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ANALISIS DINA
DATOS DEL ANALISIS ESTATICO:
NIVEL PESO (P) Acel. Grav. MASA=(P/g)1 304.26 tn 9.80 m/seg2 31.0469
2 304.26 tn 9.80 m/seg2 31.0469
3 208.16 tn 9.80 m/seg2 21.2408
CALCLO DEL CENT!OIDE DE LA MASA DE LA PLANTA DE LA LOSA
CALCLO DEL CENT!O DE LA MASA DE LA
NIVEL Larg" (#) A$c%" (%) &' '
1 3 1.3 15 5.15
2 3 1.3 15 5.15
3 3 1.3 15 5.15
C""r*e$a*a+ *el Ce$,r" *e Ma+a:
1-. m
-.1- m
CA!ACTE!ISTICAS GEOMET!ICAS MASA INE!CIAL
E$ la *'recc'"$ &
2731.8175 0
= 2731.8175 0
= 231.1- 0
CALCLO DE LAS CA!ACTE!ISTICAS GEOMET!ICAS DE LOSA
NIVEL SECCION
1 1 0.00 0.00 0.00
∑=
Calcl" *e M"e$," *e I$erc'a 4ara la Pla$,a *e la L"+a: Secc'"$ !ec,a$glar:
=Σ
Σ=
A
Ai Xi X
.
=
Σ
Σ=
A
AiYiY
.
==12
* 3
1
hb Ixx
12
* 3
2
hb Ixx =
12
* 3
3
hb Ixx =
YYi−
X i X
−
( ) xA i2
XXi−
1
b Iyy =
2
b Iyy =
1
*3
b Iyy =
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ICO
OSA
A &'5A' '5A'
309.00 m2 4635.00 1591.35
309.00 m2 4635.00 1591.35
309.00 m2 4635.00 1591.35
62. 2 136-. 00.-
E$ la *'recc'"$
= 23175 0
= 23175 0
= 23175 0
I77' I88' I77 I88
0.00 2731.8175 23175 2731.82 23175.00
( ) xAi2YYi −
2
* 3h
2
3h
3h
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3 1 0.00 0.00 0.00
CALCLO DE MOMENTO DE INE!CIA POLA! GEOMET!ICO MOMENTO POLA! DE INE!CIA D
M"e$," *e I$erc'a P"lar Ge"9,r'c" ():
Ma+a I$erc'al
NIVEL PESO (P) A.G.= (g) MASA (M=P/g)
1 25906.82 m4 304.26 tn 6. 31.0;60
2 25906.82 m4 304.26 tn 6. 31.0;60
3 25906.82 m4 208.16 tn 6. 21.202
31.0469387755 0 0
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0.00 2731.8175 23175 2731.82 23175.00
E LA MASA
M"e$," P"lar
A!EA (A)
309.00 m2 2;3.12163
309.00 m2 2;3.12163
309.00 m2 1.00106
0.475619
a Ø1=
=
1.078214
0.036415 1.000008
0.445113
a Ø2= 1.062209
M"e$," P"lar *e I$erc'a *e la Ma+a (IѲ):
IѲ=J*(M/A)
D*ØU
D*ØU
( ) xAi X i X Iyyi 2−Σ+Σ
AREA
Masa J I
*=
θ
Gravedad
Peso Masa =
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3er ',erac'"$
0.015330
0.036705 N"ral'?ac'"$ *e a
0.034623
0er ',erac'"$0.015307
0.036659 N"ral'?ac'"$ *e a
0.034586
-," ',erac'"$
0.015305
0.036655 N"ral'?ac'"$ *e a
0.034583
;,a ',erac'"$
0.015305
0.036654 N"ral'?ac'"$ *e a
0.034583
a ',erac'"$
0.015305
0.036654 N"ral'?ac'"$ *e a
0.034583
va ',erac'"$
0.015304
0.036654 N"ral'?ac'"$ *e a
0.034582
6$a ',erac'"$
0.015305
0.036654 N"ral'?ac'"$ *e a
0.034583
1a ',erac'"$
0.0153040.036654 N"ral'?ac'"$ *e a
0 034582
D*Ø2
D*Ø3
D*Ø4
D*Ø5
D*Ø6
D*Ø7
D*Ø8
D*Ø9
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0.442771
a Ø3=
=
1.060126
0.034623 1.000002
0.442575
a Ø4=
=
1.059932
0.034586 1.000014
0.442556
a Ø5=
=
1.059911
0.034583 1.000013
0.442550
a Ø6=
=
1.059898
0.034583 1.000002
0.442544
a Ø7=
=
1.059886
0.034583 0.999991
0.442552
a Ø8=
=
1.059904
