cros de tres niveles wilhurto1111

METODO DE CROSS

DIAGRAMA GRAFICO PORTICO DE 3 NIVELES

Q3 4.00 TN/M Q3 4.00 TN/M Q3 4.00 TN/M

P3 8 TN

D 1 EI E 1 EI L 1 EI M

2 EI 2 EI 2 EI 3.00 M

Q2 9.00 TN/M Q2 9.00 T/M Q2 9.00 TN/M

P2 6 TN

C 1 EI F 1 EI K 1 EI N

3 EI 3 EI 3 EI 3.00 M

Q1 9.00 T/M Q1 9.00 T/M Q1 9.00 T/M

P1 4 TN

B 1 EI G 1 EI J 1 EI O

4 EI 4 EI 4 EI 4.00 M

A H I

L1= 4.50 L1= 5.75 L3= 2.90

A) DETERMINACION DE LAS RIGIDECES

NUDOS A,H,I

KAB = KBA = 1.000 EIKHG = KGH = 1.000 EI K = I = 4 EI = 1.000 EI

KIJ = KJI = 1.000 EI L 4.00

NUDOS B,G,J

KBC = KCB = 1.000 EIKGF = KFG = 1.000 EI K = I = 3 EI = 1.000 EIKJK = KKJ = 1.000 EI L 3.00

NUDOS C,F,K

KCD = KDC = 0.667 EIKFE = KEF = 0.667 EI K = I = 2 EI = 0.667 EIKKL = KLK = 0.667 EI L 3.00

NUDOS D,C,B

KDE = KED = 0.222 EIKCF = KFC = 0.222 EI K = I = 1 EI = 0.222 EIKBG = KGB = 0.222 EI L 4.50

NUDOS E,F,G

KEL = KLE = 0.174 EIKFK = KKF = 0.174 EI K = I = 1 EI = 0.174 EIKGJ = KJG = 0.174 EI L 5.75

NUDOS L,K,J

KLM = KML = 0.345 EIKKN = KNK = 0.345 EI K = I = 1 EI = 0.345 EIKJO = KOJ = 0.345 EI L 2.90

PROYECTO: LOCAL COMERCIAL CURSO: ANALISIS ESTRUCTURAL IICARRERA: INGENIERIA CIVIL LUGAR: ABANCAYDOCENTE: ING. RAUL MANRIQUE PADILLA CODIGO: 2008147812ALUMNO: ERWIN BALLON SAAVEDRA FECHA: NOVIEMBRE - 2010

