CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
PANEL ZONE DISTORTION IN MOMENT RESISTING FRAMES .
A Graduate Project submitted in partial satisfaction of
the requirements for the degree of Master of Science 1n
Engineering
by
Hooshang Nadershahi
May, 1986
The Graduate Project of Hooshang Nadershahi 1s approved:
Dr. Roger Di Julio, Chair
Professor Leonard Spunt
I
Professor Astrid Levine
California State University, Northridge
ii
TABLE OF CONTENTS
PAGE
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.
v
LIST OF TABLES...............................
vi
TABLE OF SYMBOLS.............................
vii
ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
COMPUTER MODELING............................
8
THEORY.......................................
15
VERIFICATION OF COMPUTER MODELS..............
22
ANALYZING NEED FOR COLUMN STIFFNERS AND
WEB DOUBLERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
RESULTS AND DISCUSSION.......................
38
CONCLUSIONS AND RECOMMENDATIONS..............
52
BIBLIOGRAPIIY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
APPENDICES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
APPENDIX !(Computer output for model No. 1)..
57
APPENDIX 2(Computer output for model No. 3)..
71
LIST OF FIGURES
FIGURE
PAGE
Photograph of a panel zone
1.
7
Inflection points, shown on the deflected
structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2.
Isolated joint of a structure . . . . . . . . . . . . . 4
3.
Beam-to-column connection . . . . . . . . . . . . . . . . . 5
4.
Structure's specifications . . . . . . . . . . . . . . . . 9
5.
Model No. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6a.
Model No. 2(front view) . . . . . . . . . . . . . . . . . . . 13
6b.
Model No. 2(three dimensional view) ....... 13
7a.
Model No. 3(front view) . . . . . . . . . . . . . . . . . . . 15
7b.
Model No. 3(three dimensional view) ....... 15
8a.
Structural Loading(front view) . . . . . . . . . . . . 16
8b.
Structural Loading(three dimensional view) 16
9.
Numbering Convention for slopes
and displacements . . . . . . . . . . . . . . . . . . . . . . . . . 20
10.
Shape functions. . . . . . . . . . . . . . . . . . . . . . . . . . . 21
11.
Sections where
th~
Bending Stresses are
Evaluated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
12.
Sections where the Shear Stresses are
Evaluated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
12a. Column flange before using stiffners ...... 33
i·v ·
12b. Column flange after us1ng stiffners ....... 34
13.
Column flange considered as a plate ....... 35
14.
Behavior of Column Web due to load from
Beam Flange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
15.
The distorted shape of model 1 . . . . . . . . . . . . 40
16a. The distorted shape of model 2(front view) 41
16b. The distorted shape of model 2(isometric). 41
17a. The distorted shape of model 3(front view) 42
17b. The distorted shape of model 3(isometric). 42
.. 18.
The elements for which the bending stresses
are determined(in the panel zone) . . . . . . . . . . 44
19.
Column Flange acting like a cantilever beam46
20.
The elements for which the bending stresses
are determined(in the column flange) ....... 47
21.
Distorted Shape of Panel Zone without
connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
22.
Distorted Shape of Panel Zone with
connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
v·
LIST OF TABLES
TABLE
PAGE
1.
Comparison of displacements between
computer output and hand calculation ...... 26
2.
Comparison of bending stresses between
model No. 1 and model No. 3 . . . . . . . . . . . . . . . 29
3.
Comparison of shear stresses between
model No. 1 and model No. 3 . . . . . . . . . . . . . . . 32
4.
Comparison of bending stresses for model
No. 3 with and without the stiffners and
doubler plates. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.
Comparison of bending stresses in the
column flange for both models with and
without the stiffners and doubler plates .. 48
vi
LIST OF SYMBOLS
[K] = STIFFNESS MATRIX
y
=
DEFLECTION
X
=
DISPLACEMENT
v
=
STRAIN ENERGY
T
=
KINETIC ENERGY
I
=
MOMENT OF INERTIA
tf
= FLANGE THICKNESS
t
w
= WEB THICKNESS
c
= COLUMN FLANGE THICKNESS
t
wc = COLUMN WEB THICKNESS
Af = FLANGE AREA
bb = BEAM'S FLANGE WIDTH
tb = BEAM'S FLANGE THICKNESS
A = CROSS SECTIONAL AREA
E = MODULUS OF ELASTICITY
L = LENGTH
f = FORCE
v
= SHEAR FORCE
K = EFFECTIVE LENGTH FACTOR
o< = VERTICAL SIDE ANGLE OF PANEL ZONE
~ = HORIZONTAL SIDE ANGLE OF PANEL ZONE
){ = TOTAL DISTORTED ANGLE OF PANEL ZONE
lf/ =
SHAPE FUNCTION
8 = AVERAGE ROTATION ANGLE
. v
vii
ABSTRACT
PANEL ZONE DISTORTION IN MOMENT RESISTING FRAMES
by
Hooshang Nadershahi
Master of Science 1n Engineering
A panel zone of a beam-to-column connection was
analyzed, and it was observed that unless the column
flange 1s extremely thick, flange stiffners must be added
to the column in line with the beam flanges. Such
stiffners keep the column flanges from deflecting and
prevent stress concentrations in the column· flanges and
web and in the weld which joins them to the beam .
.
\)
It was also observed that web doubler plates must be
added to the panel zone(column web) in order to increase
the shear capacity and to prevent excessive panel zone
distortion.
Three finite element models were constructed using
beam and plate elements.
The most complete model was
composed of 507 nodes and 534 plate elements.
Res'ul ts of the analysis are presented, discussed and
comparisons are made for the most complete model(no.3),
with and without stiffners and doubler plates.
x·
INTRODUCTION
A frame structure will deflect when subjected to
lateral loading and the joints will rotate. Inflection
points occur in each of the beams and columns.
See Figure 1.
, inflection
--points
FIGURE 1
(Deformation of a rigid frame)
Where the joints rotate the members maintain the same
angular orientation with respect to each other.
The
inflection points generally occur near the mid span of
each beam and column.
Since the a1m of this project is analysis of a joint
(panel zone), a single joint is isolated from the
structure. The same boundary conditions must be modeled,
however.
See Figure 2.
~
relative deflection
~
inflection points
FIGURE 2
Isolated Joint
The inflection points are at the points of zero moment.
Therefore a beam and column model with rollers and pins
located at the inflection points was used.
3).
(See Figure
The details of this model will be discussed later.
3
FIGURE 3
Beam-to-column connection
The panel zone of conventional beam-to-column
connections developes high shear stresses in the column
web(panel zone), high bending stresses in the column
flanges and a stress· concentration at the center of the
beam flanges where they attach to the column, when beam
moments produced by seismic events approach the plastic
moment capacity of the beam.
Thtrefore, the complete
design of a steel moment frame requires among other
things the analysis of the stresses
~n,
and the
4
distortion of the joints.
Nevertheless, due to the
complexity of the required analysis, the distortion of
joints is usually ignored.
The objective of this project is to determine the
effect of stiffening the panel zone by means of stiffners
and web doubler plates.
Making the panel zone rigid by
such connections, was found to reduce the shear and
bending stresses and the panel zone distortion.
A typical panel zone in a building is shown
photograph 1.
' v
in
5
Photograph 1
Panel zone in a typical building
.
.
6
~n
-A doubler plate is a plate welded to the column web
the _panel zone to provide panel zone shear capacity
sufficient to resist forces due to imposed loads.
Stiffners are added to the column flanges in the panel
zone to protect the column flanges from the forces
transmitted by the connecting beam flanges.
If the
column flange is thick enough, stiffners are not
required.
The exact theoretical solution for such a structure
~s
not possible.
A numerical procedure which provides an
approximate, but acceptable solution is required.
The
most widely used numerical method is the finite element
method.
In the finite element method the continium
~s
idealized as a structure consisting of a number of
individual elements connected only at the nodal points.
The Structural Analysis Program for Static and Dynamic
(SAP V) is used for the analysis presented in this paper.
For the purpose of the analysis, two structures with
the same numbers will be compared, one with stiffners and
doubler plates and the other without.
The specifications
of this structure are shown in Figure 4.
7
Specifications of the Beams and Column
BEAM
1n. 4
I
= 9760
tf
=
1.020
tw
=
0.63
A
= 47.1
~n.
.------------------~n.
~n.
2
COLUMN
I
= 2890
~n
t£
= 1.40
~n
tw
= 0.88
~n
A
= 84.40
80.00 11
4
~n
2
u
36.0 11
J
1~:-145.01 ~-
T
1
1.40 11
-•
14.72 11
FIGURE 4
DIMENSIONS OF THE STRUCTURE
8
COMPUTER MODELING
Three models were constructed.
All three modelfi have
the same members, dimensions, and boundary conditions.
Model No. 1
Beam elements were used to construct the first model.
This which is the simplest of the three models, contains
eleven nodes and nine beam elements.
The beam element in
the SAP V program considers torsion, bending, axial and
shearing deformation.
All forces and moments are
calculated in the local coordinate system.
In order tb
define a beam element, coordinates i and j are used to
delineate the end points for a beam and k is used to
define a principle axis direction.
the model.
Figure 5
repres~nts
9
Elements one, five, six and eight are -made as long as the
width and height of the panel zone, and are rigid, to
This model was
simulate the rigidity of the panel zone.
used to determine the rotation of the joint without
considering the shear defamation.
3
2
4
1
5
6
7
8
9
FIGURE 5
Model No. 1
Model No. 2
Plate elements were used in the second model to
represent the beam and column ·structure.
consists of 110 nodes
~nd
This model
98 plate elements.
This model
was mainly used to verify the third model which uses more
nodes and elements. The plate element is a plane stress
element which may be used for analyzing plates and
• ti
10
shells.
The points where the stresses are calculated are
located equidistant from the coordinates of the three or
four corner nodes.
The element has six degrees of
freedom per node.
Plate elements were used to determine the distortion of
the panel
~one
due to rotation and shear.
represented in figures 6a and 6b.
Model No. 2 is
11
I
I
r
-~-
FIGURE 6a
Model No.2, front view
~=
I
,--
:::::
I
~
FIGURE 6b
Model No. 2, isometric view
12
Model No. 3
The third model which 1s
si~ilar
to the second model,
but has more nodal points and plate elements.
This model
consists of 507 nodes and 534 plate elements.
The finer
mesh was used in the area around the panel zone to more
accurately represent the stresses in the panel zone which
is the area of interest.
See Figures 7a and 7b.
13
1\
K
f\
~
I~ /
1"-.
/
./
/
......_ /'"
/
~
V"'
lj
v
~
f.--,
/
'-
FIGURE 7a
Model No.3(front view)
1\
I\
1\
-=
1\
p-
~
=--
-
E; /
~<
/ 5~
L: s~
~
~
--:::>
1/
ll
1/
L
FIGURE 7b
Model No. 3(isometric view)
14
Loading
In order to study the effect of loading in the panel
zone a lateral load of 100,000 lbs was applied to the
column in all three models. The applied load
~s
shown for
model number one and three in figures 8a and 8b
respectively.
100,000 lb
;/
FIGURE 8a
Applied load to model No. 1
II
v
v
-
=--------
I----
k?
--:::>
c~ 7
~
/_
I?
L.. ~
<:
l---
----=
\
\
FIGURE 8b
Applied load to model No. 3
15
THEORY
Assumed-Mode Method.
Application of Lagrange's equations to continuous
models:
An assumed-mode, or shape function,
1s an admissible
function that is used to approximate the deformation of a
continuous system.
To create a generalized-parameter
single degree of freedom system model of a continuous
system, a single assumed-mode is used.
For example, the
deflection curve of a beam may be approximated by
(1)
y(x,t) =rcx)y(t)
where 'fCx) J.s any admissible shape function and y(t) 1s
the generalized displacement for this single degree of
freedom system.
To generate a multi- degree of freedom
mod~l
of a
continuous system equation (1) is expanded to include N
functions'
ri
(x) .
Thus y(x,t) will become
y(x,t)
(2)
N
y (x, t)
=
L__'fi
L=-1
Cx)y 1 <tl
(3)
16
The strain energy ln a beam lS given by
L
~
V = 1/2
2
EI (y") dx
(4)
0
and kinetic energy due to transverse displacement y(x,t)
is given by
L..
2
T = 1/2) ,.0 A(y) dx
(5)
0
where~
is the mass per unit volume and A is the cross
sectional area.
When equation 3 is substituted in
equation 4, the resulting expression for potential energy
may be written in the form
N
v =
1/2
N
~ ~-K .. y.y.
L L
(·=
1
lJ
l
(6)
J
~-::.1
where
L
Kij =
S
EI
'f'\ (x) 'f" j (x) dx
0
lS the stiffness coefficient.
(7)
17
Finite Element
Finite element modeling of a structure may be
considered to be an application of the assumed-mode
method where the~i's represent the deflection shapes
over a portion of the structure, with the elements being
assembled to form the structural system.
The elements
are jointed together at nodes, and displacement
compatibility is enforced at these joints.
Although the
finite element method has a very wide range of
capability, emphasis will be placed on one-dimensional
elements such as the beam element.
It is beyond the scope of this paper, however, to
present a thorough discussion of the finite element.
Transverse Motion of a Beam(Beam Element)
Consider a uniform beam element of length L, mass
density ;o, elastic modulus E, Cross sectional area A, and
moment of inertia I.
Let the diplacement coordinates for
transverse motion be the end displacements and the slopes
numbered as shown in Figure 9.
18
FIGURE 9
Let
y (x, t)
~
z
if
(8)
'fi (t)yi (t)
(. :=.1
where the functions ri(x) satisfy the boundary conditions
,
I
lf1 (0)
=
lf~ (L) =
lf 1 (L) =
'f1 (0)
=
1
'f'2(0)
=
1
lf 2 (O)
=
lf2(L)
lf'3 (L)
=
1
lf ~ (0)
=
'f3 (O) = 'f3(L)
lf 4 (L)
=
1
lf4 (O)
=
'f4 (0)
I
I
0
I
=
0
=
0
= lf4(L) =
0
=
lf2(L)
I
I
(9)
Appropriate shape functions can be easily derived by
considering the beam element in Figure 9 to be loaded
statically by shears and moments to produce the various
static deflection shapes that satisfy equation 9. Thus,
for a beam loaded only at its· ends the equilibrium
equation is
(Eiyu)u
=0
(10)
19
The shape functions can be graphically represented as
follows:
X
X
X
L
.;,4 (x)
FIGURE 10
Shape functions
The general solution to equation (8) for a uniform
beam is a cubic polynomial
y(x)
(11)
Note that (x/L) is used instead of x so that all C.'s
l.
have the same dimensions. Substituting the four sets of
boundary conditions of equation 9 into 11 we obtain the
following shape functions:
20
2
3
3(x/L) + 2(x/L)
. 2
3
2L(x/L) + L(x/L)
lf2 = X
. 2
3
lf3 = 3(x/L) - 2(x/L)
2
3
= -L(x/L)
+ L(x/L)
lf/1 = 1
(12)
'f4
recall that
K ..
~J
~~
L EI
'f:'
lf/
(7)
dx
0
substituting equation 12 into equation 7 we obtain a
symmetric matrix which is called stiffness matrix.
12
K
=
(EI/L 3 )
6L
-12
6L
4L2
-6L
2L 2
12
-6L
(13)
4L2
I..
where:
E
I
L
~s
~s
~s
the elastic modulus.
the moment of inertia
the length
j
21
The stiffness matrix is used in the following form in
order to determine the displacement of every node in the
structure.
{F} = [K]{x}
{x}
=
(14a)
[K]- 1 {F}
(14b)
Where {x} 1s the displacement matrix.
