Download - Metodo Cros
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MÉTODO CROSS
W=3.797 W=3.92 W=3.873 W=3.92H4=9.493Tn
T U V W X
W=3.797 W=3.92 W=3.873 W=3.92H3=16.612Tn
O P Q R S
W=3.797 W=3.92 W=3.873 W=3.92H2=21.358Tn
K L M N Ñ
W=3.797 W=3.92 W=3.873 W=3.92H1=23.732Tn
F G H I J
A B C D E
6.00 4.50 5.00 4.50
ELEMENTOS ESTRUCTURALES MODULO DE ELASTICIDAD DEL CONCRETO
ELEMENTO SECCIÓN INERCIA E = 234787.137637COLUMNA: 0.35 X 0.35 0.001251
VIGA P : 0.25 X 0.50 0.002604VIGA S : 0.25 X 0.40 0.001333
CARGAS
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CARGAS HORIZONTALESH1 = 23.732 TnH2 = 21.358 TnH3 = 16.612 TnH4 = 9.493 Tn
PESO DE CARGAS DISTRIBUIDAS ( W )TRAMO 1 TRAMO2 TRAMO3 TRAMO4
WFG = 3.797 Tn/m WGH = 3.920 Tn/m WHI = 3.873 Tn/m WIJ = 3.920WKL = 3.797 Tn/m WLM = 3.920 Tn/m WMN = 3.873 Tn/m WNÑ = 3.920WOP = 3.797 Tn/m WPQ = 3.920 Tn/m WQR = 3.873 Tn/m WRS = 3.920WTU = 3.797 Tn/m WUV = 3.920 Tn/m WVW = 3.873 Tn/m WWX = 3.920
LONGITUDES
LONGITUD DE VIGASFG = KL = OP = TU = 6GH = LM = PQ = UV = 4.5HI = MN = QR = VW = 5IJ = NÑ = RS = WX = 4.5
LONGITUD DE COLUMNASAF = BG = CH = DI = JE = 2.9FK = GL = HM = IN = JÑ = 2.9KO = LP = MQ = NR = ÑS = 2.9TO = PU = QV = RW = SX = 2.9
RIGIDECES RELATIVAS
RIGIDECES RELATIVAS K = I/LC KAF = 4.312E-04 C KFK = 4.312E-04 C KKO = 4.312E-04 C KOTC KBG = 4.312E-04 C KGL = 4.312E-04 C KLP = 4.312E-04 C KPUC KCH = 4.312E-04 C KHM = 4.312E-04 C KMQ = 4.312E-04 C KQVC KDI = 4.312E-04 C KIN = 4.312E-04 C KNR = 4.312E-04 C KRWC KEJ = 4.312E-04 C KJÑ = 4.312E-04 C KÑS = 4.312E-04 C KSX
V KFG = 4.340E-04 V KKL = 4.340E-04 V KOP = 4.340E-04 V KTUV KGH = 5.787E-04 V KLM = 5.787E-04 V KPQ = 5.787E-04 V KUVV KHI = 5.208E-04 V KMN = 5.208E-04 V KQR = 5.208E-04 V KVWV KIJ = 5.787E-04 V KNÑ = 5.787E-04 V KRS = 5.787E-04 V KWX
MᵒFG = - MᵒGF = - 11.391 MᵒGH = - MᵒHG = - 6.615MᵒKL = - MᵒLK = - 11.391 MᵒLM = - MᵒML = - 6.615MᵒOP = - MᵒPO = - 11.391 MᵒPQ = - MᵒQP = - 6.615MᵒTU = - MᵒUT = - 11.391 MᵒUV = - MᵒVU = - 6.615
MOMENTOS DE EMPOTRAMIENTO ( Mᵒ )
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MᵒHI = - MᵒIH = - 8.069 MᵒIJ = - MᵒJI = - 6.615MᵒMN = - MᵒNM = - 8.069 MᵒNÑ = - MᵒÑN = - 6.615MᵒQR = - MᵒRQ = - 8.069 MᵒRS = - MᵒSR = - 6.615MᵒVW = - MᵒWV = - 8.069 MᵒWX = - MᵒXW = - 6.615
CROSS SIN DESPLAZAMIENTO
MOMENTOS DE EMPOTRAMIENTOS
MᵒFG = - MᵒGF = - 11.391MᵒKL = - MᵒLK = - 11.391MᵒOP = - MᵒPO = - 11.391MᵒTU = - MᵒUT = - 11.391
MᵒGH = - MᵒHG = - 6.615MᵒLM = - MᵒML = - 6.615MᵒPQ = - MᵒQP = - 6.615MᵒUV = - MᵒVU = - 6.615
MᵒHI = - MᵒIH = - 8.069MᵒMN = - MᵒNM = - 8.069MᵒQR = - MᵒRQ = - 8.069MᵒVW = - MᵒWV = - 8.069
MᵒIJ = - MᵒJI = - 6.615MᵒNÑ = - MᵒÑN = - 6.615MᵒRS = - MᵒSR = - 6.615MᵒWX = - MᵒXW = - 6.615
FACTORES DE DISTRIBUCIÓN
1ER NIVEL 1ER NIVEL 2DO NIVEL 3ER NIVEL
NUDO NUDO NUDO NUDO
A AF = 0.000F
FA = 0.333K
KF = 0.333O
OK = 0.333B BG = 0.000 FK = 0.333 KL = 0.335 OP = 0.335C CH = 0.000 FG = 0.334 KO = 0.332 OT = 0.332D DI = 0.000
G
GB = 0.230
L
LG = 0.230
P
PL = 0.230E EJ = 0.000 GF = 0.231 LK = 0.231 PO = 0.231
GL = 0.230 LP = 0.230 PU = 0.230GH = 0.309 LM = 0.309 PQ = 0.309
H
HC = 0.220
M
MH = 0.220
Q
QM = 0.220HG = 0.295 ML = 0.295 QP = 0.295HM = 0.220 MQ = 0.220 QV = 0.220
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
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H
HI = 0.265
M
MN = 0.265
Q
QR = 0.265
I
ID = 0.220
N
NI = 0.220
R
RN = 0.220IH = 0.265 NM = 0.265 RQ = 0.265IN = 0.220 NR = 0.220 RW = 0.220IJ = 0.295 NÑ = 0.295 RS = 0.295
JJE = 0.299
ÑÑJ = 0.299
SSÑ = 0.299
JI = 0.402 ÑN = 0.402 SR = 0.402JÑ = 0.299 ÑS = 0.299 SX = 0.299
TO TU UT UP UV0.498 0.502 0.301 0.299 0.400
-11.39 11.39 -6.615.67 5.72 -1.44 -1.43 -1.911.89 -0.72 2.86 -0.55 0.27-0.58 -0.59 -0.78 -0.77 -1.03-0.69 -0.39 -0.29 -0.13 0.200.54 0.54 0.07 0.07 0.090.16 0.03 0.27 0.12 0.03-0.10 -0.10 -0.13 -0.13 -0.17
0.00 6.89 -6.89 0.00 11.95 -2.82 -9.14
OK OT OP PO PL PU PQ0.333 0.332 0.335 0.231 0.230 0.230 0.309
-11.39 11.39 -6.613.79 3.78 3.82 -1.10 -1.10 -1.10 -1.481.89 2.84 -0.55 1.91 -0.27 -0.71 0.21-1.39 -1.39 -1.40 -0.26 -0.26 -0.26 -0.35-0.54 -0.29 -0.13 -0.70 -0.07 -0.39 0.080.32 0.32 0.32 0.25 0.25 0.25 0.330.17 0.27 0.12 0.16 0.06 0.03 -0.04-0.19 -0.19 -0.19 -0.05 -0.05 -0.05 -0.07
0.00 4.06 5.34 -9.40 0.00 11.59 -1.44 -2.23 -7.92
KO KF KL LK LP LG LM0.332 0.333 0.335 1 0.231 0.230 0.230 0.309 1
-11.39 11.39 -6.613.78 3.79 3.82 -1.10 -1.10 -1.10 -1.481.90 1.90 -0.55 1.91 -0.55 -0.55 0.21-1.08 -1.08 -1.09 -0.24 -0.24 -0.24 -0.32-0.70 -0.22 -0.12 -0.54 -0.13 -0.18 0.09
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0.34 0.35 0.35 0.18 0.18 0.18 0.240.16 0.12 0.09 0.17 0.12 0.03 -0.03-0.12 -0.12 -0.12 -0.07 -0.07 -0.07 -0.09
0.00 4.29 4.73 -9.02 0.00 11.70 -1.78 -1.93 -7.99
FA FK FG GF GB GL GH0.333 0.333 0.334 1 0.231 0.230 0.230 0.309 1
-11.39 11.39 -6.613.79 3.79 3.80 -1.10 -1.10 -1.10 -1.48
1.90 -0.55 1.90 -0.55 0.21-0.45 -0.45 -0.45 -0.36 -0.36 -0.36 -0.48
-0.54 -0.18 -0.22 -0.12 0.110.24 0.24 0.24 0.05 0.05 0.05 0.07
0.17 0.03 0.12 0.09 0.00-0.07 -0.07 -0.07 -0.05 -0.05 -0.05 -0.06
0.00 3.52 5.05 -8.57 0.00 11.73 -1.45 -2.03 -8.24
AF BG0.00 0.001.90 -0.55-0.22 -0.180.12 0.03-0.03 -0.021.76 -0.73
6.89 -2.82
T U
2.90 2.90
O P4.22 -1.74
5.34 -2.23
H4
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4.06 -1.44
O P
2.90 2.90
K L2.88 -1.11
4.29 -1.78
4.73 -1.93
K L
2.90 2.90
F G3.37 -1.37
5.05 -2.03
3.52 -1.45
F G
2.90 2.90
H1
H2
H3
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A B1.82 -0.75
1.76 -0.73
ECUACIONES DE EQUILIBRIO
1ER NIVEL
R1
∑V + ∑H - R1 - R2
0.4 + 71.195 - R1 - R2
R1 + R2 + R3
2DO NIVEL
∑V + ∑H - R2 - R3
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝐻 + ∑▒𝑅 = 0
