alternancias takabella-1
DESCRIPTION
ingenieria civilTRANSCRIPT
DISEÑO SISMORESITENTEING. METODO DE TAKABEYA Lamina
H.J.T.H MT-01
ESTADO 1 :Máximos Momentos negativos en la estructura adjunta por el método de Fukuhey Takabeya:
W1 W2 W3 Datos:H1
m n o p W1 = 4.00 Tn/m h1 =
h1 W2 = 4.00 Tn/m h2 =
W4 W5 W6 W3 = 4.00 Tn/m h3 =
H2 W4 = 5.00 Tn/m H1 =
i j k l W5 = 5.00 Tn/m H2 =
h2 W6 = 5.00 Tn/m H3 =
W7 W8 W9 W7 = 6.00 Tn/m VigaH3 W8 = 6.00 Tn/m b =
e f g h W9 = 6.00 Tn/m h =
h3 L1 = 7.20 m. Columna a y dL2 = 6.30 m. b =
a b c d L3 = 7.00 m. h =
L1 L2 L3 Columna b y cb =
h =
Momento de empotramiento Perfecto (M°ik) Cargas distribuidas
Momento de Inercia (I) Viga seccion rectangular
Coeficiente de Rigidez (K) K = Iik/Lik Elementos con nudos rígidos
Tramo L Carga Carga M. Empot. Perf. Sección I
Coeficiente de Rigidez (K)Distribuida P l1 l2 Tn-m b h
m Ton/ml Tn m m. M°ik M°ki cm cm cm4 K Representación
mn 7.20 4.00 0.00 0.00 0.00 -17.28 17.28 30.00 60.00 540000 750 0.93
no 6.30 4.00 0.00 0.00 0.00 -13.23 13.23 30.00 60.00 540000 857 1.06
op 7.00 4.00 0.00 0.00 0.00 -16.33 16.33 30.00 60.00 540000 771 0.96
ij 7.20 5.00 0.00 0.00 0.00 -21.60 21.60 30.00 60.00 540000 750 0.93
jk 6.30 5.00 0.00 0.00 0.00 -16.54 16.54 30.00 60.00 540000 857 1.06
kl 7.00 5.00 0.00 0.00 0.00 -20.42 20.42 30.00 60.00 540000 771 0.96
ef 7.20 6.00 0.00 0.00 0.00 -25.92 25.92 30.00 60.00 540000 750 0.93
fg 6.30 6.00 0.00 0.00 0.00 -19.85 19.85 30.00 60.00 540000 857 1.06
gh 7.00 6.00 0.00 0.00 0.00 -24.50 24.50 30.00 60.00 540000 771 0.96
im 3.30 0.00 0.00 0.00 0.00 0.00 0.00 35.00 45.00 265781 805 1.00
jn 3.30 0.00 0.00 0.00 0.00 0.00 0.00 30.00 40.00 160000 485 0.60
ko 3.30 0.00 0.00 0.00 0.00 0.00 0.00 30.00 40.00 160000 485 0.60
lp 3.30 0.00 0.00 0.00 0.00 0.00 0.00 35.00 45.00 265781 805 1.00
ei 3.30 0.00 0.00 0.00 0.00 0.00 0.00 35.00 45.00 265781 805 1.00
fj 3.30 0.00 0.00 0.00 0.00 0.00 0.00 30.00 40.00 160000 485 0.60
gk 3.30 0.00 0.00 0.00 0.00 0.00 0.00 30.00 40.00 160000 485 0.60
hl 3.30 0.00 0.00 0.00 0.00 0.00 0.00 35.00 45.00 265781 805 1.00
ae 4.30 0.00 0.00 0.00 0.00 0.00 0.00 35.00 45.00 265781 618 0.77
bf 4.30 0.00 0.00 0.00 0.00 0.00 0.00 30.00 40.00 160000 372 0.46
cg 4.30 0.00 0.00 0.00 0.00 0.00 0.00 30.00 40.00 160000 372 0.46
dh 4.30 0.00 0.00 0.00 0.00 0.00 0.00 35.00 45.00 265781 618 0.77
Tal que
Kik Pi =2∑Kik ikƔ ∑ ikƔ
1 . Momento de Inercia y Momento de Empotramiento perfecto
