 speci-

mens associated with testing Program A are listed in column 7 of Table 1

and those associated with the 10 specimens of testing Program B are listed

in column 5 of Table 2. The recorded experimental buckling load for each

specimen of either testing program was characterized by a distinct loss in

load carrying capacity. Loss of load carrying capacity was detected readily

from the load-dial of the Tinius-Olsen hydraulic testing machine, and was

always accompanied by a sudden shift in the equilibrium configuration of

the specimen that was clearly audible and visible.

21

SECTION IV

EXPERIMENTAL AND NUMERICAL RESULTS

(IV-l). ANALYSIS OF RESULTS OF TESTING PROGRAM A. The theoretical buckling

loads shown in column 8 of Table 1 were calculated assuming that each panel

was subjected to a force that was uniformly applied along its curved edge.

The bifurcation branch of CLAPP was used to calculate these buckling loads.

Consequently, the theoretical buckling loads listed in Table 1 correspond

to bifurcation under a uniformly applied axial compression using both a 12

x 12 and a 20 x 12 finite difference grid. For this bifurcation analysis the

20 x 12 grid yielded a bifurcation load less than three percent smaller than

the 12 x 12 grid. Nevertheless, numerical calculations for the bifurcation

load for each of the remaining specimens were obtained using either a 20 x

12 or a 16 x 12 finite difference grid. The clamped boundary condition along

a curved edge of a specimen requires the transverse displacements be zero

along a line of nodal points coincident with the curved boundary and along

a parallel line of nodal points just inside the boundary. The larger num-

ber of grid points was always taken along the generators of a specimen to

minimize this internal constraint.

SPECIMENS WITH SIMPLY-SUPPORTED STRAIGHT EDGES. Table I shows that the bifur-

cation load predicted by CLAPP was greater than its corresponding set of

experimental buckling loads except for one specimen. The ratio of the modi

fied experimental load to the numerical bifurcation load is shown in the last

column of Table 1 for each specimen. The modified experimental buckling load

was obtained by assuming that the observed experimental buckling load was

uniformly distributed along the curved edge of a specimen and only the portion

22

of the curved edge between the book-ends contributed to the buckling of a

specimen.

The ratio of the modified experimental buckling load to the theoretical

bifurcation load fell in the range 0.5 < p < 1.0 for eighteen of the twenty

specimens with simply-supported straight edges. The ratio was 0.458 for

one specimen and 1.072 for another. We remark that theoretical bifurcation

loads predicted by the energy method represent upper bounds to the classical

bifurcation loads associated with the test specimens. Moreover, in the

presence of initial geometric imperfections the experimental buckling loads

can be expected to be less than the classical bifurcation load if the speci-

ment is imperfection sensitive. If a specimen is not sensitive to initial

imperfections its experimental buckling load can be expected to compare

favorably with the theoretical bifurcation load.

Another complicating factor is the nature of the simply-supported boun-

dary condition. Actually two different types of the simply-supported boun-

dary conditions must be recognized. Normally, a simply-supported boundary

condition implies the bending moment and transverse displacement are zero.

In addition to these conditions, in-plane displacements or membrane forces

must be specified. Consequently, with reference to the simply-supported

test specimens, circumferential displacement can be prevented, can be

allowed to occur freely, or, there can be some intermediate partial restric-

tion of circumferential displacements. The theoretical bifurcation loads

listed in Table I correspond to freely occurring circumferential displace-

ments along the straight edges.

The foregoing observations are offered in explanation of the rather

large difference between the experimental buckling load and the theoretical

bifurcation load for some test specimens and the much better agreement

23

between the two loads for other specimens. The ratio 1.072 for one test

specimen is believed to be a quirk arising out of the way the modified

experimental buckling load is defined.

Figure 10 shows the experimental and numerical load versus end-

shortening curves for a 16 in. x 16 in. panel with simply-supported

straight edges. The numerical load vs end-shortening curve was obtained

using measured initial imperfections. A plot of the normalized buckling

determinant is also shown in the figure. We note that the numerical curve

is essentially linear even though initial imperfections are present.

Furthermore, the panel buckled apparently by bifurcation as indicated by

the system buckling determinant becoming negative.

CLAPP was modified to provide the capability of prescribing uniform

end displacements as opposed to prescribing uniform end load.

Figure 11 shows the experimental and theoretical load versus end-

shortening curves for the 16 in. x 8 in. specimen with the [0/9032s fiber

pattern. The theoretical bifurcation loads for conceptual models with

simply-supported edges are 2522 lb when circumferential displacements occur

freely, and 4311 lb when circumferential displacements are prevented at the

straight edges. The experimental buckling loads for the two test specimens

are 2500 lb and 3240 lb.

Thcre is, perhaps, better agreement between the theoretical bifurcation

loads and the experimental buckling loads than is immediately obvious. Con-

sider the experimental curve labeled 1 in Figure 11. The urosual shape of

this load versus end-shortening curve appears to be the result of the panel

slipping circumferentially in the book-ends at a load near 300 lb. In this

test it becomes clear that the friction forces exerted by the vertical

24

pressure blocks on the specimen was not sufficient to prevent circumferen-

tial displacements. Consequently, at approximately 300 lb the book-ends

allowed circumferential displacements to commence. However, the specimen

edges apparently made contact with back surfaces of the book-ends and

circumferential displacements were prevented from approximately 1500 lb

onward. One expects the experimental buckling load for this specimen to

fall between the two theoretical bifurcation loads.

The behavior exhibited by the experimental curve labeled 2 in Figure

11 can be explained in a similar manner. Initially the friction forces

exerted by the vertical pressure blocks on the specimen is sufficient to

prevent circumferential displacements. At a load of approximately 800 lb

a gradual slippage occurs and, finally at a load of approximately 2250 lb

the friction forces were not sufficient to prevent or restrict these dis-

placements any longer. A sudden slippage occurred that resulted in the

buckling of the specimen before its straight edges made contact with the

back surfaces of the book-ends. Accordingly, one expects the experimental

buckling load for this specimen to agree closely with the theoretical

bifurcation load corresponding to the simple-support condition when circum-

ferential displacements occur freely.

The experimental strain distribution shown in Figure 12 shows an en-

couraging resemblance to the calculated nodal load distribution shown in

Figure 13.

SPECIMENS WITH UNSUPPORTED STRAIGHT EDGES. Table 1 shows that the bifurca-

tion load predicted by CLAPP was less than its corresponding set of experi-

mental loads for every specimen. This unexpected behavior can be explained

as follows. Because the radius of a specimen was less than 12.0 in,

25

Panel Dimensions: 16 in x 16 in2 00O - Fiber Pattern: [0/+45/90] s

Boundary Conditions: Clamped curved edges, Bifurcation atSimply-supported straight edges 8125 lb

IOOO Finite-Difference Grid: 20 x 12 Lost load carry in" o€ ./ capacity 5700 lb

AA

- 00 •i Y

o LOAD IHTETV'i.yf3

400 A

El - numerical200 --- experimental

00 I I I

0 0.5 1.0 1.5 2.0 2.5 3.0AVERAGE END SHORTENING, in x 10-2

FIGURE 10. Numerical and experimental load versus end-shortening curvesfor a 16 in x 16 in panel with simply-supported straightedges.

26

4400Buckling Limit When Circumferential .- 31 1 1L,.

4,200 Displacements are Precluded cliverqeuce at 0.01975

On0

3800

3600 Analytical Equilibrium Path,,

3400

3200 - 210 b.b c l(

3000

2800

2600 Bucklinq Limit When-z_ 52 bCircumferential 22 b 0

2400 Displacements Occur -

Freely 11250

2200

2000 0 _,-Experimental EquilIibrium~ Pa-th,

1800

- 1600

0400

1200

10("o PANL; 16 in x 8 in

800 FIBER PATTERN: 10/901EDGE CONDITIONS: Clamped Curved Edges

600 S impl v-supported st ra ighted a s

400

200

0.0 0.,2 0.4~ 0.6 0.3 1.0 1.2 1.14 1.6 1.8 2.0 2.2 ?.4 2.6 2.5 3.0

End-Shn)rtenin 1 (x 10- ) ( inches)

FIGURE I. Analytical and exter imt'ntal loaid vs. end-'.horioni nn cuives for p~iflt' Iwiji h imoily-suippoirtd ',traioht eqs

27

>L

U- -u C

E W a Q)

:) 'a

7 7p

-L H- wiC

'i:C:

a~ 0

C- L) -

- Lc3

C) C C)

-C: ) ) C: C) C ) C - 0 )0 0 C: ) 0j CD C1 C

N N - CIS C t

C) C '.C H '

28 >

C:

o

0~

-Cc,

C)D E

01) r-.u

u ~0 4) (

0z n

CIO C)C

CC00

-' C)

j c

IVOON

29

distortions of the straight edges of a specimen occurred upon clamping

its curved edges in the testing fixture. The experiment buckling load is

believed to correspond to a limit point load that is greater than the

bifurcation load for a perfectly cylindrical geometry. In other words,

the initial distortion of the straight edge- of a specimen prevents an

experimental detection of a bifurcation load corresponding to a wrinkling

of these edges for a perfect cylindrical geometry under a uniformly dis-

tributed edge compression.

We remark that the bifurcation loads predicted by CLAPP correspond to

cylindrical specimens without initial imperfections under forces that are

uniformly distributed along the curved edges. It is important to note

that axial and circumferential dispiacements along the curved edges are

not specified. Consequently, theory predicts a specimen will collapse at

the bifurcation load.

The experimental model is clamped tightly in the head-plate and in the

base-plate so that circumferential displacements along the curved edges are

prevented. More importantly, axial deformations are restricted by the

relative movement of Lhe cross-head and the platten of the testinq machine.

Consequently, when the straight edges buckle the testing fixture prevents

the collapse that theory predicts for the specimen under uniform load. As

a result of the clamp conditions the specimen retains significant load

carrying capacity. In fact, the experimental buckling loads correspond to

limit points in the post buckled region.

A close inspection of the strain data indicates the strain at the

straight edges changed sign at loads that are in the appropriate neighbor-

hoods of the theoretical bifurcation loads. The sign change on the edge

30

strains corresponds to the observed severe distortion of the straight edges

of a specimen. The load levels at which the sign change occurred depended

on the initial imperfection in the specimen.

CLAPP was modified so that the buckling behavior of specimens under

prescribed uniform end-displacements could be studied.

Figure 14 shows the experimental equilibrium paths for the 16 in. x

8 in. specimens with the [0/90]2s fiber pattern. It also shows equilibrium

paths predicted by CLAPP for initial imperfections of the form W (x,y) =

WI(l+cosrx/2a) for amplitudes WI = 0.0, +0.005, and -0.010. The limit point

buckling loads discussed previously are clearly evident. The ratios of the

experimental buckling loads to the theoretical limit load for a perfectly

cylindrical specimen are 0.85 and 0.83. The ratios of the experimental

buckling loads to the theoretical limit load for an initial imperfection

of amplitude 0.005 are 0.93 and 0.91. Even better agreement is expected

for the exact imperfection distributions.

Figure 15 shows the strain distribution at various load levels for the

specimen discussed in the previous paragraph. Evidently, the force applied

to the curved edges of the specimen was uniform during the early stages of

the loading process; that is, during the initial increments of prescribed

end-displacements. Accordingly, the bifurcation load predicted by CLAPP

for a uniformly applied end-load should agree qualitatively with the load

at which the sign change occurred for the edge strains. The theoretical

bifurcation load from fable 1 is 476 lb and the load at which the axial

edge strain ceased to increase was near 600 lb.

Figure 16 shows the nodal forces predicted by CLAPP for the same speci-

ment distribution. During the initial increments of prescribed end-

31

0 7

C,

C C

C) co-L C

C)C

- L-) C

LL- L. CC

xo '

w LLJ0 z CL.)0 Lj >> - .s *C~

vi~~- 4)L;)L0

(T\ --4

00

LU a. m

o 00 0 00 00 0 0

(qi) avo ivio

32-

500 *STRAINI GAGE LOCATION

FINITE-DIFFERENCENODAL POINT

400 -PANEL: 16 in. x 8-i

- (o/9012s

S300- ime

curve edge

200 2

-~jX:I.'0CzL.J H

2.. 34 8 9 i

GAGE LOCATION

FIGURE 15. Experimental strains corresponding to prescribed Values,of end-shor ten ing for test -.pec i ins Wit h LmflSLpporte.I

t ro i (Ilit edge,,.

33

cc

Cr~l U

cc,-

Z - c c

c C) ) \

LLJ~- -- 0

-IT~' z -o

C3 Co_C ~~~ LuDw-

J)

-vi

CC

AO c

C- 001

C C ,

U

- 0

C-,

0 0 0 3 0 03 0 0 0DLI' n ~ N - 0 C 0) \ Ul -T (N -

(qi) avoi IVOON

314

displacements the strain distributions and the nodal force distributions

are nearly uniform. These distributions become nonuniform as the loading

process continues; however, there is a visible agreement between the

experimental strain distribution and the calculated nodal load distribution

for all levels of prescribed end-displacements.

(IV-2). ANALYSIS OF RESULTS OF TESTING PROGRAM B. The theoretical buckling

loads shown in column 6 of Table 2 were calculated assuming that each panel

was subjected to prescribed end-displacements that were uniform along the

curved edges. Calculations were made for 16 x 11 and 20 x II finite-

difference grids to check the convergence of the numerical process.

SPECIMENS WITH SIMPLY-SUPPORTED EDGES. The experimental equilibrium paths

for five 16 in. x 12.83 in. specimens with the (0/+45/901 s fiber pattern

and simply-supported straight edges are shown in Figure 17. The load at

which each specimen buckled is marked on the graph beside the corresponding

equilibrium path. The theoretical equilibrium path is also shown in the

same figure for the perfect panel and for an initial imperfection amplitude

of -0.010 in. The two paths essentially coincide except that their termina-

tion points (buckling loads) are different (8064 and 6608 lb. for the per-

fect and imperfect panels, respectively). These buckling loads correspond

to a 16 x 11 finite-difference grid. A 20 x 11 finite-difference grid was

also used to calculate the buckling loads for the same perfect and imperfect

panels. The equilibrium paths in this case were indistinguishable from

those obtained using the 16 x 11 finite-difference grid except that their

termination points (buckling loads) are somewhat less (6950 and 5622 lb.

for the perfect and imperfect panels, respectively) than those associated

with the 16 x 11 finite-difference grid.

35

Figure 18 shows theoretical equilibrium paths for the perfect panel and

the imperfect panel (WI = -0.010 in.) where, instead of using end-displacement

as a measure of the system displacement, the norm of the transverse displace-

ments is used. These curves exhibit more clearly the nonlinear character of

the equilibrium path. These curves correspond to the 20 x 11 finite-

difference grid. Also note the mathematical form of the geometric initial

imperfection shown on the same figure.

The theoretical buckling load was detected numerically as a change in

the system buckling determinant from positive to negative. This indicates

that the simply-supported panel experienced bifurcation buckling. A plot

of the normalized buckling determinant versus total end load for an initial

imperfection amplitude of -0.010 in. is shown in the upper left hand corner

of Figure 18.

The initial imperfection amplitude corresponds to a radial deviation

from a perfect cylinder of 0.020 inches at the geometric center of the panel,

which is approximately equal to one half the panel thickness. This is a

rather large initial imperfection. The magnitudes of the measured initial

imperfections were frequently larger than 0.020; however, the distribution

of the imperfections were different. Generally, the largest imperfections

occurred near the edges of a specimen with somewhat smaller ones occurring

near the centerline.

The 16 x II and 20 x 11 finite-difference grids gave 8064 lb and 6950

lb as the bifurcation loads for the perfect panel. That is, the 20 x II

grid predicted a bifurcation load 13.8% lower than the 16 x 11 grid. Further

improvement in the theoretical buckling load is expected with a further

refinement in the finite-difference grid. CLAPP is presently dimensioned to

36

In) In en )

Inn

-~S-

1.0 .0 oC- In O .Cco C0 r-

CD. .0 "a(Zr .0 0: C0

11 S5- '- k.0 LO) 0

-: 00 U

-0 I (j C 0:2cC\J -0 (Nj 4-

S.. - 2 (A:9 I~ CCC -

E- ~Cj CD (= - k C\j ca_

-C L) . ( x LOV) E

Alo U) a ~ -. ~w+Jo .0- D s- - s-

_0~~ c 0cI 'a 0- oo F

-0 4-3 SO.- CL E1x10 ) cCl 0 ) S0 -4- V)- a

*- .. > o U C') LU C)( I. - CL (V-- -

+1 C) :30 EO .. Wc S.. O0) u :3-0 c0O= +)0

x LOJ a)04 L.-L'(V---- c

+i E C. a) G

O o .-

LUJ

F- U CA

0a. LO 4-3 a)03 - 5-..-

C) L C) CL

a- La.. Co L) 1O(.C')

C:)oD 0) 0) CD C0 0) 0 C0 0D 0 00 0 0D 0 0D C0 0D 0 0 0D0D 0) 0 0 0D CD C= C CD 0

0D (n 0; rl: I. ) 1r CO; (N-7

qt 'aVOI OlN] lVioi

37

C)

5- - ) EE LnO*I a0) 4-1

LO (J 4- ( UU CL-a)L(L\ s 0 0) V)0 Cr a4)E

ea c. LA >' C4) 0 C -0)

on w 0 :

,n-0" )-C a) 0) I- Q) (N. +-.W )v C: -C~ I I -0 - C) C = C) 0-0' a - C0) 1 If 00 -:T.- ) a C

4)4-) iLA OLLn N O *~-a.'1O 0 CD 0--0I) * v

- = S-

0)4-4- E 0

- C) 0) U

4- S-u- 0M~ < CD U-

CL C:) a) 0L) CL

ULU L.1 U- ( )= C _- .C:< - CD co 4-) -

CL U- wi C) '0S- S-

C) o0+-)4- i

C C=

S-c-

C~ C) 4)0

LO - C) -N a)

-u LJn

* 4-)

a m ro =

-4- CLS

0- C) Ci

oM 0-

09 0 0D C ) C

m ~ ~ o 0;L; 0

qL -IVO 0N IVI>

038

handle a maximum 20 x 12 finite-difference grid, so that further refine-

ments were not undertaken in this investigation.

