-
ELSEVIER PII: S0141-0296(97)00173-3
Engineering Structures, Vol. 19, No. 11, pp. 879-890, 1997 1997
Elsevier Science Ltd
All rights reserved. Printed in Great Britain 0141-0296/97
$17.00 + 0.00
Nonl inear dynamic response of a
guyed tower to a sudden guy
rupture Nabi l Ben Kah la
Department of Civil Engineering, Ecole Nationale D'lng~nieurs de
Gab~s, Route de Medenine, 6029 Gabbs, Tunisia (Received July 1996;
revised version accepted November 1996)
The geometrically nonlinear dynamic response of a three-dimen-
sional model of a guyed tower, when a selected guy suddenly rup-
tures, sending an impulsive shock to the entire structure is
studied. The sudden rupture of a guy is simulated by the
instantaneous removal of its end tension, applied as an external
force at its mast attachment point. A 500 ft tall tower with three
stay levels was ana- lysed. The analysis was performed for a
nominal wind speed acting in the plane of the ruptured guy, assumed
to be a windward one. The mast was modelled by a three-dimensional
space truss and the guys by three-dimensional elastic catenaries.
1997 Elsevier Science Ltd.
Keywords: guyed towers, sudden rupture, dynamic response, non-
linear analysis
1. Introduction
The sudden rupture of a guy in a guyed tower acts as a
triggering mechanism, subjecting the mast to a load imbal- ance.
The load imbalance causes an impulsive shock to the structure,
giving the system an initial acceleration and set- ting it into a
free vibration motion. The resulting time dependent forces and
displacements can be large enough to provoke the collapse of the
system.
If the guyed tower is a part of a communication network, its
collapse causes the loss of serviceability and if built in an urban
area, human casualties and considerable economic losses could be
expected. For these reasons, the Inter- national Association For
Shell and Spatial Structures (lASS) ~ recommend that guyed towers
of class I be designed to withstand the rupture of one arbitrarily
selected guy. The analysis is performed for a nominal wind speed
acting in the plane of tile ruptured guy, assumed to be a windward
one. The static wind pressure is maintained on the structure after
rupturing of the guy.
The purpose of this ,audy was to investigate the geo- metrically
nonlinear dynamic response of a guyed tower to the sudden rupture
of a guy, using a detailed finite element model. This model
incorporates catenary elements to rep- resent guy cables, accounts
for mechanical, structural and aerodynamic damping and includes
geometrical non- linearities. The dynamic analysis is illustrated
with a three- dimensional example tower having three stay
levels.
2. Guyed tower model
Figure la illustrates the profile of the 500 ft tall guyed tower
that was analysed. The elevation of the tower is shown in Figure
lb. The triangular cross-section mast (see Figure lc) is made up of
50 identical panels, each having a width and length of 10 ft. A
typical panel consisting of nine pinned end members is shown in
Figure ld. The struts are 2 in diameter steel pipes, the diagonals
are 3 in diameter steel pipes and the chords are 3.5 in solid
rounds. The com- pression and tension capacities of each member are
given
J
Z
s
~.." =)
o N
3
q i , d)
b)
Y
)
Figure 1 Example tower: (a) profile; (b) elevation; (c) cross-
section; (d) typical mast panel
879
-
880
Table I Compression/tension capacities of mast members
Compression capacity, Ib Tension capacity, Ib
Struts 13162 Diagonals 29798 Chords 146298
Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla
Table 3 Windward guys' end tensions: preliminary design
Guy cable X-component, Ib Z-component, Ib
38520 G 1 22393 -28898 80280 G2 27014 -22614 346356 G3 23075
-9763
in Table 1. The mast is laterally supported at three levels by a
set of three 1 in diameter guys. The guys have a break- ing tension
of 122 000 lb. The guys attached to the mast at the level of 480 ft
have a pretension of 11% of their break- ing tension, those at
level 320 ft: 12% and finally those at 160 ft: 13%. The structure
is subjected to a static wind pressure, computed according to the
EIA standard 2, with a velocity of 75 mph at a reference height of
33 ft acting at 180 from the X-axis. The ground exposure is of type
C.
