August 2010 

NASA/TM-2010-216839 

Design of 8-ft-diameter Barrel 

Test Article Attachment Rings for 

Shell Buckling Knockdown Factor Project 

Andrew E. Lovejoy and Mark W. Hilburger 

Langley Research Center, Hampton, Virginia 
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August 2010 

NASA/TM-2010-216839 

Design of 8-ft-diameter Barrel 

Test Article Attachment Rings for 

Shell Buckling Knockdown Factor Project 

Andrew E. Lovejoy and Mark W. Hilburger 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

The use of trademarks or names of manufacturers in the report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
iii 

Preface 

The Shell Buckling Knockdown Factor Project (SBKF), NESC Assessment #: 07-010-E, was established 

in March of 2007 by the NASA Engineering and Safety Center (NESC) in collaboration with the NASA 

Constellation Program (CxP). The SBKF Project has the goal of developing and experimentally 

validating improved (i.e., less-conservative, more robust) shell buckling design factors (a.k.a. knockdown 

factors) and design technologies for launch vehicle structures. 

Preliminary design studies indicate that implementation of these new knockdown factors can enable 

significant weight savings in these vehicles and will help mitigate some of NASA’s future launch vehicle 

development and performance risks, e.g., reduced reliance on large-scale testing, high-fidelity estimates 

of as-built structural performance, increased payload capability, and improved structural reliability. 

To this end, a series of detailed Project Reports are being published to document all results from the 

SBKF Project and including design trade studies, test article and test facility design, analysis and test 

data, technology development white papers and state-of-the-art assessments, and finally shell design 

guidelines to update and/or augment the existing NASA SP series publications for the design of bucklingcritical thin-walled shell structures. A select group of significant results, in whole or in part, will be 

published as NASA Technical Memorandums (TM). 

Any documents, that are published as a part of this series, that refer to or report specific designs or design, 

analysis, and testing methodologies are to be regarded as guidelines and not as NASA requirements or 

criteria, except as specified in formal project specifications. 

Comments concerning the technical content of this NASA TM are welcomed. 

The following Project Report was used to create this TM: 

SBKF-P2-TR-2008-007 
iv

Table of Contents 

Nomenclature ............................................................................................................................................. viii

1.0 Introduction .............................................................................................................................. 1

2.0 Summary of Results ................................................................................................................. 1

3.0 Physical Description of Test Setup/Test Assembly ................................................................. 1

4.0 Design/Test Requirements and Criteria ................................................................................... 2

4.1 Structural Design .......................................................................................................................... 2

4.2 Factors of Safety and Knockdown Factors ................................................................................... 5

4.3 Margin Calculations ...................................................................................................................... 5

4.4 Material Properties ........................................................................................................................ 6

4.5 Loads ............................................................................................................................................. 6

5.0 Approach .................................................................................................................................. 6

5.1 Purpose .......................................................................................................................................... 6

5.2 Assumptions .................................................................................................................................. 7

5.3 Rationale ....................................................................................................................................... 8

6.0 Results ...................................................................................................................................... 8

6.1 Bolt Patterns .................................................................................................................................. 8

6.2 Multiple-Piece Designs ................................................................................................................. 9

6.3 Single-Piece Design .................................................................................................................... 22

7.0 Conclusions ............................................................................................................................ 27

8.0 References .............................................................................................................................. 28

Appendix A: Closed-Form Solution Spreadsheet Description .................................................................. 29

Appendix B: Bolt Pattern Design FEM ..................................................................................................... 32

B-1 Two-Row, In-Line ................................................................................................................. 32

B-2 Two-Row, Staggered ............................................................................................................. 33

B-3 Two-Row, Staggered, Gapped ............................................................................................... 34

Appendix C: Multiple-Piece Design FEM ................................................................................................. 35

C-1 Design MP-1 .......................................................................................................................... 35

C-2 Design MP-2 .......................................................................................................................... 37

C-3 Design MP-3 .......................................................................................................................... 55

Appendix D: Single-Piece Design FEM .................................................................................................... 56
v

List of Figures 

Figure 3.1. SBKF sub-scale cylinder test assembly. .................................................................................... 2

Figure 4.1. Initial two-piece attachment ring design concept (MP-1). ........................................................ 3

Figure 4.2. Two-piece attachment ring design concept with outer band (MP-2). ........................................ 3

Figure 4.3. Three-piece attachment ring design concept (MP-3). ................................................................ 4

Figure 4.4. Single-piece attachment ring design concept (SP-1). ................................................................ 4

Figure 5.1. Sketch depicting clamped boundary for finite element analyses (MP-1). ................................. 8

Figure 6.1. Two-row bolt patterns investigated. .......................................................................................... 9

Figure 6.2. MP-1 design cross-section definition (not drawn to scale). ..................................................... 10

Figure 6.3. MP-1 design inner and outer ring locations. ............................................................................ 11

Figure 6.4. MP-1 design circumferential bolt spacing. .............................................................................. 11

Figure 6.5. MP-2 Design cross-section definition (not drawn to scale). .................................................... 15

Figure 6.6. Typical MP-2 buckling mode, shown for tw,L = tw,B = 0.5 inch. ............................................... 16

Figure 6.7. Local solid model MP-2 design cross-section deformation at Nx = 5,050 lb/in (magnification 

factor of 5). ............................................................................................................................. 17

Figure 6.8. Local solid model MP-2 design, L-shaped ring vonMises stresses at Nx = 5,050 lb/in. .......... 18

Figure 6.9. Local solid model MP-2 design, band vonMises stresses at Nx = 5,050 lb/in. ........................ 19

Figure 6.10. MP-2 design cross-section definition (not drawn to scale). ................................................... 21

Figure 6.11. SP-1 design cross-section definition (not drawn to scale). .................................................... 27

Figure A.1. Example spreadsheet for bolted joint in tension. .................................................................... 29

Figure A.2. Example spreadsheet for bolted joint in single shear. ............................................................ 30

Figure A.3. Example spreadsheet for bolted joint in double shear. ........................................................... 31

Figure B.1. Two-row, in-line bolt pattern FEM (compression case). ........................................................ 32

Figure B.2. Two-row, staggered bolt pattern FEM (compression case). ................................................... 33

Figure B.3. Two-row, staggered, gapped bolt pattern FEM (compression case). ...................................... 34

Figure C.1. MP-1 FEM. ............................................................................................................................. 35

Figure C.2. MP-1 FEM isometric view. ..................................................................................................... 36

Figure C.3. MP-1 FEM applied load.......................................................................................................... 37

Figure C.4. MP-2 FEM to examine thickness of L-bracket web and band. ............................................... 38

Figure C.5. Close-up of MP-2 FEM to determine required thickness of L-bracket web and band. .......... 39

Figure C.6. Use of dummy ply to remove offsets. ..................................................................................... 40

Figure C.7. Nonlinear deformation for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch (contours 

indicate radial displacement). ................................................................................................. 41

Figure C.8. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article weld 

land inner surface. .................................................................................................................. 42

Figure C.9. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article weld 

land outer surface. .................................................................................................................. 43

Figure C.10. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article skin 

inner surface. .......................................................................................................................... 44

Figure C.11. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article skin 

outer surface. .......................................................................................................................... 45

Figure C.12. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article 

stringer Z1 ("bottom" of element) surface. ............................................................................. 46

Figure C.13. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article 

stringer Z2 ("bottom" of element) surface. ............................................................................. 47

Figure C.14. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article Lshaped ring web inner surface. ............................................................................................... 48

Figure C.15. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article Lshaped ring web outer surface. ............................................................................................... 49
vi

Figure C.16. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article band 

inner surface. .......................................................................................................................... 50

Figure C.17. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, test article band 

outer surface. .......................................................................................................................... 51

Figure C.18. Local MP-2 FEM to examine contact response of L-bracket web and band. ....................... 52

Figure C.19. Locations of bolts (black) in local MP-2 FEM. .................................................................... 53

Figure C.20. Contact surface locations for local MP-2 FEM. ................................................................... 54

Figure C.21. Attachment ring modeled in MP-3 shell FEM. ..................................................................... 55

Figure D.1. SP-1 ABAQUSTM shell FEM. ................................................................................................ 57

Figure D.2. SP-1 ABAQUSTM shell FEM, laminated end. ........................................................................ 58

Figure D.3. SP-1 ABAQUSTM shell FEM, bolted end. .............................................................................. 59

Figure D.4. SP-1 ABAQUSTM shell FEM attachment bolt beams (shown in black). ................................ 60

Figure D.5. SP-1 nonlinear deformed shape, LC1 at 2220 lb/in, AISI 1025 steel attachment rings 

(deformations magnified x50). ............................................................................................... 61

Figure D.6. SP-1 nonlinear deformed shape with radial deflection contours, LC1 at 2220 lb/in, AISI 

1025 steel attachment rings (deformations magnified x50). .................................................. 62

Figure D.7. SP-1 vonMises stress (psi) in inner flange inner surface at laminated end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. .......................................................................................... 63

Figure D.8. SP-1 vonMises stress (psi) in inner flange outer surface at laminated end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. .......................................................................................... 64

Figure D.9. SP-1 vonMises stress (psi) in inner flange inner surface at bolted end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. .......................................................................................... 65

Figure D.10. SP-1 vonMises stress (psi) in inner flange outer surface at bolted end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. .......................................................................................... 66

Figure D.11. SP-1 vonMises stress (psi) in outer flange inner surface at laminated end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. .......................................................................................... 67

Figure D.12. SP-1 vonMises stress (psi) in outer flange outer surface at laminated end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. .......................................................................................... 68

Figure D.13. SP-1 vonMises stress (psi) in outer flange inner surface at bolted end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. .......................................................................................... 69

Figure D.14. SP-1 vonMises stress (psi) in outer flange outer surface at bolted end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. .......................................................................................... 70

Figure D.15. SP-1 vonMises stress (psi) in weld land inner surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. .................................................................................................................... 71

Figure D.16. SP-1 vonMises stress (psi) in weld land outer surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. .................................................................................................................... 72

Figure D.17. SP-1 vonMises stress (psi) in acreage skin inner surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. .................................................................................................................... 73

Figure D.18. SP-1 vonMises stress (psi) in acreage skin outer surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. .................................................................................................................... 74

Figure D.19. SP-1 vonMises stress (psi) in intermediate skin inner surface, LC1 at 2220 lb/in, AISI 1025 

steel attachment rings. ............................................................................................................ 75

Figure D.20. SP-1 vonMises stress (psi) in intermediate skin outer surface, LC1 at 2220 lb/in, AISI 1025 

steel attachment rings. ............................................................................................................ 76

Figure D.21. SP-1 vonMises stress (psi) in ring inner surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. .................................................................................................................... 77

Figure D.22. SP-1 vonMises stress (psi) in ring outer surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. .................................................................................................................... 78

Figure D.23. SP-1 vonMises stress (psi) in stringer inner surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. .................................................................................................................... 79
vii

Figure D.24. SP-1 vonMises stress (psi) in stringer skin outer surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. .................................................................................................................... 80

Figure D.25. SP-1 nonlinear contact region deformation at weld land, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings (deformations magnified x50). ................................................................... 81

Figure D.26. SP-1 nonlinear contact region deformation at acreage (center of panel), LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings (deformations magnified x50). ......................................... 82

List of Tables 

Table 4.1. Attachment ring material properties. .......................................................................................... 6

Table 6.1. Bolt load distribution between bolt rows in two-row patterns. ................................................... 9

Table 6.2. MS for MP-1 attachment ring design. ....................................................................................... 10

Table 6.3. Critical LC1 linear buckling loads for design MP-2, various attachment ring designs. ........... 13

Table 6.4. Nonlinear LC1 instability loads for design MP-2, various attachment ring designs. ............... 13

Table 6.5. Maximum LC1 nonlinear vonmises stresses for design MP-2, various attachment ring designs.

