Effect of variation of member stiffness on behavior to timber bridge floor systems
by Arne Bengt Riple
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil
Engineering
Montana State University
© Copyright by Arne Bengt Riple (1985)
Abstract:
This paper investigates the effects incurred in a bridge floor system resulting from variation in member
stiffnesses. If the stiffness in one stringer is reduced, without reducing the stiffness in the other
members, a higher load must be carried by the nonreduced members. The increased loading condition
results in reduced capacity for the floor system. The study is accomplished using a computer simulation
to analyze the member reactions in the floor system. Using a structural grid as a model for the bridge
floor, a matrix solution based on the stiffness method is solved by computer. Figures are presented to
show the effects on member reactions resulting from variation in stiffness and loading conditions.
Results show the effects occurring in both exterior and interior stringers as well as in the floor planks.
The governing effects from these members are combined to show the effects in the floor system.
Reducing the stiffness in an exterior stringer results in a greater reduce tion in capacity of the floor
system, compared to reduction in capacity due to reduction in an interior stringer. EFFECT OF V A R IA T IO N OF MEMBER STIFFNESS ON BEHAVIOR
OF TIM BER BRIDGE FLOOR SYSTEMS
by
Arne Bengt Riple
A thesis submitted in partial fulfillment
of the requirements for the degree
of
I
Master of Science
.
in
Civil Engineering
M O NTA NA STATE U N IV E R S IT Y
Bozeman, Montana
June 1985
/V 3 7 g
K4«5
C-op. %
ii
APPROVAL
of a thesis submitted by
Arne Bengt Riple
This thesis has been read by each member of the thesis committee and has been found
to be satisfactory regarding content, English usage, format, citation, bibliographic style,
and consistency, and is ready for submission to the College of Graduate Studies.
/ W
z /, /
Date
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Mpproveo ror me major Department
//
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Date
Approved for the College of Graduate Studies
(T Date
Graduate Dean
iii
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Permission for extensive quotation from or reproduction of this thesis may be granted
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either, the proposed use of the material is for scholarly purposes. Any copying or use of
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.................. il gain shall not be allowed without my permission.
Signature
Date
i l
m
s
iv
ACKNOW LEDGMENTS
This research was made possible in part by support from the Engineering Experiment
Station at Montana State University.
The author expresses his appreciation to Dr. Fred F. Videon for the opportunity to
conduct this study and for the guidance provided throughout the study.
V
TABLE OF CONTENTS
Page
A P P R O V A L ..................................
ii
S TATEM ENT OF PERMISSION TO USE.............................................................................
jii
ACK NO W LEDG M ENTS.....................................................................
iv
TABLE OF C O N TE N TS ..............................
v
L IS T O F TABLES................................................................
vi
L IS T O F FIG URES....................................................................................................................
vii
A B S T R A C T ................................................................................................................................
xi
Chapter
1
IN T R O D U C T IO N ......................................................................................................
I
Background..........................................................................................................
Objective...............................................................................................................
I
2
2
ANA LYSIS OF FLOOR S Y S T E M ................................................... : ..................
3
3
R E S U LTS ....................................................................................................................
12
Bending in Stringers.......................................................................
Reduced Stiffness in Center Stringer........................................................
Reduction in Exterior Stringer.................................................................
Bending in Floor P lank......................................................................................
Reduced Center Stringer..............................................
Reduced Exterior Stringer..........................................................................
Combined Effects in F lo o r...............................................................................
Deflection and Shear......................................................................
12
12
16
21
30
30
30
41
4
SUM M A RY AND C O N C LU SIO N .......................................
44
REFERENCES C IT E D .........................................................
46
APPENDIX — Computer R uns.......................................
48
vi
LIST OF TABLES
Tables
Page
1.
Variation in Stiffness for the Grid Members...........................................................
5
2.
Moment Capacity for Reduced S trin g er.................................................................
13
vii
LIST OF FIGURES
Figures
Page
1.
Grid model of floor system........................................................................................
3
2.
Bending moment in stringers at location of floor plank due to a
unit load P at the exterior stringer............................................................................
6
Bending moment in stringers at location of floor plank due to a
unit load P at the first interior stringer...................................................................
6
Bending moment in stringers at location of floor plank due to a
unit load P at the first interior stringer...................................................................
7
Bending moment in stringers at location of floor plank due to a
unit load P at the second interior stringer..............................................................
7
Bending moment in stringers at location of floor plank due to a
unit load P at the center stringer...............................................................................
8
7.
Bending moment in stringers at location of floor plank................ ......................
8
8.
Distribution of bending moment from the exterior stringer to
first interior stringer...................................................................................................
10
Distribution of bending moment from first interior stringer to:
----- exterior stringer;-------- interior stringer...........................................................
10
Distribution of bending moment from second interior stringer
to first interior stringer....................
11
Distribution of bending moment from center stringer to second
interior stringer.............................................................................................................
11
12.
Reduction of stiffness in center stringer.................................................................
12
13.
Reduced stiffness in center stringer. Effect in center stringer—
IsZL = 32.7 in3 .....................................................................
14
Reduced stiffness in center stringer. Effect in center stringer —
IsZL = 22.2 in3 ...................................................................
14
Reduction of stiffness in center stringer. Effect in center stringer —
IsZL= 16.8 in3 ..........................................................................................................
15
3.
4.
5.
6.
9.
10.
11.
14.
15.
viii
Figures
16.
17.
18.
19.
Page
Reduction of stiffness in center stringer. Effect on second interior
stringer - ls/L = 32.7 in3 ..........................................................................................
17
Reduction of stiffness in center stringer. Effect in second interior
stringer - ls/L = 22.2 in3 ..........................................................................................
17
Reduction of stiffness in center stringer. Effect in second interior
stringer - ls/L = 16.8 in3 ..........................................................................................
18
Reduction of stiffness in exterior stringer. Effect in exterior stringer
— IsZL = 32.7 in3..........................................................................................................
19
20.
Reduction of stiffness in exterior stringer. Effect in exterior stringer
— IsZL = 22.2 in3 ............................................................................
21.
Reduction of stiffness in exterior stringer. Effect in exterior stringer
— IsZL = 16.8 in3 ..............................................................................................................
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
20
Reduction of stiffness in exterior stringer. Load at exterior stringer.
Effect in first interior stringer — IsZL = 32.7 in3 ...................................................
22
Reduction of stiffness in exterior stringer. Load at exterior stringer.
Effect in first stringer — IsZL = 22.2 in3 . .............................................................
22
Reduction of stiffness in exterior stringer. Load at exterior stringer.
Effect in first interior stringer — IsZL = 16.8 in3 ...................................................
23
Reduction of stiffness in exterior stringer. Load at first interior
stringer. Effect in first interior stringer — IsZL = 32.7 in3 ..............; ..................
24
Reduction of stiffness in exterior stringer. Load at first interior
stringer. Effect in first interior stringer — IsZL = 22.2 in3 ...................................
24
Reduction of stiffness in exterior stringer. Load at first interior
stringer. Effect in first interior stringer — IsZL = 16.8 in3 ...................................
25
Reduction of stiffness in exterior stringer. Effect in first interior
stringer from combined loading conditions — IsZL = 32.7 in3 ............................
26
Reduction of stiffness in exterior stringer. Effect in first interior
stringer from combined loading conditions - IsZL = 22.2 in3 ............................
26
Reduction of stiffness in exterior stringer. Effect in first interior
stringer from combined loading conditions — jsZL = 16.8 in3 ............................
27
Moment diagram in floor plank. Load is located at exterior stringer.................
28
Load is located between the exterior and first interior stringer
...................
28
ix
Figures
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
Page
Moment diagram in floor plank. Load is located at center stringer.
The effect of reduced center stringer is displayed.............................................. ..
29
Reduction of stiffness in center stringer. Effect in floor plank IsZL = 32.7 in3 ................................ .................................................................... ......
31
Reduction of stiffness in center stringer. Effect in floor plank IsZL = 22.2 in3.........................................................................................................
31
..
Reduction of stiffness in center stringer. Effect in floor plank IsZL = 16.8 in3 ....................................... ................................................................
32
Reduction of stiffness in exterior stringer. Load at exterior stringer.
Effect in floor plank — IsZL = 32.7 in3 ....................... ..........................................
33
Reduction of stiffness in exterior stringer. Load at exterior stringer.
Effect in floor plank — IsZL = 22.2 in3 ...................................................................
33
Reduction of stiffness in exterior stringer. Load at exterior stringer.
Effect in floor plank - IsZL = 16.8 in3 ...................................................................
34
Reduction of stiffness in exterior stringer. Load between exterior
and first interior stringer. Effect in floor plank - IsZL = 32.7 in3 .....................
35
Reduction of stiffness in exterior stringer. Load between exterior
and first interior stringer. Effect in floor plank - IsZL = 22.2 in3 .....................
35
Reduction of stiffness in exterior stringer. Load between exterior
and first interior stringer. Effect in floor plank - IsZL = 16.8 in3 .....................
36
Reduction of stiffness in exterior stringer. Effect in floor plank due
to combined loading conditions — IsZL = 32.7 in3 ..............................................
37
Reduction of stiffness in exterior stringer. Effect in floor plank due
to combined loading conditions — IsZL = 22.2 in3 ......... ............... ....................
37
Reduction of stiffness in exterior stringer. Effect in floor plank due
to combined loading conditions — IsZL = 16.8 in3 ..............................................
38
Reduction of stiffness in exterior stringer. Governing effect in floor
system due to combined loading conditions - IsZL = 32.7 in3 .........................
39
Reduction of stiffness in exterior stringer. Governing effect in floor
system due to combined loading conditions - IsZL = 22.2 in3 ......... ...............
39
Reduction of stiffness in exterior stringer. Governing effect in floor
system due to combined loading conditions — IsZL = 16.8 in3 ..........................
40
X
Figures
49.
50.
51.
Page
Reduction of stiffness in interior stringer. Governing effects in floor
system due to combined loading conditions — ls/L = 32.7 in3 ..........................
42
Reduction of stiffness in interior stringer. Governing effects in floor
system due to combined loading conditions — ls/L = 22.2 in3 ..........................
42
Reduction of stiffness in interior stringer. Governing effects in floor
system due to combined loading conditions — ls/L = 16.8 in3 . ; .....................
43
xi
ABSTRACT
This paper investigates the effects incurred in a bridge floor system resulting from var­
iation in member stiffnesses. If the stiffness in one stringer is reduced, without reducing
the stiffness in the other members, a higher load must be carried by the nonreduced mem­
bers. The increased loading condition results in reduced capacity for the floor system. The
study is accomplished using a computer simulation to analyze the member reactions in the
floor system. Using a structural grid as a model for the bridge floor, a matrix solution
based on the stiffness method is solved by computer. Figures are presented to show the
effects on member reactions resulting from variation in stiffness and loading conditions.
Results show the effects occurring in both exterior and interior stringers as well as in the
floor planks. The governing effects from these members are combined to show the effects
in the floor system. Reducing the stiffness in an exterior stringer results in a greater reduc­
tion in capacity of the floor system, compared to reduction in capacity due to reduction in
an interior stringer.
I
CHAPTER I
IN TRO DUC TIO N
Background
Bridges are an important part of the United States road network. Over the last years,
the traffic situation has become much heavier than many older bridges were designed for.
In addition to the increased loading conditions, the bridges have also been deteriorating
and several bridges are structurally deficient to handle present-day loading conditions [ I ] .
This deficiency has proved to be a severe problem for many highway departments.
The Federal Highway Administration (FHWA) [1] has worked together with the highway
departments to find suitable solutions to solve these problems. Several methods of renova­
tion have been considered.
A survey conducted by the author reveals that many highway departments feel that
replacement of the older bridges is the best solution, and they are currently replacing the
older bridges as soon as funding is available.
