January 2011 

NASA/TM-2011-216875 

ARL-TR-5123 

Pre-Test Analysis Predictions for the 

Shell Buckling Knockdown Factor Checkout 

Tests – TA01 and TA02 

Robert P. Thornburgh 

U.S. Army Research Laboratory, Vehicle Technology Directorate 

Langley Research Center, Hampton, Virginia 

Mark W. Hilburger 

Langley Research Center, Hampton, Virginia 
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January 2011 

NASA/TM-2011-216875 

ARL-TR-5123 

Pre-Test Analysis Predictions for the 

Shell Buckling Knockdown Factor Checkout 

Tests – TA01 and TA02 

Robert P. Thornburgh 

U.S. Army Research Laboratory, Vehicle Technology Directorate 

Langley Research Center, Hampton, Virginia 

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 Test Reports were combined to create this TM: 

SBKF-P2-TR-2008-008; Pre-Test Analysis Report – Test Article 1 

SBKF-P2-TR-2009-001; Pre-Test Analysis Report – SBKF-P2-CYL-TA02 Test 
iv 

Table of Contents 

Nomenclature .............................................................................................................................................. vii

Part 1: Pre-Test Analysis Report – Test Article 1 SBKF-P2-TR-2008-008 .......................................... 1

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

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

3.0 References ...................................................................................................................................... 16

Part 2: Pre-Test Analysis Report – SBKF-P2-CYL-TA02 Test ........................................................... 17

1.0 Introduction .................................................................................................................................... 17

2.0 Summary of Results ....................................................................................................................... 17

3.0 References ...................................................................................................................................... 37

List of Figures 

Part 1: Pre-Test Analysis Report – Test Article 1 SBKF-P2-TR-2008-008 

Figure 2.1. Analysis coordinate system. ..................................................................................................... 2

Figure 2.2. Measure geometric imperfection for TA01. ............................................................................. 3

Figure 2.3. Predicted load-shortening response for the TA under uniform axial loading. ......................... 4

Figure 2.4. Predicted buckling mode shapes at varying load levels for the TA under uniform 

 axial loading. ............................................................................................................................ 5

Figure 2.5. Predicted out-of-plane deformation at varying load levels for the TA under uniform axial 

 loading. ..................................................................................................................................... 6

Figure 2.6. Predicted axial strain on the outer surface at varying load levels for the TA under uniform 

 axial loading. ............................................................................................................................ 7

Figure 2.7. Predicted circumferential strain on the outer surface at varying load levels for the test 

 article under uniform axial loading. ......................................................................................... 8

Figure 2.8. Predicted out-of-plane displacement at the center of the panels during uniform axial load. ... 9

Figure 2.9. Predicted out-of-plane displacement at the center of the axial weld lands during uniform 

 axial load. ................................................................................................................................. 9

Figure 2.10. Predicted out-of-plane displacement at the dent and buckling initiation site during uniform 

 axial load. ............................................................................................................................... 10

Figure 2.11. Predicted load-shortening response for the TA under combined bending and axial 

 loading. ................................................................................................................................... 11

Figure 2.12. Predicted buckling mode shape for the TA under combined bending and axial loading 

 based on eigen analysis at the limit load. ............................................................................... 11

Figure 2.13. Predicted out-of-plane deformation at varying load levels for the TA under combined 

 bending and axial loading. ..................................................................................................... 12

Figure 2.14. Predicted axial strain at varying load levels for the TA under combined bending and axial 

 loading. ................................................................................................................................... 13

Figure 2.15. Predicted circumferential strain at varying load levels for the TA under combined 

 bending and axial loading. ..................................................................................................... 14

Figure 2.16. Predicted out-of-plane displacement at the center of the panels during combined bending 

 and axial load. ........................................................................................................................ 15

Figure 2.17. Predicted out-of-plane displacement at the center of the axial weld lands during combined 

 bending and axial load. .......................................................................................................... 15

Figure 2.18. Predicted out-of-plane displacement at the dent and buckling initiation site during 

 combined bending and axial load. .......................................................................................... 16
v 

Part 2: Pre-Test Analysis Report – SBKF-P2-CYL-TA02 Test 

Figure 2.1. Analysis coordinate system. ................................................................................................... 18