The guys are assumed to be perfectly flexible, i.e. with- out
any bending stiffness. They are considered to have a uniform
section between their attachment points and are modelled by elastic
catenaries 3. To account for the energy dissipation in the material
and the friction due to inner strand rubbing, fictitious linear
viscous dampers are inserted in parallel with each guy 4,5. Seven
equally spaced nodes are defined on each guy attached to the mast
at levels 480 ft and 320 ft and only five on those attached at
level 160ft. The total number of cable elements, nodes and degrees
of freedom used for the analysis is given in Table 2.
The mast is composed of individual members welded together. The
welded connections provide some bending rigidities which are
neglected, thus assuming the joints to act as smooth hinges. The
mast is then modelled by a three- dimensional space truss made up
of 450 members (labelled in descending numbers). This model does
not account for mast structural damping.
3. Solution method
First, a geometrically nonlinear static analysis of the guyed
tower under the wind loading was performed to determine the
windward guys' end tensions. These forces are summar- ized in Table
3.
A lumped mass idealization is used at the element level and 20
frequencies and mode shapes of the intact guyed tower were
obtained. The frequencies were determined for vibration of the
structure about its deflected position under the static wind
pressure and are listed in Table 4. This table also contains the
frequencies and periods of the damaged structure (for three
different cases of guy ruptures). The sudden rupture of a single
windward guy is simulated as follows: the guy is replaced by its
end tension which is applied as an external force to the point
where the guy was
attached to the mast. At time t = 0 s, this force is removed
instantaneously from the structure, while maintaining the static
wind pressure on it, causing a force imbalance at the location of
the rupture. This imbalance initiates the motion of the system
resulting in an initial acceleration.
The highly nonlinear dynamic equations of motion are solved
using a step-by-step numerical integration method. The linear
acceleration method, together with an iterative scheme to ensure
dynamic equilibrium within each time step, is used 5-7. The
fraction of critical damping used for the fictitious linear viscous
dampers was 5% and the maximum imbalance force allowed was 1 lb.
The time domain was 60 s with a time step for the numerical inte-
gration of 0.0005 s.
4. Results and discussion
Table 5 summarizes the peak lateral mast displacements at guy
attachment points (parallel to the direction of the wind, computed
as the average of the displacements of nodes A, B and C shown in
Figure lc) and the dynamic amplifi- cation factors of guys' end
tensions at mast attachment points. The results are presented for
three different cases of guy ruptures. The dynamic amplification
factor is defined as the ratio of the peak transient guy end
tension to the initial guy end tension. Table 5 gives also the
initial dis- placements and guys' end tensions, calculated under
static wind pressure, before the sudden rupture of a selected guy.
The lateral mast displacements are measured with respect to the
mast static unloaded equilibrium position (i.e. no wind is acting
on the structure).
When windward guy G1 suddenly breaks, violent motion of the mast
is observed at this guy attachment point with a peak transient
lateral displacement of-13.68 ft. This can be seen in Figure 2, by
inspection of the plot of X-480 (X refers to the direction of the
motion, 480 the level of the mast considered). This lateral motion
of the mast becomes less important for elevations lower than 320ft
(see Figure 2, plots of X-240, X160 and X-80). At an elevation of
320 ft, the peak transient lateral displacement of the mast is
-3.81 ft. At the time when this peak is reached, guy G2 becomes
very taut, resulting in a large end tension. Figure 3 shows the
time variations of the guys' end tensions at mast attachment
points. The variables T7, T8 andT9 are the end tensions of the guys
attached to the mast at level 480 ft, at
Table 2 Total number of cable elements, nodes and degrees of
freedom
Number of cable elements Number of nodes Number of degrees of
freedom
Entire guyed tower Guyed tower without G1 Guyed tower without G2
Guyed tower without G3
48 195 567 42 190 552 42 190 552 44 192 558
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Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla
Table4 Guyed tower frequencies (rad/s) and period(s)
881
Intact structure Damaged structure
Rupture of G1 Rupture of G2 Rupture of G3
No Freq. Period Freq. Period Freq. Period Freq. Period
1 2.403 2.614 1.927 3.260 1.907 3.295 2.258 2.782 2 2.861 ;!.