As of 1981, based on a study by Koppers Co. [2] using a National Bridge inventory
maintained by FHWA, over. 71,000 bridges in the U.S. used timber as a major material of
construction. About 86% of these are off the Federal Aid system. Further, of the 297,566
off-system bridges of all materials and types, 33.4% were classified as structurally deficient
and 27.4% were classified as functionally obsolete. It is reasonable to assume that the per­
centage for timber bridges are at least as high as these overall figures.
Through personal communication with Don Harrison, Bridge Superintendent in Cas­
cade County in Montana [3 ], several aspects of bridge maintenance in the off-system were
2
discussed. Due to lack of funds the off-system bridges are seldom, replaced at the same rate
as the Federal Highway bridges. One problem that was discussed is the deterioration of the
top sides of the stringers due to trapped moisture between floor planks and stringers. As
the top sides of the stringers deteriorate, the connection between stringer and floor plank
tend to become insufficient. To obtain adequate connection between stringer and plank,
the stringer has in several cases been turned upside down instead of being replaced. The
effect of such a deteriorated stringer can be compared to a stringer with reduced volume,
and thereby reduced stiffness.
Objective
The purpose of this research is to examine the effects on a bridge floor system due to
reduction of stiffness in one stringer. The theoretical model of the floor system is discussed
in Chapter 2. The effects of reduced stiffness in interior and exterior stringers are exam­
ined using the computer model. These effects are studied to determine the strength reduc­
tion of the bridge floor.
3
CHAPTER 2
ANA LYSIS OF FLOOR SYSTEM
The floor system is analyzed using a structural grid as a model, as proposed by Ghali
and Neville [4 ]. A structural grid is defined as a frame structure with rigid joints whose
members and joints lie in a common plane, with all applied force loads being out of the
plane and normal to the plane of the structure. The model grid is a rectangular system
consisting of seven stringers and one floor plank as shown in Figure I.
top view
plank
I
I
I
I
I
I
stringer
end view
Figure I . Grid model of floor system. "J_" member number; " I " joint number.
4
Plank decks consist of individual planks spiked across the stringers. Since the planks
are not connected to each other, all bending in the longitudinal y-direction occur in the
stringers. The use of one floor plank is therefore sufficient to examine the transverse dis­
tribution of bending moment in the floor system. For maximum bending effects in the
stringers, the plank is located at the center of the stringers.
A t the supports, the stringers are unrestrained for bending rotation about the x-axis,
but are restrained for translation in the z direction and torsional rotation about the y-axis.
To solve the structural grid, the stiffness method as presented by Weaver and Gere
[5] is used. The theory behind the stiffness method is not discussed in this paper, but the
computer program is listed in the Appendix.
The dimensions used in the floor system are based upon requirements set by
AASHTO [6 ]. To avoid the effects of buckling, the width to depth ratio, d/b = 2.0. From
the length to depth ratio L/d = 15.0, the dimensions of the stringers are:
b = 10.0 in
d = 20.0 in
The dimensions of the reduced stringers are:
1. b = 10.0 in
d = 18.0 in
2.
b = 10.0 in
d = 16.0 in
For the floor plank, the minimum thickness is 3.0 in. The width b of the floor plank is set
to be 12.0 in, but the thickness is varied in one inch crements from 3.0 in to 6.0 in.
According to these dimensions, the computer simulation is run with a variation in the
member stiffness as shown in Table I .
5
Table I . Variation in Stiffness for the Grid Members.
L/d
Is/L (in3 )
IrsZL (in3 )
Ip/S (in3 )
10.2
32.680
32.680
23.824
16.732
1.125
15.0
22.222
19.8
16.835
22.222
16.200
11.378
16.835
12.273
8.620
2.667
5.208
9.000
Is - moment of inertia of stringer; Irs = moment of inertia of deteriorated stringer; Ip =
moment of inertia of floor plank; L = length of stringers; S = spacing of stringers; d = depth
of stringer.
The analysis of the grid is based on four loading conditions. A unit load P is individu­
ally placed at these locations:
1. Exterior stringer, joint 2
2.
First interior stringer, joint 5
3.
Second interior stringer, joint 8
4.
Center stringer, joint 11
Each of these loading conditions give a set of influence lines that show the bending
moment in each stringer, Figures 2-6. The bending moment in the loaded stringer is used
as reference moment, and the bending moments in the other stringers are shown as a per­
centage of this reference moment.
Figures 3 and 4 show the bending moment in the stringers at the location of the plank
with the load P located at joint 5. In Figure 3 the curves show the variation in the stringer
stiffness. Figure 4 shows the variation in the stiffness in the floor plank.
Notice is Figure 4 that the bending moment in the exterior stringer for lp/S = 9.0 is
actually greater than the bending moment in the loaded first interior stringer. The low
stiffness in the stringers, ls/L = 16.8, allow large deflections, and the high stiffness in the
6
40..
-
12.0 ft
20. .
Figure 2. Bending moment in stringers at location of floor plank due to a unit load P at
the exterior stringer. Curves show the effect of variation in stringer stiffness.
p
r
S
I
I
T
1 0 0 ..
8 0 ..
6 0 ..,
- 2 0 ..
12.0 ft
Figure 3. Bending moment in stringers at location of floor plank due to a unit load P at
the first interior stringer. Curves show the effect of variation in stringer stiffness.
7
I
I
I
I
%
no..
-1 6 .8
100..
6 0 ..
4 0 ..
1 2 .0
ft
Figure 4. Bending moment in stringers at location of floor plank due to a unit load P at
the first interior stringer. Curves show the effect of variation in plank stiffness.
p
:
r
100..
6 0 -.
4 0 --
-20- .
12.0
ft
Figure 5. Bending moment in stringers at location of floor plank due to a unit load P at
the second interior stringer. Curves show the effect of variation in stringer
stiffness.
8
p
:
r
100..
12 .0 f t
Figure 6. Bending moment in stringers at location of floor plank due to a unit load P at
the center stringer. Curves show the effect of variation in stringer stiffness.
Figure 7. Bending moment in stringers at location of floor plank. Curves show the varia­
tion in location of the unit load P.
9
floor plank make the floor system act with a higher rigidity. This results in larger deflec­
tion and higher bending moment in the exterior stringer than in the first interior stringer.
As the stringer stiffness is increased, the distribution of bending moment from the
loaded stringer to the adjacent stringer is reduced. This effect is reversed when looking at
the stiffness in the plank. As the stiffness of the plank is increased, better distribution of
bending moment is achieved. This capability of distributing the moment is important when
looking at the effects of having a stringer with reduced stiffness.
When designing the stringers for maximum bending moment, the exterior stringers are
designed for a larger moment than the interior stringers. All interior stringers are designed
for the same maximum bending moment. Figure 7 shows the four loading conditions and
the difference in bending moment between exterior and interior stringers.
When investigating the effects of a stringer with reduced stiffness, the greatest effects
are noticed in the reduced stringer and the first adjacent stringer. Figures 8-11 show the
percentage distributed bending moment from the loaded stringer to the first adjacent
stringer. The curves show the effect of the variation in stringer and plank stiffnesses. As the
stringer stiffness is decreased, more moment is distributed to the next stringer. This is
reversed for the stiffness in the floor plank. Interpolation between the curves is possible for
other magnitudes of member stiffness.
When investigating the effects of having the stiffness in one stringer reduced, it is only
necessary to reduce the center stringer and the exterior stringer. The reduction in the
center stringer is representative for all interior stringers, whereas the exterior stringer has to
be investigated separately.
10
J i
L
3 2 .0 .: 2 8 .0 ..
2 4 .0 ..
. ..
20 0
1 6 .0 .:
1 2 .0
..
8 .0
..
4 .0 ..
20
30
40
SO
60
70
80
80
100
Figure 8. Distribution of bending moment from the exterior stringer to first interior
stringer. Load is located at exterior stringer.
L
3 6 .0 ..
3 2 .0
2 8 .0 ..
2 4 .0 ..
2 0 .0
..
16.0.:
1 2 .0
..
8 .0
..
4 .0 . .
20
30
40
SO
60
70
80
90
100
110 %
Figure 9. Distribution of bending moment from first interior stringer to:
------- exterior stringer
------- interior stringer
Load is located at first interior stringer.
11
H L
lP
3 6 .0 .
'" X
s
3 2 .0 .
2 8 .0 .
2 4 .0 .
2 0 .0 .
\
^
\
\
\
-
1 6 .0 .
1 2 .0 .
8 .0 .
4 .0 .
--------1--------1------- 1—
10
20
30
i--------;—
40
90
i------- 1---------1—
60
70
80
i--------1------------90
IOO
X
Figure 10. Distribution of bending moment from second interior stringer to first interior
stringer. Load is located at second interior.
Jj l
L
3 6 .0 .
—— — — — — —
^
QO
\
Ol
3 2 .0 .
2 8 .0 .
2 4 .0 .
\
2 0 .0 .
\
V A
i.i'
1 6 .0 .
1 2 .0 .
8 .0 .
4 .0 .
—
I—
10
I—
20
I—
30
I—
40
i—
50
i—
60
i—
70
i—
80
I—
90
i------------100
%
Figure 11. Distribution of bending moment from center stringer to second interior stringer.
Load is located at center stringer.
12
CHAPTER 3
RESULTS
Bending in Stringers
Reduced Stiffness in Center Stringer
When the stiffness in the center stringer is reduced, the two adjacent stringers must
help carry the extra load the center stringer can no longer carry itself. The bending moment
in the reduced center stringer is reduced whereas the bending moments in the two adjacent
stringers are increased, Figure 12.
p
100 . .
4 0 ..
2 0 ..
12 .0
ft
Figure 12. Reduction of stiffness in center stringer. Curves show the effect in bending
moment in stringers.
Finding the governing effects of bending moment in the stringers requires two loading
conditions.
13
1. unit force P at center stringer, joint 11.
2.
unit load P at second interior stringer, joint 8
Reducing the stiffness in the center stringer results in decreased moment capacity for
this stringer. This reduction in moment capacity must be considered when comparing the
effects o f the change in bending moment in the stringers.
The moment capacity in a stringer is given in Equation I .
M = fb * sx
( I)
For a stringer with reduced stiffness, the moment capacity is
Mr = V
sxr
(2)
The relationship between these two equations is
(3)
This gives
The moment capacity for the reduced stringer used in this analysis is calculated using
Eq. 4 and is listed in Table 2 as a function of IrsZls-
Table 2. Moment Capacity for Reduced Stringer.
IrsZIs
1.0
0.73
0.51
MrZM
1.0
0.81
0.64
With a reduction in stiffness to 51% of the full stiffness, the moment capacity is
reduced to 64%.
The governing effects of a load placed at the reduced center stringer is noticed in the
center stringer. Figures 13-15 show the effects in the center stringer. The straight line
14
100..
9 0 ..
80_.
60- 50- 40- _
10- -
0.1
0.2
0.3
0.4
0 .5
0.6
0.7
0 .8
0 .9
1 0 I r s / ls
Figure 13. Reduced stiffness in center stringer. Effect in center stringer — ls/L = 32.7 in3
100..
8 0 -
6 0 ..
50 —
30-1.
20.1 0 ..
0.1
0 .2
0 .3
0.4
0.5
0.6
0.7
0.8
0 .9
1.0
Irs Z Is
Figure 14. Reduced stiffness in center stringer. Effect in center stringer — ls/L = 22.2 in3
15
100..
80 - 7 0 ..
6 0 ..
4 0 ..
3 0 ..
2 0 ..
10..
0.2
0 .3
0.4
0 .5
0.6
0.7
0.8
09
1.0 I r s / l s
Figure 15. Reduction of stiffness in center stringer. Effect in center stringer — I /L
16.8 in3.
16
represents the moment capacity of the stringer. When the moment curve is above the
moment capacity, the effect of bending is increased in the center stringer. Measuring the
difference between the moment curve and the moment capacity gives a direct indication of
the reduction in capacity of the member.