Figure 2.2. Measure geometric imperfection for TA02. ........................................................................... 19

Figure 2.3. Predicted load-shortening response for the TA under uniform axial loading. ....................... 20

Figure 2.4. Predicted out-of-plane deformation and outer surface strains at varying load levels for the 

 TA under uniform axial loading at 0.20 Pcr. .......................................................................... 21

Figure 2.5. Predicted out-of-plane deformation and outer surface strains at varying load levels for the 

 TA under uniform axial loading at limit load of 554.37 kips. ............................................... 22

Figure 2.6. Predicted out-of-plane displacement at the center of the panels during uniform axial load. . 23

Figure 2.7. Predicted out-of-plane displacement at the center of the axial weld lands during uniform 

 axial load. ............................................................................................................................... 23

Figure 2.8. Predicted buckling mode shape for the TA under combined axial loading and positive 

 bending. .................................................................................................................................. 25

Figure 2.9. Predicted load-shortening response for the TA under combined axial loading and positive 

 bending. .................................................................................................................................. 25

Figure 2.10. Predicted out-of-plane deformation and outer surface strains for the TA under axial 

 loading and positive bending at 0.2 Pcr + 0.3 Mcr. ................................................................. 26

Figure 2.11. Predicted out-of-plane deformation and outer surface strains for the TA under axial 

 loading and positive bending at 0.3 Pcr + 0.45 Mcr. ............................................................... 27

Figure 2.12. Predicted out-of-plane deformation and outer surface strains for the TA under axial 

 loading and positive bending at limit load. ............................................................................ 28

Figure 2.13. Predicted out-of-plane deformation and outer surface strains for the TA under axial 

 loading and positive bending after buckling. ......................................................................... 29

Figure 2.14. Predicted out-of-plane displacement at the center of the panels during combined axial 

 loading and positive bending. ................................................................................................ 30

Figure 2.15. Predicted out-of-plane displacement at the center of the axial weld lands during combined 

 axial loading and positive bending. ........................................................................................ 30

Figure 2.16. Predicted buckling mode shape for the TA under combined axial loading and negative 

 bending. .................................................................................................................................. 31

Figure 2.17. Predicted load-shortening response for the TA under combined axial loading and negative 

 bending. .................................................................................................................................. 31

Figure 2.18. Predicted out-of-plane deformation and outer surface strains for the TA under axial 

 loading and negative bending at 0.2 Pcr  0.3 Mcr. ................................................................. 32

Figure 2.19. Predicted out-of-plane deformation and outer surface strains for the TA under axial 

 loading and negative bending at 0.3 Pcr  0.45 Mcr. ............................................................... 33

Figure 2.20. Predicted out-of-plane deformation and outer surface strains for the TA under axial 

 loading and negative bending at limit load. ........................................................................... 34

Figure 2.21. Predicted out-of-plane deformation and outer surface strains for the TA under axial 

 loading and negative bending after buckling. ........................................................................ 35

Figure 2.22. Predicted out-of-plane displacement at the center of the panels during combined axial 

 loading and negative bending. ................................................................................................ 36

Figure 2.23. Predicted out-of-plane displacement at the center of the axial weld lands during combined 

 axial loading and negative bending. ....................................................................................... 36
vi 

List of Tables 

Part 1: Pre-Test Analysis Report – Test Article 1 SBKF-P2-TR-2008-008 

Table 2.1. Acreage Design for Checkout TA. ............................................................................................ 1

Table 2.2. Linear Buckling Response the Ideal TA Design. ...................................................................... 2

Part 2: Pre-Test Analysis Report – SBKF-P2-CYL-TA02 Test 

Table 2.1. Acreage design for checkout TA. ............................................................................................ 17

Table 2.2. Linear buckling response the ideal TA design. ....................................................................... 18
vii 

