p/p - scielo.br · p/p cr1 w/l q=5000 kn q=30000 kn ... 8.5 x 10 7 t (sec)) p0= 0.45 pcr1 alpha =...
TRANSCRIPT
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3
P/Pcr1
w/L
Q=5000 kN
Q=30000 kN
Q=59897.6 kN
Q=59897.7 kN
Q=72000 kN
Q=78553.7 kN
Q=72000 kn
Q=78553.7 kN
Pcr1
Pcr2
Pu-wu
Pc-wc
Qcr2
Qcr1
Pcr1
Pcr2
wc
wu
(
√ ) ( )
√
√
( )
√ ( )
√ ( )
( )
( ) ( ) ( ) √ ( )
( ) ( ) ( )
( ) (5)
0 0.5 1 1.5 2 2.5 3 3.53
4
5
6
7
8
9
10x 10
-3
rf
w (
m)
Large Deformations
small Deformations
P0=4500kNq0=QcB=1wn=18.32rad/sw(0)=0.0033102 mv(0)=0
alpha = 0.5
0 200 400 600 800 1000 1200 1400 1600 1800 20002
2.5
3
3.5
4
4.5
5x 10
-3
t (sec)
w (
m)
0 20 40 60 80 100 120 140 160 180 200-4
-2
0
2
4
6
8
10x 10
-3
t (sec)
w (
m)
B=1rf=1.994
B = 1rf = 0.997
( )
1995 1996 1997 1998 1999 20002
2.5
3
3.5
4
4.5
5x 10
-3
t (sec)
w (
m)
2 2.5 3 3.5 4 4.5 5
x 10-3
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
w (m)
v (
m/s
)
1995 1995.5 1996 1996.5 1997 1997.5 1998 1998.5 1999 1999.5 20002
3
4
5
6
7x 10
6
t (sec)
P (
N)
1995 1996 1997 1998 1999 20001.5085
1.509
1.5095
1.51
1.5105
1.511
1.5115x 10
8
t (sec)
K (
N/m
)
B = 1rf =1.994wr =18.26 rad/swf = 36.53rad/sn=2
0 0.5 1 1.5 2 2.5 3 3.50
0.02
0.04
0.06
0.08
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.53.3
3.35
3.4
3.45
3.5
3.55x 10
-3
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.53
4
5
6
7x 10
-3
rf
w (
m)
0 0.5 1 1.5 2 2.5 30
0.01
0.02
0.03
0.04
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.50
0.02
0.04
0.06
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.50
0.005
0.01
0.015
0.02
rf
w (
m)
q0=QcP0=4500kNwn=18.3rad/sw(0)=0.003317v(0)=0t=200s
alpha=0.75
alpha=0.5
alpha=0.1
alpha=1
alpha=0.25
alpha=0.01
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5
α
rf
Min1
Max1
Min2
Max2
195 196 197 198 199 2002
3
4
5
6
7x 10
6
t (sec)
P (
N)
195 196 197 198 199 2000.4
0.6
0.8
1
1.2
1.4
1.6x 10
8
t (sec)
K (
N/m
)
195 196 197 198 199 200-0.02
-0.01
0
0.01
0.02
0.03
0.04
t (sec)
w (
m)
-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
w (m)
v (
m/s
)
q0=QcP0=4500kNalpha=0.5n=1
rf = 0.594wr=10.9 rad/s=wfwn=18.32rad/sw(0)=0.003317 mv(0)=0
195 196 197 198 199 200-2
0
2
4
6
8
10
12
14x 10
-3
t (sec)
w (
m)
0 0.005 0.01 0.015 0.02-0.15
-0.1
-0.05
0
0.05
0.1
w (m)
v (
m/s
)
195 196 197 198 199 2002
3
4
5
6
7x 10
6
t (sec)
P (
N)
195 196 197 198 199 2000.4
0.6
0.8
1
1.2
1.4
1.6x 10
8
t (sec)
K (
N/m
)
wr = 12.938 rad/swf = 25.876 rad/sn=2rf=1.414alpha=0.5
0 0.5 1 1.5 2 2.5 3
0.305
0.306
0.307
0.308
0.309
rf
w (
m)
0 0.5 1 1.5 2 2.50.3
