ship hull girders unstiffened plates

SSC-217
COMPRESSIVE
STRENGTH
OF
SHIP HULL GIRDERS
PART I
UNSTIFFENED PLATES
This document has been approved
for public release and sale; its
distribution
is unlimited.
..,
SHIP STRUCTURE
COMMITTEE
1970
—
-.
_..
----
.
SHIP
STRUCTURE
COMMITTEE
AN INTERAGENCY ADVISORY
COMMITTEE DEDICATED TO IMPROVING
THE STRUCTURE OF SHIPS
MEMBER AGENCIES:
ADDRESSCORRESPONDENCETd:
LINITED STATESCOAST GUARD
SECRETARY
NAVAL S}{IP SYSTEMS COMMAND
SHIP STRUCTURE COMMITTEE
MILITARY SEALIFT COMMAND
U.S. COAST GUARD HEADQUARTERS
WASHINGTON, D.C. 20591
MARITIME ADMINISTRATION
AMERICAN BLIREAU OF SHIPPING
*
1970
Dear
Sir:
The
interest
tural
been
Ship
in
Structure
ultimate
strength
In connection
components.
sponsored
investigating
structural
models
dinal,
transverse
The
reported
Committee
the
results
the
has
a continuing
of ship hull
strucwith
this,
research
strength
of
under various
combinations
and normal
loads.
of
the
first
phase
of
this
has
small
of
longitu–
project
are
herein.
Sincerely,
W.
F.-RE&
Rear
Chairman,
—
111
Admiral,
—
Ship
——.—
U.S.
Coast
.Structure
.- -
Guard
Committee
.—
.
.
I
SSC-217
Technical Report
on
Project SR-193, “Small Hull Girder Model”
COMPRESSIVE STRENGTH OF SHIP HULL GIRDERS
PART I
UNSTIFFENED PLATES
by
H. Becker, R. Goldman, J. Pazerycki
Mithras
under
Department of the Navy
Naval Ship Engineering Center
Contract No. NOO024-69-C-5413
document has been appwved
fop public ~eleaze and saZe;
its dist~ibution is unlimited.
ThLs
U.S. Coast Guard Headquarters
Washington, D.C.
1970
ABSTRACT
This
is Part
the compressive
fened
plates
Three
(to account
ence
strength
while
1.
areas
of normal
Tests
pres sure
plates
Hypotheses
4.
have
5.
were
a negligible
of plates
, which
Ref.
The
The
tion
of plate
well
7.
strength,
-
up to 11 psi
indications
strength
presented
in
However,
pressure
reduction
in biaxial
similar
the
stress
in plate
with
established
that
control
Furthermore,
and were found
demonstrated
strength
of plates
to exceed
mass
of more
recent
data.
ii
older
the actual
the weldof the weld-
stress
field
measured
the material
design
be optimistic
and
b/t.
knowledge
were
(Ref.
propor-
with b/t
predicting
residual
and is
plates
although
decreasing
stresses
may
decrease
from
the
that the
axial
scale
for
strength
found
re suits
affecting
= 30,
of weld-
It was
on large
at b/t
rapidly
strength
the influence
strength-
should
was
= 90.
strength.
experimental
tests
that
in steels
was
for b/t
predicting
on plate
current
showed
and biaxial
reduction
for
the
.
50.
A, foundation
It was
inves
with
predictions
pressure
a moderate
induced
centerlines
column
= 30 and
increases
the plate.
for
the
the biaxial
agreement
transverse
residual
ing parameters
this
for
with
with
loss
preceded
is true
stresses
vanish
residual
with
on the longitudinal
with
developed
theory
essentially
6.
same
was
2).
strength
agrees
theoretical
that normal
agrees
residual
in agreement
on
is applied
determining
on wide
with
= 70 and a 40 percent
to correlate
Data
project.
loading
in general
influence
for b/t
induced
for
are
conducted
to induce
A theory
this
that
sea),
and the influ-
result
Study
evolved
agree
demonstrated
for b/t
This
-
strength
by the
in the longitudinal
50.
unstif
data.
exerts
strengths
biaxial
induced
membrane
They
.
R was
observed
covers
by welding.
during
reduction
been
of which
1.
are
into
1).
experimental
results
Part
on strength,
induced
30 and
of plates
Experiments
strength
loadings
transverse
‘
(R.ef.
strength
3.
girder
in the Feasibility
tigation
the
This
plates.
obtained
a large
with b/t
prediction
girders.
stresses
when
of investigation
stiffened
loadings
were
reveal
on a year
membrane
problems
of a plate
2.
cover
of Hull
of residual
to these
report
of ship hull
H will
the transverse
on strength
solutions
Part
problem
for
the influence
I of a two-part
chart
in
at weld
yield.
for
compared
uni to the
CONTENTS
Page
INTRODUCTION. . . . . . . . . . . . .
.
STABILITY THEORIES AND HYPOTHESES
SPEC MEN CHARACTERISTICS.
. . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.1
1
.
.2
.
.15
LOAD APPLICATION DEVICES. . . . .
.
.
.
.
.
.
.
.
.
.
.18
DATA ACQUISITION.
.
.
.
.
.
.
.
.
.
.
.24
SUMMARY OF EXPERIMENTAL DATA. . .
.
.
.
.
.27
RESIDUAL STRESS.
.
.
. . . . . . .
. . . .
.
.
.
.
.
.
.
.
.
.
.30
.
.
.
.
.
.
,
.
.
DISCUSSION OF UNIAXIA , COMPRESSION DATA .
.
.
.
.
.
.
.
.
.
DISCUSSION OF BIAXIAL COMPRESSION DATA.
.
.
.
.
.
.
.
.
.
EFFECT OF NORMAL PRESSURE . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.54
.
.
.
.
.
.
.
.
.58
.
.
.
.
.
.
.59
.
.
.
.
.60
CONCLUSIONS.
. . . . . . . . . . . . .
RECOMMENDATIONS
REFERENCES.
.
. . . . . . . . . . . . .
.
.
. . . . . . . . . . . . . . .
.
.
. . .
111
.
.
.
.38
.45
NOM.ENGLATIJRE
Sym
bols
a
length
b
width
b
of plate,
in.
of plate,
in.
(outside
effective
width
of equivalent
D
bending
stiffness
of plate,
E
Young’
s modulus
secant
and tangent
e
E
s’
Et
F
(t/b )(E/cry)
g
multiplier
h
x
k
of tube)
flange,
in.
Et3/[12(1
(1 msi
moduli,
–V2)],
= 106
in-lb.
psi)
msi
1/2
converting
number
0tome
Cy
of effective
biaxial
k
, msi
dimensions
transverse
flanges
in a plate
at
failure
longitudinal
buckling
transverse
coefficient
buckling
coefficient
Y
multiplier
1
width
for
of weld
centerline,
number
m
N
x
N
converting
tension
plate
stress
x
P
(t) to effective
on one
side
of weld
in.
of longitudinal
plate
longitudinal
plate
transverse
half
loading,
waves
tox’
loading,
tu
Y
P
thickness
region
in buckled
plate
lb/in.
= O. 707
Py/a,
lb/in.
Y
force
applied
longitudinally
force
applied
diagonally
to tube,
transverse
lb.
to tube,
lb.
Y
‘2
equivalent
at yield,
fore e developable
by pair
lb.
2betu
CY ‘
P
-..
pressure
acting
normql
Iv
to plate,
psi
of effective
flanges
s
parameter
in theoretical
relation
for
uniaxial
longitudinal
strength
t
thickness
v
shear
w
deflection
w
of plate,
force
residual
normal
central
o
in
in.
longitudinal
Y
transverse
c!
effectiveness
E
strain
T
plasticity
v
Pois
Ci
stress,
normal
coordinate
factor
reduction
lb,
plane
of plate,
to prebuckling
of plate,
coordinate
sonf
field,
to prebuckling
deflection
x
stress
for
in.
in.
residual
factor
of plate,
in.
of plate,
for
plane
in.
stresses
inelastic
buckling
s ratio
ksi
Subscripts
e
along
r
residual,
u
ultimate
x,
y,
z
cr
Cy
Combined
edge
of plate
or
coordinate
(also
related
to
elastic
when
residual
referring
to
v )
stress
directions
critical,
or buckling
compressive
yield
always
identified
subscripts
may
(in this
as
be
report
compressive
formed
x cr
x- direction
(or
longitudinal)
w
y- direction
(or
transverse)
from
a reference
to yield
yield)
the
critical
ultimate
above.
For
or buckling
example:
is
SHIP STRUCTURE COMMITTEE
The SHIP STRUCTURE COMMITTEE is constituted to prosecute a research
program to improve the hull structures of ships by an extension of knowledge
pertaining to design, materials and methods of fabrication.
RADM W. F. Rea, III, USCG, Chairman
Chief, Office of Merchant Marine Safety
U. S. Coast Guard Headquarters
Capt. J. E. Rasmussen, USN
Naval Ship Engineering Center
Prince Georges ’ Center Building
Capt. T. J. Banvard, USN
Maintenance and Repair Officer
Military Sealift Command
Mr. E. S. Dillon
Chief
Office of Ship Construction
Maritime Administration
Mr. C. J. L. Schoefer, Vice President
American Bureau of Shipping
SHIP STRUCTURE SUBCOMMITTEE
The SHIP STRUCTURE SUBCOMMITTEE acts for the Ship Structure Committee
on technical matters by providing technical coordination for the determination
of goals and objectives of the program, and by evaluating and interpreting the
results in terms of ship structural design, construction and operation.
NAVAL SHIP ENGINEERING CENTER
U. S. COAST GUARD
Mr.
Mr.
Mr.
Mr.
Mr.
LCDR C. S. Loosmore, USCG - Secretary
CDR C. R. Thompson, USCG - Member
CDR J. W. K!me, USCG - Alternate
CDR J. L. Coburn - Alternate
P.
J.
G.
H.
I.
M. Palermo - Chairman
B. O’Brien - Contract Administrator
Sorkin - Member
S. Sayre - Alternate
Fioriti - Alternate
NATIONAL ACADEMY OF SCIENCES
MARITIME ADMINISTRATION
Mr.
Mr.
Mr.
Mr.
F. Dashnaw
A. Maillar
R. Falls Raymond F,
- Member
- Member
Alternate
Coombs - Alternate
Mr. R. W. Rumke, Liaison
Prof. R. A. Yagle, Liaison
SOCIETY OF NAVAL ARCHITECTS & MARINE
ENGINEERS
AMERICAN BUREAU OF SHIPPING
Mr. T. M. Buermann, Liaison
Mr. S. G. Stiansen - Member
Mr. F. J. Crum - Member
AMERICAN IRON AND STEEL INSTITUTE
OFFICE OF NAVAL RESEARCH
Mr. J. M. Crowley - Member
Dr. W. G. Rauch - Alternate
NAVAL SHIP RESEARCH & DEVELOPMENT CENTER
Mr. J. R. Lecron, Liaison
BRITISH NAVY STAFF
Dr. V. Flint, Liaison
CDR P. H. H. Ablett, RCNC, Liaison
Mr. A. B. Stavovy - Alternate
WELDING RESEARCH COUNCIL
MILITARY SEALIFT COMMAND
Mr. R. R. Askren - Member
Lt. J. G. T. E. Koster, USN, - Member
—.
Mr. K. H. Koopman, Liaison
Mr. C. Larson, Liaison
INTRODUCTION
Aims
of the
The
tity
Proiect
purpose
of the
of experimental
data
under
various
transverse
rnore,
combinations
membrane
it is
with
the
plates
edge
ultimate
of square
load
the
structural
stability
ual
stress
studies
the
current
State
of the
this
retiew
in the
accomplistients
their
The
recent
results
test
current
are
reported
been
on biaxial
the
there
was
should
across
The
would
exist
be
concern-.
architecture.
is
no scale
In
factor
demonstrated
, therefore,
aims
presented
status,
of the
resulting
in
in the
resid-
it is felt
that
project.
in Table
inves
A resume
appears
plates
many
of the
in the
art
1.
The
are
indi–
specific
summary
(Ref.
of
Z ) provide
an
Furthermore,
and thereby
of the
of the
tigatio~,
information.
on large
for
state
appears
and Ractliffe
available
on stability
1 ) of the
this
table.
studies
of Dwight
to the
from
in the
current
obtained
effects
(Ref.
A. summary
positions
re .mlts
provide
studies
a direct
performed
in
effort.
Experimental
have
doubt
considerations
began.
input
were
of scale
the
continuity
in a ship.
bottom
to naval
1 that
This
satisfied
was
of the
report.
irnpo rtant
stiffened
results
.
The
in which
investigation.
have
by X at several
this
of the
investigation
advancements
cated
data
Art
A, detailed
before
),
l%rther-
experimental
of plates
little
out in Ref.
of these
studies
(N
(p).
of ways
compression.
the behavior
experiments
On the basis
of a number
and therefore
of this
r plates
loading
pressure
the
quan.
a large.
of rectangular
membrane
of a longitudinally
pointed
to obtain
to support
uniaxial
applicability
it was
was
strength
and normal
is one
simulates
in the tubes
direct
addition,
),
pro~ect
tubes
behavior
tests
.
under
of the tube
reproduced
ing
of this
can be tested
each
(N
explanations
use
tube
of longitudinal
loading
intent
theoretical
The
square
on the ultimate
here
seen
data
for
on biaxial
the
before.
first
compression
time
In addition,
compression
strength
.
No test
strength
results
the influence
was
examined
presumably
on this
problem
.pres sure
of normal
experimentally.
Terminology
used
are
in this report
synonymous.
to identify
ilBucklingll and IIcriticalll
Several
from
state
in accordance
with
the flat
terms
to the bent
of instability.
sharp.
,:.’..
are
For
edge-
In actuality,
pattern
begins
uration
commonly
supported
it marks
to form
and
termed
flat
a load
starts
plates
range
to deepen
‘la buckle!
1.
They
instability.
refer
the
this
to the
classical
change
is
in which
a visible
into
geometric
the
change
notions
seldom
wave
config-
Table I.
Status of Theory and Experiment on Pertinentl
Features of Plate Buckling and Strength Data
Feature
Quantity
Theory
Experiment
Uniaxial
Comp.
‘c r
Extensive
Extensive
Uu
Yes
Yes
Biaxial
Cornp.
‘cr
Yes
No
Uu
No X
No X
Uniaxial
Comp.
‘c r
Yes
Yes
~u
No
No X
No
No
No
No X
Zero
Pressure
Finite
Pressure
Biaxial
Comp.
I
Effects
1
Yes
of Residual
- Data
data .
They
this
to the upper
may
refer
report
The
ing upon
is
ude
extreme
preceding
of the upper
existence
of these
a state
descriptor.
three
may
carrying
terms
is
be either
Yes
X
- No published
synonyms
capability
confined
carrying
capacity
numerical
which
previous
per-
of a structure.
structure.
to test
In
values.
or nouns,
, however,
and is not a test
of an associated
of the
adjectives
“Strength”
structure,
of load
are
or to a property
usage.
limit
X
No
studies.
and !Ifailurell
value,
terms
of the
ing the
previous
of the load
to a test
the idiomatic
Yes
X
contribution.
, llu~timatell
the usage
a property
from
X.-Current
“Maximum”
tain
exist
Stress
X
depend-
is a noun only.
It
value.
It is the magnitof a structure
imply-
value
and is
only
indirectly
STABILITY THEORIES AND HYPOTHESES
Buckling
The
differential
equation
for buckling
of a flat
plate
is
(Ref.
3)
a4W/8X4
+ 284W/8X28y2
+84w/8y4+ (Nx/D) a2w/ax2
+ (N
/
for
which
chosen
the
general
~)a2W/a Y2 = o
biaxial
compressive
buckling
solution
may
be
in the form
w = wosin(mrx/a)
—-
(1)
sin(n~y/b
)
(2)
-3For
narrow
tion
and none
tions
column
also
apply
x-dependent
solution
buckling
there
reasonably
component
to Eq.
(1) for
wide
stress
exists
not influence
would
have
supported
The
with
preceding
buckling
problem.
element
since
at the free
tion
edges.
ling.
will
for
be
seen
residual
and
strength.
For
of Eq.
to influence
general
where
would
residuals
of a simply
plates
the
with
wide
column
will
column
be in hand,
in which
that
, use
The
project
theoretical
(a/b
coordinates
case
type
longitudi-
of instability
of the
solution
+ rnb/a)2
(4)
(5)
= 3) consists
a pictorialization
(6)
kx = 4 precisely.