METODO DE CROSS


B) CALCULO DE LOS FACTORES DE DISTRIBUCION

NUDO B

FD BA = KBA = 1 = 0.450

KBA + KBG + KBC 1 + 0.222 + 1

FD BG = KBG = 0.222 = 0.100 = 1.000

KBG + KBC + KBA 0.222 + 1.000 + 1.000

FD BC = KBC = 1.000 = 0.450

KBC + KBA + KBG 1.000 + 1.000 + 0.222

NUDO C

FD CB = KCB = 1.000 = 0.529

KCB + KCF + KCD 1.000 + 0.222 + 0.667

FD CF = KCF = 0.222 = 0.118 = 1.000

KCF + KCD + KCB 0.222 + 0.667 + 1.000

FD CD = KCD = 0.667 = 0.353

KCD + KCB + KCF 0.667 + 1.000 + 0.222

NUDO D

FD DC = KDC = 0.667 = 0.750

KDC + KDE 0.667 + 0.222

= 1.000

FD DE = KDE = 0.222 = 0.250

KDE + KDC 0.222 + 0.667

NUDO E

FD ED = KED = 0.222 = 0.209

KED + KEL + KEF 0.222 + 0.174 + 0.667

FD EL = KEL = 0.174 = 0.164 = 1.000

KEL + KED + KEF 0.174 + 0.222 + 0.667

FD EF = KEF = 0.667 = 0.627

KEF + KEL + KED 0.667 + 0.174 + 0.222

NUDO F

FD FC = KFC = 0.222 = 0.108

KFC + KFE + KFK + KFG 0.222 + 0.667 + 0.174 + 1.000

FD FE = KFE = 0.667 = 0.323

KFE + KFK + KFG + KFC 0.667 + 0.174 + 1.000 + 0.222 = 1.000

FD FK = KFK = 0.174 = 0.084

KFK + KFG + KFC + KFE 0.174 + 1.000 + 0.222 + 0.667

FD FG = KFG = 1.000 = 0.485

KFG + KFC + KFE + KFK 1.000 + 0.222 + 0.667 + 0.174

NUDO G

FD GB = KGB = 0.222 = 0.093

KGB + KGF + KGJ + KGH 0.222 + 1.000 + 0.174 + 1.000

FD GF = KGF = 1.000 = 0.417

KGF + KGJ + KGH + KGB 1.000 + 0.174 + 1.000 + 0.222 = 1.000

METODO DE CROSS


FD GJ = KGJ = 0.174 = 0.073

KGJ + KGH + KGB + KGF 0.174 + 1.000 + 0.222 + 1.000

FD GH = KGH = 1.000 = 0.417

KGH + KGB + KGF + KGJ 1.000 + 0.222 + 1.000 + 0.174

NUDO L

FD LE = KLE = 0.174 = 0.207

KLE + KLK 0.174 + 0.667

= 1.000

FD LK = KLK = 0.667 = 0.793

KLK + KLE 0.667 + 0.174

NUDO K

FD KL = KKL = 0.667 = 0.362

KKL + KKF + KKJ 0.667 + 0.174 + 1.000

FD KF = KKF = 0.174 = 0.094 = 1.000

KKF + KKJ + KKL 0.174 + 1.000 + 0.667

FD KJ = KKJ = 1.000 = 0.543

KKJ + KKL + KKF 1.000 + 0.667 + 0.174

NUDO J

FD JK = KJK = 1.000 = 0.460

KJK + KJG + KJI 1.000 + 0.174 + 1.000

FD JG = KJG = 0.174 = 0.080 = 1.000

KJG + KJI + KJK 0.174 + 1.000 + 1.000

FD JI = KJI = 1.000 = 0.460

KJI + KJK + KJG 1.000 + 1.000 + 0.174

NUDO A

FD AB = 0.00 CONDICION: POR EMPOTRAMIENTO PERFECTO

NUDO H

FD HG = 0.00 CONDICION: POR EMPOTRAMIENTO PERFECTO

NUDO I

FD IJ = 0.00 CONDICION: POR EMPOTRAMIENTO PERFECTO

NUDO L

FD LM = 0.00 CONDICION: POR SER VOLADIZO

NUDO K

FD KN = 0.00 CONDICION: POR SER VOLADIZO

NUDO J

FD JO = 0.00 CONDICION: POR SER VOLADIZO

C) CALCULO DE LOS MOMENTOS DE EMPOTRAMIENTO

AB = BA = 0.00Me Me

METODO DE CROSS


BC = CB = 0.00

CD = DC = 0.00

DE = = -4 x 4.50 = -6.75

12 12

ED = = 4.00 x 4.50 = 6.75

12 12

EF = FE = 0.00

FG = GF = 0.00

GH = HG = 0.00

EL = = -4.00 x 5.75 = -11.02

12 12

LE = = 4.00 x 5.75 = 11.02

12 12

LM = = -4.00 x 2.90 = -16.82

2 2

ML = = 0.00 x 0.00 = 0.00 (VOLADIZO)

2 2

LK = KL = 0.00

CF = = -9.00 x 4.50 = -15.19

12 12

FC = = 9.00 x 4.50 = 15.19

12 12

FK = = -9.00 x 5.75 = -24.80

12 12

KF = = 9.00 x 5.75 = 24.80

12 12

KN = = -9.00 x 2.90 = -37.85

2 2

NK = = 0.00 x 0.00 = 0.00 (VOLADIZO)

2 2

KJ = JK = 0.00

BG = = -9.00 x 4.50 = -15.19

12 12

GB = = 9.00 x 4.50 = 15.19

12 12

GJ = = -9.00 x 5.75 = -24.80

12 12

Me Me

Me Me

Me -WL2 2

Me WL2 2

Me Me

Me Me

Me Me

Me -WL2 2

Me WL2 2

Me -WL2 2

Me WL2 2

Me Me

Me -WL2 2

Me WL2 2

Me -WL2 2

Me WL2 2

Me -WL2 2

Me WL2 2

Me Me

Me -WL2 2

Me WL2 2

Me -WL2 2

METODO DE CROSS


JG = = 9.00 x 5.75 = 24.80

12 12

JO = = -9.00 x 2.90 = -37.85

2 2

OJ = = 0.00 x 0.00 = 0.00 (VOLADIZO)

2 2

JI = IJ = 0.00

Me WL2 2

Me -WL2 2

Me WL2 2

Me Me

METRADO DE CARGAS

TABLA DETERMINACION DE LAS LONGITUDES

DESCRP.DESCRIPCION DATOS R1 R2 ASUM.DISTANCIAS CALCUL.

