PORTICO PRINCIPAL - EJE A-A ∆3
3.10
∆3
3.10
∆3
3.10
10.23 T K=0.00046
N 0 2 . 3
6 1 0 0 0 . 0 = K
K=0.0009
O
P
6 1 0 0 0 . 0 = K
3.10
∆2
K=0.00046
6 1 0 0 0 . 0 = K
3.10
∆2
6 1 0 0 0 . 0 = K
∆2
3.10
8.85 T K=0.00046
J 0 2 . 3
6 1 0 0 0 . 0 = K
K=0.0009
K
L
6 1 0 0 0 . 0 = K
∆1
3.10
K=0.00046
6 1 0 0 0 . 0 = K
3.10
∆1
6 1 0 0 0 . 0 = K
∆1
3.10
4.33 T K=0.00046
E 0 2 . 3
6 1 0 0 0 . 0 = K
K=0.0009
F
G
6 1 0 0 0 . 0 = K
A
6 1 0 0 0 . 0 = K
B
HA
K=0.00046 6 1 0 0 0 . 0 = K
C
HB
HC
5.6
2.9
HD 5.6
ESPRESIONES DE MOMENTOS
NUDO
NUDO
NUDO
A
E
J
MAE =
0.00016(2ΘA+ΘE - 3Ψ1)
MEA =
0.00016(2ΘE + ΘA - 3Ψ1)
MEI =
0.00016(2ΘE + ΘJ - 3Ψ2)
MEF =
0.00046(2ΘE + ΘF)-8.1
MJE =
0.00016(2ΘJ + ΘE- 3ψ2)
MJK =
0.00046(2ΘJ + ΘK)-8.1
MJN =
0.00016(2ΘJ + ΘN-3ψ3)
NUDO
NUDO
NUDO
MNJ =
0.00016(2ΘN +ΘJ - 3ψ3)
C
G
L
MCG =
0.00016(2ΘC+ΘG -3ψ1)
MGC =
0.00016(2θG + ΘC-3ψ1)
MGL =
0.00016(2θG +ΘL -3ψ2)
MGH =
0.00046(2θG +ΘH)-8.1
MGF =
0.0009(2θG + ΘF)+2.17
MLG =
0.00016(2θL+ ΘG- 3ψ2)
MLP =
0.00016(2θL+ΘP-3ψ3)
MLM =
0.00046(2θL +ΘM)-8.1
MLK =
0.0009(2θL +ΘK)+2.17
ESPRESIONES DE MOMENTOS
NUDO
NUDO
NUDO
A
E
J
MAE =
0.00016(2ΘA+ΘE - 3Ψ1)
MEA =
0.00016(2ΘE + ΘA - 3Ψ1)
MEI =
0.00016(2ΘE + ΘJ - 3Ψ2)
MEF =
0.00046(2ΘE + ΘF)-8.1
MJE =
0.00016(2ΘJ + ΘE- 3ψ2)
MJK =
0.00046(2ΘJ + ΘK)-8.1
MJN =
0.00016(2ΘJ + ΘN-3ψ3)
NUDO
NUDO
NUDO
NUDO
N
MNJ =
0.00016(2ΘN +ΘJ - 3ψ3)
MNO =
0.00046(2ΘN + ΘO)-8.1
NUDO NUDO
NUDO
NUDO
B
F
K
MBF =
O
MFK =
0.00016(2θF + Θk -3ψ2)
MFB =
0.00016(2θF+ ΘB- 3ψ1)
MFG =
0.0009(2θF+ΘG)-2.17
MFE =
0.00046(2θF +ΘE)+8.1
MKF =
0.00016(2θk+ΘF-3ψ2)
MKO =
0.00016(2θk+θO-3ψ3)
MKL =
0.0009(2θK +θL)-2.17
MKJ =
0.00046(2θK+θJ)+8.1
MOK =
G
L
P
0.00016(2ΘB + ΘF - 3Ψ1)
NUDO
NUDO
NUDO NUDO
C
D
Q
M
0.00016(2θo+ΘK-3ψ3)
MCG =
0.00016(2ΘC+ΘG -3ψ1)
MGC =