M°ik = ±Wik. L2ik
I = bh3/12
2 . Factores de Giro (Ɣik)Ɣik= -Kik / PiƔik= -Kik /2∑Kik ∑ Ɣik = -0.500
Nudo Tramo Kik Pi =2∑Kik ikƔ ∑ ikƔ
mmn 0.930 3.860 -0.241
-0.500mi 1.000 3.860 -0.259
nnm 0.930 5.180 -0.180
-0.500no 1.060 5.180 -0.205
nj 0.600 5.180 -0.116
oon 1.060 5.240 -0.202
-0.500op 0.960 5.240 -0.183
ok 0.600 5.240 -0.115
ppo 0.960 3.920 -0.245
-0.500pl 1.000 3.920 -0.255
iim 1.000 5.860 -0.171
-0.500ij 0.930 5.860 -0.159
ie 1.000 5.860 -0.171
j
jn 0.600 6.380 -0.094
-0.500ji 0.930 6.380 -0.146
jk 1.060 6.380 -0.166
jf 0.600 6.380 -0.094
k
ko 0.600 6.440 -0.093
-0.500kj 1.060 6.440 -0.165
kl 0.960 6.440 -0.149
kg 0.600 6.440 -0.093
llp 1.000 5.920 -0.169
-0.500lk 0.960 5.920 -0.162
lh 1.000 5.920 -0.169
eei 1.000 5.400 -0.185
-0.500ef 0.930 5.400 -0.172
ea 0.770 5.400 -0.143
f
fj 0.600 6.100 -0.098
-0.500fe 0.930 6.100 -0.152
fg 1.060 6.100 -0.174
fb 0.460 6.100 -0.075
g
gk 0.600 5.780 -0.104
-0.500gf 1.060 5.780 -0.183
gh 0.770 5.780 -0.133
gc 0.460 5.780 -0.080
hhl 1.000 5.460 -0.183
-0.500hg 0.960 5.460 -0.176
hd 0.770 5.460 -0.141
Nudo TramoMomen. Empot. Perf.
iƬ i / ρiƬ
M°ik M°ki
m mn -17.280 17.280 3.86 17.280 4.477
n no -13.230 13.230 5.18 -4.050 -0.782
o op -16.33 16.333 5.24 3.103 0.592
p 3.920 -16.333 -4.167
i ij -21.600 21.600 5.860 21.600 3.686
j jk -16.537 16.537 6.380 -5.063 -0.793
k kl -20.417 20.417 6.440 3.879 0.602
l 5.920 -20.417 -3.449
e ef -25.92 25.92 5.400 25.920 4.800
f fg -19.85 19.85 6.100 -6.075 -0.996
g gh -24.50 24.50 5.780 4.655 0.805
h 5.460 -24.500 -4.487
3 . Momento de Giro ( i/ρi )Ƭ
ρi =2∑Ki
4 . Factor de desplazamiento (tik ) 5 . Momentos de Piso
KikTramo Piso Kik hr Hr
im 1.000 6.400 -0.469
1
1.000 3.300 6.400 4.000
jn 0.600 6.400 -0.281 0.600 3.300 6.400 4.000
ko 0.600 6.400 -0.281 0.600 3.300 6.400 4.000
lp 1.000 6.400 -0.469 1.000 3.300 6.400 4.000
ei 1.000 6.400 -0.469
2
1.000 3.300 6.400 7.000
fj 0.600 6.400 -0.281 0.600 3.300 6.400 7.000
gk 0.600 6.400 -0.281 0.600 3.300 6.400 7.000
hl 1.000 6.400 -0.469 1.000 3.300 6.400 7.000
ae 0.770 4.920 -0.470
3
0.770 4.300 4.920 9.000
bf 0.460 4.920 -0.280 0.460 4.300 4.920 9.000
cg 0.460 4.920 -0.280 0.460 4.300 4.920 9.000
dh 0.770 4.920 -0.470 0.770 4.300 4.920 9.000
DIAGRAMA DE ITERACIONES
m
-0.2
41
-0.1
80 n
-0.2
05
-0.2
02 o
-0.1
83
-0.2
45 p
-0.259 -0.116 -0.115 -0.255-2.062 4.477 -0.782 0.592
-2.776 4.244 -1.376 1.681