For
transverse
loading
1. 23 approximately.
buckling
of the transition
combinations
stresses
or
buck-
that biaxiality
n = 1 )
= (a/rob
loa~alone,
l/9),
func-
conditions
(3) but no solution
on wide
buckling
curvature
deflection
boundary
Eq.
to affect
compressive
)2ky
with
buckling,
be expected
(for
various
column
to a lineal
the antic lastic
stresses
solution
limited
the precise
agrees
when
would
for
to utilize
solution
t-o the wide
= kyr2D/b2t
y cr
For longitudinal
alone,
k y=(l+
with
residual
v
= kxr2D/b2t
x Cr
r
ing
that
solution
properly
for
(1) yields
kx + (a/rob
implies
precisely
of longitudinal
biaxial
(2) in F,q.
sion
of the plate)
the Ny buckling
good
it is more
not account
effect
stresses
upon
a reasonably
It is conceivable,
nal
effect
cornpres
width
= 3.
column
the
entire
It also
It is necessary
wide
of any
the
buckling.
by Tirnoshenko
The
3).
is provided
component
However,
it does
provided
(Ref.
is
and a simplified
is
(3)
small
a/b
discarded
buckling
almost
column
a relatively
plate
is
N
)
across
wide
wave in the y direc= o.
These
situa Xy
column.
Consequently
the
to a wide
deflection
column
that the longitudinal
(which
one half
Furthermore,
well
of the
w = wosin(ny/b
It follows
is only
in the x direction.
interaction
of 3 straight
points
of the buckle
are
curve
lines
as
identified
mode
shape
for
the plates
shown
in Fig.
on the figure,
in each
zone
of this
1.
The
together
of the load-
.
It also follows
that the presence
of longitudinal
due to welding
should degrade
elastic
biaxial
buckling
stresses
,
-4-
I-EE ,Y4 TY
_“
1.5
I
I
P
m’l~m=2~m=3.
I
(0, 1.235)
I.0 -
kY
0.5 -
(3.445,
a/b = 3
w :wo$in(mmx/a)
sin(my/b)
(TIMOsHENKOIS
SOLUTION,
I
I
00
0.555)
Ref.3)
I
2
I
3
4
kx
Fig. 1.
IJniaxial
Strength
The
tially
result
Theories
ultimate
the
same
transverse
expected
Biaxial Compression Buckling Interaction Curve
for Simply Supported Rectangular Plates
load
as the buckling
membrane
to agree
of Eq.
carrying
capacity
load
compression
with
(Ref.
l).
loading,
the prediction
(6) with k
of a narrow
using
colurnnis
Consequently
the
strength
the classical
essen-
foruniaxial
might
wide
be
column
= 1.
Y
The
strength
calculated
advanced
of a plate in uniaxial
1 using a modification
in Ref.
by
several
writers
“xU/” Cy=
(Refs.
[s/(S+
4,
be/b
and u~ #rcy
It is
when
= 0.626
is found
seen
s=8.
can be fitted
(t/b) (E/ucy)
from
to fit the
Through
to the more
Fig.
scatter
choice
5).
1)][1/s
-1- (1 – 2be/b)(crx
where
The
theoretical
relation
is
+ 2be/b
(7)
cr/ucy)]
l/2
(8)
2,
band
of another
recent
longitudinal
compression
was
of the two-flange
hypotheses
data.
of the older
value
for
experimental
s , the hypothesis
data
.5Biaxial
Strength
The
Hypotheses
calculation
compression
and consideration
ferent
failure
mate
load
know
modes
small
permissible
k
b/t,
The
Instead
shown
was
as r/r
.
as t~e
was
For
strength
under
same
the above
For
utilizes
to predict
ridge
line
the longitudinal
comprised
plate.
of a transverse
This
longitudinal
waves
lines
, the
flanges
.
= 30,
be
expressed
the
should
same
occur
Consequently
and possibly
of failure
of the
was
to the
to the
them.
to
hypo-
experiments
employed
of biaxial
.
above
that
induce
with b/t
large
the hinge
transverse
lines
for
beyond
which
levels
are
longitudinal
at the nodes
enough
lines
loads
actually
of the
at low load
buckles
and one or more
ridge
is
behavior
declares
wave
strength
deflection
in transverse
become
carry
may
type
4) which
stresses
In plates
rid~es
that
equal
and failure
to b/t
hypothesis
half
results
is
1 is
It is also
a different
large
and transverse
waves.
This
form.
, the ultimate
loading
e between
hypothesis
The
mernb rane
strength.
of the postbuckling
loaded
load
biaxial
observation
(Fig.
curve.
altered
N
/u
after
general
for
both buckling
concept
rse
ratio
however,
longitudinal
t-ransve
ultimate
be applicable
uniaxial
The
biaxially
b/t,
be
transverse
sca Fe of Fig.
diffe”renc
required
interaction
uniaxial
)/(u
/rcy).
e%achc~ube .Xu
little
as
it may
the abscissa
loading.
(r
b/t
the flange
a description
be
to occur
case
in a somewhat
uniaxial
as
should
to be
must
= 3.
under
small
larger
appears
The
for
with
a/b
strength
ratio
hypothesis
= 50.
thesis
range
of a
that
coefficient
and as a result
relatively
of well
approach
expected
For
for
with
chosen
3.
be
since
synonymous
the buckling
It is the
in the plastic
ridge
scale
force
the ulti-
in terms
solution
of the buckling
retained
plates
by 4 in Fig.
~~mate
plate.
form
be
of the longitudinal
longitudinal
verse
may
used
divided
quotient
would
entire
be
supported
of enumerating
ratio
half
1 may
horizontal
of a rigorous
failure
the
a modified
and failure
of multiple
to characterize
ed plate
theory,
the dif-
investigation.
biaxial
of Fig.
with
hypothesis
it is an engineering
evolution
involving
on simply
load
cornpress
The
to use
scale
buckli~g
loads
an attempt
biaxial
deflection
interact
The
represents
At present
buckling
as they
field.
in a general
to large
of a ‘biaxially
nature.
For
of a plate
recourse
forms
stress
to a subsequent
plastic
This
of the
phenomena.
deferred
strength
involves
of the mode
behavior
conceptual
b/t
field
components
flange
The
of the
stress
to develop
equivalent
buckling
of the
the
transup to the
ultimate.
If the plate
waveform
In the presence
the buckle
given
were
in a plate
of residuals
waveform
biaxial
initially
should
field.
may
The
be
flat
and residual-free,
developed
(and also
differ
effect
from
then the buckle
in accordance
initial
imperfections
the configuration
of an initial
imperfection
with
Fig.
1.
, possibly)
in Fig.
1 for
may
be large
a
-6.
I
\
\
EMPIRICAL FIT TO DATA ABOVE
PROPORTIONAL
LIMIT
0.8
0.6
‘x cr/Ucy
0.4
SCATTER BAND FOR EXPERIMENTALDATA
0.2
00
8
6
2
l/F~(b/t)(ucy
PLATE
/E)l’2
BUCKLING
DATA
1.0
0.8
0.6
ax u / Ucy
0.4
0.2
00
2
4
1/2
I/F= (b/t) (ucy/E)
PLATE
Fig. 2.
Buckling
STRENGTH
6
8
DATA
and Strength of Longitudinally
Rectangular Flat Plates
Compressed
-71,5
1
1
1
(0, 1.235)
1.0 -
[0.662,
0.s -
I
1
0.25
o!0
,
I
0,75
0.50
G-x
0.5551
1, o
/uxu
Hypothesis for Biaxial Strength of Simply
Fig. 3.
Supported Rectangular Plates with a/b = 3
for
tramverse
or biaxial
imperfection
eye,
but it could
manner
form
ab/
=3.
points .
This
take
could
In fact,
for
appeared
to buckling
further
in biaxial
induce
ridge
lines
that now the effective
Suppose
the material
as a flange.
would
each
This
when
From
this
if the failure
for
would
the buckling
line
acts
ridge
is
stress
the
plate
the
ridge
be altered.
as an invisible
plate
of a flange
the
at the node
to be present,
might
behave
occurs
selected
then
providing
were to be less than 3, and the
in the same manner
as above
in Fig,
failure
hypothesis
the plate
were
would
is depicted
flange
sion,
1,
,
.
4.
stiffener.
in the
Failure
on either
ultimate
at the yield
is utilized.
load
level,
The
Then
same
of the
side
manner
plate
of each
can be compand the
rela -
expression
be
in which
IT’
12(1
the plasticity
hinged
flange.
investigations,
failure
may
all the quantities
in Eq.
a given
k
E(t/be)2
9)
V2)
reduction
reduction
for
–
In the
and no plasticity
flange
of the
of the
stress
= qk
oCY
y
a long
ridge
side
situation
be expected
ridge line.
uted
that
on each
a/b
Nevertheless
on Fig.
across
stiffener
influence
experiments
cornpres
shown
in the
The
study.
An
to the
somewhat
in the current
any of the three
if a transverse
field
loading.
apparent
in a cylinder.
would be enforced
even though b/t
buckling
stress
could be computed
except
tion
is loaded
may
directly
in a biaxial
a subject
have
to longitudinal
notbe
imperfection
is
undoubtedly
If a plate
buckle
may
the pattern
imperfections
effects
lines
plate
affect
compared
of i/100
of a corresponding
of initial
the
loading
of the order
factor,
case
be assumed
need
(9) are
~,
would
of the mild
(tentatively)
be considered.
known
steel
except
be equal
used
tO
for
to occur
Es/E
for
the current
at yield
Consequently,
since
the effective
width of the
then
Y’
be/t
= 0.63(kyE/mcy)
1/2
(10)
-8-
4
NOMINAL+
NY
4
v ////
Tm
Ny ALONE
N, ALONE
FAILURE
UNDER
N,
OR N“
t
ENFORCED IDE
ENFORCEDNODE
ENFORCEDNODE
NY -
F
kLzziz
1
ENFORCEDNODE
ENFORCED )DE
ENFORCEDNODE
4 FLANGES
2 FLANGEs
6 FLANGES
FAILURE UNDER Nx COMBINED
Fig. 4,
For
ky=
Equivalent Flange Concepts for Rectangular Plates
a long
0.433.
length.
width,
b,
then
be/b.
For
nation
for
from
Since
it is only
shorter
necessary
to determine
values
as well
of be/b
flange
Fig.
result
for
a hinged
values
flange
is the
relation
of ~
provides
flanges
length)
of ky depends
(Ref.
3).
upon
plate
to
data
on this
The
determi-
width may then be pursued
in an iterative
5 contains
t-he intermediate
data and the
data.
desired
the
Timoshenko
as clamped
those
the theoretical
than the flange
the value
of the transverse
hinged
final
less
flanges
the length
selected
here
2.
(be considerably
for
of the effective
fashion
Table
flange
However,
the flange
relation
WITH NW
flange.
of flange
width
For
the four
and
force
cases
at yield
of interest
appear
in
-91
I
I
1
I
6
4
2
30
I
1
40
50
I
60
b/t
I
0
1
I
I
2
I
I
70
I
80
90
I
3
I
4
I
5
b/be
Fig. 5.
.:._
Effective Widths and Buckling Coefficients for
Equivalent Hinged Flanges
3
-1oTable II.
b/t
Effective Flange Dimensions and Forces
50
70
90
o J$o
1.50
2.10
2.70
1.64
0.70
0.63
0.61
1.65
1.48
1.43
30
~,:
b (in.)
be(in.
)
P2’~(103
‘:Load
per
If a three
tance
equal
to
one flange
region
exceed
flange
lobe
the
for
same.
those
cases
ling.
However,
perimental
may
b/t
could
preceding
as to the exact
The
discussion
Influence
there
be helpful
The
was
plate,
nature
of this
ult-imate
the plate
for
case
the
a form
appears
dimensions
of the flange
of plate
Failure
plastic
buck-
to be a possibility
that
the observed
strength
a means
either
ex-
plate
the
For
be some
condition
section
ques -
during
on biaxial
tests.
strength.
of residual
has
the
b/t),
or
(large
b/t).
In either
the failure
in the
of
along
if the influence
can be established
data
hinged
failure
(small
as though
Therefore,
process
of resid-
elastic
or in-
the influence
may be applied
to
is not rigorous.
It is offered
as
the observations
be determined
before
as a whole
ed plate
configuration
of flanges
is computed
buckling
cornpress
postbuckling
long
it is hypothesized
that
This hypothesis
also.
influence
may
Comments
as a pair
buckle
buckling.
of explaining
may
boundary
This
ridgelines.
there
in the
plastically
the experimental
The
to be hinged.
interior
of a longitudinally
of the plate
of plastic
upon
range,
for
however,
as though
which
buckles
strength
stress
strength
plates
which
were
strength
would
Stresses
representable
edges
relating
lobar
width-s
= 50 these
assumed
of the flange
factor
theoretically
is
as a plate
plate
since
each
flange
in explaining
assumption
of the
of Residual
treated
elastic
be a dis-
or “borderline.
appears
Introductory
ual
within
in the manner
the flange
edges
tion
plate
b/t
would
Obviously,
the usefulness
be doubtful
more
to be a reasonable
the two loaded
been
there
of the ridgeline
for
w
= 39.2ksi
Cy
data.
In the
appears
side
then
of ridgelines.
Therefore
larger
hypothesis
occur,
pair
be since
= 30 the two effective
to occur
for
0.03
Furthermore,
the
be expected
the flange
at b/t
width.
would
should
each
on each
4) then
plate
39,200x
buckle
lie
be almost
hypothesis
pair,
b between
would
(Fig.
would
---
lb)
of this
on the influence
stresses
investigation
on uniaxial
with the aid of two
and of cor-
of residuals.
compressive
principles
of plate
instability y:
.-
.11.
1.
After
a plate
the plate
any additional
two flange-like
tains
For
2.
strips
to plates
below
plates
which
stressfirst
Gerard
for
critical
is
sustained
supported
across
mainly
edges.
stresses
second
by
This
per-
considerably
flange
strain
may
and then
entering
the
well-known.
It is discussed
was
critical
employed
that the proper
the
be accomplished
a suitable
stress.
in Ref.
successfully
plasticity
1,
by
reduction
is Es/E.
use
In the following,
or inelastically,
stress
to determine
principle
6) to demonstrate
a hinged
elastically
critical
curve
is generally
The
(Ref.
factor
buckle
the
strain
principle
example.
have
is
the unloaded
of the critical
by computing
The
along
which
load
load
yield.
determination
for
the critical
buckles,
while
is made
influence
of residual
stresses
influence
diminishes
to a negligibly
of these
on plate
principles
strength
small
to calculate
and to show
amount
as b/t
the
that the
becomes
small.
Outline
The
important
schematically
features
in Fig.
6.
to the curve
stress
when
account.
the
For
modulus
of the calculation
An appropriate
at the top in nondimensional
rection
form.
to reveal
a flange
plasticity
a simply
;
are
relation
factor
is necessary
supported
plate,
appears
involves
between
reduction
depicted
curve
modification
2
l–v
~.
The
no modification
For
s cherne
stress-strain
the proper
appropriate
governs.
of Procedure
the cor-
strain
and
is taken
since
the
how~ver,
into
secant
(Ref.
1)
.
(Es/E)
[(1/2)
+ (1/4)(1
+ 3Et/Es)l/2]
l–v
and consequently
more
Fig.
complex
2 are
suitable
done
The
ratio
employed,
relation
in Fig.
gether
the relation
have
the modified
strain
to be changed
to reflect
if the experimental
curve
and buckling
will
reflect
That
stress.
this
data
of
this
more
has
been
6.
trend
with
then
between
would
Actually,
expression.
of UK Cr /crcy
the appropriate
is shown
stress-
as afunction
strain
curve.
of b/t
The
in Fig.
critical
6.
strain
is
E
utilizing
x cJ’cy
an elastic-
= 3. 62(t/b)2/<
plastic
stress-
(11)
Cy
strain
curve
so that
~
= o-cy/E.
Y
to.
-12-
A(t
!
duc~
I
I
Fig. 6.
(12) comes
Eq.
compressive
buckling
Determination of Effective Residual Stresses
from
the expression
stress
of a simply
in Eq.
(8) for
supported
flat
the elastic
plate
2
=km
0x cl-
where
12(1
k = 4 and Poisson’s
strain
Eq.