196 2.318 2.711 2.557 2.457 2.511 2.502 3 3.108 ;!.022 3.262 1.926
2.622 2.396 2.657 2.365 4 3.508 1.791 3.316 1.895 3.162 1.987 3.357
1.872 5 3.719 1.689 3.423 1.836 3.628 1.732 3.753 1.674 6 3.869
1.624 3.615 1.738 3.784 1.661 3.832 1.640 7 4.012 1.566 3.713 1.692
4.089 1.536 3.918 1.604 8 4.688 1.340 3.822 1.644 4.546 1.382 3.992
1.574 9 4.777 1.315 4.200 1.496 4.654 1.350 4.464 1.408
10 4.864 1.292 4.542 1.383 4.859 1.293 4.537 1.385 11 4.947
1.270 4.747 1.323 4.930 1.274 4.838 1.299 12 5.038 1.247 5.397
1.164 5.036 1.248 4.952 1.269 13 5.107 1.230 5.484 1.146 5.277
1.191 5.046 1.245 14 6.095 1.031 5.547 1.133 5.485 1.145 5.263
1.194 15 6.147 1.022 5.985 1.050 6.029 1.042 5.374 1.169 16 6.389
0.983 6.380 0.985 6.259 1.004 6.029 1.042 17 6.617 0.950 6.545
0.960 6.348 0.990 6.185 1.016 18 6.918 0.908 6.662 0.943 6.475
0.970 6.500 0.967 19 7.105 0.884 6.770 0.928 6.667 0.942 6.685
0.940 20 7.205 0.872 6.837 0.919 6.801 0.924 6.727 0.934
Table5 Summary of response
Initial guy tension (Ib) at Dynamic amplification factor
Level Initial Rupture Peak mast (ft) displ. (ft) A B C of guy
displ. (ft) A B C
480 -1.52 14613 14467 36559 G1 -13.68 1.51 1.53 G2 -3.37 1.44
1.48 1.76 G3 -1.86 1.38 1.41 1.23
320 -0.99 11281 11281 35231 G1 -3.81 1.47 1.46 2.84 G2 -3.43
1.79 1.79 G3 -1.64 1.47 1.48 1.43
160 -0.33 12541 12690 25056 G1 0.35 1.54 1.45 1.16 G2 -1.12 1.22
1.22 2.05 G3 -1.27 1.38 1.38
points A, B and C, respectively. The plot of T9 is left blank to
remind the reader that guy G1 has ruptured. T55, T56 and T57 are
the end tension of the guys attached to the mast at level 320 ft at
A, B and C, respectively. Finally T103, T104 and T105 are the end
tensions of the guys attached to the mast at level 160 ft.
The effect of the impulsive shock is especially felt in guy G2.
The plot of guy G2 end tension (T57) gives a peak transient tension
of 100 000 lb for an initial tension of 35 231 lb, therefore a
dynamic amplification factor of 2.84. The time variations of the
end tensions of the other guys show small peak tensions.
Table 6 summarizes the initial axial forces (I.F.), peak
compression (P.C.) and ?eak tension (P.T.) forces in each member of
selected mast panels. To study the effect of the sudden rupture of
guy G1 on individual members of the mast, the time variations of
the axial forces were plotted for each member of selected mast
panels. Those plots are given in Figures 4-10 for the levels 480
ft, 400 ft, 320 ft, 240 ft, 160 ft, 80 ft and 10 ft, respectively.