As the stiffness in the floor plank is increased, less effect in the reduced center stringer
is noticed. The same effect is observed for the reduction in stringer stiffness.
For the second loading condition, where the load is located at the second interior
stringer, the governing effect is noticed in the second interior stringer. Figures 16-18. As
the stringer has no reduction in stiffness, the moment capacity is constant at 100%. The
moment capacity for the full stiffness stringer is indicated by a straight line at 100% in the
figures.
When the stiffness in the center stringer is reduced, deflection of the stringer will be
increased. As the relative displacement between the reduced stringer and the main stringers
is increased, the moment in the floor plank will also be increased. A higher stiffness in the
floor plank will then transfer more moment to the adjacent stringers. High stiffness in the
floor plank will therefore increase the effects in the adjacent stringers and reduce the
effects in the reduced stringers.
Reduction in Exterior Stringer
Reducing the stiffness in the exterior stringer affects both the exterior and first
interior stringers. To investigate the effects in the stringers, two loading conditions are used.
1. unit load P at exterior stringer, joint 2
2.
unit load P at first interior stringer, joint 5
Since the exterior stringer does not have the advantage of having stringers on both
sides, all distribution of forces go only in one direction. Because of this, the effects in the
exterior stringer are more noticeable than in the center stringer. Figures 19-21 show the
17
200
-
180- 160- 140 - 120. -
100..
8 0 ..
20.-
01
0.2
0.3
0.4
0.5
0.6
0.7
0 .8
0.9
1.0
Irs /ls
Figure 16. Reduction of stiffness in center stringer. Effect in second interior stringer
IsZL = 32.7 in3 .
%
2 0 0 ..
Y
-22 .2
180- 1 6 0 ..
140- -
120..
i£.
S
100-.
8 0 ..
60- -
I
40- -
------ 1-------1------ 1------ 1------ f------1----- M— I------ 1-------- 1—
0.1
0 .2
0 .3
0 .4
0.5
0.6
0.7
0 .8
0.9
1.0
Irs /ls
Figure 17. Reduction of stiffness in center stringer. Effect in second interior stringer
IsZL = 22.2 in3 .
18
20 0 . .
1 8 0 ..
1 6 0 ..
1 4 0 ..
120..
100..
8 0 ..
6 0 ..
4 0 ..
20..
0.1
0.2
0.3
0 .4
0.5
0 .6
0.7
0.8
0.9
1.0 IrsZ Is
Figure 18. Reduction of stiffness in center stringer. Effect in second interior stringer —
IsZL = 16.8 in3 .
19
100..
9 0 ..
7 0 ..
5 0 ..
4 0 ..
3 0 -.
2 0 ..
= 3 2 .7
1 0 ..
0.1
0.2
0 3
0 .4
0.5
0 .6
0.7
0.8
0 .9
1.0
I r s / ls
Figure 19. Reduction of stiffness in exterior stringer. Effect in exterior stringer 32.7 in3.
L /L
s
100..
8 0 ..
6 0 ..
3 0 ..
=
0.1
0.2
22.2
0 .3
0.4
0.5
0.6
0.7
0 .8
0.9
1.0 I r s / ls
Figure 20. Reduction of stiffness in exterior stringer. Effect in exterior stringer - L /L
22.2 in3.
20
100..
9 0 ..
8 0 ..
6 0 ..
0.1
0 .2
0.3
0.4
OS
0.6
0.7
0 .8
0.9
1.0
IrsZ Is
Figure 21. Reduction of stiffness in exterior stringer. Effect in exterior stringer — L /L =
16.8 in3.
21
changes of bending moment in the exterior stringer. The moment capacity is represented
by the same line as for the reduced center stringer.
When investigating the effects in the first interior stringer,, both loading conditions are
considered. Figures 2 2-24 show the changes in bending moment for the first interior
stringer when the load is located at the exterior stringer.
Placing the load at the first interior stringer gives different results for the bending
moment in the first interior stringer. Figures 25-27.
As the stiffness in the stringers are reduced from 32.7 in3 to 16.8 in3, the governing
effects change with the loading condition. With high stiffness in the stringers, the effect
o f increased bending moment is governed by the second loading condition. This is reversed
when the stringer stiffness is reduced.
The combined effects of these two loading conditions must therefore be considered
to find the maximum effects in the first interior stringer, Figures 29-31.
Bending in Floor Plank
Reducing the stiffness in a stringer results in increased deflections. This deflection
creates higher bending moment in the floor plank, so it is important to investigate the
effects in the floor plank the same way as for the stringers.
To investigate the full effects, three loading conditions are used. Figures 31-33 show
the moment distribution of the floor plank using these loading conditions. The maximum
bending moment in the plank is used as reference for the percentage moment distribution.
22
200 . .
-T - - 3 2 . 7
1 8 0 ..
1 6 0 ..
1 4 0 ..
120 . .
100..
6 0 ..
20..
0.1
0 .2
0 .3
0.4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0
Irs Z Is
Figure 22. Reduction of stiffness in exterior stringer. Load at exterior stringer. Effect in
first interior stringer — ls/L = 32.7 in3 .
200..
1 8 0 ..
1 6 0 ..
1 4 0 ..
120. .
100..
6 0 ..
2 0 ..
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0 I r s / ls
Figure 23. Reduction of stiffness in exterior stringer. Load at exterior stringer. Effect in
first stringer — IgZL = 22.2 in3.
23
200. .
1 4 0 ..
120. .
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0
l r s/ Is
Figure 24. Reduction of stiffness in exterior stringer. Load at exterior stringer. Effect in
first interior stringer — ls/L = 16.8 in3 .
24
%
200. _
Y
-3 2 .7
1 8 0 -.
1 6 0 ..
140- 120. .
100..
80. _
6 0 -4 0 ..
20. .
4------- 1------ V —
Ol
0.2
0.3
0.4
as
I--------H —
\ ------- 1--------- 4
0 .6
ttS
0.7
09
1.0 Ir s /ls
Figure 25. Reduction of stiffness in exterior stringer. Load at first interior stringer. Effect
in first interior stringer — ls/L = 32.7 in3 .
200 -
-
1 8 0 ..
1 6 0 ..
1 4 0 ..
120-100..
0.2
0.3
0 .4
0.5
0.6
0.7
0.8
0 .9
1.0 Ir s / ls
Figure 26. Reduction of stiffness in exterior stringer. Load at first interior stringer. Effect
in first interior stringer — ls/L = 22.2 in3 .
25
200 - 1 8 0 ..
1 6 0 ..
1 4 0 ..
1 2 0 ..
100..
8 0 ..
6 0 ..
4 0 ..
0.1
0.2
0.3
0.4
0.5
0 .6
0.7
0 .8
09
1.0 Ir s / ls
Figure 27. Reduction of stiffness in exterior stringer. Load at first interior stringer. Effect
in first interior stringer — ls/L = 16.8 in3 .
26
200 .
.
1 8 0 ..
1 6 0 ..
140. _
120. .
100..
60. .
4 0 ..
0.1
0.2
0.3
0.4
0.5
0 .6
0.7
0.8
09
1.0 lr s /|s
Figure 28. Reduction of stiffness in exterior stringer. Effect in first interior stringer from
combined loading conditions — ls/L = 32.7 in3 .
200. .
—
=22 2
1 8 0 ..
1 6 0 .1 4 0 -.
1 2 0 ..
100..
8 0 ._
60. _
4 0 ..
20-
-
0.1
0.2
0.3
0.4
05
0.6
0.7
0 .8
0 .9
1.0 Ir s /ls
Figure 29. Reduction of stiffness in exterior stringer. Effect in first interior stringer from
combined loading conditions — IsZL = 22.2 in3 .
27
200..
1 8 0 .1 6 0 ..
(— 9 .0
L_ i .i
ioo .
20. .
0.1
0.2
0.3
0.4
OS
0.6
0.7
0.8
0 .9
1.0 Ir s / ls
Figure 30. Reduction of stiffness in exterior stringer. Effect in first interior stringer from
combined loading conditions — ls/L = 16.8 in3 .
28
p
r
I
I
i
i
i
4 0 ..
12.0 ft
2 0 ..
=
22.2
-6 0 ..
-
8 0 ..
- 100 . .
Figure 31. Moment diagram in floor plank. Load is located at exterior stringer.
I
I—
100..
r
-—
I
I
I
I
I
I
I
-iT =22.2
8 0 ..
6 0 ._
2 0 ._
- 2 0 ..
-4 0 ..
12.0 ft
Figure 32. Load is located between the exterior and first interior stringer.
29
p
2 0 0 ..
- ! f -2 2 .2
1 6 0 ..
120 ..
-4 0 ..
1 2 .0 ft
Figure 33. Moment diagram in floor plank. Load is located at center stringer. The effect
of reduced center stringer is displayed.
30
Reduced Center Stringer
The effect of reduced stiffness in the center stringer is showed by Figure 33. This
reduction in stiffness increases the bending moment in the floor plank markedly.
A load is located at the center stringer to create the governing effects in the floor
plank as the center stringer is reduced. The increase in bending moment in the plank is
shown in Figures 34-36. As for the stringers, the moment capacity is constant at 100%.
Reduced Exterior Stringer
When the stiffness in the exterior stringer is reduced, two loading conditions must be
considered. The first location for the load is at the exterior stringer, Figure 31. The second
location is at the center of the floor plank, between the exterior and first interior stringer.
Figure 32.
Figures 3 7-39 show the effects of the first loading condition and Figures 4 0-42 show
the effects of the second loading condition. These two sets of curves are combined to give
the maximum effect in the floor plank when the exterior stringer is reduced. Figure 43-45.
Combined Effects in Floor
The governing effects of a reduction of stiffness may be in any of the three investi­
gated members, depending on the member stiffnesses.
. Figures 4 6 -4 8 show the effects of reduced stiffness in the exterior stringer. These
curves are a combination of the maximum effects in the investigated members. The hori­
zontal line at 100% is the bending moment capacity of the floor system. The difference
between the curves and the line of capacity is a direct measurement for the reduction in
capacity of the floor system.
31
200..
1 8 0 ..
1 6 0 ..
1 4 0 ..
120. .
100-8 0 ..
6 0 ..
4 0 ..
20..
0.1
0 .2
0 .3
0.4
0 .5
0 .6
0.7
0 .8
0 .9
1.0
Irs /ls
Figure 34. Reduction of stiffness in center stringer. Effect in floor plank - ls/L = 32.7 in3 .
200..
—
=
22.2
1 8 0 ..
1 6 0 ..
1 4 0 ..
120..
100..
8 0 ..
6 0 ..
2 0 ..
0.1
0.2
0 .3
0.4
0 .5
0 .6
0.7
0 .8
0 .9
1.0
Ir s /ls
Figure 35. Reduction of stiffness in center stringer. Effect in floor plank - ls/L = 22.2 in3.
32
200..
1 8 0 ..
1 6 0 ..
1 4 0 ..
120..
100..
8 0 ..
20.
-
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1 .0
I r s / ls
Figure 36. Reduction of stiffness in center stringer. Effect in floor plank — ls/L = 16.8 in3 .
33
3 2 .7
1 8 0 ..
1 6 0 ..
1 4 0 ..
1 2 0 ..
100..
8 0 ..
6 0 ..
4 0 ..
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0
I r s / ls
Figure 37. Reduction of stiffness in exterior stringer. Load at exterior stringer. Effect in
floor plank - ls/L = 32.7 in3.
200. .
-Vl = 2 2 . 2
1 8 0 ..
1 6 0 ..
140. .
1 2 0 ..
100..
8 0 ..
6 0 ..
20.-
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0
I r s / ls
Figure 38. Reduction of stiffness in exterior stringer. Load at exterior stringer. Effect in
floor plank - Is/L = 22.2 in3.
34
2 0 0 ..
1 8 0 ..
1 6 0 ..
1 4 0 ..
