N S
Technical emorandum
NASA
T

108427
NI\S \
National Aeronautics and Space Administration
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NASATMIOB427) A SIMPLISTIC
LOOK
T
LIMIT STRESSES
FROM
R NDOM
LO DING
NASA) 22
P
A SIMPLISTIC
LOOK
AT
LIMIT
STRESSES
FROM
RANDOM LOADING ByH.M.
Lee
Structures and Dynamics Laboratory Science and Engineering Directorate
October
1993
N94 1S710
Unclas
G3/39
0190896
George
C
Marshall Space Flight Center
MSFC·
Form
3190
Rev. Mev
1983
T BLE
O
CONTENTS
Page IN1 R.ODUCTION THE
CONTINUOUS BE M
3
SSUMPTIONS
.
5
C LCUL TION
OF
BEAM
FREQUENCIES
6
PEAK ACCELERATION
FOR
EACH MODE
7
M XIMUM
DISPLACEMENT
FOR
EACH MODE
8
THE
STRESS EQUATION
8
COMP RISON
WITH TEST
SIMULATION
2
CONCLUSIONS............................................................................................................................
4
REFERENCES
....
7
PPENDIX
18
iii
PMeEOfN
PAGE BLANK
NOT
Ftl
Mi
Figure
1
2
3
4
5
6 7
8
9
1
11
12
LIST
OF
ILLUSTR TIONS
Title Statistical philosophy
flow
.......................................................................................... .
Continuous
beam
model
Pinned pinned beam modes 1
to
4 .............................................................................. . Peak acceleration for each mode ................................................................................. . Mass loading effect on beam ...................................................................................... . Maximum displacement for beam modes ................................................................... .
Beam stress
with
Mlln
=
0
Beam stress with
Mlm
=
3.0 ...................................................................................... . Multiple mode stress versus test simulation ............................................................... . First mode stress versus test simulation ...................................................................... . AEPI flight instrument ................................................................................................ . AEPI static tests .......................................................................................................... .
iv
Page 2
4
7
7
9
1
11
12
13
15 15
TECHNICAL MEMORANDUM
A
SIM PLISTIC LOOK AT LIMIT STRESSES FROM RANDOM LOADING INTRODUCTION
Since
random
loads
play such
an
important
role
in
the
design,
analysis,
and
testing of most space shuttle payload components
and
experiments,
the
structures
and
dynamics community
has
long desired
to
more
fully understand
the
relationship
between
the
random
load environment
and
the
actual stresses resulting
from
that environment.
The
current philosophy
at MSFC
for
calculation of
random
load factors embraces a statistical philosophy
which
utilizes Miles equation:
where
pk
=
peak
random
load factor (limit)
Q
=
esonant amplification
fa,ctor
fn
=
component natural frequency,
Hz
PSD
j
=
input qualification criteria
atfn,
G
2
/Hz.
This equation involves calculation of
the
loads based
on
(1)
analytical or tested values for significant resonant frequencies
lfn),
(2)
an
historically
based damping value
of 5 percent
(Q
=
10)
or component measured damping
from
testing,
(3)
the
magnitude of
the
maximum
expected flight environment at resonance
(PSDj),
and (4)
a statistically 30 definition of
peak
load.
f
you
remove
the
crest factor of 3
from
the
equation,
the
remaining expression,
J 1'
Q
n
.
P
S
j
represents
the
root
mean
square response
(Grms)
of
the
component. This assumes that
the
component
is
a single degreeoffreedom harmonic oscillator driven
at
all
frequencies
by
a
white
noise
environment at constant
PSD
level and that
the
component does
not
affect
the
input.
From
a statistical
point
of
view,
the
Grms
response can
be
set equal
to
the
standard deviation
(0 )
by
assuming
that
the
realized ensemble of
random
input
time
histories
are
best represented
by
a Gaussian distribution
with
a
mean
of
zero.
Under
these
conditions
the
Grms
response is a
10
response. Multiplying
the
Grms
by
the
crest
factor
3 produces
the
well
known
30
response value
which has
a 99.73percent probability of
being
greater
than any
instantaneous
random
load encountered.
In
Miles equation,
the
other critical probabilistic
term
is the
qualification input criteria value
(PSDj)
at
the
component s natural
frequency
lfn)
From the
historical data base, a 97.50percent probability level
is
calculated
(a
1.960 value).
This level
then
becomes
the
basis
from
which
the
actual component criteria is developed
(fig.
1).
Statistically,
the
criteria assures
the
analyst that
the
flight loads
have
only a 2.5percent probability of
an
exceedance. Further confidence
in
the
analytically derived criteria
s
gained
from
the
fact
that
the
criteria
is
created
from
straightline enveloping of
the
data, and
from
the
requirement
to
hard mount
components
during
vibration testing.