The 16 x 11 and 20 x 11 finite-difference grids predicted bifurcation

loads of 6608 and 5622 lb for the imperfect panel (WI - -0.010 in.). Thus,

the 20 x 11 grid predicted a bifurcation load 14.9% lower than the 16 x 11

grid for the imperfect panel. Again, improvement in the theoretical buckling

load for the imperfect panel can be expected for a more refined finite-

difference grid.

Figure 18 shows that the experimental buckling loads are not grossly

misrepresented by the buckling load predicted by the 20 x 11 grid for the

imperfect panel. Based on the buckling load predicted by the 20 x 11 grid

for the perfect panel (6950 Ib) the ratios of the experimental to the theore-

tical buckling load for the five specimens are 0.831, 0.793, 0.741, 0.716,

and 0.668. The last ratio really should not be counted because this speci-

men had been tested previously with very loose straight edges, Based on

the buckling load predicted by 20 x 11 grid for imperfect panel (5622 lb)

these ratios become 1.03, 0.980, 0.918, 0.885, and 0.818.

The theoretical curves, and thus the theoretical buckling loads, upon

which the foregoing ratios are based correspond to simply-supported straight

edges for which circumferential displacements are unrestrained. It is

impossible to be certain of the nature of the boundary condition along the

straight edges of the test specimens. As an example of the uncertainty of

the type of boundary condition that existed along the straight edges of a

test specimen consider the test specimen for which the experimental buckling

load was found to be 5775 lb, the largest of the bucklinq loads of the five

specimens. For this test the shoulders of the vertical pressure blocks

39

were filed to a rounded configuration so that the blocks contacted the speci-

men along a straight line. In the other tests these contacting surfaces

were flat and tended to bend the panel when the pressure was applied. The

former, it is expected, allowed a more freely occurring rotation at the

edge for which the corresponding buckling load should be expected to be

less than that for the latter case. As can be seen this was not the case.

All this suggests that the edge conditions at the straight edges of the

test panel are uncertain.

It is felt that the conditions along the straight edges of the test

specimens is the principal source of the difference exhibited between the

experimental and theoretical buckling loads. It is also felt the CLAPP is

much less at fault for the difference referred to.

It should also be noted that any pressure exerted by the vertical pres-

sure blocks on the panel tends to retard the free occurrence of axial dis-

placements along the straight edges. This could give rise to shearing

stresses in the panel which would lead to lower axial buckling loads.

Finally, the clamping mechanism prevents circumferential displacements from

occurring freely along the curved edges. This could cause local distortions

near the curved edges that could lead to lower buckling loads. The model

for which the theoretical buckling loads were computed assumed that axial

displacements along the straight edges and circumferential displacements along

the curved edges are unimpeded.

SPECIMENS WITH UNSUPPORTED STRAIGHT EDGES. The experimental equilibrium

paths for six 16 in. x 12.83 in. specimei. with the [0/9012s fiber pattern

and unsupported straight edges are shown in Figure 19. The load at which

each specimen buckled is marked on the graph beside the corresponding

40

equilibrium path. The theoretical equilibrium path is also shown in the

same figure for initial imperfection amplitudes of -0.0025 and -0.005. As

was the case for specimens with simply-supported straight edges, the theore-

tical equilibrium paths for the 16 x 11 finite-difference qrid essentially

coincide for initial imperfection amplitudes of -0.0025, -0.0050, and -0.010

in. Moreover, the buckling loads corresponding to these iniitial imperfec-

tion amplitudes differed only slightly, as can be seen from Figure 20.

The equilibrium path corresponding to a 20 x 11 f.inite-difference grid

differs only slightly from that corresponding to a 16 x H1 grid. The

buckling loads for the 16 x 11 and 20 x 1) grids for an initial imperfec-

tion amplitude of -0.01 in. are 3416 and 3320 lb, respectively. In this

case the refined finite-difference grid did not influence the buckling load

nearly as much as it influenced the buckling loads for the simply-supported

panel.

The experimental equilibrium paths depicted in Figure 19 indicate that

the stiffness of each test specimen changes noticeably in the load range

400-1000 lb. This change in stiffness coincides also with the observed

reversal of the axial strains at the straight edges of the test specimens.

Consequently, it is believed that this change in stiffness signifies the

load-level at which the straight edges of a specimen lost their capahility

to resist greater axial loads.

The theoretical equilibrium paths shown in Figure 20 for various initial

imperfection amplitudes reveal that a bifurcation occurs at approximately

1134 lb for a perfect panel This agrees well with the experimental loads

corresponding to the changes in stiffness of the test specimens as shown

in Figure 19.

41

Using the limit load (3320 ib) corresponding to an initial imperfection

amplitude of -0.010 and the 20 x 11 finite-difference grid, the ratios of

the experimental limit load to the theoretical limit load are 0.818, 0.753,

0.741, 0.693, and 0.652. The theoretical limit load used to calculate

these ratios are based on an axially symmetric distribution of initial

imperfections (W° = WI (l+cosnF/a)). The actual distributions of initial

imperfections indicated a pronounced distortion of the straight edges of

the general shape represented by the mathematical equation expressed above,

that dimenished as the specimen centerline was approached. Actually the

center region of the test specimens were relatively straight in comparison

to the straight edges. This observation is revealed by the imperfection

data listed in Appendix C.

The equilibrium path for an initial imperfection distribution given by

W = WI (l+cosns /a) (n/b) is shown in Figure 20. This distribution more

closely represents the actual imperfection distributions. This equilibrium

path coincided with the other paths shown in Figure 20. The limit point load

for this imperfection was 3460 lb. which is essentially the same as the limit

point loads for the other initial imperfections.

42

3400

3200 - 3416 lb 16x1l grid, WI -0.010 in-

Theoretical 3320 lb 20xll grid, WI -0.010 in3000 equilibrium paths /

for WI = -0.0025 and

-0.0050 in.2800

2600

2715 lb

2400 -

2500 lb

2200 -2460 lb

2300 lb

2000 2165 lb

S 1800

S 1600

U-i_j 1400 -~ Experimental equilibrium paths

1200

1000 PANEL 16 in x 12.83 in.

FIBER PATTERN: [0/90]2s

800 / BOUNDARY Clamped curved edges,-CONDITIONS : unsupported straight

edges600

400

300 - w° = WI (1 + cos x/a)

200

0 25 50 75 100 125 150 175 200

END SHORTENING, x 10" in.

Figure 19. Theoretical and experimental equilibrium paths for specimens

of Program B with unsupported straight edges.

43

f I ~Ln- a)

LUj C-0 -

C LUJ 4-)

CC:)LUJ -: -

cr cl L LU

%D CD c

.- -D C) 0)I~ UL 0 - 4-'

c - : 0l - ) L

LL- o - CD +

.0ia C J ) c 9 iI

S- - 2-- C D71 WMI LU U- < M) 0V

CA a.C CL LL- -L C O

.- LI) >)(90

S- Lo C) )CD C~ C) C-). ( 100)

C.. CD C) II

.4-'C 4- 4-~C a .

0~( 04 m. (m C\ - U-

oZ C L0

C- n (~C) -0

0)~~C CM In ( >

C) C) CD C: ) :)(9C C )

CD9( ( C) 0 C) C-) ) CC:)~~C'H U' D L -) " Z

cl0(9 aj44

if if f IS:3

IqL SVIO3 ~

SECTION V

LONGITUDINAL STIFFENERS

(V-1). INTRODUCTION. The compute- program CLAPP was modified to include

the effect of longitudinal stiffeners on the buckling behavior of fiber-

reinforced panels by adding the total potential energy of the stiffeners

to the total potential energy of the panel. Accordingly, the total poten-

tial energy of a stiffener element is developed in this section.

The stiffeners considered in this section have thin-wall open cross

sections and are assumed to coincide with the finite difference grid lines

that are parallel to the generators of the panel. It is not necessary

that a stiffener be associated with every finite difference grid line.

A stiffener is assumed to be made from an homogeneous isotropic mater-

ial; however, the developments remain valid for quasi-isotropic, fiber-

reinforced stiffeners. The special properties of quasi-isotropic, fiber-

reinforced stiffeners are described later. It is further assumed that

the cross section of a stiffener does not vary along its length, and that

each stiffener is free of externally applied forces.

Each stiffener is assumed to be rigidly attached to the panel along a

finite-difference grid line. A point of attachment is defined as the

point on the reference surface of the panel that lies on the normal throug '

the centroid of the stiffener cross section. Mathematically, the displace-

ment components associated with the panel and the displacement components

associated with the stiffener are required to be continuous along this

contact line.

45

(V-2). STIFFENER STRAIN ENERGY. An expression for the strain energy asso-

ciated with small displacements of straight beams with thin-wall, open cross

sections is given by Bleich and Bleich [41

2 ~ 2 2U =2 E s + +JG(') + EA()+ dz (V-l)Sf ; S C

The quantities appearing in Eq. (V-1) are defined as follows. The rectangu-

lar coordinates ; and n coincide with the principal centroidal axes of

inertia, and z signifies a coordinate measured along the centroidal axis of

the beam. Thus, I,., and I are principal centroidal moments of inertia,

A denotes the cross sectional area, J is the torsional constant, and 7 is

the warping coefficient for the cross section. Young's modulus and the

shearing modulus are denoted by E and G, respectively. Finally, U and V

are components of displacement of the shear center parallel to the and n

axes, respectively, W is the axial displacement of the centroid of thec

cross section, andA3 is the unit angle of twist that the section experiences.

The first two terms in Eq. (V-l) represent strain energy due to bending'

about the principal axes of inertia, while the next two terms represent

strain energy caused by twisting and axial deformation, respectively. The

last term represents strain energy associated with warping of the cross

section. The strain energy associated with warping is usually discarded in

stiffener analyses; it is also discarded in the present analysis.

Since it is assumed that every stiffener is free of externally applied

forces, Eq. (V-1) also represents the total potential energy of a stiffener.

Energy methods have been employed by several investigators to examine

the effect of stiffeners on the buckling behavior of plates and panels.

46

These investigators do not agree universally on the terms that need to be

retained in the stiffener energy expression. Donnell [51 discards the

strain energies associated with axial deformations and bending about an

axis perpendicular to the reference surface of the panel. Thus Donnell

assumes that the dominant actions of a stiffener are bending about an axis

parallel to a circumferential tangent, and twisting. Szilard [6] adopts

the same reasoning, but argues that strain energy due to twisting can be

discarded for closely spaced stiffeners. Palamarchuk and Polyakov [7]

retain the same bending and twisting energies, but include terms that

represent the effects of externally applied forces and initial geometric

imperfections.

The investigations cited consider only stiffeners with symmetrical

cross sections. Stiffeners with unsymmetrical cross sections are treated

in the present developments.

(V-3). STIFFENER ENERGY IN MATRIX FORM. The total potential energy for a

stiffener can be expressed in matrix form as

El 0 0 0 U"

0 E 0 0 V1

V = [ v', ', w dz (v-2)0 0 JG 0 IB'

0

0 0 O EA wC

As was stated previously, U and V are components of displacement of the5 5

shear center along the t and n axes, w is the axial displacement of thec

centroid, and 2 is the rotation of the cross section per unit length.

Connectivity of a stiffener to the panel is accomplished by expressing

these displacement variables in terms of the displacements (UD ' V D ) of the

47

point of contact of a stiffener

with the panel. The situation

is depicted in Figure 21.

It is shown in Ref. [41 that, x

for small displacements, the dis-

placement components for a generic

point in the rigid cross section

of a stiffener are I / .-

FIGURE 21. General thin-wall openU =U + (n scross section.

(v-3)

v = V - )

At the contact point D, Fi, =D and j =

TD' so that, with the aid of Eqs.

(V-3),

U s 1 0 - (n s -j D U UD

V = 0 V (V-4)

S0 0 1 1

Because plane sections remain plane (r = 0) the axial displacement of

the contact point, wD1 is

wD = w - F r D V (V-5)D c D c 9 c

where uc and vc are centroidal displacements along the t and n axes as

shown in Figure (21), and ( )' indicates differentiation with respect to

z. From Eq. (V-3),

48

r.I

U = Us + n IL (v-6)

V =V - nlVC VS S

so that Eq. (V-5) becomes

= w - F lDVn (V-7)wD = W D U - D VD ( -7

Eqs. (V-4) and (V-5) lead to the following transformation

Uls 1 0 -(n -n) 0 l

v,, o ooVl01 0 0 21s D DD (V-8)

1 0 0 1 0 0 So

B' 0 0 0 1 0]CL D nD [W0I

Eq. (V-8) permits the strain energy of a stiffener to be expressed in terms

of the displacements experienced by the point of contact of a stiffener

with the panel.

(V-4). DISPLACEMENT CONTINUITY. To enforce the required displacement con-

tinuity along the line of contact of a stiffener with the panel, it is

necessary to project the displaceme,. vector of the contact point along the

circumferential tangent and along a normal to the panel. According to

Figure 21,

UDi VCosat sinciUcos n= U (V-9)

viD I-sina cosa n

where Ut and Vn are the circumferential and normal components of displace-

ment of the contact point D.

49I

Accordingly, the contact point displacement vector appearing on the

right-hand side of Eq. (V-S) is expressed as

Ul cosct s i nc 0 0 0 UID t

Vo -sint cosa 0 0 0 U"D n

B" 0 0 1 0 0 B" (V-10)

(' 0 0 0 1 0 a'

!w; 0 0 0 0 I

The assumption is made that the panel thickness is small compared to

the dimensions of a stiffener normal to the panel. This permits the con-

tact point D to lie in the reference surface of the pancl.

Continuity of the displacements associated with the contact point on

the stiffener and the displacements associated with the contact point on

the panel requires that

U =V, B=Wt ,y

U =W, 3'=W , (V-Il)n , yx

wD U, B" = WWDUB ,yxx

Here U, V, W are the displacement components of a point on the reference

surface of the panel.

Eqs. (V-2), (V-8), (V-10), and (V-11) yield the following matrix formu-

lation for the strain energy of a stiffener:

V [d]T[A]T[B]T[S)[B][A)[d] dz, (V-12)

0

50

where

[A] = cosa sinca 0 0 1-s i nc Cosc 0 0

0 0 1 0 0 (V-13)

0 0 0 ! 0

0 0 0 0 I

[B] I 0 0

0 1 S D 0 0(V-14)

0 0 0 1

L D 11 D 0I_

[S] El 1, 0 0 0

0 El r "" (V-15)

0 0 JG 0 1

0 0 0 EA]

and

(d]T (V W W W U I (V-16a)

,xx ,xx ,xxy , xy X

To interface with the computer program CLAPP, the elements of the

stiffener displacement vector [d] are rearranged so that

T[d] T [U , V , W , W , W I (V-16b),x , X XX ,x X~ ,xy

The total potential energy of a stiffener becomes

V = J [dIT [PAS2] [d] dz (V-17)

0

51

The matrix [PAS2) results from carrying out the operations indicated in

Eq. (V-12) taking into account the alterations of the matrices [A], [B],

and [S] because of the rearrangement of the elements in the [d] matrix.

The elements of [PAS2] are given in Figure 22.

A final transformation is required to express the total potential

energy in terms of the finite-difference grid point displacements.

(V-5). FINITE-DIFFERENCE CONSIDERATIONS. The strain energy density of

a stiffener element is assumed to be constant over the length of the

element. Moreover, the strain energy density is assumed to be equal to

its values at the midpoint of the element length. Consequently, the total

potential energy for a stiffener-element is taken as the product of the

strain energy density at the midlength of the element and the length of

the element. Symbolically,

V = [d T[PAS2][d] x (V-18)e

where [d] is the displacement vector associated with the midpoint of the

stiffener-element.

Nine different stiffener-elements are required. These stiffener-

elements correspond to the nine types of area-elements used in CLAPP, one

interior stiffener-element, four boundary stiffener-elements, and four

corner stiffener-elements. The nine stiffener-elements are shown in

Figure 23, which also shows the stiffener-element orientation and midpoint

along with the local numbering system for the surrounding finite-difference

grid points.

For each stiffener-element the midpoint displacement vector (Eq. (V-16b))

is transformed to the local grid point displacement vector

52

CD CD C) C)

6 66 6 r_ (A

tU a 0

0 0- 0 0

C. kPC, LP

I a + +

mn Ln0o) 6 u Z

0 ) (N (n kP 0

+ 6 n 0 -. -6 (An - 0 U LiiL nrC 0 L) a 04(

u U N + .~-- CD an- a C a 6 m 0 U

a) LLI m Wn m Vn N' klP C3 XIP- X 0 'J CL r_- 5= - C-

n ~ (\ .- < in cc 01ccP C.- <~ 0m i~ n uiJ I~P LIi r-

1 Lii Lo. LIi

<C + I + I Lii Csj

LCL.

3X

an P C, u C a)

C L 6 0 C)

a* a anC, -06 0 CM )

o -6 l 0 o CA 0LA - 0 C-

0z 0 gr Nu. U Cz < 03 Gi

w UP~ Lii _rC 4-'

- + a I ILL) Lii La-

C4a)

S.-

53

o-Tc -' ar\ an -

Q) E)

L. C

u. tA w 0I- (

C "- E L

c - a- :3.-w

L. Q 0)-0Q) r-C. E.CLA 0 L- Q)

IN ~ ~ ~ a C:0- ~ .C)C(U -C U~) (DE

E -3

r-.m Q) c. C)

S-u Cl w'

(a 4.C .0

=) .- 00V0)

C)Q n* C.

I- 0 -' I\ '.

(~ 0 0 -0 e~ C

a)0

C)0

C )L

(V c

0 0 )

u i0) >-v

co C>- 00 -M 0 0 ,

r44

514

T

[q] = (Wi , UI , V1 W 2 U 2 , V2 . W9 U9 , V9 ] (V-19)

through the relations

d. = c.j q. (V-20)i j IJ j

where the matrix [C] is composed of coefficients that depend on the vari-

able spacing of the finite-difference grid. Accordingly, the total poten-

tial energy for a stiffener-element is

V T [CTVe = 2 [q] [c] [PAS2][C][q] Z (V-21)

The transformation matrix [C] depends on the location of the stiffener-

element in the global system. To illustrate the procedure used to estab-

lish these matrices, the transformation matrix for the interior stiffener-

element shown in Figure 24 is derived.