1 2 0 ..
100..
8 0 ..
6 0 ..
4 0 ..
20-
-
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1 .0
I r s / ls
Figure 39. Reduction of stiffness in exterior stringer. Load at exterior stringer. Effect in
floor plank — ls/L = 16.8 in3.
35
200-.
180. „
1 6 0 ..
1 4 0 ..
120 . .
100..
6 0 ..
4 0 ..
20. _
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0 I r s / ls
Figure 40. Reduction of stiffness in exterior stringer. Load between exterior and first
interior stringer. Effect in floor plank - ls/L = 32.7 in3 .
200-.
1 8 0 ..
1 6 0 -1 4 0 ..
120..
100..
8 0 -.
6 0 -.
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0 I r s / l s
Figure 41. Reduction of stiffness in exterior stringer. Load between exterior and first
interior stringer. Effect in floor plank - ls/L = 22.2 in3.
36
200..
1 8 0 ..
1 6 0 ..
1 4 0 ..
120. .
10 0. .
8 0 ..
V . 9 .0
6 0 ..
4 0 ..
20..
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0 I r s / l s
Figure 42. Reduction of stiffness in exterior stringer. Load between exterior and first
interior stringer. Effect in floor plank — ls/L = 16.8 in3.
37
200. .
-V - = 3 2 .7
1 8 0 ..
1 6 0 ..
1 4 0 ..
120. .
100 . .
8 0 ..
6 0 ..
2 0 ..
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1.0 I r s / l s
Figure 43. Reduction of stiffness in exterior stringer. Effect in floor plank due to com­
bined loading conditions — ls/L = 32.7 in3.
200..
-V - = 2 2 .2
1 8 0 -1 6 0 ..
140- -
120..
10 0. .
8 0 ..
6 0 ..
4 0 ..
0.1
0 .2
0 .3
0 .4
0 .5
0 .6
0.7
0 .8
0 .9
1.0
I r s / ls
Figure 44. Reduction of stiffness in exterior stringer. Effect in floor plank due to com­
bined loading conditions — ls/L = 22.2 in3.
38
200. .
- V - = 1 6 .8
1 8 0 ..
1 6 0 ..
1 4 0 ..
120. .
100 - .
4 0 -.
0.1
0 .2
0 .3
0 .4
0 .6
0 .6
0 .7
0 .8
0 .9
1.0 I r s / l s
Figure 45. Reduction of stiffness in exterior stringer. Effect in floor plank due to com­
bined loading conditions — ls/L = 16.8 in3.
39
200..
-V - = 3 2 . 7
18 0 . 1 6 0 ..
1 4 0 ..
120. .
100. .
80+
60- 4 0 ..
0.1
0 2
0 .3
0 4
0 .5
0.6
0.7
0.8
0.9
1.0 Irs /ls
Figure 46. Reduction of stiffness in exterior stringer. Governing effect in floor system due
to combined loading conditions — ls/L = 32.7 in3.
200..
- 15-
=
2 2 .2
1 8 0 ..
1 6 0 ..
1 4 0 ..
120. .
100 . .
4 0 --
0.1
0 .2
0 .3
0.4
0.5
0 .6
0.7
0.8
0.9
1.0 Ir s /ls
Figure 47. Reduction of stiffness in exterior stringer. Governing effect in floor system due
to combined loading conditions — Is/L = 22.2 in3.
40
200 . .
-V- =16 8
1 8 0 ..
1 6 0 ..
1 4 0 ..
120..
100 . .
8 0 ..
0.1
0 .2
0 .3
0.4
0.5
0 .6
0.7
0 .8
0 .9
1.0
I r s / ls
Figure 48. Reduction of stiffness in exterior stringer. Governing effect in floor system due
to combined loading conditions — ls/L = 16.8 in3.
41
Figures 49-51 show the effects of reduced stiffness in the interior stringer. These
curves display the same effect as Figures 4 6 -4 8 . Notice that the reduction in capacity is
less for the reduction in interior stringer compared to the exterior stringer.
Deflection and Shear
To find the total effects in the floor system, increased effects in shear and deflection
must also be considered. As the stiffness is reduced in a stringer, the deflection in this
stringer will be increased. This, in turn, results in the floor plank having to carry increased
load to the adjacent stringers.
Deflection and shear are not as thoroughly investigated as the effects of bending. How­
ever, the analyses show that these effects are of about the same magnitude as the effects
due to bending.
Less, stiffness in the floor plank seems to increase the effects of both shear and deflec­
tion.
Further analyses of the effects of shear and deflection are recommended. For the
effect of shear in the stringers, the floor plank is suggested moved to the end of the
stringers.
42
200 -
-
- f - -3 2 .7
1 8 0 -160- _
1 4 0 ..
120- -
100. .
80- _
60- _
20-
-
0.1
02
0 .3
0 .4
0 .5
0 .6
0.7
0.8
0 .9
1.1
Irs /ls
Figure 49. Reduction of stiffness in interior stringer. Governing effects in floor system due
to combined loading conditions — ls/L = 32.7 in3 .
200 -
.
1 8 0 ..
1 6 0 ..
14 0 - 120. .
100- 80- _
60+
40420-.
0.1
0 .2
0.3
0.4
0 .5
0 .6
0.7
0.8
0.9
1.0
I r s / ls
Figure 50. Reduction of stiffness in interior stringer. Governing effects in floor system due
to combined loading conditions — ls/L = 22.2 in3.
43
200-
-T- = 1 6 8
_
1 8 0 ..
1 6 0 ..
1 4 0 ..
120. .
100..
6 0 ..
CU
0 .2
0 .3
0.4
0 .5
0 .6
0.7
0.8
0 .9
1.0
Ir s / ls
Figure 51. Reduction of stiffness in interior stringer. Governing effects in floor system due
to combined loading conditions - ls/L = 16.8 in3.
44
CHAPTER 4
SU M M A R Y AND CONCLUSION
The results of this investigation are best separated into two categories.
1.
effect in floor system due to reduced stiffness in exterior stringer
2.
effect in floor system due to reduced stiffness in interior stringer
Three members have been investigated for each reduction in stiffness and loading con­
dition.
1. stringer with reduced stiffness
2.
first adjacent stringer to the reduced member
3.
floor plank
For each member and loading condition, three sets of curves have been developed.
These curves show the increased bending moment in each member as a percentage of the
maximum design moment for that specific member.
A horizontal line at. 100% shows the maximum design moment for the floor plank
and for a stringer having full stiffness. The reduced stringer has reduced moment capacity
according to the reduction in section modulus. Table 2.
It is evident that a reduction of stiffness in a stringer has adverse effects on the floor
system. Reducing the stiffness of the exterior stringer results in a more severe reduction in
the capacity of the floor system than if an exterior stringer is reduced.
The effects on the floor system due to the reduction of member stiffness in one
stringer depend on the combination of stiffnesses between the stringers and the planks.
Reducing the exterior stringer depth from 20.0 in to 16.0 in reduces the capacity of the
floor system by about 50% for ls/L = 16.8 in3 and lp/S = 9.0 in3, and by about 20% for
45
ls/L - 16.8 in3 and Ip/S - 1.1 in3. Lesser stiffness in the floor plank show less reduction
of capacity for this condition.
Reducing the center stringer depth from 20.0 in to 16.0 in reduces the capacity of the
floor system by about 25% for ls/L = 32.7 in3 and lp/S = 9.0 in3, and by about 5% for
ls/L = 22.2 in3 and IpZS = 1 . 1 in3 . As the stiffness in the stringers is reduced, less reduc­
tion of capacity is obtained with increased stiffness in the floor planks.
It is recommended that the deteriorated stringers be replaced, and not simply turned
over. If deteriorated stringers are turned over, the reduced depth of the stringer should be
carefully examined, and the effects on the floor system should be investigated for the
actual loading condition allowed on the bridge.
46
REFERENCES .CITED
47
REFERENCES CITED
1.
Federal Highway Administration. "Upgrading deficient through truss bridges."
FHW A/RD-82/041. Washington, D.C., April 1983.
2.
Itani, R. Y ., and Faherty, K. F. "Structural wood research." ASCE. New York, New
York, 1983.
3.
Personal communication, Don Harrison, Bridge Superintendent in Cascade County.
February 1985.
4.
Ghali, A., and Neville, A. M. "Structural analysis, a unified classical and matrix
approach." 2nd edition. Chapman and Hall, London, 1978.
5.
Weaver, W. Jr., and Gere, M. M. "Matrix analysis of framed structures." 2nd edition.
D. Van Nostrand Company, New York, 1980.
6.
American Association o f State Highway and Transportation Officials. "Standard spec­
ifications for highway bridges." AASHTO . 12th edition. Washington, D.C. 1977.
48
APPENDIX
COMPUTER RUNS
49
12:05
J UN
o ribsle
I?
a
on
! E GRI DA
E D I T S03
I .000
2.000
3.000
4 .000
5.000
6.000
7.000
8.000
9.000
10.000
11 . 0 0 0
12.000
13.000
14.000
15.000
16.000
17.000
13.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
31 . 0 0 0
32.000
33.000
34.000
35.000
36.000
37.000
38.000
39.000
40.000
4 1 . OQO
42.000
43.000
44.000
45.000
46.000
47.000
48.000
49.000
50.000
51.000
52.000
53.000
54.000
55.000
56.000
'85
L E N E . I CE F V 0 0 5
11:42
04/12/85
HERE
C
C
C
C
C
C
************************************ ************************
*
*
GRI D PROGRAM, NAMED
I C E F V C 0 3 , RI PLE
483
640
460
720
*
*
* * * * * ** * * ** * ** * * ** * ** * * ** * * ** * ** * * ** * ** * * ** * * ** * ** * * ** * * ** * *
DI ME NS I ON
DI MENSI ON
DI I E N S I ON
DI MENSI ON
DI MENSI ON
C
C
C
GRI D
INPUT
X ( 1 0 0 ) , Y ( I 0 0 ) , J J ( I 0 0 ) , J K ( I 0 0 ) , X I (5 0 ) , Y I ( 5 0 )
A ML ( 6 , 5 0 ) , J R L ( 3 0 0 ) , E L ( 5 0 ) , C X ( 5 0 ) , C Y ( S O )
I D ( 3 0 0 ) , S F F ( 3 0 0 , 1 0 0 ) , S M S ( 6 , 6 ) , I M ( 6 ) , LML( SO)
AR(300),AE(300),AJ(300),AC(300),OJ(500),DF(300)
A M 0 ( 4 ) , K ( I O O ) , A M ( 6 ) , K 9 ( 1 0 0 ) , KC( SO)
STATEMENTS
I SN = I
I C HNGE = O
W R I T E * , " F O R PRESET GR I D P R I N T I , ELSE 0 "
I N P U T PRESET
I F ( P R E S E T . EU. 0 ) GOTO 6 3 0
W R I T E * , " I N P U T NUMBER OF S T R I N G E R S "
I N P U T NST
W R I T E * , " I N d UT LENGTH OF S T R I N G E R S "
I N d UT ST L
W R I T E * , " I N P U T S P A C I N G OF S T R I N G E R S "
I N P U T STS
WR I T E * , " I NRUT DEPTH D, AND WI DTH B ( i n ) OF S T R I N G E R S "
I N P U T O S , BS
W R I T E * , " I N P U T DEPTH D, AND WI DTH B ( i n ) OF P L A N K "
INP UT DP,BP
W R I T E * , " I N P U T D I M E N S I O N S OF REDUCED STRI NGER , D AND B ( i n ) "
I N P U T R OS , RBS
WR I T E * , " I NPUT L O C A T I O N OF REDUCED S T R I N G E R , S T R I N GE R NUMBER"
I N P U T RST
W R I T E * , " I N DUT L O C A T I O N OF P L A N K , AS F RACTI ON OF S T R I N G p R L ENGT H"
I NPUT LFP
W R I T E * , " I N P U T E AND G"
I NPUT E , G
WR I T E * , " I N d UT NUMBER OF LOADED J O I N T S ( N L J ) , AND"
W R I T E * , " N U M B E R OF L OADED MEMBERS ( N L M ) "
I N d UT N L J , NLM
W R I T E * , " I N D'JT NUMBER OF R E S T R A I N T S ( NR ) "
I N P U T NR
W R I T E * , " I N P U T NUMBER OF R E S T R A I N E D J O I N T S ( N R J ) "
I N P U T NRJ
STSI=STS*12
S TL I = S TL * 1 2
NJ=i*NST
M = ( 3* NS T ) - 1
ND J = 3
NO = NOJ * N J
N=ND-NR
DO 7 2 0 J = I , ND
AR(J)=O.C
AE(J)=O.C
C ON T I N U E
DO 7 3 0 1 = 1 , M
50
57.000
55.000
59.000
60.000
61.000
67.000
63.000
64.000
65.000
750
66.000
67.000
68.000
69.000
70.000
71 . 0 0 0
72.000
73.000
74.000
75.000
76.000
77.000
78.000
79.000
80.000
81 . 0 0 0
82.000
83.000
84.000
85.000
86.000
87.000
88.000
89.000
90.000
91 . 0 0 0
92.000
93.000
94.000
95.000
96.000
97.000
98.000
99.000
700
I 0 0 .00 0
I 01 . 0 0 0
I 02.000
I 03.000
I 04.000
105.000
I 06.000
I 07.000
I 08.000
I 09.000
110.000
111.000
I 12.000
113.000
I 14.000
115.000
I 16.000
I 17.000
73?