0.00016(2θG + ΘC-3ψ1)
MGL =
0.00016(2θG +ΘL -3ψ2)
MGH =
0.00046(2θG +ΘH)-8.1
MGF =
0.0009(2θG + ΘF)+2.17
MLG =
0.00016(2θL+ ΘG- 3ψ2)
MLP =
0.00016(2θL+ΘP-3ψ3)
MLM =
0.00046(2θL +ΘM)-8.1
MLK =
0.0009(2θL +ΘK)+2.17
MPL =
0.00016(2θP+ 0.00016(2θP+ ΘL-3 ψ3)
MPQ =
0.00046(2θP +ΘQ)-8.1
MPO=
0.0009(2θP +ΘO)+2.17
MDH =
0.00016(2θD + ΘH -3ψ1)
MQM =
0.00016(2θQ+θM- 3ψ3)
MQP =
0.00046(2θQ +ΘP)+8.1
MMQ =
0.00016(2θM+ΘQ0.00016(2θM+ΘQ- 3ψ3)
MMH =
0.00016(2θM+θH- 3ψ2)
MML =
0.00046(2θM +ΘL)+8.1
MHD =
0.00016(2θH +θD -3ψ1)
MHM =
0.00016(2θH+θM 0.00016(2θH+θM - 3ψ2)
MHG =
0.00046(2θH + θG)+8.1
MON = 0.00046(2θO+ΘN) +8.1 MOP = 0.0009(2θO +θP)-2.17
NUDO
H
NUDO
NUDO
F
K
MFB =
0.00016(2θF+ ΘB- 3ψ1)
MFG =
0.0009(2θF+ΘG)-2.17
MFE =
0.00046(2θF +ΘE)+8.1
MKF =
0.00016(2θk+ΘF-3ψ2)
MKO =
0.00016(2θk+θO-3ψ3)
MKL =
0.0009(2θK +θL)-2.17
MKJ =
0.00046(2θK+θJ)+8.1
NUDO
O
MOK =
Q
NUDO
NUDO NUDO
D
M
0.00016(2θo+ΘK-3ψ3)
MDH =
0.00016(2θD + ΘH -3ψ1)
MQM =
0.00016(2θQ+θM- 3ψ3)
MQP =
0.00046(2θQ +ΘP)+8.1
MMQ =
0.00016(2θM+ΘQ0.00016(2θM+ΘQ- 3ψ3)
MMH =
0.00016(2θM+θH- 3ψ2)
MML =
0.00046(2θM +ΘL)+8.1
MHD =
0.00016(2θH +θD -3ψ1)
MHM =
0.00016(2θH+θM 0.00016(2θH+θM - 3ψ2)
MHG =
0.00046(2θH + θG)+8.1
MON = 0.00046(2θO+ΘN) +8.1 MOP = 0.0009(2θO +θP)-2.17
H
NUDO
ECUACION DE CONDICIÓN
NUDO E : ΣME = 0
NUDO K : ΣMK = 0
MEA +MEJ +MEF =
ΣMP= 0
NUDO P :
MKF + MKO + MKL + MKJ =
NUDO J : ΣMJ = 0
MPL + MPQ +MPO =
NUDO F : ΣMF = 0
MJE +MJK+MJN =
ΣMQ = 0
NUDO Q :
MFK + MFB + MFG + MFE =
NUDO N: ΣMN = 0
MQM + MQP =
NUDO G : ΣMG = 0
MNJ+MNO =
ΣMM = 0
NUDO M :
MGC + MGL + MGH +MGF =
NUDO O: ΣMO = 0
MMH + MMQ + MML =
NUDO L : ΣML = 0
MO MOK + MON + MOP =
ΣMH = 0
NUDO H :
MLG + MLP + MLM + MLK =
MHD + MHM + MHG =
CORTANTES ACTUANTES VA + VB + VC + VD + 7.80 + 15.93 + 18.42 = 0 MAE + ME