0.034582 1.000008
0.442547
a Ø9=
=
1.059892
0.034583 0.999996
0.442554 a Ø10=
=
1.059910
0 034582 1 000014
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
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11ava ',erac'"$
0.015305
0.036654 N"ral'?ac'"$ *e a
0.034583
1 "*" *e v'#rac'"$
0.442544
[D]*[Ø4] 1.059885
0.034583 0.999990
1= .30-3
w=
Brece$c'a
T= 2π=
1.1;0--;-2w
Calcl" *el 2*" "*" *e V'#rac'"$
D= mat!" #!nam!$a
S= mat!" #e %a!#&
M5= 'a t!" genea(!"a#a #e( )!me m&
M5= Ma,r'? ge$eral'?a*a *el 4r'er "*"
0.4425440468 1.0598851304 0.9999901566
S= 'at!" #e a!#&
1
1
D*Ø10
+1=
w2
['!*]=
[,]1 =
^∗=_ [∅]_^ ]" " [[ ∅]____________
]_1 − 1/ ^∗ )[ = (_ [∅]_1 [∅]_^ ][
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0.442549
a Ø11=
=
1.059898
0.034583 1.000002
-.33-00600
segn#&s
* 13.7396379273 = ;2.16-3260
32.9061887522
21.2406072442
0 0160777977
0.442544
@ * 1 059885
D*ØU
seg-1
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1
1
1
1
0.9022406398 -0.234131931 -0.1511297594
-0.234131931 0.4392581847 -0.361953089
-0.2209009444 -0.5290538377 0.6585011755
D= mat!" #!nam!$a
0.000910 -0.001810 0.001516
-0.001810 -0.004440 0.005507
-0.003027 -0.005965 0.007661
1
ØU= 1
1
1er ',erac'"$
0.000616
-0.000743 N"ral'?ac'"$ *e a
-0.001330
2er ',erac'"$
-0.000084
-0.003865 N"ral'?ac'"$ *e a
-0.005730
3er ',erac'"$
-0.000308
-0.002486 N"ral'?ac'"$ *e a
-0.003595
0er ',erac'"$
-0.000342
-0.002281 N"ral'?ac'"$ *e a
-0.003276
-," ',erac'"$
-0.000351
-0.002227 N"ral'?ac'"$ *e a
-0.003193
;," ',erac'"$
[,]1 =
[D]2=
D*ØU
D*Ø1
D*Ø2
D*Ø3
D*Ø4
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0.999990
0.0977593602 0.234131931 0.1511297594
@ 0.234131931 0.5607418153 0.361953089
0.2209009444 0.5290538377 0.3414988245
0.097759 0.234132 0.151130
0.234132 0.560742 0.361953
0.220901 0.529054 0.341499
0.462819
a Ø1=
=
-0.558591
0.001330 -1.000007
-0.014592
a Ø2=
=
-0.674447
0.005730 -1.000070
-0.085774
a Ø3=
=
-0.691642
0.003595 -0.999962
-0.104345
a Ø4=
=
-0.696178
0.003276 -1.000007
-0.109799
a Ø5=
=
-0.697519
0.003193 -1.000035
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
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-0.000353
-0.002212 N"ral'?ac'"$ *e a
-0.003169
a ',erac'"$
-0.000354
-0.002207 N"ral'?ac'"$ *e a
-0.003161
va ',erac'"$
-0.000354
-0.002205 N"ral'?ac'"$ *e a
-0.003159
6$a ',erac'"$
-0.000354
-0.002205 N"ral'?ac'"$ *e a
-0.003158
1 a ',erac'"$
-0.000354
-0.002205 N"ral'?ac'"$ *e a-0.003159
11ava ',erac'"$
-0.000354
-0.002204 N"ral'?ac'"$ *e a
-0.003158
2 M"*" *e V'#rac'"$
-3.663881
[D]*[Ø11 -9.202791
0.003169 -9.022886
1= 0.003169
w=
e$en$!a
T= 2π=
.3-3;
D*Ø5
D*Ø6
D*Ø7
D*Ø8
D*Ø9
D*Ø10
+2
=
w2
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-0.111443
a Ø6=
=
-0.697855