∑▒ 〖𝐹 _ = 0𝑋 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
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0.67 + 47.463 - R2 - R3
R2 + R3 + R4
3ER NIVEL
∑V + ∑H - R3 - R4
0.57 + 26.105 - R3 - R4
R3 + R4 = 26.675
4TO NIVEL
∑V + ∑H - R4 = 0
0.97 + 9.493 - R4 = 0
R4 = 10.463
SOLUCION DE SISTEMA DE ECUACIONES
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
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R4 = 10.463 Tn
R3 = 16.212 Tn
R2 = 21.458 Tn
R1 = 23.452 Tn
CROSS DESPLAZAMIENTO 1ER NIVEL
CON:
∴ M = -5
FACTORES DE DISTRIBUCIÓN
1ER NIVEL 1ER NIVEL 2DO NIVEL 3ER NIVEL
NUDO NUDO NUDO NUDO
A AF = 0.000F
FA = 0.333K
KF = 0.333O
OK = 0.333B BG = 0.000 FK = 0.333 KL = 0.335 OP = 0.335C CH = 0.000 FG = 0.334 KO = 0.332 OT = 0.332D DI = 0.000
G
GB = 0.230
L
LG = 0.230
P
PL = 0.230E EJ = 0.000 GF = 0.231 LK = 0.231 PO = 0.231
GL = 0.230 LP = 0.230 PU = 0.230GH = 0.309 LM = 0.309 PQ = 0.309
H
HC = 0.220
M
MH = 0.220
Q
QM = 0.220HG = 0.295 ML = 0.295 QP = 0.295HM = 0.220 MQ = 0.220 QV = 0.220HI = 0.265 MN = 0.265 QR = 0.265
I
ID = 0.220
N
NI = 0.220
R
RN = 0.220
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
- 6𝐸𝐼"Δ" /𝐿^2 =𝑀_((𝐴𝐿𝐸𝐴𝑇𝑂𝑅𝐼𝑂))
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I IH = 0.265 N NM = 0.265 R RQ = 0.265IN = 0.220 NR = 0.220 RW = 0.220IJ = 0.295 NÑ = 0.295 RS = 0.295
JJE = 0.299
ÑÑJ = 0.299
SSÑ = 0.299
JI = 0.402 ÑN = 0.402 SR = 0.402JÑ = 0.299 ÑS = 0.299 SX = 0.299
TO TU UT UP UV0.498 0.502 0.301 0.299 0.400
0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.000.14 0.00 0.00 0.00 0.00-0.07 -0.07 0.00 0.00 0.00-0.02 0.00 -0.03 -0.03 -0.010.01 0.01 0.02 0.02 0.03
0.00 0.06 -0.06 0.00 -0.01 0.00 0.02
OK OT OP PO PL PU PQ0.333 0.332 0.335 0.231 0.230 0.230 0.309
0.00 0.00 0.00 0.00 0.00 0.00 0.00-0.83 0.00 0.00 0.00 0.00 0.00 0.000.28 0.28 0.28 0.00 0.00 0.00 0.000.10 0.00 0.00 0.14 0.00 0.00 0.08-0.03 -0.03 -0.03 -0.05 -0.05 -0.05 -0.07-0.08 -0.03 -0.03 -0.02 -0.01 0.00 -0.030.05 0.05 0.05 0.01 0.01 0.01 0.02
0.00 -0.52 0.25 0.27 0.00 0.09 -0.05 -0.04 0.00
KO KF KL LK LP LG LM0.332 0.333 0.335 1 0.231 0.230 0.230 0.309 1
5.00 5.00-1.66 -1.67 -1.68 -1.16 -1.15 -1.15 -1.550.00 0.00 -0.58 -0.84 0.00 0.00 -0.740.19 0.19 0.19 0.36 0.36 0.36 0.490.14 0.14 0.18 0.10 0.00 0.07 0.21-0.15 -0.15 -0.15 -0.09 -0.09 -0.09 -0.12-0.02 -0.03 -0.04 -0.08 -0.03 -0.05 -0.09
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0.03 0.03 0.03 0.05 0.05 0.05 0.070.00 -1.47 3.51 -2.05 0.00 -1.64 -0.85 4.20 -1.71
FA FK FG GF GB GL GH0.333 0.333 0.334 1 0.231 0.230 0.230 0.309 1-5.00 5.00 -5.00 5.000.00 0.00 0.00 0.00 0.00 0.00 0.00
-0.83 0.00 0.00 -0.58 0.000.28 0.28 0.28 0.13 0.13 0.13 0.18
0.10 0.07 0.14 0.18 0.08-0.05 -0.05 -0.05 -0.09 -0.09 -0.09 -0.12
-0.08 -0.05 -0.03 -0.04 -0.050.04 0.04 0.04 0.03 0.03 0.03 0.04
0.00 -4.74 4.45 0.28 0.00 0.18 -4.93 4.63 0.12
AF BG0.00 0.00-5.00 -5.000.00 0.000.14 0.07-0.03 -0.050.02 0.01-4.87 -4.97
0.06 0.00
T U
2.90 2.90
O P0.11 -0.01
0.25 -0.04
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-0.52 -0.05
O P
2.90 2.90
K L-0.69 -0.31
-1.47 -0.85
3.51 4.20
K L
2.90 2.90
F G2.75 3.04
4.45 4.63
-4.74 -4.93
F G
2.90 2.90
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A B-3.31 -3.41
-4.87 -4.97
ECUACIONES DE EQUILIBRIO
1ER NIVEL
∑V + Q11 - Q21
-16.9 + Q11 - Q21
- Q11 + Q21 + Q31
2DO NIVEL
∑V - Q21 - Q31
14.71 - Q21 - Q31
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝑄 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
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14.71 - Q21 - Q31
Q21 + Q31 + Q41
3ER NIVEL
∑V - Q31 - Q41
-2.42 - Q31 - Q41
Q31 + Q41 = -2.420
4TO NIVEL
∑V - Q41 = 0
0.25 - Q41 = 0
Q41 = 0.250
SOLUCION DE SISTEMA DE ECUACIONES
Q41 = 0.250 Tn
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
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Q41 = 0.250 Tn
Q31 = -2.670 Tn
Q21 = 17.130 Tn
Q11 = 31.590 Tn
CROSS DESPLAZAMIENTO 2DO NIVEL
CON:
∴ M = -5
FACTORES DE DISTRIBUCIÓN
1ER NIVEL 1ER NIVEL 2DO NIVEL 3ER NIVEL
NUDO NUDO NUDO NUDO
A AF = 0.000F
FA = 0.333K
KF = 0.333O
OK = 0.333B BG = 0.000 FK = 0.333 KL = 0.335 OP = 0.335C CH = 0.000 FG = 0.334 KO = 0.332 OT = 0.332D DI = 0.000
G
GB = 0.230
L
LG = 0.230
P
PL = 0.230E EJ = 0.000 GF = 0.231 LK = 0.231 PO = 0.231
GL = 0.230 LP = 0.230 PU = 0.230GH = 0.309 LM = 0.309 PQ = 0.309
H
HC = 0.220
M
MH = 0.220
Q
QM = 0.220HG = 0.295 ML = 0.295 QP = 0.295HM = 0.220 MQ = 0.220 QV = 0.220HI = 0.265 MN = 0.265 QR = 0.265
I
ID = 0.220
N
NI = 0.220
R
RN = 0.220IH = 0.265 NM = 0.265 RQ = 0.265
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
- 6𝐸𝐼"Δ" /𝐿^2 =𝑀_((𝐴𝐿𝐸𝐴𝑇𝑂𝑅𝐼𝑂))
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IIN = 0.220
NNR = 0.220
RRW = 0.220
IJ = 0.295 NÑ = 0.295 RS = 0.295
JJE = 0.299
ÑÑJ = 0.299
SSÑ = 0.299
JI = 0.402 ÑN = 0.402 SR = 0.402JÑ = 0.299 ÑS = 0.299 SX = 0.299
TO TU UT UP UV0.498 0.502 0.301 0.299 0.400
0.00 0.00 0.00 0.00 0.00-0.83 0.00 0.00 -0.58 0.000.41 0.42 0.17 0.17 0.230.10 0.09 0.21 0.21 0.10-0.09 -0.09 -0.16 -0.16 -0.21-0.07 -0.08 -0.05 -0.06 -0.070.07 0.07 0.05 0.05 0.07
0.00 -0.41 0.41 0.00 0.23 -0.35 0.12
OK OT OP PO PL PU PQ0.333 0.332 0.335 0.231 0.230 0.230 0.3095.00 5.00-1.67 -1.66 -1.68 -1.16 -1.15 -1.15 -1.550.00 0.00 -0.58 -0.84 -0.29 0.00 -0.740.19 0.19 0.19 0.43 0.43 0.43 0.580.00 0.21 0.22 0.10 0.11 0.09 0.21-0.14 -0.14 -0.14 -0.12 -0.12 -0.12 -0.150.00 -0.05 -0.06 -0.07 -0.03 -0.08 -0.090.03 0.03 0.03 0.06 0.06 0.06 0.08
0.00 3.42 -1.41 -2.01 0.00 -1.59 4.01 -0.77 -1.65
KO KF KL LK LP LG LM0.332 0.333 0.335 1 0.231 0.230 0.230 0.309 15.00 -5.00 5.00 -5.000.00 0.00 0.00 0.00 0.00 0.00 0.00-0.83 0.83 0.00 0.00 -0.58 0.58 0.000.00 0.00 0.00 0.00 0.00 0.00 0.000.10 -0.10 0.00 0.00 0.21 -0.18 0.000.00 0.00 0.00 -0.01 -0.01 -0.01 -0.01-0.07 0.03 0.00 0.00 -0.06 0.04 0.000.01 0.01 0.01 0.01 0.01 0.01 0.01
