Validation of the ULSAP Closed-Form Method for Ultimate Strength Analysis of Cross-Stiffened Panels Samuel M. Dippold Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University In partial fulfillment of the requirements for the degree of Master of Science In Ocean Engineering Dr. Owen F. Hughes, Chair Dr. Alan J. Brown Dr. Eric R. Johnson Date June 20, 2005 Blacksburg, Virginia
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Validation of the ULSAP Closed-Form Method for Ultimate Strength Analysis of Cross-Stiffened Panels
Samuel M. Dippold
Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University
In partial fulfillment of the requirements for the degree of
Master of Science In
Ocean Engineering
Dr. Owen F. Hughes, Chair Dr. Alan J. Brown
Dr. Eric R. Johnson
Date June 20, 2005
Blacksburg, Virginia
Validation of the ULSAP Closed-Form Method for Ultimate Strength Analysis of Cross-Stiffened Panels
Samuel M. Dippold
(ABSTRACT)
This thesis presents the results of 67 ABAQUS elasto-plastic Riks ultimate strength
analyses of cross-stiffened panels. These panels cover a wide range of typical geometries.
Uniaxial compression is applied to the panels, and in some cases combined with lateral pressure.
For eight of the panels full-scale experimental results are available, and these verified the
accuracy of the ABAQUS results. The 67 ABAQUS results were then compared to the ultimate
strength predictions from the computer program ULSAP. In all but 10 cases the ULSAP predicted
strength is within 30% of the ABAQUS value, and in all but 4 cases the predicted failure mode
also agrees with that of ABAQUS. In one case the ULSAP predicted ultimate strength is 51%
below the experimental value, and so this case is studied in detail. The discrepancy is found to
be caused by the method which ULSAP uses for panels that experience overall collapse initiated
by beam-column-type failure. The beam-column method program ULTBEAM is used to predict
the ultimate strength of the 61 panels that ULSAP predicts to fail due to overall collapse of the
stiffeners and plating which may or may not be triggered by yielding of the plate-stiffener
combination at the midspan (Mode III or III-1). ULTBEAM is found to give more accurate results
than ULSAP for Mode III or III-1 failure. Future work is recommended to incorporate ULTBEAM
into ULSAP to predict the ultimate strength of panels that fail in Mode III or III-1.
Acknowledgements
I would like to thank my advisor and committee chair Dr. Owen Hughes for all of his
support and guidance over the past two years.
I would also like to thank Dr. Alan Brown and Dr. Eric Johnson for being members of my
advisory committee. In addition, I would like to thank Dr. William Hallauer for being Dr. Johnson’s
proxy.
Finally, I would also like to thank Jason Albright and Dhaval Makhecha for all of their help
with this work.
iii
Table of Contents
LIST OF FIGURES ____________________________________________________________ V
LIST OF TABLES ____________________________________________________________ VI
NOMENCLATURE ___________________________________________________________ VII
5. COMPARISON OF ULTIMATE STRENGTH PREDICTIONS ______________________ 27
5.1. 1½ BAY MODEL RESULTS ____________________________________________________ 27 5.2. SMITH PANEL RESULTS_______________________________________________________ 31 5.3. SMITH PANEL 6 _____________________________________________________________ 33
6. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK _______________ 36
6.1. CONCLUSIONS ______________________________________________________________ 36 6.2. RECOMMENDATIONS FOR FUTURE WORK _________________________________________ 36
APPENDIX A _______________________________________________________________ 38
APPENDIX B _______________________________________________________________ 69
VITA ______________________________________________________________________ 78
iv
List of Figures
Figure 1.1 A three-bay stiffened panel under uniaxial compression .............................................. 1 Figure 1.2 Stiffened panel under uniaxial compression and lateral pressure ................................ 1 Figure 1.3 Cross-section of a plate-stiffener combination.............................................................. 2 Figure 1.4 Mode I - Overall collapse of a cross-stiffened panel ..................................................... 3 Figure 1.5 Mode II - Collapse due to biaxial compression ............................................................. 3 Figure 1.6 Mode III - Beam-column-type collapse.......................................................................... 3 Figure 1.7 Mode III-2 - Local S-shaped mechanism ...................................................................... 4 Figure 1.8 Mode IV - Local buckling of stiffener web ..................................................................... 4 Figure 1.9 Mode V - Stiffener tripping ............................................................................................ 4 Figure 2.1 Symmetry about midspan of middle bay in 3 bay panel ............................................... 5 Figure 2.2 Proportional loading with an unstable response (ABAQUS User's manual)................. 6 Figure 2.3 Idealized elastic-perfectly plastic stress-strain curve .................................................... 7 Figure 2.4 Finite element mesh for 1½ bay model ......................................................................... 8 Figure 2.5 Initial imperfections in the 1½ bay panel models .......................................................... 