The first three plots of each figure represent the time variations
of the axial forces in the struts, from left to right in members
1-2, 2-3 and 1-3, respectively, (with reference to Figure lc).
The
second set of plots is that of the forces in the diagonals, from
left to right in members 1-5, 2-6 and 3-4, respectively. The bottom
three plots are of the forces in the chords, in members 1-4, 2-5
and 3-6, respectively.
The peak axial forces in the members of the panel located at
level 480ft are below their compression/tension capacities as seen
in Figure 4 and do not fail. Figure 5 shows that only strut 2-3
fails by exceeding its compression capacity. The peak transient
compression force is -23 7491b (see Table6), while the struts
compression capacity is -13 162 lb (see Table 1). The impact of the
sud- den rupture of guy G I is strongly observed in the panels
located between guys attachment points at levels 320 ft and 160 ft.
This is best appreciated by looking at Figures 6-8. The peak
transient compressive forces in chords 1-4 and 2- 5 exceed their
compressive capacities which were calcu- lated to be -146 298 lb.
These peak forces are, respectively, -305 370 lb and -303 908 lb at
level 320 ft, -217 426 lb and -216011 lb at level 240 ft, and -166
728 lb and -167 191 lb at level 160 ft. This is true for all the
chords of type 1-4 and 2-5 of all the panels between levels 320 ft
and 160 ft. In addition, the peak transient tension force in chord
2-6 of the panel at level 320 ft was found to be
-
882
Figure 2
Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla
5
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Figure3 Time variations of guys' end tensions at mast attachment
points after sudden rupture of G1
-
Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla
Figure 4
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Time variations of mast member forces in panel at elevation 480
ft after sudden rupture of G1
883
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Time (s) Figure5 Time variations of mast member forces in panel
at elevation 40Oft after sudden rupture of G1
-
884
Figure 6
Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla
x 104 41
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Time var iat ions of mast member forces in panel at elevation
320 ft after sudden rupture of G1
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Figure 7 Time variat ions of mast member forces in panel at
elevation 240 ft after sudden rupture of G1
-
Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla 885
Figure 8
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Time variations of mast member forces in panel at elevation 160
ft after sudden rupture of G1
Table6 Initial and peak transient forces in mast members (sudden
rupture of G1)
Member
Level (ft) Type 1-2 2-3 1-3 1-5 2-6 3-4 1-4 2-5 3-6
480 I.F. 3981 11840 8634 ~,25 -6667 5306 -13742 -9537 -30920
P.C. -11221 -11378 -3077 -12837 -6872 -23376 -23005 -34553 -30920
P.T. 13620 11840 17187 13908 24378 5306 10426 254 26395
400 I.F. 111 -524 1690 -562 1440 -2653 -4182 -4719 -56585 P.C.
-9535 -23749 -676 -12718 -3686 -29176 -139941 -160629 -56585 P.T.
9899 2146 21378 10315 32935 3407 268026
320 I.F. 4538 10205 12702 -965 -5693 3362 -44487 -41085 -27935
P.C. -3661 -11538 -28464 -216 -305370 -303908 -27935 P.T. 9129
23542 31670 10435 164 24560 498371
240 I.F. 533 -20 1839 -1056 556 -2792 -38804 -38935 -47050 P.C.
-8522 -2643 -14522 -11911 -21674 -6034 -217426 -216011 -50649 P.T.
9243 15504 3901 9527 2956 21229 324705
160 I.F. 6964 9816 12563 -1412 -3459 679 -70141 -67666 -18275
P.C. -2535 -9686 -22383 -2821 -166728 -167191 -35660 P.T. 15923
24612 13301 7615 1848 19957 165960
80 I.F. 907 101 1943 -1430 116 -2849 -71228 -72168 -24002 P.C.
-7260 -2108 -13114 -13451 -17217 -6230 -96709 -99078 -49111 P.T.