-2.815 -0.469 4.699 -0.281 -1.482 -0.281 1.532 -0.469
-2.889 4.735 -1.533 1.627
-2.950 4.915 -1.545 1.588
-3.078 5.175 -1.531 1.518
-3.341 5.722 -1.473 1.332
-3.902 6.870 -1.336 0.926
-5.102 9.327 -1.037 0.049
-7.674 14.590 -0.392 -1.833
-13.186 25.869 0.991 -5.868
-25.002 50.047 3.957 -14.518
-0.171 -0.094 -0.093 -0.169
i
-0.1
59
-0.1
46 j
-0.1
66
-0.1
65 k
-0.1
49
-0.1
62 l
-0.171 -0.094 -0.093 -0.169-3.609 3.686 -0.793 0.602
-3.995 3.197 -0.730 1.645
-3.845 -0.469 3.196 -0.281 -0.688 -0.281 1.397 -0.469
-3.690 2.623 -0.733 1.749
-3.340 1.692 -1.004 2.473
-2.609 -0.303 -1.660 4.127
-1.049 -4.528 -3.093 7.685
2.293 -13.579 -6.181 15.327
9.455 -32.971 -12.805 31.713
24.808 -74.537 -27.008 66.840
57.717 -163.636 -57.454 142.139
111.764 -354.629 -122.720 303.550
-0.185 -0.098 -0.104 -0.183
e
-0.1
72
-0.1
52 f
-0.1
74
-0.1
83 g
-0.1
33
-0.1
76 h
-0.143 -0.075 -0.080 -4.487-7.866 4.800 -0.996 0.805
-26.197 6.079 -0.841 2.524
T=2∑Kik tik=-3kik/2∑Kik Tr =2∑Kik
4 . Distribución de los Momentos de Giro y desplazamientos
-65.233 -0.470 8.828 -0.280 0.079 -0.280 -0.969 -0.470
-148.930 14.208 3.192 -8.935
-328.338 25.684 10.056 -26.315
-712.919 50.192 24.848 -63.620
-1537.302 102.717 56.588 -143.620
-3304.445 215.295 124.636 -315.116
-7092.480 456.614 270.508 -682.737
### 973.902 583.201 -1470.769
### 2082.757 1253.488 -3159.989
-199.759 4459.689 0.000 -6780.990
a b c d
Mik =Kik(2mi+mk+mrik) + M°ik Momento final nudo izquierdo
Mki = Kik(2mk+mi+mrki) + M°ki Momento final nudo derecho
CUADRO DE MOMENTOS FINALES EN VIGAS
Tramo
Coef. De Rigidez Mom. Emp. Perf. Momentos de giro Momentos de desplazmiento Mom. Finales
K K M°ik M°ki mi mk mrik mrki Mik
mn 750 0.93 -17.28 17.28 50.047 3.957 0.000 0.000 79.487
no 857 1.06 -13.23 13.23 3.957 -14.518 0.000 0.000 -20.231
op 771 0.96 -16.33 16.33 -14.518 5.227 0.000 0.000 -39.190
ij 750 0.93 -21.60 21.60 -354.629 -122.720 0.000 0.000 -795.339
jk 857 1.06 -16.54 16.54 -122.720 303.550 0.000 0.000 45.059
kl 771 0.96 -20.42 20.42 303.550 0.000 0.000 0.000 562.399
ef 750 0.93 -25.92 25.92 4,459.689 0.000 0.000 0.000 8,269.101
fg 857 1.06 -19.85 19.85 0.000 -6,780.990 0.000 0.000 -7,207.694
gh 771 0.96 -24.50 24.50 -6,780.990 0.000 0.000 0.000 -13,044.000
CUADRO DE MOMENTOS FINALES EN COLUMNAS
Tramo
Coef. De Rigidez Mom. Emp. Perf. Momentos de giro Momentos de desplazmiento Mom. Finales
K K M°ik M°ki mik mki mrik mrki Mik