9 Figure 2.6 Transverse and longitudinal edges of a stiffened panel.............................................. 10 Figure 3.1 Finite element mesh for Smith panel 6........................................................................ 14 Figure 3.2 Initial imperfections in Smith panel models ................................................................. 15 Figure 3.3 Photo of the post collapse condition of Smith panel 6 ................................................ 16 Figure 3.4 Initial Imperfections of Smith Panel 6.......................................................................... 16 Figure 3.5 Residual stress in stiffened panels (Smith, 1975)....................................................... 17 Figure 3.6 LTF - Large Testing Frame (Smith, 1975)................................................................... 19 Figure 3.7 Transverse and longitudinal edges of a stiffened panel.............................................. 20 Figure 4.1 Membrane stress in an orthotropic plate..................................................................... 23 Figure 4.2 Plate induced failure (a) & stiffener induced failure (b) in a beam-column ................. 24 Figure 5.1 Panel vt009 at collapse ............................................................................................... 30 Figure 5.2 Subdivision of cross-section into 'fibres' (Smith, 1992)............................................... 32 Figure 5.3 Subdivision of stiffened panel into elements (Smith, 1992) ........................................ 32 Figure 5.4 Weld-induced residual stress in a stiffened panel (Smith, 1992) ................................ 32 Figure 5.5 Photo of the post collapse condition of Smith panel 6 ................................................ 35 Figure 5.6 ABAQUS results for Smith panel 6 at collapse ........................................................... 35
v
List of Tables
Table 1.1 Modes of Failure (Paik and Thayamblalli, 2003) & (Hughes, 1988) .............................. 2 Table 2.1 Material Properties for 1½ Bay Panels........................................................................... 7 Table 2.2 Elements in 1½ bay finite element model of 3 bay panel............................................... 8 Table 2.3 Boundary Conditions for 1½ Bay Models ..................................................................... 10 Table 2.4 Geometric Properties of 1½ Bay Panels ...................................................................... 11 Table 3.1 Geometric and Material Properties of the Smith Panels .............................................. 13 Table 3.2 Elements in FE Model of Smith Panel 6....................................................................... 14 Table 3.3 Residual Stress in Smith Panels .................................................................................. 18 Table 3.4 Boundary Conditions for Full Panel ABAQUS Model.................................................. 19 Table 5.1 1½ Bay Model ABAQUS and ULSAP Results ............................................................. 27 Table 5.2 Smith Panel Results ..................................................................................................... 31 Table 5.3 ULTBEAM vs. ULSAP for Smith panels not failing by Mode III or III-1 ........................ 33
vi
Nomenclature
Geometric Properties a length of one bay; spacing between adjacent transverse frames
Am amplitude of the added lateral deflection due to load
A0m amplitude of the initial deflection
Asx cross-sectional area of longitudinal stiffeners
Asy cross-sectional area of transverse frames
b spacing between adjacent longitudinal stiffeners
B breadth of stiffened panel
bf flange breadth
hw web height
M0 initial bending moment
ns number of longitudinal stiffeners
nf number of transverse frames
t plate thickness
tf flange thickness
tw web thickness
teq equivalent plate thickness
wos initial deflection of a stiffener
wosm maximum initial deflection of a stiffener
wot initial sideways tilt of a stiffener
wotm maximum initial sideways tilt of a stiffener
wopl initial deflection of the plating between longitudinal stiffeners
woplm maximum initial deflection of the plating between longitudinal stiffeners
Z section modulus
0δ initial deflection
∆ total eccentricity
η eccentricity ratio
λ column slenderness parameter
µ dead load bending term
ρx correction factor to account for variation in the true deflection pattern from the assumed
sinusoidal pattern
vii
Material Properties and Strength Parameters E Young’s modulus
Ex effective Young’s modulus in the x direction
Ey effective Young’s modulus in the y direction
p applied lateral pressure
ν Poisson’s ratio
σx applied longitudinal compressive stress
σY yield stress
σYp yield stress of plating
σYs yield stress of longitudinal stiffeners
σYf yield stress of transverse frames
σYeq equivalent yield stress of plating, longitudinal stiffeners, and transverse frames
σrc compressive residual stress
σYC yield stress of plating under compression due to residual stress
σYT yield stress of plating under tension due to residual stress
σYT equivalent yield stress for orthogonally stiffened panels
σx applied longitudinal compressive stress
viii
1. Introduction
Modern ships encounter extreme loads while performing daily tasks and must have
adequate structural strength. In order to provide the necessary strength, while minimizing cost,
most ships today are constructed using stiffened panels. Stiffened panels are generally
comprised of a plate, longitudinal stiffeners, and transverse frames. Each section between
transverse frames is referred to as a bay. For example, Figure 1.1 is a three-bay stiffened panel.