In the longitudinal direction, the midpoint (subsequently referred to

as the stiffener-element centroid) of the stiffener-element contains the

centroid of the corresponding area-element. This follows from the defini-

tions of an area-element and of a stiffener-element. The corners of an

area-element are the centroids of the areas contained between adjacent

grid lines. The length of the corresponding stiffener-element is equal to

the dimension of the area-element parallel to the generator of the panel.

A derivative of a centroidal displacement with respect to the lonqitu-

dinal direction x, denoted by ( )', can be expressed as a linear combina-

tion of displacements at the three finite-difference grid points (i-1, i,

i+l) lying on the longitudinal grid line.

A general one-dimensional centroidal function, f, and its derivatives

are expressed as linear combinations of the function values at the three

55

0

E

.7# 4, j+l

centroid M

3 2longitudinal

h k direction

6 29

• -- h ' = k

i- i+l

FiGURE 24. interior stiffener-element with qrid spacinq

and grid line notations.

56

node points on the jth grid line as

f (k-h) (3h+k) f + (h+3k) (3h+k) f (k-h) (3k+h)i 6k(h+k) i+l 16hk i 16h(h+k) i-l'

f, L f + (L L) f + - (V-23)i 2k i+l 2h 2k 2h i-V

and

f,. 2 f f + 2 (V-24)k(h+k) i+l hk i h(h+k) i-

where h and k are longitudinal spacings between the grid lines i-l and

i, and i and i+l, respectively.

A derivative of a centroidal displacement with respect to the circum-

ferential coordinate y, denoted by C ), can also be expressed as a linear

combination of displacements at suitable finite-difference grid points by

means of a Taylor series. Accordingly, a Taylor series expansion about

the point (i, j) yields the two linear equations

fj+l = f " + m f. + m2 f. (V-25)

and

fj i = f " - Q f. + Z2 f., (V-26)j- j JJ

where Q. and m are spacings between the j-1 and j, and j and j+l circumfer-

ential grid lines. Eqs. (V-25) and (V-26) lead to the first-order central

difference formulas

Sf (.-m)f m (V-27j M(P+m) j+l Zm j P. f+M) i-I

57

and

". 2 2 f + 2 (V-28)j m(+m) j+1 -m j (M+ fj

The centroidal displacement vector [d] includes mixed derivatives also.

The coefficients in the transformation matrix [C] that correspond to deri-

vatives with respect to x are obtained from Eqs. (V-23) and (V-24) for an

interior stiffener-element. The coefficients in the transformation matrix

[C] corresponding to the mixed derivatives are determined by appropriate

combinations of Eqs. (V-23), (V-24), and (V-26).

A general two-dimensional centroidal function, g, has the mixed deri-

vative

I + (V-29)2 =k gi+l 2h 2k i gi-l"

Using Eq. (V-26) yields

I, z O(-m) mg= 1 ___ tm - m(v-3o)2k m( +m) gi+l, j+l Zm gi+l, j 7m gi+l, j+(3l

1 - 1 _ 9. (-m) - m (V-31)

2h 2k m(9+m) gi, j+l Zm i, i z gi, i

+ z (Z-M) - m (V-32)

2h inF+m- g-I j+ I in gi-l, j -m gi-], j- I

Identification of the nine surrounding grid points with the local num-

ber system determines the coefficients in the transformation

g =ci gi i = 1, 2,... 9. (V-33)

58 "

The coefficients for the mixed derivative g" are obtained in a similar

manner.

The total potential energy for any stiffener-element is expressei ai

V [q) T [CAS2][q] x . (V-e

where

[CAS2] = (C]T [PAS2] [C] V-35)

Eq. (V-34) is the formulation of the total potential energy for any

stiffener-element that interfaces consistently with the area-elements used

in CLAPP.

(V-6). INCORPORATION INTO CLAPP. The incorporation of lonaitudinal stiffe-

ners in the computer program CLAPP is accomplished with three subroutines.

The first of these three stiffener subroutines is named SCOEF. SCOEF

calculates the elements of the matrix [PAS2]. Since [PAS21 depends only on

the material and geometric properties of the stiffener cross section it is

calculated once for each element and stored.

SCOEF permits the user to select any of seven stiffener cross sections.

It also provides for any other cross section through a user's choice ontion.

For the various stiffener cross sections included in SCOEF see the user's

manual in APPENDIX D.

The second stiffener subroutine is named STFDIF. It calculate, the

elements of the transformation matrix [C] of Eq (V-20). The subroutine

FDIFF of CLAPP performs similar calculations for each area-element. Con-

sequently, when FDIFF is called to calculate [C] for an area-element

STFDIF is subsequently called from FDIFF to calculate [C] for the corres-

59

ponding stiffener element.

The third stiffener subroutine is named ATBAS. It performs the matrix

multiplications indicated in Eq (V-35). This subroutine is called from

the subroutine STFDIF. ATBAS has been constructed to take advantage of

the numerous zeros that occur in the matrix [C].

The main program and the subroutine FDIFF of CLAPP are modified so

that longitudinal stiffeners can be included when appropriate. Additions

to the main program read in stiffener indices indicating (a) that stiffe-

ners are to be included, (b) the choice stiffener cross section, (c) whether

stiffeners are located on the inside or outside of the panel, and (d) if

stiffeners occur on every finite-difference grid line. The main program

calls SCOEFF to construct the matrix [PAS2]. The additions to the subrou-

tine FDIFF determine when the stiffener energy is required in an analysis

that does not include stiffeners at every grid line. When it is appropriate,

STFDIF is called to calculate the stiffener-element energy which is imme-

diately added to the correspoinding area-element energy. The procedure

used by CLAPP to assemble the -,ystem stiffness matrix for area-elements

proceeds in precisely the sa.e manner when stiffeners are present.

(v-7). QUASI-ISOrROPIC FIBER-REINFORCED STIFFENERS. A strain energy

expression for a quasi-isotropic, fiber-reinforced stiffener that is ana-

logus to the strain energy expression for an isotropic stiffener is estab-

lished in this section. For the purpose of the present development a

quasi-isotropic material is defined as one possessing midplane symmetry

and alternate zero and 90 degree fiber directions. Thus, for a stiffener,

the zero fiber direction is assumed to coincide with the longitudinal axis

of the stiffener, and the 90 degree fiber direction is perpendicular to

60

this axis.

The stress-strain relations [2] for a general fiber-reinforced laminate

are

N All A1 2 A 1 6 e BIl B1 2 B 1 6 Kx lx 3 x

N = A 1 2 A 2 2 A 2 6 e + B12 B2 2 B2 6 K (V-36)

N A 1 6 A 2 6 A 6 6 2e B16 B26 B6 6 2K

M B11 B12 B16 e DI, D12 D16 K

My B12 B2 2 B2 6 e + D12 D22 D26 K (V-37)y y y

M B16 B26 B6 6 2e D16 D26 D66 2Kxy xy xy

Formulas connecting the elements of the laminate stiffness matrices [A],

[B], and [0 with the material properties and the geometric locations of the

individual layers are

A. Qijk - (V-38)B k=l (h k-IV

tj 2 k ij k k-

N

D.. = Z (h3 - h3 ) (i,j = 1, 6). (V-40)iJ k=l ij k k-I

Pertinent geometric quantities appearing in these relations are defined in

Figure 25.

The laminate is assumed to possess midplane symmetry so that the B..

are identically zero in Eqs. (V-36) and (V-37). It is also assumed that

61

the stiffener experiences a membrane state of stress like the one shown

in Figure 26. Consequently, the dominant bendi g action results from the

moment caused by the membrane force Nx

If the cross section of a stiffener is assumed to be rigid, then e = 0y

so that

N = A l l ex + A1 (2e xy) (V-41)

and

N = A1 6 e + A6 6 (2e ) (V-42)xy x xy

Now A1 6 0 because of the laminate fiber directions are either parallel

or perpendicular to the longitudinal axis of the stiffener. Consequently,

the stress-strain relations appropriate to an analysis of fiber-reinforced

stiffeners under the foregoing restrictions are

N = All e (V-43)x x

and

N A66 (2e ). (V-44)xy xy

These relations are analogous to the isotropic stress-strain relations

used by Bleich and Bleich [4] to arrive at their expression for the strain

energy of stiffeners made from isotropic materials. All that is required

to make the isotropic strain energy expression valid for quasi-isotropic

stiffeners is to appropriately identify E and G of the isotropic case with

All and A6 6 for the quasi-isotropic case.

To do this, consider that

62

UWANOW

K z& layer

aer number1

FIGUR 2a5e Cros_ sec ionfla inat

FIGURE 25. Cers secton of litre ,,fraifnr

S6

N N

N -k N kAll = E --0. 1 (h k -hEk ) t z (V45k=l k=l

and

N N-k -A6 6

= Z --066k (hk - hkl) = t Z (V-46)

k=l k=l

if the thickness of each layer is the same.

The subscript k signifies that the k-th layer is under consideration.

The Qij are symmetrical and are the material coefficients referred to a

generic set of axis. They are expressed in terms of the material coeffi-

cients, Qij, associated with the material axes of a layer through the trans-

formation:

Q1,I = Qlcos" 0 + 2 (Q12 + 2 Q66) sin2 0 cos 2 0 + Q2 2 sink 0,

Q12 = (QIl + Q22 - 4 Q66) sin 2 a cos2 6 + 012 (sink e + cos 4 e),

Q22 = Qll sink 0 + 2(Q12 + 2 Q6 6) sin2 0 cos 2 0 + Q2 2 cos4 e, (V-47)

16 = (Qii- Q12 - 2 Q66 ) sin 0 cos3 0 + (Q12 - Q22 + 2 Q66) sin 3 e cos 0,

Q26 = (Ql Q - 2 Q66) sin3 0 cos + + (Q12 - Q2 2 + 2 Q66 ) sin 0 cos

3 ,

Q66 = (Qil + Q22- 2 Q12 - 2 Q66) sin 2 6 cos 2 0 + Q66(sin 4 0 + cos4 .).

The quantities Q are related to the enqineerinq material constants

through the relations:

64

E11

lv2v,,1

v-2 Ell v2 1 E2 2

Q12 = Q21 = v 1 2v 2 1 - V1 2 2 1 (v-48)

E22

Q22 = )-v 1 2 v 2 1

Q66 = G12 .

Ell, E22 are Young's modulii of elasticity parallel and perpendicular to

the fiber direction, respectively; G12 is the shearing modulus of elasti-

city associated with the directions parallel and perpendicular to the fiber

direction; and v12, v2 1 are Poisson ratios. v12 is associated with a

strain in the ]-direction due to a stress in the 2-direction and v2] is

associated with a strain in the 2-direction due to a stress in the 1-

direction. It is convenient to let the ]-direction coincide with the

fiber direction.

From Eqs. (V-47) and (V-48)

k Ell

= j = 12"2 for fibers parallel to the stiffener axis

Qk= (V-49)

k E22

Q2 2k = for fibers perpendicular to the stiffener]-12V21 axis

and

Ak

Q66= Q66= G12 (V-50)

for either fiber direction.

65

If N is the number of layers in the laminate, then from Eqs. (V-44)

and (V-49)

Nt E l + E22 Ell - E22

A1 ll -V12 V21 2 (V-51)

where

0 if N is evenx= (V-52)

I if N is odd.

Note that when N is odd, the middle or odd layer is assumed to be parallel

to the stiffener axis. If the middle or odd layer is perpendicular to the

stiffener axis Ell and E22 interchange positions in Eq (V-51).

Finrily,

A6 6 = Nt G 12 (V-53)

for N even or odd. Notice that Nt is the total thickness of the laminate

from which the stiffener is constructed.

Now if E and G in the isotropic strain energy expression for thin-wall

open sections is replaced with

All Ell + E22 Ell - E22E Nt 2 + A( 2N ) (V-54)

and

A66= G12, (Y-55)

one arrives at a strain energy expression for the quasi-isotropic material

considered in this section.

66

REFERENCES

I. Bauld, Nelson R., and Satymurthy, Kailassam, Collapse I Analysisfor Plates and Panels, AFFDL-TR-79-3038, Air Force Fliq DynamicsLaboratory, Air Force Wright Aeronautical Laboratories, Air ForceSystems Command, Wright-Patterson Air Force Base, Ohio, May, 1979.

2. Jones, Robert M., Mechanics of Composite Materials, McGraw-Hill,1975.

3. Wilkins, D. J., "Compression Buckling Tests of Laminated Graphite-Epoxy Curved Panels," AIAA Journal, Vol. 13, No. 4, April, 1975.

4. Bleich, F., Buckling Strength of Metal Structures, H. H. Bleich, Ed.,

New York: McGraw-Hill, 107-116, 1952.

5. Donnell, L. H., Beams, Plates, and Shells, McGraw-Hill, 204-209, 216-218, 1976.

6. Szilard, R., Theory and Analysis of Plates: Classical and NumericalMethods, Prentice-Hall, Inc., 540-547, 1974.

7. Palamarchuk, V. G., and Polyakov, P. S., "Rational Stringer Reinforce-ment of a Shell with Initial Deflections," Soviet Applied Mechanics,Vol. 12, No. 3, 229-234, 1976.

67

APPENDIX A

STRAIN, END-SHORTENING, AND IMPERFECTION MEASUREMENTS FORTEST PANELS WITH SIMPLY-SUPPORTED STRAIGHT EDGES

CLAMPED CURVED EDGES

TESTING PROGRAM A

68

C14 en_-a UNT

E c. .u- L C14 - T L r

CD~~ '.0.0 a'o C1 LT+ -7 U\ r olo(1

I- C,4 - LA U.\ C -I 0 LA CO r OD LA' :r r ) C'00 -f' C', m~ -I _:r _:O -.3 LA O\

uj ~I r- C -\D mN C4, (N \ (N \ .' r-I'LN a

IDLrLr 0 C M OU\ r- 0A. m UO % co CD 0 I- -C (N (.7 LA m- -T LA L-. 0 I'). UL\ '. \.1 0 '.

Cl

'0 0 N- (N ' rn-T \.O - LA c0 \-r. ~ 7 0 .f LA)LN- LO V)- O ~ O - L N- ~L O 0 N

'0 N I- C

C: )

IQAL)

IA -N I- m0.T - 0

a- (DO 00=--T LA a) PC C00 0 0 0 0 0000wa)aa\ 0 0 0 C c

(30 cc-~

0 ,D 0 COO , (N N- -'0-3 LA'\ 0 z . COC ON -N

0C :3 -7 00 r\ C 7 U\ 0 N - CO -T0 - (N &)' r, LA 0 N- M~ 0 -T 0a. C-4 COC (N\-t . r- -

U- CYC

c~ z

'0- '0u'- ~ ~ ~ ~ ~ ~ ~ .(N -70 L' -N -C O)0 0 0 0

Z ) M (N) (N C N r , (' LA 'N LA '0 '0 ' D N -N- N-

uj~~~~~~~- M T UN of-m m m

0- (N +1 (N (' ' A A L . 0 - N - N

C Z

C) CD CD (D -> C)- Coc 0 0 LNCD 0 a

.4 m IA

0 -c, C: r r , 0 N Nr

w 0) 0- C > 0'0 0C -- 0 C.) LA C N 0~ (N A (N ' D0 (~ 0 CD 0 0' V)

C> (N 0 Ar C) LA '0 '. 0 Ln CO U"\ 0- Cr - - (N IQI c, ', 0

10 C14 LAO I-a" U\ 0 r LU*\ ~ ~ ~ ~ ~ ~ ~ ~ ~ ( C4 C C' " \- -r-l Z f r

-7 C 69

EOL Co '. ' Ln '.D m' N '

Z ~ 0 cCO 0 - ' Ln F- CD -T

Qi)

C3 \,D'0 O' -T LA' LAO 0 rr

0~ ~ o. ,N 0 \ 0 u-, L(n O -, C) CD0 0 C-4 N

~~N'0 0 -40 r- x - 0 0\ "~ Nrr~LN N . 0- r- - r- CO 00 L

4.n --c

Cc 00 ) CDC 00 CO 00 NI 04

x( m0'0 C - N N c. 'D0 LA r-

I C-

000 0 . 0 0 0 0 0 r)

N -) c-N. . . . Ci CI C4C

a'~~~ CDOO 0) - 0 N (D- r' 0r C O U\

0 0 00 0 0 0 0 010 0 "A00 0 0 0 " 0 T 0" 10 0 N

~-T LA\ n LA\ ULA U\ Lr\ Lr\ Lr LA\ LA

m' en u- c,4 N o. L\ Lr\ 'L. u\ 0 ""I u-\ -TLn 'D0 \ CO C ~ ' 0 N- 0"% 0 N, C, ff" LA\

.0 0 00C 0 - M -T 0 LA\ CO L\-T LA'0 '0E '0m C ' CO ('0 CO - -T 00 -T co

W 0 N r- N C CO ON m- O\ 0O\ 0 0 - -

z

C) C O 'D Co mO CO t-C O O C ,

4-,

In

Li

o I -0 -0 -m -, LA a LALAILALA'C 0 '0 '0 '0 'I.,3

I 0 -o L

< )L OLA 0000 LA COLA U\ LA 0

0-70

C 0 O'\ C) r- (N M0 C CO r - . o, , m m C) f.'I '0 mLA 4 Ln c LA N C)LA -T r- (N r- C) (n r Ln (N 00 CD - I'D

-- C14 c(N m' (\ ~ -T LAN LA LrN LA L LA '.0 '. 'o0 '0

2

M T~OL C) ) C m ~ 0 Mm r- 0 Ln -'T " AC C )r- 'c' .) ( A ' 0 ,O% CD (N .0 01) - 0. -T c* L.A LA\ 1- - (N- N( N (N4 m fn -T _z0 UL\ 100 '.0 (N (N

ro0)C N L -Z '.0 CD '.0 C) U-\ (N 00 mNf LA\ cr LA\ 00 - C)

m, ~~\' LA\ - '.D - -T 00 (N '.0 m -7 (N C) m LAr co m, -:I(u - N 0N M M rn -:1-~ -7 LA\ ULA '0 ' '0 '0 (N (Nco

(D m CA ( C) CO cc C\01 -T r-- (N -- CO ;3 CO LA\ f- CA, f(N Lf\C14 -T r- CD -r rN- -T~ CO C14 rN- LA\ CO\ fA (N - Lr\ 0'\ (N UL\

C C1 C- en _4 I -T I I I I I I ID In ID II I

IC)

Ifl ) C)C (N 0O C Lr. C) (N C) C) C) C) CD C) C C) C) C) c. C) C) (1)

0) s- - (N - L AA( LA CAN ..Z LA CA- AL C Ar.LAL \- 0 0~ QY m (N( C)CA( T. LC\ L'\ Lr\ '0 '.0 r (N CO) u

mO L Ln.