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0.00 4.21 -4.22 0.01 0.00 0.00 4.58 -4.57 0.00
FA FK FG GF GB GL GH0.333 0.333 0.334 1 0.231 0.230 0.230 0.309 10.00 -5.00 0.00 -5.001.67 1.67 1.67 1.16 1.15 1.15 1.55
0.00 0.58 0.84 0.00 0.74-0.19 -0.19 -0.19 -0.36 -0.36 -0.36 -0.49
0.00 -0.18 -0.10 0.00 -0.210.06 0.06 0.06 0.07 0.07 0.07 0.10
0.00 0.04 0.03 0.00 0.07-0.01 -0.01 -0.01 -0.02 -0.02 -0.02 -0.03
0.00 1.52 -3.48 1.96 0.00 1.61 0.84 -4.17 1.72
AF BG0.00 0.000.00 0.000.83 0.58-0.10 -0.180.03 0.04-0.01 -0.010.76 0.42
-0.41 -0.35
T U
2.90 2.90
O P-0.63 -0.39
-1.41 -0.77
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3.42 4.01
O P
2.90 2.90
K L2.63 2.96
4.21 4.58
-4.22 -4.57
K L
2.90 2.90
F G-2.65 -3.01
-3.48 -4.17
1.52 0.84
F G
2.90 2.90
![Page 19: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/19.jpg)
A B0.79 0.43
0.76 0.42
ECUACIONES DE EQUILIBRIO
1ER NIVEL
∑V - Q12 + Q22
2.77 - Q12 + Q22
Q12 - Q22 + Q32
2DO NIVEL
∑V + Q22 - Q32
-14.5 + Q22 - Q32
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝑄 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
![Page 20: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/20.jpg)
- Q22 + Q32 + Q42
3ER NIVEL
∑V - Q32 - Q42
14.36 - Q32 - Q42
Q32 + Q42 = 14.360
4TO NIVEL
∑V - Q42 = 0
-2.38 - Q42 = 0
Q42 = -2.380
SOLUCION DE SISTEMA DE ECUACIONES
Q42 = -2.380 Tn
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
![Page 21: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/21.jpg)
Q32 = 16.740 Tn
Q22 = 28.810 Tn
Q12 = 17.220 Tn
CROSS DESPLAZAMIENTO 3ER NIVEL
CON:
∴ M = -5
FACTORES DE DISTRIBUCIÓN
1ER NIVEL 1ER NIVEL 2DO NIVEL 3ER NIVEL
NUDO NUDO NUDO NUDO
A AF = 0.000F
FA = 0.333K
KF = 0.333O
OK = 0.333B BG = 0.000 FK = 0.333 KL = 0.335 OP = 0.335C CH = 0.000 FG = 0.334 KO = 0.332 OT = 0.332D DI = 0.000
G
GB = 0.230
L
LG = 0.230
P
PL = 0.230E EJ = 0.000 GF = 0.231 LK = 0.231 PO = 0.231
GL = 0.230 LP = 0.230 PU = 0.230GH = 0.309 LM = 0.309 PQ = 0.309
H
HC = 0.220
M
MH = 0.220
Q
QM = 0.220HG = 0.295 ML = 0.295 QP = 0.295HM = 0.220 MQ = 0.220 QV = 0.220HI = 0.265 MN = 0.265 QR = 0.265
I
ID = 0.220
N
NI = 0.220
R
RN = 0.220IH = 0.265 NM = 0.265 RQ = 0.265IN = 0.220 NR = 0.220 RW = 0.220
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
- 6𝐸𝐼"Δ" /𝐿^2 =𝑀_((𝐴𝐿𝐸𝐴𝑇𝑂𝑅𝐼𝑂))
![Page 22: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/22.jpg)
I
IJ = 0.295
N
NÑ = 0.295
R
RS = 0.295
JJE = 0.299
ÑÑJ = 0.299
SSÑ = 0.299
JI = 0.402 ÑN = 0.402 SR = 0.402JÑ = 0.299 ÑS = 0.299 SX = 0.299
TO TU UT UP UV0.498 0.502 0.301 0.299 0.4005.00 5.00-2.49 -2.51 -1.51 -1.49 -2.000.00 -0.75 -1.26 0.00 -0.950.37 0.38 0.66 0.66 0.880.07 0.33 0.19 0.09 0.35-0.20 -0.20 -0.19 -0.19 -0.25-0.03 -0.09 -0.10 -0.05 -0.160.06 0.06 0.09 0.09 0.13
0.00 2.79 -2.79 0.00 -2.10 4.10 -2.00
OK OT OP PO PL PU PQ0.333 0.332 0.335 0.231 0.230 0.230 0.309-5.00 5.00 -5.00 5.000.00 0.00 0.00 0.00 0.00 0.00 0.000.83 -1.25 0.00 0.00 0.00 -0.75 0.000.14 0.14 0.14 0.17 0.17 0.17 0.23-0.10 0.19 0.09 0.07 0.04 0.33 0.02-0.06 -0.06 -0.06 -0.11 -0.11 -0.11 -0.140.04 -0.10 -0.05 -0.03 -0.03 -0.09 -0.040.04 0.04 0.04 0.04 0.04 0.04 0.06
0.00 -4.11 3.96 0.15 0.00 0.15 -4.88 4.60 0.13
KO KF KL LK LP LG LM0.332 0.333 0.335 1 0.231 0.230 0.230 0.309 1-5.00 0.00 -5.00 0.001.66 1.67 1.68 1.16 1.15 1.15 1.550.00 0.00 0.58 0.84 0.00 0.00 0.74-0.19 -0.19 -0.19 -0.36 -0.36 -0.36 -0.490.07 -0.14 -0.18 -0.10 0.09 -0.07 -0.210.08 0.08 0.08 0.07 0.07 0.07 0.09-0.03 0.03 0.03 0.04 -0.05 0.05 0.07-0.01 -0.01 -0.01 -0.03 -0.03 -0.03 -0.03
0.00 -3.42 1.43 1.98 0.00 1.62 -4.14 0.81 1.71
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FA FK FG GF GB GL GH0.333 0.333 0.334 1 0.231 0.230 0.230 0.309 10.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00
0.83 0.00 0.00 0.58 0.00-0.28 -0.28 -0.28 -0.13 -0.13 -0.13 -0.18
-0.10 -0.07 -0.14 -0.18 -0.080.05 0.05 0.05 0.09 0.09 0.09 0.12
0.04 0.05 0.03 0.03 0.05-0.03 -0.03 -0.03 -0.02 -0.02 -0.02 -0.03
0.00 -0.25 0.53 -0.27 0.00 -0.18 -0.06 0.36 -0.12
AF BG0.00 0.000.00 0.000.00 0.00-0.14 -0.070.03 0.05-0.01 -0.01-0.13 -0.03
2.79 4.10
T U
2.90 2.90
O P2.33 3
3.96 4.60
-4.11 -4.88
![Page 24: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/24.jpg)
O P
2.90 2.90
K L-2.6 -3.11
-3.42 -4.14
1.43 0.81
K L
2.90 2.90
F G0.68 0.4
0.53 0.36
-0.25 -0.06
F G
2.90 2.90
![Page 25: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/25.jpg)
A B-0.13 -0.03
-0.13 -0.03
ECUACIONES DE EQUILIBRIO
1ER NIVEL
∑V - Q13 - Q23
-0.34 - Q13 - Q23
Q13 + Q23 - Q33
2DO NIVEL
∑V - Q23 + Q33
2.49 - Q23 + Q33
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝑄 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
![Page 26: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/26.jpg)
+ Q23 - Q33 + Q43
3ER NIVEL
∑V + Q33 - Q43
-14.5 + Q33 - Q43
- Q33 + Q43 = -14.450
4TO NIVEL
∑V - Q43 = 0
13.72 - Q43 = 0
Q43 = 13.720
SOLUCION DE SISTEMA DE ECUACIONES
Q43 = 13.720 Tn
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
![Page 27: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/27.jpg)
Q33 = 28.170 Tn
Q23 = 16.940 Tn
Q13 = -2.830 Tn
CROSS DESPLAZAMIENTO 4TO NIVEL
CON:
∴ M = -5
FACTORES DE DISTRIBUCIÓN
1ER NIVEL 1ER NIVEL 2DO NIVEL 3ER NIVEL
NUDO NUDO NUDO NUDO
A AF = 0.000F
FA = 0.333K
KF = 0.333O
OK = 0.333B BG = 0.000 FK = 0.333 KL = 0.335 OP = 0.335C CH = 0.000 FG = 0.334 KO = 0.332 OT = 0.332D DI = 0.000
G
GB = 0.230
L
LG = 0.230
P
PL = 0.230E EJ = 0.000 GF = 0.231 LK = 0.231 PO = 0.231
GL = 0.230 LP = 0.230 PU = 0.230GH = 0.309 LM = 0.309 PQ = 0.309
H
HC = 0.220
M
MH = 0.220
Q