7276 11977 5599 10862 2788 16662 49616
10 I.F. 934 -1169 3142 -1383 1772 -4509 -85614 -88337 -3375 P.C.
-6930 -7978 -13698 -13451 -20144 -14747 -92009 -88337 -140211 P.T.
8556 12817 10619 10688 12239 20073 3906 53422
498 371 lb which is beyond the 346 356 lb tension capacity of
the chords. The peak transient compressive force in strut 1-3 of
the panel at level 240 ft, computed to be -14 522 lb, also exceeded
its compressive capacity The failure of all
those members will eventually cause the collapse of the guyed
tower. For the mast panels below level 160 ft, no member failure
occurs (see Figure 9), except for strut 1-3 at the bottom of the
mast (level l0 ft) for which the peak
-
886
Figure 9
Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla
4 x 104
0 20 40 60 Time (s)
4 x 104
Ckl 0 IJ,~ ..... ,:~-,,-,,~" L--'J~',l
~:-~I . . . . . . . ' . . . . . . . . . . . . . . 1 -41 /
0 20 40 60 Time (s)
x 10 4
"2 I ....... i ....... i ......
Time (s) x 104
o[21(2Li:2 oo
_4 ~ i i 0 20 40 60
Time (s) x 105 x 105
2 . . . . . . . . . . . . . . . . . . . . _
_ , _ ..... :] 0 20 40 60 0 20 40 60
Time (s) Time (s)
4x104
0 20 40 60 Time (s)
4 x 104. .
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0 20 40 60 Time (s)
x 105
~ ; W 14" ..... : ....... ~ ..... ] ~ op; : -~? , , i .... ~-~I
- - . . . . . : . . . . . . . ~ . . . . . 0 20 40 60
Time (s)
Time variations of mast member forces in panel at elevation 80
ft after sudden rupture of G1
4 x 104
. . . . . . . : . . . . . . . . . . . . . t -4 / /
0 20 40 60 Time (s)
x 104
LL -2
-40 20 40 60 Time (s)
x 10 5 4 . ,
~Wii ........ i ...... . . . . . . . : . . . . . . . . . . . .
.
.41 0 20 40 60
Time (s)
x 104
L"':-'Z-i.171U',i2
LL - " . . . . . . . . . . . . . . .
-4~1 2:0 4:0 60 Time (s)
X 10 4 ._..4
0 20 40 60 Time (s)
4 xlSr-
2[ - . . . . . . ~ . . . . . . . ; . . . . . . .
-2F . - . " ....... ~ ....... -4'
0 20 40 60 Time (s)
X 10 4
~- 0 ~ ' ' - -~ ..... i " " - - *
-% ~o ,::o 6'0 Time (s)
X 104 . . . .4 .
0 20 40 60 Time (s)
x 105
0 0 - " "~: :C -.- : ij~
0 20 40 60 Time (s)
Figure 10 Time variations of mast member forces in panel at
elevation lo f t after sudden rupture of G1
-
Nonl inear dynamic response o f guyed tower to sudden guy
rupture : N. Ben Kah la
F igure 11
x 1134 10 : :
._. 8 ....... i ....... i ......
O~ 2'0 40 60 Time (s)
x 10 4
.~ . . . . . . . i . . . . . . . i . . . . . . ~" 6 . . . . . .
. : . . . . . . . : . . . . . .
~ 4I ....... ~ ....... ~ . . . . . .
0 40 60 Time (s)
x 10 4 10 : :
8 . . . . . . . : . . . . . . . ~ . . . . . .
c~ 6 . . . . . . . i . . . . . . . i . . . . . .
o 4
~-" 2 . . . . . . . : . . . . . . . ~ . . . . . . LItd._ :~ ~L/
: -_ - . ~. ~ .L
u 20 40 60 Time (s)
l oX-1 - 4
..... ....... ...... 1 e 6 ....... i ....... i ...... co 4 . . .