CL

C)C C) C) C) 0)C )C C CC) C) C) D C) CC CC) C CD CD

LAjLA, C) LA C C LA\ C) LA\ C) LA\ CD LA\ CD Ul\ C) L\ C) U\ C) LN LA

LA (N W, C) CN "A -- \ '0 -0 C)\ CO '0 (N1 m0 )C N( .CN ~ ~ .CC) (N en MN I -:-U

C - (N CA\ C A)'0 (N( No N(L '0, -0 -- j co m 1 N0 (N (NI Cn- (Nm

m0U m -T -4 U* n 1 - ro- '-

E CD -:3 r- 00C CO - CO CA' -'0 r- co

"- '0t 'T :0 (N -) MO (N, (N - NC

0 ~ - C\c " - m--.r ' - I(D C( C,4 -0 MO '0 I" (N CO . D '0 (N C ( C) 1 (n O-(

U-\ LA O\' -r (N - L U\ r- -T (N C) (N -T LA\ ' WO MS(1( C14 mA m -7 -7 _ LA\ LA\ LA LA\ LA LA LA\

~ ))C) '0 r, -' 0AC CD (N4 MA' - 'D LA 'D0 -7(N CO '0 -T mA (N-' C) LAo0 A LA 9% m(% N C4- '0 mO

(Ui - l (NC nC- - 3 LA LAl LA% '0 '0 (N (N 00 CO CO CO

- CI'. CO LA mAC C) O C) M - r- C0O' C4 (N CO L \ LA L'0 CAN C '0 CO - " CA' m - CA-\'o mO mA C) " M:

- CN N 4 C14 C14 CA. .C) l m -T _:r -T LA '0 '0 '0 '0

C)C C) CD LA ) C) C) LA\ C) C) LA LA LA C) LA LA\ C)

-C) (N .-I CO -:T C) CA C) - ( C) '10 CA CO CA - CO

.- 0N lzA CA% - LA\ LA '0 '0 (N- CO 00 M C(N (NN Z)- CC - - o

0-)

(U LA C)C)OC) ) LAC) L C) LA Q) LA\ C) LA\ C) LA C) C C) (NxO LAO LA C) (N4 LA (N CN Ln r-N C4 (N \ LA (N OC

-~~3 - N( ( NC C ACA. r -- -T -'r LA\ LA LA,\

71

IMPERFECTION MEASUREMENTS

(x io-3 in)

BCP 9824-A-2-1 CS BCP 9824-A-2-2 CS

-6 -6 -5 0 -6 -2 -6 -4 -7 -4 !-4 0 -3 -3 -13-14

-6 -5 -3 2 -5 2 -5 -2 7 -6 -3 0 -5' -1 -15 -15

-6 -6 -5 1 -8 0 -6 -3 i -7 -9 -4 -2 -6 -2 -17 -13

-7 -6 -5 1 -9 "1 -7 -5 -8 -9 -5 -4 -8 -61-18-15

-5 -5 -6 0 -7 -2 -7 -5 -11 -9 -7 -5 -8 -81-16 -15

- - 1

BCP 9810-B-4-1 CS BCP 9810-B-4-2 Cs

-1 -- 1 -7 0 -2 0 -2 2 -

-5 -3 -2 0 -1 1 3 o 2-15 -7 03 0 2

-4 -4 -3 1 3 -I -] -l -13 -15 -7 -1 -2 -2 -5 0

-4 -4 -3 1 -2 1 2 2 -15 -14 -8 -2 -3 -3 -7 -1-5 -5 -6 L0 -4 - 1 0 -12 -13 -9 -7 -8 -5 1-12 -5

-8 -6 -5 -1 -5 -2 0 -1 -Hl -11 -8 -11 -9 -13 -9

18.513"

2 5/1611TYP

, 3 15/32" TYP0.5" o LEVEL

r=

8.0"

72

C) CD -- 10 c - ('4z'- co -z (3 -o 0 C ) D Q

-N P- N4 ('4-7 0 C (31 \Dc)

L.7 CD '.0 -- C'4 - CO F-, CM t. CO, LP (N4 ('4C'4 (' C4 10 co) (' 01 C) M CO - :I r ('4 -7r

r - - (' C-4(' -7 ' 'D r, f- .0

LI ~ l C) -7 3 -C -Z3 W.. r-5 ( C '-7 C:;CL (' C14C 0- C - C S) CO 00 P- -7 r - C*

C* C')

C/7

Q) U

) ('4 1 0

ct LI) 0 C) -C) C) ) C)( C) 0) ') U ) C 0 C) CD C-) ) C

CL0 --7' -T '0 U) 0o1- ('a) oiC4 r'4 (

C'0C

CL CL(D C3CCCD C

m - ) C ) C), 0 ) I ) C) C - o) C \ E ) C C: ) CD (n CDCN 0_ ('C'1)(" "C K 4 cc '. ( rCO C C,

CD LI) _T - C) LA C C-4 L T C) r C ) C) -C) C) C)

CO LA - 0C) ('-so rCC CC N.4 r-

C) D -z'- CS) -- --C C r- O rl r Z c

Q ) CLA -7 C-4 C14 ('4j LAN ('4 -7 C) - -IZ

-C o CTN C) N -- "e\ C") m ) 0e j C , C 'o-7 so r-()

CD

-3(C C) \ U-\ LA 0, L C) so C) rl, AD U"lco) -7- uL D '-

U ' ", N N' . ) C" , C m' a') c' r (-,4 mO -Z o)4') -z ('4 ('4 M" CI) --T (n (('o ('r--- 0C

LU

C14 U')I U -

-7

)I0 0. 0)C) C C) CD Lr\In U'L L ) L A A C, LA UN LAU A C L

I 00 -P C14 C' Z LI) so C- o N 3* 10C C ' C'-7 L\- C

co M A U'\ C\ LA U LA C) LA C LA' ) LA\ C) U", C) LA Cz) U') C) LA.- m ('4 U-) T-- C) C) LA N C LA r-- 4C) C4 LAr f- C) (' LA\ N.

xC 0 C'4 C-4 ('4t (4 C")j C", M" r-\ -.r7 -- t -

Co (NJ M) JD -:I" C) m ~ C) f\ (NCO ~ ~ ~ ~~C Co Co -o Co 0'c o00 0 0 00 C)\ -\ owo ~ cc Co 00 co-

0 M C,- C1 D - m \ 0 CO r_- - CD u, -T - -

z 'D0 w CD C-, -T C) (N -~ CN4 Id LA\ '.0 '. -7 CO CO (Dw~ (N r o ) Coo C- -\ Co \ 0) Co Co Co Co' Co Co Co C CD C)

CImo U'\ a) '0 M) Co Co - C:) UN (- CN (. 10 r Co0

m~ OD' MoCo C ) CD m' -:! Cj (N x Ln U-\ '. 'D0 C(N oN C) ffNr - r- 00 Co) Co CX-) Co Co Co o r- Co Co Co C C 00 ' a, o', -

L C o m- U-\ Co '0 ) - (N o - A U'\ cc :I - in LD C-\-o - - WN '00 Co m4 o- 0N 0N _ C 4 C ( N ' N Mf M( _: - :r

- ~ ~~~~~ -i r N o C o C o C ) C - - -N -N -N -( (- -~ -a

rox (N- 0o -T r- C' (N C N4 _. o ) - (J C) 0o Co-\ cn

-< - ) Co NJ 0 cc, 'D0 Co C(N L C) -T C 0 -\ L\ U (\ - - 'D0 - N

LiJ

(N

4l C - -o - - - - C4C

- LL ' ) c

(NJ~ ~~~ CD o. C) o. Co o( oN- - 0. ) ' N N N ( C N 0

Co ~ - c0 0 C( - N -7 UI r- w. m. (NT (N- Co Co Co) Co Cm) - -

Lin L).

Ln

Co Co o o (

-:I((N - C,.\ N NJ C

(U

C

C C Co '3 - .

LI ) - - (N N N

- " L "

<i -

- IC)

C) II (N - (N ( 0 Q) 00- ~ C o o - N (

-7 LA r, ( - 0 ( O'% 10 O'\ (n (N L"\ -o '0 a,\ Co\ CCA-N -Z (N C0 a, LA 10 '0 '0 0 0 ' '0 '0 0

-T~( (N (1CN (cN (N (N (N (N4

C) -7 '0 CC rN- (NJ CX -T LA 0') - '0 (- LA' C) C -r 0 Co' C'r,) CA N o (N\ LA\ r- C) M LAN 0\ - LA' C) LAl r- Co ) C(N -:r

- 1 (N 4 (N 4 (N 1 (N CA -.7 -Zr -11 -Z L ULA uLA

CO

(DC -zr (N , Co o '0 '0 mA r- - N 4( C 14 M 00C C) C)m4( A( LA C)-T co fA( - -T m -T Co C - CA '0 r-,

(Ai - ( N N CA -r -3- -Z LA\ LA\ '0 '0 '0 '0 '0

X( c) - r LA (cr\ LA\ C) C) 'aoCo C)oC C C LA Co) Co- mA ( N ' - L o C N ( -:T Co mA ( Co Co ' ( --r- 1 - l mN ( N A C -7 -:1 -zr LA LA LA LA'0 a C '0

LU

C14X

Q) C A Co LA (N Co LA' CA Co\ Co LA Cr A 0 U'\ Co - C 0 C N

- 00 - C'. (N T'- - - L ' (N co (71 0o C C) C) C)

Co. LU t--u

LA\ LA C) LA C aC LA C) LA C) LA CD LA C) C C- C(N LA (N C) ( LA (N C) (N4 LA r- C) (N4 LA '0Z ( CoC 1

- 4 (N (N (N N Cn A C A C A

C) 00 (N4 '0 rN-~ _ 0 ' C - Co'rN A - C LA' LAa) ( A ( ) C C14 - (N \ r C - C)' C) -7r -:T LAr Cor ( C

=1 - (N*' (N (N (N -zt O M Cr - C) U\ (

z C)T -o C A C - - -o (N LA M CA r '0 ' fo CoI LA- CA

CD ~ ~ '0 '0 Cor Ll -r '0 Co CA w ' \D m \.o LA C)4 - co C)cll Cr\Lr\- -- - -M -- ( "\ Nr (N C*- TA CA -~ CA "I

C- )C o L N L Co - C - C, : Co '0 Col '0 Cr (N1 U-\ \ CO Co\

Co CA0 co 10 -T -' CA C)r CD (N - L.(0A C L )

(UN (N L - N C o Co o Nr Co r CA uN \ '0 '0\ (N C mU o - (N N ( 10 -rl -o LA LA '0 '0 (N (N Co Co Co

LA

wU ) ) C) '0 C) 0 ' 0 C) C) (N\ 0 N '0 LA N LA C) CA \

o c- -- Nr CA-Z - D r, LA 0A0 '0 '0 N (N Co CO

-o I IC)

0) Co)j LA A ) C) C) C) C) C) LA\ C ) LA 0 UN C) L % C) C C) LA C- ( C*- A Co '0 LAZr - (N\ Co (N LA r- Co '0 C o'r 0 Co C- C-

C) 0 - N -C - LA LA '0 ( C o fCo M C) 0" - - --N (N

Co LU (A75

m A e r- m 0o SN LA \ - -T-C) C) , 0\ - C - S

z c'. 00 '0 -T o'. '.o 00 LA\ r--7 ) 4S -:r -7 '.D r- ON.

On I'_ 0m_ " -T I'.0 '.0 Lr\ - U ' 0 C) C

(D

L) r- - -' - r- r- 00 CO

0 SN 0, -T -CDLA~. )in '0 r- . r- r- r- r- r- co

-ci

C4

a) X C) '.0 5- ) 0~ C D r- (D wL. - r ir- a) 0\, ID mN - A )

C) ) C) CD C) C) C) C) C) C) C)m LA C) 0 .75--- C (~'0 CD -

-a -T SN N AS r- (\ m

0

:3 - C ) M .m

C) %0 1 -(N

C

(-C)

00 00 C- 00

CC_

in X O a) r, C) a r- w- ;

co) m) 0 01\

IC)

I C) LA C) LA C)D CI) ~ X .

* L '0 LAC) 0 0-S 04 S M ' M U- CCC - - - - C)

cca000

0-

(0iC C) C) C) LA( 0 La '0 N- N-

)x 0 -T -:T _: -T -T

76

IMPERFECTION MEASUREMENTS

(x lo-3 in)

BCP 9121-A-5-I ES BCP 9921-A-5-2 ES

-10 -1 2 0 5 3 -2 -2 -9( 0 0 0 4 -4 -9 -8

-13 5 6 2 8 6 -8 0 -12 3 2 2 6 -2 -14 -9

-18 3 10 1 8 7 -13 -2 I -16 2 2 0 Lt -1 -17 -9

16 0 8 2 5 8 -I 0 L20 I I -1 2 -5 -18 -7

10 3 7_ L 6 -6 3 -15 -3 -3 -4 -4 -6 -5 -7

BCP 8910-B-2-1 ES BCP 8910-B-2-2 ES

-16 -7 -2 0 -2 1 -3 -6 -6 1 1 0 0 -1 -3 -2 -12

-21 -6 1 1 -3 0 -5 -5 5 5 2 1 0 -6 -13 -10

-22 -9 2 0 -3 -1 -4 3 -5 5 2 2 0 -7 -12 -7

-22 -8 2 -2 -4 -3 -4 3 -8 -1 -2 -3 -2 -9 -11 -4

-17 -8 -3 -5 -8 -6 -8 -1 -8 -3 -5 -5 -7 -8 -1

18.5 13'' 5

2, TYP

SI ".. 32

LEVEL

_ L - . I--. - - 2

12. O''-T 34

5

77

0 (N UN UN, 0sN 03 N ao r- 00 C) - mN-- O >4 LI - U-\ UnUN, (Ni UN C UN% \D '. N (N 0 - ( --r Un r- co ON ,N (

L ( 'J ( N(N -T -T T0 -ZT -Z -:r _T -T N

-0

Z -T CD LN '. ) . UN\ '0 C) CD (4 in UN\ --T (- ON '0 U" -7- in CO

a,) 1'. CN 1N C4 C) ('-4 (-, (N

CD

C" C '% . N (N - -o r-- m ~ ('N -:3 m C) (' (' C) r, '.0 UN

m ('N U-\ (N O - -r '0 COON' C) - n (N r' -Z 'D0 'o

V) 0) ( (N C -7 . ~ (N 3 C -zr r-8 CN-% ~- - - C

1.3 0N -n 03 ( N- O ' CD - N -Z U", WN a. ) N_. -, -- N ( ( ' (N ( __r m) ( 'N )- r -T

C) U

U) -T -00-

F- (

F) - c(N ) U\0 CD (N (N Q (D NO LJ N (N- N C) N -0 UN UN '0 ON ON

C) (N) U"\D-

CL -C-

a_ L-) C) C N C C) UN C) CD UN UN C) C) C) C) C ) UN C ) C

C) in in C) -n UNC>~- C N UN U 00 C-. CD CD CD - C)-' -r (N "' (' - N' 'D (N- cc- (N - O N O N C

ON 0 04- l 4 " C4 r, r

-

:3) 0 ) C C ) C ) C C ) C ) C C ) C ) C

V) V U N C N C N C N C U ) C ) C ) C ) C ) C

0-

o -Z C:) r'NO ON C) (NJ 0-\ O (N '.0 UoCN CO 0(N 0 O N ('N c C) a) mOO

UN (N UN 03 (N '.0 a- -N -T ON ('N ON - N N (N O 00

40 m

0 C) (' I- '.0

MU 0 -r m. (' 0U ('N 00 _r C)\ a,' CD-' c t~ ~ ' N r- 0

L- UNZU U-N '. a-, (n- W>

uj C) (N m) UN\ 0 0N C) C) (N C), C) (N4 C' (N r4 C) 0) C)UND

0.- C) (N O :Z N (N 00 (N r- (N (N (-4 - C) - (0 (N - C)

-< CN(' 4 U 0 ( -- TC ONT C)\ -\ ( N U N '..0 I'(N-r-

CC

CD UN C) UN C)0 ) C) UN C) UN c UNc C) U\ UN in

C)0C) 0 C C ) C)r C)\ C) C C) m C) C)\ C)I C C) C 0 C

(N Q N <D - C) Q UN 0 C) 0 (N IND (- I) (D 0N (N 2D N

L I N P - - (N (N4 (N (N K78

OD a)'0 - ) L c . ~ c c LA\ -T 00a) U'% LA ZA LAof '. . . - N- - r-cw co

LA c) -TC - -z OC) 0-' 0' C) cc M C) 0' -7 C, - U'\ r,* '.0 '.0C-7 cc c ) N N -.T U% r- r- co mc 00 CD - CN c) NQ - (Ni (N4 M~ fN fN M~ ( M re M" ( C. -:T -:T Ln Ln LA Lfn Ln LA- (C

C) -

WC.0 r 0 cc M - n '0 O -7 CO cc N C 'N cO '.D m~ m '.