710
661
LIL(I)=O-O
C ONT I NUE
XST=<3S*CDS**3)+DS*(0$*»3))/12
YST=RS* ( 0 S * « 3 ) / 1 2
XFDa(gp*(DP**3)+DP*(8P**3))/12'
Y FP = B d * ( D P * * 3 > / I 2
X R S T = C R B S * ( RDS* * 3 ) + R D S * < R B S * * 3 ) ) / 1 2
YRST=RBS*(R0S**3)/12
NK = NJ
KXO=O.0
DO 7 0 0 I = 1 / N K , 3
X(I)=KXO
X(I*1)=KX0
X ( I + 2 ) = KX0
Y(I)=O.O
Y(I+1)=STLI/LFP
Y ( I + 2 ) = STLI
KXO = KXO T S T S I
JJ(I)=I
JK(I)=ITl
JJ(ITl)=ITl
JK(ITl)=ITE
XI(I)=XST
XI(ITI)=XST
YI(I)=YST
Y I ( I T 1 ) =YST
IF d
. L T . NK) THEN
J J ( IT 2 ) =ITl
J K ( I T ? ) = IT4
X I (IT?)=XFP
Y I (IT?)=YFd
ENDI F
C ONT I NUE
JP=3*RST
XI(JP-I)=XRST
Y I ( J P - I ) =YRST
X I ( J P - 2 ) =XRST
YI(JP-Z)=YRST
WRITE*," "
I F ( I CHNGE . GT . 0 ) THEN
W R I T E * , " I F ANY CHANGES HAS BEEN MADE TO THE RE ST R A I N E D J OI N T S
W R I T E * , " CHANGES MUST RE RECORDED I N THE J O I N T R E S T R A I N T L I S T .
W R I T E * , " P R I N T I TO PERFORM THESE CHANGES, P R I N T O TO CONTI NUE
I N d UT CHJRL
I F ( C H J R L . EQ. 0 ) GOTO 661
ENDI F
DO 7 3 2 J = 1 , NO
JRL(J)=O
C ONT I NUE
W R I T E * , " I N P U T J OI NT RESTRAI NT L I S T "
WRITE*,"K,JRL(3K-2>,JRL(3K-1),JRL(3K)"
DO 7 1 0 1 = 1 , NRJ
I NPUT K ( I ) , J R L ( 3 * K ( I ) - 2 ) , J R L ( 3 * K ( I ) - D , J R L ( 3 * K ( I ) )
CONT I NUE
I F ( I CHNGE . GT. 0 ) THEN
W R I T E * , " I F ANY CHANGES HAS BEEN MADE TO THE J O I N T L O A D S , "
W R I T E * , " T H E N CHANGES MUST BE RECORDED"
W R I T E * , " P R I N T I TO PERFORM THE CHANGES, P R I N T O TO C ON T I N U E "
I N P U T CHJ L
I F ( C HJ L . E Q . 0 ) GOTO 6 6 2
ENDI F
51
I I S . 000
I 19.000
120.000
733
I 21 . 0 0 0
I 22.000
I 23.000
I 24.000
I 25.000
1 2 6 . 0 0 0 74 4
I 27.000
1 2 8 . 0 0 0 662
129.000
I 3 0 . 0 00
I 31 . 0 0 0
I 32.000
I 33.000
I 34.000
I 35.000
I 36.000
I 37.000
I 3 8 . 0 0 0 735
I 3 9 , 0 0 0 734
I 40.000
141.000
I 42.000
I 43.000
I 44.000
I 45.000
I 4 6 . 0 0 0 745
I 47.000
I 4 3 . 0 0 0 663
I 49.000
I 50.000
I 51 . 0 0 0
I 52.000
I 53.000
I 54.000
I 55.000
I 56.000
I 57.000 C
I 5 8 . 0 00 6 3 3
I 59.000
I 60.000
I 61 . 0 0 0
I 62.000
I 63.000
I 64.000
I 65.000
I 66.000
I 67.000 C
I 69.000 C
I 69.000 C
I 70.000
I 71 . 0 0 0
I 72.000
I 73.000
I 7 4 . 0 0 0 350
I 75.000
I 76.000
I 77.000
I 7 9 . 0 0 0 370
DO 7 33 J * I / ND
A J ( J ) = O 1C
C ONT I NUE
I F C N L J . N E . 0 ) THEN
W R I T E * , " I N P U T J O I N T L OA D S "
WR I T E * , " K , A J ( 3 K - 2 ) , A J ( 3 K - 1 ) , A J ( 3 K ) "
DO 7 4 4 1 = 1 , NLJ
I NPUT K 9 ( I ) , A J < 3 * K 9 ( I ) - 2 ) , A J ( 3 » K B < I ) - 1 ) , A J < 3 * K d ( I ) >
C ONT I NUE
ENDI F
I F d C H N G E . GT. 0 ) THEN
W R I T E * , " I F ANY CHANGES HAS BEEN MADE TO TH E MEMBER L O A D S , "
W R I T E * , " T H E N THESE CHANGES MUST BE RECORDED"
W R I T E * , " P R I N T I TO RECORD THE CHANGES, P R I N T O TO C ON T I N U E "
I N P U T CHML
I F ( CHML . E R . 0 ) GOTO 6 6 3
ENDI F
DO 7 3 4 1 =1 , M
DO 7 3 5 J = 1 , 6
AML( J , I > = 0 . 0
C ON T I N U E
CON T I N U E
I F ( NLM . N E . 0 ) THEN
W R I T E * , " I NPUT MEMBER L OA D S , I , A M L ( I , I ) , A M L ( 2 , I ) , A M L < 3 , I ) "
WRITE*,"AML(4,I),AML(5,I),AML(6,I>"
DO 7 4 5 1 = 1 , NLM
I N P U T K C ( I ) , AML ( 1 , K C ( I ) ) , A M L ( 2 , K C ( I ) ) , A M L ( 3 , K C ( I ) ) , A M L ( 4 , K C ( I ) ) ,
* AML ( 5 , KC ( I ) ) , A ML ( 6 , K C ( D )
C ONT I NUE
ENDI F
WR I T E * , " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
W R IT E *,"*************************+***********.******.**,***+..
LOD=STLI/DS
WRITE*,"SPACING*",STS
WRITE*,"L/D=
",LOD
W R I T E * , " M A I N S T RI NGERS
: " , R S , " * " , OS
W R I T E * , " R E D U C E D ST RI NGE RS : " , RB S , ” * " , RDS
WRITE*,"PLANK
:",0°,"*",B P
GOTO 6 9 9
WRITE*,"INPUT
WRITE*," "
WRITE*," "
STATEMENTS
START"
WRITE*,"INPUT M,NJ,NR,NRJ,E,G"
I NPUT M , N J , N R , N R J , E , G
WRITE*,"
"
NO J = 3
ND = NDJ * N J
N= ND- NR
CLEARI NG
MATRI XES
DO 35 0 J = 1 , ND
AR(J)=O1C
AJ(J)=O1C
A E ( J )= O 1C
C ONT I NUE
DO 3 6 3 1 = 1 , M
DO 3 7 0 J = I , 6
AM L ( J , I ) = 0 . 0
CON T I N U E
52
I 79.000
I 8 0 . 0 0 0 360
I 81 . 0 0 0
I 82.000
I 8 3 . 0 0 0 17 0
184.000 C
I 85.000 C
I 86.000 C
I 87.000
I 88.000
I 89.000
I 9 0 . 0 0 0 I OO
I 91 . 0 0 0
192.000
I 93.000
I 94.000
1 9 5 . 0 0 0 110
I 96.000
I 97.000
I 98.000
I 99.000
2 0 0 . 0 0 0 120
2 C l .000
202.000
203.000
204.000
205.000
206.000
207.000
2 0 8 . 0 0 0 130
209.000
210.000
211.000
2 1 2 . n 00
213.000
214.000
2 1 5 . 0 0 0 140
216.000
217.000 C
218.000 C
219.000 C
2 2 0 . 0 0 0 699
221.000
222.000
223.000 I
224.000
225.000 2
226.000
227.000
228.000
229.000 3
230.000
231.000
232.000 4
2 3 3 . 0 0 0 150
2 34.000
235.000
236.000
23 7 . 0
00
238.000
239.000
5
L M L ( I ) = O. O
CON T I N U E
DO I 7 0 J = I , NO
JRL(J)=O
C ONT I NUE
CONTI NUATI ON
OF
I NPUT
WRITE*,"INPUT X ( J ) , Y ( J ) "
DO I OO J = I , NJ
I NPUT X ( J ) , Y ( J )
C ONT I NUE
WRITE*," "
WRITE*,"INPUT J J ( I ) , J K ( I ) , X I ( I ) , Y I ( I ) "
DO 1 1 0 1 = 1 , M
I NPUT JJ ( I ) , J K d ) , XI ( I ) , Y K I )
C ONT I NUE
WRITE*,"
"
WRITE*,"INPUT K , J R L ( 3 * K - 2 > , J R L ( 3 * K - 1 ) , J R L ( i * K > "
DO I 21 1 = 1 , NRJ
I NPUT K ( I > , J R L ( 3 * K ( I ) - 7 > , J R L ( 3 * K ( I > - 1 ) , J R L ( 3 * < ( I > >
C ONT I NUE
WRITE*,"
"
WR I T E * , " I N P U T NL J , NL M"
I N P U T N L J , NLM
WRITE*,"
"
WRITE*,"INPUT K , A J ( 3 * K - 2 ) , A J ( 3 * K - 1 > , AJ(3*K>"
DO I 30 1 = 1 , NLJ
I NPUT K 9 ( I ) , A J ( 3 * K 8 ( I ) - 2 ) , A J ( 3 * K B ( I ) - 1 ) , A J ( 3 * K 9 ( I ) )
CON T I N U E
WRITE*,"
"
W R I T E * , " I N P U T I , AML( I , I ) , A ML ( 2 , I ) , A ML ( 3 , I ) , A M L ( 4 , I )
*AML(6,I)”
DO I 4 0 1 = 1 , NLM
,I),
I NPUT K C ( I ) , A M L ( 1 , K C ( I ) ) , A M L ( 2 , K C ( I ) ) , A M L ( 3 , K C ( I ) ) ,
*AML(5,KC(I)),AM L(6 ,KC(I))
CON T I N U E
WRITE*,"
"
KC( I ) ) ,
SDATA
4
WRITE*,"
"
WRI TE*, "STRUCTURAL
WRITE(108,1)
PARAMETER S"
F0RMAT(6X,"M",4X,"N",3X,"NJ",3X,"NR",2X,"NRJ",8X,"E
WRITEd 08,2)M,N,NJ,NR,NRJ,E,G
F0RMAT(2X,5I5,2F9.2)
WRITE*,"
"
W R I T E * , " J O I N T C OOR D I N A T E S "
WRITE(108,3)
FORMAT(2X,"JOINT” , 9 X , " X " , 9 X , " Y " )
DO I 50 J = I , NJ
WR I T E d 0 8 , 4 ) J , X ( J ) , Y ( J )
F0RMATC2X,I5,2F10.5>
C ONT I NUE
WRITE*#"
"
WR I T E * , " ME M3 E R I NFORMATI ON"
WRI T E ( I 0 8 , 5 )
FORMAT!2X,"MEMSER",2X,"JJ",3X,"J K " , 8 X , " X I " , 3 X , " Y I " , R X ,
*"EL",SX,"CX",3X,"CY")
MD = 2 * N D J
fi ")
53
?40.mo
2 4 1 .onn
2 4 2 . non
243.000
244.000
245.000
246.000
247.000
248.000
249.000
250.000
251.000
252.000
253.000
254.000
255.000
256.000
257.000
258.000
259.000
260.000
261.000
262.000