Nomenclature 

Acronyms 

Al-Li Aluminum-Lithium 

CxP Constellation Program 

kips Kilopounds (1000 pound force) 

lbm Pounds Mass 

lbs Pounds 

LV Launch Vehicle 

LVDT Linear Variable Differential Transformer 

MSFC Marshall Space Flight Center 

NESC NASA Engineering and Safety Center 

SBKF Shell Buckling Knockdown Factor 

TA Test Article 

TM Technical memorandum 

List of Symbols 

br Ring Spacing 

bs Axial stiffener spacing 

H Total panel thickness 

h Stiffener height 

L Cylinder specimen length 

Mcr Buckling bending moment 

Ncr Running load at buckling 

Pcr Total axial load at buckling

Plimit Total axial load at limit point 

R Radius of Cylinder 

t Skin thickness 

teff Effective orthogrid wall thickness 

tr Thickness of Rings 

ts Axial stiffener thickness 

cr Axial end-shortening at buckling

limit Axial end-shortening at limit point 

cr Average axial strain at buckling 

xx Axial membrane stain 

yy Circumferential membrane strain 
1 

Part 1: Pre-Test Analysis Report – Test Article 1 

1.0 Introduction 

This report summarizes the pre-test analysis predictions for the SBKF-P2-CYL-TA01 shell buckling test 

that was conducted at the Marshall Space Flight Center (MSFC) in support of the Shell Buckling 

Knockdown Factor (SBKF) Project, NASA Engineering and Safety Center (NESC) Assessment #: 07-

010-E. The test article (TA) is an 8-foot-diameter aluminum-lithium (Al-Li) orthogrid cylindrical shell 

with similar design features as that of the proposed Ares-I and Ares-V barrel structures. The testing 

included four sub-critical load sequences, meaning loads that will not cause buckling or failure of the TA, 

and one test to buckling or failure. The load sequences included uniform axial compression loads and 

combined axial compression and bending. In support of the testing effort, detailed structural analyses 

were conducted and the results were used to monitor the behavior of the TA during the testing. A 

summary of predicted results for each of the five load sequences is presented herein. 

2.0 Summary of Results 

The first TA design was intended to be a relatively simple and predictable specimen to be used to verify 

the design methods, experimental setup, loading fixture and testing process in the SBKF test program (see 

Reference 1 for details on the design). The acreage design chosen for the checkout specimen is shown in 

Table 2.1. The skin is relatively thick at 0.100 inch to prevent pocket buckling. The stiffeners were 

chosen to be very short with a small height-to-thickness aspect ratio (h/ts = 3). This resulted in a design 

with a large radius to effective shell wall thickness ratio (R/teff) which would be representative of very 

large launch vehicle (LV) barrel design. 

Table 2.1. Acreage design for checkout TA. 

Dimensions Design 1 Checkout 

t (in) 0.100 

H (in) 0.400 

h (in) 0.300 

bs (in) 4.00 

ts (in) 0.100 

br (in) 4.00 

tr (in) 0.100 

R/teff 230.9 

Areal Weight (lbm/in2) 0.0113 

Analysis results are presented using the coordinate system shown in Figure 2.1. Although the TA is 78 

inches long, it is clamped on each end by attachment rings that extend 4.625 inches from each end of the 

TA. The axial coordinate measurements start from the top edge of the lower attachment ring and the 

circumferential coordinate measurements start from the zero index, which is at the center of Panel A. It is 

important to note that the circumferential coordinate is positive in the clockwise direction when viewed 

from the top (or towards the left when the cylinder is viewed from the outside). 

Table 2.2 shows the buckling loads from a linear eigen analysis for the checkout TA design subjected to 

uniform axial compression. The results include both the predicted values for a simple analysis that 

assumes smeared-stiffener properties in the acreage along with the values for a reinforced design, which 

includes weld lands and reinforced stiffeners adjacent to the axial weld lands. Also shown are the total 

load carried by the cylinder (Pcr) and the average stress resultant (Ncr), along with the end shortening at 

buckling (cr) and the average axial strain at buckling (cr/L). A bending analysis was also performed on 

the TA model and a critical bending moment (Mcr) of 17.883 × 106

 in-lb was calculated. The Pcr and Mcr
2 

values for the reinforced design are used to determine the applied loading of the TA during subcritical 

testing (i.e., initial test loading to load levels that do not cause buckling or failure). 

Figure 2.1. Analysis coordinate system. 

Table 2.2. Linear buckling response the ideal TA design. 