0.003169 -0.999940
-0.111961
a Ø7=
=
-0.698043
0.003161 -1.000034
-0.112118
a Ø8=
=
-0.698087
0.003159 -1.000042
-0.112178
a Ø9=
=
-0.698171
0.003158 -1.000147
-0.112161
a Ø10==
-0.6979790.003159 -0.999866
-0.112168
a Ø11=
=
-0.697991
0.003158 -0.999881
1.;3623
segn#&s
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
seg-1
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Calcl" *el 3er "*" *e V'#rac'"$
D= mat!" #!nam!$a
S= mat!" #e %a!#&
M5= 'a t!" genea(!"a#a #e( )!me m&
M5= Ma,r'? ge$eral'?a*a *el +eg$*" "*"
['*]= -3.663880945 -9.2027912391 -9.022886212
S= mat!" #e %a!#&
1
1
1
1
1
1
1.000000 -0.002811 -0.007061
0.000000 0.992939 -0.017735
0.000000 -0.006923 0.982612
D= mat!" #!nam!$a
0.000910 -0.001810 0.001515
-0.001810 -0.004442 0.005503
-0.003027 -0.005967 0.007655
CALCLO DEL TE!CE! MODO DE VI!ACION
[,]1 =
[,]1 =
[D]2=
ω^ [Ø]−=[][[[[[[[[[[[ -1 [Ø]0
^∗=_ [∅]_^ ]" " [[ ∅]____________
]_1 − 1/ ^∗ )[ = (_ [∅]_2 [∅]_^ ][
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* -113.75228738 = 0-.0066-233
-285.71849616
-191.65346876
0.0002094044
-3.663881
@ * -9.202791-9.022886
0.000000 0.002811 0.007061
@ 0.000000 0.007061 0.017735
0.000000 0.006923 0.017388
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-3.663880945
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648.212055 -369.768501 117.847636
-369.768501 493.726615 -329.009954
80.625662 -225.092723 231.810300
1
1
1
1er ',erac'"$
396.291191
-205.051839 N"ral'?ac'"$ *e a
87.343239
2er ',erac'"$
3926.985816
-3165.813123 N"ral'?ac'"$ *e a
1126.062999
3er ',erac'"$
3417.962747
-3006.588258 N"ral'?ac'"$ *e a
1145.806524
0er ',erac'"$ 3021.746524
-2727.571620 N"ral'?ac'"$ *e a
1062.959913
-," ',erac'"$
2909.394671
-2647.085504 N"ral'?ac'"$ *e a
1038.601627
;," ',erac'"$2876.088586
-2623.189945 N"ral'?ac'"$ *e a
1031.358014
," ',erac'"$
2865.960579
-2615.922573 N"ral'?ac'"$ *e a
1029.154679
," ',erac'"$2862.853828
[D]-1=
Ø0=
D*Ø0
D*Ø1
D*Ø2
D*Ø3
D*Ø4
D*Ø5
D*Ø6
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4.537171
a Ø1=
=
-2.347656
87.343239 1.000000
3.487359
a Ø2=
=
-2.811400
1126.062999 1.000000
2.983019
a Ø3=
=
-2.623993
1145.806524 1.000000
2.842766
a Ø4=
=
-2.566016
1062.959913 1.000000
2.801261
a Ø5=
=
-2.548701
1038.601627 1.000000
2.788642
a Ø6=
=
-2.543433
1031.358014 1.000000
2.784771
a Ø7=
=
-2.541817
1029.154679 1.000000
2.783581
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
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1028.478791
6," ',erac'"$
2861.898207
-2613.007572 N"ral'?ac'"$ *e a
1028.270891
1," ',erac'"$
2861.604010
-2612.796468 N"ral'?ac'"$ *e a
1028.206887
11," ',erac'"$
2861.513416
-2612.731461 N"ral'?ac'"$ *e a
1028.187178
12 ',erac'"$
2861.485515
-2612.711440 N"ral'?ac'"$ *e a