0.305
0.31
0.315
0.32
rf
w (
m)
0 0.5 1 1.5 2 2.5
0.35
0.4
0.45
0.5
rf
w (
m)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
rf
w (
m)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
rf
w (
m)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
rf
w (
m)
P0 = 0.9pcr2wn=16.8016rad/sw(0)=0.30478mv(0)=0t=200sq0=Qcp0=0
alpha=0.01
alpha=0.1alpha=0.25
alpha=0.5
alpha=0.75
alpha = 0.001
0 0.5 1 1.5 2
1.4
1.6
1.8
2
2.2
2.4
2.6
t (sec)
w (
m)
0 0.5 1 1.5 2-1
0
1
2
3
4
5
6
7
8
t (sec)
v (
m/s
)
1.4 1.6 1.8 2 2.2-1
0
1
2
3
4
5
6
7
w (m)
v (
m/s
)
0 0.5 1 1.5 20
1
2
3
4
5
6x 10
7
t (sec)
K (
N/m
)
P0=0.65pcr1q0=72000kNw(0)=1.3498mv(0)=0wn=10.89rad/st=1.759s
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.50.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
rf
w (
m)
P0 = 0.45pcr1alpha=0.01wn=13.6396rad/sw(0)=0.8601mv(0)=0t=200sq0=72000kN
495 496 497 498 499 5000.75
0.8
0.85
0.9
0.95
1
t (sec)
w (
m)
0.75 0.8 0.85 0.9 0.95 1 1.05 1.1-1.5
-1
-0.5
0
0.5
1
1.5
w (m)
v (
m/s
)
495 496 497 498 499 5001.105
1.11
1.115
1.12
1.125
1.13
1.135x 10
9
t (sec)
P (
N)
495 496 497 498 499 5007.9
8
8.1
8.2
8.3
8.4
8.5x 10
7
t (sec)
K(N
/m)
P0= 0.45 Pcr1alpha = 0.01rf = 0.905wf = wr =12.344 rad/sn = 1
495 496 497 498 499 5000.83
0.84
0.85
0.86
0.87
0.88
0.89
0.9
0.91
t (sec)
w (
m)
0.84 0.86 0.88 0.9 0.92 0.94-0.6
-0.4
-0.2
0
0.2
0.4
w (m)v
(m
/s)
495 496 497 498 499 5001.105
1.11
1.115
1.12
1.125
1.13
1.135x 10
9
t (sec)
P (
N)
495 496 497 498 499 5008.3
8.32
8.34
8.36
8.38
8.4
8.42
8.44x 10
7
t (sec)
K (
N/m
)
P0 = 0.45pcr1alpha=0.01rf = 1.993wf=27.184rad/swr=13.6 rad/sn=2
495 496 497 498 499 5000.8
0.82
0.84
0.86
0.88
0.9
t (sec)
w (
m)
0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
w (m)
v (
m/s
)
495 496 497 498 499 5001.105
1.11
1.115
1.12
1.125
1.13
1.135x 10
9
t (sec)
P (
N)
495 496 497 498 499 5008.3
8.32
8.34
8.36
8.38
8.4
8.42
8.44x 10
7
t (sec)
K (
N/m
)
P0 = 0.45 Pcr1rf = 0.499alpha =0.01wr= wf =6.8062 rad/sn = 1
( B) ( l )
l3
l3[
B ( B){ (g
L) (g
L)3}]
0 0.5 1 1.5 2 2.50
0.02
0.04
0.06
rf
w (
m)
0 0.5 1 1.5 2 2.5 30
0.01
0.02
0.03
0.04
rf
w (
m)
0 0.5 1 1.5 2 2.53.3
3.34
3.38x 10
-3
rf
w (
m)
0 0.5 1 1.5 2 2.5 33
3.5
4
4.5
5x 10
-3
rf
w (
m)
0 0.5 1 1.5 2 2.5 32
4
6
8
10x 10
-3
rf
w (
m)
0 0.5 1 1.5 2 2.5 30
0.005
0.01
0.015
0.02
0.025
rf
w (
m)
q0=QcPa1=4500kNwn=18.3rad/sw(0)=0.003317v(0)=0t=200s
alpha=0.75xi=0.03
alpha=1.0xi=0.03
alpha=0.5xi=0.03
alpha=0.25xi=0.03
alpha=0.1xi=0.03
alpha=0.01xi=0.03
3
3
0 0.5 1 1.5 2 2.5 3 3.50
0.01
0.02
0.03
0.04
rf
w (
m)
0 0.5 1 1.5 2 2.5 33