 ................................................................................................................................................ 13

Table 6.6. MS for MP-2 attachment ring design, load case LC1. .............................................................. 14

Table 6.7. MS for MP-2 attachment ring design, load case LC2 ............................................................... 14

Table 6.8. MS for MP-3 attachment ring design, load case LC1. .............................................................. 20

Table 6.9. MS for MP-3 Attachment Ring Design, Load Case LC2 ......................................................... 20

Table 6.10. Response summary for SP-1 AISI 1025 steel attachment ring design. ................................... 23

Table 6.11. Response summary for SP-1 7075-T651 aluminum attachment ring design. ......................... 23

Table 6.12. MS for SP-1 AISI 1025 steel attachment ring design, LC1 scaled to 5050 lb/in. ................... 24

Table 6.13. MS for SP-1 7075-T651 aluminum attachment ring design, LC1 scaled to 5050 lb/in. ......... 24

Table 6.14. MS for SP-1 AISI 1025 steel attachment ring design, load case LC2. ................................... 25

Table 6.15. MS for SP-1 7075-T651 aluminum attachment ring design, load case LC2. ......................... 25

Table 6.16. MS for SP-1 AISI 1025 steel attachment ring design, load case LC3. ................................... 26

Table 6.17. MS for SP-1 7075-T651 aluminum attachment ring design, load case LC3. ......................... 26
viii

Nomenclature 

Acronyms 

AISC American Institute of Steel Construction 

AISI American Iron and Steel Institute 

Al Aluminum 

Al-Li Aluminum Lithium 

ASTM American Society for Testing and Materials 

FEA Finite Element Analysis 

FEM Finite Element Model 

FS Factor of Safety 

IU Instrument Unit 

ksi Thousand Pounds Per Square Inch 

LC1 Load Case #1 

LC2 Load Case #2 

LC3 Load Case #3 

LH2 Liquid Hydrogen 

LOX Liquid Oxygen 

MP-1 Multiple-Piece Design #1 

MP-2 Multiple-Piece Design #2 

MP-3 Multiple-Piece Design #3 

MS Margin of Safety 

Msi Million Pounds Per Square Inch 

MSFC Marshall Space Flight Center 

OML Outer Mold Line 

psi Pounds Per Square Inch 

SAE Society of Automotive Engineers 

SBKF Shell Buckling Knockdown Factor 

SF Safety Factor 

SP-1 Single-Piece Design #1 

List of Symbols 

Abond Bonding area (in2

) 

E Elastic modulus (psi, Msi) 

I Moment of inertia (in4

) 

Nx Uniform stress resultant (lb/in) 

Nx,crit Critical uniform stress resultant (lb/in) 

Nx,unst Nonlinear analysis unstable uniform stress resultant (lb/in) 

Papplied Applied load (lb) 

Sy Allowable shear stress, yield (psi) 

tw,B Thickness of band (inch) 

tw,L Thickness of L-shaped section web (inch) 

Z1 Finite element inner surface location 

Z2 Finite element outer surface location 

 Poisson’s ratio 

allow Allowable stress (psi, ksi) 

bru Allowable bearing stress, ultimate (psi, ksi) 

bry Allowable bearing stress, yield (psi, ksi) 

calc Calculated stress (psi) 
ix

shear Calculated shear stress in the adhesive layer 

u Allowable stress, ultimate (psi, ksi) 

vonM vonMises stress (psi) 

y Allowable stress, yield (psi, ksi) 
Abstract 

The Shell Buckling Knockdown Factor (SBKF) project includes the 

testing of sub-scale cylinders to validate new shell buckling knockdown 

factors for use in the design of the Ares-I and Ares-V launch vehicles. 

Test article cylinders represent various barrel segments of the Ares-I and 

Ares-V vehicles, and also include checkout test articles. Testing will be 

conducted at Marshall Space Flight Center (MSFC) for test articles 

having an eight-foot diameter outer mold line (OML) and having lengths 

that range from three to ten feet long. Both ends of the test articles will 

be connected to the test apparatus using attachment rings. Three 

multiple-piece and one single-piece design for the attachment rings were 

developed and analyzed. The single-piece design was chosen and will be 

fabricated from either steel or aluminum (Al) depending on the required 

safety factors (SF) for test hardware. This report summarizes the design 

and analysis of these attachment ring concepts. 

1.0 Introduction 

The SBKF project includes the testing of sub-scale cylinders to validate new shell buckling knockdown 

factors for use in the design of the Ares-I and Ares-V launch vehicles. These sub-scale test articles 

represent various barrel segments of the Ares-I and Ares-V vehicles, and also include several checkout 

test articles. Testing will be conducted at MSFC on eight-foot diameter test articles having lengths that 

range from three to ten feet long. The test setup, described in detail in Section 3 and shown in Figure 3.1, 

and is designed to test articles of various length by using different length extension rods to attach the 

upper and lower portions of the test fixture at the load cell locations. The upper and lower portions of the 

test fixture are connected to the test article using attachment rings. These attachment rings act as the 

interface between the test article and the transition section sections of the test fixtures. This report 

summarizes the design and analysis of the test article attachment rings. 

2.0 Summary of Results 

Three multiple-piece and one single-piece attachment ring designs were developed and analyzed. While it 

is possible to use a multiple-piece design to satisfy strength requirements, manufacturing and assembly 

considerations lead to choosing the single-piece design. The single-piece design reported herein shows 

positive margins for the three design load cases examined. However, depending on SF requirements, the 

attachment ring will be fabricated from either American Institute of Steel Construction (AISI) 1025 steel 

or 7075-T651 Al. In particular, if a minimum SF = 3 for adhesive shear is required for the compression 

load case, then AISI 1025 steel is required for the current design. If a minimum SF = 2 is acceptable for 

the compression load case, then 7075-T651 Al can be used for the current design. 

3.0 Physical Description of Test Setup/Test Assembly 

Testing will be conducted at MSFC on sub-scale cylinder test articles. Test articles are representative of 

scaled Ares-I and Ares-V barrel segments such as the liquid oxygen (LOX) tank, liquid hydrogen (LH2) 

tank and instrument unit (IU). Additionally, there will be checkout articles that will be used to verify the 

test setup and process. The basic test setup comprises the test towers and the test assembly. The test 

assembly comprises the test article, attachment rings, transition sections, struts, spider beams and eight 

load lines. The load lines connect the upper and lower spider beams, and comprise load cylinder, load 

cell, extension rods, adapters and clevises. Test articles of various lengths (approximately 3 feet, 6 feet 

and 10 feet) can be accommodated by using different length extension rods. The test assembly portion of 

the test setup, with a typical six-foot-long test article, is shown in Figure 3.1. The load lines attach to the 
2

load spiders, which transfers load through the struts and transition sections into the test article. 

Attachment rings connect the test article to the upper and lower portions of the test fixture at the transition 

sections. The attachment rings that connect the test article to the transition sections are indicated in the 

figure, and are the focus of this design report. 

Figure 3.1. SBKF sub-scale cylinder test assembly. 

4.0 Design/Test Requirements and Criteria 

4.1 Structural Design 

Four different attachment ring designs were investigated. Several designs were multiple-piece designs. 

One design is a single-piece ring design with an integrally-machined grove into which the test article is 

inserted. Descriptions of these two designs are given in the following subsections. 

4.1.1 Multiple-Piece Designs 

Three multiple-piece designs (MP) were examined. The initial multiple-piece design comprises two Lshaped rings that are attached to the inside and outside of the test article as shown in Figure 4.1. 

Subsequently, the outer L-shaped ring was replaced by a band as shown in Figure 4.2. Lastly, an annular 

ring was added to the base of the L-shaped rings to form a three-piece attachment fixture as shown in 

Figure 4.3 to aid in assembly and alignment. The two-piece design of Figure 4.1 was designated MP-1, 

the two-piece design of Figure 4.2 was designated MP-2 and the three-piece design of Figure 4.3 was 

designated MP-3. Designs MP-1 and MP-2 were designed to have all load transfer from the transition 

structure through bearing on the L-rings, then transfer load to the test article through bearing at bolts 

through the rings and test article. That is, no bearing of the test article end against the transition structure 

was permitted. The locations of the bolts are not indicated in the cross-section sketches depicted in the 

figures because they are dependent upon the bolt pattern development described in Section 6.1 and the 
3

subsequent analyses. The MP-2 banded design was developed in an effort to reduce the manufacturing 

and installation complexity and cost. Design MP-3 was developed to assist in alignment of the parts, and 

to permit the test article to bear upon the annular ring, thus shifting the load transfer from bearing at bolts 

through the test article to bearing through the test article at the interface between the test article and the 

annular ring. 

Figure 4.1. Initial two-piece attachment ring design concept (MP-1). 

Figure 4.2. Two-piece attachment ring design concept with outer band (MP-2). 
4

Figure 4.3. Three-piece attachment ring design concept (MP-3). 

4.1.2 Single-Piece Design 

Based upon the analysis and design of MP-3, a single-piece (SP) was developed in order to simplify 

assembly, reduce part count, and decrease cost. The single-piece design essentially takes the MP-3 design 

and makes it a single piece by integrally-machining the attachment ring from a single piece of material. 

This single-piece design concept is shown in Figure 4.4 and is designated SP-1. This design utilizes an 

adhesive/potting material in the gap between the test article and the attachment ring as the primary 

attachment mechanism in order to reduce bolt count. A small number of attachment bolts (not shown) are 

retained from previous designs for fail-safe purposes in the event that the adhesive potting material fails 

during handling or testing.. 