1028.181108
13',erac'"$
2861.476922
-2612.705274 N"ral'?ac'"$ *e a
1028.179239
10" ',erac'"$
2861.474275
-2612.703374 N"ral'?ac'"$ *e a
1028.178663
1- ',erac'"$
2861.473460
-2612.702789 N"ral'?ac'"$ *e a
1028.178485
3 M"*" *e V'#rac'"$
2.783051
[D]-1*[Ø15] -2.541098
1028.178485 1.000000
1= 12.10-
w=
D*Ø8
D*Ø9
D*Ø10
D*Ø11
D*Ø12
D*Ø13
D*Ø14
+ 3
=
w2
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1028.478791 = 1.000000
2.783214
a Ø9=
=
-2.541167
1028.270891 1.000000
2.783101
a Ø10=
=
-2.541119
1028.206887 1.000000
2.783067
a Ø11=
=
-2.541105
1028.187178 1.000000
2.783056
a Ø12=
=
-2.541100
1028.181108 1.000000
2.783053
a 13=
=
-2.541099
1028.179239 1.000000
2.783052
a 10=
=
-2.541099
1028.178663 1.000000
2.783051
a 1-=
=
-2.541098
1028.178485 1.000000
32.;-222
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
D*ØU
seg-1
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9
t&ss
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e$en$!a
T= 2π=
.16-6-1w
M"*" *e v'#rac'"$ ,",al
0.442544 -3.663881 2.783051
= 1.059885 -9.202791 -2.541098
0.999990 -9.022886 1.000000
=
=
=
2.783051048 -2.5410983099 0.9999999476
!IGIDES GENE!ALIADAS
0.442544 1.059885 0.999990
-3.663881 -9.202791 -9.022886
2.783051 -2.541098 1.000000
MASA PA!TICIPANTE
MASA PA!TICIPANTE DESPLAAMIENTO
2.502419
-21.889558
'*1 = [ +1]T ['] [+
1]
'*2 = [ +2]T ['] [+
2]
'*3 = [ +3]T ['] [+
3]
*1 = [ +1]T [] [ +
1]
* 2= [ + 2]T [] [ +
2]
* 3= [ +3]T [] [ +
3]
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segn#&s
31.0469387755 0 0
0 31.0469387755 0
0 0 21.2408163265
20125 -11480.18 2503.18-11480.18 15328.7 -6988.44
2503.18 -6988.44 4923.84
20125 -11480.18 2503.18
-11480.18 15328.7 -6988.44
2503.18 -6988.44 4923.84
20125 -11480.18 2503.18
-11480.18 15328.7 -6988.44
2503.18 -6988.44 4923.84
O!IONTAL EN S TOTALIDAD
31.0469387755 -1 = @.;620-60
31.0469387755 -1 = ;6.;3630
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;2.16-3260
0-.0066-2326-
0;2.1;;313
2717.0328716543
199976.79445602
471605.04832966
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1.241953
ECACION DEL MOVIMIENTO
62.1975732904
4775.4499523295
462.186631038
@@@@@F
1
1
1
CALCLO DE LAS E!AS INE!CIALESCDINAMICAS
= 0.45
U = 1.3
, = 1.1
= 8
g = 9.81
= 2.5
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21.2408163265 -1 = @2;.30
2717.0328716543 . = -77.692459847 s
199976.794456019 . = 679.603779347 s
471605.048329657 . = -26.380088884 s
43.6839048201 . = -1.2491236512 s
41.8760109419 . = 0.1423119886 s
1020.3779526693 . = -0.0570767026 s
Sa = 1.6226;-
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12.232416 0 0
m= 0 12.232416 0
0 0 12.232416
20125 -11480.18 2503.18= -11480.18 15328.! -6"88.44
2503.18 -6"88.44 4"23.84
0.0001381"5 0.000202502 0.00021!15!