Smeared Reinforced 

Pcr (lb) 669,200 714,020 

Ncr (lb/in) 2219 2368 

cr (in) 0.1279 0.1234 

cr (103) 1.850 1.795 

Mass (lbm) 235.0 266.9 

Detailed measurements of the as-built TA were obtained, giving a mapping of geometric imperfection or 

deviation from an idealized geometrically perfect cylinder, and were incorporated into the finite-element 

analysis of the TA. The measured imperfection for the TA installed in the attachment rings is shown in 

Figure 2.2. Overall, the TA is within 0.1 inch of the nominal geometry. There is some erroneous data 

across the top edge, due to the presence of the attachment ring, but this was filtered out of the data. Unlike 

the imperfection used in the design analysis, this imperfection signature shows little influence by the axial 

weld lands on the overall geometry, and thus indicates the potential for a buckling load very close to the 

predicted Pcr for the perfect cylinder. 
3 

Figure 2.2. Measure geometric imperfection for TA01. 

Testing consisted of applying two types of loading to the TA: uniform axial compression and combined 

bending and axial compression loading in which equal fractions of Pcr and Mcr are applied 

simultaneously. A nonlinear static analysis was performed on the imperfect TA for both of these load 

types up to the buckling limit load. At various load levels a linear eigen analysis was performed to 

determine the predicted buckling mode shape. By using this method, the nonlinear effect caused by the 

geometric imperfection can be observed and the mode shape at the limit load can be used to predict the 

initiation location for the collapse of the cylinder. Finally a nonlinear static analysis combined with a 

transient collapse analysis was performed to simulate the unstable buckling response of the TA under 

uniform axial compression. This allows prediction of the post-buckled response of the TA and the 

remaining load-carrying capability. The finite element model used during the analysis included the load 

introduction cylinders and the load spiders to predict accurately the effects of the test hardware stiffeners 

on the response. 

The predicted limit load for the cylinder under uniform axial loading was 608,530 lbs, which corresponds 

to a knockdown factor of 0.852 (85.2% of the classical linear bifuraction buckling load). The loadshortening response of the cylinder with uniform axial compression is shown in Figure 2.3. The 

prebuckling response of the cylinder is linear and, following collapse, the load is reduced to 

approximately 235,000 lbs. The increase in end shortening during collapse is a result of strain energy in 

the test fixtures and loading structure being released. However, the modeling of the test fixtures and 

loading structure was not exact, so differences in the axial stiffness mean that the end shortening 

following collapse is not an exact prediction, but is qualitatively correct. 
4 

Figure 2.3. Predicted load-shortening response for the TA under uniform axial loading. 

The linear bifurcation buckling mode shapes at various load levels are shown in Figure 2.4. The initial 

unloaded mode shape suggests that buckling will initiate at the axial weld land, but at larger load levels it 

becomes clear that the nonlinear influence of the imperfection will cause buckling to initiate in the 

acreage of Panel A. The out-of-plane deformation predicted by a nonlinear analysis at selected load levels 

is shown in Figure 2.5. An inward deformation can be seen forming near the axial center line of the 

cylinder. At first glance, the imperfection signature does not suggest this behavior at this region, since 

there is no distinct inward imperfection present in this location. However, there are two outward 

imperfection humps on each side of this area, which align with the outward deformation created by the 

axial compression of the cylinder in the presence of the axial weld lands, as shown in the deformation 

results at 0.2 Pcr. As adjacent areas deform outward, the area where instability initiates is driven inward 

until the cylinder collapses. Figures 2.6 and 2.7 show the strain at the cylinder outer surface at varying 

load levels, and the buckling initiation site is the primary area to note. The out-of-plane displacements at 

the linear variable differential transformer (LVDT) locations are shown in Figures 2.8 and 2.9, and the 

out-of-plane displacement at the buckling initiation site is shown in Figure 2.10. The LVDTs at the center 

of Panel A and at the weld lands appear to be the best predictors of the onset of instability. 
5 

Figure 2.4. Predicted buckling mode shapes at varying load levels for the TA under uniform axial 

loading. 
6 

Figure 2.5. Predicted out-of-plane deformation at varying load levels for the TA under uniform axial 

loading. 
7 

Figure 2.6. Predicted axial strain on the outer surface at varying load levels for the TA under uniform 

axial loading. 
8 

Figure 2.7. Predicted circumferential strain on the outer surface at varying load levels for the TA under 

uniform axial loading. 
9 

Figure 2.8. Predicted out-of-plane displacement at the center of the panels during uniform axial load. 