+
3.20
MBF + MFB
+
3.20
MCG + MGC
+
3.20
MDH+MHD
+
42.15
=
0.00
+
34.35
=
0.00
3.20
VE + VF + VG + VH + 15.93 + 18.42 = 0
MEJ + M
+
MFK +MKF
+
MGL +MLG
+
MHM + MMH
NUDO N: ΣMN = 0
NUDO G : ΣMG = 0
MNJ+MNO =
ΣMM = 0
NUDO M :
MGC + MGL + MGH +MGF =
NUDO O: ΣMO = 0
MMH + MMQ + MML =
NUDO L : ΣML = 0
MO MOK + MON + MOP =
ΣMH = 0
NUDO H :
MLG + MLP + MLM + MLK =
MHD + MHM + MHG =
CORTANTES ACTUANTES VA + VB + VC + VD + 7.80 + 15.93 + 18.42 = 0 MAE + ME
+
3.20
MBF + MFB
+
3.20
MCG + MGC
+
MDH+MHD
3.20
+
42.15
=
0.00
+
34.35
=
0.00
+
18.42
=
0.00
3.20
VE + VF + VG + VH + 15.93 + 18.42 = 0
MEJ + M
+
3.2
MFK +MKF
+
3.20
MGL +MLG
+
MHM + MMH
3.2
3.2
VJ + VK + VL + VM + 18.42 = 0 MJN + M
+
3.2
MKO +MOK 3.20
+
MLP +MPL
+
MMQ + MQM
3.2
3.2
MOMENTOS FINALES
A
E
MAE =
-15.90
MEA =
-11.01 -7.22 18.21
MEJ = MEF =
NUDO
NUDO
C
G
MCG =
-18.82
MGC =
-16.84 -14.95 8.92 23.08
MGL = MGH =
MJE =
J
MJK = MJN =
-8.69 10.40 -1.98
MGF =
MLG =
NUDO
L
MLP = MLM =
N
MNJ = MNO =
-3.05 2.73
MLK =
NUDO
B
-20.06
P
MPL =
-15.40 -7.02 4.15 18.22
-7.70 -3.11
MOMENTOS FINALES
A
E
MAE =
-15.90
MEA =
-11.01 -7.22 18.21
MEJ = MEF =
NUDO
NUDO
C
G
MCG =
-18.82
MGC =
-16.84 -14.95 8.92 23.08
MGL = MGH =
MJE =
J
MJK = MJN =
-8.69 10.40 -1.98
MGF =
MLG =
NUDO
L
MLP = MLM =
N
MNJ = MNO =
-3.05 2.73
MLK =
NUDO
B
MBF =
MFK =
F
MFB = MFG = MFE =
P
-20.06 -18.42 -19.32 13.21 24.00
MPO=
-7.70 -3.11 10.46 -17.91
MPL = MPQ =
NUDO
D
MDH =
NUDO
Q
MQP =
MQM =
K
MKF =
-18.62
MKO =
-10.51 9.45 19.35
MKL = MKJ =
MMQ =
NUDO
O
MOK = MON = MOP =
M
-11.39 12.06 -0.64
MMH = MML =
MHD =
NUDO
H
-15.40 -7.02 4.15 18.22
MHM = MHG =
-9.81 9.71
-7.71 -13.82 21.22
-15.02 -12.80 27.45
MKO = MKL = MKJ =
-10.51 9.45 19.35 MMQ =
NUDO
O
MOK = MON = MOP =
M