Although there are many types of stiffeners, T-shaped stiffeners and frames will be used in this
thesis and are illustrated in Figure 1.3.
Stiffened panels are designed to support axial loads as well as lateral pressure as shown
in Figure 1.1 and Figure 1.2. For the purposes of this thesis, stiffened panels will be analyzed
using uniaxial compression in the longitudinal direction and in some cases combined with lateral
pressure.
Figure 1.1 A three-bay stiffened panel under uniaxial compression
Figure 1.2 Stiffened panel under uniaxial compression and lateral pressure
1
Figure 1.3 Cross-section of a plate-stiffener combination
Stiffener and frame scantlings (geometric properties) and spacings have a great influence
on the strength of a panel as well as the way in which the panel fails. Collapse behavior of
stiffened panels can be divided into six different modes (Paik and Thayamblalli, 2003). A seventh
mode (III-2) was added from (Hughes, 1988) to help describe a mode of failure that is often
mistaken for tripping. These modes are listed in Table 1.1 and are shown in Figure 1.4–Figure
1.9.
Table 1.1 Modes of Failure (Paik and Thayamblalli, 2003) & (Hughes, 1988)
Mode Type Description
I overall collapse plating and stiffeners collapse together as a unit
II biaxial compression collapse plate-stiffener intersection yields at the corners of plating between stiffeners
III beam-column-type collapse plate-stiffener combination yields at midspan
III-1 overall collapse initiated by beam-column-type collapse
plate-stiffener combination yields at midspan and leads to plating and stiffeners collapsing together as a unit
III-2 local S-shaped mechanism a local plastic mechanism forms in the flange causing a local sideways deflection due to flange yielding
IV local buckling of stiffener web stiffened panel reaches ultimate strength immediately after stiffener web buckles locally
V Stiffener tripping stiffened panel fails immediately after lateral-torsional buckling (tripping) of stiffeners
2
Figure 1.4 Mode I - Overall collapse of a cross-stiffened panel
Figure 1.5 Mode II - Collapse due to biaxial compression
Figure 1.6 Mode III - Beam-column-type collapse
3
Figure 1.7 Mode III-2 - Local S-shaped mechanism
Figure 1.8 Mode IV - Local buckling of stiffener web
Figure 1.9 Mode V - Stiffener tripping
4
2. 1½ Bay ABAQUS Model for Ultimate Strength Analysis of 3 Bay Panel
(Ghosh, 2003) determined that in inelastic analysis a 1 bay panel model can be
misleading. Axial compression causes a panel to deflect upward and downward in alternating
bays. A bay with a downward deflection will have stiffener-induced failure while a bay with an
upward deflection will have plate-induced failure. A multi-bay panel with equal upward and
downward deflections will have stiffener-induced failure (Chen, 2003). Modeling only 1 bay can
be misleading based on the fact that the analysis may indicate plate-induced failure due to the
initial eccentricity. A 3 bay model incorporates both upward and downward deflections and is
therefore more suitable for this type of analysis. Moreover, transverse frames cannot merely be
modeled as a simply supported loaded edge as the actual boundary conditions at a frame are
between simply supported and clamped boundary conditions. This further demonstrates the
need for a 3 bay model.
Symmetry about the midspan of the middle bay of a 3 bay model can be used to
minimize the complexity of the analysis thereby reducing the time necessary to generate results.
This symmetry results in a 1½ bay model, as shown in Figure 2.1
Figure 2.1 Symmetry about midspan of middle bay in 3 bay panel
The ABAQUS analysis of the 1½ bay panel models was done following the same
procedure outlined in (Ghosh, 2003). Uniaxial compression in the direction of the longitudinal
stiffeners was applied to the model as concentrated nodal forces. A “dead load” was applied to
the model before a “live load” was applied during the Riks analysis.