E
is obtained
(12).
strain.
The
The
V2)
= 0.28
by transposing
remaining
elastic
ratio
-
quantity
portion
(12)
(t/b)2
of the
E
for
mild
to the bottom
on the right
•xcr/~cy
The
steel.
of the left
becomes
function
may
critical
side
of
the critical
be extended
-13.
as a high
as
effective
residual
The
cancels
required
to permit
stress
residual
completing”
the construction
strain
ratio
is
simply
ur/r
function
of b/t,
curves
of Fig.
which
on the
right
stress-
strain
influence
increases
are
curve
plots
of ~r/~cy
downward
the critical
Both
by the residual.
6 contains
strain
plots
The two
line reduced
in evaluating
is depicted
Enter the lower
diagram
elastic
values
of rr and Ux cr.
b/t and identify
the corresponding
.Er/~cy
and ~x ~r/ccV,
to the modified
is apparent
stress
that when
degradation.
stress
Effect
That
According
into
the effect
gible,
gain would
capacity
bent
would
.
of
of normal
sion
included
is
the influence
of
a few
may
predictions
a plate
to a segment.
in
of the
of a
of Levy
may
and his
col-
large)
increase
in buckpressures.
However,
in cylindrical
increase
shells
be so small
is taken
as to be negli-
at most.
of this
information
be .surnmarized
of normal
of the nature
plate
(even a very
large
lateral
imperfections
percent
appears
compression.
7), a significant
be expected
for
of initial
pressure
an examination
of the flat
in longitudinal
to the
effect
in the conjec~re
or maximum
plate
of pres sure
on
that an inappreciable
as
load
the result
carrying
of the
pressure.
is loaded
membrane
be to produce
have
1 to O as b/t
of the effect
compressed
column.
a from
in controlling
in the buckling
When
It
a will
(13)
be anticipated
transverse
for
relation
of a longitudinally
application
would
discussion
significance
plates
of unity
of plasticity
the anticipated
or only
The
hull
transition
to the theoretical
(Ref.
would
account,
the limit
Rise
rr/crcy.
“J”cy
Cy =
by the conversion
loaded
leagues,
ling load
as at A.
t-he effective
Pressure
discus
increase
cylinder
when
+v/fl
x
the role
of Normal
1.
B
at a selected
on strength.
A detailed
Ref.
at
the general
The
reflects
residual
load
CY
be applicable.
decreased
and read
occurs
rr/rcy
Therefore,
UC+
curve
the
for
zero.
At ~ and above the value of a approaches
positions
on the Ur curve
a undergoes
a rapid
have been reached.
Between
these two
would
- strain
as a
and the modified
form are used
The process
on strength.
stress
modulus
and ~x ~r/~cy
in nondimensional
of residual
Young’s
in the f~gure.
and the critical
line,
nondimensional
since
Cy
top and bottom.
The bottom
of the
relation.
simultaneously
compression,
an initial
Timoshenko
a degrading
has
effect
imperfection,
shown
upon
by normal
the effect
the
(Ref.
similar
3) that
strength
pressure
of the normal
and
pressure
to a slightly
such
an initial
of the column
and
pre load
-14could
degrade
action
both
it considerably
it is
of normal
pressure
transverse
more
ination
of this
for
strengths
longitudinal
effect
slightly
was
bent
made
(Ref.
not close
to the observations
warrants
further
For
some
equal
cases
yielding.
in general
use
that
to adapt
study
much
Timo
exam-
shenko ts
the predictions
was
halted.
This
studies.
plate
instability
theories
(see
upon
investigated.
the largest
the nature
The
algebraic
may
Ref.
for
shear
in principal
by
example)
of the material
~aximum
difference
be controlled
8,
and the
theorY
stres
re -
ses
is
to the yield
=cr
‘=Y
whichever
x
—
‘Y’
‘Y–
‘~’
while
2cr:Y
G-)z+(m-u)
is little
the plane
= (mx –
stress
difference
case
will
‘z–
the octahedral
Yz
between
them
(rz = ()) when
as in the current
Use
‘r
is greatest,
Y
sign
be degraded
A preliminary
However,
and the
yielding
depending
being
F
There
alone.
in subsequent
of loading,
Two
of problem
quires
pursuit
3).
compression,
may
of Yielding
material
type
sim
by attempttig
columns
area
are
membrane
of a plate
compres
were
Theories
normal
pressures
are
that under the combined
and transverse
and biaxial
than under
data
when large
conceivable
Consequently,
applied.
2
shear
as may
Ux and ~
of these
theories
Y
theory
be seen
are
that
(15)
x
of the
in evaluattig
data.
requires
2
+(U–u)
z
investigation.
be made
(14)
‘x
in Fig.
7 for
same
algebraic
biaxial
strength
OCTAHEDRAL
SHEAR THEORY
I.c
*
MAXIMUM
SHEAR
THEORY
Uy
/uc~
o
0
Fig. 7.
1,
Plane Strength Theories
.
-15-
SPECIMEN CHARACTERISTICS
Shapes
and Dimensions
All
strength
fabricated
from
welding
along
section,
flat
Fig.
Material
specimens
were
rectangular
the four
Residual
thick.
plates
The
edges.
Stresses.
8 depicts
square
by the use
details
section
tubes
of electron
beam
of the welding
The material
the specimens
cross
was
appear
nominally
and shows
in the
0.030
inch
the dimension
ranges.
Properties
All
steel
test
test
stock.
specimens
AISI
No.
foot
by 8 foot
1020,
insuring
were
The material
commercial
sheets.
the
from
22 GA.
sheets
of composition
readily
0.0299
cold
quality,
AU
uniformity
fabricated
was
inch
rolled
were
available
nominal
steel
part
received
of the
and properties
sheet
thickness
same
within
in 3
mill
run,
reasonable
limitations.
The
3
x
8
2 foot
sections.
which
it had been
1200°F
sheets
were
Each
section
cut.
in an inert
Additional
jected
to another
remove
identify
The
The
to-point
was
E
for
The
of this
the
buckles
They
along
and
the 3
process
the parent
with
1 foot
by
8 from
x
-annealed
at
plate
4 tube
and were
samples
sub-
in order
to
shape
in the
value
the
of the
yield
ratio,
performed
were
and the yield
curve
back-to-back
modulus.
value,
secured
pairs
as
was
to
strength.
obtained
strain
gages
It is evident
and agreed
with
load
, which
9.
a
3 that this
the compres-
preventing
in Fig.
and Ractliffe’s
by a pointto obtain
in Table
well
in a buckleshown
of 29 to 30 msi.
steel
-Strain
investigation
specimen
were
gage
tests
3.
stress-strain
fr orn Dwight
F for
were
cut from
using
Young’s
strain
Stress
to obtain
then
stress-strain
of the usual
the usual
Effective
to identify
were
Poisson’s
tension
E values
5/6
by 2 foot
and oven-cooled.
cycle
in Table
process
values.
calculating
for
were
elastic
employing
were
samples
shown
value
that the
atmosphere
modulus.
are
in the range
sion
jig
gas
2 foot
marked
sections
and compression
loading
reference
was
into
stresses.
Young’s
results
The
annealing
residual
Tension
sheared
compress
ion
It is interesting
shortening
they
data
employed
in
specimens.
Curve
compressive
region
were
strips
of extremely
stress
for the material
This
fabricated,
to buckle
short
at a stress
wavelength,
-strain
from
arose
close
curve
was
difficult
which the specimens
from the tendency
to yield.
as would
The
be expected
for
-161.
THICKNESS ! 0.0293-0.0303
rlT
rl
cROSS-SECTION
61
b/t = 90
—
FicI.8.
.SDecimen Dimensions Showinq Maxima and
Minima on Sketches of Tub;s
Table 3.
Test
Type
c
c
c
c
c
c
c
c
c
c
c
Material Properties Tests
Specimen
Type
Sheet
38,!5
Sheet
39,4
Sheet
39.2
Shcet
39.6
Shmmt
38.6
Sheet
b/k=
{
z,.,
39.4
I
15, box
40.0
b/t = 30, box
.274
b/t=
50, box
.289
b/t=
70, box
b[t=
90, box
T
Sheet
c
c
c
She et$,
-1=+=
39.0
Sheetf,
38.2
Sheet,$
41.2
C - Compression
+
v
T - Temion
Eearmealed Specimene
,282
.280
0.28
av
-17-
Fig. 9.
material
a
Luders
was
found
ever,
with
bands.
a tangent
to have
For
form
was
shown
calculation
should be employed.
are plotted against
stress
has
-strain
been
E
x cr
may
For
zero
yield
and which
the tangent
practical
exhibits
modulus
purposes,
how-
elastic-plastic.
10,
but with
buckling
It approached
a sharper
knee.
stresses,
which relate
rx cr/rcy
be constructed
10 by making
=o- ~ cr/E
TYPICAL
CARBON
PROPORTIONAL
LIMIT
\
in Fig.
of plastic
in Fig.
beyond
of O. 8 rnsi.
essentially
If the strains
the corresponding
curve
done
approaching
at strains
a value
the material
schematic
modulus
Actually,
Sheet Compression Test Jig
use
for
the curve
of Fig.
material.
IL;’’T”M
This
relation
= 3. 62(t/b)2
Low
STEEL
2
to each value of b/t
value,
then an effective
the model
of the
the
(16)
TYPICAL
‘T
~
u
r
OF
0
I
I
).002 +
SCHEMATIC
CURVES
Fig. 10.
..,
.
I
4
1
3
E (microinch/inch)
EFFECTIVE
Stress-Strain Curves
1
2
SHIP STEEL CURVE
1
5
LOAD APPLICATION DEVICES
Equipment
The
variety
unstiffened
of load
plate
types
with
a length
equal
The
problem
was
face
with no frictional
and in a manner
experiments
to square
to three
to apply
times
section
the application
sheet
the dimension
the forces
resistance
that would
involved
cross
meet
of a side
uniformly
to Pois son
metal
along
ratio
the boundary
each
of the
square.
each
strain
of a
tubes,
loaded
sur-
tendencies,
conditions
stipulated
for
the tests.
Two
testing
accomplish
column
testing
25,000
machines
the project
machine
pounds
through
the manner
of a deadweight
generated
pounds
capacity
chines
incorporate
of the applied
Fixtures
in Fig.
12,
pres sion
for
which
load
On the
small
although
of three
sure
similar
The
gage
for
was
details
in
smaller
for
4,000
both
great
mastability
for
of the uses
in the following discussions
of the large
comof the
machine
interpolation
2 pounds
employable
most
and
is grad-
to 10 pounds.
1 pound
during
res pec -
the
compared
in the
significant
which
of a test
of the machine
adequate
for
shown
13.
frequently
machine
of load
which
device
A schematic
is minuscule
on conventional
loads
are
project,
to the
size
data.
the conduct
variations
tests
face
are
each
are
The
property
for
much
with
provide
support
reliable
calibrated
on the large
possible
employed
The
machine
to the tubes
sheet.
in Fig.
values
were
during
This
therefore,
these
machines
specimen.
during
of thin
with
precision
minimizing
was
the lateral
on the dial
machines.
columns
of applying
11).
which
to
by a three-
bellows
systems
application
appears
increments
testing
of stability
(Fig.
pneumatic
features
in the experimental
standard
capable
pressurization
tests
system
scale
the load
Both
displays
machines
of the scatter
other
also
machine
Both
tively.
applied
actuated
applicator
load
property
in 20 pound
manufacture,
balancing
transverse
loading
The
uated
The
employed
were
at any level.
material
transverse
11).
load
load
load
were
loads
pneumatically
by a two-column
(Fig.
fixtures
The large
of unique
of force
loads
were
and several
goals.
did not
same
imparts
would
have
machines.
the purposes
of this
of the machines
on the types
The
the virtue
of
could
smaller
type
occur
machine
of stability
and,
investigation.
and fixtures
of tests
mea-
compression
which
this
as all
is the use
a greater
on a slender
distributions
require
manner
departure
conducted
are
included
on the tubes.
-19.
4
I
a.
25,000
pounds
b.
4000 pounds showing
sion fixture
in place.
Fig.
a.
transverse
compression
11.
fixture
compres-
Testing Machines
b.
sion
Fig, 12.
transverse
stabilization
of
property
tests
Closeups of Fixtures
sheet
during
compres–
-20STATIONARY,HEAQ
‘4
I
I
nil.
A
SELF ALIGNING
s(DE LO$OING HEAD
A = STEEL SHIM STOCK
U
PIVOTED
4CT1VE
LOAO HEAD
B EBERYLLIuM
COPPER SHIM STOCK
&
‘Y
LOAD
‘ppLlcATION
- TopVIEW
Schematic of Transverse Compression
Fixture
Fig. 13.
h
k
ACTIVE
y&G
TEST MACHINE EASE
LOAD APPLICATION - SIDE VIEW
Nx
Uniaxial
Com~res
The
test
sim
condition
of a compressive
tube
while
enforcing
of the plates.
inhibiting
load
in the
conditions
that have
been
actually
reason
confining
for
deviations
the data
tional
cantly.
the
may
under
would
expected
were
test
met
The
the loading
in the
restraint
Some
14 which
during
these
tests
restraint
Rotational
because
about
for
met
and Poisson
that
to increase
of support
the belief
this
7 percent
point
may
increase
to the plane
effects
presuma-
patterns
amount
the buckling
that
by the frictional
buckle
a small
the
the
not influence
normal
well
Uniaxial
whether
However,
would
of three-lobe
not tend
section,
= 3 was
of movement
would
only
the longitudinal
of the above
experiments.
conditions
and the knowledge
reveals
edges
freedom
so as to avoid
to determine
to a/b
plates
measure
edges
in the
to be reasonably
head.
not be important
the loaded
accompany
described
boundary
be assumed
of each
of instability
data for long plates
and which receives
some
substanconducted
specified
the application
to permit
the existence
was
the current
along
the loaded
would
was
of symmetry
important
accepting
experiment
significantly.
plate
forces
I?ig.
from
for
(Nx)
axis
conditions
which
in the past,
No direct
of loading
along
expansion
is the agreement
in the buckling
conditions
bly
y direction
obtained
Compression.
of the
boundary
theoretically
The basis
boundary
type
the longitudinal
also
the Pois son
application.
tiation
this
along
hinged
It was
of movement
for
force
stress
be gained
to be
of rotasignififrom
in the buckling
..
.
_21_
Ic
I
I
I
I
8
6
LOADED EDGES CLAMPED
Fig. 14.
Buckling Data
edges
fully
for
kx
4
/
EDGES SIMPLY SUPPORTED
LOADED
2
mx ~, ,
c
-
(%)
I
4
3
2
c./b
stress
The
of a plate
realization
highly
for
unlikely,
strength
flat
to a few
section
to within
loaded
edges
deviate
significant
load
of longitudinal
the order
th~se
ture
criteria
potential
clamped.
edges
gain
is
in plate
lie
lateral
moments
appeared
the edges
of the tube
when
the edges
are
inches
or less.
in a plane
from
along
the tube
acress
to have
the
been
to avoid
length,
thereby
satisfied
section
by the
order
axis
axis
square
all four
the same
of the load
the tube
polished
In addition,
to within
displacement
inches
variations
along
only
of
cannot
inducing
minimizing
of the tube.
careful
All
rnanufac
-
of the tubes.
Biaxial
Compression
The
loading
permit
more,
the criteria
successful
two most
loading
tube
section
partially
for
re strained
compression
followed
effective
required
by construction
implementation
of that
longitudinal
load
the development
of fixtures
which
Further-
concept.
application
still
in complexity
by the same general
requirements
and finally
complicated
by the requirements
loading,
simultaneous
transverse
cross
concept
the eflective
applied,
multiplied
for the transverse
The
of biaxial
application
of a feasible
would
for
must
0.001
bending
distribution
the
loading
possible
the
than
reduces
of 0.0001
of a tube
are
at the unloaded
at most.
is generally
more
the loaded
restraint
which
percent
Finally,
tolerance.