-11.39 12.06 -0.64
MMH = MML =
MHD =
NUDO
H
MHM = MHG =
-7.71 -13.82 21.22
-15.02 -12.80 27.45
∆3
Q 1.- MOMENTOS DE EMPOTRAMIENTO
4. CALCULO Columnas
∆2
M
∆1
H
EF = -
FE=
JK = -
K J=
NO = -
ON=
-8.10 -8.10 -8.10
b= h= I=
OP = -
PO=
KL = -
L K=
FG = -
GF=
GH = -
HG=
MLM = -MML= PQ = -
QP =
-2.17 -2.17 -2.17 -8.10
Vigas
-8.10 -8.10
I=
b= h=
∆3
Q 4. CALCULO
1.- MOMENTOS DE EMPOTRAMIENTO
Columnas ∆2
M
∆1
H
EF = -
FE=
JK = -
K J=
NO = -
-8.10 -8.10 -8.10
ON=
b= h= I=
OP = -
PO=
KL = -
L K=
FG = -
GF=
GH = -
HG=
MLM = -MML= PQ = -
QP =
-2.17 -2.17 -2.17 -8.10
Vigas
-8.10 -8.10
I=
b= h=
5. CALCULO 2.- INCOGNITAS + ECUACION DE CONDICION Columnas =
D
ΘA = ΘB = ΘC = ΘD = ΣME= ΣMF=
0 0 0 0 0
ΘE = ΘF = ΘG = ΘH = ΘJ = ΘK =
ΣMG= ΣMH=
0 0 0 0 0 0 0 0 0 0
ΘL = ΘM =
ΣMJ= ΣMK= ΣML= ΣMM= ΣMN= ΣMO= ΣMP= ΣMQ=
ΘN = ΘO = ΘP = ΘQ =
?
Vigas= Para: E,F = I,J
? Vigas= Para: Para: F,G F,G = J,
? ? ? ?
3.- DESPLAZAMIENTOS DESPLAZAMIENTOS
COLUMNAS AE, BF, CG, DH =
SE DESPLAZAN
COLUMNAS EI,FJ,GK,HL=
SE DESPLAZAN Δ2
COLUMNAS IM,JN,KO,LP =
SE DESPLAZAN Δ3
Δ1
ΣMG= ΣMH= ΣMJ= ΣMK= ΣML= ΣMM= ΣMN= ΣMO= ΣMP= ΣMQ=
0 0 0 0 0 0 0 0 0 0
ΘL = ΘM = ΘN = ΘO = ΘP = ΘQ =
? ? ? ?
3.- DESPLAZAMIENTOS DESPLAZAMIENTOS
COLUMNAS AE, BF, CG, DH =
SE DESPLAZAN
COLUMNAS EI,FJ,GK,HL=
SE DESPLAZAN Δ2
COLUMNAS IM,JN,KO,LP =
SE DESPLAZAN Δ3
Δ1
6.- ROTACION EN CUERDAS
E INERCIA ΨAE = ΨBF = ΨCG = ΨDH =
Δ1 .
=
ΨEI = ΨFJ = ΨGK = ΨHL =
3.20
=
0.40 m
Ψ1
0.25 m 0.00052
ΨIM = ΨJN = ΨKO = ΨLP = 0.25 m 0.50 m 0.00260
Δ3- Δ2- Δ .
=
Ψ3
6.- ROTACION EN CUERDAS
E INERCIA ΨAE = ΨBF = ΨCG = ΨDH =
Δ1 .
=
ΨEI = ΨFJ = ΨGK = ΨHL =
3.20
=
0.40 m
Ψ1
0.25 m 0.00052
ΨIM = ΨJN = ΨKO = ΨLP = 0.25 m 0.50 m 0.00260
E RIGIDEZ 0.00016 0.00046 = M,N = O,P = K,L = G,H 0.0009
K = N,O
Δ3- Δ2- Δ .