263.000
264.000
265.000
266.000
267.000
268.000
269.000
270.000
271.000
272.000
273.000
2 7 4 . 0 00
275.000
276.000
277.000
278.000
2 7 9 . 0 00
280.000
281.000
282.000
283.000
284.000
285.000
286.000
287.000
288.000
289.000
290.000
291.000
292.000
293.000
294.000
295.000
296.000
297.000
298.000
299.000
300.000
NB = O
DO I 6 0 1 = 1 , M
NB I = NOJ * < AB S ( J K ( I ) - J J d ) ) + ! )
I F ( N 9 I . GT. NB) NB = NBI
XCL = X ( J K ( I ) ) - X ( J J d ) )
YCL = Y U K ( D ) - Y ( J J d ) )
E L ( I ) =SQRT( XCL*XCL+YCL*YCL)
CX( D = X C L Z E L ( I )
CY ( D = Y C L Z E L ( I )
6
160
7
8
181
190
C
C
C
21 O
200
W R I T E d O 8 , 6 ) 1 , J J ( I ) , J K ( I ) , X I ( D , Y I ( I ) , EL ( I ) , C X ( I ) , C Y ( I )
F0RMAT(2X,3I5,5F10.3)
CON T I N U E
WRITE*," "
W R I T E * , " J O I N T RESTRAI NTS"
WRITE(108,7)
F ORMAT ( 2 X , " J 0 I N T " , 2 X , " J R 1 " , 2 X , " J R 7 " , 2 X , " J R 3 " )
DO 1 80 I = D N R J
W RITE(108,S)K(D,JRL(3*K(D-2)»JRL(3*K(I)-1),JRL(3*K(I)>
FORBAD 2 X , 415)
CON T I N U E
WRITE*," "
NI =O
DO 1 9 0 J = D N D
NI=NDJRL(J)
I F ( J R L C J ) . GT. 0 ) THEN
I D ( J ) = N + NI
ELSE
ID(J)=J-NI
ENDI F
C ONT I NUE
STIFF
4
DO 2 0 0 J = D N
DO 2 1 0 K A = I , NB
SFF ( J , K 4 ) = 0 . 0
CON T I N U E
CONT I NUE
DO 2 2 0 1=1, 14
SC M IaG iX K D ZEL(I)
S C M 2=4.0*E *YI(D ZEL(I)
S C M3 = 1 . 5 * S C M 2 Z E L ( I )
SCM4 = ? . 0 * S C i M 3 Z E L ( D
S M S ( D I ) = S C M 1 * C X ( D * C X ( D +S C "42 * C Y ( D * C Y ( I )
S M S ( D 2 ) = ( S C MI - S C M2 ) * C X ( D * C Y ( D
SMS(1,3)=SC43*CY(D
S M S ( D 4 ) = - S C M 1 * C X ( I ) * C X ( I ) +0 . 5 * S C M 2 * C Y ( D * C Y ( D
SMS(D5)=-(SCMD0.5*SCM2)*CX(I)*CY(I)
SMS ( 1 , 6 ) = - S M S ( D 3 )
S MS ( 2 , 2 ) = S C M I * C Y ( I ) * C Y ( I ) + S C M 2 * C X ( I ) * C X ( I )
SMS( 2 , 3 ) = - S C M 3 * C X ( D
SMS ( 2 , 4 ) = S M S d , 5 )
S M S ( 2 , 5 ) = - S C M D C Y ( I D C Y d ) + n . 5 * S C M2 * C X ( I ) * C X ( D
SMS ( 2 , 6 ) = - S M S ( 2 , 3 )
S MS ( 3 , 3 ) = S C M4
S MS ( 3 , 4 ) =SMSC I , 3 )
S 4S(3,5)«SMS(2,3>
S MS ( 3 , 6 ) = - S CM4
S M S ( 4 , 4 ) = SMS( I , 1 )
SMS ( 4 , 5 ) = S M S ( D 2 )
SMS ( 4 , 6 ) = S M S d , 6 )
54
i Cl . n o n
302.000
303.030
304.000
305.000
306.000
307.000
308.000
309.000
310.000
311.000
312.000
313.000
314.000
315.000
316.000
317.000
318.000
319.noo
320.000
321.000
322.000
323.000
324.000
3 2 5 . 0 0 0 240
3 2 6 . 0 0 0 230
3 2 7 . 0 0 0 770
328.000
329.000 C
330.000 C
331.000 C
337.000
333.000
334.000
335.000
336.000
337.000
338.000
339.000
340.000
341 . 0 0 0
342.000
343.000
3 4 4 . 0 0 0 410
345.000
3 4 6 . 0 0 0 400
3 4 7 . 0 0 0 601
348.000
349.000
350.000
351.000
3 5 2 . 0 0 0 470
353.000
354.000
3 5 5 . 0 0 0 390
356.000 C
357.000 C
358.000 C
359.000 C
360.000 C
361.000
SMS C 5 , 5 ) = S M S ( 2 , 2 )
SMS( 5 , 6 >= S M S ( 2 , 6 )
S M S ( 6 , 6 > =SCM4
IM (1 )= 3 *JJ(I)-2
IM (2 )= 3 *JJ(I)-1
IM (3)=3*JJ(I)
IM (4)-3 *JK (I)-2
IM (5)=3*JK (I)-1
I.M (6>*3*JK(I>
DO 2 3 0 J = 1 ,MD
II= IM (J)
I F ( J R L t I I ) . GT . 0 ) GOTO 2 3 0
DO 2 4 0 K A = J ,MD
I2=IM (K A)
I F ( J R L ( I 2 ) . GT . 0 ) GOTO 2 4 0
IR = ID (II)
IC = ID (IZ )
I F d R . G T. I O
THEN
ITEM=IR
IR = IC
I C = I TEM
EN DI F
IC =IC -IR tI
S F F U R ,I O =S F F U R ,IO tS M S U ,
C ON T I N U E
CON T I N U E
CON T I N U E
N R ITE*," "
BANFAC
I F ( S F F ( 1 , 1 ) . L E . 0 . 0 ) GOTO <
DO 3 9 0 J = 2 , N
JI=J-I
J2=J-NBt1
I F ( J 2 . L T. I ) J2 = 1
I F ( J I . EQ. I ) GOTO 601
DO 4 0 1 1 = 2 , J l
II= I-I
I F ( 1 1 . L T . J 2 ) GOTO 4 0 0
SU' 4 = SFF ( I , J - I t l )
DO 4 1 3 K A = J Z , I l
SU M= SUM- SFF( K A , I - K A t I ) * S F F ( K
C ON T I N U E
SFF ( I , J - I t D =SUM
CON T I N U E
SUM=SFF( J , 1 )
DO 4 2 0 KA = J Z , J I
TEMP=SFF( K A , J - K A t I ) / S F F ( K A , I
SUM = S U M - TEMP» S F F ( K A , J - K A t I )
S F F ( K A , J - K A t I ) =TEMP
CONT I NUE
I F ( S U M . L E . 0 . 1 ) GOTO 6 0 0
S F F ( J , I ) =SUM
CON T I N U E
LDATA
4
WR I T E * , " STRUCTURE
NO." , I S N
KAtl )
55
162.000
363.000
364.000
365.000
366.000
367.000
368.000
369.000
370.000
371.000
372.000
373.000
374.000
375.000
376.000
377.000
378.000
379.000
380.000
381.000
382.000
383.000
384.000
385.000
386.000
387.000
388.000
389.000
390.000
391.000
392.000
393.000
394.000
395.000
396.000
397.000
398.000
399.000
400.000
401.000
402.000
403.000
404.000
4 05.000
406.000
407.000
408.000
409.000
410.000
411.000
412.000
413.000
414.000
415.000
416.000
417.000
418.000
419.000
420.000
421.000
422.000
O
10
11
12
250
I 3
14
260
C
r
C
270
280
C
C
C
WRITEd 0 8 ,9 )
FORMAT( 4 X , " N L J " , 2 X , " N L ^ " )
WR I T E ( I 0 8 , 1 0 ) N L J , N L M
F O R M A T ! 2 X , 2 I 5)
W RITE*," "
I F C N L J . N E . 0 ) THEN
W R I T E * , " A C T I O N S AT J O I N T S "
WR I TEC I 0 8 , 1 1 )
F0RMATC2X," J O I N T " , 7 X , " A J I " , 7 X , " A J 2 " , 7 X , " A J 3 " )
DO 2 5 0 J = I , N L J
W R ITEC 108,12)K8C J),A JC 3*K B C J)-2),A JC 3*K B C J)-1),A JC 3*KB C J))
F0RMATC2X,I5,3F10.3)
C ON T I N U E
END I F
W RITE*," "
I F C N L M . N E . 0 ) THEN
WR I T E * , " A C T I O N S AT ENDS OF R E S T R A I N E D MEMBERS DUE TO LOADS
WRITEC108,13)
FORMAT!2X,"MEMBER",5 X , " AMLI" , 6 X , " A M L 2 " , 6 X , " AML3 " , 6 X , " A M L 4 "
*6X ,"A M L5",6X ,"A M L6")
DO 2 6 0 1 = 1 , NLM
W R I T E C 1 0 8 , 1 4 ) K C ( I ) , A M L C 1 , K C ( I ) ) , AMLC2,K C C I ) ) , AMLC3,K C C I ) ) ,
*AM L(4,KC C I)),AM LC 5,KC C I)),AM LC 6,KC C I))
F0RMATC2X,I5,6F10.3>
LMLCKCCI ) ) = 1
C ON T I N U E
W RITE*,"
"
EN DI F
LOADS
4
I F C N L M . N E . 0 ) THEN
DO 2 7 0 1 = 1 , M
I F C L M L C I ) . N E . 0 ) THEN
J l = 3 * J J CI ) - 2
J2 = 3 * J J C D - I
J 3 = 3 * J J CI )
K l = 3 * J K CI ) - 2
K2=$*JK C D - I
K3 = 3 * J K C I )
A E C J I ) = AECJ1 ) - C X C I ) * A M L C 1 , I ) * CYC D * A M L C 2 , D
AECJ2) = A E ( J 2 ) - C Y C D * A M L C 1 , D - C X C D * A M L C ? , D
A E (J3)=A E C J3)-A M L(3,I)
AECK1) = A E C K 1 ) - C X C D * A M L C 4 , D + C Y C D * A M L C 5 , D
A E C K 2 ) * A E C K 2 ) - C Y C D * A M L C 4 , D —C X C D * A M L C 5 , D
AE(K3) = AECK3)-AMLC6,D
ENDIF
C ON T I N U E
EN DI F
DO 2 8 0 J = I , ND
JR=IDCJ)
AC C J R ) = A J CJ >* AEC J )
CON T I N U E
BANSOL
DO 4 3 0 1 = 1 , N
J=I-N B tI
I F C I . L E . NB)
SJM = ACC I )
K I= I-I
J=I
56
4?3.0m
4 ?4.non
4 25.000
426.000
427.000
4 28 . 0 0 0
429.000
450.000
431.000
432.000
433.000
4 34.000
435.000
436.000
437.000
438.000
439.000
440.000
441.000
442.000
443.000
444.000
445.000
446.000
447.000
448.000
449.000
450.000
451.000
452.000
453.000
454.000
4 55.000
4 56.000
457.000
458.000
4 59.000
460.000
461 . 0 0 0
462.000
463.000
464.000
465.000
466.000
467.000
