Metodo Cros

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

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 )

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




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

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

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

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 〗

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 〗

R4 = 10.463 Tn

R3 = 16.212 Tn

R2 = 21.458 Tn

R1 = 23.452 Tn

CROSS DESPLAZAMIENTO 1ER NIVEL

CON:

∴ M = -5



NUDO NUDO NUDO NUDO

A AF = 0.000F

FA = 0.333K

KF = 0.333O


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





- 6𝐸𝐼"Δ" /𝐿^2 =𝑀_((𝐴𝐿𝐸𝐴𝑇𝑂𝑅𝐼𝑂))

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

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

-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

A B-3.31 -3.41

-4.87 -4.97


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 〗

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


Q41 = 0.250 Tn

∑▒ 〖𝐹 _𝑋 = 0 〗

∑▒ 〖𝐹 _𝑋 = 0 〗

Q41 = 0.250 Tn

Q31 = -2.670 Tn

Q21 = 17.130 Tn

Q11 = 31.590 Tn

CROSS DESPLAZAMIENTO 2DO NIVEL

CON:

∴ M = -5



NUDO NUDO NUDO NUDO

A AF = 0.000F

FA = 0.333K

KF = 0.333O


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


I

ID = 0.220

N

NI = 0.220

R

RN = 0.220IH = 0.265 NM = 0.265 RQ = 0.265






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

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

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

A B0.79 0.43

0.76 0.42


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 〗

- 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


Q42 = -2.380 Tn

∑▒ 〖𝐹 _𝑋 = 0 〗

∑▒ 〖𝐹 _𝑋 = 0 〗

Q32 = 16.740 Tn

Q22 = 28.810 Tn

Q12 = 17.220 Tn

CROSS DESPLAZAMIENTO 3ER NIVEL

CON:

∴ M = -5



NUDO NUDO NUDO NUDO

A AF = 0.000F

FA = 0.333K

KF = 0.333O


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


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






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

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

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

A B-0.13 -0.03

-0.13 -0.03


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 〗

+ 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


Q43 = 13.720 Tn

∑▒ 〖𝐹 _𝑋 = 0 〗

∑▒ 〖𝐹 _𝑋 = 0 〗

Q33 = 28.170 Tn

Q23 = 16.940 Tn

Q13 = -2.830 Tn

CROSS DESPLAZAMIENTO 4TO NIVEL

CON:

∴ M = -5



NUDO NUDO NUDO NUDO

A AF = 0.000F

FA = 0.333K

KF = 0.333O


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


I

ID = 0.220

N

NI = 0.220

R

RN = 0.220IH = 0.265 NM = 0.265 RQ = 0.265






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

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

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

A B0.01 0

0.01 0.00


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 〗

+ 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


∑▒ 〖𝐹 _𝑋 = 0 〗

∑▒ 〖𝐹 _𝑋 = 0 〗

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

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

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

MÉTODO CROSS

2.90

2.90

2.90

2.90

TRAMO43.920 Tn/m3.920 Tn/m3.920 Tn/m3.920 Tn/m FACTORES DE DISTRIBUCIÓN


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





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



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

-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

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

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

- R4 = 0

= 48.133

= 0

= 0

26.675


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



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

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

-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

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

- Q41 = 0

= 14.710

= 0

= 0

-2.420


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



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


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


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

0.00 0.00 4.55 -4.55 0.00 0.00 0.00 4.59 -4.59 0.00 0.00


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

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

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

= -14.450

= 0

= 0

14.360


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



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


-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


-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


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

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

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

= 2.490

= 0

= 0

-14.450


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



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


-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


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

0.00 -0.13 0.34 -0.09 -0.12 0.00 -0.10 0.34 -0.06 -0.17 0.00


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

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

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

= -0.260

= 0

= 0

2.200

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

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

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


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



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

-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

-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

+E-0.89

-0.86

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

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

-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

E-3.34

-4.90

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

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

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

E0.69

0.67

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

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

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

E-0.1

-0.10

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

-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

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

E0.01

0.01

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

-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

2.90

J

-7.31

-6.64

J

2.90

E

-7.82

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

CALCULO DE "C" POR MATRICES

#VALUE!

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

C1 = ###C2 = ###C3 = ###

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