5
2.1. ABAQUS – Modified Riks Analysis
The finite element analysis (FEA) program ABAQUS was used in order to perform
inelastic analyses on stiffened panels. More specifically, a static analysis was done in ABAQUS
using the modified Riks method (ABAQUS, 2002). This method is valid for cases where the load
magnitude is proportional to a single scalar parameter. This scalar, λ , is known as the load
proportionality factor. The current loading on the model, , can be determined using the
following equation:
totalP
( )00 PPPP reftotal −+= λ
Here, is the dead load and is the reference load vector. 0P refP
The modified Riks method is also capable of providing a solution for cases with unstable
responses. This type of response is shown in Figure 2.2. This capability was unnecessary in all
but one of the ABAQUS analyses evaluated for this thesis.
Figure 2.2 Proportional loading with an unstable response (ABAQUS, 2002)
2.2. Material Properties
The stiffened panels analyzed using the 1½ bay models had material properties as
shown in Table 2.1.
6
Table 2.1 Material Properties for 1½ Bay Panels
Material Mild Steel
Young’s Modulus (E) 205800 MPa
Poisson’s Ratio (ν ) 0.3
Yield Stress ( Yσ ) 352.8 MPa
The ABAQUS models incorporated an idealized elastic-perfectly plastic stress-strain
The results of the 1½ bay models are shown below in Table 5.1. Plots of the panels at
collapse are shown in Appendix A.
Table 5.1 1½ Bay Model ABAQUS and ULSAP Results
Panel No.
Y
ABQult
σσ ,
Y
ULSAPult
σσ ,
ABQult
ULSAPult
,
,
σσ
Y
ULTBEAMult
σσ ,
ABQult
ULTBEAMult
,
,
σσ
ABAQUS Failure Mode
ULSAP Failure Mode
vt001 0.521 0.395 0.757 0.548 1.052 III-1 III or III-1 vt002 0.675 0.526 0.780 0.684 1.013 III-1 III or III-1 vt003 0.780 0.609 0.780 0.816 1.046 III-1 III or III-1 vt004 0.515 0.226 0.439 0.513 0.995 III-1 III or III-1 vt005 0.528 0.288 0.546 0.530 1.005 III-1 III or III-1 vt006 0.585 0.427 0.730 0.601 1.027 III-1 III or III-1 vt007 0.664 0.528 0.796 0.670 1.009 III-1 III or III-1 vt008 0.592 0.425 0.717 0.628 1.061 III-1 III or III-1 vt009 0.684 0.486 0.711 0.723 1.057 III-1 III or III-1 vt010 0.828 0.593 0.716 0.910 1.098 III-1 III or III-1 vt011 0.892 0.656 0.736 0.914 1.025 III-1 III or III-1 vt012 0.709 0.872 1.230 0.849 1.198 III III or III-1 vt013 0.810 0.773 0.954 0.896 1.106 III III or III-1 vt014 0.637 0.607 0.953 0.764 1.199 III-1 III or III-1 vt015 0.545 0.520 0.954 0.694 1.273 III III or III-1 vt016 0.682 0.789 1.157 ⎯ ⎯ IV IV vt017 0.705 0.688 0.975 0.977 1.385 III III or III-1 vt018 0.715 0.690 0.965 0.827 1.157 III III or III-1 vt019 0.511 0.266 0.520 0.620 1.212 III-1 III or III-1 vt020 0.528 0.348 0.658 0.654 1.239 III-1 III or III-1
27
1½ Bay Model ABAQUS and ULSAP Results
Panel No.