Figure 4.4. Single-piece attachment ring design concept (SP-1). 
5

4.2 Factors of Safety and Knockdown Factors 

SFs were used in the design process. Knockdown factors were not used in the design process as they were 

not applicable to the design of the attachment rings. The SFs were applied to numerous failure modes and 

included limit (yield) stress, bolt shear, test article and attachment ring bearing, net tension failure, shear 

out and tensile tear out. For the multiple-piece design, the SFs applied to the design analyses were as 

follows: 

 Limit = 1 or 3 

 Bolt Shear = 1 

 Net Tension Failure = 1 

 Bearing, Test Article = 1 

 Bearing, Attachment Ring = 1 

 Bolt Tension = 1 

For the single-piece design, the SFs applied to the design analyses were the following: 

 Limit = 1 or 3 

 Bolt Shear = 1, 3 or 4 

 Net Tension Failure = 1, 3 or 4 

 Bearing, Test Article = 1, 3 or 4 

 Bearing, Attachment Ring = 1, 3 or 4 

 Bolt Tension = 1.5 

 Adhesive Shear = 3 or 4 

Multiple SFs were applied to some of the failure modes considered in the design analyses because it was 

uncertain what the required SFs were. Using multiple SFs provided the opportunity to evaluate the 

designs for SFs that were anticipated as potentially being required to meet imposed testing safety 

standards. 

4.3 Margin Calculations 

Margins of safety (MS) were calculated based upon allowable values or design requirements. Therefore, 

the generic form of the MS calculation equation is: 

  1 _

_   SF Calculated ValueSpecified Value MS

where SF represents the applicable SF. For example, a stress margin of safety calculation used the 

following equation: 

   1

calc

allow

SF

MS





where allow is the allowable stress (yield for limit and ultimate for ultimate), and calc is the calculated 

stress. The attachment rings are not permitted to yield, so ultimate stress failure was not examined for the 

attachment rings. 
6

4.4 Material Properties 

Test article designs utilized Al alloy aluminum lithium (Al-Li)-2195. The properties for Al-Li-2195 were 

initially provided by MSFC, and are also found in References 1 and 2. Room temperature values used in 

the design study were E = 11.0 Msi (L-direction),  = 0.33, y = 66 ksi (45°-direction) and u = 73 ksi 

(45°-direction), and are for stock with a thickness range of 1.5-1.85 inches. The weight density was 

provided as 0.098 lb/in3

 (Ref. 1). 

Attachment rings were designed and analyzed as being fabricated from either steel or Al. Two steel alloys 

were chosen, AISI 4130 and AISI 1025, and the chosen Al alloy was 7075-T651. The properties for these 

three materials are shown in Table 4.1 and were obtained from Reference 3. Bolts used for all attachments 

were assumed to be Society of Automotive Engineers (SAE) 5, American Society for Testing and 

Materials (ASTM) A325 (Type 1) with y = 92 ksi and u = 120 ksi as obtained from Reference 4. The 

adhesive/potting material selected was Hysol EA-9394 manufactured by Henkel. Properties for EA-9394 

were given as E = 0.59 Msi and  = 0.37 in Reference 5, and Sy = 4.2 ksi in Reference 6.

Table 4.1. Attachment ring material properties. 

Property AISI 4130 Steel AISI 1025 Steel 7075-T651 Al 

E (Msi) 29.0 29.0 10.3 

 0.32 0.32 0.33 

y (ksi) 70.0 36.0 56.0 

u (ksi) 90.0 55.0 66.0 

bry (ksi) (e/D = 2.0) 120. N/A 98.0 

bru (ksi) (e/D = 2.0) 190. 90.0 124. 

4.5 Loads 

Three load cases were used to design the attachment rings. The first load case (LC1) was a uniform 

running load of 5,050 lb/in, representing the maximum applied test load, which could be applied in either 

compression or tension. For designs MP-1 and MP-2, this was the only load case considered. The second 

load case (LC2) represents an assembly lifting load. The total weight to be lifted was assumed to be 

approximately 1160 lb. This weight comprises the test article and the complete attachment ring at one 

end, and represents the weight that is being lifted by the attachment ring at the opposite end. The resulting 

running load is Nx = 3.846 lb/in in this case. Using a 1-g acceleration during the lifting process with a 

factor of safety (FS) of 3, the design load becomes Nx = 11.54 lb/in for LC2. Lastly, a 10 psi internal 

pressure load case (LC3) was considered whereby pressure on the test assembly ends generates a tension 

load in the test article of Nx = 240 lb/in (Nx = 720 lb/in including FS = 3). Load cases LC2 and LC3 were 

included with LC1 for the analysis and sizing of designs MP-3 and SP-1. 

5.0 Approach 

The approach for designing the attachment rings used both closed-form and finite element solutions. First, 

closed-form solutions were used to provide the basic thicknesses of the attachment rings. Second, finite 

element analysis (FEA) was performed to verify the closed-form solutions and to examine detailed 

response not possible using the closed-form solutions. 

5.1 Purpose 

5.1.1 Closed-Form Solutions 

Close-form solutions were used for calculating the response of the connection between the attachment 

rings and the test article and transition section. Primarily, this encompassed calculations to determine the 

bolt spacing and diameters, and the thickness of the parts involved. The equations used for the 

calculations were found in Reference 7, and were used to calculate bolt load factor (bolt in tension), bolt 
7

shear, net tension failure, bearing (test article), bearing (attachment ring), shear out and tensile tear out. 

Shear out and tensile tear out are only important for situations where the bolt is close to the edge, so the 

designs developed were such that the distance from the bolt to the edge was at least two bolt diameters. 

Therefore, the shear out and tensile tear out calculations were not performed as they were deemed 

unnecessary. The closed-form, bolted-connection calculations were made by implementing the equations 

in Microsoft Excel workbooks, the details of which are presented in Appendix A. 

Additional closed-form calculations were used to examine the response of the adhesive potting layer 

subjected to the second and third load cases, assembly and internal pressure, respectively. For these two 

load cases, the bond area was calculated, and the associated stress was calculated using the total load for 

the load case. Mathematically, this is equivalent to: 

bond

applied

shear A

P

 

where shear is the calculated shear stress in the adhesive layer, Papplied is the applied total load, and Abond is 

the bond area. Note that the bond area accounts for adhesive on both the internal and external test article 

surfaces, i.e., there are two bonding surfaces at each test article/attachment ring interface. 

5.1.2 Finite Element Solutions 

FEA was used for two main purposes. First, FEAs were performed to determine the effect of bolt pattern 

on the bolt load sharing. Second, the overall performance of the test article/attachment ring combination 

was examined using FEA. FEAs were performed using the NASTRANTM (Ref. 8) or ABAQUSTM (Ref. 

9) finite element codes. 

5.2 Assumptions 

5.2.1 Closed-Form Solutions 

It was assumed that the thickness of the test article was 0.25 inch thick in the region where it interfaces 

with the attachment rings. Most assumptions related to the bolted connection calculations can be found in 

Reference 7 and are not repeated herein. Specific assumptions made about the bolt calculations for this 

report are described in Appendix A. It is important to recognize that the initial calculations assumed that 

the load was evenly distributed to all bolts in the pattern. In later calculations, that assumption was 

changed so that bolt load distribution was based on the FEA results for the bolt patterns as described in 

Section 6.1. The FEA led to the assumption that the load was distributed evenly among the bolts within 

each row. Finally, the assumption on the adhesive layer closed-form calculation was that the adhesive acts 

in shear, only. 

5.2.2 Finite Element Solutions 

It was assumed that the test article/attachment ring combination was clamped at the circumferential edges 

of the test article (see example in Figure 5.1 for design MP-1). This assumption requires that the transition 

section and attachment ring flange connection to the transition section be sufficiently stiff to approximate 

a clamped condition. It was determined that this boundary condition was sufficient for the design of the 

attachment ring and its components. Other assumptions were made for the various analyses and are 

described in the sections with their associated modeling descriptions and results. 
8

5.3 Rationale 

Both closed-form and finite element solutions were used to provide design data in the most efficient 

manner. The closed-form solutions were used to simplify analyses and provide design-level results in 

order to evaluate the designs. Finite element solutions were used where closed-form solutions were 

unavailable and where more detailed information was required. 

Figure 5.1. Sketch depicting clamped boundary for finite element analyses (MP-1). 

6.0 Results 

6.1 Bolt Patterns 

Based on experience with the design of other test fixtures, it was assumed that the MP-1 design would 

have two rows of bolts of equal diameter. The primary purpose of the bolt pattern analysis was to 

examine the load sharing by the bolts. Therefore, FEAs were used to determine the pattern that would 

provide the most even distribution of load between the bolts in the two rows. Three bolt patterns were 

examined and are shown in Figure 6.1. The patterns of Figure 6.1a and Figure 6.1b have the same number 

of bolts in the two rows, while the pattern of Figure 6.1c has half as many bolts in the row interior to the 

test article as it does at the article edge. The finite element models (FEM) used in the analyses and their 

descriptions are provided in Appendix B. The load distribution between the two rows for the three bolt 

patterns are shown in Table 6.1. It is evident that for the in-line and staggered bolt patterns, the interior 

row carries a significant portion of the load. With equal numbers of bolts in the two rows, this means that 

the individual bolt load on the interior row is over three times that of the edge row. Conversely, the two 

rows carry nearly equal load in the staggered and gapped bolt pattern, so the individual bolt load on the 

inner row is only about two times that of the edge row since the inner row has half the number of bolts. 

Therefore, the staggered and gapped bolt pattern was chosen because the individual bolt loads are closer 

between the edge and inner rows, resulting in more efficient load sharing. Sizing of the MP-1 design was 

then performed on this staggered and gapped bolt pattern. In order to be conservative, sizing used only the 

load carried by the inner row of bolts. In the later designs (MP-2, MP-3 and SP-1), only a single row of 

bolts was used so the bolt row load distribution analysis was not needed. 
9

Table 6.1. Bolt load distribution between bolt rows in two-row patterns. 

Bolt Pattern Edge Row, 

percent 

Interior Row, 

percent 

In-line 20.8 79.2 

Staggered 23.1 76.9 

Staggered, Gapped 48.4 51.6 

a) In-line b) Staggered c) Staggered, gapped 

Figure 6.1. Two-row bolt patterns investigated. 

6.2 Multiple-Piece Designs 

Details of the analyses and the results for each of the three multiple-piece designs are presented in the 

following three sub-sections. 

6.2.1 MP-1 

Multiple-piece design MP-1, shown in Figure 4.1, was assumed to be fabricated from AISI 4130 steel. 

The cross-section for the design MP-1 is shown in Figure 6.2, and this cross-section was used for both the 

inner and outer L-section rings for the design. The locations of the inner and outer L-section rings are 

shown in Figure 6.3. MS were calculated using both the closed-form solutions and FEA. Closed-form 

solutions were used for all MS calculated at the bolt locations including the bolts, test article and 

attachment rings. FEA was used to examine the stresses within the attachment ring L-section. Details of 

the FEM and analysis are provided in Appendix C. Lastly, the bolt spacing and locations were developed 
10

so as to satisfy the clearances needed for assembly by using the AISC stagger for impact wrench 

tightening requirement (Ref 10). The circumferential bolt spacing is shown in Figure 6.4. 

MS were calculated using only the LC1 load case and are summarized in Table 6.2. For this design, all SF 

= 1.0 in the MS calculations. The most critical margin was bearing yield in the test article with a value of 

MS = 0.4625. 

Table 6.2. MS for MP-1 attachment ring design. 