= 3 when
rotational
however,
Uniformity
cross
a/b
of full
load
difficult
along
problems
the length
dimensions
along
application.
were
the achievement
of the tube
induced
in spite
by Poisson
the longitudinally
loaded
of the varying
strains
faces
01 uniform
which
were
but which
were
Plates
-22unrestrained
frictional
in the middle
resistance
transversely
with
and
loaded
reasonably
in Fig.
tained
good
values
letely.
less,
effort
may
on the basis
The wide
column
result
to meet
does
up to
before
data
satisfactory
required
satis-
friction
comp-
be reduced
loading.
obtained
for
during
the small
of the project.
loading
machine
with no forces
applied
simple
support
tests on plates
at the tube ends in order to perform
transverse
with all edges hinged were unsuccessful
unless
longitudinal
force
of cement
were
applied
appeared
to help.
The
~n addition,
on the short
Both
support
of these
latter
in which
a small
axial
internal
vacuum
to the s pecimen.
stress
Pressure
was
internal
possible
loading
through
passed
arrangements
monorneter
dial
Interpolation
of
in a
by the appli-
The
resultant
strength.
and POsitive
internal
pres sure
and tubing
applications
in the upper
longitudinal
compression
from
Sketches
of the vacuum
the testing
and positive
in Fig.
while
These
gage.
to 0.05
system
pressure
was
read
with a
positive
pres sure was measured
with a
both permitted
direct
reading
to 0.1 psi.
psi was
provided
Vacuum
15.
The bleed
possible.
the
same
degree
control
of load
for
the pres-
stability
as in the
machines.
Material
Property
Tests
The determfiation
yield
strength
sion
properties
thick
edges
taken
of the longitudinal
of the perforations
which
appear
standard
square
induced
the use
into the specimen.
mercury
surization
vacuum
with the use
platen
machine
testing
of 1 percent
was
were
load
a small
Tests
Both
were
of the order
load
steps
cation
axial
to achieve
of simple
few experiments
of a small
attempts
to the specimen.
to aid the acquisition
the plate
ends.
to
Nevert-he the tests the
the purposes
only
to the specimen
criteria
it could
of the transverse
gage
of preliminary
the above
not eliminate
be required
tests
of the
attained
depicted
the distributions
the final
still
percent
judged
avoiding
features
were
of the fixtures
to measure
was
of the strain
was
These
the use
for
motions
tests.
fixture
of one
fixture
and by the need
and transverse
Data on the degree
of uniformity
and longitudinal
loads were ob-
that failed
present
fraction
current
in biaxial
configuration
Further
a small
13.
gaging
concepts
The
through
in Fig.
strain
The fixture
factorily.
of the tube.
success
of failure
with other
tube,
of the transverse
by extensive
90 percent
test-s
edges
12 and sketched
proper
of each
to the longitudinal
were
of Young’s
accomplished
were
measured
tube manufactured
sheet
from
which
single
plates
were
shown
in Fig.
9.
in the jaws
ratio
was
tests
by employment
the test
accomplished
ratio
of ways.
The
= 15,
specimens
tests
machine.
during
of suitable
were
Direct
= 6,
were
using
made.
tests
jig
column
below.
inch
manner
of Poisson’s
e of the wide
described
on a
the 0.030
In addition,
in the usual
measurement
gages
and the
compres-
in the stabilization
conducted
the performance
strain
compression
and a/b
ed longitudinally
tension
of the small
Poisson’s
by longitudinal
to b/t
compress
The
modulus,
in a variety
-23-
1
P
LOADING
HEAD
J
LOADING
PLATEN
REGULATOR
1T
~
u
PRESSURE
INPUT
FROM
NITROGEN
BOTTLE
\
TUBING
!
PRESSURE
PORT
UNSTIFFENED
BOX
MODEL
o
PRESSURE
GAGE
DUCT SEAL
\
\
~TEST
\ \ \
\ \
MACHINE BASE
\\
COMPOUND
‘
MODEL
TEST
WITH
INTERNAL
PRESSURE
U----@””’
LOADING
PLATEN
NOMET “ER
P
4
TEST
MACHINE
BASE
‘.
‘
MODEL TESTS
Fig. 15.
WITH INTERNAL
Sketches
VACUUM
of Pressurization
Systems
-24-
DATA ACQUISITION
Load
The
brated
load
magnitudes
dial
rate
verse
gages
controllers
forces
pounds
point-by-point.
one
throughout
rate.
on load
cases
readable
and 2 pounds
with the cali-
employment
the longitudinal
static
to near-impact.
combinations
held
were
aided
static
recorded
manual
is reproduced
of 10 pounds
compares
for
load
was
and time
to a precision
This
to apply
from
measured
Through
01 the
and trans
Most
-
were
while
applied
the other
to
was
varied
range.
a stopwatch
record
were
were conducted
with a load application
The transverse
loads were applied
when
of the components
A typical
strain.
tests
a preselected
Data
In many
rate
per minute.
However,
loads
machines.
possible
any
compression
of 1,000
tubes,
it was
at virtually
longitudinal
rate
of the applied
on the testing
well
the large
with
on a Mosley
control
in Fig.
in load
the dial
and small
16.
and
gage
testing
X-Y
recorder.
of the longitudinal
The
5 micro
scales
inch/inch
precision
machines,
load
are
in
of 20 pounds
respectively.
Pressure
The
(either
pressures
positive
so that the pressure
This
is
subject
dynamic
preferable
to errors
which
were
in the
the
to the interiors
measured
specimen
to reading
when
applied
were
or vacuum)
interior
the inlet
pressurization
of the tubes
by a tap placed
pressure,
gas
could
be read
which
is flowing
in the line
directly.
procedure
because
is
of the
head.
5000
4000
Fig. 16. Typical
Load-Time Trace
3000
P (lb,)
2m
100a
o
TIME/SEC
v25Strain
Strain
were
read
data
were
directly
obtained
with bonded
to 5 microinch/inch
electric
with
strain
inch/inch,
Model
in size
of properties
using a BLH Strain Indicator
and characteristics.
The range
4.
Table
Table 4,
gages
interpolation
120
C.
which
to 1 microThe
gages
is listed
varied
in
Strain Gages
Gage
Type
Transverse
Correction
Gage
Factor
Resistance
ohms
Gage
Length
in.
90
70
50
FAE-50-1256
120
2.05
-0.2’70
.
FAE-12-1256
120
2.01
+0.
. 125
370
b/t
50
30
They
were
membrane
two buckling
during
with
used
stresses
studies
stages
the
are
stress-strain
biaxial
was
data
to maximize
No data
because
from
of the lack
stresses,
of instability
of preliminary
prosecuted.
however,
residual
the onset
of the investigation
project
reported,
data,
loading,
and a variety
experiments,
the early
which
to obtain
during
in
obtained
the efficiency
the
preliminary
of relation
to the
project.
All
back
strain
to obtain
mean
periment,
for
curvatures.
only,
used
data
In fact,
specimens
principal
The
0.030
less
width
8.
(b/t
percent.
gages
no strain
gages
required
right
and also
were
at minimum
applied
pairs
were
calculation
of
Because
of
field.
a minimum
in order
to obtain
cost
to the
to the longitudinal
and the cross
those
angle
investigation
specimen
exbending
longitudinally
to permit
stress
in this
on each
to obtain
aligned
required
membrane
load
from
were
summed
(the buckling
differences
In others
were
time,
the ultimate
t-e sts
in back-towere
section
the
proj-
strength
area
were
the
tests.
Errors
maximum
The
inches,
than
the
performed
in minimum
data
Experimental
Fig.
of tests
was employed
since
strain
material
the outputs
other
the
tests.
strains
sheet
cases
while
of the biaxial
number
of gages
pertinent
locations
stress-strain
components
the large
utilized
the Poisson
on the
In some
strains
example)
some
mounted
17).
membrane
as in the
number
were
(Fig.
At
where
the two
ect.
gages
arrangement
range
extreme
was
2 percent,
1 percent.
= 30)
was
Therefore,
of specimen
variation
The
use
but the mass
largest
2 percent.
dimensions
in thickness,
deviation
All
others
of the nominal
may
from
of data
from
were
cross
be seen
the nominal
yielded
a variation
the nominal
of the order
section
area
in
of
of
specimen
of 1/2
(instead
of
-26-
Fig. 17. Strain Gage
Application
TRANSVERSE
NOMINAL
SHEET GAGE
0.030 in.
GAGE
LONGITUDINAL
GAGE
the directly
3 percent
measured
for
elastic
30 and
the maximum
thermore,
b/t
lJ/t ‘
value)
longitudinal
have
have
percent
1.5
departure
buckling
= 30 but would
could
stress
been
less
involved
a maximum
allother
for
from
nominal
could
have
than
error
specimens.
of
Fur-
of the theoretical
been
3 percent
6 percent
for
b/t
for
greater
than
30.
All
less,
specimen
which
buckling
tion
have
es
curve
of 4 percent
percent
The
accuracy
is flat
at a/b
a negligible
= 3.
transverse
load
apply
reliable
than nominal
on strength
in the theoretical
maximum
considered
smaller
introduced
at the longitudinal
would
were
(and probably
in the applied
percent
are
would
stress
coefficient
lengths
variation
or
on longitudinal
since
the buckling
There
could be a maximum
wide column
buckling
stress
deviaand ,?
stress.
could
compression
to the transverse
to better
effect
also)
by 1 percent
than
have
failure
forces.
1 percent.
been
no more
loads,
The
than
and the
strain
1/2
same
gage
data
-27-
SUMMARY OF EXPERIMENTAL DATA
Tables
5,
experiments
strength
6,
of ship
approximately
conducted.
hull
half
In a sense,
The
use
long
edges
tests
flat
of each
distribution
of the tube
Mode
Shapes
AS might
observed
alone,
result
of the four
edges
similar
have
been
The
three
loading
phase
aspects
of the behavior
was
the manner
buckles
form
at N
From
half
that
process
along
N
for
were
applied
It was
failures
form.
of
in
tile
was
the
the long
of failure.
was
wa ~ e .
buckle
buckle
in the
not observed
it did occur
at an intermediate
One of the most interesting
.
of the biaxially
the buckles
&lost
plates
occur
shapes
When
this
loading
However,
than failure
planned
the
standpoint
3-90-11
to test
the ultimate
pressure
Wide
mode
buckle.
exhibited
face
in a
sec-
to emphasize
flanges
of one transverse
column
cross
at the inception
.
shown
loaded
began
and then
specimens
as clas sical
snapped
into
of large
three
the wide
b/t
lobe
column
at failJre.
specimens
this
tubes
of the tests
in which
less
of the eight
various
tube.
in several
tend
proper-
is
four
would
the
simultaneous
of the
to all
would
expected,
longitudinal
failed
edges
be an averaging
in unison
tubes
of four
the tubes
which
to act
wide
lobe
in any biaxially
failure
would
tests.
along
and material
all
can be applied
compressed
compressed
a set
If the loaded
Each
consisted
to a classical
the biaxially
near
tend
the
were
of four
support
in geometry
readjustments
plates.
in the biaxially
permits
throughout
load
actually
would
the buckle
the average
simple
report.
at loads
The
during
which
represents
identical
slight
acquired
guarantees
of geometry
of this
data
of experiments
and therefore
nearly
then the
unifo rrnity.
strengths
test
so that uniform
tube,
stress
tube
plates
section
are
number
hypothetically
uniformity
preceding
tion
girders.
tube
the pertinent
phase of the project
on the compressive
The tests iu those tables
represent
of the total
of each
The
in this
each
of tubes
on four
ties.
and 7 contain
conducted
whether
strength
also,
of significance
and 6-90-16
that
are
the loading
of a plate
result
is
to the project,
the most
would
They
be important
loading.
Sine e
sequence
in combined
deferred
the tests
important,
to that
subsequent
it
on
were
to
involves
section
of
report.
Columns
The
in Table
experimental
8,
while
buckling
the buckle
coefficients
shapes
appear
for
in Fig.
wide
31.
columns
appear
Table 5.
b~k
Model
No.
1-30-7
4060
30
1-30-8
3810
30
1-30-11
2420
30
1-30-12
30
1-30-14
30
30
P
psi
c
b
Load
Sequence
ax
ksi
1
‘Y
Model
No.
ksi
b/t
30
30
a
Px
lb.
Strength ‘data
1-30-17
N
x
p Nx
36.91
36.63
26OO
KTXN
23.30
800
3400
Nx N
1350
36OO
2s00
4000
50
1-50-6
5500
50
1-50-7
5330
50
9-50-15
Y
5540
7, 70
13, 00
Nx N;
3200
Nx N
3040
i-30-16
1-30-2
10.6
N
1335
26.90
Y
38.50
N“x
30.47
P %
30,46
15io
Ny N
2100
N
50
9-50-12
50
9-50-11
4800
2000
50
9-50-13
2960
26OO
50
9-50-17
3500
1800
50
1-50-16
2960
3500
10.4
50
1-50-18
2660
9.9
50
9-50-14
1380
2680
50
i-50-i9
3580
2240
30
x
NY ~Tx
Nx ii
Y
Ny N
x
N-~P
‘Y
PN
Y
Nx N
Y
Nx p ii
Y
?0
2-70-3
5060
7-70-5
5260
70
7-70-1
5060
-10
8-’70-13
3800
70
8-70-15
2530
2610
?0
0-70-18
1270
299o
-10
2-70-6
70
2-70-16
3800
244Il
10.9
70
7-70-12
2530
2440
10.3
70
2-70-19
1270
248o
10.5
NXPN
70
0-70-17
0000
1500
10.0
70
7-70-14
2530
23OO
lb.
p LT
Y
Xxp
N
294o
28.00
11.70
lb:
lb?
Load
Sequence
P
psi
9-90-1
5250
Nx
16.43
90
10-90-3
5360
Nx
16, 65
90
8-90-5
5090
10,6
p CNx
16, 00
90
9-90-4
5130
10.5
p Nx
16, 11
90
3-90-8
2650
3860
90
3-90-11
2650
2290
11.6
NM
XY
NxpN
3980
3690
10-90-7
90
3-90-18
3980
2000
8-90-10
1330
3480
8.34
Y
ITx N
Y
Nx P N},
10,8
31, 60
7.94
11,02
90
8-90-9
1330
2535
10.6
Nx PYN
2’?. 40
10, 50
90
8-90-6
0000
1520
10.5
16.88
13.65
90
3-90-19
0000
1325
90
8-90-12
2650
530
2230
3200
~ ~r
Y
N
Y
e
90
6-90-16
2650
2340
19.95
9.46
16.90
1s.40
14.00
7.88
14.10
20.40
11.77
21.30
N“x
20.32
Nx h~
15.39
Nx Ny
Y
10.24
9.81
5.14
11.22
‘x
ksi
90
90
N
x
p xx
Nx N
1470
31.50
P
90
Y
70
10.6
29. so
26.60
Y
c
10.6
22. so
b
a
P
8.34
12, 50
12,50
4, 18
NTx N
10.6
4.18
Y
0
0
8.34
1.67
8.34
Nx N>,pf
20.32
Y
5.53
N
Y
Nx P IT
Y
Nx p Ny
15.39
9.18
10.24
9.18
5.14
9.32
Y
Y
a
Internal
7-70-14
b
Px/[4bt(l
c
0.707
11.04
0
5.64
10.24
8.64
dr
em
f
x
x
vacuum except for 1-50-19
(16 psi internal
pressure)
–
pr
t/b)]
P\,/3bt
+
15.Oksi,
+
8,341
Failed
(30 psi internal
ksi,
IT +
Y
u
ll,7ksi,
+
6.531
Y
1 to 2 Minutes
after
u +
x
ksi,
u
x
Vacuum
38.5
+
ksi
1.67
(Failure)
ksi,
r
+
Y
was
Applied
F
-29-
Table 6.
b/t
Experimental Buckling Data
Model
No.
P
r
lbx
ksi
x
70
7-70-1
424G
16.82
90
9-90.1
2930
9.04
Table 7,
Centerline Measured Residual Stresses
b/t
30
k:i
14-.2
70
50
r
30
0.91
k
4.8
de Column Failure Data
Tab” e8.W
b/t
8.5
50
70
90
1.05
1.02
1.11
Y
The
retical
average
value
ky=
The
Table
measured
5.
of these
of unity.
1.105
value
four
It was
values
obtained
is
1.05
compared
by transposing
to the theo-
Eq.
(6) to the form
(uP/E)(b/t)2
of the applied
(31)
stress,
~
yu
was
obtained
from
-30-
RESIDUAL STRESSES
Introduction
Data
on the hypothetically
by the electron
the
beam
specimens
the basis
fabricated
for
describes
current
made
and after
after
have
been
They
vitiated.
new method
because
of trepanning
Analyses
were
between
Data
welding.
influence
the weld
zone.
was
region
1.
the
conducted
were
8 to 10 inches
waviness
might
long,
have
residuals
of several
plate
gages
to furnish
agreement
test
plates.
interior.