Figure 2.9. Predicted out-of-plane displacement at the center of the axial weld lands during uniform axial 

load. 
10 

Figure 2.10. Predicted out-of-plane displacement at the dent and buckling initiation site during uniform 

axial load. 

The predicted limit load for the cylinder under combined bending and axial loading was 0.85(0.5Pcr + 

0.5Mcr). The load-shortening response of the cylinder with combined bending and axial loading at the 

LVDT locations used during testing is shown in Figure 2.11. LVDT 1 is at 0° where peak compression 

occurs. LVDTs 2, 3 and 4 are at 90°, 180°, and 270°, respectively. The prebuckling response of the 

cylinder is linear. 

The predicted buckling mode shape from an eigen analysis at the limit load (Figure 2.12) shows that 

buckling under combined bending and axial load initiates at the same location as the uniform axial load 

case. The out-of-plane deformation predicted from a nonlinear analysis for selected load levels is shown 

in Figure 2.13. The deformation response of the cylinder is dominated by global bending as expected. 

Figures 2.14 and 2.15 show the strain at the cylinder outer surface at varying load levels. The buckling 

initiation site is the primary area of note. The out-of-plane displacement at the LVDT locations are shown 

in Figures 2.16 and 2.17, and the out-of-plane displacement at the dent and the buckling initiation site are 

shown in Figure 2.18. For this load case only the LVDT at the center of Panel A is a good predictor for 

the onset of instability. 
11 

Figure 2.11. Predicted load-shortening response for the TA under combined bending and axial loading. 

Figure 2.12. Predicted buckling mode shape for the TA under combined bending and axial loading based 

on eigen analysis at the limit load. 
12 

Figure 2.13. Predicted out-of-plane deformation at varying load levels for the TA under combined 

bending and axial loading. 
13 

Figure 2.14. Predicted axial strain at varying load levels for the TA under combined bending and axial 

loading. 
14 

Figure 2.15. Predicted circumferential strain at varying load levels for the TA under combined bending 

and axial loading. 
15 

Figure 2.16. Predicted out-of-plane displacement at the center of the panels during combined bending 

and axial load. 

Figure 2.17. Predicted out-of-plane displacement at the center of the axial weld lands during combined 

bending and axial load. 
16 

Figure 2.18. Predicted out-of-plane displacement at the dent and buckling initiation site during combined 

bending and axial load. 

3.0 References 

1. Thornburgh, R. P.; and Hilburger, M. W.: Design of Orthogrid Cylinder Test Articles for the Shell Buckling 

Knockdown Factor Assessment. NASA/TM-2010-216866, November 2010. 
17 

Part 2: Pre-Test Analysis Report – SBKF-P2-CYL-TA02 Test 

1.0 Introduction 

This report summarizes the pre-test analysis predictions for the SBKF-P2-CYL-TA02 shell buckling test 

that was conducted at the MSFC in support of the SBKF Project, NESC Assessment #: 07-010-E. The TA 

is an 8-foot-diameter Al-Li orthogrid cylindrical shell with similar design features as that of the proposed 

Ares-I and Ares-V barrel structures. The testing included three sub-critical load sequences, meaning loads 

that will not cause buckling or failure of the TA and two tests to buckling or failure. The load sequences 

included uniform axial compression loads and combined axial compression and bending. In support of the 

testing effort, detailed structural analyses were conducted and the results used to monitor the behavior of 

the TA during the testing. A summary of these results is presented herein. 

2.0 Summary of Results 

The second TA, TA02, used the same stiffener design as the first TA, TA01, but was intended to be tested 

to failure with combined bending and axial loading. The TA design was intended to be a relatively simple 

and predictable specimen used to verify the design methods, experimental setup, loading fixture and 

testing process in the SBKF test program. See Reference 1 for more information on the TA02 design. The 

acreage design chosen for the checkout specimen is shown in Table 2.1. The skin was relatively thick at 

0.100 inch to prevent pocket buckling. The stiffeners were chosen to be very short with a small height-tothickness aspect ratio (h/ts = 3). This results in design with a large radius to effective shell wall thickness 

ratio (R/teff) which would be representative of a very large launch vehicle barrel design. 