-li -cc cc CD~ C) C) flN C'- r- rA LA m. .f . c c o C

C4 - (N C c .c -D LA 00 0- U\ 00. c c ( A 00 m - - U\ r- m C -)

-0 OD cc LA C)r- c c - C) C) C N C- - .o -Z mc LA (N r, CF.-X - C) CD M WN(N - (N \~L LA '.0 '0 LA D. N-c Co cc)a- C) - C) '10 IDc '. D '. D '.0 D \,c '0 '.0 ' 0 '0 D. '. . . . .o'0 N - N - (

ci

0 - 0 )C T L- --- - - - - - - - - - - - - - - - - - - - - - -

IN C) N N Z

L-) C) 0 LACC) C ) L A C ) C ) C C) C) C) LA C) C) C) (mc m A cc 0 C- 0 0 LA cc cc cc L C) '. A ~ 0 0 -- cc CD-.- )C oa -r -0 cN w -a, C) LA LA 'r N-\ ( r co cccm C) - 0 : U o r

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c c

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-79

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01 mn rn --T .n 10 0o r- r- m~O Co m~ EN U O P--. Cc)

D. 0i 00 *- co aN 0 C4 -T (- -o-Z i'l ('. - 0 --7 C o ,-T e - 0\ U-% ( '0 ,\ w~ _PS '.T I- 0-. CD .o o 0T

-o

00 10 41 N 0 -' N mn m (N fl- D 0F' 10 r, U\

C', T-. C14 M ~ C , -T -l- LIN 'N - 0 (N a N- Z (' N a %

co "N r- 0) 0's CO -o UUN OON ('N -T- n r- 00 0'~(' 4 (N" M N CCZ -Z \ U'\ 7r \UN In Sn U '0

CD 0-Z (' n DUN 0 OC) .0 F- '0 a0 N. N 0 cC " O Z C N U ON ('N\ OND UN, rN ON S --i -Zrl 0 - -,\

0N a) C'S4 0 T UN m0 -'.n -T ( O ( -~ - w m' N

UN N- -r- COci ' o U - -N -N - - ON N- - O-o V) N eN (N -r - N N U n S n S n N

I )00 0 0 0 0 0 0 0 0 0 0 0 0 0 0U' 0 r ('N ON n - r\ UN'. CD F- N n C - U'\ 0 '.00 -7n C

-7l ra -(> "' Z UN . '- ON 0 N ' -%r P- N- N. Co co(N - q ( 14mC CC e, - : z

UN UN 0 UN.0 U 0 T O'\ 0 N 0 N 0 N 0' UN 0 0 0%q) UNT N. 0l (N4 UN O- F N r L- co~U N- OD - co ccN

-r - - - C14 (N ( ( ' ( z(' -7 7 _r 7T

0 C) ('N ON Co % (N N N Lr s0 0 N P- C- tX\ .4-. CO N- 'NLUN 4 Z- ( -0 N UN* L 0 UNr 0N '0 r- '04 CON - 00 (' -n 0

C% - ( (N (VN..m --T UlCN '.0 N-o ON 00 0 a

0o ON N-i C> mN m' 0- ('N (' N o 0- O Co 0, CN UN: UN- - N- O' 0 (N N- C(4 '0 ONi 'o UN 0 0- wN 0 1oCo

-I \ e -- (N (N (N ('N (' r(N-7 w o -7 -7 -7

GoN (D o. CD, cN UN 0nN 0 N-( o 0 CoO - (r4 n - C) (N - 0' ('N ('N UN - CA~ Sn N - Co) ON ON

('90

(N C'J '.V - 01) a) UN -7 a) r- C) _:t C C) 0 'ena LA.0CD C%4 UN0 0T' MN L Lr\ CC'r~ Ln 00 - "N 0N rn a) r- eIN

L )- N r4 (N4 CN M' Cn)C)~ ) UN LALA \f U)\ U)\r

M e CO en, a- 0) '. OC W O( 0,\ c. C) M) C) 'D0 CO C) r-D '.CC -4 \D 0) "N '. -- C) (' -4 LA CC 0-\ " -T O (D CO U-Z '0 '0 r-- r- r- r- cr) CO CC Oa) 0) 0)1 a) 0,\ C) C C) C)- C) :3

0m

roLO 0) C, en a) '.0 C) (Ni N-- 0L C, UA '.0 '0 (N CD '.0 CO N--

-T ',C r- 00 CD 04- Mn -T LA \D a) 0 "-. '.0 O) 04 '0 - -- If.4c4 C'D '.0 '.0 '.C ' - r- r- r- r- N- r- U) CO O CC all m) C

o 0)N r- en '.0 -- CD C 00 m N- (Na) '. ' C LA %N(N .Da LA a)CI MN ") (N \ LA ff% C) N e - w) C) -rn4 N - CO 0-) C4 -7r LA LA

0\ ---- ---- ---- .- m m --7: CDr, C-1 C1

0 .. 0)\ a) eIN (D r- mN en CO \ LA\ (N( 1. Ne A- 0 e -co

< N- - r- N- N- N- r, c co0 CCOa 00)0 a) - 0) C) C)-

C%

I (i C) ) C) C) C) C) C) C) C) C) C) C) C) CD CDC CD C) CD C CDa) Lj CO (N C) .0 -:r o) '. - r- N- r Na LA \u - N- mn o\ "N :- 0)C a', 000\) C)4 C)- m mN( ne -Z -r ULA LA\ '0 N-Nr-C 0) C)CN C.. C -- (4 N ( N (N NC(4 (Nj N- "' ('4 IN ('1 C.)C*. CIA M'

00 (/1.)0"\

a-L.)0) L) C C CD C CD C) C C) ) C) CD C) C) C) C) CD ) C- C) C)C) C) C' (D C) C) C C C) C) C () C) C CD C) C) C) C) CD CD

-7LA a) N- a) 0a\ CD - "N en -Z LA a) r. , 0y ) C:) - C,4 r') -Z~-- -T --3 -zt -T LA LA LA\ LA LA LA\ LA% LA\ LA U 'D a) ID a) a)

(NN n enL~r LA(r - 0)\

zm) m CD en

)-Zr CO CO C) 0)cr -T -:r LA -T

CD

W, 0 Dr

en uI o

C C

01\ LA a) ) (- 0 If( LA a'\ C) C

C4 C .- r - - " -

0 '0 CD C) 0 0o -0 C:) (D 0) C)

< - -

IMPERFECTION MEASURFMENTS

(x io3 in)

BCP 9824-A-3-I AS BCP 9824-A-3-2 AS

4 0 3 0 -8 -4 -5 -3 4 1 5 0 -I 0 -5 -5

4 -4 0 -4 -10 -6 -1 0 0 4 2 3 0 2 -2 -2

6 -2 4 -2 -9 -3 3 4 10 0 7 5 1 -1 0

12 3 7 5 -4 2 II 11 16 4 10 9 5 8 5 613 4 8 6 -l 5 11 14 20 8 13 13- 10 10 10 12

12 8 7 7 2 8 12 14 18 8 II 141 11 13 , 112

10 10 8 12 6 1i 11 12 16 12; 12 15 13 14 i 15 16

BCP 9810-B-3-I AS BCP 9810-B-3-2 AS

2 -1 0 0 -3 -2 -3 1 -3 -1 -2 0 -I 0 -1 -1

0-4 -2 -2 -6 -2 -2 2 -4 I 0!-3-2 0 -2

4 - 2 -2 -1 -5 I 6 8 10-3 3 3 -3 0 I v10 I 1 3 -3 5 12 12 12 -1 7 5 1 4 5 5

Il 4 4 7 -1 7 14 15 _ 13 01 71 6 3 5' 7! 7

12 3 5 5 0 9 16 15 -10 2 8 6 3 7 6 8

10o 6 7 7 2 8 10 1-2 8' 9 1

2L 1 5 -1, TYP

S8

8513'

1 TYP

32 LEVEL

I2"' TY T16.0", T

82

0 Ur\ - N U. (N 0 N - o0 Lf% ('( '.L- U'A '.0 \- 0 r- '' 0iI I -7 C) _:r N . L\ -

I E- -N -' -- 0-O\ 0

z 0 0'.0w 03 r- m r- co - Nl-~ w30 01\ 0 "- '.0

-Z m r" D m C1 r (I 0' - -N -v "

C1 0l Lf''. 0 - - _r\ LA.- Un 0o (N (N '0 - o

La L

0-\~0 -. N- O ' -:r LI' m'' 0 .- , U 'o - T t'. - m~M in ( '.0 N N 0 -T~ -CC) . N-4 N - -:, 00 -

C', C' -q (N (N, - ,I, '. '. - L"\ 03, Q. '.

C) 41 00) - ID O'\ r.-.' 00U\ 3- 0 U' -'. 0r a,\- V) C14 00 LI'. r-' C11 - = ' 0 O '. m I' t -- 03 C

LO- (N 1 5""a ('. .0 r-T UN C (Nr c, c

x -r- 0 LA C

(D - U'\0

F-- 03 ~ ) LI'. 0 0 0(9 9t' . .i' .I* . .I

a- -0 0 (T-' "N -1- '.00w30m 0 -=Q-c- c0 C -' a-I'0 5. - 5' U.'. L'

S 0-1 winV-

co U' 0 0 LA 0 'D 0 C'. 0 0' 0 UCD 0 0 0 0 0 0(l LN 0Ln C) 0 r (N U'. 0 (NL", 0 -C) CD C) -LA0

Ln - - N ( N mN m' mIN. N ' N

CL

~.Ji.. 0 0 - 03 C'. N 3* C'I (N '( 03 3 - -4 '. i' CN ' (N C(N

ar00- - -00 01'- C).0030 03 N' M L4 LA. 00{ (

03 -T m' N-a- 0 ''\ - U'. 0 '.0 (N UlA O 0 N' (N L 3

0f (V- ( N N. n' -:3- -T- -: - \ U'. l\ LA LA\ ' .W '.

M -T CD m '

o' N 0 ~. e. N -x r-, "N r- m'- U'\ r- 0 CNJ - 1.0c - ( (N4 (N4 &) M rn -I* _:T . -:r U'\ ulA Ul\ L

F-4i 0 -T U'. Ul\ r, _:r 00 -T U'. 0 0 m N'0 03 m 0GOi ( -41 r- 0> m N- " m' 0'.% -;; 0 %0 '0 1\ C11%' 0'. m m -

La C4 m -Z U(N (N %'0 L 0 '0 %.0 '- rN - .00 00

Xa

a

03 wi 0 0 Ln 0 0 L, Lm ID 0 0 0 0 U'. 014 00

0 0 al -N V\ - 00 N' 0 N-0' -N r-\

0'.

CV~ A LA 'A U'.0 iA 0 "0 00 00 00LA (N L N (N LA C N. 0 (4 LA'0 I'- a- ' o - r, *-:r

-' -- - N ( ( N ( N. N '' ' '

83

- - - -) - - ~ (- r - -- -- C - - -) (D -7 - C -

L- LA LA C: d0O .- r N. - N A - 0 - CC) - r- (D 04

1A

O ~ L o - - A o~ eJ L . 0 C A-o r-- co U\U- -\ 0

- r - 00 C o O Oaio 00 0- - AlA MN MC'- D) CD)

O O. CD '.0 1.0 --T M~ M M -: ) CD ) - \ U\ 0, -T -- r C)re 0 o - z '0 C - -T -,D M~ " A U'\ ( ) 0 m Ln 00 C rn -c W

(D - -" r- - r- --- w w- m -,0 0 c

U) Co ' 00 ) 0 C CD C - - - -) -) C- rC'I m'~ m) CA -T -T -

4- C

oCD U'% C) C) LA) LA LA\ LA\ C) C CD LfA ) Ul\ LA C) -\ ULA ulA ULAI- Co - 0 Ca .) -T - C - . -CO CO C C CA 0) LA\

1 -00 Cp LA '.0 \.D N. r- 00 M 0 0 C), - 1 - A 1A C"' MA -zr -T LA\ L '0

C14 c LA c . N. -o - - - A) C - LA '.0 N. i Coi 0)0i C

u --- 1 C) 0)C C) CD C CD 0 C C CC) 0 C) C) (D C) C CDI u' 0 0 0 0 0C 0CD0 00 C) CD

A 0A Cm (IN C\ .-T --T z -T -T - :r -T T -T 4r -T LA QLA LA LA LA\ LA

841

Ln 0,- -c:T* CN r"c '.0 0 ca Vn O an -

C1 C11 -;j- ,T - -T - :

C:

0 04 C14 rLA C - : LA 1*- 110 fl- P-~ C- ( 0 C*a ,N

'U. M CO -l TI o-,NI (S ~ (N 4 4 4 -

CL 01 C,%o --t -!r Co U-\ ' 00 0 r-.0 - 00 00 'n0 a,

0 m - cLA -:3 C - O rh-- CO 0o kt)-. C AO .

c- ((NO N-(VC A - '. ' )C ~ -~J N C O

a - N 0 L LA LAN '0 U'% C) N% n an an o0 oC14 U- r -u--u , r - ( ) L N r

C' OC-" O f' ' - 0 D - 0 u, - Z -

C)0 0 C,4 m ~ r- U'\ 0 o t(n Ul -T '. )L - r--o N (m -J LA 'o-a -Ly, "4 w.A '30 tV-\ Co 0 co CN

. 4 s I

Co

7A w 0 LA 0 A0 0 0 0 A 0 LA 0 LA 0 0 0 N 0

0r LA m. C4 CAl 0T LM N. P- 03" CD - A (N 04 -- - '0f- C C ~ N ( C A ( 0 - -( -( -~ -A -. -n - -

to

(v '1 LA N. CA u-l -0 W- 0 C) WIN c * LA . 03 40 nN-C

C4 0 r- C14 0n r~0 - 0 LA ". LA f,0 O £f en -3 T 0 n -3 -(NJ ~ ~ ~ C1 LAq M0 mO. C." LA m-a. L - - ~ --

L r L

0 0

a, C

c

00

CD 0- C

If))

M 0 -T 10 -

-T LP -o

a' Lo 'D - "0

DODC 0 C- - -

'.0 '0 0 c-L_:I -T c- - 0 )

cI .

0 x -~ 0 .0 '" :T 00 001j '-D uQJ-7 C. 4 -I' -L '. C c

IC)

(D a ')0 ) r 0 0- -7 C-o -7 -7 -

00

CL

L.)

0~ Co 0' CO Co C ''a C9N 0 0- .0 LA r 0\ C) D

< ICC C, C' ~- 86

IMPERFECTION MEASUREMENTS

(x 1o-3 in)

BCP 9921-A-8-1 DS BCP 9921-A-8-2 DS

9! 8 4 0 4 6 5 5j - - -4 0 6 9 3 -3

5 0-1 2 7 .7K 5 - 7, -2j 4 6 -3 -41017 2 -I 7 12 12 / O1 - -3' 6 2 -? -5

15 8 2 2 9 13 14i 14 9 11 3 1 13' 15 3 0

n15 1 8 8 10 15 19 18 12 .12 4 5 16 18 5 3

16 13 11 13 16 17 20 22 16, 14 7 9 16 20 9 5

19 14 15 18 20 18 20 22 15 14 9 11, 15 15 14 10

BCP 9810-B-1-1 DS BCP 9810-B-1-2

1 0 I 1 0 2 I -1 -1 3 3 2 0 - -0 -1 -20

2I, -2 0 -1 -2 -2 I 5 5 0 1 0-15 -2.24;

0- -- -- 2

Ii I 9 4 -1 4 3 I I 3 1 12 9 13 3 I -23 -20

23 19 12 5 9 10 10 9 19 18 1 t0 9 8 -I0 -13 -13

34 28 12 4 8 12 13 15 21 18 11 10 9 -6 12 -8

39 29 12 6 12 14 19 19 2120 13 12 13 0 -3; 2

3629 15 10 16 16 19 21 20 I3 17 16 17 10 3 12

13.566"1 11/16 "

TYP

I''2 9/ 16'''-':-LEVEL

2''- 6

87

I I - III I I -3,7

EXPERIMENTAL AND NUMNERICAL ANALYSIS OF AXIALLY COMPRESSED CXRCU--ETC(U)OCT 81 N R BAULD F33615-79-C-3030

UNCLASSIFIED AFWAL-TR-61-3156 NL22 AIflffffllllffff2EEE~hhE

7m EA1275 DATNU hV O E S EARChINh E E I 11

11120

11111 1.25 14 I8;

0 0 ) (r CN -74 C.0 '.0 - C

E 0 N 00 C 00C -7- w. C- 00 0 C=l~ -7 '.- -7 - ---I, - n

Z N -l %N N 1 0 0. C'.)0 ro

C1 - - -. -O m- -T - -7 N ; 0r

C 00 ) 0 N C 4 04 M0 m - U o-n N N- 7 7 - -)

I.L -T -- Nr oo'0 '. ~

LnJ

HU 0 N) C.0 'DC.C D 0 C - CO 0 t - O0 0 .0 O0 -

F- X 9 9

C) 0 0)o o - c -I I D I0- -coc- - - - - --0

0L Ir C- L

CD) CZ) 000 0 C 00 0 0 l00 0 0 0

0- 0- L 0 NO C 0O- 0 '0 N C O u CD

C14 CO CC. 4

LA , mA 0 0 0 0 0 0 0 0 0 0 0 0N. LA rn - 0 - r- 'r\- U-% r- M' 0 - M r, - C)

'/) _ _ IN C r -

x

z 0)

0T L, M %D 0. N : m~. CO 0 C14 ',.\ 0 N- Cm C r'W A I. . C- m- r-\ m r-T r-M 00 - n 0 r- o r- - Cv.) >.-

0 O

Ln

CO m

\. 0 ' -0 CO CO M~)C 00 t- LA co~e. m . N - -T U,\ L - w-~~~-. "A ON 0. -I -; - 0.Z'. CO C C f -. u) e.)

m~~ ~ ~ ~ %.0 0ow w m r o

w )C 0 0 LA"\ CO A 0 %D 0 --T O'\. 0 -T M~ rZ 0.)' 4 N .0 *-0- '. 0 0 CO L% e.) .- 0a -% . N, C'o. t- rn oo-r r )r- en

X N 1 Me. -Z i. LA '. 0 0 --- Nec -7 LA L'.wj 0 01-

LA .T .. L

L -.T11. 0.)'7 C N r: - LJ.C COO.) UA I. CO V; U0)-0 N -T %D CO c' -r cN m~ -7 . Ir - o N L7'0 C-

- c~ - - - " N1 N1 N1 (14 .M ' M~. M~. (n .0COLLJ Cf.