Y
ABQult
σσ ,
Y
ULSAPult
σσ ,
ABQult
ULSAPult
,
,
σσ
Y
ULTBEAMult
σσ ,
ABQult
ULTBEAMult
,
,
σσ
ABAQUS Failure Mode
ULSAP Failure Mode
vt021 0.585 0.537 0.918 0.761 1.301 III-1 III or III-1 vt022 0.703 0.670 0.953 0.844 1.200 III-1 III or III-1 vt023 0.467 0.404 0.864 0.568 1.214 III-1 III or III-1 vt024 0.639 0.590 0.924 0.752 1.177 III-1 III or III-1 vt025 0.717 0.665 0.928 0.822 1.147 III-1 III or III-1 vt026 0.808 0.770 0.952 0.962 1.190 III III or III-1 vt027 0.831 0.819 0.986 0.943 1.135 III III or III-1 vt028 0.760 0.609 0.801 0.816 1.073 III III or III-1 vt029 0.531 0.395 0.743 0.548 1.033 III III or III-1 vt030 0.661 0.526 0.796 0.684 1.034 III III or III-1 vt031 0.462 0.325 0.704 0.494 1.068 III-1 III or III-1 vt032 0.435 0.254 0.584 0.445 1.023 III-1 III or III-1 vt033 0.807 0.652 0.808 0.928 1.150 III III or III-1 vt034 0.508 0.226 0.446 0.513 1.010 III-1 III or III-1 vt035 0.527 0.288 0.547 0.530 1.006 III-1 III or III-1 vt036 0.585 0.427 0.730 0.601 1.027 III-1 III or III-1 vt037 0.660 0.528 0.800 0.670 1.015 III-1 III or III-1 vt038 0.583 0.423 0.725 0.628 1.077 III-1 III or III-1 vt039 0.527 0.485 0.919 0.723 1.371 III-1 III or III-1 vt040 0.763 0.592 0.775 0.736 0.964 III III or III-1 vt041 0.796 0.655 0.823 0.914 1.148 III III or III-1 vt042 0.542 0.520 0.959 0.694 1.280 III III or III-1 vt043 0.691 0.690 0.998 0.827 1.197 III III or III-1 vt044 0.778 0.773 0.994 0.896 1.151 III III or III-1 vt045 0.793 0.829 1.046 0.900 1.135 III III or III-1 vt046 0.644 0.526 0.817 0.684 1.061 III III or III-1 vt047 0.735 0.609 0.828 0.816 1.110 III III or III-1 vt048 0.513 0.395 0.769 0.548 1.069 III III or III-1 vt049 0.457 0.325 0.712 0.494 1.080 III-1 III or III-1 vt050 0.420 0.254 0.605 0.445 1.060 III-1 III or III-1 vt051 0.767 0.652 0.850 0.928 1.210 III-1 III or III-1 vt052 0.483 0.226 0.468 0.513 1.060 III III or III-1 vt053 0.511 0.288 0.565 0.530 1.039 III-1 III or III-1 vt054 0.578 0.427 0.739 0.601 1.039 III-1 III or III-1 vt055 0.653 0.528 0.808 0.670 1.025 III1 III or III-1 vt056 0.564 0.421 0.747 0.628 1.114 III-1 III or III-1 vt057 0.627 0.483 0.771 0.723 1.154 III-1 III or III-1 vt058 0.766 0.591 0.772 0.910 1.188 III III or III-1 vt059 0.738 0.654 0.887 0.914 1.238 III-1 III or III-1
Mean: 0.799 Mean: 1.116 COV: 0.206 COV: 0.087
28
Table 5.1 shows the ABAQUS, ULSAP, and ULTBEAM results for the 1½ bay panel
models described in Section 2. These results indicate that ULSAP generally gives fairly good,
although slightly conservative, predictions for the ultimate strength of stiffened panels. Analyzing
the results further shows that ULSAP predictions for panels with medium to large stiffeners are
more accurate than predictions for panels with small stiffeners.
ULSAP does a good job predicting the mode of failure of the panels as well. All 59
panels in this series feature either beam-column-type failure or overall buckling triggered by
beam-column-type yield. ULSAP predicts all but one of these panels to fail either in a pure Mode
III, beam-column-type failure, or a combined (III-1) failure, which means overall (Mode I) collapse
triggered by a Mode III beam-column yield. Figure 5.1 shows one of the panels in this series with
combined beam-column failure and overall collapse. Yielding occurs in the web and flange of the
longitudinal stiffeners in the middle bay due to compression from the downward deflection. The
flange in the end bay is also yielding due to tension from the upward deflection. The failure of this
panel is very similar to beam-column stiffener-induced failure shown in Figure 4.2 (b). It is
important to note that because von Mises stress is being plotted, the sign of the stress cannot be
used to determine if a region is in tension or compression. Instead, deflections can be used to
establish tension and compression regions.
For the panels ULSAP predicts to fail by Mode III or III-1, ULTBEAM was also used to
predict the ultimate strength. ULTBEAM ultimate strength predictions shown in Table 5.1
correspond very well with the results given by the ABAQUS analyses. The error in the ULTBEAM
results is less than 60% of the error in the ULSAP results. Also, the coefficient of variation of the
ULTBEAM results is less than half of that of ULSAP.