=
Ψ3
ANALISIS ANALISIS DE PORTICO POR EL MOTODO DE CROSS DATOS
LONGITUD RI RIGIDEZ K
FD
NUD O A
AE
3.2
0.00016
0
EA
3.2
0.00016
0.21
EF
5.6
0.00046
0.59
EJ
3.2
0.00016
0.21
JN
3.2
0.00016
0.21
JK
5.6
0.00046
0.59
JE
3.2
0.00016
0.21
NO
5.6
0.00046
0.74
NJ
3.2
0.00016
0.26
BF
3.2
0.00016
0
FG
2.9
0.0009
0.54
FK
3.2
0.00016
0.1
FB
3.2
0.00016
0.1
FE
5.6
0.00046
0.27
KO
3.2
0.00016
0.1
KL
2.9
0.0009
0.54
18.42 T
E
J
N B
F
15.93 T
ANALISIS ANALISIS DE PORTICO POR EL MOTODO DE CROSS DATOS
LONGITUD RI RIGIDEZ K
FD
NUD O A
AE
3.2
0.00016
0
EA
3.2
0.00016
0.21
EF
5.6
0.00046
0.59
EJ
3.2
0.00016
0.21
JN
3.2
0.00016
0.21
JK
5.6
0.00046
0.59
JE
3.2
0.00016
0.21
NO
5.6
0.00046
0.74
NJ
3.2
0.00016
0.26
BF
3.2
0.00016
0
FG
2.9
0.0009
0.54
FK
3.2
0.00016
0.1
FB
3.2
0.00016
0.1
FE
5.6
0.00046
0.27
KO
3.2
0.00016
0.1
KL
2.9
0.0009
0.54
KF
3.2
0.00016
0.1
KJ
5.6
0.00046
0.27
OP
2.9
0.0009
0.59
OK
3.2
0.00016
0.11
ON
5.6
0.00046
0.3
CG
3.2
0.00016
0
GL
3.2
0.00016
0.1
GH
5.6
0.00046
0.27
GF
2.9
0.0009
0.54
GC
3.2
0.00016
0.1
LP
3.2
0.00016
0.1
LM
5.6
0.00046
0.27
LK
2.9
0.0009
0.54
LG
3.2
0.00016
0.1
PQ
5.6
0.00046
0.3
PL
3.2
0.00016
0.11
PO
2.9
0.0009
0.59
DH
3.2
0.00016
0
HM
3.2
0.00016
0.21
HD
3.2
0.00016
0.21
HG
5.6
0.00046
0.59
MQ
3.2
0.00016
0.21
MH
3.2
0.00016
0.21
ML
5.6
0.00046
0.59
QM
3.2
0.00016
0.26
QP
5.6
0.00046
0.74
Mto. DE EMPOTRAMIEMTO
18.42 T
E
J
N B
15.93 T
F
K
7.80 T O C
G
L
P D H
M
Q
MEF=MJK=MNO=MGH=MLM=MPQ MFG=MKL=MOP
8.10 2.17
CALCULO DE PÓRTICO SIN DESPLAZAMIENTO (Mi) NJ
NO
0.260
JN
OK
0.300
-8.100
8.100
2.106
5.994
-1.779
-0.652
-3.499
0.851
-0.890
2.997
-0.297
1.749
0.010
0.029
-1.335
-0.489
-2.625
-0.116
-0.667
0.014
-0.168
1.313
0.204
0.580
-0.348
-0.127
-0.684
3.05
-3.05
7.65
-1.73
-5.92
JK
0.210
KJ
KF
0.590
0.270
-8.100
8.100
0.100
0.110
OP
0.740
JE
0.210
ON
0.590 -2.170
KO 0.100
KL 0.540 -2.170
1.701
1.701
4.779
-1.601
-0.593
-0.593
-3.202
1.053
0.851
-0.801
2.390
-0.297
-0.326
1.601
-0.232
-0.232
-0.651
-0.909
-0.337
-0.337
-1.819
0.005
-0.005
-0.455
-0.325
-0.185
-0.245
0.909
0.096
0.096
0.268
-0.042
-0.015
-0.015
-0.083
2.62
2.41
-4.96
7.61
-1.43
-1.52
-4.76
EA
EJ
0.210
EF
FK 0.100
FB 0.100
FG
0.590
0.270