Equation 13 can be used to determine the stiffness
matrix for the simplest of the three models(no.1). This
model was used for checking the more complicated models.
The stiffness matrix is an 8 X 8 symmetric matrix given
by equation 15. The unit of [K] is (lb/in).
29.87 .2322 4.888 -.306
.0142 .3055 -.013
19.16
[K]=10
.000 3.828 3.828 2.394
.000
.000
.000 -.073
.000 -.282
.000
.000
.000
.024 -.011
.000
.000
.000
.011
.000
.000
.000
7.655
.000
.000
7.655
.000
9
4.788
(15)
22
The output of the
SAP V program provides moments per
unit length and membrane stresses in the plate elements.
Thus for a plate the stresses are determined by:
6( = P/A
+ 6M/t
2
(16)
where:
P/A is the axial stress
M is the moment/unit length
t is the element thickness
The outputs for models one and three are presented 1n
appendices one and two.·
VERIFICATION OF COMPUTER MODELS
In order to verify the accuracy of the computer
models, the results obtained from such models must be
compared with theoretical solutions or simple models.
Such a comparison has been made using the first and the
third models.
23
Verification of the model No. 1
ThE' stiffness matrix obtained (equation 15) can be
used Lo dPLcrminc t.hc displacements of every node of
model number one.
These displacements can then be
compared to the displacements obtained from the computer.
The displacements are obtained as follows:
{x}
=
[k]- 1 {f}
(in)
(14b)
.721 75.70 -.080 127.4 89.27 -.360 -.360 0.800
0
40000 -16.2 40000 40000 -37.9 -37.9 637.0
0
2.302 -226. -48.6 0.040 0.040 -2.34
0
46000 53000 -45.6 -45.6 535.4
10
40000 -44.6 -44.6 546.3
0
1.487 0.180 -0.40
0
1.487 -0.40
0
0.114
0
-to
{x}=10
5
24
The results are compared 1n the table below.
Table 1
Comparison of displacements obtained from hand
calculation solution and the SAP V program for the
simple model(No. 1)
node number
1
2
3
4
5
6
7
8
hand
calculated
displacements
(in)
Computer
displacements
(in)
1.275
4.00
2.262
4.830
5.890
6.361
6.361
5.534
1.275
3.924
2.256
4.850
5.970
6.370
6.370
5.368
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
10- 3
10- 1
10- 3
10-l
10- 1
10- 3
10- 3
10- 3
As 1s observed from Table 1, the results are very close.
The bending and shear stresses were calculated at
several locations using equations 17 and 18 which follow.
25
Bending Stress
The bending stress !or model No. 1 at any location
can be determined from the following equation.
s' =
My/I + P/A
(17)
where:
M is the moment at the location where the stress 1s
to be evaluated.
y is the distance from the neutral ax1s.
I is the moment of inertia.
Bending stresses at five different locations shown 1n
figure 11 are evaluated
FIGURE 11
Sections where the Bending stresses are evaluated
26
Bending stress can be evaluated for point A using the
following procedure, and the internal forces from model 1
e! =
MC/I + P/A
M
=
4.791724 X 10
p
=
0
6
lb-in
c = 8.575 J.n
I
=
er=
=
9760 J.n
4
6
(4.791724 X 10 )(8.575)/9760
4209.0 psi
comparing this value with the stress obtained for
computer model No.3, by using equation 16, as follows
2
~
=
6M/t
M
=
0
P/A
=
3910 ·psi
~computer =
% difference =
3910 psl.
+ P/A
(16)
(4209.0 - 3910.0)/4209
=
7.0%
Similarly, the stress at sections B,C,D, and E are
determined in the same manner.
The following table
presents the results of these calculations.
27
Table 2
Comparison of bending stress between model No. 1 and
model No. 3.
Sections
for model 1
ps1
for model 3
psi
% difference
A
4209.
3910.
7.0
B
9542
9192
3.6
c
3130
3161
0.1
D
13,785
15,080
8.0
E
3147
3130
0.5
As can be seen from the table the max1mum difference
between the hand calculated and the stress obtained from
the computer model is 8.0 percent. Finer mesh elements
might have reduced this difference.
28
Shear Stress
The maxlmum shear stress for model No. 1 can be
evaluated from the following equation;
L =
VQ/It
(18)
where:
V is the resultant internal force at the section
the shear stress is to be evaluated.
Q lS the first moment of area.
I is the moment of inertia.
t lS the thickness.
Shear stress for the six· different sections shown ln
Figure 12 are evaluated below.
FIGURE 12
Sections where the shear stresses are evaluated
29
The shear stress can be determined for point A, using
model No. 1 and the following procedure;
~
=
v =
VQ/It
10
5
lb.
Q = [(7.705) (16.130)(1.4)
+ (4.455) (5.81)(.88)]
3
=
196.8 in
I
=
2890 in
t
=
0.88 in
~
=
5
(10 )(196.8)/(2890)(.88)
=
7736.0 psi
4
Comparing this stress with the shear stress obtained
from the model No.3, where the stress is taken directly
from output of SAP V program.
C computer
=
7307 ps1
% difference
=
=
(7736 - 7307)/7736
5%
Similarly, the shear stress at the sections B,C,D,E and F
can be determined 1n the same manner.
The results of
such calculations are presented in table 3.
30
Table 3
Comparison of the shear stress between model No.1 and
model No.3.
Sections
for model 1
psl.
for model 3
psi
% difference
A
7736
7306
5.0
B
2079
2038
0.1
c
2019
2027
0.3
D
7448
7900
5.6
E
7090
7909
10.0
F
2028
2115
4.0
As can be seen from table 3, the max1.mum difference
between the shear stress for model No. 1 and the shear
stress obtained from the computer model No.3 1.s
10 percent. This can account for the fact that the beam
model does not permit to capture the stress concentration
in the panel zone.
31
ANALYZING NEED FOR COLUMN STIFFNERS AND WEB DOUBLERS
If the flange of the supporting column is too thin
the forces transmitted by the connecting beam flanges
will load the outstanding portion of the column flange as
a cantilever beam and cause it to deflect as shown in
Figure 12a.
stress concentrations
FIGURE 12a
Column Flange without stiffners
As this deflection takes place it reduces the stress in
the outer edges of the beam-to-column welds, and as a
result increases the stress in the center portion of the
weld in line with the column web.
32
Unless the column flange is sufficiently thick,
flange stiffners must be added to the column in line with
the beam's top and bottom flanges. Such stiffners keep
the column flange from deflecting and load the weld
uniformly, as shown in figure 12b.
FIGURE 12b
Column Flange with stiffners
Analysis of Stiffner Requirements in the Tension Region
of the Connection(Elastic Design)
The following is adapted from "Welded Interior
Beam-to-Column Connections", AISC 1959.
33
The column flange can be considered as acting as two
plates, both of type ABCD; See Figure 13.
FIGURE 13
(From Blodgett, Omer W., 1966)
The beam flange 1s assumed to place a line load on each
of these plates.
The effective length of these plates
(p) is assumed to be 12 times the thickness of the column
flange (12t ) and the plates are assumed to be fixed at
c
the ends of this length.
The plate is also assumed to be
fixed adjacent to the column web.
34
Analysis of this plate by means of yield line theory
leads to the equation for the m1n1mum column flange
thickness requirement, which is
or
tc
~
0.40
tc
~
0 . 40
Af
(19a)
bb tb
(19b)
...---
v
where bb and tb are beam's flange width and thickness
respectively.
If the thickness of the column flange(t ) meets the
c
above requirements, column stiffners are not needed in
line with the tension flanges of the beam.
If the actual thickness of the column flange (t ) is
c
less than this value, stiffners are needed.
35
Analysis of Stiffner Requirements 1n Compression Region
of Connection (Elastic Design)
It is assumed that the concentrated compression force
from the beam flange spreads out into the column web at a
slope of 2.5 until it reaches the K line or toe of the
fillet, as is illustrated in Figure 14.
I
t
+
5K
l
Column web
FIGURE 14
(From Blodgett, Omer W., 1966)
Equating the resisting force of the column web to the
applied.force of the beam flange will result in an
equation for the minimum web thickness requirement for
the column
or
we 2
we 2
Af/(tb + SKC)
(19a)
bbtb/(tb + SKC)
(19b)
36
If the thickness of the column web(W ) meets the
c
above requirement, column stiffners are not needed in
line with the compression flanges of the beam.
If the actual thickness of the column web(W ) 1s less
c
than this value the web must be stiffened in some manner.
These two criteria are used to determine whether the
column in the joint being studied need to be stiffened.
Column flange thickness
t
c L 0.40
-J bbtb
bb
=
12 1n
tb
=
1.02 1n
(0.40)~(12) (1.02)
t
c .L
t
1.399 1n
c ~
Since the actual column flange used very close to this
value the stiffners are not required.
37
Column web thickness
wc
~ bb tb/(tb + SK c )
=
tb =
Kc =
bb
wc
12 l.n
1.02 l.n
2 9/16 in
~ (12) (1.02)/[(1.02) + (5) (2 9/16)
J =
0.88 l.ll
Since the actual column web is the same as this, the
doubler plates are not required.
38
RESULTS AND DISCUSSIONS
The following three figures represent the distorted
shapes of all three models.
I
I
FIGURE 15
Distorted shape of model No.1
39
rn
I I I
I I I
I I I
/-f-f
~odel
FIGf.JR.E 16a
Distorted shape of
No.2(front view1
~odel No.2(iso~etric view)
FIGf.JR.E 16b
Distorted shape of
40
FIGURE 17a
Distorted shape of model No.3(front view)
FIGURE 17b
Distorted shape of model No.3(isometric view)
41
The shear stress is the most important factor in the
analysis of panel zone, because it is the shear stress
which distorts the panel zone and can cause failure and
additional distortions of the structure.
In the previous calculations it was found that there
was no need for stiffners and web doublers in the
structure. In other words the column elements used were
thick enough to carry the load from the beam. However,
the shear stress varies linearly with the cross sectional
area of the web, according to equation 18.
The addition
of doublers increased the web thickness by 30% and this
reduced the shear stress by 32%.
42
However, the bending stress in the column web near
beam flanges was reduced by about 50 percent due to
addition of stiffners and doubler plates.
These,results
are summarized in table 4, for the elements shown in
figure 18.
~II\I
1 2
~/
v
~
v
3 4- 5
I~
~
/
-~
/
~
/
~~
/
~
/
~L/
/
/
~
/
~
~
~
/
6
7-
8 9
/
~
7
~
7
~
II\II\
FIGURE 18
The bending stress was determined for the elements
indicated above
' v
43
Table 4
Comparison of bending stress near the panel zone,
for model No.3 (with and without the stiffners and
doubler plates for the members indicated in figure 18.
Bending
stress
without
stiffners
and
doublers
(psi)
Bending
stress with
stiffners
and
doublers
(psi)
% change
1
18410.0
8676.0
52.3
2
7991.0
3691.0
53.2
3
20540.0
9682.0
52.8
4
9089.0
4211.0
53.6
5
-1056.0
-464.0
56.0
6
-23330.0
-11950.0
49.0
7
-10400.0
-5193.0
50.0
8
-22240.0
-11800.0
47.0
9
-9409.0
-4721.0
50.0
Element
Number
As can be observed from the table 4, the bending stresses
in the panel zone, in the neighborhood of beam's top and
bottom flanges are reduced about 50 percent by adding
stiffners and doubler plates to the panel zone .
. ll
44
The beam's top and bottom flanges cause the column
flange to bend and act like a cantilever beam in the
neighborhood of the panel zone.
See Figure 19.
FIGURE 19
Column Flang Acting Like a Cantilever Beam
The addition of
stiffne~s
reduc~s
the bending stress in
the column flange by an average of 37%. These results are
summarized in table 5 for elements shown in Figure 20.
45
II\/\I\
13
I~
15
1 g 9
Lt 5 6
12 3
IO 11 12
V\ V\
\I
FIGURE 20
The bending stresses in the column flange near the panel
zone are determined for members indicated above
46
Table 5
Comparison of bending stress in the column flange for
model No.3(with and without the stiffners and doubler
plates for elements indicated in figure 20) .
Element
Number
Bending
stress
without
stiffners
(psi)
Bending
stress with
stiffners
% change
(psi)
1
397.1
271.0
31.6
2
-5294.8
-3805.5
28.1
3
2336.1
1215.5
48.0
4
293.8
225.6
23.0
5
1058.0
1032.0
2.4
6
6341.1
3945.3
37.8
7
557.4
300.3
47.0
8
4454.6
3413.0
23.4
9
2790.0
1552.6
44.0
10
1843.0
1228.0
33.4
11
7602.7
5427.1
. 29.0
12
2136.4
747.0
65.0
13
1493.7
883.0
40.0
14
5697.5
3660:2
35.7
15
2709.3
902.5
65.0
These results indicate that even though there was no
design requirement for stiffners, the column flange
stresses can be reduced significantly by the addition of
st:l.ffners.
47
Distortion of Panel Zone
As was previously mentioned, there is no design
requirement for stiffners and web doubler plates 1n the
panel zone of the structure which was modeled.
In other
words, the panel zone is sufficiently stiff to prevent
overstress.·
However, there is distortion in the panel
zone which contributes to
structure.
th~
overall flexibility of the
As the stiffners and web doubler plate are
added, the distortion is reduced by 3.25 percent.
This
reduction would probably have been considerably higher if
the beams and column used had thinner web and flanges.
Figure 21 and 22 present the distorted shapes of the
panel zone drawn over the undistorted shapes for model
No.3, without and with the stiffners and web doubler
plate.
The displacement of each node A,B,C and D is
I
I
taken relative to node A and is indicated by A , B , C
and D" .
The displacements are magnified several times,
so that the distorted shapes could be observed more
clearly.
I
48
The shear distortion angles are obtained from the
equation
(o<-(3)
where
and
(20)
are the panel zone's side angles as shown
in figure 21 and 22.
If o<
and~
were equal, there would
have been no shear distortion of the panel zone.
In
other words, the panel zone would be subjected to pure
rotation.
The average rotation of panel zone 1s obtained from
the equation
e=
1/2C~+f3)
(21)
49
c
a; r--- -----------
-----------~C
,
1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I~
.....---; o<
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
0
--! ----
I
---
-
-
'o'
. ...J
FIGURE 21
Distorted shape of panel zone, without the sti££ners
and web doubler plate
Corresp·onding shear distortion:
<;(
= (o< -
=
f.; )
(0 .. 00157 - 0. 003904)
=
1.167 X 10-
3
rad
I
50
c
r-8~--
--- --- - ---- --- ----- -- -- f-l c '
I
I
I
I
I
I
r
I
I
I
I
I
I
:~
o( _.,..-.
I
I
r
I
I
~~~~~--0-~~------~o~~
---f-- -- -- --- _J
DI
FIGURE 22
Distorted shape of the panel zone, with the stiffners and
doubler plate
Corresponding shear distortion:
'i=(o<-(3)
=
(.0011461 -
.0030844)
=
9.6915 X 10-
4
rad
51
The distortion due to pure rotation was found
directly from the computer output of model No. 1 to be
.
e = 1.107
X 10
-3
rad.
The average rotation of panel
zone was found from equation (21) to be
rad, using model No. 3.
e=
2.53 X 10
-3
This is nearly twice the
rotation of the simple model (model No. 1), which
represents a significant contribution of the overall
flexibility of the joint.
This additional flexibility 1s
not included in the beam model (No. 1).
The shear distortion was found from equation (20) to
~
be~=
2.747 X 10 -3 rad. When stiffners and doubler plates
were added to the panel zone the shear distortion
was
reduced by 30.0%.
Note that the shear distortion is of the same order
of magnitude as the rotation due to bending.