Description MS 

Bolt shear, yield, attachment ring to test article 1.464 

Bolt shear, ultimate, attachment ring to test article 2.213 

Net tension failure, yield, attachment ring to test article 1.292 

Net tension failure, ultimate, attachment ring to test article 1.535 

Bearing - test article, yield, attachment ring to test article 0.4625 

Bearing - test article, ultimate, attachment ring to test article 0.6176 

Bearing - rings, yield, attachment ring to test article 3.653 

Bearing - rings, yield, attachment ring to test article 4.983 

Bolt tension, attachment ring to transition section 1.283 

Attachment ring stress, yield 1.917 

Attachment ring stress, ultimate 2.750 

Figure 6.2. MP-1 design cross-section definition (not drawn to scale). 
11

Figure 6.3. MP-1 design inner and outer ring locations. 

Figure 6.4. MP-1 design circumferential bolt spacing. 
12

6.2.2 MP-2 

Multiple-piece design MP-2, shown in Figure 4.2, was assumed to be fabricated from AISI 1025 steel. 

The cross-sections for the L-shaped ring and band for the MP-2 design are shown in Figure 6.5, where the 

L-shaped ring is internal to the test article and the band is external. Both the L-shaped ring and band were 

assumed to be adhesively bonded to the test article using EA-9394, but include bolts through the test 

article connection as a fail-safe measure. The web thicknesses that attaches to the test article are given 

thicknesses defined by tw,L and tw,B. The values for tw,L and tw,B were set to be equal, and a design study 

was conducted where the values of these thicknesses ranged from 0.1 and 0.625 inch. The final thickness 

value was set to 0.25 inches. MS were calculated using both the closed-form solutions and FEA. Closedform solutions were used for all MS calculated at the bolt locations including the bolts, test article and 

attachment rings. FEA was used to examine overall buckling of the test article, and the nonlinear stresses 

in the test article, the L-shaped ring and the band. Details of the FEM and analysis are provided in 

Appendix C. Lastly, the bolt spacing and locations were based upon the MP-1 design. The bolts attaching 

to the transition structure remain the same as those for MP-1 shown in Figure 6.4. However, the row of 

bolts closest to the L-section elbow (2-degree arc spacing) has been removed while the 4-degree arc 

spacing bolts through the test article remain. 

A test article buckling analysis study was conducted using NASTRANTM and the shell FEM, which is 

described in Appendix C. The study was used to examine the effect of the attachment ring on the overall 

buckling of the test article. For buckling of the test section only, which is defined as the portion of the test 

article not connected to the two attachment rings, the fundamental buckling load was 2,272 lb/in. Table 

6.3 shows the buckling loads for various values of tw,L and tw,B, and Figure 6.6 shows a typical 

fundamental buckling mode for a design where tw,L and tw,B are equal to 0.5 inch. It was determined from 

this study the thickness of the L-shaped ring web and the band have little effect on the overall buckling 

load. Therefore, the buckling response did not appear to drive the attachment ring design. Nonlinear 

analysis was then performed using NASTRANTM, and the LC1 loads at which the nonlinear analysis 

became unstable for various values of tw,L and tw,B are shown in Table 6.4. All web thicknesses shown 

result in designs that become unstable for a load slightly higher than 2,300 lb/in, so Table 6.5 shows the 

maximum vonMises stress for the various components at a load of 2,300 lb/in. Since the attachment ring 

components appear to behave linearly (very small deformations in this region), the stresses in Table 6.5 

are scaled to a load of 5,050 lbs/inch (LC1 maximum expected load for all test articles) in the MS 

calculations for the attachment ring. Finally, a nonlinear analysis using ABAQUSTM and a local 24-degree 

arc section solid FEM described in Appendix C was used to examine the response if no adhesive was 

used between the attachment ring and test article, so that only the fail-safe bolts were attaching the 

components. ABAQUSTM was used to enforce contact relationships between the test article and 

attachment ring components. The nonlinear deformation from this analysis is seen in Figure 6.7 for 5,050 

lb/in uniform axial compressive load, and separation between the attachment ring and test article are 

clearly evident. Attachment ring vonMises stresses are shown in Figures 6.8 and 6.9 for the L-shaped ring 

and band, respectively. The maximum vonMises stress observed in the L-shaped ring was 44,700 lbs/in2

and in the band was 77,200 lb/in2

. These maximum values were concentrated in the region of the bolt 

locations, and were ignored due to the coarseness of the FEM at the bolt holes, and because the behavior 

in the vicinity of the bolt holes was determined using the closed-form solutions. The maximum values of 

vonMises stress used to calculate MS were taken to be body stresses removed from the bolt locations, and 

were 10,000 lb/in2

 and 22,000 lb/in2 for the L-shaped ring and band, respectively. 

MS were calculated using the LC1 and LC2 load cases and are summarized in Tables 6.6 and 6.7, 

respectively, for tw,L and tw,B a value of 0.5 inch is assigned. In the MS calculations, attachment ring 

stresses were scaled to a load of 5,050 lb/in for LC1. In the bolt MS calculations it was assumed that the 

inner L-shaped ring took all loads transferred from the test article as a fail-safe condition with no EA9394. Additionally, for this MP-2 design, all SF = 1.0 inch the MS calculations. The most critical margin 

was yield due to joint bending of the test article with a value of MS = 0.6370 for LC1. These 
13

calculations apply to a fail-safe condition so they may not be appropriate. However, examination of the 

remaining MS shows the bolt tension joint has a negative margin of MS = 0.1336 for LC1 in tension. 

Therefore, design MP-2 was deemed not satisfactory for the LC1 tension case, and design MP-3 was 

developed and analyzed. 

Table 6.3. Critical LC1 linear buckling loads for design MP-2, various attachment ring designs. 

tw,L and tw,B (inch) Nx,crit (lb/in) 

0.1 2,285 

0.125 2,288 

0.25 2,293 

0.375 2,298 

0.5 2,302 

0.625 2,305 

Table 6.4. Nonlinear LC1 instability loads for design MP-2, various attachment ring designs. 

tw,L and tw,B (inch) Nx,unst (lb/in) 

0.1 2,367 

0.125 2,383 

0.25 2,320 

0.375 2,313 

0.5 2,344 

0.625 2,344 

Table 6.5. Maximum LC1 nonlinear vonmises stresses for design MP-2, various attachment ring designs. 

 Maximum vonM (psi) at Nx=2300 lbs/in 

tw,L and tw,B (inch) L-shaped ring* Band* Test Article 

0.1 13,900 16,200 44,500 

0.125 11,900 14,100 44,500 

0.25 6,800 8,200 44,500 

0.375 4,750** 5,900*** 46,000 

0.5 3,700** 4,700*** 45,600 

0.625 3,050** 3,950*** 45,700 

 *Occurs at the weld land locations. 

 ** Adjusted from mid-surface value based on values seen in 0.1, 0.125 and 0.25 cases, added 200 psi. 

 *** Adjusted from mid-surface value based on values seen in 0.1, 0.125 and 0.25 cases, added 

 900 psi. 
14

Table 6.6. MS for MP-2 attachment ring design, load case LC1. 

Description MS 

Bolt shear, yield, attachment ring to test article 0.3841 

Bolt shear, ultimate, attachment ring to test article 0.1966 

Net tension failure, yield, attachment ring to test article 1.780 

Net tension failure, ultimate, attachment ring to test article 2.075 

Bearing - test article, yield, attachment ring to test article 0.2687 

Bearing - test article, ultimate, attachment ring to test article 0.1912 

Bearing - rings, yield, attachment ring to test article 0.2023 

Bearing - rings, yield, attachment ring to test article 0.2188 

Joint bending - bolt, yield 1.847 

Joint bending - bolt, ultimate 2.713 

Joint bending - test article, yield 0.6370 

Joint bending - test article, ultimate 0.5985 

Joint bending - L-shaped ring, yield 0.2079 

Joint bending - L-shaped ring, yield 0.2101 

Bolt tension, attachment ring to transition section 0.1415 

Attachment ring stress, L-shaped ring, yield 3.431 

Attachment ring stress, L-shaped ring, ultimate 5.770 

Attachment ring stress, band, yield 2.489 

Attachment ring stress, band, ultimate 4.330 

Test article stress, yield (at 2,300 lbs/in) 0.4474 

Test article stress, ultimate (at 2,300 lbs/in) 0.6009 

Table 6.7. MS for MP-2 attachment ring design, load case LC2 

Description MS 

Bolt shear, yield, attachment ring to test article 268.5 

Bolt shear, ultimate, attachment ring to test article 350.6 

Net tension failure, yield, attachment ring to test article 1215. 

Net tension failure, ultimate, attachment ring to test article 1344. 

Bearing - test article, yield, attachment ring to test article 319.0 

Bearing - test article, ultimate, attachment ring to test article 352.9 

Bearing - rings, yield, attachment ring to test article 348.1 

Bearing - rings, yield, attachment ring to test article 532.3 

Joint bending - bolt, yield 1245. 

Joint bending - bolt, ultimate 1624. 

Joint bending - test article, yield 157.9 

Joint bending - test article, ultimate 174.7 

Joint bending - L-shaped ring, yield 345.6 

Joint bending - L-shaped ring, yield 528.6 

Bolt tension, attachment ring to transition section 499.5 
15

a) Band b) L-section 

Figure 6.5. MP-2 Design cross-section definition (not drawn to scale). 
16

Figure 6.6. Typical MP-2 buckling mode, shown for tw,L = tw,B = 0.5 inch. 
17

Figure 6.7. Local solid model MP-2 design cross-section deformation at Nx = 5,050 lb/in 

(magnification factor of 5). 
18

Figure 6.8. Local solid model MP-2 design, L-shaped ring vonMises stresses at Nx = 5,050 lb/in. 
19

Figure 6.9. Local solid model MP-2 design, band vonMises stresses at Nx = 5,050 lb/in. 

6.2.3 MP-3 

Multiple-piece design MP-3 was assumed to be fabricated from AISI 1025 steel and is attached to the test 

article using both EA-9394 and bolts. The cross-section for the design MP-3 is shown in Figure 6.10. The 

L-shaped rings are attached to the annular ring, and are separated at a distance of 0.5 inch, which results 

in 0.125-inch regions of EA-9394 between the test article and L-shaped ring webs. MS were calculated 

using both the closed-form solutions and FEA. Closed-form solutions were used for all MS calculated at 

the bolt locations including the bolts, test article, and attachment rings. FEA was used to examine the 

stresses within the attachment ring L-section. Details of the FEM and analysis are provided in Appendix 

C. Lastly, the bolt spacing and locations were based upon the MP-2 design. The bolts attaching to the 

transition structure remain the same as those for MP-1 shown in Figure 6.4. The number of bolts through 

the test article was determined through analysis. 

Closed-form solutions for design MP-3 are different than for design MP-2 for load case LC1 due to the 

double-shear condition in the attachment ring. However, assuming the test article bears on the transition 

sections, and that the adhesive connects the test article to the attachment ring, only the tension case of 

LC1 was analyzed for design MP-3. Also, due to the same FEM being used, finite element results for 

design MP-3 are identical to those for design MP-2 for load case LC1. Load case LC2 was examined as a 
20

fail-safe condition where only the bolts hold the load for assembly. The number of bolts used around the 

test article circumference was varied, and included 90 (same as MP-2), 45, and 18. No adhesive 

calculations were performed for design MP-3. 