im 805 1.00 0.00 0.00 -354.629 50.047 -25.002 25.002 -684.212
jn 485 0.60 0.00 0.00 -122.720 3.957 -25.002 25.002 -159.891
ko 485 0.60 0.00 0.00 303.550 -14.518 -25.002 25.002 340.548
lp 805 1.00 0.00 0.00 0.000 5.227 -25.002 25.002 -19.775
ei 805 1.00 0.00 0.00 4,459.689 -354.629 111.764 -111.764 8,676.513
fj 485 0.60 0.00 0.00 0.000 -122.720 111.764 -111.764 -6.573
gk 485 0.60 0.00 0.00 -6,780.990 303.550 111.764 -111.764 -7,887.999
hl 805 1.00 0.00 0.00 0.000 0.000 111.764 -111.764 111.764
ae 618 0.77 0.00 0.00 0.000 4,459.689 -199.759 199.759 3,280.146
bf 372 0.46 0.00 0.00 0.000 0.000 -199.759 199.759 -91.889
cg 372 0.46 0.00 0.00 0.000 -6,780.990 -199.759 199.759 -3,211.144
dh 618 0.77 0.00 0.00 0.000 0.000 -199.759 199.759 -153.815
Vik = +Vºik-(Mik+Mki)/ Lik Fuerza cortante en el nudo izquierdo
Vki = -Vºki-(Mki+Mik)/ Lki Fuerza cortante en el nudo derecho
CUADRO DE CORTANTES FINALES EN VIGAS
5 . Momentos finales
6 . Cortantes finales
Tramo W L Vºik Vºki Mik Mki Vik Vki
mn 4.00 7.20 14.4 -14.40 79.49 71.18 -6.526 -35.326
no 4.00 6.30 12.6 -12.60 -20.23 -13.35 17.931 -7.269
op 4.00 7.00 14.0 -14.00 -39.19 12.43 17.823 -10.177
ij 5.00 7.20 18.0 -18.00 -795.34 -536.46 202.973 166.973
jk 5.00 6.30 15.8 -15.75 45.06 529.98 -75.526 -107.026
kl 5.00 7.00 17.5 -17.50 562.40 311.82 -107.389 -142.389
ef 6.00 7.20 21.6 -21.60 8,269.10 4,173.43 -1,706.529 -1,749.729
fg 6.00 6.30 18.9 -18.90 -7,207.69 -14,355.85 3,441.685 3,403.885
gh 6.00 7.00 21.0 -21.00 -13,044.00 -6,485.25 2,810.893 2,768.893
CUADRO DE CORTANTES FINALES EN COLUMNAS
Tramo W L Vºij Vºji Mij Mji Vij Vji
im 0.00 3.30 0 0 -684.21 -229.53 276.893 276.893
jn 0.00 3.30 0 0 -159.89 -53.88 64.780 64.780
ko 0.00 3.30 0 0 340.55 179.71 -157.654 -157.654
lp 0.00 3.30 0 0 -19.77 35.46 -4.752 -4.752
ei 0.00 3.30 0 0 8676.51 3638.67 -3,731.873 -3,731.873
fj 0.00 3.30 0 0 -6.57 -214.32 66.938 66.938
gk 0.00 3.30 0 0 -7888.00 -3771.39 3,533.149 3,533.149
hl 0.00 3.30 0 0 111.76 -111.76 - -
ae 0.00 4.30 0 0 3280.15 7021.74 -2,395.786 -2,395.786
bf 0.00 4.30 0 0 -91.89 91.89 - -
cg 0.00 4.30 0 0 -3211.14 -6146.62 2,176.225 2,176.225
dh 0.00 4.30 0 0 -153.81 153.81 - -
Ubicación punto de inflexión de los cortantes Momento Máximo Positivo
Se calcula la distancia al punto de inflexión para conocer Aplicamos un corte en el punto de inflexión del cortante
la ubicación de momento máximo positivo en el DMF de en el tramo ik.