52
CONCLUSIONS AND RECOMMENDATIONS
A beam-to-column connection of a moment resisting
frame was studied to determine the stress and distortion
in the panel zone.
The structure was first modeled with
beam elements, which capture only the bending effects.
Then the structure was modeled using finite elements.
the finite element model identified stress concentrations
in the panel zone near the top and bottom flanges of the
beam, and more rotatl.on and shear distortion of the panel
zone.
The shear distortion was found to be of the same
order of magnitude as the bending rotations.
In order to m1n1m1ze these effects stiffners and web
doubler plates are in practice added to the panel zone.
The addition of stiffners and web doublers
significan~ly
reduced the bending stresses in the column flange, the
shear stress in the panel zone and the shear distortion
of the panel zone.
It is suggested that for further research on the
effect of stiffners and web doubler plates, beams and
columns with thinner flanges and webs· be chosen. This
53
will better illustrate the usefulness of stiffners and
web doubler plates.
In addition, for more accurate results, a finer
element mesh should be used, particularly in the areas of
high stress concentration.
54
BIBLIOGRAPHY
1.
Blodgett, Orner W., Design of Welded Structures,
Cleveland: James F. Lincoln Arc Welding Foundation,
1966
2.
Craig, Roy R. Jr. Structural Dynamics, John Wiley and
Sons, New York 1981.
3.
Laible P. Jeffrey, Structural Analysis, New York, NY
1985. Holt, Rinehard and Winston.
4.
Slutter, Roger G., Tests of Panel Zone Behavior in
Beam-to-Column Connections, for American Institute of
Steel Construction, INC. 1977.
5.
Stevens, Karl K., Statics and Strenth of Materials,
Prentice-Hall, New Jersey, 1979.
6.
Timoshenko, S. Theory of Plates and Shells, 2nd
Edition, McGraw-Hill, 1959.
Computer Program Manual:
7.
"SAP IV: A structural Analysis Program for Static and
Dynamic Response of Linear Systems", University of
California, Berkeley, 1Q73. ·
55
APPENDICES
56
APPENDIX 1
57
COMPUTER OUTPUT FOR MODEL NO. 1
C 0 N T R 0 L
I N F 0 R MA T I 0 N
11
NUMBER OF NODAL POINTS
=
NUMBER OF ELEMENT TYPES =
1
NUMBER OF LOAD CASES
1
=
NUMBER OF FREQUENCIES
=
0
ANALYSIS CODE (NDYN)
0
=
EQ.O,
STATIC
EO. 1, MODAL EXTRACTION
EQ.2,
FORCED RESPONSE
EQ.3,
RESPONSE SPECTRUM
EQ.4,
DIRECT INTEGRATION
EQ.5,
FREQUENCY RESPONSE
SOLUTION MODE (MODEX)
=
0
EQ.O,
EXECUTION
DATA CHECK
EO. 1,
NUMBER OF SUBSPACE
ITERATION VECTORS (NAD) =
0
EQUATIONS PER BLOCK
=
0
TAPE10 SAVE FLAG (N10SV) =
0
GRAVITATIONAL CONSTANT
= 386.40
TOTAL BLANK COMMON (MTOT)=25000
,..
STRUCTURE PLOTTING IS REQUESTED
REQUIRED BLANK COMMON FOR THIS STEP=
111
NODAL POINT INPUT DATA
NODE
BOUNDARY CONDITION CODES
y
NUMBER X
z XX VY
1
1
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
4
1
1
0
0
0
5
1
0
1
0
0
6
1
1
1
0
0
7
0
0
0
0
0
8
0
0
0
0
0
9
0
0
0
0
0
10
0
0
0
0
0
11
1
1
1
1
1
zz
0
0
0
0
0
0
0
0
0
0
1
NODAL POINT COORDINATES
X
v
.000
.000
.000
48.000
.000
98.000
-153.400
.000
153.400
.000
-98.000
.000
-7.400
.000
.000
18.000
7.400
.000
.000
-18.000
160.000
160.000
z
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
T
0
0
0
0
0
0
0
0
0
0
0
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
U1
<X>
GENERATED NODAL DATA
NODE
BOUNDARY CONDITION CODES
y
NUMBER X
z XX yy
1
2
3
4
5
6
7
8
9
10
11
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
zz
0
0
0
0
0
0
0
0
0
0
1
NODAL POINT COORDINATES
X
y
.000
.000
.000
-153.400
153.400
.000
-7.400
.000
7.400
.000
160.000
.000
48.000
98.000
.000
.000
-98.000
.. 000
18.000
.000
-18.000
160.000
z
T
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
()"1
~
EQUATION NUMBERS
y
N
X
1
1
2
3
4
5
6
7
8
9
10
11
6
12
16
20
0
27
33
39
45
0
2
7
0
0
0
0
28
34
40
46
0
z
0
8
0
0
0
0
29
35
41
47
0
XX
3
9
13
17
21
24
30
36
42
48
0
yy
4
10
14
18
22
25
31
37
43
49
0
zz
5
11
15
19
23
26
32
38
44
50
0
REQUIRED BLANK COMMON FOR THIS STEP=
147
"'
0"1
0
3
I
D
NUMBER
NUMBER
NUMBER
NUMBER
B E A M
DF
OF
DF
OF
E L E ME N T S
BEAMS
=
GEOMETRIC PROPERTY SETS=
FIXED END FORCE SETS
=
MATERIALS
=
9
4
0
1
MATERIAL PROPERTIES
MATERIAL
NUMBER
VOUNG•S
MODULUS
POISSON•S
RATIO
MASS
DENSITY
WEIGHT
DENSITY
.3000E+08
.3000
.OOOOE+OO
.OOOOE+OO
BEAM GEOMETRJC PROPERTIES
,,.
SECTION
NUMBER
AXIAL AREA
A( 1)
SHEAR AREA
A(2)
SHEAR AREA
A(3)
TORSION
J( 1)
INERTIA
I(2I
INERTIA
I (3 I
1
2
3
4
.4710E+02
.8440E+02
.4710E+02
.8440E+02
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
. 1240E+02
. j080E+03
. 1000E+05
. 1000E+04
.2950E+03
. 1470E+04
. 1500E+05
.5000E+04
.9760E+04
. 3910E+04
.2200E+06
. 2000E+05
ELEMENT LOAD MULTIPLIERS
A
B
X-DIR
.OOOOOOE+OO
.OOOOOOE+OO
V-OIR
.OOOOOOE+OO
.OOOOOOE+OO
Z-DIR
.OOOOOOE+OO
.OOOOOOE+OO
c
.OOOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+OO
SECTION
S(2)
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
D
.OOOOOOE+OO
.OOOOOOE+OO
:OOOOOOE+OO
Q')
1-'
3/D BEAM ELEMENT DATA
BEAM
NUMBER
NODE
-I
NODE
1
2
3
8
2
3
4
4
5
6
7
8
7
1
1
8
2
7
1
9
9
1
10
-J
9
5
10
6
NODE
-K
MATERIAL
NUMBER
11
11
11
11
11
11
11
11
11
1
1
1
1
1
1
REQUIRED BLANK COMMON FOR THIS STEP=
SECTION
NUMBER
1
1
1
ELEMENT END LOADS
A
B
c
D
4
0
2
2
1
3
3
1
.o
4
2
0
0
0
0
0
0
0
0
0
0
0
(j
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
END CODES
-I
-J BAND
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
38
33
10
17
32
44
25
. 50
27
167
,,.
())
N
E Q U AT I 0 N
P A R A ME T E R S
TOTAL NUMBER OF EQUATIONS
=
BANDWIDTH
=
NUMBER OF EQUATIONS IN A BLOCK =
NUMBER OF BLOCKS
=
50
50
50
1
,..
0'1
w
,.
N 0 D A l
NODE
NUMBER
2
(S T A T I C)
l 0 A D S
0 R
MA S S E S
(D Y N A M I C)
X-AXIS
FORCE
Y-AXIS
FORCE
Z-AXIS
FORCE
X-AXIS
MOMENT
Y-AXIS
MOMENT
Z-AXIS
MOMENT
1. OOOOOE+05
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
LOAD
CASE
All EQUATIONS HAVE STIFFNESS ATTACHED
STRUCTURE
LOAD CASE
ELEMENT
A
.000
LOAD
MULTIPLIERS
D
B
c
.000
.000
.000
STIFFNESS MATRIX PARAMETERS
MINIMUM NON-ZERO DIAGONAL ELEMENT= 9~800E+05
MAXIMUM DIAGONAL ELEMENT
7.402E+12
MAXIMUM/MINIMUM
7.553E+06
AVERAGE DIAGONAL ELEMENT
3.382E+11
DENSITY OF THE MATRIX
5.6 PCT.
REQUIRED BLANK COMMON FOR THIS STEP=
118
0)
.j:::.
B E A M
BEAM LOAD
NO.
NO.
2
1
E L E M E N T
F 0 R C E S
A N·D
M0 M E N T S
AXIAL
R1
SHEAR
R2
SHEAR
R3
TORSION
M1
BENDING
M2
BENDING
M3
1.028E-06
-1.028E-06
1 .OOOE-~>05
-1. OOOE+05
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
-3.000E+06
4.800E+06
1. 031 E -06
-1.031E-06
1. OOOE+05
-1. OOOE+05
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
1.669E-06
3.000E+06
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
8.047E-07
-2.980E-07
P/A+M2/S2
P/A-M2/S2
:
3
1
1. 031E-06
-1.031E-06
-7.451E-09
7.451E-09
If"
4
1
.OOOE+OO
.OOOE+OO
-4.759E+04
4.759E+04
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
-6.948E+06
5
1 -7.153E-07
7. 153E-07
-4.759E+04
4.759E+04
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
6.948E+06
-7.300E+06
6
1
4.768E-07
-4.768E-07
-4.759E+04
4.759E+04
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
-7.300E+06
6.948E+06
7
1
·.OOOE+OO
.OOOE+OO
-4.759E+04
4.759E+04
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
-6.948E+06
2.980E-08
8
1 -1.020E-06
1. 020E-06
1. OOOE+05
-1. OOOE+05
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
9.800E+06
-8.000E+06
0'1
U1
9
-1.033E-06
1.033E-06
S T AT I C
1.000E+05
-1.000E+05
S 0 L U T
EQUATION SOLUTION
=
DISPLACEMENT OUTPUT=
STRESS RECOVERY
=
ON.
.OOOE+OO
.OOOE+OO
.OOOE+OO
.OOOE+OO
TIME
.OOOE+OO
.OOOE+OO
8.000E+06
.OOOE+OO
L 0 G
.41
.10
. 19
w
())
())
S A P - C S U C
S T R U C T U
~
E
P L 0 T T E R
TEKTRONIX PLOT10 PREVIEW PLOTTING IS REQUESTED
REQUIRED BLANK COMMON FOR THIS STEP =
CPU TIME FOR PLOT FILE SETUP
=
111
.07
FOR PLOT GROUP
PLOT TYPE (ITYPE)
EO. 1, STRUCTURE PLOTS
VERTICAL AXIS (IAXIS)
EO. 1, X AXIS IS VERTICAL
2, Y ~XIS IS VERTICAL
3, Z AXIS IS VERTICAL
VERTICAL AXIS INCLINATION (ALPHA)
ROTATION ABOUT THE VERTICAL (BETA)
FLAG FOR DELETING NODES (IDEL)
EQ.1, NODES ARE TO BE DELETED
FLAG FOR NODE LABELING (NODLBL)
EQ.1, THE NODES WILL BE LABELED
NUMBER OF DEFORMED SHAPES/MODES
TO BE PLOTTED (NMODE)
LT.O, ALL WILL BE PLOTTED
EQ.O, NONE WILL BE PLOTTED
GT.O, NMODE WILL BE PLOTTED
FLAG FOR COORD. SYSTEM AXES (LABAX)
EQ.1, THE AXES WILL BE DRAWN
FLAG FOR TYPE OF DEFORMED PLOT (IDEF)=
EQ.O DEFORMED STRUCTURE
EQ.1 VECTORS FROM UNDEFORMED
EQ.2 DEFORMED OVER UNDEFORMED
FLAG FOR BOXING THE STRUCTURE (IBOX)=
PLOT MARGIN, PCT OF PLOT HEIGHT
MAXIMUM CONNECTIVITY BETWEEN NODES
REQUIRED BLANK COMMON FOR THIS STEP=
XMAX
XMIN
YMAX
YMIN
XHT
YHT
DELP
2
.000
.000
0
0.
IJ'
-1
0
0
0
10.00
5
111
= 160.00
= -153.40
= 160.00
= -98.000
= 313.40
= 258.00
= 39.619
())
'-J
PSF
=
PLTMAR=
.25240E-01
.44400
CPU TIME FOR UNDEFORMED PLOT
REQUIRED BLANK COMMON FOR THIS STEP
CPU TIME FOR DEFORMED PLOTS
1. 00
184
1. 28
lj'
()")
00
S A P - C S U C
S T R U C T U R E
P L 0 T T E R
FOR PLOT GROUP 1
PLOT TYPE (ITYPE)
EQ. 1, STRUCTURE PLOTS
VERTICAL AXIS (IAXIS)
EQ. 1, X AXIS IS VERTICAL
2,
Y AXIS IS VERTICAL
3, Z AXIS IS VERTICAL
VERTICAL AXIS INCLINATION (ALPHA)
ROTATION ABOUT THE VERTICAL (BETA)
FLAG FOR DELETING NODES (IDEL)
EQ.1, NODES ARE TO BE DELETED
FLAG FOR NODE LABELING (NODLBL)
EQ. 1, THE NODES WILL BE LABELED
NUMBER OF DEFORMED SHAPES/MODES
TO BE PLOTTED (NMODE)
LT.O, ALL WILL BE PLOTTED
EQ.O, NONE WILL BE PLOTTED
GT.O, NMODE WILL BE PLOTTED
FLAG FOR COORD. SYSTEM AXES (LABAX)
EQ. 1, THE AXES WILL BE DRAWN
FLAG FOR TYPE· OF DEFORMED PLOT (IDEF)=
EQ.O DEFORMED STRUCTURE
EQ.1 VECTORS FROM UNDEFORMED
EQ.2 DEFORMED OVER UNDEFORMED
FLAG FOR BOXING THE STRUCTURE (IBOX)=
PLOT MARGIN, PCT OF PLOT HEIGHT
MAXIMUM CONNECTIVITY BETWEEN NODES
REQUIRED BLANK COMMON FOR THIS STEP =
2
.000
.000
0
0
- 1
IJ"
0
0
0
10.00
5
111
XMAX
160.00
XMIN
-153.40
YMAX
160.00
YMIN
-98.000
XHT
313.40
YHT
258.00
DELP
50.877
PSF
. 19655E-01
PLTMAR= .92000
CPU TIME FOR UNOEFORMED PLOT
REQUIRED BLANK COMMON FOR THIS STEP
.46
184
(})
\.0
S T AT I C
AN A L YS I S
LOAD CASE
DISPLACEMENTS/ROTATIONS OF UNRESTRAINED NODES
NODE
NUMBER
1
2
XTRANSLATION
2.77816E-01
3.43264E-01
4.23640E-01
2.77816E-01
2.77816E-01
v-
TRANSLA TI ON
3.98848E-14
2.03619E-14
6
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
7
2.77816E-01
2.98874E-01
2. 778H3E-01
2.55408E-01
8.16126E-03
3.25790E-14
-8.16126E-03
3.26366E-14
3
4
5
e
9
10
zTRANSLATION
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
XROTATION
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
v-
ROTATION
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
zRDTATION
- 1. 10690E -03
- 1. 60753E -03
-1.60753E-03
6.33304E-04
6.33304E-04
-4. 10195E -03
-1.09891E-03
-1.22390E-03
-1.09891E-03
-1.37390E-03
,..