QM = 0.220HG = 0.295 ML = 0.295 QP = 0.295HM = 0.220 MQ = 0.220 QV = 0.220HI = 0.265 MN = 0.265 QR = 0.265
I
ID = 0.220
N
NI = 0.220
R
RN = 0.220IH = 0.265 NM = 0.265 RQ = 0.265
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
- 6𝐸𝐼"Δ" /𝐿^2 =𝑀_((𝐴𝐿𝐸𝐴𝑇𝑂𝑅𝐼𝑂))
![Page 28: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/28.jpg)
IIN = 0.220
NNR = 0.220
RRW = 0.220
IJ = 0.295 NÑ = 0.295 RS = 0.295
JJE = 0.299
ÑÑJ = 0.299
SSÑ = 0.299
JI = 0.402 ÑN = 0.402 SR = 0.402JÑ = 0.299 ÑS = 0.299 SX = 0.299
TO TU UT UP UV0.498 0.502 0.301 0.299 0.400-5.00 -5.002.49 2.51 1.51 1.49 2.000.83 0.75 1.26 0.58 0.95-0.79 -0.79 -0.84 -0.83 -1.11-0.30 -0.42 -0.40 -0.30 -0.450.36 0.36 0.35 0.34 0.460.14 0.17 0.18 0.14 0.24-0.16 -0.16 -0.17 -0.17 -0.22
0.00 -2.43 2.43 0.00 1.89 -3.75 1.86
OK OT OP PO PL PU PQ0.333 0.332 0.335 0.231 0.230 0.230 0.309
-5.00 -5.001.67 1.66 1.68 1.16 1.15 1.15 1.550.00 1.25 0.58 0.84 0.29 0.75 0.74-0.61 -0.61 -0.61 -0.60 -0.60 -0.60 -0.81-0.14 -0.39 -0.30 -0.31 -0.15 -0.41 -0.320.28 0.28 0.28 0.27 0.27 0.27 0.370.06 0.18 0.14 0.14 0.07 0.17 0.16-0.13 -0.13 -0.13 -0.13 -0.13 -0.13 -0.17
0.00 1.13 -2.76 1.63 0.00 1.37 0.90 -3.80 1.52
KO KF KL LK LP LG LM0.332 0.333 0.335 1 0.231 0.230 0.230 0.309 1
0.00 0.00 0.00 0.00 0.00 0.00 0.000.83 0.00 0.00 0.00 0.58 0.00 0.00-0.28 -0.28 -0.28 -0.13 -0.13 -0.13 -0.18-0.30 0.00 -0.07 -0.14 -0.30 0.00 -0.080.12 0.12 0.12 0.12 0.12 0.12 0.160.14 0.02 0.06 0.06 0.14 0.01 0.06-0.07 -0.07 -0.07 -0.06 -0.06 -0.06 -0.08
![Page 29: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/29.jpg)
0.00 0.44 -0.20 -0.24 0.00 -0.15 0.34 -0.07 -0.12
FA FK FG GF GB GL GH0.333 0.333 0.334 1 0.231 0.230 0.230 0.309 1
0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00-0.14 0.00 0.00 -0.07 0.00
0.05 0.05 0.05 0.02 0.02 0.02 0.020.06 0.01 0.02 0.06 0.01
-0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.030.00 0.02 -0.05 0.03 0.00 0.02 -0.01 -0.01 0.00
AF BG0.00 0.000.00 0.000.00 0.000.00 0.000.02 0.01-0.01 -0.010.01 0.00
-2.43 -3.75
T U
2.90 2.90
O P-1.79 -2.6
-2.76 -3.80
![Page 30: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/30.jpg)
1.13 0.90
O P
2.90 2.90
K L0.54 0.43
0.44 0.34
-0.20 -0.07
K L
2.90 2.90
F G-0.09 -0.03
-0.05 -0.01
0.02 -0.01
F G
2.90 2.90
![Page 31: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/31.jpg)
A B0.01 0
0.01 0.00
ECUACIONES DE EQUILIBRIO
1ER NIVEL
∑V - Q14 - Q24
0.02 - Q14 - Q24
Q14 + Q24 + Q34
2DO NIVEL
∑V - Q24 - Q34
-0.26 - Q24 - Q34
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝑄 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
![Page 32: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/32.jpg)
+ Q24 + Q34 - Q44
3ER NIVEL
∑V - Q34 + Q44
2.2 - Q34 + Q44
+ Q34 - Q44 = 2.200
4TO NIVEL
∑V + Q44 = 0
-11.6 + Q44 = 0
- Q43 = -11.560
SOLUCION DE SISTEMA DE ECUACIONES
∑▒ 〖𝐹 _𝑋 = 0 〗
∑▒ 〖𝐹 _𝑋 = 0 〗
![Page 33: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/33.jpg)
Q44 = 11.560 Tn
Q34 = 13.760 Tn
Q24 = -2.460 Tn
Q14 = 0.280 Tn
CALCULO DE MOMENTOS FINALES
CUADRO DE MATRICES
i i1 23.452 31.590 17.220 -2.830 0.280 1 23.452 31.5902 21.458 17.130 28.810 16.940 -2.460 2 21.458 -17.1303 16.212 -2.670 16.740 28.170 13.760 3 16.212 2.6704 10.463 0.250 -2.380 13.720 11.560 4 10.463 -0.250
i1 2.0642 4.6293 6.643 MOMENTOS FINALES
Ri Qi1 Qi2 Qi3 Qi4 Ri Qi1
Ci
∑▒ 〖𝐹 _𝑋 = 0 〗 → −𝑅 _1+𝐶_1 𝑥𝑄_11−𝐶_2 𝑥𝑄_12− _𝐶 3 _1𝑥𝑄 3− _𝐶 4 _1𝑥𝑄 4 = 0∑▒ 〖𝐹 _𝑋 = 0 〗 → −𝑅 _2−𝐶_1 𝑥𝑄_21+𝐶_2 𝑥𝑄_22− _𝐶 3 _𝑥𝑄 23− _𝐶 4 _𝑥𝑄 24 = 0∑▒ 〖𝐹 _𝑋 = 0 〗 → −𝑅 _3−𝐶_1 𝑥𝑄_31−𝐶_2 𝑥𝑄_32+ _𝐶 3 _𝑥𝑄 33− _𝐶 4 _𝑥𝑄 34 = 0∑▒ 〖𝐹 _𝑋 = 0 〗 → −𝑅 _4−𝐶_1 𝑥𝑄_41−𝐶_2 𝑥𝑄_42− _𝐶 3 _𝑥𝑄 43+ _𝐶 4 _𝑥𝑄 44 = 0
![Page 34: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/34.jpg)
4 7.881 MOMENTOS FINALES
4.50 -6.73
T U
2.90 2.90
O P
3.85 -5.27
0.46 -8.24
O P
2.90 2.90
K L
1.49 -7.16
0.37 -9.57
K LH2
H3
H4
![Page 35: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/35.jpg)
2.90 2.90
F G
1.20 -9.45
-0.71 -8.24
F G
2.90 2.90
A B
-5.51 -9.06
H1
![Page 36: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/36.jpg)
MÉTODO CROSS
2.90
2.90
2.90
2.90
![Page 37: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/37.jpg)
TRAMO43.920 Tn/m3.920 Tn/m3.920 Tn/m3.920 Tn/m FACTORES DE DISTRIBUCIÓN
1ER NIVEL 1ER NIVEL 2DO NIVEL 3ER NIVEL
NUDO NUDO NUDO NUDO
A AF = 0.000F
FA = 0.333K
KF = 0.333OB BG = 0.000 FK = 0.333 KL = 0.335
C CH = 0.000 FG = 0.334 KO = 0.332D DI = 0.000
G
GB = 0.230
L
LG = 0.230
PE EJ = 0.000 GF = 0.231 LK = 0.231GL = 0.230 LP = 0.230GH = 0.309 LM = 0.309
H
HC = 0.220
M
MH = 0.220
QHG = 0.295 ML = 0.295HM = 0.220 MQ = 0.220HI = 0.265 MN = 0.265
I
ID = 0.220
N
NI = 0.220
RIH = 0.265 NM = 0.265IN = 0.220 NR = 0.220
= 4.312E-04 IJ = 0.295 NÑ = 0.295= 4.312E-04
JJE = 0.299
ÑÑJ = 0.299
S= 4.312E-04 JI = 0.402 ÑN = 0.402= 4.312E-04 JÑ = 0.299 ÑS = 0.299= 4.312E-04
= 4.340E-04= 5.787E-04= 5.208E-04= 5.787E-04
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
![Page 38: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/38.jpg)
FACTORES DE DISTRIBUCIÓN
3ER NIVEL 4TO NIVEL
NUDO
0.333 T TO = 0.4980.335 TU = 0.5020.332
UUP = 0.299
0.230 UT = 0.3010.231 UV = 0.4000.230
VVQ = 0.282
0.309 VU = 0.3780.220 VW = 0.3400.295
WWR = 0.282
0.220 WV = 0.340
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
![Page 39: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/39.jpg)
0.265W
WX = 0.3780.220 X XS = 0.4270.265 XW = 0.5730.2200.2950.2990.4020.299
VU VQ VW WV WR WX0.378 0.282 0.340 0.340 0.282 0.3786.61 -8.07 8.07 -6.610.55 0.41 0.49 -0.49 -0.41 -0.55-0.96 0.16 -0.25 0.25 -0.16 -1.900.39 0.29 0.35 0.61 0.51 0.68-0.52 0.06 0.31 0.18 0.17 0.360.06 0.04 0.05 -0.24 -0.20 -0.270.05 -0.03 -0.12 0.03 -0.11 -0.210.04 0.03 0.03 0.10 0.08 0.11
0.00 6.23 0.97 -7.20 0.00 8.50 -0.12 -8.38