Table 2.1. Acreage design for checkout TA. 

Dimensions Design 1 Checkout 

t (inch) 0.100 

H (inch) 0.400 

h (inch) 0.300 

bs (inch) 4.00 

ts (inch) 0.100 

br (inch) 4.00 

tr (inch) 0.100 

R/teff 230.9 

Areal Weight (lbm/in2) 0.0113 

Analysis results are presented using the coordinate system shown in Figure 2.1. The TA is 78 inches long 

and was clamped on each end by attachment rings that extended 4.625 inches from each end of the TA. 

The axial coordinate measurements start from the top edge of the lower attachment ring and the 

circumferential coordinate measurements start from the zero index, which is at the center of Panel A. It is 

important to note that the circumferential coordinate was positive in the clockwise direction when viewed 

from the top (or towards the left when the cylinder is viewed from the outside). For this test, bending 

moment was applied about the axis formed by Y = 270o, and positive bending moment was defined such 

that maximum axial compression of the TA occurs at Y = 0o. 

The buckling loads predicted from a linear eigen analysis of the checkout TA design subjected to uniform 

axial compression are shown in Table 2.2. The results include both the predicted values for a simple, 

smeared-stiffener analysis of the acreage along with the values for a reinforced design, which includes 

weld lands and reinforced stiffeners adjacent to the axial weld lands. The total load carried by the cylinder 

(Pcr) and the average stress resultant (Ncr) are shown, along with the end shortening at buckling (cr) and 

the average axial strain at buckling (cr/L). A bending analysis was also performed on the TA design and 
18 

a critical bending moment (Mcr) of 17.883 × 106 in-lb was calculated. The Pcr and Mcr values for the 

reinforced design were used to determine the applied loading of the TA during subcritical testing. 

Figure 2.1. Analysis coordinate system. 

Table 2.2. Linear buckling response the ideal TA design. 

Smeared Reinforced 

Pcr (lb) 669,200 714,020 

Ncr (lb/in) 2219 2368 

cr (inch) 0.1279 0.1234 

cr (103) 1.850 1.795 

Mass (lbm) 235.0 266.9 

Detailed measurements of the as-built TA were obtained, giving a mapping of geometric imperfection or 

deviation from an idealized geometrically perfect cylinder, and were incorporated into the finite-element 

analysis of the TA. The measured imperfection for the TA installed in the attachment rings is shown in 

Figure 2.2. Overall, the TA is within 0.1 inch of the nominal geometry and is very similar to the measured 

geometry of TA01. There was some erroneous data across the top edge, due to the presence of the 

attachment ring, but this was filtered out of the data. Unlike the imperfection used in the design analysis, 

this imperfection signature shows little influence by the axial weld lands on the overall geometry, and 

thus indicates the potential for a buckling load very close to the predicted Pcr for the perfect cylinder. 
19 

Figure 2.2. Measure geometric imperfection for TA02. 

Testing consisted of applying three types of loading to the TA: uniform axial compression and two 

combined bending and axial load cases. For the combine load cases, bending and compression are applied 

in a ratio of 3:2, respectively, with one case using a positive bending moment and the other using a 

negative bending moment. This allows the TA to be tested to failure twice, once with the maximum 

compression occurring at the center of Panel A (0o) and once with the maximum compression occurring at 

the weld land between panels B and C (180o). A nonlinear static analysis was performed on the imperfect 

TA for each of these load cases up to the buckling limit load. At various load levels during the nonlinear 

analysis, a linear eigen analysis was performed to determine the predicted buckling mode shape. By using 

this method, the nonlinear effect caused by the geometric imperfection can be observed and the mode 

shape at the limit load can be used to predict the initiation location for the collapse of the cylinder. 

Finally, a nonlinear static analysis combined with a transient collapse analysis was performed to simulate 

the unstable collapse of the TA under combined bending and axial compression. This allows prediction of 

the post-buckled response of the TA and the remaining load carrying capability. The finite-element model 

used during the analysis included the load introduction cylinders and the load spiders. The modeling 

approach used for this loading structure has been improved, since the pre-test predictions were performed 

for the first TA, TA01, and the model used herein more closely replicates the physics of the load system 

used during the test. 
20 

The predicted limit load for the cylinder under uniform axial loading was 554,370 lbs, which corresponds 

to a knockdown factor of 0.776. The load-shortening response of the cylinder with uniform axial 

compression is shown in Figure 2.3, and the pre-buckling response of the cylinder is very linear. 