C). - -1

COT - l\ LA 0 LA 0 LA. 0 U) 40 If. 0 0 0 0 0D 0 0 0 0 0 CO*-IO N LA. r-- ONcl LA r-. ON " U.'1.0 CrC 0.M 0 - N C..). -T 0C

x 0 ~ ~ - - -N 4 N 14 N N N N e. Cl~ e.% C^~ Ce. M

88

N-I C) 0D m N (N% (N 00 -

UI - 0 (N

E.: LA -, OD00 - J I' N- ON C4 u\ 34 -ZS0 -j (n -D %0 N- N 0.0 N- 0 n - ((U. '.0 '.0 0.0 000 D0 '.0. . s N N N

C(4 -T (N N - r - N r- (N N- Z CN -

L. (Nr. - r- - r- -4 04 C4 '0 % 0' 0.~~_Z N- N- N-% 03 3 3 3 3 3 3 3 3

C: (a0 (N4 Cn~0 C~~ L~ NO 0 ( N

U x 0 ( -T Un N- N- - C N M -7 u01 all~ m~ m' m- m~ (D C 0 00 0

(I)

(10

0) Lf\ 0 Ul\ 0 LP( 0 LP. U-\ 0 0 00D LC\ U%

1 L1 (N N-- -(N - - 0 - ~ -3 (NC

N-o o N- - N- WO WO M0\ N ) 0. C' 0 0 --~ ~ ~ 1 C4C----------------------( (N (N (N (N4 M

al 0 0 0 0 0 0 0 0 0 0 0 0 0

0. X. ND - N-> 3 0. 0' N (

.0 -

1 ~ ( U'. 0 3C

-7 a i' CO 0

(U .

-Li , I

o -0( C 0 - NU - 0'n .o N -

sO0NmCm m<- --

U89

0 -T m~ m M - - -T '. \ %D M. U"\L -:2 MO CN %0 M 0 o-,UL -; 01 LA_ 0- 14 0 LACw - -a,01 O -:r O' - 0% O -c7 w

Q) m m m _:r :r -W L A'0 '0 \ r- r--

LA\ r- -T ~r Q'T M~ -T0 0 - r- r- LAOZ- \D 00 (n .0 r- M~ 0 CN -T '0 r- M~ (N -7 LA\ 0O 0 -Tw- ( 4 C14 MN fn ff 01 M~ f -7 -r -T -Z U\ LA

0-D C, -:I0 m- 01) m w~ %D mO (N ' - m-0~.m LA 0 '0o co 0 (N 0 N- O 0" C N -T '.0 r- 0 -

(a MN ffN C(N M ON M~~c W - -T -T LA\ LA LA\

1- I I I I III I I I IO I- I T

Id,

_ 0 L -T r- m~ ULA (N - L\ - -T -r7 \.o00 LA .0 -x N- 0 -r -T M \D -0 C; - 0\O N A-

(N -,

0 00 00CD0 00 0 00C 0 0 0 0 0 0 0 0 0

(N C 'l LA '.0 '.0 N- N- CO j 0 -* N IU - L .

0\ LLJ(/n

0l Cl 0 0' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0(N LA\ r- 0l -4 (N) -TL . N O .~ N LA

- - - - - -- - - - - - -( 04 (N 4 (N N C(N

0) MN - ' r- 0 M LA (1 0 0 (N M .1'0 -7 - N 0L \ (LA C- C1 MN 0N'\ r-~ \0 \D '.0 O N " 0 %Q CD a -:r

z'' L ' - N N-C CO\ o" r- %0 0

(N r~ ~ - -7 N LA C O ('' 0 0

(U\Lf __ __ - - - - - -- - -- - -w

0 LA (N -l a\ -T '0 N- -7 - 'mO - O .- (-l (N r-. 00 CO '0, LA Lm"~' 0 N- 0 ~ N

0 C C ' C C'I ( o Q~ - (N '0 LA 1 - 10 CO

m ~ ~ N CO r- 0-- mN (N3 o~r 00 -7%00 L

m c,, z -- -T--. LA\ LA LA '0

COC

x 0I.- -T 0 0 0 0 0 0 0 0 0 0 0 0

U,\ N ',\0 (N 0 U LA -'0 0~ -7 (N - 0 C DI '0- v m~ LA r- '0 0 C4 U-% 0N%- - C ( N 0'- LAT.

(N 0 - - - - - - - - c fN

.90

L.. LAl (N M (N -:r r- "N m Mw) w ON a% m C 000

E-

zIr- 0 3 --7 m- w -T '.

QJ o "~ .0 -T (n00' -T D. "L-A' %. .D) '0 r- r-c0o

%-' '. LAC 0D a% .0 LAO0MV m' Ln m~ -T %D - (N 00

LAN LA'. '.0 %D % r- i'- rl-

C (

0

< - r T 00 COCOO' 0 0"0 (ON (N

x C%-

C)0 0 0 0) 0 0 0n

- L 0 r- -0 0 O O 0 U:

cC C: - - - - (N ( N(

0 0 0 0D 0 0 0 00 LA 0 0 0 0) LA 0 "N

'.0 00 COM 0 - -(N m~(

91

IMPERFECTION MEASUREMENTS

(x 1O-3 in)

BCP 9817-B-7-1 BS BCP 9817-B-7-2 BS

1 _9_ 6 1 0 1 -3 L.-7 -5 1 1-2 0 1 0 2

13 10 1 -5 1-8 5 I1 -3 -4 -3 -3 -'18 12 3 -3-I - 1 6 1 -1 -2 1 3

23 17 7 2: 0 3 13 10 5 4

23 17 10 5i4 7 16 9 7 5 6 10

21 15 8 7 5 7 i 20 12 10 10 8; 12 _

15 12 9 9 8 9 21 13 15j15'13 15

BCP 9921-A-7-1 BS BCP 9921-A-7-2 BS

S40'3 _5_ -1 -5 0 9 8 3

12 1 -2 15 19 6 -2 5 25 31 17

15 3 12 19 12 _ 15 35 45 31

21 9 4 5 13 21 18 11 22 38 41 32

22: 12 5 4 10 18 23 17 26 361 37 32

21 13 7 7 12 17 27 20 25 32 36 38

18 13 11 11 12 17 31 32 33 39,

I " TYPLEvEL

_L U1 ,2,,,12" TYPI P

TYP3r2'' -

16.0" -

- -7

92

APPENDIX B

STRAIN, END-SHORTENING, AND IMPERFECTION MEASUREMENTS FORTEST PANELS WITH UNSUPPORTED STRAIGHT EDGES

AND CLAMPED CURVED EDGES

TESTING PROGRAM B

93

o) CO 00 m, '0 IDN ~- Ol ~- 0 n 'Lr LA M m m~o m0~ - r- '.D CO " C r-~r lN

- - N m -- - I V .0 1. No - N C on on 1O 0'" IO-

z m W I'C ~ - ~ o - CD M' Ln - CN CO U\-T ff-% M LA M~ - M~ CO r- N -T '0 0 " LA C N L, CO

- C o 0 LAN N-C A . C% Ln OW CO - N- C - O J

m m w~c c--C w -,o o -n- CO r-)'0 N C- N N m M M~ -:7 -T -. -T -T - - LA L

c

00 M 0 CO rCo ,C C", N- - C 14 m.n N (~C N C -T e- )f,. CO f4 - -T- 0"% -= M -T Co - C" LA - mO - -- U-\ L -

n -O~ on" -n 0 C . ~ N C ND '.0 MOf'

H- - r4 en -Z- Ln V .0 N-N - CO CO CO CO mO mO

C-' C-L

ISJ~C -0 Lr C0 - U '\ n 0 . r n .- C - C :)

ui CO r-, Cc 0 ' m 0 C

o: 0- - - - - - - - - - - W

0 0

z o C C C C C C C C C C C C C C C) C C wA, LAO LA C' UL\ C Ul CD U\ C C C C C C C C C. C 4

N \ LA - C0 A N C 1 U' LA '. r-C 00 C N C14 - C~

C N -- . . . . .Nn I ' -. UC

H .- 4,

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C1on4CO '0 F COJ r N- - \- LA N- %D CD r- t-- LA

Lu~~ ~ ~ ~ Cn r O C- :M fl - A - T - - - - -M -- - - - - - - - - -n

Ln 00 -T N10 '0 '0C'" Co LC r - o N -\ 0 '0 c~(Cm -T -T LA LA% LA '0A '0 'D0 N- N- N-

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(N Ln 0 N '00 -7 m- -r w0 o~ - w '0 -7 - ~(- N "N (N C"% C-' m . (N .N (N C4 - - -

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x A-C (N oA - (N L 'D0 r- t-- c 0 a a-, 000 -

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LA CD LA ON M -o M .r- 0-; C 0 LA m - CO 0 0 (N Z.0 -, m -I -- (o (N (N (N (N ( ( '4 (4

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(N 0' N- - ' CO 0 - NJ (N .0 C14. C4 CN C04 0

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0> C)-0 W 0 W M M - -: - O 0n r-" \N 0 \0L - LA(N LA "O (N\ \'c mO (N LA 0-0 (i LC N

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-r -T i D o c:> I IA- 00 M C I r- C14 2 I-CqC%-n

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(N 00 0 0 000000 A 0CD>I :U4( -T '0 CO- "N -0' '0r CO 000 -- -

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96

LA% 'D0 Co

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r- CN OD( , C T CV O - C'lC4 n - -

C%4 jr U- .%.oi r- r- r -- \. 01 an~ -:r 0n '0 LA .0N C, LnL O A F

00

LA.

co La 4L LA '0 '0 C> r- CO 0~0 0 - N C1A LA '. 0 '0 CO

ON L A -r '0 N\ LA U'\ 0 ~ UN'. C'C, L0 '\ ND 0 0~ '0 LA

C^c~ - -z rA -, U-\ LA LA '.0 r- 0 0-. (7\ () - N C-4 t" '-T0- 0 rCA CA 41 (14 CAJ V4 CAJ N CA C-4 C14 [ CN CA . .,- - %141 r"

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.c~J 98

IMPERFECTION MEASUREMENTS

(x i0-3 in)

BCP 9824-A-2-I CF BCP 9824-A-2-2 CF

-4 -6 +1 +7 0 -14 -l 1-8 -2 +3 II -12 -6 0 +6 i+18 +13+3 1 1 1 -6 0 3

-8 0 13-5l12 I-7 +2 +3 -8G12 -8 0 -5 +5 +16 418

-51-10 -6 -7 -9 -I9 !-141 -9 +1 +4 -8 -10 -7 -3 -4 +5 +14 +21_____ ~ ll ! -61 -7 -

-9-1 -12 -9 -II -1913 -8 +3 +4 -6 10 -5 -7 0 +9 +16

-10 -13 -13 -12 -13 -15 -13 -1 +9 +3 -4 -9 -8 -3 - +4 +12 +20

BCP 9810-B-4-1 CF BCP 9810-B-4-2 CF

+201+12 +4 0 1 0 -1 +2 +3 +8 1 +1 +1 +8 +5 o -0 '-2 1 '-28 -15+22 +14 +5 +1 +2 +2 +6 +9 +16 -+1 0 +6 +4 -3 -14 -18 -23 -

+21 +12 +4 +1 +1 0 +7 +9 1+19 0 -2 0 0 -6 -13 -I'-19 -24+33 +25 16 +9 +8 +6 +9 +11 +18 0 -4 -1 -5 -10-14 -14 -16 -6

+33 26 17 +12 1+10 +8 i+1 1+14 !+20 -7 -10 -10 -11 -6 -6 +6-I- !i -' .

17. 513''

2 3/16''P

3 9/16" TYP0.5" LEVEL

II

2F T

8.0"-8 - 5 _

This imperfection data is questionable. Imperfection measuring device

was not mounted accurately enough.

99

a~~~( r- (N r,) (N<D o,

Ln 0 1 0'L"O-- 0 ( A '0 -Z 'D 0 a) L r, 0 r n0 a

EN -T 0 r Co 'D 0 C) L 0 C 0 ( ' A 'z ~ ~~ ~ ~ ~ CN -70 (DL" 0I N (-) (n (N

- - '0 '. C) 0 N ~ ACDo a -.Z -4 0 - M0F-.m l -- C' 1 l l o 0 N _ (N, -j - _ J (

u -- ---- ----- - - ci C4 C. N C

~. 0 - LA CO r-- -o cc '.0 j rn -. r- r- LA\ WC CC 0

LA N - (N C) L .0 N o a -c- c - - L -- - -) - (N ruJOL

ML 0 - a a r) 0 LA C r- 11n '4D "'I -T 11 0,1 ) 00 -1x -T-r' -- ' 0 ' - - '0 0a -:3 r-. 0 r-' o ( -T- N-

Z~ C- -. Z - N (N (T~c~rLD

- LU

CD C, r"10L 1 0 r0 0c-

C0 00 c 0c ) 0 ( . N '. 0 C o

=> C, - 0 - -D -) CD (N C) - ~ CD a 0 UCOD Co , 0 CDC

m. aD 011 1 oJ L D )-DI

CC -

100CD 0 \0 0) o00 0-,-0c 0C40 0 0 0 0 0 0 0 'D .C 0

(N L 0 0n 0o 0 - 0 0 0 C0 0- 0D a, " 0 0- - ' - ) 0 -C4 I'n en LA f'0 -T

LAD

z

'0

00m '00C r- -0 CC (0 '14 0 '01 (N\C14 C '0 0 - 0 - ON r- Ul O 0 " ( O - -% -

04- -1 (N \ (N fl -0 -* 0 m C Nm

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T ' n 0 co 0 '0 C o C % A L ra 0 \ - e

F- r-

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co. 0 o (N ) 0 0 a) 0 -3 '0 Co I 0 IN - (N CD0 Cm(' N LA0 U' IN (N\ a)L ) ( A ' o 0 0 Co n 0Na '0:31

mA C'1 -' r 0 U\1- (N (N (n IN r w IN 0 N IN

.x 0 -N .o .-0 .'00 (NO e% "N 0

- ( ( IN (N (N 0 ) N L a (N LA O

L - C N- 0 -T C) (N CD raJ u*D %D C. -) a) '.D

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4) r- -z MN (N co l a) t , oC -a t co -z -Z N- 'o ' .0D-C

Cv (4 C.~ C ',~ - C LI\ It\ 9. '.0 '.

0'% '.o o r- C N- - 1 0- 0 m) CD o C :0 C.. C (N - N- o C) -, 00 7 .l -

V) C14 C (4 -7 -4 r.- -T -7 '0 r 0 C 0(4 -7 C,4 %D N- 00 OCC N C. -T - Tt

- 1 ( N , (N (N (N (N, C14 C-4 rI M~ M

<~- 0' ~0 O% - - D ' w 0 C> N- (-C,( U, N- m- C'4 -7 'D w) C C - '4

00 - all -O N-N---

0 0 o 0 0 o 'UJ 0) C 4 m~ _NW -n a r- . W C

Id\ C j C Cr

a_0 C1C4 C C C- C C- C ~ mACL

coo

00 0oO -T '.0 m .0 -O C - f 0 -n CN '.0;;C) 1

-f) - -7 CNO C o 0 .0 '. 0 Co Lr - co coL 0- r) -7 -Z7 '.0 '. D '.0 r2 r, r,0

El

0 T C 1 -Z0 r-7 Co- f-7 10 oP Co0

0 r.,( - -7 CD C"0 '.0 ff 0 '.0cu -N -: - - - -n --

0 o Co o -- on-0 Co w

C(N '.0 0 -7 Co 0, Co 0 Lf -T '

'V - (N4 (N -7'.:.0 '0

C o -T 0 Co4 %L m _; 0 0 ( c

x M -r Co ("' (N 0n oN L o -T .7 - CD0 --l (T (N) LA) rA' '0 '0 N - Co Co

(N -

La'

eu LA L L x0 A 0 0 0 0T 0 LA

-0 (N (N (m70 '. - 0 0 -

0-0

a.V

0 '.C,0 I 0- 0 N- 0 C 0 LA D f0 D (N '0 O CCo LA 0 L AO ' U'0 Co o N- D~ o o o (

r- -o (NCDAI~I ~ N Co C

11. - - -- -- - -- -

EV3 - ( A ( - C ~ 0 n .. c' - O -

~- ( O L ON ' o (0 \ 0 W '.0 r- m( %D~ (N

c, (N (N In m~ -*- -T .-- 7 - "1

a -70 '. 0 - "o w 0 a. Co 'I- N-0 -C 0- N %.D e -. T % 00 CD '0 N-N-N-Co -

U-7

-0 0

co L 0 W % O 0 00 \0 U% Co -C ( r4 Co -0 o- 0 r

M. 0-" LA .0 N - "~ 0 j M L \ '.0 N- - r-

74 C4. . .

.10

IMPERFECTION MEASUREMENTS

(x io-3 in)

BCP 9921-A-6-1 EF 3CP 9921-A-6-2 EF

1+28J+35 +36 +23 O -5 +28 +50+52 ,+0 13 26 +14 0 +2 !+24 :+44 +69+241+35 +38 +30 +Ri +8+35 , +52+56 +731+48+33 + 02 +35 +59

+261+33 +42 +33 ! +18 J+4 _ 1+55V 6 , +52 ,42 +40 +30 +22 +26 +1,? +62 +72+++ i--1---+32 1+36 1+44 +38 +26 +26 i+50 '+ +61 30 42 +43 +38 +32 34 +52 '+62 80

+39 +36 +45 +40 +37 1+40 +39 +64 +72 +48 +46 +48 +43 +44 +45 +6l +69 +85

_+64 +72_ +48_ +4 +8 4 4

BCP 9817-B-5-1 EF BCP 9817-8-5-2 EF

+68+551+31 o+Io l40 +59 +66 +25 +24 i+2j' ,. 0 +1 +2 2 !+525 1+ 3 +2 0 1++66 +54 +;20 +12 j+1+44 +s 8 +5 1+ +8 +~2~+65 +57 '+48 '+36 +28 + 30 +51 '2 5 + + 32 29 +21+32 +33 +34 +28 1+5 1+13 +3

0 +29 +21

+60 +61 +56 +41 +40 +44 +53 +57 4Ao + +3 +2 + +

+55 +53 +55 +48 +50+5i,5+58+56 + + + +

S+2 29 32 1+30 i+ 25 +25 +32 +33

17.513''211, TYP

3 TYP

LEVEL"IT -.1 • il II-- I

1 -- 2

2''TYP 312.0 T'-

- S

This imperfection data is questionable. Imperfection measuring devicewas not mounted accurately enough.