29
Figure 5.1 Panel vt009 at collapse
30
5.2. Smith Panel Results
The results of the analyses of the Smith Panels are shown in Table 5.2. Plots of the panels
at collapse are shown in Appendix B.
Table 5.2 Smith Panel Results
Panel No. Y
EXPult
σσ ,
Y
SFEAult
σσ ,
EXPult
SFEAult
,
,
σσ
Y
ABQult
σσ ,
EXPult
ABQult
,
,
σσ
Y
ULSAPult
σσ ,
EXPult
ULSAPult
,
,
σσ
Y
ULTBEAMult
σσ ,
EXPult
ULTBEAMult
,
,
σσ Exp.
Collapse Mode
ABAQUS Collapse
Mode
ULSAP Collapse
Mode
1a 0.76 0.69 0.908 0.858 1.128 0.762 1.003 ⎯ ⎯ V V IV 1b 0.73 0.57 0.781 0.718 0.984 0.571 0.782 ⎯ ⎯ V V II 2a 0.91 0.81 0.890 0.960 1.054 0.816 0.897 0.923 1.014 IV V & III-2 III or III-1 2b 0.83 0.82 0.988 0.940 1.132 0.841 1.013 ⎯ ⎯ IV V & III-2 V 3a 0.69 0.63 0.913 0.755 1.094 0.589 0.854 0.763 1.105 IV III-2 III or III-1 3b 0.61 0.60 0.984 0.701 1.149 0.609 0.998 ⎯ ⎯ IV & V V & III-2 V 5 0.72 0.55 0.764 0.770 1.069 0.549 0.763 ⎯ ⎯ IV & V V & III-2 V 6 0.49 ⎯ ⎯ 0.554 1.131 0.238 0.486 0.410 0.837 I III-1 III or III-1
(Smith, 1992) is the fourth of a series of papers in the same series as (Smith, 1975). In
this paper, a computer program was developed to analyze the collapse and post-collapse
behavior of stiffened panels. This program was used to analyze the series of panels that was
constructed and tested in (Smith, 1975).
A beam-column finite element model was used to analyze the panels under the
assumption that the panels contained a large number of longitudinal stiffeners that behaved
identically. The model contained one stiffener-plate combination as shown in Figure 5.2, and
represented two adjacent bays. Each bay was assumed to be symmetric about a central plane,
so only half of the interframe span was modeled for each bay as shown in Figure 5.3. Boundary
conditions were applied to the model instead of adding physical transverse frames. These
frames were assumed to be flexurally rigid but torsionally weak and therefore simple support
boundary conditions were used. The boundary conditions, and the assumption of a center plane
of symmetry in the interframe spans, mean that this model actually represents an infinitely long
structure that repeats every two bays.
31
Figure 5.2 Subdivision of cross-section into 'fibres' (Smith, 1992)
Figure 5.3 Subdivision of stiffened panel into elements (Smith, 1992)
Residual stress was added to the FE model as shown in Figure 5.4. The yield stress of
the plating and stiffeners was modified to account for the presence of compressive and tensile
stresses due to the weld-induced residual stresses. This method is similar to the method outlined
in Section 3.4, with the addition of taking residual stress in the web of the stiffener into account.
The results from the FE analyses in (Smith, 1992) are shown in Table 5.2 as σult,SFEA.
Figure 5.4 Weld-induced residual stress in a stiffened panel (Smith, 1992)
ULSAP ultimate strength results are shown in Table 5.2. The ULSAP results have good
agreement with the experimental results for the majority of the Smith panels analyzed. The
32
prediction of failure mode for the Smith panels is acceptable, although the mode is not predicted
correctly in a few cases.
ULTBEAM results for the Smith panels predicted to fail by Mode III or III-1 failure by
ULSAP are shown in Table 5.2. The table clearly shows that ULTBEAM gives more accurate
ultimate strength predictions for Mode III or III-1 failure than ULSAP.
ULTBEAM was also used to find the ultimate strength of the Smith panels that were not
predicted to fail by Mode III or III-1 by ULSAP. These results are shown in Table 5.3. Since
ULSAP predicts a different mode of failure, it is expected that ULTBEAM will predict a higher
ultimate strength for these cases. For all but one of the panels ULTBEAM does predict a higher
ULTIMATE strength than ULSAP. For the case in which ULTBEAM is lower than ULSAP, the
values given by the two programs are virtually identical.
Table 5.3 ULTBEAM vs. ULSAP for Smith panels not failing by Mode III or III-1