........
0
71
APPENDIX 2
COMPUTER OUTPUT FOR MODEL NO. 3
ssssssssss
ssssssssssss
ss
ss
ss
sss
sssssssss
sssssssss
sss
ss
ss
ss
ssssssssssss
ssssssssss
AAAAAAAAAA
AAAAAAAAAAAA
AA
AA
AA
AA
AA
AA
AAAAAAAAAAAA
AAAAAAAAAAAA
AA
AA
AA
AA
AA
AA
AA
AA
AA
AA
PPPPPPPPPPP
PPPPPPPPPPPP
pp
pp
pp
PP
pp
PP
PPPPPPPPPPPP
PPPPPPPPPPP
pp
PP
PP
pp
PP
-----------
CSUC VERSION
cccccccccc
cccccccccccc
cc
cc
cc
cc
cc
cc
cc
cc
cc
cc
cccccccccccc
cccccccccc
ssssssssss
ssssssssssss
ss
ss
ss
sss
sssssssss
sssssssss
sss
ss
ss
ss
ssssssssssss
ssssssssss
uu
uu
uu
uu
uu
uu
uu
uu
uu
UU,
uu
uuuuuuuuuuuu
uuuuuuuuuu
uu
uu
uu
uu
uu
uu
uu
uu
uu
cccccccccc
cccccccccccc
cc
cc
cc
cc
cc
cc
cc
cc
cc
cc
cccccccccccc
cccccccccc
JULY 1, 1983
85/12/04.
'I
PANEL ZONE DISTORTION IN MOMENT RESISTING FRAMES
•-J
1-.)
C 0 N T R 0 L
I N F 0 R M A T I 0 N
NUMBER OF NODAL POINTS
= 507
NUMBER OF ELEMENT TYPES =
2
NUMBER OF LOAD CASES
1
=
NUMBER OF FREQUENCIES
=
0
ANALYSIS CODE (NDYN)
0
=
EQ.O,
STATIC
EO. 1,
MODAL EXTRACTION
EQ.2,
FORCED RESPONSE
EQ.3,
RESPONSE SPECTRUM
EQ.4,
DIRECT INTEGRATION
EQ 5,
FREQUENCY RESPONSE
SOLUTION MODE (MODEX)
=
0
EQ.O,
EXECUTION
EO. 1,
DATA CHEC.K
NUMBER OF SUBSPACE
ITERATION VECTORS (NAO)
=
0
EQUATIONS PER BLOCK
0
=
TAPE10 SAVE FLAG (N10SV) =
0
GRAVITATIONAL CONSTANT
= 386.40
TOTAL BLANK COMMON (MTOT)=25000
if"
BANDWIDTH MINIMIZATION IS REQUESTED
STRUCTURE PLOTTING IS REQUESTED
REQUIRED BLANK COMMON FOR THIS STEP=
5071
NODAL POINT INPUT DATA
NODE
BOUNDARY CONDITION CODES
y
NUMBER X
z XX yy
1
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
6
0
0
0
0
0
7
0
0
0
0
0
9
0
0
0
0
0
10
0
0
0
0
0
12
0
0
0
0
0
13
0
0
0
0
0
15
0
0
0
0
0
16
0
0
0
0
0
17
0
0
0
0
0
18
0
0
0
0
0
zz
0
0
0
0
0
0
0
0
0
0
0
0
0
NODAL POINT COORDINATES
y
X
.000
.000
.000
.000
.000
20.000
.000
20.000
.000
35.000
.000
35.000
.000
49.000
.000
49.000
.000
61.000
.000
61.000
.000
71.000
.000
71.000
.000
71.000
z
.000
16. 130
.000
16. 130
.000
16.130
.000
16. 130
.000
16.130
.000
2.065
8.065
T
0
1
0
1
0
1
0
1
0
1
0
0
0
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
-....)
w
19
20
21
22
26
27
28
29
33
34
35
45
47
57
59
69
71
81
'83
93
95
105
107
117
118
46
58
70
82
94
106
119
120
124
125
126
127
129
130
131
133
134
136
137
139
140
142
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o·
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.000
.o·oo
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
71.000
71.000
76.000
76.000
76.000
76.000
79.510
79.510
79. 510
79.510
82.000
112.000
82.000
112.000
82.000
112.000
82.000
112.000
82.000
112'!ooo
82.000
112.000
82.000
112.000
114.490
114.490
114.490
114.490
114.490
114.490
114.490
118.000
118.000
118.000
118.000
123.000
123.000
123.000
123.000
133.000
133.000
145.000
145.000
159.000
159.000
174.000
174.000
14.065
16. 130
.000
2.065
14.065
16. 130
.000
2.065
14.065
16. 130
16. 130
16.130
14.065
14.065
11.065
11.065
8.065
8.065
5.065
5.065
2.065
2.065
.000
.000
.000
16.130
14.065
11.065
8.065
5.065
2.065
.000
2.065
14.065
16. 130
.000
2.065
14.065
16. 130
.000
16. 130
.000
16. 130
.000
16. 130
.000
16.130
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
·o
1
0
1
0
1
0
0
0
0
0
0
0
Q
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
-.....J
-&:::>
143
145
146
147
148
149
150
151
152
153
154
155
156
157
160
161
162
165
166
167
170
171
172
182
184
194
196
206
208
218
220
230
183
195
207
219
231
232
235
236
237
240
241
242
243
244
245
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
I)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
ci
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.000
.000
6.000
14.717
6.000
14.717
6.000
14.717
6.000
14.717
6.000
12.000
14.717
3.000
12.000
14.717
3.000
12.000
14.717
3.000
12.000
14.717
3.000
3.000
6.000
6.000
9.000
9.000
12.000
12.000
14.717
14.717
3.000
6.000
9.000
12.000
14.717
3.000
12.000
14.717
3.000
12.000
14.717
6.000
12.000
14.717
6.000
194.000
194.000
.000
.000
20.000
20.000
35.000
35.000
49.000
49.000
61.000
61.000
61.000
71.000
71.000
71.000
76.000
76.000
76.000
79 ;r510
79.510
79.510
82.000
112.000
82.000
112.000
82.000
112.000
82.000
112.000
S2.000
112.000
114.490
114.490
114.490
114.490
114.490
118.000
118.000
118.000
123.000
123.000
123.000
133.000
133.000
133.000
145.000
.000
'16. 130
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.ooo·
.000
.000
.000
.000
.000
.000
.ooo
.000
.000
.000
.000
.000
.000
.000
.000
-.J
U1
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
289
291
301
303
313
315
325
327
337
339
349
290
302
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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:ooo
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CJ)
314
326
338
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
375
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378
379
381
382
384
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420
421
422
408
423
424
411
425
426
413
427
428
415
429
430
417
431
432
436
437
439
440
442
443
445
446
448
449
451
452
462
464
468
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471
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1..0
44
45
46
47
48
49
50
51
52
. 53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
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72
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120
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N
138
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140
141
142
143
144
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147
148
149
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151
152
153
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159
160
161
162
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164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
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159.000
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185
186
187
188
189
190
191
192
193
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199
200
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206
207
208
209
210
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212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
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232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
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252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
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293
294
295
296
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305
306
307
308
309
310
311
312
313
314
315
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0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
24.717
24.717
24.717
34.717
34.717
34.717
49.717
49.717
69.717
69.717
94.717
94.717
18.717
18.717
18.717
18.717
24.717
24.717
34.717
34.717
49.717
49.717
69.717
69.717
94.717
94.717
-145.000
-145.000
-145.000
-145.000
-145.000
-145.000
-145.000
159.717
159.717
159.717
159.717
159.717
159.717
159.717
165.000
103.000
109.000
114.490
91.000
103.000
114.490
97.000
114.490
97.000
114.490
97.000
114.490
114.490
114.490
114.490
114.490
114.490
114.490
114.490
114'! 490
114.490
114.490
114.490
114.490
114.490
114.490
114.490
97.000
79.510
79.510
79.510
114.490
114.490
114.490
97.000
79.510
79.510
79. 510
114.490
114.490
210.000
I
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
8.065
2.065
5.065
11.065
14.065
2.065
14.065
2.065
14.065
2.065
14.065
2.065
14.065
2.065
14.065
8.065
8.065
8.065
14.065
2.065
2.065
14.065
8.065
8.065
8.065
2.065
14.065
2.065
14.065
8.065
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
<.0
0
EOUIITION NUMBERS
y
N
X
1
2
3_
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
3"1
32
33
34
35
36
37
38
39
40
41
42
43
44
45
1
7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
103
109
115
121
127
133
139
145
151
157
163
169
175
18 i
187
193
199
205
211
217
223
229
235
241
247
253
259
265
2
8
14
20
26
32
38
44
50
56
62
68
74
80
86
92
98
104
110
116
122
128
134
140
146
152
158
164
170
176
182
188
194
200.
206
212
218
224
230
236
242
248
254
260
266
z
XX
YY
zz
3
9
15
21
27
33
39
45
51
57
63
69
75
81
87
93
99
105
111
117
123
129
135
141
147
153
159
165
171
177
183
189
195
201
207
213
219
225
231
237
243
249
255
261
267
4
10
16
22
28
34
40
46
52
58
64
70
76
82
88
94
100
106
112
118
124
130
136
142
148
154
160
166
172
178
184
190
196
202
208
214
220
226
232
238
244
250
256
262
268
5
11
17
23
29
35
41
47
53
59
65
71
77
83
89
95
101
107
113
119
125
131
137
143
149
155
161
167
173
179
185
191
197
203
209
215
221
227
233
239
245
251
257
263
269
6
12
18
24
30
36
42
48
54
60
66
72
78
84
90
96
102
108
114
120
126
132
138
144
150
156
162
168
174
180
186
192
198
204
210
216
222
228
234
240
246
252
258
264
270
,__.
.<-0
9l
9<\
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
1 17
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
553
559
565
571
577
583
589
595
601
607
613
619
625
631
637
643
649
655
661
667
673
679
685
691
697
703
709
715
721
727
733
739
745
751
757
763
769
775
781
787
793
799
805
8~ 1
817
823
829
554
560
566
572
578
584
590
596
602
608
614
620
626
632
638
644
650
656
662
668
674
680
686
692
698
704
710
716
722
728
734
740
746
752
758
764
770
776
782
788
794
800
806
812
818
824
830
555
561
567
573
579
585
591
597
603
609
615
621
627
633
639
645
651
657
663
669
675
681
687
693
699
705
711
717
723
729
735
741
747
753
759
765
771
777
783
789
795
801
807
813
819
825
831
556
562
568
574
580
586
592
598
604
610
616
622
628
634
640
646
652
658
664
670
676
682
688
694
700
706.
712
718
724
730
736
i42
748
754
760
766
772
778
784
790
796
802
808
814
820
826
832
557
563
569
575
581
587
593
599
605
611
617
623
629
635
641
647
653
659
665
671
677
683
689
695
701
707
713
719
725
731
737
743
749
755
761
767
773
779
785
791
797
803
809
815
821
827
833
558
564
570
576
582
588
594
600
606
612
618
624
630
636
642
648
654
660
666
672
678
684
690
696
702
708
714
720
726
732
738
744
750
756
762
768
774
780
786
792
798
804
810
816
822
828
834
\.0
w
HO
141
14 2
14 J
14<1
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
835 836
841
842
847. 848
853 854
859 860
865 866
0
0
874 875
880 881
886 887
892 893
898 899
904 905
910 911
916 917
922 923
928 929
934 935
940 941
946 947
952 953
958 959
964 965
970 971
976 977
982 983
988 989
994 995
1000 1001
1006 1007
1012 1013
1018 1019
1024 1025
1030 1031
1036 1037
1042 1043
1048 1049
1054 1055
1060 1061
1066 1067
1072 1073
1078 1079
1084 1085
1090 1091
1096 1097
1102 1103
1108 1109
837
843
849
855
861
867
0
876
882
888
894
900
906
912
918
924
930
936
942
948
954
960
966
972
978
984
990
996
1002
1008
1014
1020
1026
1032
1038
1044
1050
1056
1062
1068
1074
1080
1086
1092
1098
1104
1110
838
844
850
856
862
868
871
877
883
889
895
901
907
913
919
925
931
937
943
949
955
961
967
973
979
985
991
997
1003
1009
1015
1021
1027
1033
1039
1045
105.1
1057
1063
1069
1075
1081
1087
1093
1099
1105
1111
839
845
851
857
863
869
872
878
884
890
896
902
908
914
920
926
932
938
944
950
956
962
968
974
980
986
992
998
1004
1010
1016
1022
1028
1034
1040
1046
1052
1058
1064
1070
1076
1082
1088
1094
1100
1106
1112
840
846
852
858
864
870
873
879
885
891
897
903
909
915
921
927
933
939
945
951
957
963
969
975
981
987
993
999
1005
1011
1017
1023
1029
1035
1041
1047
1053
1059
1065
1071
1077
1083
1089
1095
1101
1107
1113
\0
.j::.
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
1114
1120
1 126
1132
1138
1144
1150
1156
1162
1168
1174
1180
1186
1192
1198
1204
1210
1216
1222
1228
1234
12·10
1246
1252
1258
1264
1270
1276
1282
1288
1294
1300
1306
1312
1318
1324
1330
1336
1342
1348
1354
1360
1366
1372
1378
1384
1390
1115
1121
1127
1133
1139
1145
1151
1157
1163
1169
1175
1181
1187
1193
1199
1205
1211
1217
1223
1229
1235
1241
1247
1253
1259
1265
127 I
1277
1283
1289
1295
1301
1307
1313
1319
1325
1331
1337
1343
1349
1355
1361
1367
1373
1379
1385
1391
1116
1122
1128
1134
1140
1146
1152
1158
1164
1170
1176
1182
1188
1194
1200
1206
1212
1218
1224
1230
1236
1242
1248
1254
1260
1266
1272
1278
1284
1290
1296
1302
1308
1314
1320
1326
1332
1338
1344
1350
1356
1362
1368
1374
1380
1386
1392
1117
1123
1129
1135
1141
1147
1153
1159
1165
1171
1177
1183
1189
1195
1201
1207
1213
1219
1225
1231
1237
1243
1249
1255
1261
1267
1273
1279
1285
1291
1297
1303
1309
1315
1321
1327
1333
1339
1345
1351
1357
1363
1369
1375
1381
1387
1393
1118
1124
1130
1136
1142
1148
1154
1160
1166
1172
1178
1184
1190
1196
1202
1208
1214
1220
1226
1232
1238
1244
1250
1256
1262
1268
1274
1280
1286
1292
1298
1304
1310
1316
1322
1328
1334
1340
1346
1352
1358
1364
1370
1376
1382
1388
1394
1119
1125
1131
1137
1143
1149
1155
1161
1167
1173
1179
1185
1191
1197
1203
1209
1215
1221
1227
1233
1239
1245
1251
1257
1263
1269
1275
1281
1287
1293
1299
1305
1311
1317
1323
1329
1335
1341
1347
1353
1359
1365
1371
1377
1383
1389
1395
....