103

a I I I I I I I I I I I

L

C) 0 0 LA% (N r - ( 7 r, - L -T r-Z~ m-zr 7 U A-% 'D0 ( C-4 CT L%. O' M - ,, 0

W "4 N (N ~ r- -_r -T- -T -T Ln Ln L LA%

4' 0 rn LA% LA% (N 0 00 (N %.0 - L . CN-4mr -T m~ LA -'. - C0 m 0 0 C,4 LA% N-

- 1 YN fn _:% _z - 7-T -T LA\ UN LA\ u

CL

lb -, -Ar - - 0%UCL 0 co C^ 1. N -T 0 -T r00 z. 00 0- - o~li '

V). - N tv, M C. -Z -T -z- 7 LA% LA

0A 0 \U - ----- -" ' ; C1 c

W C,\ 0 COW LA LA -l N-\ rf ~ - I -. e - 00

X:- < (Nl ( rn if -T -.T -T LA LA LAr LA LA

C.7 LL.< 4

C4 -T

CA-n ~ 0 1 O 0 - 'N r- Ch 0 CO r4 0 WO LAN C) 0 q

O o a - -

w tn

LiL

zu LA 0 LAOLA 000000 LA-- ID (NO0 (N A I- - ( .A '. ON- r-

x~~~~or -T -n -. r, c' a ( ( N ( (

LAJ

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CC

j 0 iLA 0 r- -o CO 00 %.D r-t 0 %0 ..

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0cc ( C 4 N '0 (IN -T _CO-T LO 'D-0 (N '

-J -le- ~ C O ( - - o4L (N ( NuC A ( A -

I-. - - - - - - - - - -

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'0 - - ---- -- - -

; - - r 1 C .

10

O cC -T LAO LAO LA en '.0 LAO '0D LA\ LA - .I .I Ic Io -1 m CT 0

E -

LoZ 0 00-T 0' - CO ~ f~A - C A'0 0 LA C-4o

(D I N ( ( N LA C-4A C n LA M. A -\ MN -:

I ' Il -T I In (N\ U% N O

O CO" -n w A- 0 :2 (N C D LA w~ 0 A-0 r 0 oo a, LA r-<- CN A-4 CN 04 C(4 IC A 0 4 C- 4 0AA- (N C4 '.0 C OO c" 1

C 0

SN -~ -T LA - .0 A- a) ID U' -m ) L - C ( - 0 a

0 or

X - LA\ LA 0 CD C) 'D.0 C. CD A- COC CD CO cO CO 0 0 C A-e A - (N (N (N (N " -T (N (N (N (N CN (N N (N -T (N \

(N - - - - C1 1 4 C

C- 0

C, m 00 N' L\ M0 LA- (N 00 LAO m 00 LAOF-Ul-l - 0 -T C1 -T r, M -

+) 3TI - E

C. 4 C - 0 L o r

C)

0 0r 0- 0 0 0- 0T 0 0 , 0 0 0 0 0 0 0D 0 0 0-'V (N L -z. A-O a)r 0 ON - '0 A-O M ) 0- (N N LAm

. - - - - - - - -- 4 0

72

10 (N \ 0 LA ) A- M 0 f' - 0 O 0 LA N\ ( U ' 0 A- LA

0 E

0 0 N) C) LA CO A- CO CO '0 LA '0 0 0 LA -a \0 ( D -D ) A- 0 CD LA0 a ) a A- C '\ '0 A- n

x 0 - - - - - C (N C(N "D -0 C4 C4<V L

CD 05

'- ---- = M o n I I I I I I I I I I

(D Dr (N 0mD'~

E

110 -T 00 (N U'\'

cm (N4 C, (N4 C14 (

C)(D ) m C LA~ r- 0 riNc-T -T -T Ln If' rl-

fL- m. m. . r- L r ) ,

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0

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a, CO0) CD 0 a a

C-CC

.10

IMPERFECTION MEASUREMENTS

(x o-3 in)

BCP 9824-A-4-I AF BCP 9824-A-4-2 AF

+31 +221+15 +5 O -2 +51+10 +1] +.)8 +16 10 0 0 -5 +2 1 +6 +7

+32 +25 +16 -4 -21 +l1 +8 I+13 +20 +28 +19 +12 +2 +I "4 +4 !+ 10 +6

+34 +26 +19 +6 +4 +41+11 +17 +22 j+16 1 1+16 +" -2 0 +;i !+13 +6

+39 +31 +22 +10 +8 +io +19 +25 +29 +30 +30 i+27 +16 +l 1i+15 +31 +23 1+11

+45 +35 +27 +16 +14 +17 +26 +30 +37 +34 +31 .+32 +22 +17 +2 +39 '+34 '- 9

+451+37 +29 +21 +22 +24 +33 +40 +46 +32 4+33 +34+23 +19 +25 +4 1 +36 +16

+43 +37 +34 +28 +31 +33 +43 +50 +62 +34 +36 +35 !+28 +29 +32 +47 42 +3CF

BCP 9817-B-8-1 AF BCP 9817-B-8-2 AF

+30 +14 +6 0 o-1 +5:+15 +30 +15 11+139+92 +3 0 38 -6 6 -961-33

+29 +16 +9 +3 +5 +2 +7 +22 +38 +179+132+88 +45 +3 -25 -50 -72 106

+38 +25 k16 +10 +10 +10 +15 +28 +40 + 1674+127+88 +53 1+21 -9 -30 -42 -55

+47 +33 k25 -19 +18 -19 +24 +34 +-41 +158+124+90 +59 +33 +11 -5 -11 -I1

.+60 +43 I-36 t+29 +28 1-30 34 +39 +46 +145+117+90 +(65 -+46 +28 +16 +16 +21

69 50 44 +38 +36 38 +41 +45 +48 +130+1111+90 +72 4+6 +46 +39 +443 !+52

71 8 51 44 +42 45 +50 +50 57 +_114+10390 +75+67 +61 +60 !+67 +75

17.513"

2 3/16'TYP

i- 3 9/16" TYP

1'' I LEVEL

2"TYP 4_ 5

6

I 7I _- 8I I - 9

This imperfection data is questionable. Imperfection measurinq devicewas not mounted accurately enough.

107

LU fC CO 0i NO m~. mt E' -o '.0 N- '0 m.- C O 0-0 1

zu

Q) CC 'N LA.7 N- LAOw -7 -7 0 WAO'\ CO LA C.

mA 2 ' LA .0 COO.' f C.'. C14 M ~'0'. (CIC

c.

L'i T

< C) LA LA% - CO r N N " O ' - - ". U'\ 0 (N IN Ca,% ( .0 ( ON CO LT CO ' C(N U,\ O r- M '0 " .m (N"

LCJ - - (N (N\ UN 1A\ \.O r-" -o tf. A0 '.0 Nl , r - =C 0

x -

-C L0 - - - - - - -" - - - - - - -: - - - -U' W 0'

a_, 0 C

CD 00 c:z0A a,\ .0 V-

- 00 0 00C 0C "' 00O C:I0O O 0 0 0 C C C C, D 0 0 C m'

M- m. U' 0 r ., :x 0 - - - - - - - .O '24

<(A

(N II co C4 U

L-. I I -rn. -:r _r CA 7. :r L L

EE

-7(C) C A N 0'. mN r- LA N-\ CO C C AC

C14- - ( ( 4 (N en. Z - -T LA\

O o '.0 00 LAO CA N-O 00 ( N C"\ - rOO '. 4 (N a,\'04C. L O.- C ' O C4 .C '-(4 C C4 MA. Cn m -T _r -7v

z -LA) 'V (I A C - -4 c o 0

L C N- 0 C L AO 0' 0'.C C * C') LA\ LA LA N'o 0(A - (N I mA mA _r' LA LA Ul\ V\\ r'- fl- CO m a"O' ' 0 L.

L- - - - - - - - - - - - - - - -- 0 00.'-

0 '0 '0 (C4 0~ ( O. CO ~ ( 00 CO N- LA C'-T

vN (N mA -T -_ LA" LA LA L A '0i ' ' ' 'D0 N- N- N-- c

7 C,'

-7 C* 4 -4 O C-- -T -I7

c 0m - r L \ c r

S- CL C

V 0 0 00 CA.? '- (N '.O C - CO 0D

L l% Ul%

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U' ~ 0O~

C.109

C)C4L\ -T -T0

C) (N LI)-f(NC ' ' Ua) UA Lr a) 0 -1c ' J, '-

CC) 0 U. . I .~ cc I' cc c) m) 'o N- a) C a C - NU' ~ CD L -- * - - - 0- u c c, L

0% a) C.0 4 -7 - U (N4 CD wC w) - l- m' CC -7 00 r-

(N i (N N (Nc ') C) '

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C) C) (N N- -- .0 IC'. CD '.0 '0 --T -_ -Z C') -, a) '0 N< - - U C - N N 04N ( "I (N i (N N (N! - - C)

- -- CN ~ (N -(N i (N 4 (N4 (N4 ( (N N C ' (N INj (N

I. C- OC-C C) C) n U) C Z) C)--C) C 0 a C) M) a)3 a) a) a) a)

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(N 0. c)1) L) C ~ C) ( C! C D - c- (N I) 0 CD N

C) 0 0 CD CD CD CD CD I C ) C 0 C, C ) CD

a) 0.C cc M C-TOs - )M C

0.< - - - --- - - - - - - - - - - - - C1

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(u) LIT '. No - _ ;) C). m (N C') 00 LI) CN4(a !C

U. - - - - - - - - - -- n - -.: -Z 0

Cr

-u 0 -n 'D LI) CD-~ a -1, %0 N- C) r- a) Lr) C) I' . a) ,\)L :r w (NN U) a) a) C) (N\ U) aa.,N ) ( ) O C ) )

-T -o 0 - 0-\ 0' 00 M ~ -~ E

C, ~ C . - - . 0 1 ) 0 ' CM N-2 a). '\ m~ -A -0 (N

x~ ~ 0 N C) L) N 00 a)\ ( - - C) (N U) \ '.0 C\ C) C -

< ' - r C CD) LI C ( 00 -n 00 (N \ '. \ 00 00 C) (N C') 0 )

v 0 - r

(N ~ C -.IN ( U - C A (N '.0 C m. - 0 C) ) a) c') C) (N'D 0 (n - ( (N ( ) ' . - -L - -I LI . - - .

m ' ,\0 ' 0 C C) 0 N- cI C) a) LI C) ) 0- CO ) C' - LI C' LI N-u C ) N- C) C )> -(D c: C c LICD - 0 ) )C a C U-\ '0 a)

x 0 C4 :t ,0 l C M(N- (N4 Cf') C') Cc ') C') ') C') 0 ) 0 (N m

110

IMPERFECT0N MEASUREMETS

x 10-3 in)

BCP 9817-B-6-1 DF BCP 9824-A-1-2 DF

+19 k12 +6 1+3 0 0 0 0 -0 -10 -12 -16 -11 1 11 -3 -3 0

+12 +6 -2 -7 -9 -6 -6 -3 -9 -15 -16 -20 ,-13 -9 -12 -12 -1 +7+10 +4 -5 1JO -12 -9 -6 +2 +3 -14 -15 -16 -12 -11 -9 -8 O+13

+ 12 + 6 -I -6 -II -6 -2 - +12 + 2 1 -9 - 10 - 1 1 -8 -7 -6 - + 7 + 17+ + 7 1 0 -3 - 7 -5 + 3 + 18 + 3 1 + 1 + 1 - 3 -2 0 + 3 + 4 i+ I4 + 29

+5+2 -3 -4 -9 -5 +3 +19 +31 1+-11 +5 -1 +21 +4 1+3 + r 1+17+30'

5

17+2+ 1, I : =

14 +9 +6 1+4 0 +2 +7 +16 +23 +17+12 +6 +11 +15 '+20 +28 +38

BCP 9824-A-1-I DF BCP 9817-B-6-2 OF

+71 0i +2 +5 0 - 2 +6 18 +19 +13 +10 +8 0 +2 +4 +i0 +15

+6 +3 +1 +3 +3 + +3 -4 +5 18 +16 +12 +8 +5 -4 -5 -1 +11 +22

+8 +5 +6 +7 +6 +2 +1 +8 +20 +15 +10 +6 +3 -7 -9 -5 +9 +24

+13 + I1 +10 +12 +9 +6 +8 15 +23 +18 +14 +9 +4 -5 -7 -21+12 +26

+19 +18 +14 +16 +16 '+15 +14 +22 +29 +17 +14 +9 +5 -4 -6 -I +13 +22

+24 +20 +18 20 +20 '+19 +21 28 +36 +14 .+1l +7 +2 -4 -8 +1 +10 +17

+30 +27 '2 5 k25 +29 +28 +32 +40 +50 +8 +8 +7 +5 +2 +7 +10 +1R +25

12. 566"

I9/161"TYP

2 11/32" TYP1'' 1LEVEL

T- 2

2 " T Y 1 4

16.o0" T 67

8_ I 9

This imperfection data is questionable. Imperfection measurinq device

was not mounted accurately enough.

111

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I.MPERFECTION MEASUREMENTS

(x ]o-3 in)

BCP 9921-A-7-1 BF BCP 9921-A-7-2 BF

+30i+27 +22 p14. 0 -7 -8 -3 1-6 +9 10 1+9 +5 0 -3 -6 1-8-10

+61 +45 +28 k15 -1 12 -12 +-4 -14 +21 +20 k15 +10 0 -10 -20 -29 -36

+8L +60 +36 11 13 +34 +25 k17 -4 1-1 6 -26 i-40 -57

+24 +2160 +10 + 4 - +. 4 03 - + -2 5~-- - -1 -6 ,+83 +60 +35 +14 -1 -8 -]1 -10 -10 +39 +30 +21 +11 -2 -14 -26 -48 -71

+63 +51 +31 +13 +2 -5 -5 -8 - +3 +33 ,+24 +12 -3 -161-26 _-43 -64- - I -25

+44 +36 +24 +12 +3 -2 -1 -2 -2 +33 +30 +22 +12 -2 1-12 -17 -38

+24 +21 ]+16 +10 +4 +3 + 0 +2 +21 i+19 +13 +7 -3 -3 -8 -11 -15

BCP 9817-B-7-1 BF BCP 9817-B-7-2 BF

+6 1+ +3 +2 0 -2 3 - - 1 +1+4

+12 +8 +3 +2 - 1 -5 -8 10-1 6 1-.16 +12 1+5 -2 -6 -5 0 +5 J+2+13 +8 +3 0 -4 -8 -9 -12 -16 +20 +13 +8 0 -3 -4 0 +4 +1

+18 +12 +5 +1 -2 -6 -6 -7 -9 +23;+16 +6 +1l-3 -4 -1 +2

+13 + II +5 +1 -2 -5 -5 -5 -6 +20 +15 +7 +2 -3 -3 -3 -2 -9

+16 +5 j +2 0 -2 -4 -3 -3 -4 +19 +14 +10 +5 ' 0 -1 -2 -2 1-13

+4 +4 +3 +3 +2 0 +1 0 0 +14 +12 ,+10 +8 i +4 +3 +2 0 -9

8. 156"

1 1 /64'TY P

1 33/64" TYP

"£ I LEVEL

j A1 10 IIi _-2

2"TYP 4

6 OI ___

_6

7I __8

9

117

APPENDIX C

STRAIN, END-SHORTENING, AND IMPERFECTION MEASUREMENTSFOR TEST PANELS FOR TESTING PROGRAM B

118

is. 5CQi

.I

I II I

3 4.i 7 F I ~~

. - - 3

1 6 4L

FIGURE Locations for strain and imperfection measurements for 16- x I?panels with [0/9012s fiber pattern and unsupport-d straiohtedcnes. For 16 x 12 panels with [0/+45/90]s fiber pattern and

j simply-supported straight edges only the axial strains at thethree interior locations were recorded, and the imperfect datawere recorded for the seven interior imperfection grid lines.

a (Circumferential dimensions shown correspond to the panelswith unsupported straight edges. Subtract one inch for simply-supported panels.)

119

Imperfection measurements (xlO'3 in) for l6x12 panels with fiber pattern[O/+45/90] s and simply-supported straight edges (curved edges clamped).

Collapse load in parentheses.rounded edges

DS-A9-l (4600 lb) freely DS-A9-2 (4975 Ib) 30 in-lb on side bars

31 8 8 6 8 6 2 6 3 3 2 8 6 3

-2 7 7 3 4 7 0 5 4 4 3 5 8 7

-2 7 7 3 4 5 -1 8 4 3 3 4 9 6-2 4 4 3 1 3 -3 8 2 3 2 3 7 6

-4 2 2 -1 -2 1 -2 4 -2 -2 -l -l 6 3

0 2 1 -1 -2 I -2 5 -1 2 2 1

1 1 0 -l -2 -1 0 1 1 3 4 3 6 3

DS-A1O-I (5775 Ib) 10 in-lb DS-A1O-2 (5510 ib) 30 in-lb on side bars

0 4 5 4 7 7 6 19 13 6 5 8 12 9

-4 2 4 4 6 6 9 33 22 5 2 7 12 10

-7 0 7 7 6 7 9 33 28 2 -2 4 15 18

-10 -2 3 4 4 4 7 30 31 1 -4 2 18 22

-12 -5 2 0 0 3 3 30 24 01-10 -3 16 17

-12 -4 1 1 1 1 0 0 21 -1 -7 -4 10 13

-6 -2 0 -I 2 0 -l 19 1 i-2 -4 -I 6 8

DA-AII-1 (5160 Ib) nearly freely

-61 -7 -3 0 0 -6 -2

-10 -6 0 5 -1 -8 -8

-7 -4 7 10 4 -6 -7

-6 -7 6 10 3 -8 -12

-40.-- -I 5 I -9 -13-6 -7 2 4 0 -7 -8

-6 -4 -2 0 o -4 1 -7

120

Imperfection measurements (xlO-3 in) for 16-12 panels with fiber pattern

[0/901, and unsupported straight edges (curved edges clamped). Collapseload in parentheses.