The
together
data
occur-
may
2) measured
edges
in the
is felt
were
of the conclusions
strain
with
of high
a
reliability
of buckling
in the current
determined
and beyond
results
are
from
at the weld
More
recent
theory
project.
Feb.
1969)
thick
readings
were
then
converted
hardness
-yield
centerline
features
are
exceeded
in Fig.
of prime
and Moxham,
be examined
stresses
18 as
stress
zone
of the weld
itThe
in a subsequent
yield
was
through
steel.
in terms
as a multiple
metal
in
the weld
for
importance.
the base
side
surveys
beyond
into
the
beam
sheets.
chart
expressed
of the hardened
on either
(Dwight
well
conversion
graphically
steel
microhardness
region
shown
and electron
4340
plate
and the width
will
inch
10) to determine
welding
the
thickness
data
(Ref.
TIG
by conducting
into
centerline
25 percent,
of the plate
from
the weld
Two
thickness.
by Buehler
on 0.062
obtained
of a standard
The
2/3
conducted
were
of the distance
about
the free
of residuals
the residuals
The hardness
the use
stress
some
of excellent
on the effect
small,
and compares
Status
difference
plate
in which
electric
which
of the achievement
Previous
The
bonded
to
details
the measurements
lines
by extensometers
employed
and experiment
of scribed
along
been
analysis
and Ra ctliff e 1 (Ref.
Dwight
section
have
However,
of which
pseudo-welds
study
should
literature
on plates
residual
This
the residuals,
9).
the lengths
as a result
measured
current
(Ref.
stresses
to be inapplicable
investigators.
and extensive
welding,
welding
by generating
of previous
at Lehigh
by comparing
before
red
tests
and Tall
of residual
found
investigation.
to measure
to those
Numerous
by Rao
this
control
were
that the residuals
experiments
results
process
for
the belief
the
excellent
welding
The
of the
plate
strength
only
centerline.
Structural
investigation.
by
about
The
Engineer”,
-31-
—HARDENED
EB
ZONE
&HARDENED
ZONE
25C
T! 1G
DATA OF Ref. 10 ON
0.062 ,“, THICK STEEL
SHEETS OF AISI 4340
22!
TIG
Ea
Fig. 18. Material Strength Variations
the Region of a Weld
20(
TENSILE
;TR~lNGTH
17!
]
EB
;:~:ERED
1
~,
15(
DISTANCE y = J!
TEWJ~ED
-
a
1
I
12!
~ esulting
about
1
plate
were
for
plates
stock
made
for
sheets
As
proper
cross
section.
with
heat
ber
of the
lished
the square
tube
machine
have
have
been
been
of the current
tests
were
milled
only
almost
project.
sheared
to size.
at high
rotation
of residual
of the plates
against
The
apparatus
for
The
speed
stresses.
welding,
an aluminum
provided
action.
EBW
would
from
the an-
final edge cuts
and low feed
The
cuts
were
no
inches.
This
sink
plates
and then were
preparation
orientation
stress
= 30 and would
b/t
the induction
O. 010
b/t
Boxes
in a milling
than
for
the larger
for
to minimize
deeper
compression
of the yield
Procedure
The
nealed
rate
centerline
small
Welding
1
3
2
5 percent
negligibly
‘“
accurate
mandrel
they
mandrel
were
which
clamped
was
in
square
in
positioning
of the plates
together
rotatable
in the vacuum
cham-
was
so that all four
corner
welds
could
be accomp-
in one pumpdown.
The
welds
the work
held
minute.
The
were
made
5 inches
beam
from
was
at 26 kilovolts
and
the gun a-t a feed
approximately
O. 010
10 milliamperes
speed
with
of 100 inches/
inches
wide
at the work
surface.
After
each
completion
end to the length
in the sketches
fabricator
after
of welding
the boxes
and squareness
of Fig.
grinding.
8.
A rigorous
The
boxes
were
surface
tolerances
which
inspection
was
were
inspected
ground
are
conducted
again
on
reflected
for
by the
flatness
in
-32and general quality
to the nearest
of the workmanship.
0.0001
All
dimensions
were
measured
inch.
insure
Prior
to testing,
the ends of each box were
surface
lapped to
maximum
uniformity
of contact with the loading
heads,
which
were
flat
boxes
and
square
required
sisted
of a su~face
which
comprised
O. 010
inches
General
grinding
inches.
at 45
edges
degrees
The transversely
loaded
before
testing.
This con-
to the planes
The grinding
was applied
the desired
contact
uniformity.
to achieve
Character
plate
nature
of residuals
sketch
appears
curves
simplified
0.6C
of the residual
in Fig.
of
stress
distribution
in a
19.
This agrees
with with the general
by Dwight and Ractliffe
and by the current
measured
The
be somewhat
of the plates
to a depth
of Residuals
A conceptual
investigators.
O. 0001
of the long
the boxes.
welded
may
to within
preparation
are
shown
smooth
as compared
1
and symmetrical,
to actual
which
stresses.
I
I
I
I
I
I
40
I
50
I
60
I
70
I
80
1
I
0.40
0.3C
q/q UCy
0.2C
0.10
0.08
ur/gucy:~1/2~Hb/t)
- 1]-’
\
I
20
0.06
I
30
b/t
Fig.
19,
Theoretical
Residual
Stress Curves
I
90
I o
-33The
sketches
The
duction.
ized
rectangular
to the actual
may
be graphed
Dwight
that
during
this
than crcyj
cussed
the manner
raises
questions
at the
plate
component
of I for
stick-welded
measurements
that the edge
was
used
ski-ess
made
can be much
and Tall
(Ref.
of the multiplier,
of measurement
as to the proper
As
plate.
entire
pletely
weld
should
reversal
strip
used
9),
g in
by different
procedure,
region
equal
as
dis.
strain
from
region
are
beyond
accounts
wider
for
shown
yield,
obtained
is much
the
stress
the
relation
of 39.2
edge
band
the higher
of increased
manner.
for
appear
in Fig.
in Fig.
23,
the
of the
by Rao
larger
stress
and Tall,
than in Fig.
stress
plate
distribution
which
hardness
field
center
found
fields
does
obtained
and yield
agree
9,
with
and by Buehler.
18 which
is
of the specimens
as compared
to
Evidently,
not account
strength.
Ref.
of the order
by Buehler
The
reveals
with
in the current
residuals.
at the weld
was
g was
22.
which
in agreement
Therefore,
ksi.
hardness
between
of
theoret-
in the center
except
The edge stresses
based on hardness
measurements.
in the current
study were of the order
of 45 to 50 ksi,
The
cen-
edge
stress
accumulated
the details
of those
yield
each
in a uniform
t-repanning,
operations
stresses
Furthermore,
the material
and
to the plate
the longitudinal
before
the shaving
considerably
tension
t-repan-
ses
sign.
from
nature
The
stres
centerline
plate
tests,
the Poisson
field.
strips
used
relations
appear
in Fig.
21.
When
the plate should have been com-
removed,
the residual
residual
the general
stress
the entire
was
preliminary
registered
of narrow
removed,
gages
centerline
the weld
across
reconstructed
The
from
was
from
only
residual
increment
edge
example.
of longitudinal
the weld
and the longitudinal
data
stresses
uniaxial
was
stress
in algebraic
The
found,
to reveal
elastically
of the
relaxed
gages
having
the machining
each
relaxed
details
pair
of stresses
It involved
ically
zone
plates
were
of Rao
the use
at the centerline
of the basically
procedure
terline.
for
(17)
19.
a single
after
gages
the distribution
the
study,
centerline
that transverse
The
approximation
yields
Procedure
In the current
the
in-
above.
Trepanning
ning
stress
If the ideal-
balance
the results
Hence
residual
r
values
with
10) and others.
investigators
u
in Fig.
show
agrees
Furthermore,
force
However,
which
which
2~t)
reported
g = 1.
investigation
(Ref.
17.
(b–
for
the sketch.
to be a close
a simple
shown
and Ractliffe
larger
Eq.
as
from
is as sumed
then
= 2gQtcrCy=
e
the model
self-evident
distribution
on the assumption
Buehler
20 depict
is
distribution,
2! tr
which
of Fig.
behavior
of 1.25.
studies
the narrow
properly
through
use
for
of
-34-
m’
ab -
+’4
IDEALIZATION
APPROXIMATION
TO ACTUAL
JI —
‘r
,
t
.
V: INTERNAL
Fig.
20.
FORCES
fied Residual Stress Fie’d Showing
ante of Internal Forces
$impl
Ba’
/r
EDGE
RESIDUAL
+,
abz -
I
Ab,TENSION
1
Amrl
to
Acr2
+
COMPRESSION
b -2Ab,
G-e, = —
b-2iAb,
‘e2 =
Am,,
2Ab,
+~bl)
2Abz
Au, z-(Am,,)
cej = b-2X:Abi Aurm-1,‘-’ Amc,
2Abm
Fig. 21.
Details of Edge Showing Procedure to Reveal
Residual Stress Field
T35500
T
400
h
b/t= 30
3-
b/t.50—
300
* (10–4)
200
100
—
0
.10
.20
~ - DISTANCE
Fig,
FROM EDGE IN,
Strain Gage Data from Shaving Operations
22.
—b/t=30
–_—_b/yz50
—_—b/,
,70
.
0 -
—
\
..
\
0.10
0.20
W-DISTANCE
Fig.
23.
Residual
FROM
Stress
0.30
EDGE IN
Distribution
-36-
Residual
stress
and the test
data
constructed
from
was
made
value
with
for
unity,
I
was
By
was
Eq.
converted
to the
curve
as
and the data
shown
A point-by-point
present
time
residual
because
stress
As
creasing
For
from
tion.
transition
The
residual
large
test
which
comparison
b/t
from
residual
of this
occurs
for
greater
the annealed
zone
prediction
each
appear
these
= 45
to impose
is the confrontation
in the following
to lie
section.
curve
T~ese
of the older
annealed
generally
plate
along
appropriate
that
at the
of specific
specimen.
60 the
b/t
of data.
band
and the absence
diminishes
residual
without
(from
appears
(and certainly
no penalty
with
with
apparently
curve
extremes
of the residual)
Below
to be
the Wr/wc
the current
or residual-free
between
assumed
data.
sets
of residuals
than
fraction
45 to 60.
stresses
data
was
s tatter
appear
data
of a reported
this
did not appear
the influence
to a vanishing
range
since
data
were
experimental
above,
the two
of the
2,
of the meager
can be seen,
b/t.
24,
of Ref.
information
subtracted
b/t
in Fig.
for
test
curves
e in the literature,
of 7 for
described
d e bottom
datat
The
this
to the evident
value
from
data,
current
results,
arr/rc
strength
the current
24.
In the absence
the operations
subtracted
through
e in Fig.
fit to the
be contrary
strength
line.
The
and 1 = 3.5.
at an average
performing
were then
drawn
and Ractliffe’s
it may
chosen
are
and Ractliff
(17).
g = 1.25
g in Dwight
although
while
curves
of Dwight
fully
effective
in the
= 30)
on strength.
the experimental
be
diminu-
to occur
at b/t
de-
may
the
The
data
-37-
0.5
0.4
0.3
q /vc y
0.2
0. I
Eq. (17); g= 1.25,
A
Ref. 2
0
CURRENT
1=3.5
o
TESTS
t
o
I
30
I
40
I
50
I
60
I
70
I
80
I
I
I
90
b/t
I .0
I
I
I
BOTTOM OF SCATTER
OLDER DATA
0.8
0.6
BAND,
THEORY
FOR
CURRENT
SPECIMENS
mxui~cy
(g=l,25
0.4
,1=3,5)
THEORY
FOR Ref.2
/
SPECIMEN
(g=l,l=7)
0.2
0
I
30
I
40
I
I
I
I
50
60
70
80
b/t
Fig. 24.
—.
Theoretical Effect on Compressive Strength
of Residual Stresses in Plates
90
-38-
DISCUSSION OF UNIAXIAL COMPRESSION DATA
Historical
Review
For
several
the uniaxial
rived
from
(more
Naval
Ship
Vasta
the basic
strength
the experimental
Basin
recently
results
The
scatter
= Z.25F
–
has
Basin,
Center)
band for
derived
determination
been
de.
Model
and currently
by Frankland
the data
from
of
the curve
at the Experimental
Model
and Development
12) et al.
of data for
plates
obtained
Taylor
with the plot of the equation
‘#
source
of ship
the David
Research
(Ref.
along
decades
longitudinal
the
(Ref.
appears
11),
in Fig.
25
the data,
1. Z5F2
(18)
=Y
where
F = (t/b) (E/cry)
The
experiments
one aluminum
and in the conduct
edges
Care
small
order
each
relative
More
recently,
the needs
models.
hinged
of which
Among
14,
flange.
Dwight
investigations
recent
data
early
Model
Basin
of the aircraft
industry
known
all four
data
are
stimulated
tests
the results
re-
field
appear
Data.
=
the data to the relation
(t/b) 3/4
conducted
for
They
as were
example.
of endeavor
in Fig.
(19)
by the Model
and steels,
in England,
this
more
along
loaded
the best
1/2
were
and Ractliffe
for
support
individually.
The “models
Thicknesses
were of the same
investigation
(that is, 0.030 inch).
He fitted
15 and 16) on aluminums
bibliography
was
simple
and on
of the experiments
(Ref.
13) who subjected
square
and rectangular
forces
and related
the ultimate
strengths
to that
(cru/mcy) (rcy/E)
Further
of steels,
in the design
to achieve
in the current
ported by Needham
tubes to compression
of a long,
on a variety
taken
to ship dimensions.
as the models
on aluminum
conducted
was
of the tests
of the plates,
were
were
alloy.
1/2
also
Staff
in Ref.
17’. )
general
These
with the outlines
reproduced
(Refs.
by
(An extensive
appears
Z 5 together
are
Basin
researches
of the
on the logarithmic
plot of Fig.
Z6 to depict the character
of the scatter
band which results
in order to assess
the utility of the relation
advanced
by Needham
(Eq.
19) who derived
The
his
result
information
from
shown
such
in Figs.
plots.
Z5 and 26,
together
with Eqs.
(18) and (19),
represent
inception
of this project.
amount
seen
of scatter
to exist
mendations
for
between
have
been
the status of uniaxial
strength
data at the
From
Fig.
25, which reveals
the smaller
a
significant
discrepancy
is
each group of data,
Recomthe earlier
and the more
recent
studies.
made
to employ
relations
other
than Eq.
(18) in
-39-
W, u
/9
pLATE STRENGTH DATA
(NOtc:
This is Figure
Fig.
2 plus lest points of current
investigation.
)
25. Scatter Bands for Older and
More Recent. Strength Data
10
,0
00,
t
Fig.
!
1
1
I
I
I
1
1
I
10
~
26.
Logarithmic Presentation of Strength
Data Based on Eq. (19)
100
-40order
to reflect
this
of the current
order
to ascertain
Strength
Data
The
which
points
were
appear
as
the
from
2).
is little
be through
achieved
Bonndarv
Boundary
restraints
conditions
plate.
It probably
hand,
the difficulty
which
were
able
ideal
lie
be open
for
appear
and
seeking
of
in Fig.
27.
Ractliffe
in which
recent
recent
nature
They
boundary
in a range
and more
and more
Dwight
to measure
were
relate
plane
data.
a resolution
data.
That
of the boundary
to the control
of a plate,
to
would
conditions
During
most
of the plate
support
test
load
and Ractliffe
2 percent
segmented
of transmitting
into the
in spite
employed
load
longitudinal
it is
on a single
On the other
freedom
in single
possible
to effect
plate
supports
which
of the considerable
to avoid
transfer
and therefore
test
tests.
It is also
transfer
In fact,
plate
the
to the edges
However,
rotational
to experimentalis’cs.
the edge
programs
parallel
in a practical
complete
over
and to the rotational
or is not considered.
simple
of achieving
to the edges.
capable
may
lower
of
test
investigation.
the
by Dwight
is t-rue that w = O in most
known
actually
in
strengths
Three
patterns
of results
in the plane
of longitudinal
run parallel
along
the early
the edges.
to be nonexistent
is well
sets
usually
to the
along
to achieve
amount
by this
obtained
the early
of deformations
tions
those
represent
str~sses.