4
5
6
7x 10
-3
rf
w (
m)
0 0.5 1 1.5 2 2.5 3
0.005
0.01
0.015
0.02
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.50
0.02
0.04
0.06
0.08
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.50
0.02
0.04
0.06
rf
w (
m)
0 0.5 1 1.5 2 2.5 33.3
3.35
3.4
3.45x 10
-3
rf
w (
m)
alpha = 0.1
P0 = 4500kNq0=Qcw(0)=0.0033mv(0)=0wn=17.335rad/st=200s
alpha =0.25
alpha = 0.01
alpha = 0.75 alpha = 1
alpha =0.5
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5
α
rf
Min1
Max1
Min2
Max2
195 196 197 198 199 200-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
t (sec)
w (
m)
-0.05 -0.025 0 0.025 0.05 0.075 0.1 0.125 0.15-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
w (m)
v (
m/s
)
195 196 197 198 199 200
0
2
4
6
8
10x 10
6
t (sec)
P (
N)
195 196 197 198 199 2002
4
6
8
10
12
14
16x 10
7
t (sec)
K (
N/m
)
rf=0.554
wf = wr = 9.6rad/s
P0=4500kN
q0=Qc
alpha=1
195 196 197 198 199 200
0
2
4
6
8
10x 10
6
t (sec)
P (
N)
195 196 197 198 199 2002
4
6
8
10
12
14
16x 10
7
t (sec)
K (
N/m
)
195 196 197 198 199 200-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
t (sec)
w (
m)
-0.02 0.005 0.03 0.055 0.08 0.1-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
w (m)
v (
m/s
)
rf=1.294alpha=1q0=Qcwr=11.2 rad/swf=22.4rad/sn=2
195 196 197 198 199 2000
1
2
3
4
5
6
7x 10
-3
t (sec)
w (
m)
0 1 2 3 4 5 6 7 8 9
x 10-3
-0.05
-0.025
0
0.025
0.05
w (m)
v (
m/s
)
195 196 197 198 199 200-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
t (sec)
w (
m)
-0.02 0 0.02 0.04 0.06-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
w (m)
v (
m/s
)
rf=1.294w(0)=0.0037 mv(0)=0
rf=1.294w(0)=0.0036 mv(0)=0
195 196 197 198 199 2001
2
3
4
5
6x 10
-3
t (sec)
w (
m)
1 2 3 4 5 6 7 8
x 10-3
-0.05
-0.025
0
0.025
0.05
w (m)
v (
m/s
)
195 196 197 198 199 200-0.02
0
0.02
0.04
0.06
t (sec)
w (
m)
-0.02 0 0.02 0.04 0.06-0.4
-0.2
0
0.2
0.4
w (m)
v (
m/s
)
195 196 197 198 199 2002
3
4
5
6x 10
-3
t (sec)
w (
m)
2 3 4 5 6 7 8
x 10-3
-0.04
-0.02
0
0.02
0.04
0.06
w (m)
v (
m/s
)
mass=0.99M
mass=M
mass=0.98Mrf=1.294w(0)=0.0033 mv(0)=0
M = 450,000 kg
0 0.5 1 1.5 2 2.5 3 3.50
0.02
0.04
0.06
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.50
0.01
0.02
0.03
0.04
rf
w (
m)
0 0.5 1 1.5 2 2.5 33.3
3.31
3.32
3.33x 10
-3
rf
w (
m)
0 0.5 1 1.5 2 2.5 33
3.5
4
4.5
5x 10
-3
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.50
0.01
0.02
0.03
rf
w (
m)
0 0.5 1 1.5 2 2.5 3 3.52
4
6
8
10x 10
-3
rf
w (
m)
P=4500kNq0=Qcwn=18.3352rad/sw(0)=0.0033093v(0)=0xi=0.03
alpha = 0.01alpha = 0.1
alpha = 0.25alpha = 0.5
alpha = 0.75alpha = 1