MS were calculated for design MP-3 for load cases LC1 and LC2. MS results for LC1 are summarized in 

Table 6.8. No calculations were performed for the bolts connecting the test article and attachment ring as 

it was assumed that the adhesive provided the connection. Also, no analysis of the adhesive was 

performed for MP-3. Minimum MS for LC2 for 90, 45, and 18 bolts were MS = 319.0, MS = 159.0 and 

MS = 63.00, respectively. Therefore, the closed-form bolt calculations yield significant positive margin 

when using 18 bolts, which corresponds to 20-degree arc spacing. Therefore, 18 test article/attachment 

ring bolts were chosen for design MP-3. MS results for LC2 are summarized in Table 6.9 for the 18-bolt 

design. As with design MP-2, SF = 1.0 was used in all of the MS calculations indicated in the tables. The 

most critical margin was test article yield at 2,300 lb/in load for LC1, with a value of MS = 0.4831. 

Table 6.8. MS for MP-3 attachment ring design, load case LC1. 

Description MS 

Bolt tension, attachment ring to transition section 2.283 

Attachment ring stress, L-shaped ring, yield 3.431 

Attachment ring stress, L-shaped ring, ultimate 5.770 

Attachment ring stress, band, yield 2.489 

Attachment ring stress, band, ultimate 4.330 

Test article stress, yield (at 2,300 lbs/in.) 0.4474 

Test article stress, ultimate (at 2,300 lbs/in.) 0.6009 

Table 6.9. MS for MP-3 Attachment Ring Design, Load Case LC2 

Description MS 

Bolt shear, yield, attachment ring to test article 106.8 

Bolt shear, ultimate, attachment ring to test article 139.6 

Net tension failure, yield, attachment ring to test article 1386. 

Net tension failure, ultimate, attachment ring to test article 1533. 

Bearing - test article, yield, attachment ring to test article 63.00 

Bearing - test article, ultimate, attachment ring to test article 69.79 

Bearing - rings, yield, attachment ring to test article 270.5 

Bearing - rings, ultimate, attachment ring to test article 348.1 

Bolt tension, attachment ring to transition section 999.0 
21

a) Inner and outer L-shaped rings 

b) Annular base ring 

Figure 6.10. MP-2 design cross-section definition (not drawn to scale). 
22

6.3 Single-Piece Design 

Single-piece design SP-1 was assumed to be fabricated from either AISI 1025 steel or 7075-T651 Al. The 

purpose of SP-1 was to simplify the manufacturing process by reducing the part count and assembly by 

choosing a single-piece construction. Also, the two materials were examined to simplify machining of the 

attachment ring and to potentially lighten the fixture. The cross-section for the design SP-1 is shown in 

Figure 6.11. For this design, the webs attaching to the test article have been separated such that there are 

approximately 0.125-inches of EA-9394 between each web and the test article. The EA-9394 is assumed 

to provide all attachment strength between the test article and the attachment ring, and bolts were retained 

for fail-safe consideration. MS were calculated using both the closed-form solutions and FEA. Closedform solutions were used for all MS calculated at the bolt locations including the bolts, test article and 

attachment rings. FEA was used to examine the stresses within the attachment ring. Details of the FEM 

and analysis are provided in Appendix C. Lastly, the bolt spacing and locations were identical to the MP3 design. The 18 bolts around the circumference of the test article are only present as a fail-safe 

mechanism. 

Closed-form and FEAs were conducted for load case LC1. As with design MP-3, assuming that the test 

article bears on the transition sections and that the adhesive connects the test article to the attachment 

ring, only the tension case of LC1 was analyzed using the closed-form solutions. The FEM was used to 

determine the stresses in the attachment ring webs and the test article for LC1. Only closed-form solutions 

were conducted for load cases LC2 and LC3. Load cases LC2 and LC3 were examined where either the 

EA-9394 or the bolts hold the entire load for assembly or pressure, respectively. Response summaries are 

shown in Tables 6.10 and 6.11 for the AISI 1025 steel and 7075-T651 Al attachment rings, respectively. 

Finite element results are provided for both the S4 and S4R5 elements at the load at which the nonlinear 

analysis becomes unstable, as indicated in the tables. 

MS were calculated for all three load cases and are summarized in Tables 6.12 through 6.17, where SFs 

used in the calculations are indicated in the tables. Tables 6.12 and 6.13 show the MS values for load case 

LC1 using steel and Al, respectively. Tables 6.14 and 6.15 show the MS values for load case LC2 using 

steel and Al, respectively. Tables 6.16 and 6.17 show the MS values for load case LC3 using steel and Al, 

respectively. All margins are positive with the exception of shear stress in the adhesive for LC1 subjected 

to compression. For the steel attachment ring subjected to LC1 compressive loading, positive margin is 

shown in the adhesive for a SF of 3, but becomes negative for a SF of 4. For the Al attachment ring 

subjected to LC1 compressive loading, positive margin is shown in the adhesive for a SF of 2, but 

becomes negative for a SF of 3. For LC1 in tension, only an adhesive calculation was performed because, 

based on previous analyses, for a bolted-only connection having 18 bolts, large negative margins were 

expected to exist. For tension loading, the adhesive bond must be completely intact to yield the MS values 

reported, and no analysis of partial bonds was performed to determine when the MS would become 

negative. Therefore, if a SF of at least 2 is sufficient for the adhesive subjected to LC1 loading, then all 

margins are positive for both the steel and Al designs. If a minimum SF of 3 is required, then only the 

steel design satisfies the requirement. For LC2, all margins are positive and large, indicating that LC2 is 

not critical. For LC3, the critical margin for both the steel and Al designs is bearing in the test article, 

with a value of MS = 0.02580 when SF = 3 for bearing is used. If an acceptable value of FS for the 

adhesive in LC1 is chosen (2 for Al, 3 for steel), the critical margin for both the steel and Al designs is 

bearing in the test article at the bolt locations for LC3, with a value of MS = 0.02580 for SF = 3. 
23

Table 6.10. Response summary for SP-1 AISI 1025 steel attachment ring design. 

Load Case Location Description Value 

LC1* Inner flange (S4) Max. vonMises stress 4,230 psi 

Inner flange (S4R5) Max. vonMises stress 3,820 psi 

Outer flange (S4) Max. vonMises stress 4,860 psi 

Outer flange (S4R5) Max. vonMises stress 4,590 psi 

Test article, stringer (S4) Max. vonMises stress 49,500 psi 

Test article, stringer (S4R5) Max. vonMises stress 41,800 psi 

Adhesive (S4) Max. shear stress 542 psi 

Adhesive (S4R5) Max. shear stress 487 psi 

Flange edge (S4) Max. fixture displacement 0.00402 inch 

Flange edge (S4R5) Max. fixture displacement 0.00393 inch 

Test article end (S4) Max. test article end shortening 0.137 inch 

Test article end (S4R5) Max. test article end shortening 0.133 inch 

LC2 Each bolt Bolt load 4,020 lb 

Adhesive Adhesive shear stress 25.95 psi 

LC3 Each bolt Bolt load 193.3 psi 

Adhesive Adhesive shear stress 2.00 psi 

* LC1 results at 2,336 lb/in for S4 elements and at 2,220 lb/in for S4R5 elements 

Table 6.11. Response summary for SP-1 7075-T651 aluminum attachment ring design. 

Load Case Location Description Value 

LC1* Inner flange (S4) Max. vonMises stress 2,380 psi 

Inner flange (S4R5) Max. vonMises stress 2,260 psi 

Outer flange (S4) Max. vonMises stress 3,710 psi 

Outer flange (S4R5) Max. vonMises stress 3,600 psi 

Test article, stringer (S4) Max. vonMises stress 47,200 psi 

Test article, stringer (S4R5) Max. vonMises stress 41,700 psi 

Adhesive (S4) Max. shear stress 817 psi 

Adhesive (S4R5) Max. shear stress 793 psi 

Flange edge (S4) Max. fixture displacement 0.00831 inch 

Flange edge (S4R5) Max. fixture displacement 0.00823 inch 

Test article end (S4) Max. test article end shortening 0.137 inch 

Test article end (S4R5) Max. test article end shortening 0.133 inch 

LC2 Each bolt Bolt load 4,020 lb 

Adhesive Adhesive shear stress 25.95 psi 

LC3 Each bolt Bolt load 193.3 psi 

Adhesive Adhesive shear stress 2.00 psi 

* LC1 results at 2,290 lb/in for S4 elements and at 2,220 lb/in for S4R5 elements 
24

Table 6.12. MS for SP-1 AISI 1025 steel attachment ring design, LC1 scaled to 5050 lb/in. 

Element Description MS 

S4R5 Adhesive (SF = 2) (yield, max. shear) 0.8956 

Adhesive (SF = 3) (yield, max. shear) 0.2637 

Adhesive (SF = 4) (yield, max. shear) 0.05219 

Inner flange (yield, vonMises) 3.143 

Inner flange (SF = 3) (yield, vonMises) 0.3810 

Outer flange (yield, vonMises) 2.448 

Outer flange (SF = 3) (yield, vonMises) 0.1493 

Test article, (SF = 1) (yield, vonMises) (at 2,220 lb/in) 0.5789 

Bolt, tension, transition section (SF = 1.5) 0.8847 

S4 Adhesive (SF = 2) (yield, max. shear) 0.7923 

Adhesive (SF = 3) (yield, max. shear) 0.1948 

Adhesive (SF = 4) (yield, max. shear) 0.1039 

Inner flange (yield, vonMises) 2.937 

Inner flange (SF = 3) (yield, vonMises) 0.3123 

Outer flange (yield, vonMises) 2.426 

Outer flange (SF = 3) (yield, vonMises) 0.1422 

Test article, (SF = 1) (yield, vonMises) (at 2,336 lb/in) 0.3333 

Bolt, tension, transition section (SF = 1.5) 0.8847 

N/A 

(ClosedForm)) 

Adhesive, tension load (SF = 2) (yield, max. shear) 2.847 

Adhesive, tension load (SF = 3) (yield, max. shear) 1.565 

Adhesive, tension load (SF = 4) (yield, max. shear) 0.9234 

Table 6.13. MS for SP-1 7075-T651 aluminum attachment ring design, LC1 scaled to 5050 lb/in. 