-8.100
8.100
1.701
4.779
-1.601
-0.593
0.851
-0.801
2.390
-0.297
-0.010
-0.010
-0.029
-0.997
-0.369
0.000
-0.116
-0.499
-0.015
-0.168
0.129
0.129
0.363
-0.220
-0.081
-0.081
-0.440
1.82
2.55
-4.29
7.66
-1.51
-1.04
-5.21
1.701
0.210
FE
-2.170 -0.593 -0.369
-0.005
-0.185
0.065
-0.041
BF
3.054
NJ 1.77 1.774 4
-1.995 0.997
-0.297
0.91
-3.202 1.601
0.851
AE
0.540
-0.52
2.623
2.410
JE 1.55 1.551 1
2.554
1.820
EA 0.85 0.853 3
0.910
∑ 0 =
Q31= Q21= Q11=
0.00 0.00 0.00
PORTICO PRINCIPAL - EJE A-A
∆3
N 0 2 . 3
3.10
∆3
K=0.00046
6 1 0 0 0 . 0 = K
O
3.10
∆2
K=0.00046
3.10
K=0.0009
J
K
6 1 0 0 0 . 0 = K
6 1 0 0 0 . 0 = K
∆1
3.10
E 0 2 . 3
K=0.0009
6 1 0 0 0 . 0 = K
∆2
0 2 . 3
3.10
∆1
K=0.00046
3.10
K=0.0009
F
6 1 0 0 0 . 0 = K
6 1 0 0 0 . 0 = K
A
B
HA
HB 5 .6
2 .9
PO 0.590
PL 0.110
2.170
LK 0.540
PQ
QP
0.300
0.740
-8.100
8.100
QM 0.260
3.499
0.652
1.779
-5.994
-2.106
-1.749
0.297
-2.997
0.890
-0.851
2.625
0.489
1.335
-0.029
-0.010
-1.313
0.168
-0.014
0.667
0.116
0.684
0.127
0.348
-0.580
-0.204
5.92
1.73
-7.65
3.05
-3.05
LG 0.100
LP 0.100
2.170
LM
ML
0.270
0.590
-8.100
8.100
MQ
MH
0.210
0.210
3.202
0.593
0.593
1.601
-4.779
-1.701
-1.701
-1.601
0.297
0.326
-2.390
0.801
-1.053
-0.851
1.819
0.337
0.337
0.909
0.651
0.232
0.232
-0.909
0.185
0.245
0.325
0.455
-0.005
0.005
0.083
0.015
0.015
0.042
-0.268
-0.096
-0.096
4.76
1.43
1.52
-7.61
4.96
-2.62
-2.41
GF 0.540
GL 0.100
GC 0.100
2.170 0.593
GH
HG
0.270
0.590
-8.100
8.100
1.601
-4.779
-2.390
0.801
0.997
0.029
0.015
0.499
HD
HM
0.210
0.210
-1.701
-1.701
3.202
0.593
-1.601
0.297
1.995
0.369
-0.997
0.168
0.440
0.081
0.081
0.220
-0.363
-0.129
-0.129
5.21
1.51
1.04
-7.66
4.29
-1.82
-2.55
0.369
0.185
0.005
0.041
-0.065
0.52
DH
PL 1.016
0.010 0.116
-0.851
1.734
OK -1.016
0.010
0.297
CG
-1.734
-0.851
-0.91
-1.5161
1.516
-1.426
1.426
KF -0.917
LG 0.917
-1.509
1.509
-1.044
1.044
FB -0.489
-0.522
GC 0.489
0.522
∆3
P
3.10
∆3
K=0.00046
6 1 0 0 0 . 0 = K
Q 6 1 0 0 0 . 0 = K
∆2
∆2
3.10
K=0.00046
L
M
6 1 0 0 0 . 0 = K
6 1 0 0 0 . 0 = K
∆1
∆1
3.10
K=0.00046
G
H
6 1 0 0 0 . 0 = K
6 1 0 0 0 . 0 = K
C
D
HC
HD 5.6
-3.054
QM -1.7 -1.774 74
-2.623
-2.410
MH -1.5 -1.551 51
-2.554
-1.820
HD -0.8 -0.853 53 -0.910