QP QM QV QR RQ RN RW RS0.295 0.220 0.220 0.265 0.265 0.220 0.220 0.2956.61 -8.07 8.07 -6.610.43 0.32 0.32 0.39 -0.39 -0.32 -0.32 -0.43-0.74 0.16 0.20 -0.19 0.19 -0.16 -0.20 -1.330.17 0.12 0.12 0.15 0.40 0.33 0.33 0.44-0.18 0.07 0.15 0.20 0.07 0.16 0.25 0.53-0.07 -0.05 -0.05 -0.06 -0.27 -0.22 -0.22 -0.300.16 -0.02 0.02 -0.13 -0.03 -0.09 -0.10 -0.16-0.01 -0.01 -0.01 -0.01 0.10 0.09 0.09 0.11
0.00 6.38 0.59 0.76 -7.73 0.00 8.15 -0.22 -0.18 -7.75 0.00
ML MQ MH MN NM NR NI NÑ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 16.61 -8.07 8.07 -6.610.43 0.32 0.32 0.39 -0.39 -0.32 -0.32 -0.43-0.74 0.16 0.16 -0.19 0.19 -0.16 -0.16 -1.330.18 0.13 0.13 0.16 0.39 0.32 0.32 0.43-0.16 0.06 0.08 0.19 0.08 0.17 0.14 0.44
![Page 40: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/40.jpg)
-0.05 -0.04 -0.04 -0.05 -0.22 -0.18 -0.18 -0.240.12 -0.03 0.00 -0.11 -0.02 -0.11 -0.06 -0.160.01 0.00 0.00 0.00 0.09 0.08 0.08 0.10
0.00 6.40 0.61 0.66 -7.67 0.00 8.19 -0.21 -0.18 -7.80 0.00
HG HC HM HI IH ID IN IJ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 16.61 -8.07 8.07 -6.610.43 0.32 0.32 0.39 -0.39 -0.32 -0.32 -0.43-0.74 0.16 -0.19 0.19 -0.16 -1.330.23 0.17 0.17 0.20 0.34 0.29 0.29 0.38-0.24 0.07 0.17 0.10 0.16 0.240.00 0.00 0.00 0.00 -0.13 -0.11 -0.11 -0.150.04 -0.02 -0.07 0.00 -0.09 -0.100.02 0.01 0.01 0.01 0.05 0.04 0.04 0.06
0.00 6.34 0.50 0.71 -7.55 0.00 8.24 -0.10 -0.19 -7.94 0.00
CH DI0.00 0.000.16 -0.160.08 0.140.00 -0.060.01 0.020.25 -0.05
0.97 -0.12
V W
2.90 2.90
Q R0.6 -0.1
0.76 -0.18
![Page 41: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/41.jpg)
0.59 -0.22
Q R
2.90 2.90
M N0.42 -0.15
0.61 -0.21
0.66 -0.18
M N
2.90 2.90
H I0.47 -0.13
0.71 -0.19
0.50 -0.10
H I
2.90 2.90
![Page 42: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/42.jpg)
C D0.26 -0.05
0.25 -0.05
- R3 - R4 = 0
- R3 - R4 = 0
+ R4 = 71.585
- R4 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝐻 + ∑▒𝑅 = 0
![Page 43: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/43.jpg)
- R4 = 0
= 48.133
= 0
= 0
26.675
![Page 44: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/44.jpg)
FACTORES DE DISTRIBUCIÓN
3ER NIVEL 4TO NIVEL
NUDO
0.333 T TO = 0.4980.335 TU = 0.5020.332
UUP = 0.299
0.230 UT = 0.3010.231 UV = 0.4000.230
VVQ = 0.282
0.309 VU = 0.3780.220 VW = 0.3400.295
WWR = 0.282
0.220 WV = 0.3400.265 WX = 0.3780.220 X XS = 0.427
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
![Page 45: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/45.jpg)
0.265X
XW = 0.5730.2200.2950.2990.4020.299
VU VQ VW WV WR WX0.378 0.282 0.340 0.340 0.282 0.378
0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.000.00 0.06 0.00 0.00 0.06 0.00-0.02 -0.02 -0.02 -0.02 -0.02 -0.020.00 -0.03 -0.01 -0.01 -0.04 -0.030.01 0.01 0.01 0.03 0.02 0.03
0.00 -0.01 0.03 -0.02 0.00 0.00 0.02 -0.02
QP QM QV QR RQ RN RW RS0.295 0.220 0.220 0.265 0.265 0.220 0.220 0.295
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 -0.55 0.00 0.00 0.00 -0.55 0.00 0.000.16 0.12 0.12 0.15 0.15 0.12 0.12 0.160.00 0.16 0.00 0.07 0.07 0.18 0.00 0.15-0.07 -0.05 -0.05 -0.06 -0.11 -0.09 -0.09 -0.12-0.03 -0.06 -0.01 -0.05 -0.03 -0.05 -0.01 -0.040.05 0.04 0.04 0.04 0.03 0.03 0.03 0.04
0.00 0.11 -0.35 0.10 0.15 0.00 0.11 -0.36 0.05 0.19 0.00
ML MQ MH MN NM NR NI NÑ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 1
5.00 5.00-1.47 -1.10 -1.10 -1.33 -1.33 -1.10 -1.10 -1.48-0.77 0.00 0.00 -0.66 -0.66 0.00 0.00 -1.010.42 0.32 0.32 0.38 0.44 0.37 0.37 0.490.24 0.06 0.06 0.22 0.19 0.06 0.06 0.15-0.17 -0.13 -0.13 -0.16 -0.12 -0.10 -0.10 -0.14-0.06 -0.03 -0.04 -0.06 -0.08 -0.04 -0.04 -0.09
![Page 46: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/46.jpg)
0.05 0.04 0.04 0.05 0.07 0.06 0.06 0.080.00 -1.76 -0.84 4.15 -1.55 0.00 -1.49 -0.76 4.24 -1.99 0.00
HG HC HM HI IH ID IN IJ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 1
-5.00 5.00 -5.00 5.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 -0.55 0.00 0.00 -0.55 0.000.16 0.12 0.12 0.15 0.15 0.12 0.12 0.160.09 0.16 0.07 0.07 0.18 0.15-0.09 -0.07 -0.07 -0.08 -0.11 -0.09 -0.09 -0.12-0.06 -0.06 -0.05 -0.04 -0.05 -0.040.05 0.04 0.04 0.05 0.03 0.03 0.03 0.04
0.00 0.15 -4.91 4.63 0.13 0.00 0.10 -4.94 4.64 0.19 0.00
CH DI0.00 0.00-5.00 -5.000.00 0.000.06 0.06-0.04 -0.040.02 0.01-4.95 -4.97
0.03 0.02
V W
2.90 2.90
Q R0.04 0.03
0.10 0.05
![Page 47: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/47.jpg)
-0.35 -0.36
Q R
2.90 2.90
M N-0.41 -0.39
-0.84 -0.76
4.15 4.24
M N
2.90 2.90
H I3.03 3.06
4.63 4.64
-4.91 -4.94
H I
2.90 2.90
![Page 48: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/48.jpg)
C D-3.4 -3.42
-4.95 -4.97
- Q31 - Q41 = 0
- Q31 - Q41 = 0
+ Q41 = -16.880
- Q41 = 0
- Q41 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝑄 = 0
![Page 49: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/49.jpg)
- Q41 = 0
= 14.710
= 0
= 0
-2.420
![Page 50: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/50.jpg)
FACTORES DE DISTRIBUCIÓN
3ER NIVEL 4TO NIVEL
NUDO
0.333 T TO = 0.4980.335 TU = 0.5020.332
UUP = 0.299
0.230 UT = 0.3010.231 UV = 0.4000.230
VVQ = 0.282
0.309 VU = 0.3780.220 VW = 0.3400.295
WWR = 0.282
0.220 WV = 0.3400.265 WX = 0.3780.220 X XS = 0.4270.265 XW = 0.573
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
![Page 51: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/51.jpg)
0.2200.2950.2990.4020.299
VU VQ VW WV WR WX0.378 0.282 0.340 0.340 0.282 0.378
0.00 0.00 0.00 0.00 0.00 0.000.00 -0.55 0.00 0.00 -0.55 0.000.21 0.16 0.19 0.19 0.16 0.210.12 0.16 0.09 0.09 0.18 0.21-0.14 -0.10 -0.12 -0.17 -0.14 -0.19-0.11 -0.06 -0.08 -0.06 -0.05 -0.060.10 0.07 0.09 0.06 0.05 0.06
0.00 0.17 -0.33 0.16 0.00 0.11 -0.35 0.24
QP QM QV QR RQ RN RW RS0.295 0.220 0.220 0.265 0.265 0.220 0.220 0.295