Buckle
of the actual
normal
is assumed
Part
results
Evaluation
imposed
restraint
example).
the tests.
Condition
displacements
to lie
data.
avenue
examination
during
re suits
seen
both
between
for
of these
of the differences.
of residual
between
pos sible
the discrepancy
deemed
with
to choose
one
However,
which
are
Unfortunately,
(Ref.
some
well
15,
and 26 ostensibly
of the earlier
agree
there
plates
25
to those
which
band
explanation
and free
contributed
results
difficult
flat
14 and
to examination
Investigation
in Figs.
were
2,
(Refs.
devoted
Current
crosses
scatter
The
was
a possible
results
plates
behavior
project
into
this
edge
might
precau-
effect,
they
restraints
not have
been
load.
Fig.
tudinal
Typical
27.
Iy
Compressed
Buckles
Tubes
for
Longi-
-41The
by slit
ning
unloaded
cylinders
to buckle,
transverse
loaded
then
result.
the
2 percent
grading
Residual
may
through
c+
The
current
have
+ c+
have
strength
the agreements
rise
plate
may
only
of residuals
no influence
the
importance
role
is
test
annealed
specimen
Luders
bands
several
locations.
dual
plus
this
relatively
load)
designs
s~all.
b/t
stress
abso-
In fact,
55,
only
a negli-
in reducing
carbon
was
where
at b/t
the
‘
30 reveal
strength
to scatter.
a result
strain
of considerapproach
axially
loaded
to 30 k si.
across
the full
widths
of the plates
The
hypothetical
account
low level
for
the
presence
of machine-applied
45 ksi
of the Luders
stress.
to
An unDeep
= 30 was
of about
with
)
determination.
stress
(20)
plates.
greater
yie?.ded
in
observed
total
the
a rapid
tha~ Eq.
steel
b/t,
In
influence
be considered
of the cr~~ical
strength
orI
shown.
55 there
slightly
&at
are
to indicate
be charged
conducted
with b/t
than
small
to
current
also
the results
(The
28 must
The
of decreased
must
appear
lead
of residuals
above
is toward
in plate
would
2) that the
(20) may
effective
70 on low
stresses
were
1,
b/t.
24.
less
was
which
data
exceeds
was
b/t
for
to the understanding
of residual
Fig.
results,
For
The
in Fig.
investigators,
a = 1,
small
and the trend
of residuals.
shown
An additional
able
down-
(no residuals,
of the effect
whereas
b/t
in newer
influence
as
for
of residual
01 Eq.
with
from
of the residual
when
use
plates
residual
strength.
virtually
residuals
data
(20)
general
for
is clear.
in the percentage
determining
trend
(against
test
it is impossible
(Refs.
plate
and Ractliffers
plate,
by many
(13) with
prediction
of the measured
of a perfect
The
that
good,
on strength
be used
force
a basis
in the presence
reproduced
and Dwight
data,
strength
the edge
qwcy
=
the
as
general,
Iraction
Since
un-
restraint
the early
hypothesized
of Eq.
CY
shown
strength
gible
within
of the axial
be made
of a perfect
penalties
28 contains
of residuals
each
membrane
results.
measured
been
strength
strength
severe
Fig.
been
also
the relation
Cy
data
longitudtial
recent
it cannot
along
plate
and Ractliffe),
date,
It has
to the
unnecessarily
the
in- plane
to 5 percent
is begin.
introduces
Stresses
compressive
flat)
bind
supported
wave
sinus oidally
to
were
which
data.
stresses
be related
lutely
at this
above.
longitudinal
able
with the more
tests
m a plate
a longii-udinal
but measurable
by Dwight
of Residual
reported
are
Basin
tight.
distribute
had amounted
better
the early
Influence
to form
forces
measured
that factor
Model
finger
which
a small
If this
agree
to check
as
forces
If these
edge.
may
of the early
together
the tendency
shear
restraints,
would
edges
bolted
at
(resi-
bands
at
-42l,o Y~
OOTTOM OF SCATTER BAND, OLDER DATA
0.8
“\:
\l
\
THEORY FOR CURRENT
- SPECIMENS
0,6 —
‘A
I
g.
u/o,y
0,4 —
rig.
28. Effect of Residual Stress.
Comparison of Theory with Experimental
Data
lWEORY FOR Ref. Z SPECIMENS
I
0.2 —
0
—
0
CUI?RENT —
A
Rcf, 2
I
30
50
~o
76
60
90
60
bll
In spite
agate,
time
no motion
detected
The
of the early
The load
was
appearance
maintained
of the bands
was
at one of the bands,
l/3
2 inch
modulus
buckle
the
of
of the curve
strain
increased
until
failure
for
results
of this
the end
shortening
supplied
to induce
creep
was
creep.
could
controls
increased,
transferred
Fig.
29 which
joined
to generate
tangent
and
slowly
of the
the
plate
edge
The
This
may
at an edge
continued
As
load
be s em
When
down
and the total
plates
The
load
was
did not directly
qualitatively
strip.
field.
of the center
the machine
machine
before
to move
state
the yield
in the
section
since
not large
the 3-column
stress
edge
the two are
the testing
of the combination
up a portion
was
since
not a deformation.
machine.
approach
period
reached
specimen
compressive
stress.
the unstressed
in the
strain
the 3 hour
had
the residual
the head
was
typical
the critical
during
load
residual
orI the upper
As
toward
at 36.4 ksi,
If the machine
than the center
and took
was
motion
a force
depicts
shorter
down
was
at the knee
the load
head
occurred
the
shown
sed
by the low
period,
support
occurred
have
the specimen
tension
line
buckle.
material
by machine
to the testing
increase
which
specimen
No creep
machine
ridge
of a short
the plate
constant-load
occurred,
strength.
enough
for
which
b~t = 30.
to plate
level,
A slight
indicative
did not prop-
during
.
of the data
The
they
3 hours
can be explained
curve
At the end of the 3 hour
rest
for
discernible.
possibly
wavelength
stress-
of the bands,
constant
in
strip
is
assumed
machine
it diminished
pres -
the
edge
compression.
the edge
unloaded
strips
returned
strain
at the center
(=e + EC), was transferred
to the machine.
The precise
nature of the
process
requires
measurements
w-hich could be made in a subsequent
project.
it is clear
However,
to the machine
load
will
exceed
that the
s pecimen
the end- shortening
strain
corresponding
strati
induced
by
the machine.
Buckling
Stress
Two
duals
was
face
Determination
experiments
as applied
applied
back-to-back
of a specimen
reveal
to elastic
the utility
buckling.
oriented
with b/t
= 70.
of the addition
M the first,
longitudinally
The
difference
a pair
rule
for
resi-
of strain
at the center
in strain
gages
of one
between
the
-43TOP
EOGE OF PLATE
BEFORE
LOADING
/
r 1’
WELD
SHRINKAGE
PLATE
+
L
l-h
n-!
-(a/2)cc
____ =.==-=
.- i
T’
I
+(0/2)ce
T
+Ue
1
‘Ur
,lt
L
rl—b—
+~~t
-
JOINED
SEPARATED
STRESSES
(t DEAL12ED)
,
Fig. 29. Schematic of Testina
Machine Interaction with Smal~
b/t Specimens Conta ning Residual
Stresses
FOR AN ELASTIC
STRAINS
(IDEALIZED)
PLATE,
me :Ege
Uc :- E.sC
two faces
ive
was
force
behavior
recorded
and is
ofa
solid
curve
cally
perfect
shown
plate
plate
This
the upper
of 16.8
from
Eq.
The
(5).
as sumed
to pertain
the back
extrapolation,
sum
this
appears
Fig.
of average
The
30.
the
application
rule.
is
then
of 5,4 ksi
was
(Fig.
stress
21.4
obtained
stress
would
buckling
elastic
ksi
is
24)
stress
for
This
a critical
the theoretical
rule
slope
occurred.
stress
the residual
with
in
the data
of zero
30 yielded
the buckling
with
parabolic
extrapolating
a point
buckling
value
the addition
4.1
ksi
b/t
= 90,
as
zone
buckling
in this
)
The
and
from
yield
a
stress,
buckling
Fig.
data
load
be taken
24).
This
must
because
in
strain
stres
case,
ses
experimental
appears
initially
on
at the beginning
of this
were
used
Consequently,
was
the residual
to support
the
a secon-
and theoretical
while
the
appears
the gages
pattern.
respectively,
also
yielded
which
of the insensitivity
(In this
show
ksi
of gages
load
of residual
13.0
pair
of applied
membrane
problem
of 9.0 ksi
(from
case
of instability.
postbuckling
to the
a summing
a function
experimental
consideration.
cal values
was
for
strain
to the inception
to reveal
dary
the theoreti-
b/t.
of the nonlinear
plot
of the
The
of the load-lateral
of the buckling
agreement
to substantiate
1).
between
for
of Fig.
stress
together
good
On a specimen
curve
means
at which
value
plate,
(Ref.
buckling
to obtain
the plate
to this
in reasonably
which
a possible
residual
representative
portion
beyond
of the curve
theoretical
compress-
plate.
as the load
If the
resultis
imperfection
that the curved
for
longitudinal
the difference
the plate
provides
segment
extrapolation
ksi.
This
initial
indicates
for
can be identified
backward
30.
small
as sinned
relationship
character.
of applied
and the imperfect
It is usually
which
in Fig.
witha
on the figure
deflection
from
as a function
critistress
the addition
I
I
I
I
I
500(
400(
300(
P(lb)
2001
1 %
O EXPERIMENTAL
REPRODUCTION
x-y PLOT
OF
POINTS
/
b/i:70
(9-90-1]
PC~= 4240
lb
b/t=
1001
(EKp.?r.
uC~=16. S2 ksi (Exper. ]
Ucr
~r:
‘21.40ksi
5.45
ksi
Ucr=
(Theory,
Eq. (5))
(Fig.
Curve)
24,
90
(7-70-1)
PC~=2930
)
lb {Ex Per.)
9.04
ksi
UCr =12.98
ksi
Ur’
4.13
ksi
[Exper.)
(Theory,
(Fig.24,
Eq. {5))
Curve]
/
.~
\,
30,
Effect
of
llesiduals
on
400
200
)
500
KK30
1500
STRAIN DIFFERENCE (ARBITRARY UNITS)
Fig,
I
I
I
o
STRAIN SUM (ARBITRARY UNITS)
Longitudinal
Compressive
Buckling
i
-45-
DISCUSSION OF BIAXIAL COMPRESSION DATA
Introduction
The
buckling
longitudinal
nature
and failure
or under
compression,
compression,
of uniaxial
may
occurs
and in which
cess
Furthermore,
.
uniaxial
was
be involved
plates
compression
found
longitudinal
factors
of the methods
of rectangular
transverse
to be
compression.
in the complex
under
-transverse
in conjunction
with
radically
different
from
Apparently
numerous
manner
in which
the
buckling
the buckling
process
influences
the failure
prowhen transverse
forces
are present,
the details
of testing
also
seem
to be much
more
critical
than for
te sting.
of these
Some
expositions
are
factors
are
presented
summarized
of wide
column
briefly,
after
behavior
which
and biaxial
behavior.
Wide Column buckle
Possible
Influencing
Numerous
biaxial
depth
size
stress
ratio
of transverse
also
the transverse
plates
.
The
and the character
could
loading
as well
affect
and
shape
and
be
properties
in the plate
parameter,
31.
, and the size of an imperfection
relative
significant
for transverse
loads . The
may
of material
field
could
of rectangular
imperfections
of a buckle,
uniformity
shown in Fig.
conceivably
and strength
of initial
are
Factors
factors
buckling
to the
shapes
be relevant.
to longitudinal
as the magnitude
of the
residual
Furthermore,
loading
would
of load
compared
of load
application
t-he
be a prime
to critical
stresses.
The
would
plate
could
lead
various
ratios
might
of
since
over
The
indicate
transverse
to the long
data
level
unity
head
edges
restraint
the friction-induced
of this
state
load
from
phenomenon
on the transverse
strains
in biaxial
locations
and the increasing
of the
specimen.
load
between
inner
may
be obtained
with b/t
of friction
might
edges
boundary
acting
result
in
as a result
of
and outer
from
precise
shape.
of hinged
This
long
for
trend
controllability
the loaded
as
curve
the loading
sequence
thereby
exercising
mode
due to the presence
.
a test
the
compression
stresses
Finally,
of the plate
and failure
in the
along
unequal
at various
to longitudinal
uncertainties
at the loading
of stresses
during
throughout
The shape of the stressstrain
control
the plasticity
reduction
experiment.
the po stbuckling
departures
rotational
measure
with
of stresses
be determined
of transverse
the ultimate
possible
conditions
it would
it should
theory
influence
cent-rol
localization
to failure.
and actually
correlation
uniformity
to nonlinearity
is increased
be important
factor,
some
from
the possible
and could
tlm load
for
departure
control
plates.
evaluation
Some
of the
-46-
Fig, 31,
The
columns
The
measurements
appear
scatter
smallest
percent
except
fore,
in Fig,
between
and the
must
friction.
The
strain
ratio
If the precepts
strain
would
(at one
of the inner
which
the trend
of the critical
a prime
strain
include
the
strain
arising
residual
stresses
whether
the plate
is in the prebuckling
This
would
indicate
cator
stresses
involve
the principal
The
stress
ratio
indicates
initial
formation
membrane
in the Theory
to diminish
complete
is the
was
same
increase
buckling
problem
furnish
strain
stress
ratio)
buckles
and critical
becomes
one of
.
increases
with b/t,
of the plates
action
project.
to
the transverse
buckling
A precise
of
that the
the increasing
latter
in a later
indi-
as a function
before
on transverse
stress
to
and also
residual
in susceptibility
this
to
were
a good
It is apparent
Conceivably,
Intuitively,
of this
residual
longitudinal
be expected
lines
behavior,
critical,
as the
indicate
configuration.
node
of the plate
and from
would
buckling
sine e the
the plate
influence
the transverse
should
preceding
the
applied.
the biaxiality
section.
ratio
would
applied
forces
would
transverse
parameter
reveals
of shallow
analysis
the
longitudinal
the possible
stress
reflect
table
The
ratio
to aid
strength,
parameter
external
strain
invoked
and
strain.
imperfections
in identifying
elastic
(which
that
are
or postbuckling
importantly,
then
following
which
also
b/t,
from
immediately
Most
factors
the theoretical
words,
shape
failure.
initial
There-
of transverse
buckling
a relevant
resultant
and whether
In other
of the mode
preceding
whether
significantly
be anticipated.
The
20
small.
strain/critical-
approach
to the critical
internal
be magnified
.
for
faces)
about
explanation.
and biaxial
strain
wide
as well.
with b/t
effect
applied-
that
candidate
of the applied
was
strength
than in the
for
) averaged
difference
of the longitudinal
value
end of the outer
faces
of increased
of transverse
that
the
elsewhere
a candidate
in the understanding
ratio
strain
sought
influence
then it follows
greatest
= 30 for
becomes
be the
the theoretical
for
be
in the four
shows
(at one
for b/t
strains
32 which
the
strain
an explanation
apparently
of the transverse
Wide Column Buckle Photographs
might
trend
may
as
discussed
be
expected
answer
awaits
a
-47-
1 PY
A-d
0
-b
c -Q
D-Q
1000
I
I
I
I
b/t = 30
I
x-
%
‘Y
(10-6)
~
M
B
,
H
I
I
0
I
I
Py (lb)
200
I
I
I
5000
I
I
I
160
I
I
I
I
I
I
I
b
b/t =70
b/t
=90
~-
K
P
B
100 -
80 -
g
k
@
P
H
o.
o
I
I
I
600
Fig.
I
32.
1
Transverse
I
1200
0
Strains
I
0
in
1
600
Wide Columns
I
1
1
1200
-48-
Table
G-r (ksi)’~
14.9
(k~i)>!<>x
‘:’:Eq.
For
verse
b/t
of slightly
4.16
21.5
0.19
13. o
0.32
0.25
24
= 30 a slight
nonuniform
difference
slippage
maybe
plates
initial
bowing
the transverse
Biaxial
5.46
8.00
42.0
in the two outer
of initial
rotational
90
70
(5)
strains
amount
50
0.13
of Fig.