la viga.
Se considera los cortantes como valores absolutos. Viky W x
Vikx T
i x
Mab X
La determinación de los sentidos de las fuerzas y Momentos
X de la estructura, se obtiene de los diagramas de Fuerzas
cortantes y Momentos.
L Para el desarrollo del problema se tomarán los signos, tal
como se indica en los diagramas de fuerzas cortantes y
Momentos Flectores.
Por esta razón los dos primeros monomios de la ecuación
que se expresa se ha considerado con signo positivo.
7 . Cálculo del Momento Máximo positivo M+ik y su ubicación (X,p,q)
V1
M+ik
V2
X = V1. L / (V1+V2)
M+ik =Vik. X + Mik - W.X2 /2
Longitud horizontal máxima del del diagrama de momento máximo positivo (L 1)
Nota: Los signos de los momentos que se obtienen directamente
de las cargas distribuidas y otras, se determinarán por
análisis.
+
-
Tramo W L Vik Vki Mik X p q
Tn/m m. Tn Tn m. Tn-m m. m. m.
mn 4.00 7.20 -6.526 -35.326 79.49 1.12 69.638 11.802 -4.78 0.18
no 4.00 6.30 17.931 -7.269 -20.23 10.60 -54.766 Err:502 Err:502 Err:502
op 4.00 7.00 17.823 -10.177 -39.19 16.32 -280.931 Err:502 Err:502 Err:502
ij 5.00 7.20 202.973 166.973 -795.34 3.95 -32.544 Err:502 Err:502 Err:502
jk 5.00 6.30 -75.526 -107.026 45.06 2.61 -168.780 Err:502 Err:502 Err:502
kl 5.00 7.00 -107.389 -142.389 562.40 3.01 216.561 18.614 -6.30 -5.32
ef 6.00 7.20 -1706.529 -1749.729 8269.10 3.56 2,164.469 53.721 -23.31 -23.22
fg 6.00 6.30 3441.685 3403.885 -7207.69 3.17 3,663.381 69.889 -31.78 -31.81
gh 6.00 7.00 2810.893 2768.893 -13044.00 3.53 -3,169.127 Err:502 Err:502 Err:502
8 . Diagrama de fuerzas cortantes y momentos flectores
8.01 Diagrama de fuerzas cortantes (Tn.)
-6.53 17.93 17.82
m n o p
166.97 -7.27 -10.18
M+
L1
M+ = W* L12 / 8
L1 = 2 (2 M+ / W )1/2
CUADRO DE MOMENTOS MAXIMOS POSITIVOS (M +ik) Y SU UBICACION (X, p, q)
M+ik L1
8.01.1 DIAGRAMA DE FUERZAS CORTANTES EN VIGAS
202.97 -75.53 -2395.79
i j k l
166.97 -107.03 -142.39
-1706.53 3441.69 0.00
e f g h
-1749.73 3403.89 2768.89
a b c d
m n o p
276.