5.00 5.00-1.47 -1.10 -1.10 -1.33 -1.33 -1.10 -1.10 -1.48-0.77 0.00 0.00 -0.66 -0.66 0.00 0.00 -1.010.42 0.32 0.32 0.38 0.44 0.37 0.37 0.490.29 0.00 0.08 0.22 0.19 0.00 0.08 0.15-0.17 -0.13 -0.13 -0.16 -0.11 -0.09 -0.09 -0.12-0.08 0.00 -0.05 -0.06 -0.08 0.00 -0.07 -0.080.05 0.04 0.04 0.05 0.06 0.05 0.05 0.07
0.00 -1.73 4.13 -0.85 -1.55 0.00 -1.48 4.23 -0.77 -1.98 0.00
ML MQ MH MN NM NR NI NÑ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 1
5.00 -5.00 5.00 -5.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 -0.55 0.55 0.00 0.00 -0.55 0.55 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.16 -0.16 0.00 0.00 0.18 -0.18 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00-0.01 -0.06 0.05 0.00 0.00 -0.05 0.04 0.000.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00
![Page 52: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/52.jpg)
0.00 0.00 4.55 -4.55 0.00 0.00 0.00 4.59 -4.59 0.00 0.00
HG HC HM HI IH ID IN IJ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 1
0.00 -5.00 0.00 -5.001.47 1.10 1.10 1.33 1.33 1.10 1.10 1.480.77 0.00 0.66 0.66 0.00 1.01-0.42 -0.32 -0.32 -0.38 -0.44 -0.37 -0.37 -0.49-0.24 0.00 -0.22 -0.19 0.00 -0.150.14 0.10 0.10 0.12 0.09 0.07 0.07 0.100.05 0.00 0.04 0.06 0.00 0.05-0.03 -0.02 -0.02 -0.02 -0.03 -0.02 -0.02 -0.03
0.00 1.74 0.87 -4.13 1.53 0.00 1.48 0.78 -4.22 1.96 0.00
CH DI0.00 0.000.00 0.000.55 0.55-0.16 -0.180.05 0.04-0.01 -0.010.43 0.39
-0.33 -0.35
V W
2.90 2.90
Q R-0.41 -0.38
-0.85 -0.77
![Page 53: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/53.jpg)
4.13 4.23
Q R
2.90 2.90
M N2.99 3.04
4.55 4.59
-4.55 -4.59
M N
2.90 2.90
H I-3 -3.04
-4.13 -4.22
0.87 0.78
H I
2.90 2.90
![Page 54: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/54.jpg)
C D0.45 0.41
0.43 0.39
- Q32 - Q42 = 0
- Q32 - Q42 = 0
+ Q42 = 2.770
- Q42 = 0
- Q42 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝑄 = 0
![Page 55: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/55.jpg)
= -14.450
= 0
= 0
14.360
![Page 56: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/56.jpg)
FACTORES DE DISTRIBUCIÓN
3ER NIVEL 4TO NIVEL
NUDO
0.333 T TO = 0.4980.335 TU = 0.5020.332
UUP = 0.299
0.230 UT = 0.3010.231 UV = 0.4000.230
VVQ = 0.282
0.309 VU = 0.3780.220 VW = 0.3400.295
WWR = 0.282
0.220 WV = 0.3400.265 WX = 0.3780.220 X XS = 0.4270.265 XW = 0.5730.220
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
![Page 57: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/57.jpg)
0.2950.2990.4020.299
VU VQ VW WV WR WX0.378 0.282 0.340 0.340 0.282 0.378
5.00 5.00-1.89 -1.41 -1.70 -1.70 -1.41 -1.89-1.00 0.00 -0.85 -0.85 0.00 -1.430.70 0.52 0.63 0.78 0.64 0.860.44 0.02 0.39 0.31 0.02 0.27-0.32 -0.24 -0.29 -0.20 -0.17 -0.23-0.12 -0.03 -0.10 -0.14 -0.02 -0.140.10 0.07 0.09 0.10 0.09 0.12
0.00 -2.10 3.94 -1.84 0.00 -1.70 4.14 -2.44
QP QM QV QR RQ RN RW RS0.295 0.220 0.220 0.265 0.265 0.220 0.220 0.295
-5.00 5.00 -5.00 5.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.55 -0.71 0.00 0.00 0.55 -0.71 0.000.05 0.03 0.03 0.04 0.04 0.03 0.03 0.050.12 -0.16 0.26 0.02 0.02 -0.18 0.32 0.06-0.07 -0.05 -0.05 -0.06 -0.06 -0.05 -0.05 -0.07-0.07 0.06 -0.12 -0.03 -0.03 0.04 -0.08 -0.020.05 0.04 0.04 0.04 0.03 0.02 0.02 0.03
0.00 0.07 -4.53 4.45 0.01 0.00 0.00 -4.58 4.54 0.05 0.00
ML MQ MH MN NM NR NI NÑ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 1
-5.00 0.00 -5.00 0.001.47 1.10 1.10 1.33 1.33 1.10 1.10 1.480.77 0.00 0.00 0.66 0.66 0.00 0.00 1.01-0.42 -0.32 -0.32 -0.38 -0.44 -0.37 -0.37 -0.49-0.24 0.02 -0.06 -0.22 -0.19 0.02 -0.06 -0.150.15 0.11 0.11 0.13 0.10 0.08 0.08 0.110.04 -0.03 0.04 0.05 0.07 -0.02 0.04 0.06-0.03 -0.02 -0.02 -0.03 -0.04 -0.03 -0.03 -0.04
0.00 1.74 -4.14 0.85 1.54 0.00 1.48 -4.22 0.77 1.97 0.00
![Page 58: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/58.jpg)
HG HC HM HI IH ID IN IJ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 1
0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.55 0.00 0.00 0.55 0.00-0.16 -0.12 -0.12 -0.15 -0.15 -0.12 -0.12 -0.16-0.09 -0.16 -0.07 -0.07 -0.18 -0.150.09 0.07 0.07 0.08 0.11 0.09 0.09 0.120.06 0.06 0.05 0.04 0.04 0.04-0.05 -0.04 -0.04 -0.05 -0.03 -0.03 -0.03 -0.04
0.00 -0.15 -0.09 0.36 -0.13 0.00 -0.10 -0.06 0.35 -0.19 0.00
CH DI0.00 0.000.00 0.000.00 0.00-0.06 -0.060.04 0.04-0.02 -0.01-0.04 -0.03
3.94 4.14
V W
2.90 2.90
Q R2.89 2.99
4.45 4.54
-4.53 -4.58
![Page 59: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/59.jpg)
Q R
2.90 2.90
M N-2.99 -3.04
-4.14 -4.22
0.85 0.77
M N
2.90 2.90
H I0.42 0.39
0.36 0.35
-0.09 -0.06
H I
2.90 2.90
![Page 60: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/60.jpg)
C D-0.05 -0.03
-0.04 -0.03
+ Q33 - Q43 = 0
+ Q33 - Q43 = 0
+ Q43 = -0.340
- Q43 = 0
- Q43 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝑄 = 0
![Page 61: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/61.jpg)
= 2.490
= 0
= 0
-14.450
![Page 62: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/62.jpg)
FACTORES DE DISTRIBUCIÓN
3ER NIVEL 4TO NIVEL
NUDO
0.333 T TO = 0.4980.335 TU = 0.5020.332
UUP = 0.299
0.230 UT = 0.3010.231 UV = 0.4000.230
VVQ = 0.282
0.309 VU = 0.3780.220 VW = 0.3400.295
WWR = 0.282
0.220 WV = 0.3400.265 WX = 0.3780.220 X XS = 0.4270.265 XW = 0.573
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
![Page 63: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/63.jpg)
0.2200.2950.2990.4020.299
VU VQ VW WV WR WX0.378 0.282 0.340 0.340 0.282 0.378
-5.00 -5.001.89 1.41 1.70 1.70 1.41 1.891.00 0.55 0.85 0.85 0.55 1.43-0.91 -0.68 -0.82 -0.96 -0.80 -1.07-0.56 -0.24 -0.48 -0.41 -0.26 -0.480.48 0.36 0.43 0.39 0.33 0.440.23 0.12 0.20 0.22 0.12 0.23-0.21 -0.15 -0.19 -0.19 -0.16 -0.21
0.00 1.93 -3.63 1.69 0.00 1.59 -3.81 2.22