1.0
(J1
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
1396
1402
1408
14 14
1420
1426
1432
1438
1444
1450
1456
1462
1468
1474
1480
1486
1492
1498
1502
1508
1514
1520
1526
1532
1538
1544
1550
1556
1562
1568
1574
1580
1586
1592
1598
1604
1610
1616
1622
1628
1634
1640
1646
1652
1658
1664
1670
1397
1403
1409
1415
1421
142'7
1433
1439
1445
1451
1457
1463
1469
1475
1481
1487
1493
0
1503
1509
1515
1521
1527
1533
1539
1545
1551
1557
1563
1569
1575
1581
1587
1593
1599
1605
1611
1617
1623
1629
1635
1641
1647
1653
1659
1665
1671
1398
1404
1410
14 16
1422
1428
1434
1440
1446
1452
1458
1464
1470
1476
1482
1488
1494
0
1504
1510
1516
1522
1528
1534
1540
1546
1552
1558
1564
1570
1576
1582
1588
1594
1600
1606
1612
1618
1624
1630
1636
1642
1648
1654
1660
1666
1672
1399
1405
1411
1417
1423
1429
1435
1441
1447
1453
1459
1465
1471
1477
1483
1489
1495
1499
1505
1511
1517
1523
1529
1535
1541
1547
1553
1559
1565
1571
1577
1583
1589
1595
1601
1607
1613
1619
1625
1631
1637
1643
1649
1655
1661
1667
1673
1400
1406
1412
1418
1424
1430
1436
1442
1448
1454
1460
1466
1472
1478
1484
1490
1496
1500
1506
1512
1518
1524
1530
1536
1542
1548
1554
1560
1566
1572
1578
1584
1590
1596
1602
1608
1614
1620
1626
1632
1638
1644
1650
1656
1662
1668
1674
1401
1407
1413
1419
1425
1431
1437
1443
1449
1455
1461
1467
1473
1479
1485
1491
1497
1501
1507
1513
1519
1525
1531
1537
1543
1549
1555
1561
1567
1573
1579
1585
1591
1597
1603
1609
1615
1621
1627
1633
1639
1645
1651
1657
1663
1669
1675
\.0
(j)
«<-
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
31.)3
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
1676
1682
1688
1694
1700
1706
1712
1718
1724
1730
1736
1742
1748
1754
1760
1766
1772
1778
1784
1790
1796
1802
1808
1814
1820
1826
1832
1838
1844
1850
1856
1862
1868
1874
1880
1886
1892
1898
1904
1910
1916
1922
1928
1934
1940
1946
1952
1677
1683
1689
1695
1701
1707
1713
1719
1725
1731
1737
1743
1749
1755
1761
1767
1773
1779
1785
1791
1797
1803
1809
1815
1821
1827
1833
1839
1845
1851
1857
1863
1869
1875
1881
1887
1893
1899
1905
1911
1917
1923
1929
1935
1941
1947
1953
1678
1684
1690
1696
1702
1708
1714
1720
1726
1732
1738
1744
1750
1756
1762
1768
1774
1780
1786
1792
1798
1804
1810
1816
1822
1828
1834
1840
1846
1852
1858
1864
1870
1876
1882
1888
1894
1900
1906
1912
1918
1924
1930
1936
1942
1948
1954
1679
1685
1691
1697
1703
1709
1715
1721
1727
1733
1739
1745
1751
1757
.1763
1769
1775
1781
1787
1793
1799
1805
1811
1817
1823
1829
1835
1841
1847
1853
1859
1865
1871
1877
1883
1889
1895
1901
1907
1913
1919
1925
1931
1937
1943
1949
1955
1680
1686
1692
1698
1704
1710
1716
1722
1728
1734
1740
1746
1752
1758
1764
1770
1776
1782
1788
1794
1800
1806
1812
1818
1824
1830
1836
1842
1848
1854
1860
1866
1872
1878
1884
1890
1896
1902
1908
1914
1920
1926
1932
1938
1944
1950
1956
1681
1687
1693
1699
1705
1711
1717
1723
1729
1735
1741
1747
1753
1759
1765
1771
1777
1783
1789
1795
1801
1807
1813
1819
1825
1831
1837
1843
1849
1855
1861
1867
1873
1879
1885
1891
1897
1903
1909
1915
1921
1927
1933
1939
1945
1951
1957
-o
........
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
1958
1964
1970
1976
1982
1988
1994
2000
2on6
2012
2018
2024
2030
2036
2042
2048
2054
2060
2066
2072
2078
2084
2090
2096
2102
2108
2114
2120
2126
2132
2138
2144
2150
2156
2162
2168
2174
2180
2186
2192
2198
2204
2210
2216
2222
2228
2234
1959
1965
1971
1977
1983
1989
1995
2001
2007
2013
2019
2025
2031
2037
2043
2049
2055
2061
2067
2073
2079
2085
2091
2097
2103
2109
2115
2121
2127
2133
2139
2145
2151
2157
2163
2169
2175
2181
2187
2193
2199
2205
2211
2217
2223
2229
2235
1960
1966
1972
1978
1984
1990
1996
2002
2008
2014
2020
2026
2032
2038
2044
2050
2056
2062
2068
2074
2080
2086
2092
2098
2104
2110
2116
2122
2128
2134
2140
2146
2152
2158
2164
2170
2176
2182
2188
2194
2200
2206
2212
2218
2224
2230
2236
1961
1967
1973
1979
1985
1991
1997
2003
2009
2015
2021
2027
2033
2039
2045
2051
2057
2063
2069
2075
2081
2087
2093
2099
2105
2111
2117
2123
2129
2135
2141
2147
2153
2159
2165
2171
2177
2183
2189
2195
2201
2207
2213
2219
2225
2231
2237
1962
1968
1974
1980
1986
1992
1998
2004
2010
2016
2022
2028
2034
2040
2046
2052
2058
2064
2070
2076
2082
2088
2094
2100
2106
2112
2118
2124
2130
2136
2142
2148
2154
2160
2166
2172
2178
2184
2190
2196
2202
2208
2214
2220
2226
2232
2238
1963
1969
1975
1981
1987
1993
1999
2005
2011
2017
2023
2029
2035
2041
2047
2053
2059
2065
2071
2077
2083
2089
2095
2101
2107
2113
2119
2125
2131
2137
2143
2149
2155
2161
2167
2173
2179
2185
2191
2197
2203
2209
2215
2221
2227
2233
2239
1.0
co
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
2240
2246
2252
2258
2264
2270
2276
2282
2288
2294
2300
2306
2312
2318
2324
2330
2336
2342
2348
2354
2360
2366
2372
2378
2384
2390
2396
2402
2408
2414
2420
2426
2432
2438
2444
2450
2456
2462
2468
2474
2480
2486
2492
2498
2504
2510
2516
2241
2247
2253
2259
2265
2271
2277
2283
2289
2295
2301
2307
2313
2319
2325
2331
2337
2343
2349
2355
2361
2367
2373
2379
2385
2391
2397
2403
2409
2415
2421
2427
2433
2439
2445
2451
2457
2463
2469
2475
2481
2487
2493
2499
2505
2511
2517
2242
2248
2254
2260
2266
2272
2278
2284
2290
2296
2302
2308
2314
2320
2326
2332
2338
2344
2350
2356
2362
2368
2374
2380
2386
2392
2398
2404
2410
2416
2422
2428
2434
2440
2446
2452
2458
2464
2470
2476
2482
2488
2494
2500
2506
2512
2518
2243
2249
2255
2261
2267
2273
2279
2285
2291
2297
2303
2309
2315
2321
2327
2333
2339
2345
2351
2357
2363
2369
2375
2381
2387
2393
2399
2405
2411
2417
2423
2429
2435
2441
2447
2453
2459
2465
2471
2477
2483
2489
2495
2501
2507
2513
2519
2244
2250
2256
2262
2268
2274
2280
2286
2292
2298
2304
2310
2316
2322
2328
2334
2340
2346
2352
2358
2364
2370
2376
2382
2388
2394
2400
2406
2412
2418
2424
2430
2436
2442
2448
2454
2460
2466
2472
2478
2484
2490
2496
2502
2508
2514
2520
2245
2251
2257
2263
2269
2275
2281
2287
2293
2299
2305
2311
2317
2323
2329
2335
2341
2347
2353
2359
2365
2371
2377
2383
2389
2395
2401
2407
2413
2419
2425
2431
2437
2443
2449
2455
2461
2467
2473
2479
2485
2491
2497
2503
2509
2515
2521
<.!)
<.!)
~22 2522 2523 2524 2525 2526 2527
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
2528
2534
2540
2546
2552
2558
2564
2570
2576
2582
2588
2594
2600
2606
2612
2618
2624
2630
2636
2642
2648
2654
2660
2666
2672
2678
2684
2690
2696
2702
2708
2714
2720
2726
2732
2738
2744
2750
2756
2762
2768
2774
2780
2786
2792
2798
2529
2535
2541
2547
2553
2559
2565
2571
2577
2583
2589
2595
2601
2607
2613
2619
2625
2631
2637
2643
2649
2655
2661
2667
2673
2679
2685
2691
2697
2703
2709
2715
2721
2727
2733
2739
2745
2751
2757
2763
2769
2775
2781
2787
2793
2799
2530
2536
2542
2548
2554
2560
2566
2572
2578
2584
2590
2596
2602
2608
2614
2620
2626
2632
2638
2644
2650
2656
2662
2668
2674
2680
2686
2692
2698
2704
2710
2716
2722
2728
2734
2740
2746
2752
2758
2764
2770
2776
2782
2788
2794
2800
2531
2537
2543
2549
2555
2561
2567
2573
2579
2585
2591
2597
2603
2609
2615
2~21
2627
2633
2639
2645
2651
2657
2663
2669
2675
2681
2687
2693
2699
2705
2711
2717
2723
2729
2735
2741
2747
2753
2759
2765
2771
2777
2783
2789
2795
2801
2532
2538
2544
2550
2556
2562
2568
2574
2580
2586
2592
2598
2604
2610
2616
2622
2628
2634
2640
2646
2652
2658
2664
2670
2676
2682
2688
2694
2700
2706
2712
2718
2724
2730
2736
2742
2748
2754
2760
2766
2772
2778
2784
2790
2796
2802
2533
2539
2545
2551
2557
2563
2569
2575
2581
2587
2593
2599
2605
2611
2617
2623
2629
2635
2641
2647
2653
2659
2665
2671
2677
2683
2689
2695
2701
2707
2713
2719
2725
2731
2737
2743
2749
2755
2761
2767
2773
2779
2785
2791
2797
2803
~
C)
C)
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
48g
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
2804
2810
2816
2822
2828
2834
2840
2846
28S2
2858
2864
2870
2876
2882
2888
2894
2900
2906
2912
2918
2924
2930
2936
2942
2948
2954
2958
2964
2970
2976
2982
2988
2994
2998
3004
3010
3016
3022
0
2805
2811
2817
2823
2829
2835
2841
2847
2853
2859
2865
2871
2877
2883
2889
2895
2901
2907
2913
2919
2925
2931
2937
2943
2949
0
295~
2965
2971
2977
2983
2989
0
2999
3005
3011
3017
3023
0
2806
2812
2818
2824
2830
2836
2842
2848
2854
2860
2866
2872
2878
2884
2890
2896
2902
2908
2914
2920
2926
2932
2938
2944
2950
0
2960
2966
2972
2978
2984
2990
0
3000
3006
3012
3018
3024
0
2807
2813
2819
2825
2831
2837
2843
2849
2855
2861
2867
2873
2879
2885
2891
2897
2903
2909
2915
2921
2927
2933
2939
2945
2951
2955
2961
2967
2973
2979
2985
2991
2995
3001
3007
3013
3019
3025
0
2808
2814
2820
2826
2832
2838
2844
2850
2856
2862
2868
2874
2880
2886
2892
2898
2904
2910
2916
2922
2928
2934
2940
2946
2952
2956
2962
2968
2974
2980
2986
2992
2996
3002
3008
3014
3020
3026
0
2809
2815
2821
2827
2833
2839
2845
2851
2857
2863
2869
2875
2881
2887
2893
2899
2905
2911
2917
2923
2929
2935
2941
2947
2953
2957
2963
2969
2975
2981
2987
2993
2997
3003
3009
3015
3021
3027
0
REQUIRED BlANK COMMON FOR THIS STEP=
5083
.......
0
.......
3
I
D
NUMBER
NUMBER
NUMBER
NUMBER
B E A M
OF
OF
OF
OF
E L E ME N T S
BEAMS
=
GEOMETRIC PROPERTY SETS=
FIXED END FORCE SETS
=
MATERIALS
=
222
1
0
1
MATERIAL PROPERTIES
MATERIAL
NUMBER
YOUNG*S
MODULUS
POISSDN*S
RATIO
MASS
DENSITY
WEIGHT
DENSITY
. 1000E+04
.2500
.OOOOE+OO
.OOOOE+OO
BEAM GEOMETRIC PROPERTIES
SECTION
NUMBER
AXIAL AREA
SHEAR AREA
A(2)
SHEAR AREA
TORSION
INERTIA
INERTIA
A( 1)
A(3)
J( 1)
I ( 2)
I ( 3)
S( 2)
SECTION MODULUS
Sl 31
. 1000E+OO
.OOOOE+OO
.OOOOE+OO
.5oooE-01
. 1000E+01
.2000E+01
.OOOOE+OO
.OOOOE+OO
ELEMENT LOAD MULTIPLIERS
I
A
B
c
D
X-DIR
Y-DIR
Z-DIR
.OOOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+oO
.ODOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+OO
.OOOOOOE+OO
~
0
N
3/D BEAM ELEMENT DATA
BEAM
NUMBER
NODE
-I
NODE
NODE
-J
-K
MATERIAL
NUMBER
SECTION
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
2
146
5
148
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
386
414
415
383
412
413
380
409
409
410
410
411
377
403
403
404
405
405
406
407
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
. 1
1
1
1
1
1
1
1
1
1
1
8
150
11
152
14
154
155
18
157
158
159
160
24
162
163
164
165
389
416
417
386
414
415
383
383
412
412
413
413
380
380
409
409
409
410
410
410
ELEMENT ENO LOADS
A
B
c
D
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
END CODES
-I
-J BAND
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
867
9
861
12
855
12
849
12
843
12
12
837
12
12
12
12
831
12
12
12
12
24
18
18
24
18
18
24
162
24
18
24
18
24
144
42
36
30
36
30
24
.......
0
w
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
411
411
377
403
403
403
404
404
404
405
405
405
406
406
406
407
407
407
408
373
391
392
393
394
395
396
397
398
399
400
401
402
31
167
168
169
170
71
72
73
74
75
76
77
78
79
80
407
408
373
391
392
393
393
394
395
395
396
39T
397
398
399
399
400
401
402
31
71
72
73
74
75
76
77
78
79
80
81
82
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0·
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
24
30
78
72
66
72
66
60
66
60
54
1'>0
54
48
54
48
42
42
2053
1921
1921
1921
1921
1921
1921
1921
1921
1921
1921
1921
1921
819
12
12
12
12
609
609
609
609
609
609
609
609
609
609
.......
0
+:::.
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
81
82
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
b
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
609
609
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
78
,_..
0
(.]1
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156'
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
217
218
219
82
183
195
207
219
122
232
233
234
235
128
237
238
239
240
132
242
243
135
245
·138
247
14 1
249
144
251
171
220
221
222
223
224
225
226
227
228
229
230
231
434
452
453
454
454
229
230
231
183
195
207
219
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
434
452
453
454
455
456
457
458
459
460
461
462
463
438
464
464
464
465
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
5o7
507
507
507
507
507
507
507
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
78
78
78
609
78
78
78
78
663
12
12
12
12
657
12
12
12
12
663
12
12
663
12
657
12
651
12
643
10
1582
1396
1396
1396
1396
1396
1396
1396
1396
1396
1396
1396
1396
30
78
72
66
72
I-'
0
0'\
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
455
456
456
457
458
458
459
460
460
461
462
463
438
464
464
465
466
466
467
468
468
469
441
470
470
471
471
472
444
473
474
447
475
~76
495
494
493
450
477
478
465
465
466
466
466
467
467
467
468
468
468
469
441
441
470
470
470
471
471
471
472
472
444
444
473
473
474
474
447
475
476
450
477
478
389
416
417
502
501
500
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
507
REQUIRED BLANK COMMON FOR THIS STEP=
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
p
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
60
66
60
54
60
54
48
54
48
42
42
24
144
42
36
30
36
30
24
30
24
24
162
24
18
24
18
24
18
18
24
18
18
640
472
462
314
146
136
5083
......