89
64.7
8
###
-4.7
5
i j k l
-373
1.87
66.9
4
###
0.00
e f g h
-239
5.79
0.00 ###
0.00
a b c d
X1 X2 X3
8.01.2 DIAGRAMA DE FUERZAS CORTANTES EN COLUMNAS
8.02 Diagrama de Momentos flectores en vigas (Tn-m)
-71.18 -20.23 13.35 -39.19
79.49 -12.43
m n o p
p 0.00 m. q r 0.00 m. s t 0.00 m. u
536.46 45.06 -529.98 562.40
-795.34 -311.82
i j k l
p 0.00 m. q r 0.00 m. s t 0.00 m. u
-4,173.43 -7,207.69 14,355.85 -13,044.00
8,269.10 6,485.25
e f g h
p 0.00 m. q r 0.00 m. s t 0.00 m. u
8.02.1 DIAGRAMA DE MOMENTOS FLECTORES EN VIGAS
a b c d
229.53 53.88 -179.71 35.46
m n o p
-3638.67 214.32 3771.39 111.76
i -684.21 j -159.89 k 340.55 -19.77 l
-7021.74 -91.89 6146.62 -153.81
e 8676.51 j -6.57 k -7888.00 111.76 h
a 3280.15 b -91.89 c -3211.14 -13044.00 d
9 . Diagrama de reacciones actuantes en la estructura
DIAGRAMA DE REACCIONES EN LA BASE DE LA ESTRUCTURA
4.00 Ton/m 4.00 Ton/m 4.00 Ton/m
8.02.2 DIAGRAMA DE MOMENTOS FLECTORES EN COLUMNAS
H1
m n o p
3.30
5.00 Ton/m 5.00 Ton/m 5.00 Ton/m
H2
i j k l
3.30
6.00 Ton/m 6.00 Ton/m 6.00 Ton/m
H3
e f g h
4.30
a b c d
-2395.79 Tn. 0.00 Tn. 2176.22 Tn. 0.00 Tn.
3280.15 Tn-m -91.89 Tn-m -3211.14 Tn-m -13044.00 Tn-m
-1510.08 Tn. 4799.87 Tn. -5667.55 Tn. -2616.33 Tn.
7.20 m 6.30 m 7.00 m
DISEÑO SISMORESITENTELamina
MT-01
3.30 m
3.30 m
4.30 m
4.00 Ton
3.00 Ton
2.00 Ton
Viga 30.00 cm
60.00 cm
Columna a y d 35.00 cm
45.00 cm
Columna b y c 30.00 cm
40.00 cm
Coeficiente de Rigidez (K)
Representación
0.93
1.06
0.96
0.93
1.06
0.96
0.93
1.06
0.96
1.00
0.60
0.60
1.00
1.00
0.60
0.60
1.00
0.77
0.46
0.46
0.77
-Hr. hr/Tr
-2.062
-2.062
-2.062
-2.062
-3.609
-3.609
-3.609
-3.609
-7.866
-7.866
-7.866
-7.866
p
-0.255-4.167
-2.906
-0.469 -3.125
-3.028
-3.047
-3.000
-2.908
-2.699
-2.250
-1.284
0.787
5.227
-0.169
l
-0.169-3.449
-2.923
-0.469 -3.119
-3.061
-3.148
-3.311
-3.689
-4.500
-6.245
-9.985
-18.003
0.000
-0.183
h
-4.487-4.487
31.959
-0.470 113.888
289.671
666.594
1474.642
3206.778
6919.784
14878.961
31940.199
68512.548
0.000
Mom. Finales
Mik Mki
79.487 71.183
-20.231 -13.354
-39.190 12.432
-795.339 -536.464
45.059 529.980
562.399 311.824
8,269.101 4,173.431
-7,207.694 -14,355.853
-13,044.000 -6,485.250
Mom. Finales
Mik Mki
-684.212 -229.533
-159.891 -53.883
340.548 179.709
-19.775 35.455
8,676.513 3,638.667
-6.573 -214.323
-7,887.999 -3,771.393
111.764 -111.764
3,280.146 7,021.735
-91.889 91.889
-3,211.144 -6,146.621
-153.815 153.815
q
m.
0.18
Err:502
Err:502
Err:502
Err:502
-5.32
-23.22
-31.81
Err:502
3.30 m
3.30 m
4.30 m