DS-BII-I (2460 lb) DS-Bll-2 (2715 lb)

8 8 3 8 9 11 10 11 16 9 6 5' 8 6 7 7 8 13

I 1 1012 9 9 9 4 3 6 8 9 7 6 10 1391 61 6 61 8 8 6 6 5 -2 2 7' 7 9 8 6 10O 12

51~ l0 2 4 3 4-8 -2 4 i 7 .7 I 6 5 81 HI

0 2 1 2 3 4 1 6 1 0 -1 2 -7 3 6 5 3 .. 2 5 9-7 -2 -l -2 -2 - 1 -3 l 1 6 1 -10-:O 2 1 1 - 1 5 9

-7 -3 - -3 -3 -3 -3 70 3 1 6

DS-BIO-I (2300 ib) DS-BO-2 (2495 lb)

8 3 1 0 4 8 13 12 13 16 12 7 5 7 7 9 13 21 33

11 5 1 3 9 14 12 9 11 23 14 10 12 11 13 17 38 33

13 6 4 6 10 18 14 9 8 16 9 5 6 6 8 13 21 31

5 -I -1 0 5 11 8 2. 0 If 7 5 6 4 8 11 16 23

4 0 -1 0 4 10 7 0 -2 8 1 3 2 1 4 5 7 10

4 0 -2 -1 3 7 6 0 -4 3 2 1 2 2 4 4 3 5

4 2-I _ 1 6 4 1-1 2 2 1 2 2 3 2 1 4

DS-B9-I (2165 Ib) DS-B9-2 (2410 Tb)

-6 -2 3 5 5 10 13 14 23 -4 -2 -2 2 4 8 i0 16 23

1 3 6 8 7 13 15 11 11 -1 -1 2 4 7 10 10 16 29

5 3 3 8 10 14 16 1O 8 -1 0 2 3 7 12 11 14 23

7 2 1 6 5 9 12 6 2 -1 -2 2 2 5 9 8 12 18

8 2 -1 3 2 6 6 0 -1 2 1 1 2 3 8 8 10 14

13 4 1 5 6 6 7 4 3 4 3 3 3 3 9 7 12

8 3 1 3 3 3 6 3 3 3 1 1 1 1 3 44

121

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L-Eiwwm-

APPENDIX D

USER'S MANUAL FOR COMPUTER PROGRAM~ CLAPP

133

. TCLAPP USERS MANUAL

1. TITLE CARD (18A4)

Columns 1-72 Problem description

2. CONTROL CARD (815)

Columns 1-5 IRUN - Takes integer values 1, 2, 3,according as the completion of an

analysis requires 1, 2, 3,submissions of the program.IRUN = 1 for the first submission,IRUN = 2 for the second submission,

and so forth. Valid for nonlinearanalysis only (IBIF = 0). IRUN

#ifor any analysis that is a con-tinuation of a previous application

of CLAPP.

6-l0 IEX = 0 perfect panel or plate

imperfect panel or plate

]1-)5 IBIF = fO nonlinear analysis

1I linear bifurcation analysis

0 flat plate analysis16-20 NFLAT = f

curved panel analysis

0 x and y coordinates must bepunched for input. Variablegrid capabilities.

21-25 NAUTO=11 Automatic generation of x and

y coordinates with uniform, butpossibly different, spacingsfor the x and y directions.

0 Initial imperfections are repre-

sented by a mathematicalexpression.

26-30 LGRNG =I Initial imperfections are repre-

sented by a two-dimensional

Lagrange interpolatinq function.

134

f0 When the load-deflection curveis generated in seqments thetape NTAPE contains the infor-mation required by the programto continue the calculations

beginning with the last load-level for which a convergedsolution was obtained. To con-

tinue calculations set INDEX =2, 3, ... and NUSTRT - 0.

31-35 NUSTRTI It may happen that it is desir-able to adjust the loadinqsequence to begin calculationsfor a second segment of the load-deflection curve. To do this setINDEX = 2, 3, ... , NUSTRT = I andreset the input data for PZSTRT,PXSTRT, PYSTRT, AND ZINCR, XINCR,YINCR.

36-4o NCURVE =0

3. CONVERGENCE CRITERION CARD (FIO.0, 215)

Columns 1-10 EPSI - Convergence criterion that determinesiacceptable displacements at a given

load-level (order of 10-").

11-15 ITMAX - Program terminates if converqence atany load-level has not occurred

within ITMAX iterations.

16-20 LEMAX - Program terminates after processinqLEMAX load-levels as collapse orbifurcation has not occurred.Resubmit program with IRUN = 2.

4. GRID PARAMETERS CARD (815)

I Finite-difference grid pointsnumbered consecutively along across-sectional circle

Columns 1-5 NSCHM =0 Finite-difference grid points

numbered consecutively along agenerator

135

O Panel has no cutout6-10 ICTOUT

I Panel has a cutout

11-15 NCOLS - Number of columns of grid points.

16-20 NROWS - Number of rows of grid points.

21-25 IROWI - Number of the row in which theside of the cutout nearest thefirst row of grid points lies.

26-30 IROW2 - Number of the row in which theside of the cutout furtherestfrom the first row of grid pointslies.

31-35 ICOLI - Number of the column in which the

side of the cutout nearest thefirst column of grid points lies.

36-40 ICOL2 - Number of the column in which the

side of the cutout furtherestfrom the first column of grid

points lies.

___________ NCOLS

ICOLI ICOL21_ 2 3 4 0 11 12

- ~ I If I

IROW IFOR NUMBERING OF NODESALONG A GENERATOR

NROWS CUTOUT NSCHMOI

IROW 2

136

NROWS

IROWI IROW2

I I FOR NUMBERING OF NODES

2 1 ALONG A CROSS SECTIONALI CIRCLE NSCHM=I

3ICOLI L -

NCOLS CUTOUT

ICOL2 -

11

NOTE: Node numbering must originate at the upper left-hand corner of the

finite-difference grid.

5. PANEL DIMENSIONS CARD (3FIO.O)

Columns 1-10 XDIM - Lenqth of a panel parallel toa generator.

11-20 YDIM - Length of a panel along a crosssectional circle (not the pro-jection).

21-30 R - Panel radius of curvature. (Anynumber will suffice for a plate.

6. BOUNDARY CONDITION IDENTIFIER CARD (815)

Columns 1-5 NCASE1 1

6-10 NCASE2( 2

11-15 NCASE3

16-20 NCASE4 = .3

21-25 NCASE5

26-30 NCASE6 -

31-35 NCASE7

36-40 NCASE8 5

137

NCASE_ identifies a boundary of the panel as indicated in the accompanyingfigure. An integer from I to 5 is assigned to each NCASE accordinq as thedesired support condition along the edge identified by NCASE is one of thoseshown above.

NCASEI

z Direction of az M

z NCASE7 M A Generator

NCASE3

7. RIGID BODY CONDITION CARD (415)

Columns 1-5 IRBI 1 Tangential displacement parallelto the boundary identified by

6-10 IRB2 IRB is precluded at the mid-point of the boundary for an

11-15 IRB3 even number of grid points, orat the grid point nearest mid-

16-20 IRB4 point for an odd number of qridpoints.

0 No modifications to boundaryIRBI=I U=O L conditions are made.

IRB3=l, U=O 1

8. INITIAL-LOAD CARD (4F15.O,15)

Columns 1-15 PZSTRT - Initial-load normal to the panelsurface. (Positive away from thecenter of curvature.)

16-30 PXSTRT - Initial-load parallel to a genera-

tor of the panel. (Positive inthe direction of increasing gridpoint numbers.)

31-45 PYSTRT - Initial-load tangent to a cross-sectional circle. (Positive in

the direction of increasing qridpoint numbers.

138

46-6o XDISPO - Prescribed initial axial end-displacement. Negative for com-pression.

[0 Prescribed loads61-65 MDISP

I Prescribed end-displacements

23 4 1 12 2334

12 2

23 334 PXSTRT 4

PXSTRT

POSITIVE DIRECTIONS FOR PXSTRT POSITIVE DIRECTIONS FOR PXSTRTAND PYSTRT FOR NSCHM=O AND PYSTRT FOR NSCHM=I.

9. LOAD IDENTIFICATION CARD (415)

1 Concentrated load at grid

point number LNODE.

2 Line-load along row number LROWof the finite-difference grid.

Columns 1-5 LCASE3 Line-load along column number

LCOL of the finite-differencegrid.

4 Uniform distributed load overthe entire surface.

6-10 LNODE - Number of the finite-differencegrid-point at which a concentratedload is applied.

11-15 LROW - Number of the row of finite-difference grid points along whicha line-load is applied.

16-20 LCOL - Number of the column of finite-difference grid points along whicha line-load is applied.

139

10. LOAD INCREMENT CARD (3FIO.O)

Columns 1-10 ZINCR - Load increment normal to the panelsurface.

11-20 XINCR - Load increment parallel to agenerator of the panel.

21-30 YINCR - Load increment tangent to a cross-

sectional circle of the panel.

Positive directions for load-increments are the same as those for the initialloads.

If IEX # 1 cards 11, 12, and 13 are not required.

11. INITIAL IMPERFECTION CARD (5FI0.0,15) Required only if LGRNG = 0 and IEX =I

Columns 1-10 WO - Amplitude of initial geometricimperfection.

11-20 CONSi - Wave number of the imperfection

associated with the direction ofa generator of a panel (n/halflength of panel)

O Clamped curved edges and unsup-

ported straiqht edges.21-30 CONS2 =

b Clamped curved edges and simply-

supported straight edges. b isone half of the circumferentiallength of a panel

31-40 XO - x-coordinate of geometric center

of panel measured from lower lefthand corner

41-50 YO - y-coordinator of geometric center

of the panel measured from thelower left hand corner

Initial imperfection has the formWO(x,y) - Wl*(l+cos 7r/a)(l-(r/b) 2 )(Clamped at curved edges - simply-supported along the straight edges)

51-60 IMPFORM =

Initial imperfection has the formWO(x) = WI*(I+cos 'n/a)(Clamped along the curved edgesfree at the straight edoes)

140

12. IMPERFECTION-GRID PARAMETER CARD (215) Required only if LGRNG = 1 and IEX 1

Columns 1-5 MX = Number of grid points alonq agenerator for which discrete valuesof initial imperfection are known.

Spacing of these points is requiredto be uniform.

6-10 MY = Number of grid points along a crosssectional circle for which discretevalues of initial imperfection areknown. Spacing of these points isrequired to be uniform.

MX or MY can not exceed 10 for the present dimensions of the program.

13. IMPERFECTION DATA CARD (1OF8.0) Required only if LGRNG = 1 and IEX = 1

A single card contains the known discrete value of initial imperfectionfor every grid point in a row of the imperfection-grid. Thus, MY cardsare required: one for each row of the imperfection-grid. A row isconsidered to be parallel to a generator of the panel. Imperfectionvalues are positive away from the center of curvature of the panel.

Imperfection-grid size cannot exceed 10 grid points in either directionunless internal dimensions are modified.

Imperfection-grid is parallel to finite-difference grid with origin assholen in the figure.

Direction of a

Third Card, Etc. * Generator

Second Card Row 2 . . . .

First Card Row 1 = - - 0 _

14. NODAL COORDINATE CARD (2FIO.O) Required only if NAUTO = 0

Columns 1-10 x-coordinate of a finite-difference gridpoint

11-20 y-coordinate of a finite-difference gridpoint

These cards are required only when NAUTO = 0; i.e., whenever a variablefinite-difference grid is required.

141

15. STIFFENER CARD (415)Fo no stiffeners

Columns 1-5 NSTFR I stiffeners included

6-10 NSTYP throuh 8 - cross section type(see below)

L

11-15 NSLOC = 0 located on outside of panel (+)I located on inside of panel

16-20 ISSPC =o spaced on all qrid linest1 variable spacing

16. STIFFENER CROSS SECTION INPUT CARDS only if NSTFR = I

The number and required input of these cards depend on the choice of

stiffener cross section type (NSTYP) above.

NSTYP = I (2FIO.O) (2F1O.O) rectangular plate

(1) Columns 1-10 HGHT = h11-20 WDTH = b

(2) Columns 1-10 SEMOD = elastic modulus11-20 SGMOD = shear modulus

NSTYP = 2 (4F1O.O) (2Fl0.O) symmetric I beam

(1) Columns 1-10 HGHT = h (total - tf) t I11-20 WDTI= b21-30 FLTHK = tf L

31-40 WTHK = tw

(2) Columns 1-10 SEMOD = elastic modulusi1-20 SGMOD = shear modulus

NSTYP = 3 (5F1O.O) (2FIO.O) non-symmetric I beam

(1) Columns 1-10 HGHT = h (total - tf)11-20 TWDTH = bi2 1-30 BWDTH = b231-40 FLTHK = tf r

41-50 WTHK = tw

(2) Columns 1-10 SEMOD = elastic modulus11-20 SGMOD = shear modulus

142

NSTYP = 4 ('Ff10.0) (2F10.0) inverted T f w

(1) Columns 1-10 HGHT = h (total - tf12)11-20 WDTH = bf

21-30 FLTHK -tf

31-40 WTHK =tw

(2) Columns 1-10 SEMOD =elastic modulus .

11-20 SGMOD shear modulus

NSTYP =5 (4F10.0) (2F10.0) T -beam- -

(1) Columns 1-10 HGHT = h (total - t f/2)11-20 WDTH = b21-30 FLTHK = tf31-40 WTHK = t

(2) Columns 1-10 SEMOD - elastic modulus '~11-20 SGMOD - shear modulus

NSTYP =6 (4Fl0.0) (21 10.0) C beam

(1) Columns 1-10 HGHT =h (total -tf i11-20 WDTH =b

2 1-30 FLTHK = tf L

31-40 WTHK = t .4

(2) Columns 1-10 SEMOD = elastic modulus

11-20 SGMOD = shear modulus

NSTYP = 7 (4F10.0) (21 10.0) L beam

(1) Columns 1-10 HGHT = h (total - tf/12) r11-20 14DTH = b21-30 FLTHK = tf31-40 WTHK = tw 4

(2) Columns 1-10 SEMOD = elastic modulus11-20 SGMOD = shear modulus

NSTYP = 8 (4F10.o) (5F10.0) (2F]0.0) user's choice 4

(1) Columns 1-10 SAREA = cross section area11-20 CEI = 1st principal moment of inertia, Ivv21-30 ETAI = 2nd principal moment of inertia, LM?31-40 ALPHA = angle from hori7ontal to §g-direction.

in radians

(2) Columns 1-1 CED = distance to contact point, g-direct ion11-20 ETAD = distance to contact point, I-direct ion21-30 CES = distance to shear center, 5-direct ion31-40 ETAS = distance to shear center, T-direct ion41-50 CONSTJ = twist inq constant, J

143

(3) Columns 1-)0 SEMOD - elastic modulus11-20 SGMOD - shear modulus

Refer to figure on the next page for an example of these quantities

for the user's choice stiffener, type 8.

NSTYP = 9 (4FlO.O,15)(5FO.O) QUASI-ISOTROPIC HAT SECTION

(1) Columns 1 - 10 HGHT = h

11 -20 WDTH= b

21 - 30 FLNGW = b

31 - 40 STHK = t- - - - - - - - .

41 - 45 NLAYER = No. oflayers.

(2) Columns 1 - 10 Eli = elastic UNIFoRM scCr,*,V 7WrA'ClESS

modulus parallel to

the fibers of a lamina.

II - 20 E22 = elastic modulus

perpendicular to the

fibers of a lamina.

21 - 30 G12 = lamina shear modulus

31 - 40 PNUI2 = Poisson ratio associated

with stress along fiber direction.

41 - 50 PNU21 = Poisson ratio associated

with stress perpendicular to fiber

direction.

This stiffener cross section type accomodates fiber-reinforced

stiffeners where the fiber directions are alternately zero and 90

degrees. Midplane symmetry is assumed.

144

Note that the stiffeners when located on the inside of the panel areinverted as depicted below.

.4

It __

5T/~ 0,1 aJ 7WIE 5riFFeAAEk OX.J 7-I

ouTrIp oF PANEL j.7jPE o PYAIFL.

17. NUMBER OF STIFFENERS (15) needed only if ISSPC = 1, NSTFR I

rolumns 1-5 NST = number of stiffeners if they are

not on each qrid line

18. VARIABLE SPACING STIFFENER CARDS (15) only if ISSPC = 1, NSTFR = I

Columns 1-5 NSROW = row number that locates stiffener(if NSCHM = 0)column number that locates stiffener(if NSCHM = 1)

One card is required for each stiffener, so there will be the samenumber of cards as NST above. The row (or column) numbers must be inincreasing order, i.e., 1,4,7,10, etc. not 1,7,4,10.

19. NUMBER OF LAYERS CARD (15)

Columns 1-5 KN - Number of layers in the laminate.

20. LAYER LOCATION CARDS (Flo.o)

Columns 1-10 Distance (inches) b(tween a layer surface

nearest the center of curvature and thelaminate reference surface. First layer

is considered to be the one nearest thecenter of curvature. Distances measured

toward the center of curvature are negative.

A card for the most remote surface of the last layer is required. Thus,there is required KN+I LAYER LOCATION CARDS.

145

21. MATERIAL PROPERTIES CARDS (6FIO.O) One card is required for each layer.

Columns 1-10 Modulus of elasticity parallel to the

fibers of a given layer (lb/in 2 )

11-20 Modulus of elasticity perpendicular tothe fibers of a given layer (lb/in ? )

21-30 Poisson ratio associated with strainparallel to the fiber axis due to a stressperpendicular to the fiber axis

31-40 Poisson ratio associated with strain perpen-dicular to the fiber axis due to a stress

parallel to the fiber axis.

41-50 Shearing modulus of elasticity (lb/in 2 )

51-60 Angle between the fiber direction and a

generator of the panel. This angle ispositive whenever the fiber direction issituated in a clockwise orientation relative

to the positive x-direction.

146

EXAMPLE THAT DEFINES INPUT QUANTITIES

FOR USERS CHOICE STIFFENER

C -- CEAI-T'CO/ID

CD COqrACT POINT

BETWEEN PFqAtEL

C &AND SrIFFLEAJER

_ _ x -

AREAA

.X .-t- "."r, ,.L

I - I T

"!r( ± cr'(r7

C -,TD = i.-"p + L

ETADD. Pn O-

Er, 5E

147

*U.S.Governmeflt Printing Office: 1982 5-009O5/4055