0
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108
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1-
z
UJ
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UJ
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UJ
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wcr:
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I
1-
1-
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... MATERIAL PROPERTY TABLE ...
TYPE
WEIGHT
DENSITY
.OOOE+OO
MASS
DENSITY
.OOOE+OO
... . THERMAL EXPANSION ..................... PLANE-STRESS ELASTICITY COEFICTENTS ..... .
ALPHA-X
ALPHA-Y .
C-XX
C-XY
C-XS
C-YY
C-VS
.OOOE+OO
.OOOE+OO
3.297E+07
9.890E+06
.OOOE+OO
3.297E+07
.OOOE+OO
......
0
1..0
ELEMENT lOAD CASE MULTIPLIERS
ELEMENT LOAD
CASE NUMBER
1
2
3
4
PRESSURE
,000
.000
.000
.000
XACCELERATION
y-
Z-
EFFECTS
ACCELERATION
ACCELERATION
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
THERMAL
,_.
,_.
0
THIN
PLATE/SHELL
ELEMENT
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
ELEMENT DATA
NODE-I
NODE-J
NODE-K
NODE-L
NODE-0
MATERIAL
NUMBER
AVERAGE
THICKNESS
NORMAL
PRESSURE
TEMPERATURE
DIFFERENCE
1
2
4
5
7
8
10
11
13
14
14
14
16
2
3
·5
6
8
9
11
12
14
18
19
15
17
23
18
24
25
19
26
20
22
23
24
25
26
27
29
95
96
97
98
99
100
101
102
103
104
105
30
83
84
85
5
6
8
9
11
12
14
15
17
4
5
7
8
10
11
13
14
16
0
0
19
21
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
:0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
2.0930
.o
.00
.00
.00
.00
.00
·.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
17
17
18
18
18
19
19
21
22
23
24
25
26
28
107
108
109
110
111
112
113
114
115
116
117
29
95
96
97
17
18
20
22
22
23
23
24
25
25
27
29
30
31
32
33
34
95
96
97
98
99
100
101
102
103
104
105
106
83
84
85
86
o·
0
0
0
0
0
26
28
29
30
31
32
33
107
108
109
110
111
112
113
114
115
116
117
118
95
96
97
98
.0
.o
.0
.0
.0
.0
.0
.o
.0
.0
.0
.0
.0
.0
.o
..0
.o
.o
.o
.0
.o
.o
.o
.0
.0
.0
.o
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
THERMAL
GRADIENT BAND
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.o·oo
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
30
30
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420
58
419
402
420
421
408
423
411
425
413
427
415
429
436
435
434
433
439
435
434
438
442
441
445
444
448
447
451
449
452
453
454
455
456
0
0
0
0
0
0
414
415
416
417
419
419
402
4·21
408
0
0
423
411
425
413
427
415
429
417
431
277
276
171
265
436
0
0
433
439
438
442
441
.445
444
448
450
220
221
222
223
224
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
.6530
.6530
.6530
.6530
.6530
.0
.0
.0
.0
.0
.0
.0
.0
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.0
.0
.0
.o
.0
.0
.0
.0
.o
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.0
.0
.0
.0
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.0
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.0
.0
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.0
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.0
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.0
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.0
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.00
.00
.00
.00
.00
.00
.00
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.00
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.00
.00
.00
.00
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.00
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.00
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.00
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.00
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.00
.00
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.00
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.00
.000
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.000
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.000
.000
.000
.000
.000
30
180
180
24
24
24
192
24
186
24
1951
2023
2101
2179
90
108
114
96
102
108
96
102
96
102
96
102
966
1588
1582
1026
30
30
36
42
30
30
30
30
30
30
30
30
1690
1402
1402
1402
1402
~
......
N
0
466
467
468
469
470
471'
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
224
225
226
227
228
229
230
462
461
460
460
459
458
458
457
456
456
455
454
454
453
452
434
468
468
467
466
466
465
464
464
438
471
471
470
470
441
473
444
475
447
326
231
314
302
481
463
456
457
458
459
460
461
462
468
468
468
467
467
467
466
466
466
465
465
465
464
464
464
438
472
471
471
471
470
470
470
441
441
474
473
473
444
444
475
447
477
450
481
463
480
479
469
469
457
458
459
460
461
462
463
469
462
461
468
460
459
467
458
457
466
456
455
465
454
453
464
469
472
468
467
471
466
465
470
464
472
474
471
473
470
476
475
478
477
482 .
481
463
480
484
481
225
226
227
228
229
230
231
463
0
0
0
0
0
0
0
0
0
0
0
0
0
0
452
0
0
0
0
0
0
0
0
0
0
0
0
0
0
474
473
476
475
338
326
231
314
482
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
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.6530
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.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
.6530
1. 0200
1.0200
1.0200
1.0200
1.0200
1.0200
.0
.0
.0
.0
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.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
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.0
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.0
.0
.0
.0
.0
.0
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.0
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.0
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.0
.0
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.0
.0
.0
.0
.0
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.({
.0
.0
.0
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
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.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
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.00
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.00
.00
.00
.00
.00
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.00
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.000
.000
.000
.000
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.000
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.000
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.000
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.000
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.000
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1402
1402
1402
1402
1402
1402
1402
48
48
54
54
54
60
60
60
66
66
66
72
72
72
78
186
30
30
30
36
36
36
42
180
162
24
24
24
180
180
24
192
24
186
942
1504
1498
1074
96
114
......
N
......
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
480
479
469
483
472
485
474
487
476
489
497
495
495
494
498
493
449
450
450
477
491
478
469
483
472
485
474
487
476
489
478
491
388
389
389
416
430
417
503
502
502
501
505
500
463
469
486
472
488
474
490
476
492
478
389
390
416
417
417
431
502
504
501
500
500
506
0
480
484
469
486
472
488
474
490
476
495
496
494.
493
493
499
450
451
477
478
478
492
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
1.0200
.6530
.6530
1.0200
1.0200
1.0200
1. 0200
.6530
.6530
1.0200
1.0200
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.o
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
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.000
.000
.000
.000
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.000
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108
90
108
102
102
96
102
96
102
96
658
646
640
472
490
496
326
326
314
146
164
170
I-'
N
N
B A N D WI D T H
MI N I MI Z A T
0 N
MINBND (BANDWIDTH CONTROL PARAMETER)=
REQUIRED BLANK COMMON FOR THIS STEP=
7099
WARNING -- MAXIMUM NODAL CONNECTION INCREASED TO 15
REQUIRED BLANK COMMON FOR THIS STEP=
8620
REQUIRED BLANK COMMON FOR THIS STEP=
11185
REQUIRED BLANK COMMON FOR THIS STEP=
7084
EQUATION NUMBERS AFTER BANDWIDTH MINIMIZATION
y
NClDE SEQUENCE
X
z
1
424 2530 2531 2532
2
423 2524 2525 2526
3
422 2518 2519 2520
4
463 2764 2765 2766
5
462 2758 2759 2760
6
461 275:? 2753 -2754
7
486 2902 2903 2904
8
485 2896 2897 2898
9
484 2890 2891 2892
10
500 2986 2987 2988
11
499 2980 2981 2982
12
493 2944 2945 2946
13
505 3016 3017 3018
14
501 2992 2993 2994
15
492 2938 2939 2940
16
506 3022 3023 3024
17
503 3004 3005 3006
18
495 2956 2957 2958
19
489 2920 2921 2922
20
491 2932 2933 2934
21
504 3010 3011 3012
22
502 2998 2999 3000
23
496 2962 2963 2964
24
477 2848 2849 2850
25
475 2836 2837 2838
26
470 2806 2807 2808
27
471 2812 2813 2814
28
498 2974 2975 2976
29
497 2968 2969 2970
30
494 2950 2951 2952
XX
YY
2533 2534
2527 2528
2521 2522
2767 2768
2761 2762
2755 2756
2905 2906
2899 2900
2893 2894
2989-2990
2983 2984
2947 2948
3019 3020
2995 2996
2941 2942
3025 3026
3007 3008
2959 2960
2923 2924
2935 2936
3013 3014
3001 3002
2965 2966
2851 2852
2839 2840
2809 2810
2815 2816
2977 2978
2971 2972
2953 2954
zz
2535
2529
2523
2769
2763
2757
2907
2901
2895
2991
2985
2949
3021
2997
2943
3027
3009
2961
2925
2937
3015
3003
2967
2853
2841
2811
2817
2979
2973
2955
..._.
N
w
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
7"3
74
75
76
77
'476
451
446
440
401
369
368
361
333
294
242
190
173
128
122
112
404
403
397
372
339
296
244
219
176
164
152
156
448
442
407
377
341
298
279
222
214
170
167
207
472
453
414
379
342
327
281
2842
2692
2662
2626
2395
2203
2197
2155
1987
1753
1441
1131
1029
759
723
663
2413
2407
2371
2221
2023
1765
1453
1305
1047
975
903
927
2674
2638
2431
2251
2035
1777
1663
1323
1275
1011
993
1233
2818
2704
2473
2263
2041
1951
1675
2843
2693
2663
2627
2396
2204
2198
2156
1988
1754
1442
1132
1030
760
724
664
2414
2408
2372
2222
2024
1766
1454
1306
1048
976
904
928
2675
2639
2432
2252
2036
1778
1664·
1324
1276
1012
994
1234
2819
2705
2474
2264
2042
1952
1676
2844
2694
2664
2628
2397
2205
2199
2157
1989
1755
1443
1133
1031
761
725
' 665
2415
2409
2373
2223
2025
1767
1455
1307
1049
977
905
929
2676
2640
2433
2253
2037
1779
1665
1325
1277
1013
995
1235
2820
2706
2475
2265
2043
1953
1677
2845
2695
2665
2629
2398
2206
2200
2158
1990
1756
1444
1134
1032
762
726
666
2416
2410
2374
2224
2026
1768
1456
1308
1050
978
906
930
2677
2641
2434
2254
2038
1780
1666
1326
1278
1014
996
1236
2821
2707
2476
2266
2044
1954
1678
2846
2696
2666
2630
2399
2207
2j01
2159
1991
1757
1445
1135
1033
763
727
667
2417
2411
2375
2225
2027
1769
1457
1309
1051
979
907
931
2678
2642
2435
2255
2039
1781
1667
1327
1279
1015
997
1237
2822
2708
2477
2267
2045
1955
1679
2847
2697
2667
2631
2400
2208
2202
2160
1992
1758
1446
1136
1034
764
728
668
2418
2412
2376
2226
2028
1770
1458
1310
1052
980
908
932
2679
2643
2436
2256
2040
1782
1668
1328
1280
1016
' 998
1238
2823
2709
2478
2268
2046
1956
1680
.......
N
-t::>
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
1"17
118
119
120
121
122
123
124
275
217
216
212
211
478
456
415
380
343
299
280
223
215
171
168
208
481
457
416
381
344
300
245
220
177
165
154
157
482
458
417
382
345
301
246
191
174
129
123
114
113
155
161
158
160
153
1639
1:293
1287
1263
1257
2854
2722
2479
2269
2047
1783
1669
1329
1281
1017
999
1239
2872
2728
2485
2275
2053
1789
1459
1311
1053
981
915
933
2878
2734
2491
2281
2059
1795
1465
1137
1035
765
729
675
669
921
957
939
951
909
1640
1294
1288
1264
1258
2855
2723
2480
2270
2048
1784
1670
1330
1282
1018
1000
1240
2873
2729
2486
2276
2054
1790
1460
1312
1054
982
916
934
2879
2735
2492
2282
2060
1796
1466
1138
1036
766
730
676
670
922
958
940
952
910
1641
1295
1289
1265
1259
2856
2724
2481
2271
2049
1785
1671
1331
1283
1019
100 1
1241
2874
2730
2487
2277
2055
1791
1461
1313
1055
983
917
935
2880
2736
2493
2283
2061
1797
1467
1139
1037
767
731
677
671
923
959
941
953
911
1642
1296
1290
1266
1260
2857
2725
2482
2272
2050
1786
1672
1332
1284
1020
1002
1242
2875
2731
2488
2278
2056
1792
1462
1314
1056
984
918
936
2881
2737
2494
2284
2062
1798
1468
1140
1038
768
732
678
672
924
960
942
954
912
1643
1297
1291
1267
1261
2858
2726
2483
2273
2051
1787
1673
1333
1285
1021
1003
1243
2876
2732
2489
2279
2057
1793
1463
1315
1057
985
919
937
2882
2738
2495
2285
2063
1799
1469
1141
1039
769
733
679
673
925
961
943
955
913
1644
1298
1292
1268
1262
2859
2727
2484
2274
2052
1788
1674
1334
1286
1022
1004
1244
2877
2733
2490
2280
2058
1794
1464
1316
1058
986
920
938
2883
2739
2496.
2286
2064
1800
1470
1142
1040
770
734
680
674
926
962
944
956
914
.......
N
l11
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
111
110
119
118
117
109
74
73
72
46
45
44
31
30
29
14
13
12
7
6
5
42 1
385
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2011
2005
1999
1741
1735
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1957
1939
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2006
2000
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1958
1940
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1946
133
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1959
1941
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2242
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2008
2002
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1738
1732
2683
2647
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1960
1942
1654
1648
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1582
1576
2653
2386
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1948
135
123
117
111
105
99
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2870
2864
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2714
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2015
2009
2003
1745
1739
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2684
2648
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1961
1943
1655
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2691
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2715
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2472
2466
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2244
2238
2232
2016
2010
2004
1746
1740
1734
2685
2649
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1962
1944
1656
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197
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352
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1567
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1844
1850
1508
1514
1520
1174
1180
1186
868
874
880
616
622
628
2102
1904
1923
1569
2379
2163
1917
2169
1935
1995
1929
1725
1719
1229
1253
1247
1223
1563
1557
1629
1623
1635
1617
1611
1605
1599
1593
1887
2109
2085
2115
1875
1839
1845
1851
1509
1515
1521
1175
1181
1187
869
875
881
617
623
629
2103
1905
1924
1570
2380
2164
1918
2170
1936
1996
1930
1726
1720
1230
1254
1248
1224
1564
1558
1630
1624
1636
1618
1612
1606
1600
1594
1888
2110
2086
2116
1876
1840
1846
1852
1510
1516
1522
1176
1182
1188
870
876
882
618
624
630
2104
1906
1925
1571
2381
2165
1919
2171
1937
1997
1931
1727
1721
1231
1255
1249
1225
1565
1559
1631
1625
1637
1619
1613
1607
1601
1595
1889
2111
2087
2117
1877
1841
1847
1853
1511
1517
1523
1177
1183
1189
871
877
883
619
625
631
2105
1907
1926
1572
2382
2166
1920
2172
1938
1998
1932
1728
1722
1232
1256
1250
1226
1566
1560
1632
1626
1638
1620
1614
1608
1602
1596
1890
2112
2088
2118
1878
1842
1848
1854
1512
1518
1524
1178
1184
1190
872
878
884
620
626
632
2106
1908
,_.