. . . . i . . . . . . . ! . . . . . .
0 r ..... . - - . - --1 0 20 40 60
Time (s) 0 x104. .
g
~ 4 . . . . . . . ! . . . . . . . :: . . . . . .
00~2'0 40 60 Time (s)
0x! '. .
"~Iiiiiiiiiiiiiiiiiiiii! ~ 4 ....... i . . . . . . . :~ . . . .
. .
r . . . . . . . . ; . . . . . . ; --
% 20 60 4O T ime (s )
10 x 104 / /
8 - i - - . . . . . . . . . . . . . ~ . . . . . . 4
" - " 6~::-.vi'-'::'-i:----- 4
. . . . ; . . . . . . 1 e- ..... i ....... i . . . . . .
0 / ; ; , 0 20 40 60
Time (s)
10 x 104
~- o2t .............. ! ...... t 0 20 40 60
Time (s) 10 x 104
6L:: ..... :: ....... i ...... 1 2 I ..... i ....... ! ...... 1
% 2'0 4o 6'0
Time (s)
Time variations, of guys' end tensions at mast attachment points
after sudden rupture of G2
887
4 x 104
. . . . . . . i . . . . . . . i . . . . . . .
-2 t -4
0 20 40 60 Time (s)
4 x 11) 4
2f - - - i i
, , - . ::
-% 2'o 4'0 60 T ime (s)
4 x 10 s
" - "2 JO r . .O O3 LL-2
20 40 60 Time (s)
4 x 104
oJ o r . . . . . i . . . . . - :~ : ! . . . . . :1
0 20 40 60 Time (s)
4 x 104
~" 0 " : ..=.i-:~.~..4 u_ _ : ~- . - ; .
_ .
0 20 40 60 Time (s)
4 x 10 s
oO 0 ; ; ' : : : : ' i : ' " " ' i " : ' '
-4 ' i i , 0 20 40 60
Time (s)
4 x 104
- 0 20 40 60 Time (s)
X 104 4
- ~--,i -J = T-IIT:::I~IIIZ~I:I 7 O3 LL- 2
-4 20 40 60 Time (s)
x 10 s
f iiiiii t , ~o " -2 [ . . . . . . . . i . . . . . . . . . '
""'""
-4 ; 0 20 40 60
Time (s)
F igure 12 Time variations of mast member forces in panel at
elevation 400 ft after sudden rupture of G2
-
888
Figure 13
Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla
x 104 4
~2 coO (0
u_-2 -4 0 20 40 60
Time (s) x 10 4
.-. 4 . .
o I~:.;':,.~;:,,:;~',, ~ -~I ....... : ....... ; 1 -4 / /
0 20 40 60 Time (s)
4 x105.
. . . . . . . . . . . . . i . . . . . . .
g or--:-'::--: ~--~-~ !--- :--- ~_~-- ....... ............... -4
/ 0 20 40 60
Time (s)
x 104 4
-Q2 "cO (0
U.-2 -4
0 20 40 60 Time (s)
x 104
I I - " . . . . . . . . . . . . . . . . . . . .
-4 0 20 40 60
Time (s) 4 x 10 5. .
e oF~"-!" ' -~! I
'~:~I ....... ' . . . . . . . . . . . . . . 1 0 20 40 60
Time (s)
4X104
-o2 ~0 (0 U . -2
-4 0 20 40 60
Time (s) 4x-1~.~- .
~" 2 -[- . . . . . i . . . . . . . :, . . . . . . .
eD
-4 0 20 40 60
Time (s) x 105
. _ .4 r . ' " t
g 2 . . . . . . . i . . . . . . . i . . . . . .
~ o f ....... i ....... i . . . . . . u_-2~V-'~--'~i~ , i , -
-
_4 ~ ! i 0 20 40 60
Time (s) Time variations of mast member forces in panel at
elevation 320 ft after sudden rupture of G2
10 x 104 .