Element Description MS 

S4R5 Adhesive (SF = 2) (yield, max. shear) 0.1641 

Adhesive (SF = 3) (yield, max. shear) 0.2239 

Adhesive (SF = 4) (yield, max. shear) 0.4179 

Inner flange (yield, vonMises) 9.893 

Inner flange (SF = 3) (yield, vonMises) 2.631 

Outer flange (yield, vonMises) 5.838 

Outer flange (SF = 3) (yield, vonMises) 1.279 

Test article, (SF = 1) (yield, vonMises) (at 2,220 lb /in. ) 0.5827 

Bolt, tension, transition section (SF = 1.5) 0.1247 

S4 Adhesive (SF = 2) (yield, max. shear) 0.2009 

Adhesive (SF = 3) (yield, max. shear) 0.1994 

Adhesive (SF = 4) (yield, max. shear) 0.3996 

Inner flange (yield, vonMises) 9.670 

Inner flange (SF=3) (yield, vonMises) 2.557 

Outer flange (yield, vonMises) 5.845 

Outer flange (SF=3) (yield, vonMises) 1.282 

Test article, (SF=1) (yield, vonMises) (at 2,336 lb/in) 0.3983 

Bolt, tension, transition section (SF = 1.5) 0.1247 

N/A 

(ClosedForm)) 

Adhesive, tension load (SF = 2) (yield, max. shear) 2.847 

Adhesive, tension load (SF = 3) (yield, max. shear) 1.565 

Adhesive, tension load (SF = 4) (yield, max. shear) 0.9234 
25

Table 6.14. MS for SP-1 AISI 1025 steel attachment ring design, load case LC2. 

Description MS 

Bolt shear, yield, attachment ring to test article (SF = 1) 106.8 

Bolt shear, ultimate, attachment ring to test article (SF = 1) 139.6 

Net tension failure, yield, attachment ring to test article (SF = 1) 1386. 

Net tension failure, ultimate, attachment ring to test article (SF = 1) 1533. 

Bearing - test article, yield, attachment ring to test article (SF = 1) 63.00 

Bearing - test article, ultimate, attachment ring to test article (SF = 1) 69.79 

Bearing - rings, yield, attachment ring to test article (SF = 1) 138.6 

Bearing - rings, ultimate, attachment ring to test article (SF = 1) 212.3 

Bolt shear, yield, attachment ring to test article (SF = 4) 25.96 

Bolt shear, ultimate, attachment ring to test article (SF = 4) 34.16 

Net tension failure, yield, attachment ring to test article (SF = 4) 345.8 

Net tension failure, ultimate, attachment ring to test article (SF = 4) 382.6 

Bearing - test article, yield, attachment ring to test article (SF = 4) 15.00 

Bearing - test article, ultimate, attachment ring to test article (SF = 4) 16.70 

Bearing - rings, yield, attachment ring to test article (SF = 4) 33.92 

Bearing - rings, yield, attachment ring to test article (SF = 4) 52.34 

Bolt tension, attachment ring to transition section (SF = 1.5) 823.8 

Adhesive (SF = 4) 524.0 

Table 6.15. MS for SP-1 7075-T651 aluminum attachment ring design, load case LC2. 

Description MS 

Bolt shear, yield, attachment ring to test article (SF = 1) 106.8 

Bolt shear, ultimate, attachment ring to test article (SF = 1) 139.6 

Net tension failure, yield, attachment ring to test article (SF = 1) 1386. 

Net tension failure, ultimate, attachment ring to test article (SF = 1) 1533. 

Bearing - test article, yield, attachment ring to test article (SF = 1) 63.00 

Bearing - test article, ultimate, attachment ring to test article (SF = 1) 69.79 

Bearing - rings, yield, attachment ring to test article (SF = 1) 216.2 

Bearing - rings, ultimate, attachment ring to test article (SF = 1) 255.0 

Bolt shear, yield, attachment ring to test article (SF = 4) 25.96 

Bolt shear, ultimate, attachment ring to test article (SF = 4) 34.16 

Net tension failure, yield, attachment ring to test article (SF = 4) 345.8 

Net tension failure, ultimate, attachment ring to test article (SF = 4) 382.6 

Bearing - test article, yield, attachment ring to test article (SF = 4) 15.00 

Bearing - test article, ultimate, attachment ring to test article (SF =4 ) 16.70 

Bearing - rings, yield, attachment ring to test article (SF = 4) 53.31 

Bearing - rings, yield, attachment ring to test article (SF = 4) 63.01 

Bolt tension, attachment ring to transition section (SF = 1.5) 491.2 

Adhesive (SF = 4) 524.0 
26

Table 6.16. MS for SP-1 AISI 1025 steel attachment ring design, load case LC3. 

Description MS 

Bolt shear, yield, attachment ring to test article (SF = 1) 4.184 

Bolt shear, ultimate, attachment ring to test article (SF = 1) 5.762 

Net tension failure, yield, attachment ring to test article (SF = 1) 65.70 

Net tension failure, ultimate, attachment ring to test article (SF = 1) 72.77 

Bearing - test article, yield, attachment ring to test article (SF = 1) 2.077 

Bearing - test article, ultimate, attachment ring to test article (SF = 1) 2.404 

Bearing - rings, yield, attachment ring to test article (SF = 1) 5.714 

Bearing - rings, ultimate, attachment ring to test article (SF = 1) 9.258 

Bolt shear, yield, attachment ring to test article (SF = 3) 0.7280 

Bolt shear, ultimate, attachment ring to test article (SF = 3) 1.254 

Net tension failure, yield, attachment ring to test article (SF = 3) 21.23 

Net tension failure, ultimate, attachment ring to test article (SF = 3) 23.59 

Bearing - test article, yield, attachment ring to test article (SF = 3) 0.02580 

Bearing - test article, ultimate, attachment ring to test article (SF = 3) 0.1346 

Bearing - rings, yield, attachment ring to test article (SF = 3) 1.238 

Bearing - rings, yield, attachment ring to test article (SF = 3) 2.419 

Bolt tension, attachment ring to transition section (SF = 1.5) 39.66 

Adhesive (SF = 4) 39.46 

Table 6.17. MS for SP-1 7075-T651 aluminum attachment ring design, load case LC3. 

Description MS 

Bolt shear, yield, attachment ring to test article (SF = 1) 4.184 

Bolt shear, ultimate, attachment ring to test article (SF = 1) 5.762 

Net tension failure, yield, attachment ring to test article (SF = 1) 65.70 

Net tension failure, ultimate, attachment ring to test article (SF = 1) 72.77 

Bearing - test article, yield, attachment ring to test article (SF = 1) 2.077 

Bearing - test article, ultimate, attachment ring to test article (SF = 1) 2.404 

Bearing - rings, yield, attachment ring to test article (SF = 1) 9.445 

Bearing - rings, ultimate, attachment ring to test article (SF = 1) 11.31 

Bolt shear, yield, attachment ring to test article (SF = 3) 0.7280 

Bolt shear, ultimate, attachment ring to test article (SF = 3) 1.254 

Net tension failure, yield, attachment ring to test article (SF = 3) 21.23 

Net tension failure, ultimate, attachment ring to test article (SF = 3) 23.59 

Bearing - test article, yield, attachment ring to test article (SF = 3) 0.02580 

Bearing - test article, ultimate, attachment ring to test article (SF = 3) 0.1346 

Bearing - rings, yield, attachment ring to test article (SF = 3) 2.482 

Bearing - rings, yield, attachment ring to test article (SF = 3) 3.103 

Bolt tension, attachment ring to transition section (SF = 1.5) 23.67 

Adhesive (SF = 4) 39.46 
27

3.75Ó

6.5Ó

5/8Ó Dia. Bolt (2 places)

1.375Ó

1.5Ó

1/2Ó Dia. Bolt (2 places)

0.5Ó

0.75Ó

4.625Ó

3.375Ó

0.5Ó

1.5Ó

Figure 6.11. SP-1 design cross-section definition (not drawn to scale). 

7.0 Conclusions 

Analysis and design was performed on several attachment ring concepts to connect a test article to the test 

assembly transition sections. Three multi-piece designs and one single-piece design were examined, and 

three material systems were considered, namely AISI 4130 steel, AISI 1025 steel and 7075-T651 Al. 

Designs MP-1 and MP-2 are not satisfactory particularly design MP-2 which shows many negative 

margins. Design MP-3 shows positive margins for those calculated, but in the analyses of MP-3, LC3 was 

not considered and no analysis of the adhesive was performed for any load case. However, because of the 

similarity between the two designs, the response of MP-3 is expected to be identical to SP-1 for LC3 and 

for the analyses of adhesive for all load cases. Despite the similarity in margins between designs MP-3 

and SP-1, the SP-1 single-piece design is the design of choice because not only are all MS positive, the 

single-piece design simplifies the manufacturing and assembly processes. However, the material from 

which the SP-1 attachment ring design is made depends upon the SFs required. Provided that a minimum 

SF of 2 is acceptable for load case LC1, the attachment ring can be made from either the 7075-T651 Al or 

the AISI 1025 steel. If a minimum SF of 3 is required for the adhesive subjected to LC1 loading, then the 

attachment ring must be made from the AISI 1025 steel. 
28

8.0 References 

1. Design Allowables Handbook for Aluminum-Lithium 2195 Plates, Extrusions, Forgings, & Welds. 

MSFC-HDBK-3513 (Baseline). 

2. ET Project – Design Values for Aluminum Allow 2195. MMC-ET-SE64-H, Michoud Space Systems, 

Lockheed Martin, April 1999. 

3. Metallic Materials Properties Development and Standardization (MMPDS). DOT/FAA/ARMMPDS-01, Office of Aviation Research, Washington, D.C., January 2003. 

4. Standard Specification for Structural Bolts, Steel, Heat Treated, 120/105 ksi Minimum Tensile 

Strength. A 325-06, ASTM International, West Conshohocken, Pennsylvania, August 1, 2006. 

5. Guess, T. R.; Reedy, E.D.; and Stavig, M. E.: Mechanical Properties of Hysol EA-9394 Structural 

Adhesive. SAND95-0229, Sandia National Laboratories, Albuquerque, New Mexico, February 1995. 

6. Hyson EA 9394 Epoxy Paste Adhesive. Henkel Corporation, Bay Point, California, Rev. 6/02. 

7. Shigley, J. E.; and Mischke, C. R.: Mechanical Engineering Design. Fifth, Ed., McGraw-Hill, New 

York, New York 1989. 

8. MSC.NASTRAN 2005 manuals, MSC Software, Santa Ana, California, 2004. 

9. ABAQUS V6.7 manuals, Dessault Systemes, SIMULIA Worldwide Headquarters, Providence, 

Rhode Island, 2007 

10. Manual of Steel Construction – Load & Resistance Factor Design. First Ed., American Institute of 

Steel Construction, Inc., Chicago, Illinois, 1986. 
29

Appendix A: Closed-Form Solution Spreadsheet Description 

Closed-form solutions for the bolted joints were performed using an MS Excel spreadsheet and the design 

equations from Reference 7. Three spreadsheets were developed. The first spreadsheet was for a bolted 

joint subjected to tension, an example of which is shown in Figure A.1. The second spreadsheet was for a 

bolted joint with a bolt subjected to single shear, an example of which is shown in Figure A.2. Lastly, a 

spreadsheet for a bolted joint with a bolt subjected to double shear was developed, an example of which is 

shown in Figure A.3. Assumptions inherent in the spreadsheets are noted in the figures. 