468.000
469.000
470.000
471.000
4 72.000
473.000
474.000
475.000
476.000
477.000
478.000
479.000
480.000
481.000
482.000
483.000
440
603
430
450
470
60 4
460
C
C
C
290
15
14
700
I 7
I F ( J . G T . K D GOTO 4 0 3
03 4 4 0 K A = J , K l
SUM=SUM-SFFCKA,I - K A + 1 ) = D F( KA)
CON T I N U E
OF(I)=SUM
CO J T I N U E
DO 4 5 0 1 = 1 , N
O F ( I ) =O F ( I ) / S F F ( I , I )
CON T I N U E
DO 4 6 0 1 1 = 1 , N
I =N - I D I
J=DN O -I
I F ( J . G T . N) J=N
SUM = DFC I )
K2=D1
I F ( K 2 . G T . J ) GOTO 6 0 4
DO 4 7 0 K A = K 2 , J
SUM= S U M - S FF ( I , K A - D D = D F ( K A )
CON T I N U E
O F d ) =SUM
C ON T I N U E
RESUL
4
J = N= I
DO 2 9 0 K A = I ,NO
JE=ND-KA=I
I F C J R L ( J E ) . E l . 0 ) THEN
J =J -I
DJ(JE)=DF(J)
ELSE
OJ(JE)=O.O
EN DI F
C ON T I N U E
W R I T E * , " J O I N T DISPLACEMENTS"
WR I T E CI O8 , 1 5 )
FORMAT( 2 X , " J O I N T " , 7 X , " D J I " , 7 X , " D J 2 " , 7 X , " D J 3 " )
DO 3 0 0 J = D N J
W R IT E ( 1 0 8 ,1 6 ) J ,D J ( 3 * J - 2 ) ,D J (3 * J- 1 ) ,D J ( 3 * J )
FORM AT!2X,I5,3F10.3>
CON T I N U E
W RITE*," "
W R I T E * , ” MEMBER E N D - A C T I O N S "
WR I T E ( I 0 8 > I 7 )
FORMAT ( 2 x , " MEMBER " , 6 X , " A I M 1 " , 7 X , " A M ? " , 7 X , " A M 3 " , 7 X , " AV/*'
*7X ,"A M 5",7X,"4M 6")
DO 3 1 0 I = D M
Jl = 3*JJ ( D - 2
J2=3*JJ( I ) - I
J 3 = 3 *J J ( I)
Kl = 3 * J K ( I ) - 2
K 2 = 3 * JK ( I ) - I
K 3=3*JK(I>
S C M I =G * X I ( I ) / E L ( I )
SCM 2=4.0*E*YI(I ) /E L (I)
S CM3 = 1 . 5 * S C M 2 / E L ( I )
SCM4=2.0«SCM3/EL(I>
A M D ( I ) = S C M 1 * ( ( DJ ( J I ) - D J ( K D ) * C X ( I ) + ( OJ ( J 2 ) - D J ( K 2 ) ) '
A M D (2)=SC M 2*(-(O J(JD +0.5*D J ( K D ) * C Y ( I) +(D J (J 2 )= 0 .'
**C X (I)>-SC M 3*(D J(J7)-D J(K 3>)
AMD( 3) = S C M 3 * ( ( DJ ( J I ) = D J ( K D ) *C Y ( I ) - C DJ ( J 2 ) = D J ( K 2 ) ) .
57
4 8 4 . non
485.000
486.000
487.000
4 88.000
489.000
490.000
4 9 1 . 0 0 0 520
492.000
493.000
494.000
495.000
496.000
497.000
498.000
499.000
500.000
501.000
502.000
503.000
504.000
505.000
506.000
507.000
508.000
509.000
510.000
511 . 0 0 0
512.000
513.000
514.000
515.000
516.000
517.000
518.000
519.000
520.000
521 . 0 0 0
522.000
523.000
524.000
525.000
526.000
527.000
528.000
529."00
530.000
531.000
532.000
533.000
534.000
535.000
536.000
537.000
538.000
5 39.000
540.000
541.000
542.000
543.000
544.000
* + S C 3 4 * ( BJ <J 3 J - 0 J ( K 3 ) )
AMD ( 4 ) = - A M O d )
A M O ( 5 ) = S C M 2 * ( - ( 0 . 5 * O J ( J I ) + O J ( K 1 ) ) * c Y ( I ) + (Q
‘ *CX(I)>-SCM3+(0J(J3>-0J<K3>>
A ,1 D ( 6 ) = - A M 0 ( 3 )
DO 3 2 0 J =1 ,MO
A M ( J ) = A M L U , I ) +A M O ( J )
C ON T I N U E
X F ( J R K J I ) . E 9 . I ) THEN
5 * O J ( J 2 ) + D J (K2 ) >
A R (J1)=A R (J1)+C X(I)*AM D (1)-C Y(I)+A M D (2)
EN DI F
I F ( J R L ( J 2 ) . E I . I ) THEN
A R (J2)=AR(J2)+CY(I)*AM D(1)+CX(I)*AM D(2)
ENDIF
I F ( J R L ( J 3 ) . E 3 . I ) THEN
AR(J3)=AR(J3>+AMD(3)
ENDIF
I F ( J R L ( K I ) . E 3 . I ) THEN
A R (K 1)=A R (<1)+C X (I)*A M D (4)-C Y (I)*A M 0(5)
EN DI F
I F ( J R L ( K 2 ) . E S . I ) THEN
AR (K7)=AR (K2)+C Y(I)*AM 0(4)+C X(I)+AM D (5)
ENDIF
I F ( J R L ( K 3 ) • E 9 . I ) THEN
AR(K3)=AR(<3)+AMD(5)
EN DI F
I 8
313
330
19
W R ITE (108,13)I,A M (1),A M (2),A M (3),A M (4),A M (5),A M (6)
F O RMA T ( 2 X , I 5 , 6 F 1 0 . 3 )
CON T I N U E
DO 3 3 0 J = 1 ,NO
I F ( J R L C J ) . NE. 0 ) THEN
A R (J)=A R (J)-AI(J)-A E (J)
ENDIF
C ON T I N U E
W RITE*,” ”
WRITE *, "SU PP ORT REACTIONS"
W RITE(108,19)
F0RM AT(2X,"JOINT” , 7 X , " ARI" , 7 X , " A R 2 " , 7 X , " A R 3 " )
DO 3 4 0 J = 1 , N J
J l =3*J-2
J2=3*J-1
J 3= 3*J
N1=JRL(J1)+JRL(J2)+JRL(J3)
I F ( N I . N E . 3 ) THEN
20
340
C
C
600
620
W R IT E (10 8,20 )J,A R ( J I ) , AR(J2),AR (J3)
F0RM AT(2X,I5,3F10.3)
ENOIF
C ONT I NU E
GOTO 6 2 0
U R I T E * , " S F F NOT P O S I T I V E D E F I N I T E "
WR I T E * , " * * » * * * * * * * + * * * * * ♦ * , * , * * * * * * * * , „ * , „ » , , , , „ , , , , ,
ISN=ISN+!
WR I T E * , " * * « * * * * * * * * * * * * * * * * * * * * * * * * * * * * , * * * * * , ,
W RITE*," I
NEW PRESET G R I D "
WRITE*,
2
CHANGE I N PRESET G R I D "
W RITE*," 3
NONPRESET G R I D "
W RITE*," 0
STOP "
W RITE*,"
W R I T E * , " I NPUT ONE OF THE ABOVE NUMBERS TO C O N T I N U E "
58
545.000
546.000
547.000
548.000
549.000
550.000
551.000
552.000
553.000
554.000
5 55 . 0 0 0
556.000
557.000
558.000
559.000
560.000
561.000
562.000
563.000
564.000
565.000
566.000
567.000
568.000
569.000
570.000
571.000
572.000
573.000
574.000
575.000
576.000
577.000
578.000
579.000
580.000
581.000
582.000
583.000
584.000
585.000
586.000
587.000
588.000
529.000
590.000
591.000
592.000
593.000
594.000
595.000
596.000
597.000
598.000
5 9 9 . COO
600.000
601.000
602.000
603.000
604.000
605.000
650
W R ITE*," * * * * + * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * , ,
W RITE*," * * * * * * * * * * * * * * * * * * * * * » * * * * * * * * * * , * * * * * * * * * * * * * * , * , * * * * . ,
I N P U T NEW
I CHNGE=O
I F I N E W . E Q . 0) GOTO 8 0 0
I F I N E W . E Q . 3 ) GOTO 6 3 0
I F t N E W . E Q . I ) GOTO 6 4 0
ICHNGE=ICHNGEtI
W RITE*,” * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
W R I T E * , " I NUNHER OF S T R I N G E R S "
WRITE*,
LENGTH OF S T R I N G E R S "
WRITE*,
SPACI NG OF S T R I N G E R S "
WRITE*,
DEPTH
AND WI DTH OF S T R I N G E R S "
WRITE*,
DEPTH
AND WI DTH OF P L A N K "
W RITE*,
DEPTH
AND WI DTH OF REDUCED S T R I N G E R "
W RITE*,
L OC A T I ON OF REDUCED S T R I N G E R "
WRITE*,
L OC A T I ON OF P L A N K "
WRITE*,
E AND G"
W R I T E * , " 1 0 NUMBER OF LOADED J O I N T S "
W R I T E * , " 1 1 NUMBER OF LOADED MEMBERS"
WR I T E * , " I 2 NUMBER OF R E S T R A I N T S "
W R I T E * , " 1 3 NUMBER OF R E S T R A I N E D J O I N T S "
WR I T E * , " O NO CHANGES'
WRI T E* , "
"
W R I T E * , " I NPUT ONE OF THE ABOVE NUMBERS FOR CHANGES"
W R IT E *,"***************************************************'
W R ITE*," * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * •
I N P U T CHANGE
I F I C H A N G E . E Q . I ) THEN
W R I T E * , " I NPUT NUMBER OF S T R I N G E R S "
I N P U T NST
GOTO 6 5 0
EN DI F
I F I C H A N G E . E Q . 2 ) THEN
W R I T E * , " I NP UT LENGTH OF S T R I N G E R S "
I N P U T STL
GOTO 5 5 0
EN DI F
I F t C H A N G E . E Q . 3 ) THEN
W R I T E * , " I NPUT S PA CI NG OF S T R I N G E R S '
I N 3 UT STS
GOTO 6 5 0
ENDIF
I F I CHANGE . E Q .
W R I T E * , " I NPUT
I N P U T D S , RS
GOTO 6 5 0
4 ) THEN
DEPTH 0 ,
AND
WI DTH
B OF
STRINGERS'
5 ) THEN
DEPTH D # AND
WI DTH
B OF
P L A NK'
ENDIF
I F I C H A N G E . EQ.
W R I T E * , " I NPUT
INPUT OP ,B °
GOTO 6 5 0
ENDI F
IFtCHANGE .EQ.