QP QM QV QR RQ RN RW RS0.295 0.220 0.220 0.265 0.265 0.220 0.220 0.295
-5.00 -5.001.47 1.10 1.10 1.33 1.33 1.10 1.10 1.480.77 0.00 0.71 0.66 0.66 0.00 0.71 1.01-0.63 -0.47 -0.47 -0.57 -0.63 -0.52 -0.52 -0.70-0.40 -0.06 -0.34 -0.31 -0.28 -0.06 -0.40 -0.360.33 0.25 0.25 0.30 0.29 0.24 0.24 0.330.18 0.04 0.18 0.15 0.15 0.05 0.16 0.17-0.16 -0.12 -0.12 -0.15 -0.14 -0.12 -0.12 -0.16
0.00 1.56 0.74 -3.70 1.40 0.00 1.38 0.70 -3.83 1.75 0.00
ML MQ MH MN NM NR NI NÑ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.55 0.00 0.00 0.00 0.55 0.00 0.00-0.16 -0.12 -0.12 -0.15 -0.15 -0.12 -0.12 -0.16-0.09 -0.24 0.00 -0.07 -0.07 -0.26 0.00 -0.150.12 0.09 0.09 0.11 0.13 0.11 0.11 0.140.08 0.12 0.01 0.06 0.05 0.12 0.01 0.07-0.08 -0.06 -0.06 -0.07 -0.07 -0.06 -0.06 -0.07
![Page 64: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/64.jpg)
0.00 -0.13 0.34 -0.09 -0.12 0.00 -0.10 0.34 -0.06 -0.17 0.00
HG HC HM HI IH ID IN IJ0.295 0.220 0.220 0.265 1 0.265 0.220 0.220 0.295 1
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 -0.06 0.00 0.00 -0.06 0.000.02 0.01 0.01 0.02 0.02 0.01 0.01 0.020.01 0.04 0.01 0.01 0.05 0.02-0.02 -0.01 -0.01 -0.02 -0.02 -0.02 -0.02 -0.02
0.00 0.01 0.00 -0.02 0.01 0.00 0.00 -0.01 -0.01 0.02 0.00
CH DI0.00 0.000.00 0.000.00 0.000.00 0.000.01 0.01-0.01 -0.010.00 0.00
-3.63 -3.81
V W
2.90 2.90
Q R-2.53 -2.63
-3.70 -3.83
![Page 65: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/65.jpg)
0.74 0.70
Q R
2.90 2.90
M N0.37 0.36
0.34 0.34
-0.09 -0.06
M N
2.90 2.90
H I-0.04 -0.03
-0.02 -0.01
0.00 -0.01
H I
2.90 2.90
![Page 66: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/66.jpg)
C D0 0
0.00 0.00
- Q34 + Q44 = 0
- Q34 + Q44 = 0
- Q44 = 0.020
+ Q44 = 0
+ Q44 = 0
∑▒ 〖𝐹 _𝑋 = 0 〗 → ∑▒𝑉 + ∑▒𝑄 = 0
![Page 67: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/67.jpg)
= -0.260
= 0
= 0
2.200
![Page 68: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/68.jpg)
CALCULO DE MOMENTOS FINALES
CUADRO DE MATRICES MATRIZ INVERSA
i31.590 -17.220 2.830 -0.280 1 0.06220068 0.06640481 0.06639931 0.06638208-17.130 28.810 -16.940 2.460 2 0.06665521 0.13772130 0.14221141 0.142235522.670 -16.740 28.170 -13.760 3 0.06669326 0.14208038 0.21334627 0.21794751-0.250 2.380 -13.720 11.560 4 0.06663640 0.14204137 0.21774988 0.28945699
MOMENTOS FINALES
Qi1 Qi2 Qi3 Qi4 Qi1 Qi2 Qi3 Qi4
∑▒ 〖𝐹 _𝑋 = 0 〗 → −𝑅 _1+𝐶_1 𝑥𝑄_11−𝐶_2 𝑥𝑄_12− _𝐶 3 _1𝑥𝑄 3− _𝐶 4 _1𝑥𝑄 4 = 0∑▒ 〖𝐹 _𝑋 = 0 〗 → −𝑅 _2−𝐶_1 𝑥𝑄_21+𝐶_2 𝑥𝑄_22− _𝐶 3 _𝑥𝑄 23− _𝐶 4 _𝑥𝑄 24 = 0∑▒ 〖𝐹 _𝑋 = 0 〗 → −𝑅 _3−𝐶_1 𝑥𝑄_31−𝐶_2 𝑥𝑄_32+ _𝐶 3 _𝑥𝑄 33− _𝐶 4 _𝑥𝑄 34 = 0∑▒ 〖𝐹 _𝑋 = 0 〗 → −𝑅 _4−𝐶_1 𝑥𝑄_41−𝐶_2 𝑥𝑄_42− _𝐶 3 _𝑥𝑄 43+ _𝐶 4 _𝑥𝑄 44 = 0
![Page 69: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/69.jpg)
MOMENTOS FINALES
-2.94 -4.22
V W
2.90 2.90
Q R
-2.54 -3.63
-5.35 -6.36
Q R
2.90 2.90
M N
-4.84 -5.91
-6.90 -8.09
M N
![Page 70: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/70.jpg)
2.90 2.90
H I
-6.61 -7.90
-6.21 -7.10
H I
2.90 2.90
C D
-7.97 -8.52
![Page 71: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/71.jpg)
FACTORES DE DISTRIBUCIÓN
3ER NIVEL 4TO NIVEL
NUDO
OK = 0.333 T TO = 0.498OP = 0.335 TU = 0.502OT = 0.332
UUP = 0.299
PL = 0.230 UT = 0.301PO = 0.231 UV = 0.400PU = 0.230
VVQ = 0.282
PQ = 0.309 VU = 0.378QM = 0.220 VW = 0.340QP = 0.295
WWR = 0.282
QV = 0.220 WV = 0.340QR = 0.265 WX = 0.378RN = 0.220 X XS = 0.427RQ = 0.265 XW = 0.573RW = 0.220RS = 0.295SÑ = 0.299SR = 0.402SX = 0.299
FACTORES DE DISTRIBUCION
FACTORES DE DISTRIBUCION
![Page 72: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/72.jpg)
XW XS0.573 0.4276.61-3.79 -2.82-0.27 -0.990.72 0.540.34 0.39-0.42 -0.31-0.13 -0.120.15 0.11
0.00 3.21 -3.21
SR SÑ SX0.402 0.299 0.299 16.61-2.66 -1.98 -1.98-0.21 -0.99 -1.411.05 0.78 0.780.22 0.33 0.27-0.33 -0.24 -0.24-0.15 -0.12 -0.160.17 0.13 0.134.71 -2.09 -2.61
ÑN ÑS ÑJ0.402 0.299 0.299 16.61-2.66 -1.98 -1.98-0.21 -0.99 -0.990.88 0.66 0.660.21 0.39 0.18
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-0.32 -0.23 -0.23-0.12 -0.12 -0.080.13 0.10 0.104.53 -2.18 -2.35
JI JE JÑ0.402 0.299 0.299 16.61-2.66 -1.98 -1.98-0.21 -0.990.48 0.36 0.360.19 0.33-0.21 -0.16 -0.16-0.07 -0.120.08 0.06 0.064.21 -1.72 -2.49
EJ0.00-0.990.18-0.080.03-0.86
-3.21
- X
2.90
S-2.01
-2.61
R4
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-2.09
S
2.90
Ñ-1.47
-2.18
-2.35
Ñ
2.90
J-1.67
-2.49
-1.72
J
2.90
R1
R 2
R3
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+E-0.89
-0.86
![Page 76: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/76.jpg)
XW XS0.573 0.427
0.00 0.000.00 0.000.00 0.000.00 0.11-0.06 -0.05-0.01 -0.030.02 0.02
0.00 -0.05 0.05
SR SÑ SX0.402 0.299 0.299 1
0.00 0.00 0.000.00 -0.75 0.000.30 0.22 0.220.08 0.11 0.00-0.08 -0.06 -0.06-0.06 -0.07 -0.020.06 0.05 0.050.31 -0.50 0.19
ÑN ÑS ÑJ0.402 0.299 0.299 1
5.00-2.01 -1.50 -1.49-0.74 0.00 0.000.30 0.22 0.220.25 0.11 0.11-0.19 -0.14 -0.14-0.07 -0.03 -0.03
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0.05 0.04 0.04-2.41 -1.29 3.71
JI JE JÑ0.402 0.299 0.299 1
-5.00 5.000.00 0.00 0.000.00 -0.750.30 0.22 0.220.08 0.11-0.08 -0.06 -0.06-0.06 -0.070.05 0.04 0.040.30 -4.79 4.50
EJ0.00-5.000.000.11-0.030.02-4.90
0.05
- X
2.90
S0.08
0.19
Q41
![Page 78: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/78.jpg)
-0.50
S
2.90
Ñ-0.62
-1.29
3.71
Ñ
2.90
J2.83
4.50
-4.79
J
2.90
Q31
Q21
Q11
![Page 79: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/79.jpg)
E-3.34
-4.90
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XW XS0.573 0.427
0.00 0.000.00 -0.750.43 0.320.10 0.11-0.12 -0.09-0.09 -0.060.09 0.07
0.00 0.40 -0.40
SR SÑ SX0.402 0.299 0.299 1
5.00-2.01 -1.49 -1.50-0.74 0.00 0.000.30 0.22 0.220.25 0.00 0.16-0.16 -0.12 -0.12-0.06 0.00 -0.050.04 0.03 0.03-2.39 3.64 -1.25