Bolt Grade: SAE 5, ASTM A325 (Type 1)

INPUT

Bolt Diameter (in.) 0.625

Bolt Yield (psi) 92000

Bolt Ultimate (psi) 120000

Bolt Young's Modulus (ksi) 30000

Proof Stress (psi) 85000

At (in.^2) (Table 8-2 in Shigley & Mischke) 0.226

Washer Thickness (in.) 0

Cylinder Radius (in.) 48

Bolt Distance from OML 1.25

Arc per Bolt (degrees) 4

Row Spacing (in.) 1.75

L-bracket Flange Thickess (in.) 1.5

L-bracket Yield (psi) 56000

L-bracket Ultimate (psi) 66000

L-bracket Young's Modulus (ksi) 10300

Trans. Cyl. Flange Thickness (in.) 0.75

Trans. Cyl. Flange Yield (psi) 36000

Trans. Cyl. Flange Ultimate (psi) 55000

Trans. Cyl. Young's Modulus (ksi) 29000

Axial Running Load (lbs./in.) 5050

Pressure Fruntrum Angle (degrees) 30

Safety Factor 1.5

OUTPUT

Cylinder Circumference (in.) 301.592895

Bolt Line Circumference (in.) 309.446876

Arc Bolt Spacing (in.) 3.43829863

Number of bolts 180

Force per Bolt (lbs.) 12692.0343

Pressure Fruntrum Angle (rad) 0.52359878

A (in.^2) l (in.) kb (kips/in.)

Bolt Stiffness 0.30679616 2.25 4090.61543

k, L-bracket k, Trans. Cyl. km (kips/in)

Member Stiffness* 10311.6286 37087.6108 8068.35034

C

Joint Constant 0.33642791

Fp (lbs.) Fi (lbs.) T (in.-lbs.)

Recommended Preload/Torque* 19210 14407.5 1800.9375

Sp n

Bolt Load Factor 19210 1.12471923

* Following assumptions are made: 1) joint frustrum angles assumed to be 30 degrees.

2) use washer with diameter 1.5 times bolt diameter

3) for Fi calculation, expect reused connection

4) for T, use K=0.2

Figure A.1. Example spreadsheet for bolted joint in tension. 
30

Bolt Grade: SAE 5, ASTM A325 (Type 1)

INPUT

Bolt Diameter (in.) 0.5

Bolt Yield )psi) 92000

Bolt Ultimate (psi) 120000

Cylinder Radius (in.) 48

Arc per Bolt (degrees) 4

Number of Rows 1

Row Spacing (in.) 1.75

Specimen Thickess (in.) 0.25

Specimen Yield (psi) 66000

Specimen Ultimate (psi) 73000

Flange Thickness (in.) 0.5

Flange Yield (psi) 36000

Flange Ultimate (psi) 55000

Axial Running Load (lbs./in.) 5050

OUTPUT

Cylinder Circumference (in.) 301.592895

Arc Bolt Spacing (in.) 3.35103216

Number of bolts 90

Force per Bolt (lbs.) 16922.7124

Joint Bending - Bolt

t (grip) M I c Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.75 6346.01716 0.04908739 0.25 32320 2.84653465 1.84653465 3.71287129 2.71287129

Joint Bending - Specimen

t (grip) M I c Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.75 6346.01716 0.00436332 0.125 181800 0.3630363 -0.6369637 0.40154015 -0.59845985

Joint Bending - Flange

t (grip) M I c Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.75 6346.01716 0.03490659 0.25 45450 0.79207921 -0.20792079 1.21012101 0.21012101

Bolt Shear

A Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.19634954 86186.6667 0.61591894 -0.38408106 0.80337252 -0.19662748

Net Tension Failure

A F Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.71275804 16922.7124 23742.5767 2.77981623 1.77981623 3.07464523 2.07464523

Bearing* - Specimen

A Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.125 135381.699 0.73126575 -0.26873425 0.80882424 -0.19117576

Bearing* - Flange

A Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.25 67690.8497 0.79774445 -0.20225555 1.21877625 0.21877625

Shear Out

Neglected due to requiring first row of bolts being at least 2 bolt diameters from land edge.

Tensile Tear Out

Neglected due to requiring first row of bolts being at least 2 bolt diameters from land edge.

Minimum MS: -0.6369637

* Bearing allowable assumed to be 1.5 times Fu and Fy even though provided data suggests a factor of 2.0

Figure A.2. Example spreadsheet for bolted joint in single shear. 
31

IN-LINE BOLTS, DOUBLE SHEAR

Bolt Grade: SAE 5, ASTM A325 (Type 1)

Flange Material: 1025 Low Carbon Steel

Specimen Material: Al-Li-2195

INPUT

Bolt Diameter (in.) 0.5

Bolt Yield )psi) 92000

Bolt Ultimate (psi) 120000

Cylinder Radius (in.) 48

Arc per Bolt (degrees) 20

Number of Rows 1

Row Spacing (in.) 1.75

Specimen Thickess (in.) 0.25

Specimen Yield (psi) 66000

Specimen Ultimate (psi) 73000

Flange Thickness (in.) 0.5

Flange Yield (psi) 36000

Flange Ultimate (psi) 55000

Axial Running Load (lbs./in.) 46.152

OUTPUT

Cylinder Circumference (in.) 301.592895

Arc Bolt Spacing (in.) 16.7551608

Number of bolts 18

Force per Bolt (lbs.) 773.284182

Bolt Shear

A Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.39269908 1969.152 26.9577971 25.9577971 35.162344 34.162344

Net Tension Failure

A F Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

4.0637902 773.284182 190.286443 346.845519 345.845519 383.632165 382.632165

Bearing* - Specimen

A Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.125 6186.27346 16.0031723 15.0031723 17.7004784 16.7004784

Bearing* - Flange

A Stress FS (yield) MS (yield) FS (ult.) MS (ult.)

0.25 1546.56836 34.9160123 33.9160123 53.3439077 52.3439077

Shear Out

Neglected due to requiring first row of bolts being at least 2 bolt diameters from land edge.

Tensile Tear Out

Neglected due to requiring first row of bolts being at least 2 bolt diameters from land edge.

Minimum MS: 15.0031723

* Bearing allowable assumed to be 1.5 times Fu and Fy even though provided data suggests a factor of 2.0

Figure A.3. Example spreadsheet for bolted joint in double shear. 
32

Appendix B: Bolt Pattern Design FEM 

B-1 Two-Row, In-Line 

The FEM used to analyze the bolt load distribution between bolt rows for the two-row, in-line bolt pattern 

is shown in Figure B.1. It was analyzed in MSC/NASTRAN (Ref. 8) and consisted of quadrilateral and 

triangular shell elements, along with bar elements. The shell elements represent the test article and 

therefore have a thickness of 0.25 inch and are Al-Li-2195. The bar elements are used to distribute the 

bolt load around the bolt hole circumference and to connect the shell model to ground. In the figure, shell 

elements are black and the bar elements are orange. The bar elements used to transfer load to the bolt hole 

circumference were given very large stiffness so as to remain as rigid entities. At the center of the bolt 

locations, bars were used to provide an elastic connection so as to provide a more accurate load 

distribution. The properties for the elastic connection bars were such that the axial stiffness was 

representative of a single, steel attachment flange that was 0.5 inch thick, and they were given bending 

stiffness sufficient to prevent numerical problems. These elastic connection bars connect the inner row of 

bolt centers to the edge row of bolt centers, and the edge row of bolt centers to ground points. The ground 

points are fixed in all degrees of freedom. A uniform compression or tension displacement was applied to 

the edge opposite the bolts and the bolt load distribution determined. 

Figure B.1. Two-row, in-line bolt pattern FEM (compression case). 
33

B-2 Two-Row, Staggered 

The FEM used to analyze the bolt load distribution between bolt rows for the two-row, staggered bolt 

pattern is shown in Figure B.2. Modeling was the same as that for the two-row, in-line pattern as 

described in Section B-1 with the exception of the elastic connection bars. In this model, the elastic 

connection bars were all attached to the ground point because it was quicker and easier than trying to 

connect the centers of the inner row of bolts to the centers of the edge row of bolts. Boundary conditions 

and loading were the same as for the two-row, in-line analysis. 

Figure B.2. Two-row, staggered bolt pattern FEM (compression case). 
34

B-3 Two-Row, Staggered, Gapped 

The FEM used to analyze the bolt load distribution between bolt rows for the two-row, staggered and 

gapped bolt pattern is shown in Figure B.3. Modeling, boundary conditions and loading were the same as 

that for the two-row, staggered pattern as described in Section B-2. 

Figure B.3. Two-row, staggered, gapped bolt pattern FEM (compression case). 
35

Appendix C: Multiple-Piece Design FEM 

C-1 Design MP-1 

A 20-degree arc segment solid model of the attachment ring was created to examine the stresses within 

the L-shaped section. Only the outer attachment ring was modeled under the assumption that the response 

of the inner ring would be similar. The FEM is shown in Figures C.1 and C.2. Loads applied at the bolt 

locations are shown in Figure C.3, where only tension loads were applied because they were expected to 

produce the largest stresses, particularly at the fillet. 

a) View looking radial. 

b) View looking axial. 

Figure C.1. MP-1 FEM. 
36

Figure C.2. MP-1 FEM isometric view. 
37

Figure C.3. MP-1 FEM applied load. 

C-2 Design MP-2 

Two MP-2 design FEMs were constructed and analyzed. The first model was a NASTRANTM shell FEM, 

shown in Figures C.4 and C.5 that was used to examine how the thickness of the L-bracket web and band 

affect the test article response. For these analyses, the web and band were considered to be adhesively 

bonded to the test article using the EA-9394. However, the EA-9394 was ignored in the analysis by 

creating a laminate consisting only of the ring web, test article and band with their appropriate 

thicknesses. In the first set of analyses, each component was modeled as a single layer in the laminate. 

However, to determine the stresses/strains at the surfaces of the components to assess bending, each 

component was broken up into three layers. This was done because NASTRANTM returns the mid-surface 

strain in the layers of a laminate. Therefore, the outermost layers of each component were given a 

thickness of 0.001 inch, with the central layer given a thickness appropriate to yield the total component 

thickness. Values of stress and strain were then examined in all three layers for a component, with the 
38

values in the 0.001-inch layers providing the surface values. Additionally, to provide the proper offset for 

the components, a dummy layer was used to generate laminates that positioned the component material at 

the proper location. This dummy layer was fabricated from a dummy material having E = 0.001 psi and 

= 0.3. Figure C.6 shows how the dummy ply is applied to remove the offset for a three-ply laminate that 

was modeled at the OML with an offset. For boundary conditions, the model was assumed to be clamped 

at both ends, where all degrees of freedom were fixed with the exception of the axial displacement at one 

end. At the load end, the axial displacement was free and a uniform distributed line load was applied. 

Buckling analyses used a uniform compressive axial load of 1000 lb/in, while a uniform compressive 

axial load of 2500 lb/in was used in the nonlinear analyses. At the loaded end, a set of beams was 

created around the circumference to keep the edge planar. These beams were modeled using the AISI 

1025 steel, and were given in the plane of the shell bending stiffness by assigning I = 100 in4

. The area, 

moment of inertia out-of-plane of the shell and the torsional constant were assigned values of 0.0001. 