Figure 2.3. Predicted load-shortening response for the TA under uniform axial loading. 

The out-of-plane deformation at 0.2 Pcr is shown in Figure 2.4 along with the strain at the cylinder outer 

surface. The out-of-plane deformation and outer surface strains at the limit load of 554.37 kips are shown 

in Figure 2.5. An inward deformation can be seen forming near the mid-length of the cylinder at 160o. 

This location is the predicted buckling initiation site for this TA under uniform axial load. The out-ofplane displacement at the linear variable differential transformer (LVDT) locations to be used during the 

test are shown in Figures 2.6 and 2.7. The LVDTs all show a significant amount of nonlinearity and 

should be good indicators of the onset of instability. 
21 

Figure 2.4. Predicted out-of-plane deformation and outer surface strains for the TA under uniform axial 

loading at 0.20 Pcr. 
22 

Figure 2.5. Predicted out-of-plane deformation and outer surface strains for the TA under uniform axial 

loading at limit load of 554.37 kips. 
23 

Figure 2.6. Predicted out-of-plane displacement at the center of the panels during uniform axial load. 

Figure 2.7. Predicted out-of-plane displacement at the center of the axial weld lands during uniform axial 

load. 
24 

For the combined bending and axial loading cases, an eigen analysis and a nonlinear analysis were first 

performed on the TA without any geometric imperfection included in the model. For the load case with a 

positive bending moment (maximum compression in Panel A), the predicted linear buckling load 

1.050(0.4Pcr + 0.6Mcr), and the resulting mode shape is shown in Figure 2.8. The nonlinear limit load for 

this case was 1.044(0.4Pcr + 0.6Mcr) and the buckling initiated with the same deformation pattern shown 

by the linear eigen mode shape. 

Next, the measured geometric imperfection was included in the model and nonlinear analysis was used to 

predict the expected limit loads, and a transient collapse analysis was performed to simulate the failure. 

The nonlinear limit load for the case with positive bending moment and maximum compression in Panel 

A was 0.8305(0.4Pcr + 0.6Mcr), and the resulting end-shortening response curve is shown in Figure 2.9. 

The pre-buckling response is linear and following buckling the TA is still carrying seventy percent of the 

pre-buckling load. Out-of-plane deformation and outer surface strains are shown for (0.2Pcr + 0.3Mcr), 

(0.3Pcr + 0.45Mcr), limit load and post-buckled in Figures. 2.10-2.13, respectively. These results show an 

inward deformation forming ten inches from the top of the TA at 0o, and it is at this location that buckling 

is predicted to initiate for this load case. The large post-buckled deformation is largely confined to Panel 

A, and the strains are significantly less than the yield strain for Al-Li. Thus, the second load sequence to 

failure should not be significantly influenced by this load case. The radial displacements at the center of 

the panels and the center of the axial weld lands are shown in Figures 2.14 and 2.15. Of these, the LVDT 

at the center of Panel A appears to be the best predictor of the onset of instability. 

The analysis of the TA without any geometric imperfection and with negative bending moment 

(maximum compression along the BC weld land), predicted a linear buckling load 1.062(0.4Pcr + 0.6Mcr), 

and the resulting mode shape is shown in Figure 2.16. The nonlinear limit load for this case was 

1.027(0.4Pcr + 0.6Mcr). 

Next, the measured geometric imperfection was included in the model and nonlinear analysis was used to 

predict the expected test limit loads, and a transient collapse analysis was performed to simulate the 

failure. The nonlinear limit load for the case with positive bending moment and maximum compression in 

Panel A was 0.7919(0.4Pcr + 0.6Mcr), and the resulting end shortening prediction is shown in Figure 2.17. 