W R I T E * , " I NPUT
I N P U T R OS, R9S
GOTO 6 5 0
ENDI F
I F I C HAN GE . E Q .
W R I T E * , " I NPUT
I N P U T RST
6 ) THEN
D I ME N S I O N S
7 ) THEN
L OC A T I ON
OF
OF
REDUCED
REDUCED
STR IN GE R,
STRINGER,
D AND B "
S T RI NGE R
U"
59
606.000
607.000
608.000
609.000
610.000
611.000
612.000
613.000
614.000
615.000
616.000
617.000
618.000
619.000
620.000
6 21 . 0 0 0
622.000
623.000
624.000
625.000
626.000
627.000
628.000
629.000
630.000
631.000
632.000
633.000
634.000
635.000
636.000
637.000
638.000
6 3 9 .0 0 0 "00
EOF h i t a f t e
GOTO 4 5 0
ENDIF
I F ( CHANGE . EQ• 8 ) THEN
W R I T E * , " I N P U T L OC A T I ON OF PLANK AS FRACTI ON
I NP U T LFP
GOTO 6 5 0
ENDIF
I F ( C H A N G E . EQ. 9 ) THEN
W R I T E * , " I N P U T E AND G"
INPUT E , G
GOTO 6 5 0
EN DI F
I F ( CHANGE . EQ. 1 0 ) THEN
W R I T E * , " I NPUT NUMBER OF LOADED J O I N T S "
I N P U T NLJ
GOTO 6 5 0
EN DI F
I F (CHANGE . EQ. 1 1 ) THEN
W R I T E * , " I NPUT NUM8ER OF LOADED MEMBERS"
I N P U T NLM
GOTO 6 5 0
EN DI F
I F ( CHANGE . EQ. 1 2 ) THEN
W R I T E * , " I NPUT NUMBER OF R E S T R A I N T S "
I N P U T NR
GOTO 65 I
ENDIF
I F ( CHANGE . EQ. 1 3 ) THEN
W H I T E * , " I NPUT NUMBER OF R E S T R A I N E D J O I N T S "
I N P U T NRJ
GOTO 6 5 0
ENDIF
I F I C H A N G E . EQ. 0 ) GOTO 6 6 0
END
r 4 3 9 . OOC
*
*E
! DON'T D R I i A L E
DRI B8 LE OFF 3 1 1 : 4 6
06/1 2/35
S TRI NGFR
LENGTH"
60
12:06
JUN
DRIPfl LE
! GR ID 2 ,
FOR
12
'»5
ON D
A L E N E . I C E FV093
11:59
PRESET GRI D
06/12/85
PRINT
I ,
ELSE
O
?1
INPUT
?7
MUNBER
OF
S T R I N GE R S
INPUT
?25 . 0
LENGTH
OF
S T R I N GE R S
INPUT
SPACI NG
OF
S T R I N GE R S
?2. O
INPUT
DEPTH
D,
AND
WI DTH
O (in )
OF
STRI NGERS
O,
AND
WI DTH
B (in )
OF
PLANK
? 2 0 . 0»1 0 . 0
I N P U T DEPTH
7 3 . 0 . 12.0
I NPUT DIMENSIONS
7 1 8 . 0 . 10.0
INPUT
OF
REDUCED
LOCATION
OF
REDUCED
LOCATION
OF
PLANK,
STRINGER,
S TRINGER,
D AND
STRI NGER
B (in )
NUMBER
74
INPUT
72
AS
FRACTI ON
OF
I N P U T E AND G
71400.0,10.0
I N P U T NUMBER OF LOADED J O I N T S ( N L J ) ,
NUMBER OF LOADED MEMBERS ( N L M)
71,0
INPUT
728
NUMBER
OF
RESTRAINTS
(NR)
INPUT
714
NUMBER
OF
RESTRAINED
JOINTS
INPUT J O I N T R E ST RAI NT L I S T
K , J P L ( 3 K - 2 ) » J R L ( 3 K - 1 ) , JRL(SK)
7 1 . 0 . 1.1
7 3 . 0 . 1.1
7 4 . 0 . 1.1
7 6 . 0 . 1.1
7 7 . 0 . 1.1
7 9 . 0 . 1.1
7 1 0 . 0 . 1.1
7 1 2 . 0 . 1 ,1
7 1 3 . 0 . 1 ,1
7 1 5 . 0 . 1.1
7 1 6 . 0 . 1.1
7 1 8 . 0 . 1.1
7 1 9 . 0 . 1 ,1
721 , 0 , 1 , 1
AND
(NRJ)
S TRI NGER
LENGTH
61
input
joint
loads
K , A J I 3 K - 2 ) ,AJ (TK-1 ) , A J ( 3 K )
’ 11 , o . o , o . n , - i o . o
* * , * * * * * * * * * * * * * * * * * * * * * « * * * * * * * * * * * * ‘ * * * * * * * “ *****
t**,****!*!*****************************************
SPACING= P . 0 0 0 0 0 0
L Z D = I S
M A I N STRI NGERS
REDUCED STRI NGE RS
PL A NK
:
:
:
I I . OCOOO *
1 0 . CCOOO *
3 . OOCOOO *
STRUCTURAL PARAMETERS
M
N
NJ
NR
20
35
Pl
28
J O I N T COORDI NATES
X
JOINT
. ono
I
.000
2
. 000
3
2 4 . OOO
4
74.000
5
74.000
6
43.000
7
48.000
3
48.000
9
77.000
I O
72.000
I 1
7 2 . OOO
I 2
96.000
I 3
96.000
I 4
96.000
I 5
120.000
I 6
120.000
I 7
I PO.000
I 8
I 44.000
I 9
144.000
20
144.000
21
MEMPER I N F O R M A T I ON
JJ
JK
MEMBER
I
P
I
7
3
P
P
5
3
4
5
4
5
6
5
5
3
6
7
8
7
R
9
8
O
3
I I
10
11
1O
11
12
11
11
14
I 2
13
14
I 3
14
15
I 4
14
17
I 5
16
17
16
17
18
I 7
17
PO
13
NRJ
14
20.00000
18.00000
1 2.00000
E
1400.00
G
10.00
Y
. OCO
I 5 0 . OCO
3 0 0 . CCO
. OCO
I 5 0 . CCO
3 0 0 . OCO
.000
I 5 0 . OCO
3 0 0 . CCO
. OCO
I 5 0 . OCO
3 0 0 . OCO
. OOO
I 50.000
3 0 0 . OCO
. OCO
I 5 0 . OCO
300.000
. CCO
I 50.000
3 0 0 . OCO
XI
3333.333
3333.333
4 5 9 . CCO
3333.333
3333.333
4 5 9 . OCO
3333.333
3333.333
4 5 9 . OCO
6 3 6 0 . OCO
6360.000
4 5 9 . OCO
3333.333
3333.333
4 5 9 . OCO
3333.333
3333.333
4 5 9 . OCO
YI
6666.667
6666.667
27.000
6666.667
6666.667
27.000
6666.667
6666.667
27.000
4360.000
4360.000
77.000
6666.667
6666.667
27.000
6666.667
6666.667
2 7 . 000
EL
150.000
150.000
24.000
150.000
150.000
24.000
150.000
150.000
24.000
150.000
150.000
24.000
I 50.000
150.000
24.000
150.000
150.000
24.000
CX
.000
.0 00
1.000
.000
.000
1.000
.000
.000
1.000
.0 00
.000
1.000
.000
.0 00
1.000
.000
.000
I .000
CY
I .000
I .0 0 0
.000
I .000
1.000
.000
I .000
1.000
.000
1.000
1.000
.0 0 0
1.000
1.000
.000
1.000
1.000
.000
62
19
20
19
20
20
21
J O I N T RESTRAINTS
JOINT
JRI
J R2
I
n
I
3
n
I
4
O
I
6
O
I
7
O
I
9
O
I
I O
O
I
O
I 2
I
I 3
O
I
I 5
O
I
I 6
O
I
I A
O
I
I 9
n
I
21
I
O
STRUCTURE NO.
ML»
NLJ
I
O
ACTI ONS
JO I N T
I I
3333.333
3333.333
6666.667
6666.667
150.000
150.000
.000
.000
I .000
I .000
J R3
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
AT J O I N T S
AJI
. OOO
J O I N T D I S P L A C E ME N T S
JOINT
OJ 1
I
. OOO
2
. OOO
3
. OOO
4
.000
5
.000
6
.000
7
-.002
3
. OOO
9
.002
I O
-.004
11
. OOO
I 2
.004
I 3
-.00?
I 4
.000
15
.002
I 6
. OOO
I 7
.000
I 3
. OOO
I 9
. OOO
20
. OOO
21
. OOO
MEMBER E N D - A C T I O N S
ME MBER
AMI
I
-.321
2
. 321
3
.000
4
-1.665
5
I .665
AJ 2
. CCO
AJ 3
-10.000
DJ 2
. OCO
.001
. OCO
. OCO
. 0C3
.000
. OCO
. 0C9
. OCO
. CCO
. OCO
. OCO
. OCO
-.0 09
. OCO
. CCO
- . 0C3
. CCO
. OCO
-.C C I
. OCO
DJ 3
.000
.016
.000
.000
-.019
.000
.000
-.1 66
.000
.000
-.362
.000
.000
-.166
.000
.000
-.019
.000
.000
.016
.000
A M2
. OCO
19.810
-.642
. OCO
23.555
AM3
-.132
.132
-.264
.157
-.157
AM4
.321
-.321
.000
1.665
-1.665
AM5
19.810
.000
6.9 81
-23.555
.000
AM6
.132
-.132
.2 64
-.157
.157
63
20
SUPPORT
JOINT
I
3
4
6
7
9
I O
I 2
I 3
I 5
I 6
I 8
I 9
21
. non
.000
. 000
. 000
5.091
-5.091
. OOQ
I . 46 5
- I .465
. OOO
.321
- . 321
REACTI ONS
ARI
. OOO
. OOO
. OOO
. non
. 00 0
. OOO
. OOO
. OOO
. OOO
.000
. OOO
. OOO
.000
.000
O
9
I O
I I
I 2
I 3
I 4
I 5
I 6
I 7
I 8
19
-10.311
. OCO
207.052
-19.295
. OCO
3 2 8 . 4C8
48.160
. OCO
207.052
-9.113
. OCO
23.555
-6.981
. OCO
I
8
. non
-5.091
5.091
.050
I .380
-1.380
2.811
2.189
-2.189
-2.811
1.380
- I .380
-.050
.157
-.157
.264
-.132
.132
AR2
-.321
-.321
- 1 .665
-1.665
-5.091
-5.091
. OCO
. OCO
5.091
5.091
1.665
I .665
.321
.321
A R3
-.132
-.1 32
.157
.157
1.380
I .380
2.189
2.189
1.330
I .380
.157
.157
-.132
-.132
•o
8
7
.0 00
5.0 91
-5.091
9.113
-207.052
.000
.000
.000
.000
-48.160
-328.408
.0 00
19.295
-207.052
-5.091
5.091
.000
- I . 6 65
1.665
.0 00
-.321
.321
.000
.000
10.311
-23.555
.000
.6 42
19.810
.000
******************************************************
******************************************************
1
2
T
O
NEW PRESET GRI D
CHANGE I N P RESET
NONPRESET GRI D
STOP
GRI D
I N P U T ONE OF THE ADOVE KUHHE R S TO CONTI NUE
******************************************************
******************************************************
?0
*STOP*
! DONT D R I H P L E
D R I B B L E OFF a
12:01
0 6 / 1 2/S 5
-
e0 5 0
380
380
811
I 89
I 89
811
380
380
OSO
- . I 57
I 57
- . 264
I 32
- . 132
-I
I
-2
-2
.
.
.
.
2.
2.
-I .
I .
MONTANA STATE UNIVERSITY LIBRARIES
N378
Rl+85
c o b
2