Typical nonlinear analysis deformed shape is shown in Figure C.7, and typical nonlinear vonMises stress 

results are shown in Figures C.8 to C.17 for the various parts of the attachment ring and test article. The 

figures show the stresses for the design with 0.25-inch thick L-shaped ring and band components, where 

each component was modeled using three plies. 

Figure C.4. MP-2 FEM to examine thickness of L-bracket web and band. 
39

Figure C.5. Close-up of MP-2 FEM to determine required thickness of L-bracket web and band. 
40

a) With offset. 

b) Without offset, with dummy ply. 

Figure C.6. Use of dummy ply to remove offsets. 
41

Figure C.7. Nonlinear deformation for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch 

(contours indicate radial displacement). 
42

Figure C.8. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article weld land inner surface. 
43

Figure C.9. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article weld land outer surface. 
44

Figure C.10. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article skin inner surface. 
45

Figure C.11. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article skin outer surface. 
46

Figure C.12. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article stringer Z1 ("bottom" of element) surface. 
47

Figure C.13. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article stringer Z2 ("bottom" of element) surface. 
48

Figure C.14. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article L-shaped ring web inner surface. 
49

Figure C.15. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article L-shaped ring web outer surface. 
50

Figure C.16. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article band inner surface. 
51

Figure C.17. vonMises stress for design MP-2 at 2,300 lb/in with tw,L = tw,B = 0.25 inch, 

test article band outer surface. 
52

A 24-degree arc-length solid model of the L-shaped ring and band was created to examine the stresses 

within the sections if no adhesive was used between the test article and the attachment ring. The FEM is 

shown in Figure C.18. The inner L-shaped ring and the outer band are attached to each other via beams to 

represent the half-inch diameter attachment bolts. The ends of these beams are attached to the edges of the 

bolt holes in the L-shaped ring and band that are farthest from the test article, as shown in Figure C.19. 

The test article portion of the FEM is free and independent from these bolt representations. 

Boundary conditions were applied to various parts of the model. The bolts attaching the L-shaped ring to 

the transition section were not modeled, so the entire base of the L-shaped ring was constrained as 

clamped. A clamped surface was used since it was assumed that subjected to compression, the base face 

of the L-shaped ring would be in contact with the transition section in all places. However, the bases of 

the test article and outer ring were constrained in the axial direction, only, and were free to move along 

the plane representing the transition section flange. Symmetry boundary conditions were applied to the 

ends of the three components. To provide interaction between the test article and the attachment ring 

parts, contact pairs were created at the interfaces between the test article and attachment ring as shown in 

Figure C.20. Lastly, a uniform end shortening of 0.2 inches was applied to the test cylinder edge. 

Figure C.18. Local MP-2 FEM to examine contact response of L-bracket web and band. 
53

Figure C.19. Locations of bolts (black) in local MP-2 FEM. 
54

Figure C.20. Contact surface locations for local MP-2 FEM. 
55

C-3 Design MP-3 

The multiple-piece MP-3 design was analyzed using a shell FEM identical to the one used for the MP-2 

design and described above. This model was chosen because previous analyses have shown the test article 

response is not significantly influenced by the boundary conditions on the attachment ring. This model 

equates to removing the legs of the L-shaped rings and the base annular ring as shown in Figure C.21, and 

clamping the shell model at the base of the webs. Since only the attachment ring webs are included in the 

shell model, and because the webs are attached to the test article using EA-9394, the resulting shell FEM 

is identical to the MP-2 design shell model and is shown in Figures 6.4 and 6.5. 

Figure C.21. Attachment ring modeled in MP-3 shell FEM. 
56

Appendix D: Single-Piece Design FEM 

The SP-1 design was analyzed using an ABAQUSTM shell FEM, shown in Figures D.1, D.2 and D.3. 

Each end of the model was modeled differently, with one end examining the response for a completely 

adhesive joint at the test article attachment ring interface, and the other examining the response for a 

completely bolted joint at the same location. At the adhesively-attached end, the webs of the attachment 

ring were considered to be adhesively bonded to the test article using the EA-9394. The EA-9394 was 

included in the analysis by creating a laminate consisting of the attachment ring webs, test article, and 

EA-9394 with their appropriate thicknesses. Modeling in this manner separated the attachment ring webs 

the proper distance from the test article. Similar to the previous model, to determine the stresses/strains at 

the surfaces of the components to assess bending, each component was broken up into three layers. The 

outermost layers were given a thickness of 0.001 inch, with the central layer given a thickness appropriate 

to yield the total component thickness. Values of stress and strain were then examined in all three layers 

for a component, with the values in the 0.001-inch layers providing the surface values. Although not 

necessary in the ABAQUSTM analysis, since the model was derived from the NASTRANTM for MP-2 and 

MP-3, a dummy layer was included to generate a laminate having no offsets (recall Figure C.5). This 

dummy layer was fabricated from a dummy material having E = 0.001 psi and  = 0.3. All remaining 

shell elements were defined as single layers with the appropriate offsets. At the bolted end, the inner and 

outer flanges were attached at the 18 bolt locations using beam elements to approximate the bolt stiffness 

as shown in Figure D.4. Appropriate boundary conditions were applied to each end. At the laminated end, 

which was the load end, all degrees of freedom except for the axial displacement were restrained. At the 

bolted end, each of the three components (inner flange, test article and outer flange) was clamped. 

Additionally, contact pairs were defined between the inner and outer flanges and the test article. A 

uniform compressive axial load of 2500 lb/in was used at the laminated end in the nonlinear analyses. 

As previously, at the loaded end, a set of beams was created around the circumference to keep the edge 

planar. These beams were modeled using the AISI 1025 steel, and were given in the plane of the shell 

bending stiffness by assigning I = 100 in4

. The area, moment of inertia out-of-plane of the shell and the 

torsional constant were assigned values of 0.0001. Lastly, response was examined using both the 

ABAQUSTM S4 and S4R5 shell elements. 

The typical nonlinear analysis deformed shape is shown in Figures D.4 and D.5. Typical nonlinear 

vonMises stress results are shown in Figures D.6 to D.24 for the various parts of the attachment ring and 

test article. Cross-section deformed plots in the vicinity of the contact region between the attachment ring 

flanges and test article are shown in Figure D.25 and D.26 at the weld land and in the center of a panel, 

respectively. The figures show the results for the design having AISI 1025 steel attachment rings 

subjected to LC1 at Nx = 2220 lb/in uniform loading that was analyzed using the S4R5 shell elements. 
57

Figure D.1. SP-1 ABAQUSTM shell FEM. 
58

Figure D.2. SP-1 ABAQUSTM shell FEM, laminated end. 
59

Ring

Figure D.3. SP-1 ABAQUSTM shell FEM, bolted end. 
60

Figure D.4. SP-1 ABAQUSTM shell FEM attachment bolt beams (shown in black). 
61

Figure D.5. SP-1 nonlinear deformed shape, LC1 at 2220 lb/in, AISI 1025 steel attachment rings 

(deformations magnified x50). 
62

Figure D.6. SP-1 nonlinear deformed shape with radial deflection contours, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings (deformations magnified x50). 
63

Figure D.7. SP-1 vonMises stress (psi) in inner flange inner surface at laminated end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
64

Figure D.8. SP-1 vonMises stress (psi) in inner flange outer surface at laminated end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
65

Figure D.9. SP-1 vonMises stress (psi) in inner flange inner surface at bolted end, LC1 at 

2220 lb/in, AISI 1025 steel attachment rings. 
66

Figure D.10. SP-1 vonMises stress (psi) in inner flange outer surface at bolted end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
67

Figure D.11. SP-1 vonMises stress (psi) in outer flange inner surface at laminated end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
68

Figure D.12. SP-1 vonMises stress (psi) in outer flange outer surface at laminated end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
69

Figure D.13. SP-1 vonMises stress (psi) in outer flange inner surface at bolted end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
70

Figure D.14. SP-1 vonMises stress (psi) in outer flange outer surface at bolted end, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
71

Figure D.15. SP-1 vonMises stress (psi) in weld land inner surface, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
72

Figure D.16. SP-1 vonMises stress (psi) in weld land outer surface, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
73

Figure D.17. SP-1 vonMises stress (psi) in acreage skin inner surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. 
74

Figure D.18. SP-1 vonMises stress (psi) in acreage skin outer surface, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings. 
75

Figure D.19. SP-1 vonMises stress (psi) in intermediate skin inner surface, LC1 at 

2220 lb/in, AISI 1025 steel attachment rings. 
76

Figure D.20. SP-1 vonMises stress (psi) in intermediate skin outer surface, LC1 at 

2220 lb/in, AISI 1025 steel attachment rings. 
77

Figure D.21. SP-1 vonMises stress (psi) in ring inner surface, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
78

Figure D.22. SP-1 vonMises stress (psi) in ring outer surface, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
79

Figure D.23. SP-1 vonMises stress (psi) in stringer inner surface, LC1 at 2220 lb/in, 

AISI 1025 steel attachment rings. 
80

Figure D.24. SP-1 vonMises stress (psi) in stringer skin outer surface, LC1 at 

2220 lb/in, AISI 1025 steel attachment rings. 
81

Figure D.25. SP-1 nonlinear contact region deformation at weld land, LC1 at 2220 lb/in, AISI 1025 steel 

attachment rings (deformations magnified x50). 
82

Figure D.26. SP-1 nonlinear contact region deformation at acreage (center of panel), LC1 at 

2220 lb/in, AISI 1025 steel attachment rings (deformations magnified x50). 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Design of 8-ft-diameter Barrel Test Article Attachment Rings for Shell 

Buckling Knockdown Factor Project

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Lovejoy, Andrew E.; Hilburger, Mark W.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

Washington, DC 20546-0001

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L-19913

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NASA

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Subject Category 16-Space Transportation and Safety

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

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14. ABSTRACT

The Shell Buckling Knockdown Factor (SBKF) project includes the testing of sub-scale cylinders to validate new shell 

buckling knockdown factors for use in the design of the Ares-I and Ares-V launch vehicles. Test article cylinders represent 

various barrel segments of the Ares-I and Ares-V vehicles, and also include checkout test articles. Testing will be conducted at 

Marshall Space Flight Center (MSFC) for test articles having an eight-foot diameter outer mold line (OML) and having 

lengths that range from three to ten feet long. Both ends of the test articles will be connected to the test apparatus using 

attachment rings. Three multiple-piece and one single-piece design for the attachment rings were developed and analyzed. The 

single-piece design was chosen and will be fabricated from either steel or aluminum (Al) depending on the required safety 

factors (SF) for test hardware. This report summarizes the design and analysis of these attachment ring concepts.

15. SUBJECT TERMS

Constellation Program; Shell buckling knockdown factor; Test article attachment rings; Testing methodologies

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869021.04.07.01.13

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1. REPORT DATE (DD-MM-YYYY)

01- 08 - 2010