The pre-buckling response is linear and following buckling the TA is still carrying seventy percent of the 

pre-buckling load. Out-of-plane deformation and outer surface strains are shown for (0.2Pcr + 0.3Mcr), 

(0.3Pcr + 0.45Mcr), limit load and post-buckled in Figures 2.18-2.21, respectively. These results show an 

inward deformation forming at the center of the TA near 165o adjacent to the weld land, and it is at this 

location that buckling is predicted to initiate for this load case. The radial displacements at the center of 

the panels and the center of the axial weld lands are shown in Figures 2.22 and 2.23. Of these, the LVDT 

at the center of Panel A was the best indicator of the onset of instability. 
25 

Figure 2.8. Predicted buckling mode shape for the TA under combined axial loading and positive 

bending. 

Figure 2.9. Predicted load-shortening response for the TA under combined axial loading and positive 

bending. 
26 

Figure 2.10. Predicted out-of-plane deformation and outer surface strains for the TA under axial loading 

and positive bending at 0.2 Pcr + 0.3 Mcr. 
27 

Figure 2.11. Predicted out-of-plane deformation and outer surface strains for the TA under axial loading 

and positive bending at 0.3 Pcr + 0.45 Mcr. 
28 

Figure 2.12. Predicted out-of-plane deformation and outer surface strains for the TA under axial loading 

and positive bending at limit load. 
29 

Figure 2.13. Predicted out-of-plane deformation and outer surface strains for the TA under axial loading 

and positive bending after buckling. 
30 

Figure 2.14. Predicted out-of-plane displacement at the center of the panels during combined axial 

loading and positive bending. 

Figure 2.15. Predicted out-of-plane displacement at the center of the axial weld lands during combined 

axial loading and positive bending. 
31 

Figure 2.16. Predicted buckling mode shape for the TA under combined axial loading and negative 

bending. 

Figure 2.17. Predicted load-shortening response for the TA under combined axial loading and negative 

bending. 
32 

Figure 2.18. Predicted out-of-plane deformation and outer surface strains for the TA under axial loading 

and negative bending at 0.2 Pcr  0.3 Mcr. 
33 

Figure 2.19. Predicted out-of-plane deformation and outer surface strains for the TA under axial loading 

and negative bending at 0.3 Pcr  0.45 Mcr. 
34 

Figure 2.20. Predicted out-of-plane deformation and outer surface strains for the TA under axial loading 

and negative bending at limit load. 
35 

Figure 2.21. Predicted out-of-plane deformation and outer surface strains for the TA under axial loading 

and negative bending after buckling. 
36 

Figure 2.22. Predicted out-of-plane displacement at the center of the panels during combined axial 

loading and negative bending. 

Figure 2.23. Predicted out-of-plane displacement at the center of the axial weld lands during combined 

axial loading and negative bending. 
37 

3.0 References 

1. Thornburgh, R. P.; and Hilburger, M. W.: Design of Orthogrid Cylinder Test Articles for the Shell Buckling 

Knockdown Factor Assessment. NASA/TM-2010-216866, November 2010. 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Pre-Test Analysis Predictions for the Shell Buckling Knockdown Factor 

Checkout Tests - TA01 and TA02

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Thornburgh, Robert P.; Hilburger, Mark W.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center U.S. Army Research Laboratory

Hampton, VA 23681-2199 Vehicle Technology Directorate

 NASA Langley Research Center

 Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

and U.S. Army Research Laboratory

Adelphi, MD 20783-1145

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-19958

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

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Unclassified -Unlimited

Subject Category - 16 Space Transportation and Safety

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

This report summarizes the pre-test analysis predictions for the SBKF-P2-CYL-TA01 and SBKF-P2-CYL-TA02 shell 

buckling tests conducted at the Marshall Space Flight Center (MSFC) in support of the Shell Buckling Knockdown Factor 

(SBKF) Project, NASA Engineering and Safety Center (NESC) Assessment. The test article (TA) is an 8-foot-diameter 

aluminum-lithium (Al-Li) orthogrid cylindrical shell with similar design features as that of the proposed Ares-I and Ares-V 

barrel structures. In support of the testing effort, detailed structural analyses were conducted and the results were used to 

monitor the behavior of the TA during the testing. A summary of predicted results for each of the five load sequences is 

presented herein.

15. SUBJECT TERMS

Linear variable differential transformer; Shell Buckling Knockdown Factor; Test article; NASA Engineering and Safety 

Center

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47

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(443) 757-5802

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869021.04.07.01.13

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NASA/TM-2011-216875 ARL-TR-5123

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