w
N
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
•177
478
479
48()
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
49~1
,;oo
304
284
231
228
204
186
138
93
92
91
307
252
196
151
142
90
251
194
141
195
144
145
143
103
102
57
61
62
58
88
89
99
100
98
101
96
97
94
95
235
236
238
237
239
234
233
66
1813
1693
1377
1359
1215
1107
819
549
543
537
1831
1501
1167
897
843
531
1495
1155
837
1161
855
861
849
609
603
335
359
365
341
519
525
585
591
579
597
567
573
555
561
1401
1407
1417
1411
1423
1395
1389
389
1814
1694
1378
1360
1216
1108
820
550
544
538
1832
1502
1168
898
844
532
1496
1156
838
1162
856
862
850
610
604
336
360
366
342
520
526
586
592
580
598
568
574
556
562
1402
0
1418
1412
1424
1396
1390
390
1815
1695
1379
1361
1217
1109
821
551
545
539
1833
1503
1169
899
845
533
1497
1157
839
1163
857
863
851
611
605
337
361
367
343
521
527
587
593
581
599
569
575
557
563
1403
0
1419
1413
1425
1397
1391
391
1816
1696
1380
1362
1218
1110
822
552
546
540
1834
1504
1170
900
846
534
1498
1158
840
1164
858
864
852
612
606
338
362
368
344
522
528
588
594
582
600
570
576
558
564
1404
1408
1420
1414
1426
1398
1392
392
.1817
1697
1381
1363
1219
1111
823
553
547
541
1835
1505
1171
901
847
535
1499
1159
841
1165
859
865
853
613
607
339
363
369
345
523
529
589
595
583
601
571
577
559
565
1405
1409
1421
1415
1427
1399
1393
393
1818
1698
1382
1364
1220
1112
824
554
548
542
1836
1506
1172
902
848
536
1500
1160
842
1166
860
866
854
614
608
340
364
370
346
524
530
590
596
584
602
572
578
560
566
1406
1410
1422
1416
1428
1400
1394
394
.......
w
w
501
502
503
504
505
506
507
67
69
68
70
65
6.4
507
395
405
399
411
383
377
0
0
406
400
412
384
378
0
0
407
401
413
385
379
0
396
408
402
414
386
380
0
397
409
403
415
387
381
0
BANDWIDTH PRIOR TO RESEQUENCING=
BANDWIDTH AFTER RESEQUENCING
=
398
410
404
416
388
382
0
2179
376
BANDWIDTH MINIMIZATION TIME LOG
READ FILE AND SET UP MIN1MIZATION=
PERFORM THE MINIMIZATION
=
REWRITE THE DATA FILES
=
5.51
9.43
16.81
TOTAL FOR MINIMIZATION
31.76
=
REQUIRED BLANK COMMON FOR THIS STEP=
9123
..._.
w
"""
E Q U A T I 0 N
P A R A ME T E R S
TOTAL NUMBER OF EQUATIONS
BANDWIDTH
NUMBER OF EQUATIONS IN A BLOCK
NUMBER OF BLOCKS
= 3027
= 376
= 32
= 95
.....,
w
(J1
N 0 D A L
NODE
NUMBER
135
L 0
(S T A T I C)
A D S
LOAD
CASE
0 R
MA S S E S
(D Y N A M I C)
X-AXIS
FORCE
Y-AXIS
FORCE
Z-AXIS
FORCE
X-AXIS
MOMENT
Y-AXIS
MOMENT
Z-AXIS
MOMENT
1. OOOOOE+05
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
ALL EQUATIONS HAVE STIFFNESS ATTACHED
STRUCTURE
LOAD CASE
ELEMENT
LOAD
MULTIPLIERS
A
B
C
D
.000
.000
.000
.000
STIFFNESS MATRIX PARAMETERS
MINIMUM NON-ZERO DIAGONAl ELEMENT= 1.231E+02
MAXIMUM DIAGONAL ELEMENT
2.1B9E+09
MAXIMUM/MINIMUM
1.779E+07
AVERAGE DIAGONAL ELEMENT
1.404E+08
DENSITY OF THE MATRIX
3.2 PCT.
REQUIRED BLANK COMMON FOR THIS STEP=
6084
.......
w
0"1
S T A T l
C
A N A L Y S I S
LOAD CASE
DISPLACEMENTS/ROTATIONS OF UNRESTRAINED NODES
NODE
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
~2
23
24
25
26
27
28
29
30
31
32
33
34
]5
36
37
]8
39
XTRANSLATION
TRANSLATION
4.46240E-04
3.48519E-04
4.46240E-04
1. 18104E-01
1. 17963E-01
1 . 18 104 E- 0 1
2.03229E-01
2.02980E-01
2.03229E-01
2. 77563E -01
2.77150E-01
2.77563E-01
3.35980E-01
3:34932E-01
3.35980E-01
3.81238E-01
3.80156E-01
3.78163E-01
3.80156E-01
3.81238E-01
4.01925E-01
4.00598E-01
3.98937E-01
3.9"/913E-01
3.98937E-01
4.00598E-01
4.01925E-01
4.12969E-01
4.11694E-01
4.10333E-01
4.09419E-01
4.10333E-01
4.11694E-01
4. 12969E-01
4.17910E-01
4.21615E-01
4.24175E-01
4.26388E-01
4.28546E-01
3.35362E-02
3.39129E-02
3.35362E-02
3.26230E-02
3.31398E-02
3.26230E-02
3.05694E-02
3.11209E-02
3.05694E-02
2.74516E-02
· 2.80622E-02
i.74516E-02
2.38098E-02
2.44033E-02
2.38098E-02
2.02555E-02
2.02753E-02
2.06654E-02
2.02753E-02
2.02555E-02
1.83957E-02
1.83484E-02
1. 82759E -02
1. 82485E -02
1.82759E-02
1.83484E-02
1.83957E-02
1.71669E-02
1 .. 70842E-02
1.67614E-02
1.62158E-02.
1.67614E-02
1.70842E-02
1. 71669E -02
1. 63378E -02
1.54280E-02
1.46252E-02
1.39473E-02
1.34081E-02
¥-
z-
X-
Y-
Z-
TRANSLATION
ROTATION
.OOOOOE+OO
ROTATION
ROTATION
-2.02336E-05
2.64864E-12
2.02336E-05
-3.21874E-05
2.61771E-12
3.21874E-05
-5.97512E-05
2.54502E-12
5.97512E-05
-8.90708E-05
2.47200E-12
8.90708E-05
-2.13968E-04
2.40315E-12
2. 13968E-04
-5.45829E-04
-5.17810E-04
2.27921E-12
5.17810E-04
5.45829E-04
-7. 13640E-04
-5.97097E-04
-5.63513E-04
2.01477E-12
5.63513E-04
5.97097E-04
7. 13640E -04
-7.23135E-04
-5.20402E-04
-4.65558E-04
1.86436E-12
4.65558E-04
5.20402E-04
7.23135E-04
7.11071E-04
6.27184E-04
4.71245E-04
3.03901E-04
1.56072E-04
-5.93126E-03
-5.93168E-03
-5.93126E-03
-5.80429E-03
-5.79967E-03
-5.80429E-03
-5.52125E-03
-5.50934E-03
-5.52125E-03
-5.09125E-03
-5.05515E-03
-5.09125E-03
-4.67078E-03
-4.53391E-03
-4.67078E-03
·4.35972E-03
-4.29966E-03
-4.09323E-03
-4.29966E-03
-4.35972E-03
-3.79207E-03
-3.78797E-03
-3.82134E-03
-3.75315E-03
-3.82134E-03
-3.78797E-03
-3.79207E-03
-2.45331E-03
-2.44156E-03
-2.39945E-03
-2.37815E-03
-2.39945E-03
-2.441'56E-03
-2.45331E-03
-1.55347E-03
-9.77256E-04
-7.68858E-04
-7.20976E-04
-7. 19135E-04
1. 18947E-05
1.61070E-11
-1.18946E-05
-1.99239E-04
1. 46807E -11
1.99239E-04
-4.28646E-04
1.36321E-11
4.28646E-04
-6.28359E-04
1.26967E-11
6.28359E-04
-8.49446E-04
1. 19558E-11
8.49446E-04
-1.03684E-03
-7.85627E-04
1.14235E-11
7.85627E-04
1.03684E-03
-1.08187E-03
-8.62086E-04
-5. 17885E-04
1. 11903E-11
5. 17885E-04
8.62086E-04
1.08187E-03
-9.81452E-04
-7.54275E-04
-4.33434E-04
1. 10924E-11
4.33434E-04
7.54275E-04
9.81452E-04
9.18249E-04
7.99880E-04
6.54248E-04
5. 06677E -04
3.65683E-04
-8.15090E-14
.OOOOOE+OO
.OOOOOE+OO
-6.15656E-14
.OOOOOE+OO
.e>OOOOE+OO
-7.72041E-14
.OOOOOE+OO
.OOOOOE+OO
-7.38063E-14
.OOOOOE+OO
.OOOOOE+OO
-5.69333E-14
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
-6.28963E-14
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
-2.67523E-14
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
1.87123E-04
2.10823E-04
-2.94027E-14
-2. 10823E -04
-1.87123E-04
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
,_.
w
'.1
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
"11
72
73
74
75
76
77
78
79
80
81
82
83
84
85
8G
4.30706E-01
4.32845E-01
4.34933E-01
4.37005E-01
4.39295E-01
4.42480E-01
4.46664E-01
4.16598E-01
4.20395E-01
4.23233E-01
4.25772E-01
4.28228E-01
4.30654E-01
4.33052E-01
4.35420E-01
4.37795E-01
4.40347E-01
4.43628E-01
4.47784E-01
4.14993E-01
4. 18827E -01
4.22044E-01
4.25017E-01
4.27848E-01
4.30595E-01
4.33307E-01
4.36027E-01
4.38805E-01
4.41720E-01
4.45078E-01
4.49059E-01
4.14016E-01
4. 18018E-01
4.21498E-01
4.24696E-01
4.27692E-01
4.30572E-01
4.33414E-01
4.36289E-01
4.39273E-01
4.42433E-01
4.45970E-01
4.49931E-01
4.14993E-01
4. 18827E-01
4.22044E-01
4. 25017E-01
1.30137E-02
1.27632E-02
1.26500E-02
1.26621E-02
1.27818E-02
1.29887E-02
1.32085E-02
1.62173E-02
1.52729E-02
1.44526E-02
1.37707E-02
1.32341E-02
1.28447E-02
1.26000E-02
1.24943E"02
1.25184E-02
1.26588E-02
1.28969E-02
1.31582E-02
1.58194E-02
1.47956E-02
1.39302E-02
1.32309E-02
1.26959E-02
1.23183E-02
1.20930E-02
1.20152E-o2·
1.20812E-02
1.22837E-02
1.26081E-02
1.29451E-02
1.50867E-02
1 .39472E-02
1. 30348E -02
1. 23310E-02
1. 18060E-02
1. 14505E-02
1. 12553E-02
1. 12181E-02
1.13367E-02
1. 16242E-02
1 .20853E-02
1.25954E-02
1.58194E-02
1.47956E-02
1.39302E-02
1.32309E-02
2.31819E-04
1.02728E-04
-2.39063E-05
-1.48089E-04
-2. 64103E-04
-3.58015E-04
-4.07840E-04
7.18137E-04
6.18117E-04
4.98624E-04
3.80047E-04
2.69548E-04
1.66193E-04
6.67469E-05
-3. 18783E-05
-1.30790E-04
-2.25565E-04
-3.03046E-04
-3.40368E-04
3. 952.17E-04
3.30615E-04
2.58507E-04
1.91458E-04
1.31668E-04·
7.66507E-05
2.38782E-05
-2.91253E-05
-8.45561E-05
-1.41303E-04
-1.90717E-04
-2.10770E-04
1. 10103E-11
1.09632E-11
1 . 09463E- 11
1 . 09 4 6 7 E - 1 1
1 . 096 11 E- 11
1 .. 09874E-11
1. 10246E-11
1.10719E-11
1 . 1 1 304 E - 1 1
1. 12026E-11
1 . 13005E- 11
1.14240E-11
-3.95217E-04
-3.30615E-04
-2.58507E-04
-1.91458E-04
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+()Q
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
-1.23308E-04
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
. OOOOOE-100
.OOOOOE+OO
.OOOOOE+OO
.OOOOOEtOO
.OOOOOE+OO
.OOOOOE+OO
-1. 33409E-04
-3.25586E-14
-1.50537E-14
-8.37494E-15
-2.19531E-15
3.76532E-15
9.28739E-15
1.47381E-14
2.04867E-14
2.63803E-14
3.25321E-14
5.05504E-14
4.77713E-14
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
.OOOOOE+OO
2.64589E-05
-9.99418E-05
-2.38592E-04
-3.92964E-04
-5.37506E-04
-6.17286E-04
-6.25283E-04
5.75376E-04
5.70382E-04
4.43241E-04
2.88002E-04
1.47493E-04
2.36284E-05
-9.73362E-05
-2.29657E-04
-3.74072E-04
-4.95215E-04
-5.10477E-04
-4.71466E-04
5.07114E-04
4.68147E-04
3.31719E-04
2.00246E-04
9.80646E-05
1.45104E-05
-6.68548E-05
-1.62410E-04
-2.83622E-04
-4.12553E-04
-4.64506E-04
-4.42948E-04
1. 92702E- 12
2. 11570E-12
2.33372E-12
2.52949E-12
2.67731E-12
2.76861E-12
2.79581E-12
2.74866E-12
2.62900E-12
2.44703E-12
2.23839E-12
2.13755E-12
-5. 07 114 E- 04
-4.68147E-04
-3.31719E-04
-2.00246E-04
-7. 17747E-04
-7.04530E-04
-6.87679E-04
-7.05171E-04
-8.55552E-04
-1.32012E-03
-2.07231E-.03
-1.55247E-03
-1.0413oE'-o3
-8.72755E-04
-8.26889E-04
-8. 13952E-04
-8.05739E-04
-7.95303E-04
-7.86546E-04
-8.02028E-04
-9.17459E-04
-1.32317E-03
-2.06302E-03
-1.47527E-03
-1. 13806E-03
-1.02696E-03
-9.66998E-04
-9.29680E-04
- 9. 10 17 8 E- 04
-9.05722E-04
-9.16707E-04
-9.45644E-04
-1.01509E-03
-1.27242E-03
-2.04147E-03
-1.47837E-03
-1.21179E-03
-1.11169E-03
-1.03231E-03
-9.78804E-04
-9.53211E-04
-9.52395E-04
-9.76947E-04
-1.02379E-03
-1.08726E-03
-1.29090E-03
-2.02690E-03
-1.47527E-03
-1.13806E-03
-1.02696E-03
-9.66998E-04
.......
w
(X)
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
1:l2
133
4.27848E-01
4.30595E-01
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416
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418
419
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421
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428
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432
433
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437
438
439
440
441
442
443
444
445
446
447
448
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456
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.OOOOOE+OO
.OOOOOE+OO
-5. 11493E-04
-6.49848E-04
-6.83087E-04
-7.32608E-04
-7.28653E-04
-7.14671E-04
-7. 12699E-04
-5. 12207E-04
-5.31608E-04
-4.86698E-04
-2.36587E-04
-2.20362E-04
1.44354E-04
1.37373E-04
3.99471E-04
3.91235E-04
-4.87568E-04
-4.00140E-04
-4.00140E-04
-4.87568E-04
-5.37117E-04
-5.37117E-04
-4.49514E-04
-4.49514E-04
-2.15175E-04
-2. 15175E-04
1.38800E-04
1.38800E-04
3.91794E-04
3.91794E-04
5.27240E-04
5.27175E-04
5.27876E-04
5.28225E-04
5.28225E-04
5.27606E-04
5.27606E-04
6.27558E-04
6.27499E-04
6.28172E-04
6.28541E-04
6.28541E-04
6.27945E-04
6.27945E-04
,_.