68 ifi i i i i i i i i i i i i i i i i l l j ~ ....... i . . . .
. . . :. .......
4 . . . . . . . i . . . . . . . i . . . . . .
2 O F, " - i i I 0 20 40 60
Time (s)
x 104 10[ . .
. . . 8 . . . . . . . i . . . . . . . ; . . . . . .
e 6 .............. i . . . . . .
2 ~o 4; oo Time (s)
_ _ 10 x 104 . 10 x 104
~ 8 f ] ....... i i ....... ...... ~ 8tliiiiiiiiiiiiiiiiiiiii
t
J 0 r . . . . . . -- . . . . . . . . , . . . . ] 0 20 40 60
Time (s) x 104
10~ , . /
6i . . . . . . . i . . . . . . . i . . . . . . 1 o 41 . . . . .
. . : . . . . . . . ~ . . . . . . 1
0;~ 2;0 40 60 Time (s)
0 x 104.
o~ 4 L----= . . . . . . . . . . J
0 ~ ~ 0 20 40 60 Time (s)
10 x 104.
0! ~:E :4:0 ~% 0 ~0 40 ~o Time (s) Time (s)
x 104 x 104
~ ~ g 681111111:iiiiiiiiiiiii I - . . i i ~ ~ 4 . . . . . . . i
. . . . . . . i . . . . . . . :::::::::::::::::::::: ~
....................
c~ 2'0 4'0 60' % 2'0 4'0 60 Time (s) Time (s)
Figure 14 Time variations of guys' end tensions at mast
attachment points after sudden rupture of G3
-
Nonlinear dynamic response of guyed tower to sudden guy rupture:
N. Ben Kahla
Figure 15
4 x 104
"2
~0 0 cO LL-2
-40 20 40 60 Time (S)
. x2~ .
~ ...... ~ ....... i ....... o o ~:,,%~:::;.-..::'..---::
-21 ...... : ....... ; ...... -4 i
0 20 40 60 Time (s)
4 x 105
~f- -~ ....... i ...... 2 o,-=--,,-i ..... : i " -
. . . . . . . : . . . . . . . ., . . . . . .
0 20 40 60 Time (s)
Time variat ion of mast member forces
x 104 ,-. 4 . .
" -~ I ............. ~ ...... 1 0 20 40 60
Time (s) X 104
4
Or) U_-2
-4( 20 40 60 Time (s)
4 x 105
~ ...... ~ ..... . . i . . . . . . . 0 ~:- ~,."~- :-!
.......
~2 ! i
U- "41""'210 .... 4~ .... 60 -0 Time (s)
4 x 104
.o2 v
o~0 0 cO LL-2
-4 0 20 40 60
Time (s) 4 x104 :
~f ...... ~ ....... i ....... o ~
~-2 ~ ~ .....
- ~ 6 0 Time (s)
4 x 105 .
~:EC--~:-! -: ..... i ...... 1 0 20 40 60
Time (s)
in panel at elevation 160 ft after sudden rupture of G3
889
x 1134
I -I ............ i ...... 1 -% ~:0 X0 ~0
Time (s)
4 x 10 L
l " 'WWm~
":~I .............. ~ ...... 1 0 20 40 60
Time (s)
4x_1_c~ .
Time (s)
x 104
2 . . . . . . . ~ . . . . . . . ; . . . . . . ~ 2
OL._;_"=..:-:::I:=::.~ "~ 0
" I ...... ~ ....... ! ...... l ~ -= -4 ' ' -4 0 20 40 60 q
Time (s) 4 x104 4
m
. . . . . . ' . . . . . . . . . . . . . .
0 20 40 60 Time (s)
4 x 10 s
_,,.F ~ i ] 0 20 40 60
Time (s)
"0
1.1_-2 -4
x 104
i:i-!i i i 1 ) 20 40 60
Time (s) X 10 4
t . . . . . . . . . . . . . . i . . . . . .