ÑN ÑS ÑJ0.402 0.299 0.299 1
5.00 -5.000.00 0.00 0.000.00 -0.75 0.750.00 0.00 0.000.00 0.11 -0.110.00 0.00 0.000.00 -0.06 0.040.01 0.01 0.01
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0.01 4.31 -4.32
JI JE JÑ0.402 0.299 0.299 1
0.00 -5.002.01 1.49 1.500.74 0.00-0.30 -0.22 -0.22-0.25 0.000.10 0.07 0.070.05 0.00-0.02 -0.01 -0.012.33 1.33 -3.67
EJ0.000.000.75-0.110.04-0.010.67
-0.40
- X
2.90
S-0.57
-1.25
Q42
![Page 82: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/82.jpg)
3.64
S
2.90
Ñ2.74
4.31
-4.32
Ñ
2.90
J-2.75
-3.67
1.33
J
2.90
Q32
Q12
Q22
![Page 83: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/83.jpg)
E0.69
0.67
![Page 84: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/84.jpg)
XW XS0.573 0.427
5.00-2.86 -2.14-0.94 0.000.54 0.400.43 0.05-0.27 -0.20-0.11 -0.020.08 0.06
0.00 -3.15 3.15
SR SÑ SX0.402 0.299 0.299
-5.00 5.000.00 0.00 0.000.00 0.75 -1.070.13 0.10 0.100.02 -0.11 0.20-0.05 -0.03 -0.03-0.03 0.05 -0.100.04 0.03 0.030.11 -4.23 4.12
ÑN ÑS ÑJ0.402 0.299 0.299 1
-5.00 0.002.01 1.50 1.490.74 0.00 0.00-0.30 -0.22 -0.22-0.25 0.05 -0.110.12 0.09 0.090.06 -0.02 0.03-0.03 -0.02 -0.022.36 -3.62 1.26
![Page 85: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/85.jpg)
JI JE JÑ0.402 0.299 0.299 1
0.00 0.000.00 0.00 0.000.00 0.75-0.30 -0.22 -0.22-0.08 -0.110.08 0.06 0.060.06 0.05-0.04 -0.03 -0.03-0.29 -0.20 0.49
EJ0.000.000.00-0.110.03-0.02-0.10
3.15
- X
2.90
S2.51
4.12
-4.23
Q43
![Page 86: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/86.jpg)
S
2.90
Ñ-2.71
-3.62
1.26
Ñ
2.90
J0.6
0.49
-0.20
J
2.90
Q23
Q13
Q33
![Page 87: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/87.jpg)
E-0.1
-0.10
![Page 88: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/88.jpg)
XW XS0.573 0.427
-5.002.86 2.140.94 0.75-0.97 -0.72-0.54 -0.270.46 0.340.22 0.12-0.20 -0.15
0.00 2.79 -2.79
SR SÑ SX0.402 0.299 0.299
-5.002.01 1.49 1.500.74 0.00 1.07-0.73 -0.54 -0.54-0.35 -0.11 -0.360.33 0.25 0.250.16 0.05 0.17-0.16 -0.12 -0.122.01 1.03 -3.04
ÑN ÑS ÑJ0.402 0.299 0.299 1
0.00 0.00 0.000.00 0.75 0.00-0.30 -0.22 -0.22-0.08 -0.27 0.000.14 0.10 0.100.07 0.12 0.02-0.08 -0.06 -0.06
![Page 89: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/89.jpg)
-0.25 0.42 -0.16
JI JE JÑ0.402 0.299 0.299 1
0.00 0.00 0.000.00 0.000.00 0.00 0.000.00 -0.110.04 0.03 0.030.01 0.05-0.02 -0.02 -0.020.03 0.02 -0.04
EJ0.000.000.000.000.02-0.010.01
-2.79
- X
2.90
S-2.01
-3.04
Q44
![Page 90: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/90.jpg)
1.03
S
2.90
Ñ0.5
0.42
-0.16
Ñ
2.90
J-0.07
-0.04
0.02
J
2.90
Q24
Q34
Q14
![Page 91: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/91.jpg)
E0.01
0.01
![Page 92: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/92.jpg)
MATRIZ INVERSA 0 0 0 0.1 2.0640 0 0 0.1 4.6290 0 0 0.2 6.643
0.06638208 0 0 0 0.3 7.8810.142235520.217947510.28945699
Qi4
![Page 93: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/93.jpg)
-6.02MOMENTOS FINALES
- X MAF = -5.51 MKF = 0.37MBG = -9.06 MKO = 1.49MCH = -7.97 MKL = -1.86MDI = -8.52 MLK = 17.84MEJ = -7.82 MLP = -7.16
2.90 MFA = -0.71 MLG = -9.57MFK = 1.20 0 MLM = -1.10MFG = -0.49 MML = 13.30MGF = 18.51 MMQ = -4.84MGL = -9.45 0 MMH = -6.90
S MGB = -8.24 MMN -1.57MGH = -0.82 MNM = 14.17MHG = 13.81 MNR = -5.91
-4.57 MHC = -6.21 0 MNÑ = -0.18MHM = -6.61 MNI = -8.09MHI = -0.98 MÑN = 13.26MIH = 14.63 MÑJ = -7.59
-6.28 MID = -7.10 MÑS = -5.67MIN = -7.90 0MIJ = 0.37
S MJI = 13.95MJE = -6.64 0MJÑ = -7.31
2.90
Ñ
-5.67
-7.59
Ñ
![Page 94: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/94.jpg)
2.90
J
-7.31
-6.64
J
2.90
E
-7.82
![Page 95: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/95.jpg)
![Page 96: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/96.jpg)
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+-
![Page 99: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/99.jpg)
MOMENTOS FINALES
0.37 MOK = 0.46 MTO = 4.501.49 0 MOT = 3.85 0 MTU = -4.50 0-1.86 MOP = -4.31 MUT = 13.8917.84 MPO = 16.20 MUP = -6.73 0-7.16 0 MPU = -5.27 0 MUV = -7.16-9.57 MPL = -8.24 MVU = 8.29-1.10 MPQ = -2.70 MVQ = -2.94 013.30 MQP = 11.35 MVW = -5.35-4.84 0 MQV = -2.54 0 MWV = 10.25-6.90 MQM = -5.35 MWR = -4.22 0-1.57 MQR -3.46 MWX = -6.03
14.17 MRQ = 12.35 MXW = 6.02-5.91 0 MRW = -3.63 0 MXS = -6.02 0-0.18 MRS = -2.36-8.09 MRN = -6.3613.26 MSR = 10.86-7.59 0 MSX = -4.57 0-5.67 MSÑ = -6.28
![Page 100: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/100.jpg)
0
![Page 101: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/101.jpg)
0
![Page 102: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/102.jpg)
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-
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CALCULO DE "C" POR MATRICES
#VALUE!
![Page 105: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/105.jpg)
ECUACION PARA CALCULAR LAS CONSTANTES COEFICIENTESC1 C2 C3
NIVEL = + C1*Q11-C2*Q12-C3*Q13-R1 = 0 #REF! #REF! #REF! 0NIVEL = - C1*Q21+C2*Q22-C3*Q23-R2 = 0 #REF! #REF! #REF! 0NIVEL = - C1*Q31-C2*Q32+C3*Q33-R3 = 0 #REF! #REF! #REF! -
#REF! C1 + #REF! C2 #REF! C3 = 0 MATRIS INVERSA#REF! C + #REF! C2 #REF! C3 = 0 #REF! #REF! #REF!#REF! C1 + #REF! C2 + #REF! C3 = - #REF! #REF! #REF!
#REF! #REF! #REF!
C1 = #VALUE!C2 = #VALUE!C3 = #VALUE!
MOMENTOS FINALES
MAE = #REF! MGF =MBF = #REF! MGK =MCG = #REF! MGH =MDH = #REF! MGC =MEA = #REF! MHG =MEF = #REF! MHL =MEI = MHD =MFE = MIE =MFJ = MIJ =MFG = MIM =MFB =
MJI =MMI = MJN =MMN = MJK =MNM = MJF =MNO = MKJ =MNJ = MKO =MON = MKL =MOP = MKG =MOK = MLK =MPO = MLP =MPL = MLH =
1ᵒ2o3o
![Page 106: Metodo Cros](https://reader036.vdocuments.mx/reader036/viewer/2022062520/5695d2cf1a28ab9b029bcb7b/html5/thumbnails/106.jpg)
C1 = ###C2 = ###C3 = ###