For Wide Columns
Ratio
117.0
x Cr
‘~ Curve
.
bearing
01 the box
seen
This
may
between
have
of the unloaded
as a whole,
due to a diminution
loading
the trans-
been
the result
edges
, to a small
and possibly
in alignment
to slight
of the box
within
fixture.
Compression
The
experimental
Typical
in Fig.
33.
a large
reduction
b rane
stress
results
are
is
in plate
applied
applied
stresses
plates
pertinent
which
34.
strength
with
in view
practice.
are
membrane
in Fig.
in conjunction
increases
It should be
with residual
for biaxial
appear
longitudinal
shipbuilding
to be large
mate.
results
buckles
particularly
in current
appear
b/t
equal
75 percent
results
show
mem
loading.
toward
for
-
The
small
to 70 and
strength
remembered
that the
stresses
present.
appear
clearly
transverse
longitudinal
For
as
when
data
of the trend
in transverse
as much
stresses
The
90 there
longitudinally
of the uniaxial
in Fig.
ulti-
33 pertain
to
Three
regimes
of behavior
are involved
in the plot of Fig.
33.
b/t = 30, for which the results
appear
to follow
the trend of the
For
hypothetical
occurred
there
plate
appears
This
for
Table
ported
b/t
which
latter
behavior
2 summarizes
of flanges
the
Theory
.
In this
width
for
failure
may
be assumed
plastic
plate
buckling.
from
plastic
plate
is typical
behavior
of longitudinal
is offered
as
an
to have
At “b/t = 50
to the
compression
explanation
of the
= 70 and 90.
and the assumption
(h flanges,
3,
action
by a pair
effective
of Fig.
of biaxial
to be a transition
flange
strength.
results
line
as a result
multiple
h/2
Strain
30
Er/E
the
Critical
b/t
u~ cr
b/t
9.
the loads
for
each
of a uniform
of the flange
example)
section,
initial
examination
theoretically
type,
distribution
.
If more
in accordance
then the
which
plate
2-flange
based
could
upon
of the yield
than
with
force,
of the biaxial
2 flanges
data
across
active,
advanced
can be multiplied
3 flanges
sup-
(1 O)
strength
are
the hypothesis
PZ,
be
Eq.
were
in
by
assumed
-49-
2
ky 7r2 E
G’
y(ExpE~)
12(1 -V2)
+
()
-a
-Q
kY
Q
2.0
Q
Q
G
I.0
(!)~
)
d
b/t
G
b/1 : 50
Q
b/f
= 70
b/1
❑
@
00
Q
HYPOTHETICAL
lNTERfic
TIo N
:30
h
>
CURVE
(0.862,
0.555)
90
I
0.25
I
0.50
I
0.75
ox /ux ~
Fig. 33.
Fig. 34.
-.
_
Biaxial Strength Data
Biaxial Buckle Photographs
1.00
-50active
for
b/t
assumption
which
= 70 and 4 were
would
the longitudinal
control
over
project.
pattern
in each
number
The
buckle
experimental
forms
the results
is
for
shapes
typical
wide
of several
evident
where
to the plates
more
If the capability
depends
upon
greater
with
larger.
tive
b/t
for b/t
Fig.
it is
for
expected
= 70,
shown
similarity
which
reacted
were
cemented
plates
support
in Fig.
while
merely
by cerromatrix
t~he simple
The
34,
The
ends
condi-
27.
, the
shape
typical
However,
the
heads
the head,
which
then
simple
support
the longitudinal
perhaps
and no effective
transverse
to enforce
the capability
edge
be
at that
be partially
might
be
would
be effective
would
flanges
components
pressure
could
a flange
should
effec-
be anticipated
of the biaxial
fields
for
appear
in
35.
On the basis
of effective
plotted
of the preceding
flanges
in terms
theoretical
multiple
strength
The
results
plotted
assumptions
in the various
of the ratio
longitudinal
plates
flange
strength.
ratio
discussed
appear
in Fig.
ter band
the
which
precludes
general
conservatively
The
which
drawing
time
that the
no hypothesis
conclusions
the lower
parameter
border
includes
of the
affected
can be offered
.
variable
However,
buckling
the nature
values
residuals
been
to the
is the
33.
chart,
the octahedral
shear curve,
shear theory.
The size of the scat-
to affect
the numerical
It is probable
At this
load
be presumed
to substract
along
strength
independent
of the normalized
lies
longitudinal
may
transverse
The
the number
data have
previously
and shown in Fig.
36 which contains
the normalized
reliable
character
concerning
, the biaxial
of measured
thr~e - segment
buckling
interaction
and the two lines of the maximum
has
of the
tubes.
in Fig.
were
the
that two flanges
= 30 and 50,
Typical
= 90.
test
seen
tubes
For
.
of boundary
in Fig . 33.
test
restrained
under
b/t
for b/t
of the buckle
is not certain.
smaUer
Thus
location
be
appear
of tha longitudinal
the friction
to define
30 in the
the assumptions
of several
may
specimens
condition
of
However,
than
evidence
for
pattern
measure
greater
the choice
approached
failed
of that
for
plates
internally
closely
of the longitudinally
attainment
head
some
it impossible
b/t
the
of the ends
tests
a different
the buckle
.
of the biaxial
loading
and were
behavior
make
support
columns
biaxial
the ends
by the longitudinal
edge
justification
in the
Actually,
since
on the plate.
for
to employ
in the plates
90.
exercises
lines
conditions
to provide
flanges
available
ridge
of the behavior
plate
‘
Nx/NxU
vvould induce
It is necessary
failed
for b/t
each
of interior
nature
of effective
is
for
in the boundary
the precise
current
tions
loading
the number
the uncertaintiess
reliably
assumed
be appropriate
the trend
interaction
curve,
of the band.
the
residual
of the curve.
residuals
from
the nature
to explain
stresses,
It is possible
that parameter,
of the
data in Fig.
the character
data.
The
strength
emphasis
of the current
of a rectangular”
plate,
investigation
and the influence
is upon
the longitudinal
of various
factors
36.
of the
-51upon
that
strength
to the scientific
transverse
strength
It has
longitudinal
character
The
from
which
can be
all
simplified
sine e Youngl
The
tion
of Fig.
shown
b/t.
the
.
that the critical
in deciding
the
fore es
behavior
to the elastic
This
involves
resulting
Therefore,
elastic
upon
loading.
and the associated
equal
for
and germane
the effect
strain
the externally
from
the residual
the longitudinal
strain
stresses
(32)
x
cr
or k
The
tie
.
parameter
may be chosen
the same as
When it is plotted
against
the strain
points
fall
data clearly
strength
for
each
appears
on the ordinate
into
show
b/t.
The
to be in the
axis
a fairly
well
defined
how the longitudinal
transition
region
of b/t
is the transverse
strain
between
degrada-
= 50.
buckling
The
coefficient.
= 3.
The
scatter
factors
conceivable
may
strength
33,
and enhancement
various
instructive,
to explore
cane els .
in Fig . 37,
each
affects
a/b
is
loads
= (Crx+ o-r )/o-
transverse
for
reference
for
load
to the form
s modulus
ordinate
as
felt
by the longitudinal
strain
the longitudinal
x cr
ratio
failure
longitudinal
Ex/e
ratio
is induced
force,
P , and the internal
of the c%rrent
investigation.
applied
stresses
region
it was
of the investigation,
of the transverse
resulting
the
However,
been established
in preceding
discussions
strain field should play an important
role
of the plate.
ratio
value.
character
that
be most
the application
in the data
enumerated
control
of each
group
of the boundary
important.
of N
fied
in the figure.
with
preceding
Furthermore,
before
N
in every
This
discussions
may
at the beginning
rnigh~be
conditions
section,
on the
the loading
case
important
on the buckle
be attributed
of this
except
for
pattern.
large
short
sequence
for
to the
It is
edges
involved
the few identi-
b/tin
accordance
-52-
Ipy
1000
500
I
I
I
I
I
I
I
‘B
b/t= 50
Ux /uxu =0.54
b/t = 30
rx/O-xu =0.59
b
%
PB
8
‘Y
(10-6)
b
@
$
o
I
I
I
1
5000
o
I
I
600
I
I
I
b
b/t =70
lzK/uxu=o.50
200
I
2000
I
1000
o
(lb)
‘Y
300
I
0
‘0
-
400
Q
I
I
1
b/t =90
Ux /u-xu=o.41
Q
‘D
b
I 00 -
Q
Q
‘D
b
Q
—
Q
1
o0
Fig.
35.
I
Q
I
I
1000
Strains
I
2000
Due
to
Transverse
o
I
1000
I
I
2000
,oads on Biaxially Compressed Plates
—
-53OCTAHEDRAL
SHEAR
THEORY
1.
Q
&
e[
MAXIMUM
SHEAR
THEORY
$ /Ph
Fig. 36. Normalized Biaxial
Strength Data
o.!
c
I
0.5
Px/P,u
4
1
1
b/1 :90
3
*
37.
Transverse
Plate Strenqth
as
a
Fu;ction of Lonqituilinal Strain Relative
to Critical Strain
Fiq.
MY
z
y--r
e-
——————
—--—.——
(5
1
TRANSVERSE
$TRFNGTH
DEGRADATION
e-
(b
e
h
e-
\\
b/1x50
h
b/! =3<
0,
—
.-
_54-
EFFECT OF NORMAL PRESSURE
Introduction
The
normal
with
current
b/t
plates
was
The
theories
(Ref.
stresses
relate
which
sure
under
The
seen
data
pressure
normal
pressure.
stresses.
plate
longitudinal
bending
built
in long
were
edges
which
is
with
to correlate
in the light
required
before
it
experiment.
mode
basically
alone.
the
They
shapes
same
displayed
difference
no normal
strength
was
of the plates
pressure
in
as in
the three
a slight
with
was
in the presence
10 which
of data
contains
centerlines
stresses
with
to
vacuum
applied.
38.
sets
also
and bend-
do not appear
is presented
in the centers
in Table
Both
to
rather
that
the Iailure
were
observable
to which
in Fig.
table
relate
Strength
walls
only
lengths
appear
The
of theory
compression
on longitudinal
normal
pressure
They
deflections
procedure
vacuum
tube
The
to the plates
.
of membrane
of pressure
A predictive
uniaxial
of normal
or hypothesis
of internal
form.
be
addition
on Longitudinal
in the buckle
may
appears
of transverse
data,
compressed
classical
These
of
strength
the effect
purposes
predictions
correlation
In the presence
compared
b/t
of transverse
yields
the effect
to discuss
the uniaxially
increase
influence
transverse
reduction
to the influence
of a theory
data,
factor.
of Pres
the tubes
large
predictive
growth
3) which
the absence
of an influencing
Effect
for
= 90 a large
or to the algebraic
expe rirnental
lobe
for
7) and to the
(Ref.
is possible
or upon
b/t
relate
to the expe rime ntal
In
the
for
to be useful
than to strength,
ing
identifiable
observed.
do not appear
buckling
little
strength,
However,
.
In fact,
significant.
strength
revealed
on longitudinal
the lower
to be
studies
pressure
shows
because
involve
the presence
stresses
normal
orI the assumption
of the
change
the bending
by the applied
calculated
and absence
little
symmetry
of
due to
of residual
induced
at the
pressure.
The
of completely
involved
in the tubular
construction.
As
b/t
= 90.
lower
Effect
b/t
tained
..
For
reveals
b/t
values
large
in Fig.
for b/t
, the bending
= 70 it was
it was
of Pressure
The
evident
the table
much
about
The
beyond
of yield
yield
while
for
for
the
Strength
pressure-induced
= 70.
was
smaller.
on Biaxial
39 for b/t
stress
60 percent
= 90,
reductions
while
influence
moderate
of pressure
in biaxial
strength
reductions
were
in the current
are
sus-
investi
—-
-
..-
—
—.—.
- -.
.55_
Fiq. 38. Buckle Patterns for Lonaitudinallv
‘Compressed Tubes with Internal ’~acuum”-””””
Table 10.
Effect of Pressure on Longitudinal Strength
b/t
u
XU,
pressure
u
Xu,
ksia
no pressure
- ksib
aTable
gations
it was
40 percent
loss
of the bending
Table
was
(p/Z)
21.30
16.00
36.91
30.46
20.32
16.43
4.8
13.3
26.0
42,9
@/t)2withpfrorrTable
tohavebeenn~gligibleforb/t
to bypass
testing
b/t
in strengthforb/t
stress
strength
of phenomenon
mentioned
diction
tion
30.47
induced
5
= 50,
= 30 in the
current
= 90 maybe
by the normal
and consequently
The
project.
explained
pressure
as
on the basis
shown
in
10.
This
type
36.63
b
5
appears
elected
90
70
ksia
with
‘b
50
30
with
loss
apparently
assumed
previously,
the data was
is not readily
not
available
results
from
the combined
stress
by Tirnoshenko
(Ref.
3).
However,
as
an attempt
to match
Tirnoshenkol
s pre successful.
without
Furthermore,
extensive
studies
an explanaof other
approaches
.
4
I
I
I
bit =50
‘Y
2 0{}
@
Q-
A
O-
Q-
0
I
(+
I
0.50
0
Cx
I
I.0
/axu
b/t
=50
4,
I
I
I
-0
a
Q
-Q
kY
Q
2
‘Y
Q
?
?
$
0.50
mx
b/t
p,o
o
*
*
•1b
I
o~
o
-0
2 -
1.0
oo~
/mx ~
1.0
o-~/u~
b/t=
=70
IJ
90
P<o
9-INTERNAL
VACUUM (IO.3T0
A–INTERNAL
PREss
Fig. 39.
URE(AS
11,6
sHOw
PSI)
N,psI)
Effect of Pressure on Biaxial Strength
-57The
ant
tests
sequence
brane
b/t
on specimens
to the project
as it affects
loading.
= 90.
first
case,
pressure
fir st,
time
a typical
with
the lateral
followed
three
The
vious
Nothing
seconds
more
N,
the tim~
from
failure
the three
by N
lobe
un~axial
about
was
occurred
lobe
same
type
buckle
machine
before
longitudinal
form
.
Then
snapped
to
N
was
during
were
could
was
the transverse
applied
N
was
A% that
in the tube
of the plate
of the prethe few
changed
be increased.
(ah-no
memwith
In the
~ase
observed
to the value
controls
loading
40.
as previously.
However,
the load
pattern
in Fig.
of-magnitude
increased
import-
on two tubes
Ifi the other
value
the order-
at first.
the buckle
by N
column.
most
with biaxial
depicted
followed
then
happened
were
of the pressure
conducted
are
to the
the testing
of failure
were
applied
role
in combination
as a wide
pressure
in which
strength
the
sequences
deflection
thickness.
test.
was
occurred
and 6-90-16
identified
experiments
two loading
which
3-90-11
they
plate
The
The
to failure
applied
since
to applY
At
st instantaneously)
wide
column
form.
SPECIMEN
P
.
3-90-11
8.34
/’
ksi
o
~Y
~.69ksi
‘Y
\
Fig. 40. Load Sequences for Tests 3-90-11
and 6-90-16
SPECIMEN-6-90-16
-58-
CONCLL!SIONS
The
ever,
be borne
plates
, fabricated
=3,
and with
1.
The
radically
a large
appears
tudinal
loading.
longitudinal
the mode
that
the influence
cant
the
at b/t
100.
than
stress
Beyond
stress
sible
by
less
residual
ual
under
direct
of the
by the welding
3.
Theory
of welding
uniaxial
4.
strength,
which
The
same
be
greater
may
b/t,
on the
said
with
of biaxial
a pressure
and becoming
as high
6.
that
in current
to 10 percent
greater
atl
with
.5.
model
than
This
the latest
tests
large
It appears
curve
for
use
O to
of the
resid-
it appears
posplate
parameters
with
a/b
influence
= 3 under
demonstrated
longitudinal
advanced
for b/t
was
found
hypotheses
to agree
-
.