I : :
0 20 4O 60 Time (s)
x 105
' L ~" 2 =':i,;, ..... '_: .... 0F:;-:-i ....... ~ ......
-2 I- ............ ! . . . . . . -~ 2-'0 4'0 60
Time (s)
Figure 16 Time variations of mast member forces in panel at
elevation 10 ft after sudden rupture of G3
-
890 Nonlinear dynamic response of guyed tower to sudden guy
rupture: N. Ben Kahla
transient compressive force was -13 698 lb as determined from
Figure 10. This force is larger than its compressive capacity.
The time variations of the guys' end tensions at mast attachment
points after the rupture of guy G2, are plotted in Figure 11. The
largest tensions were obtained for guys G 1 and G3. The peak
transient end tensions for G 1 and G2 are 64 344 lb and 51 365 lb,
respectively, corresponding to dynamic amplification factors of
1.76 and 2.05. The conse- quences of the rupture of guy G2 are
illustrated by the mag- nitudes of the axial forces in the members
of the panels in the vicinity of the G2 mast attachment level.
Figure 12 shows the time variations of member forces in the panel
at level 400 ft. The plot of F99 gives a peak transient axial force
of -244 002 lb in chord 3-6. For the panel at level 320 ft, the
time variations of the member forces are plotted in Figure13. The
graph of F171 shows a peak of -282 341 lb. Both of these peak
forces exceed the chord compression capacity. It is to be noted
that all the chords of type 3-6 in the panels between levels 400 ft
and 240 ft failed in compression, resulting in the collapse of the
structure.
The plots of the time variations of the guys' end tensions are
given in Figure 14 for the case when a sudden rupture of guy G3
occurred. The peak transient end tension of G 1 was computed to be
44 968 lb for a dynamic amplification factor of 1.23, that of G2
was 50 380 lb corresponding to a dynamic amplification factor of
1.43. At level 160 ft, chord 3-6 fails in compression, its peak
transient axial force as can be seen in the plot of F315 in Figure
15 was -164 349 lb. At the bottom of the mast chords 1-4 and 2- 5
failed. Both of their peak transient axial forces (respectively,
-194 692 lb and -197 339 lb) exceeded their
compression capacities. This is illustrated in the plots of F448
and F449 in Figure 16.
5. Conclusions
The present study investigated the nonlinear dynamic reponse of
a guyed tower, when a sudden rupture of a selec- ted guy occurred.
The investigation was carried out for a nominal wind speed, acting
in the plane of the ruptured guy, assumed to be a windward one. The
time variations of the guys' end tensions and mast members' axial
forces were determined for three cases of guy rupture. The analy-
ses showed that the largest tensions were obtained for the
initially windward guys and that the collapse of the struc- ture
occurs after a set of chord members lose their load carrying
capacities. Most of the time the results show that the chords fail
in compression.
References 1 'Recommendations for guyed masts', Working Group
No. 4, Inter-
national Association for Shell and Spatial Structures, Madrid,
Spain, 1981
2 EIA Standard 222-D. 'Structural standards for steel antenna
towers and antenna supporting structures', Electronics Industries
Associ- ation, Washington, DC, 1986
3 Peyrot, A. H. and Goulois, A. M. 'Analysis of cable
structures', Corn- put. Struct. 1979, 10, 805-813
4 Thomas, M. B. 'Broken conductor loads on transmission line
struc- tures', Ph.D. thesis, University of Wisconsin-Madison,
1981
5 Ben Kahla, N. 'Dynamics of a single guy cable', Comput.
Struct. 1995, 54 (6), 1197-1211
6 Ben Kahla, N. 'Dynamic analysis of guyed towers', Engng
Struct. 1994, 16 (4), 287-301.
7 Peyrot, A. H. 'Marine cable structures', J. Struct. Div., ASCE
1980, 106 (12), 2391-2404.