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B E A M
E L E M E N T
F 0 R C E S
A N D
M0 M E N T S
AXIAL
R1
SHEAR
R2
SHEAR
R3
TORSION
M1
BENDING
M2
BENDING
M3
5.809E-03
-5.809E-03
4.455E-03
-4.455E-03
-6.361E-12
6.361E-12
2. 154E-14
-2.154E-14
7.669E-13
3.740E-11
-1.774E-01
2.042E-01
2
1 -5.547E-03
5.547E-03
-7.554E-02
7.554E-02
7.051E-12
-7.051E-12
-2.204E-13
2.204E-13
-3.851E-11
-2.296E-11
-2.042E-01
-4.543E-01
3
1 -1.547E-03
1.547E-03
-5.729E-02
5.729E-02
-2.075E-12
2.075E-12
-6.808E-14
6.808E-14
7.187E-13
1.173E-11
-3.812E-01
3.740E-02
1
3.963E-03
-3.963E-03
-4.128E-02
4.128E-02
6.489E-14
-6.489E-14
-8.420E-14
8.420E-14
- 1 . 656E- 11
1.600E-11
-3.740E-02
-3.224E-01
5
1 -2.518E-03
2.518E-03
-6.509E-02
6.509E-02
-2.654E-12
2.654E-12
-9.763E-14
9.763E-14
6.164E-12
9.760E-12
-4. 129E-01
2.233E-02
6
1
3.995E-03
-3.995E-03
-4.002E-02
4.002E-02
-2.349E-13
2.349E-13
-6.703E-14
6.703E-14
-2.404E-11
2.608E-11
-2.233E-02
-3.265E-01
7
1 -3.949E-03
3.949E-03
-8.638E-02
8.638E-02
-4.741E-12
4.741E-12
- 1 . 049E- 13
1.049E-13
1.617E-11
1.228E-11
-4.747E-01
-4.356E-02
8
1
-2.554E-02
2.554E-02
-2.181E-12
2.181E-12
-8.354E-14
8.354E-14
-2.904E-11
4.805E-11
4.356E-02
-2.662E-01
BEAM LOAD
NO.
NO.
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2.281E-03
-2.281E-03
P/A+M2/S2
P/A-M2/S2
P/A+M3/S3
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"""
9
1 -7. 166E-03
7.166E-03
-1.386E-01
1.386E-01
-6.928E-12
6.928E-12
-1.095E-13
1.095E-13
2.445E-11
1. 7 12E- 11
-5.780E-01
-2.534E-01
10
1 -1.374E-03
1.374E-03
8.704E-02
-8.704E-02
-2.432E-12
2.432E-12
-9.319E-14
9.319E-14
-3.454E-11
4.913E-11
2.534E-01
2.688E-01
11
1
8.374E-03
-8.374E-03
-4.679E-01
4.679E-01
-5.343E-12
5.343E-12
-1.206E-13
1.206E-13
-7.874E-11
9.325E-11
-2.688E-01
-1.003E+OO
12
1 -1.289E-02
1.289E-02
-3.542E-01
3.542E-01
-1.510E-11
1. 510E -11
-3.237E-13
3.237E-13
2. 104E- 11
2.426E-11
-9·. 188E-01
-1.436E-01
13
1 -2.258E-03
2.258E-03
7.796E-02
-7.796E-02
4.530E-12
-4.530E-12
1.423E-14
-1.423E-14
-3.785E-11
2.426E-11
1.436E-01
9.026E-02
14
1 -5.270E-03
5.270E-03
-7.618E-02
7.618E-02
9.531E-12
-9.531E-12
8.358E-14
-8.358E-14
-4.539E-11
1.679E-11
-9.026E-02
-1.383E-01
15
1
9.255E-03
-9.255E-03
1.369E-01
-1.369E-01
6.148E-13
-6.148E-13
-3.064E-14
3.064E-14
-4.867E-11.
4.683E-11
1.383E-01
2.723E-01
16
1
1 . 062E -02
- 1. 062E -0,2
-5.171E-01
5.171E-01
-3.454E-11
3.454E-11
-2.792E-13
2.792E-13
-3.186E-11
1.257E-10
-2.723E-01
-1. 133E+OO
1'i
1
1. 192E -02
1. 192E -02
-2.726E-01
2.726E-01
·1 . 060E- 1 1
- 1 . 060E- 11
-3.527E-13
3.527E-13
- 1 . 08 3 E- 1o'
7.654E-11
-7.852E-01
-3.255E-02
18
1
7.142E-03
-7. 142E-03
1.874E-02
-1.874E-02
8.710E-12
-8.710E-12
2.625E-13
-2.625E-13
-6.850E-11
4.237E-11
3.255E-02
2.367E-02
.......
+=>
1.0
19
1 -2.531E-05
2.531E-05
-1.284E-02
1.284E-02
5.564E-12
-5.564E-12
3.660E-13
-3.660E-13
-4.007E-11
2.338E-11
-2.367E-02
-1.485E-02
20
1 -1.008E-02
1.008E-02
1.234E-02
-1.234E-02
7.570E-12
-7.570E-12
1.404E-13
-1.404E-13
-1.851E-11
-4.199E-12
1.485E-02
2.218E-02
21
1 -1.197E-02
"1.197E-02
-3.378E-01
3.378E-01
6.115E-12
-6.115E-12
-5.634E-13
5.634E-13
1 . 446E- 11
.-3.108E-11
-2.218E-02
-8.958E-01
22
1
1.969E-02
-1.969E-02
-3.392E-04
3.392E-04
-1.288E-11
1.288E-11
-7.347E-13
7.347E-13
2.014E-10
1.207E-10
1.484E-02
-2.332E-02
23
1
3.763E-05
-3.763E-05
-4.851E-04
4.851E-04
9.850E-12
-9.850E-12
1.232E-13
-1.232E-13
-1.530E-10
-9.328E-11
1.331E-02
-2.543E-02
24
1 - 1 . 97 1 E -02
1.971E-02
-3.601E-04
3.601E-04
-1.297E-11
1.297E-11
9.936E-13
-9.936E-13
2.024E-10
1.218E-10
1.478E-02
-2.379E-02
25
1
2.619E-02
-2.619E-02
-8.748E-04
8.748E-04
-1.395E-12
1 . 395E- 12
-2.436E-13
2.436E-13
2. 103E-12
2.580E-11
2.535E-02
-4.284E-02
26
1
1. 141 E -04
- 1 . 14 1E- 04
-1.067E-03
1.067E-03
2.613E-12
-2.613E-12
1.272E-13
-1.272E-13
-5.820E-11
5.935E-12
2.543E-02
-4.676E-02
:) .,.
1
··2.628E-02
2 G28E-02
-7.830E-04
7.830E-04
-1.399E-12
1.399E-12
5.285E-13
-5.285E-13
1.437E-12
2.654E-11
2.612E-02
-4.178E-02
I-'
Ul
0
28
1
2.934E-02
-2.934E-02
4.008E-04
-4.00BE-04
-B.405E-13
8.405E-13
-3.301E-14
3.301E-14
-1.466E-11
2.727E-11
3.252E-02
-2.651E-02
29
1
2.797E-03
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7.921E-03
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5.436E-13
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-3. 130E-13
3. 130E- 13
1. 186E-12
-1.146E-11
4.538E-02
1. 043E-01
30
1
1.214E-02
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-1.332E-03
1.332E-03
-3.320E-13
3.320E-13
2.159E-13
-2.159E-13
-1.397E-11
1. 933E-11
2.186E-02
-4.338E-02
31
1 -1.205E-02
1.205E-02
-1.201E-03
1.201E-03
-3.414E-13
3.414E-13
-8.817E-15
8.817E-15
-2.355E-11
2.907E-11
2.490E-02
-4.431E-02
32
1 -2.981E-03
2.981E-03
-8.037E-03
8.037E-03
-4.803E-13
4.803E-13
3.671E-13
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1. 070E- 11
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1 -2.954E-02
2.954E-02
3.813E-04
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8.450E-13
3.214E-13
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3.631E-02
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34
1
3.445E-02
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1 .073E-02
- 1 . 106E- 12
1.106E-12
6.897E-14
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35
1
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- 1 . 601 E- 11
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1.612E-02
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7.960E-13
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3.329E-11
1. 167E-01
7.122E-02
37
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8.903E-03
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1 . 401 E- 12
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38
1 -5.211E-03
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39
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40
1 -1. 182E-02
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41
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1.133E-12
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3.690E-11
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42
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3.656E-13
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43
1 -3.447E-02
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9.999E-13
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44
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1. 369E-13
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5.569E-11
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45
1
3.672E-02
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8.344E-02
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2.849E-11
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48
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49
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50
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51
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52
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53
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54
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58
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59
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69
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70
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71
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1.159E-10
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72
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6.857E-12
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73
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2.633E-11
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76
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77
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3.279E-14
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78
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79
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81
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83
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4.399E-13
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88
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95
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96
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97
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98
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99
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100
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102
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104
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5.388E-13
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105
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2.123E-12
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5.649E-13
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2.576E-11
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106
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7.340E-12
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4.617E-13
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3.204E-11
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107
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108
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109
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110
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3.712E-13
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111
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112
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114
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2.286E-03
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7.537E-02
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115
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116
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117
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118
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119
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120
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2.907E-03
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121
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8.820E-11
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123
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2.890E-01
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8.979E-12
2.642E-13
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5. 580E- 11
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124
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7.074E-03
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2.495E-01
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4.692E-13
3.652E-13
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1.294E-11
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125
1
1.733E-02
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2.048E-01
7.544E-12
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3.790E-13
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2.173E-12
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126
1
2.336E-02
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9.312E-02
9.860E-12
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1.619E-13
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9.158E-12
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127
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1.239Ef00
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3. 111 E- 11
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1.791E-13
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4.027E-11
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128
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1.359E+OO
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1. 143E-11
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5.238E-13
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129
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6.319E-11
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130
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4.326E-13
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131
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133
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134
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3.446E-03
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135
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136
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5.065E-01
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137
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2.172E-11
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4.724E-13
3.571E-11
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4.324E-01
2.385E+OO
138
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4.587E-02
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4.186E-01
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5. 166E- 11
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1.897E-14
3.938E-11
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139
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4.130E-02
3.554E-01
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4. 352E- 11
8.718E-01
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140
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8.994E-02
7.291E-12
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1.478E-13
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2.230E-11
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141
1
2.286E-03
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5.122E-02
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2.219E-12
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2.252E-13
-2.252E-13
-9.609E-12
2.952E-12
7.537E-02
7.831E-02
142
1
2.336E-02
-2.336E-02
-9.312E-02
9.312E-02
9.860E-12
-9.860E-12
1.619E-13
-1.619E-13
9.158E-12
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-7.831E-02
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143
1
4.587E-02
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4.186E-01
-4. 186E-01
5. 166E- 11
-5.166E-11
-1.897E-14
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218
1
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T H I N
P L A T E I S H E L L
ELEMENT
NUMBER
LOAD
CASE
E L E M E N T
S T R E S S E S
MEMBRANE STRESS COMPONENTS
SXX
SYY
SXY
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A N D
M0 M E N T S
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MXX
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530
1
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N
0
Ul
STATIC
531
. 1030E+04
.2569E+03
.2137E+04
.2901E-07
.2157E-06
-. 1076E-07
532
-. 1030E+04
-.2575E+03
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533
~-
t901E+04
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534
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.6902E-01
S 0 L U T
EQUATION SOLUTION
DISPLACEMENT OUTPUT
STRESS RECOVERY
0 N
T I ME
L 0 G
698.85
2.78
12.86
N
C>
0"1
s {\
p
-
c s u c
S T R U C T U R E
P L 0 T T E R
TEKTRONIX PLOT10 PREVIEW PLOTTING IS REQUESTED
REUUIRED BLANK COMMON FOR THIS STEP
5071
CPU TIME FOR PLOT FILE SETUP
2.85
FOR PLOT GROUP 1
PLOT TYPE (!TYPE)
EO. 1, STRUCTURE PLOTS
VERTICAL AXIS (!AXIS)
EO 1, X AXIS Is VERTICAL
2,
Y AXIS IS VERTICAL
3,
Z AXIS IS VERTICAL
VERTICAL AXIS INCLINATION (ALPHA)
ROTATION ABOUT THE VERTICAL (BETA)
FLAG FOR DELETING NODES (IDEL)
EO. 1, NODES ARE TO BE DELETED
FLAG FOR NODE LABELING (NODLBL)
EO. 1, THE NODES WILL BE LABELED
NUMBER OF DEFORMED SHAPES/MODES
TO BE PLOTTED (NMOQEI
LT.O,
ALL WILL BE PLOTTED
EO.O. NONE WILL BE PLOTTED
GT.O,· NMODE WILL BE PLOTTED
FLAG FOR COORD. SYSTEM AXES (LABAX)
EO. 1, THE AXES WILL BE DRAWN
FLAG FOR TYPE OF DEFORMED PLOT (IDEF)=
EQ.O DEFORMED STRUCTURE
EO. 1 VECTORS FROM UNDEFORMED
EQ.2 DEFORMED OVER UNDEFORMED
FLAG FOR BOXING THE STRUCTURE (IBOX)=
PLOT MARGIN, PCT OF PLOT HEIGHT
MAXIMUM CONNECTIVITY BETWEEN NODES
REQUIRED BLANK COMMON FOR THIS STEP
=
2
.000
.000
0
0
- 1
0
0
0
10.00
7
6085
XMAX
165.00
XMIN
-145.00
YMAX
210.00
YMIN
0.
XHT
310.00
YHT
210.00
DELP
32.248
PSF
.31010E-01
PLTMAR=
.44400
N
0
-.....!
CPU T!Mf FOR UNDEFORMED PLOT
REQUIRED BLANK COMMON FOR THIS STEP
CPU TIME FOR DEFORMED PLOTS
3. 77
10140
4.59
N
0
OJ
S A P - C S U C
S T R U C T U R E
P L 0 T T E R
FOR PLOT GROUP 1
PLOT TYPE (!TYPE)
EQ. 1, STRUCTURE PLOTS
VERTICAL AXIS (!AXIS)
EO. 1, X AXIS IS VERTICAL
2, Y AXIS IS VERTICAL
3, Z AXIS IS VERTICAL
VERTICAL AXIS INCLINATION (ALPHA)
ROTATION ABOUT THE VERTICAL (BETA)
FLAG FOR DELETING NODES (IDEL)
EO. 1, NODES ARE TO BE DELETED
FLAG FOR NODE LABELING (NODLBL)
EO. 1, THE NODES WILL BE LABELED
NUMBER OF DEFORMED SHAPES/MODES
TO BE PLOTTED (NMODE)
LT.O, ALL WILL BE PLOTTED
EO.O, NONE WILL BE PLOTTED
GT .0, NMODE WILL BE PLOTTED
FLAG FOR COORD. SYSTEM AXES (LABAX)
EO. 1. THE AXES WILL BE DRAWN
FLAG FOR TYPE OF DEFORMED PLOT (IDEF)=
EQ.O DEFORMED STRUCTURE
EO. 1 VECTORS FROM UNDEFORMED
E0.2 DEFORMED OVER UNDEFORMED
FLAG FOR BOXING THE STRUCTURE (IBOX)=
PLOT MARGIN. PCT OF PLOT HEIGHT
MAXIMUM CONNECTIVITY BETWEEN NODES
REQUIRED BLANK COMMON FOR THIS STEP =
2
.000
.000
0
0
- 1
0
0
0
10.00
7
6085
XMAX
165.00
XMIN
-145.00
YMAX
210.00
YMIN
o.
XHT
310.00
YHT
210.00
DELP
50.325
PSF
.19871E-01
PLTMAR= .92000
CPU TIME FOR UNDEFORMED PLOT
REQUIRED BLANK COMMON FOR THIS STEP
CPU TIME FOR DEFORMED PLOTS
2.34
10140
2.66
N
0
0..0