For
to degrade
the
increasing
as 40 percent
shown
neglicompres
= 50 or less.
degradation
to consider
strength
States
values
a gradual
bring
with
at b/t
with
= 90.
results
from
tests.
appropriate
in the United
would
the
were
scale
longitudinal
in the present
2.5,
of
from
a significant
to have
of 10 psi
with
design
longi-
insignifi-
of a welded
of a plate
strength
rapidly
the
plate
amount
process
previously
with
Small
strength
upon uniaxial
dramatically,
reported
steel
becomes
herein,
indicate
appear
pres sure
is in line
however,
5.
buckling.
loading.
strength
previously
by the full
both
biaxial
b/t
b/t
biaxial
is increased
displayed
strength
experiments
of normal
sive
of
smaller
and experimentally
on mild
on the welding
membrane
Current
influence
the
.
stress
transverse
to involve
40 and 60 the percentage
longitudinal
and expe rirnent
residual
For
loading
strength
reduced
data
there
of longi-
hypothesis
of plastic
stress
between
is
90,
appears
theoretically
of the data
realizable
utilization
induced
gible
the
to be that
influences
strength
b/t.
is
For b/t
accompanies
= 70 and
mode
compressive
At b/t
loading
in the presence
large
residual
uniaxial
On the basis
to predict
with
demonstrated
which
60 the
.
, with
loading.
to the two- flange
appears
40.
conducted
steels
membrane
b/t
the failure
plates
of welding
strength
HOW.
were
strength
For
strength
cases
of failure
It has been
tudinal
in longitudinal
, analogous
for
biaxial
longitudinal
loading.
transverse
strips
tests
elastic-plastic
under
under
reduction
strength
2.
failure
In these
flange
applicable.
in.
of transverse
to be greater
transverse
typically
of a plate
from
generally
that the current
from
failure
the application
maybe
in mind
t = 0.030
different
= 50 or less
plates
conclusiofis
it must
on flat
a/b
following
.
a slight
of unstiffened
The
reduction
reduction
plates
could
in
from
amount
of r
/T
for (b/t)
(m /E)l/2
X/J
C.v
diminu Ion fn the reductico K to zero
the design
curve
into
closer
agreement
data.
..
-59.
7.
current
those
From
which
been
in the latter
by the fact
plotting
encompassed
cim/wcy
mixes
this
parameter,
overridden
function
which
appears
in one parameter
of the geometric
would
scatter
terms
seem
band
the material
that is plotted
parameter
Although
of the param-
and geometric
of the
in which
the
of aU
.
a function
objection
that the width
procedures
investigators
as
material
possible
of scatter,
to be the best
by various
displays
(rcy/E)l/2,
of minimization
strength
advanced
procedure
(b/t)
in other
standpoint
of relating
have
the current
eter
the
method
is
to be
less
properties
than
are
logarithmically
as a
, b/t.
RECOMMENDATIONS
A vigorous
theory
should
during
this
program
of
be pursued
to
experimentation
broaden
and
the
base
of
development
the
data
of
established
investigation.
1.
Studies
2.
The
should
be conducted
on plates
with
a/b
between
land3.
should
type
influence
be examined
stress-strain
3.
prediction
welding
weld
procedure
strength
condition
into
theory.
The
5.
In order
with
is not size-
.
been
lost
Plates
7.
action
studies
problems
influence
knee
stresses
as the basic
should
of the
be
of shear
should
further
studies
should
of O. 060
in.
the
using
the
input.
Extended
residual
to acquire
stress
influences
the hypotheses
be included
also .
the hypothesis
be conducted
The
should
to implement
and to consolidate
to demonstrate
Stress
the best
codd
account
for
there
may
size
under
should
have
in order
b/t
that instaon plates
range
should
with
controlled
initial
imper-
correlation
be
with
conducted
suffered
to determine
strength
be
of ships
severe
damage
whether
biaxial
predic-
which
from
have
the
instability
the failure.
Syntheses
be
possible
analyses
or which
at sea,
sea,
8.
be tested
should
of the
of failure
curve
rounded
investigation
of residual
properties
of the order
to provide
tions
- strain
with
also.
6.
fections
in this
resolution
dependent,
thicknesses
extended
stress
data necessary
the influence
so as to permit
and boundary
bility
design
and plate
Biaxial
of the
on materials
instituted
the
for
parameters
data
shape
.
studies
to provide
4.
more
curves
The
be broadened
of the
by experiments
should
be performed
limitations
biaxial
loading.
on ships
based
to determine
upon
whether
the possibility
.50A.cknowledgernents
The
Colao
authors
for
Edward
his
wish
Suskevich
specimens
their
in designing
for
his
appreciation
the test
contributions
and the performance
the welding
finishing
to express
assistance
subcontractor
to Mr.
equipment,
Angelo
arid to Mr.
to the instrumentation
of the experiments
, supervised
.
of the
Mr.
James
Viall,
, welding a~rd
the machining
of the models.
REFERENCES
1.
H.,
Girders”
, National
ittee
2.
‘l Feasibility
Becker,
Report
SSC - 194,
of Model
Tests
of Sciences
May
on Ship
by Rockey
and Hill,
Hull
, Ship Structure
Comm-
1969.
llThe Strength
B. , and A. T. Ractliffe,
ion’1 , Published
in ‘l Thin Walled
Steel
Dwight,
J.
in Compress
Ed.
Study
Academy
Gordon
and Breach,
N.
of Thin
Plates
Structures”
Y.
1969,
,
PP.
3-34.
3.
N.
4.
Y.,
Bengston,
.
6.
H.
Press
T.
Thin
No.
Plates
2,
Jan.
Levy,
Long
9.
Hoffman,
ticity
for
Rae,
N.
Anon.
1940.
Plates
TN
O. , and G.
N.,
X,
and
No.
L.
80,
H.
Hi~l >
sion
and
1939,
pp.
Donnell,
. ASME
FIydro–
80-116.
“The
, APM-
pp.
and G.
Under
Tall,
Strength
54-5,
~,
plate
Insta-
Corporation,
Zibritosky,
A .,
llThe
S.
“Simply
Axial
N.
October
Strength
Supported
and Normal
to the Theory
Y.
of Plas-
1953.
Stresses
1961,
on Electron
Experimental
Load
1944.
I!Residual
Indianapolis
, U.
of the Aeronautical
38-45.
I!Introduction
Supplement,
Report
Determining
Combined
October
Sachs,
for
, Journal
Limit”
, McGraw-Hill,
, IIA Technical
J.
Method
1946,
949,
and L.
Research
Frankland,
Compres
, Trans
Modulus
Goldenberg
Engineers’1
Compression”
Sechler
E.
1 Jan.
, NACA
R.
SPJAME,
Proportional
No.
S. , D.
Buehler
11.
the
Rectangular
Welding
10.
, E.
.
in Compression”
~,
Pressure”
8.
, McGraw-
1932.
Above
Sciences,
i’.
Trans
G. , I!secan~
Gerard,
bility
Stability”
, IIship Plating Under
W.
urell
vonKarman,
of
of Elastic
1936.
static
5.
S. , llTheorY
Timoshenko,
in Welded
pp.
Beam
Plates”
468s-480s
Welding”
.
.
The
, Inc .
of Ship
Model
Plating
Basin
Under
Report
Edge
469,
,
-6112,
J. , Unpublished
Vasta,
Reports
13.
14.
ca
Needham,
R.
Structural
Sciences
Basin
Loaded
Report
Conley,
W.
Ultimate
ress
16.
F.,
J.
- ..
Progress
P.
Plates”
.
Plating
Report
304.2,
B.
ion’f , Journal
pp.
“Buckling
and
of the Aero-
217-229.
and Ultimate
, David
R.
B.
Strengths
Taylor
Allnutt,
Loaded
in
Edge
Panels’1
.
David
Strength
Model
“Buckling
Compression,
of Plating
of Adjacent
Center
Report,
, fILiterature
Lehigh
of Aluminum-Alloy
Taylor
and
Prog-
Model
Basin
1963.
- Effect
and Development
Cooper,
Basin
1960.
S. , !lu~timate
Compression
17.
Model
1954,
Compression’!
A , Becker
of
May
April
B . Allnutt,
2 - Unstiffened
1682,
Collier,
4,
April
L.
sc rength
in Compress
No.
in Edge
1419,
Strength
Report
Report
Experimental
Ultimate
Shapes
, ~,
J. , and R.
of Plating
150
A.. , 1fThe
Formed
D.
S.
1940.
nautical
Duffy,
U.
University
September
Panels”
April
Survey
Fritz
1963.
.
Loaded
Naval
in Edge
Ship
Research
1967.
on Longitudinally
Engineering
Stiffened
Laboratories
UNCLASSIFIED
Security Classification
v-
●
DOCUMENT CONTROL DATA-R&D
(Security
.Ia.sificariori
1.ORIGINATING
of title,
AC TIV17Y
body
(Corporate
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afirmrntion
must
h.
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wthor)
2m
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SECURITY
is
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C LAS
SIFICATl
OM
2b
GROUP
I
Compressive
4
the OV.,ZIII
Unclassified
U. S. Naval Ordnance Laboratory
White Oak, Maryland
r
when
REPQRT
Strength
DESCRIPTIVE
NOTES
(Type
of
5hip
oi report and:nctusive
Hull
Girder
Part
I
Unstiffened
Plates
detes)
October, 1970
5.
AuTHOR(S)
H.
(Last
name,
firsrneme,
initial)
Becker, R. Goldman, and J. Pozerycki
<. REPORT
DATE
17a.
90,
CONTRACT
b.
PROJECT
TOTAL
NO,OF
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PAGES
NO.
OFREFS
17
61
October, 1970
OR GRANT
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NOO024-69-C-5413
OR!GINATOR,S
REPORT
NUMBER(S)
I
NO.
c,
9b.
OTHER
REPORT
fhi. raport)
NO(s)
(Art~Otho.nUrnbo.a
UIetneY
be =~~idn~d
SSC-217
d.
10. AVAILABILITY/LIMITATION
NOTICES
Unlimited.
..—
11, SUPPLEMENTARY
NOTES
12. SPONSORING
MILITARY
ACTIVITY
Naval Ship Systems Command
I
13. ABSTRACT
Three problem areas of Hull girder strength are biaxial strength(to account
for the transverse membrane loadings induced by the sea), the influence of normal pressure loadings on strength, and the influence on strength of residual
stresses induced by welding. Data on solutions to these problems were obtained
during this project.
3D ,!$?%1473
~S31F1
ED
Security
Classification
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Maritime
National Academy
SHIP RESEARCH COMMITTEE
Transportation Research Board
of Sciences-National Research Council
The Ship Research Committee has technical
Ship Structure Committee’s research program:
cognizance
of the inter agency
:?
PROF. R. il. YAGLE3 Chairman,
Prof.
of flavalAm+ritieeture,
Universityof Miehigan
DF?.H. P1.ABRAMSON, E-hector Departmentof MQehanieazSciences,SouthweskRQseareh Inst.
Ckief Struetu~al C~i-kQria
and Loads, BelZ Aerosystiems
Co.
MR. W. H. BUCKLEY,
DR. D. P. CLAUSING,
MR. A. E. COX,
Senior
Senior Progmm Managex=,Newpo?tiYews Shipbuilding& DPy Dock CO.
MR. J. F. DALZELL,
Sanior .i?eseamhEngineQr, Stevens Institute of TeehnoZogy
Research Consultant,U. S. Ste&l Corpo~ation
DR. W. D. DOTY, Senior
MR. F. D. DUFFEY,
MR. D. FAULKNER,
J. E. HERZ,
MR.
G.
E.
PROF. B.
WeldingEngineer, IngaZls ShipbuildingCo~poration
Research
Chic.fStrueturalDesign Enginee?,Sun Shipbuilding& my Dock Co.
JR., Mmager, ApplicationEnginee~ing,ARMCO Steel Corporation
KAMPSCHAEFER,
R.
As~oeiate,Massachusetts-hnstitu-kof T~ehno20gy
Prof. of Civil Enginee&ng~ ~i~e~sity of IZlinois
PROF. W. J. tlALL,
MR.
Sci~ntist, U.S. Steel Corporation
NOTON,
MR. W. W. OFFNER,
of Aerospace & Civi2 Engineering,WashingtonUnive~sity
Prof.
President,
CDR R. M. WHITE, USCG, Chief,
MR.
R.
W.
X-ray
Eng-ineerz%g
International,Atomic SuppZy co~po~ation
AppLiad Engin~~tingSection. U.S. Coask Guu?d Aeademy
Executive Seereta~y,S7@ Research Comitte@
RUMKE,
“Ship Structural
Advisory Group II,
and evaluated the proposals for this project.
MR.
J.
E.
HERZ,
MR. A. E. COX,
MR.
PROF.
D.
E.
the project
prospectus
Ozief Stmctura2 Design Eng<neer,SW Sh.{pbui2d{ng
& my
Dock co.
Senior p~ogrm
Manage~, fle~o~t NaL?sShipbuilding& Dry Dock Co.
Chairman,
FAULKNER,
J.
Design” prepared
ResGaPch
GOLDBERG,
PROF. B. R. NOTON,
MassachusettsInstitute of Teehnozogy
~ssociata,
P~of. of Civi2 Engineering,Purdue Univm-wity
P~of. of Aerospace & Civil Engineering,WashingtonVnivemity
JR., l+of. & Chairmanof Departmentof Naval Amhiteeture,
Unive2wityof California
MR. D. P. ROSEMAN, Naval Architect,Hydronautics,Inc.
PROF. J. R. PAULLING,
CDR R. M. WHITE,
dance,
and
USCG, CMef,
The SR-193
Project
reviewed
the
project
PROF. J. E. GOLDBERG,
Chairman,
PROF. S. T. ROLFE, tiv;l
MR. JOHN VASTA,
—y.
,_.
App2ied Eng73zeex%zg
Sac-tion,U.S. Coast Guard Aeademy
Advisory
reports
Committee
with
the
provided
investigator
the
liaison
technical
gui-
professorof Civi2 Engineering,purdue Un{versi@
EnginQerikgDepa~tmenti,
Univwsity of Kansas
Senior Consultmti,Litton Systems, Inc. A.M.T.D.
SHIP STRUCTURE
COMMITTEE
PUBLICATIONS
These documents are distmhted by the Clearinghouse, Springfield,
Va.
22151. These documents have been announced in the Clearinghouse journal U.S. Government Research & Development
Reports
(USGRDR) under the indicated AD numbe~s.
1
SSC-202, Midship Wave Bending Moment in a Model of the Cargo Ship
“California Bear” Running at Oblique Headings in Regular Waves
by E. Numate and W. F. Yonkers.
November 1969.
SSC-203, AnnuaZ Report of the Ship Structure Committee.
AD 698847.
November
1969.
AD
699240.
SSC-204, Simulated Performance Testing for Ship Structure Components by
R. Sherman.
1970. AD 705398.
SSC-205, Structural Design Reviev of Long, Cylinbieal, Liquid-FiZled Independent Cargo Tank Barges by C. W. Bascom.
1970.
AD 708565.
SSC-206, Permissible St~esses and Their Limitations by J. J. Nibbering. AD
710520.
SSC-207, Effect of Flwne and Mechanical Straightening on Material Properties
of We2hents by H. E. Pattee, R. M. Evans, and R. E. Monroe.
1970.
AD 710521.
SSC-208, Slming
Zedge J.
of Ships; A Critical Review of the Current State of KnowR. Henry and F. C. Bailey.
1970.
AD 711267.
SSC-209, Results From Full-Scale Measurements of Midship Bending Stresses on
Three DXJyCargo Ships by 1. J. Walters and F. C. Bailey. 1970. AD
712183.
SSC-21O, Analysis of Slamming Data from the “S. S. Wolvemkg State’rby J. W.
Wheaton,
C. H. Kane,
P. T. Diamant,
F. C. Bailey.
1970.
SSC-211, Design & Installation of
a Ship Response Instxwmentation System
Aboard the Containey Vessel “S. S. Boston, by R. A. Fain, J. Q.
Cragin, and B. H. Schofield.
1970.
SSC-212, Ship Reponse Instmmentation Aboard the Container Vessel “S. S.
Boston”: Results from the 1st Operational Season in North Atlantic
Service by R. A. Fain, J. Q. Cragin, and B. H. Schofield. 1970. AD
712186.
SSC-213, A Guide for Ultrasonic Testing and Evaluation of Weld Flaw
Youshaw.
1970.
by R. A.
SSC-214, Ship Response Instrumentation Aboard the Container VesseZ “S.S.
Boston”: ResuZts from 2 Ope~at~ona_Z Saasons ik. North Atlantic
by J. Q. Cragin.
Sexwiee
lg70. AD 712187.
SSC-215, A Guide for the Synthesis of Ship Stmetures Pa~t One- The Midship
Hold of a Transversely-FramedDry Cargo Ship by Manley St. Denis. 1970.
.
---