#-1= 0.000202502 0.0004815!8 0.00058055"
0.00021!15! 0.00058055" 0.000"16686
0.0016"0461 0.0024!!0"1 0.002656356
0.0024!!0"1 0.0058"0858 0.00!101633
0.002656356 0.00!101633 0.011213284
1
$%= 1
1
1er iteraciion
0.006824
0.0154!0 &'(m*+,,+'& m
0.020"!1
2er iteraciion
0.005034
0.012253 &'(m*+,,+'& m
0.01!316
3er iteraciion
0.004"01
0.011""0 &'(m*+,,+'& m
0.01!011
4er iteraciion
0.00488"
0.011"68 &'(m*+,,+'& m
0.016"84
5to iteraciion
[D]= -1 m
D$%
D$%
D$%
D$%
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0.004888
0.011"66 &'(m*+,,+'& m
0.016"82
1 m'' +(,+'&
0.28!858
*& 1= [D][$4] 0.!04604
0.016"82 1.000001
1= 0.016"82
= 7.7371
(,&,+
==
0.8187!57&'
,*,*' * ' m'' +,,+&
=m9(+: +&m+,
#=m9(+: ((+'
M= M 9(+: 7&(*+: * (+m( m''
M= M 9(+: 7&(*+: * (+m( m''
0.28!85815 0.!04603515 1.000001041
#=m9(+: ((+'
1 0 0
0 1 0 -0 0 1
1 0 0
0 1 0 -
0 0 1
D$%
2
2;
[M]=
[S]1 =
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0."4!533266 -0.128425218 -0.182266123
-0.128425218 0.68564!!41 -0.4461410""
-0.182266123 -0.4461410"" 0.366818""4
=m9(+: +&m+,
0.000!"" 0.0002"6 -0.00043"
0.0002"6 0.000553 -0.0004!5
-0.00043" -0.0004!5 0.000461
[S]1 =
[D]2=
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0.3253"!
$1=
=
0.!3!665
0.020"!1 1.000013
0.2"06"8
$2=
=
0.!0!626
0.01!316 1.000025
0.28808"
$3=
=
0.!04862
0.01!011 1.000003
0.28!881
$4=
=
0.!04635
0.016"84 1.000015
D$%
D$%
D$%
D$%
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0.28!863
$4=
=
0.!04614
0.016"82 1.000014
3.52120064 = 1".31"02!8
8.61"00331
12.232428!
0.051!6244 0.28!858 0.28!858 0.!04604 1
0.!04604
1.000001
0.052466!3 0.12842522 0.18226612
0.12842522 0.31435226 0.4461411
0.18226612 0.4461411 0.63318101
D$%
7-1
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12.23242 0 0
0 12.23242 0
0 0 12.23242
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45/45