NOMBRE WILBER 6 3 4.50 L1 = 4.50 POR CONDICION NOTA:

CODIGO 7817 23 23 5.75 L2 = 5.75 POR CONDICIONL2/2 SUMATORIA 5.75 2.875 2.875 2.90 L3 = 2.90 POR CONDICION

DIAGRAMA GRAFICO DE LA LOSA ALIGERADA (COLUMNAS - VIGAS

PESO ESPECIFICO DEL CONCRETO

2400 Kg/M3 2.00 2.00

PESO ESPECIFICO DE TECHO ALIGERADO

350 Kg/M2 ### C VP C´ 2.725

PESO ESPECIFICO DE ACABADOS L3100 Kg/M2 VS VS 0.35

PESO ESPECIFICO DE ACABADOS DE CIELO RASO

20 Kg/M2

PESO ESPECIFICO DE MUROS

150 Kg/M2 ### B VP B´ 5.4

L2VIGA PRINCIPAL

CONDICION VP = L/10 0.54

VS VS 0.35

ASUMO VP 0.55 H

VIGA SECUNDARIA ### A VP A´ 4.325

CONDICION VS = L/12 0.33 L1

ASUMO VS 0.35 H VS VS 0.35

1.825 0.35 1.825

METRADO DE CARGA NORMA E-020 (1° NIVEL) Q1

Nº DESCRIPCION UND PESO L A H AREA Peso Kg. Peso TN.METRADO DE CARGA POR METRO LINEAL SEGÚN NORMA 020 (PRIMER NIVEL)DESCRIPCION UND FACTOR L A H AREA Peso Kg. Peso TN/M

1 PESO PROPIO DE LA VIGA T/M3 2.400 13.50 0.35 0.55 ### 6.24

2 TECHO ALIGERADO T/M2 0.350 3.65 ### 1.28

3 ACABADOS MAS CIELO RASO T/M2 0.12 3.65 438.00 0.44

4 TABIQUERIA T/M2 0.15 3.65 547.50 0.55

CARGA MUERTA TOTAL 8.506 SOBRE CARGAS : CARGA VIVA (C.V.) T/M2 0.1 3.650 365.00 0.37

CARGA VIVA TOTAL 0.37

7 Q1 TOTAL = (1.40 x CM + 1.70 x CV) SUMA TOTAL CM y CV 8.86

METRADO DE CARGA POR METRO LINEAL SEGÚN NORMA 020 (SEGUNDO NIVEL)DESCRIPCION UND FACTOR L A H AREA Peso Kg. Peso TN/M

1 PESO PROPIO DE LA VIGA T/M3 2.400 13.50 0.35 0.55 ### 6.24



4 TABIQUERIA T/M2 0.15 3.65 547.50 0.55

CARGA MUERTA TOTAL 8.50

6 SOBRE CARGAS : CARGA VIVA (C.V.) T/M2 0.10 3.650 365.00 0.37



METRADO DE CARGA POR METRO LINEAL SEGÚN NORMA 020 (TERCER NIVEL)DESCRIPCION UND FACTOR L A H AREA Peso Kg. Peso TN/M

1 PESO PROPIO DE LA VIGA T/M3 2.400 13.50 0 0.55 ### 1.32



4 TABIQUERIA T/M2 0.15 3.65 547.50 0.55

CARGA MUERTA TOTAL 3.58

6 SOBRE CARGAS : CARGA VIVA (C.V.) T/M2 0.10 3.650 365.00 0.37



SUMINOS AL ENTERO

Q1= 8.86 T/ML 9.00

PROYECTO: LOCAL COMERCIAL CURSO: ANALISIS ESTRUCTURAL IICARRERA: INGENIERIA CIVIL LUGAR: ABANCAYDOCENTE: ING. RAUL MANRIQUE PADILLA CODIGO: 2008147817ALUMNO: WILBER HURTADO TORRES FECHA: NOVIEMBRE - 2010

L1/2 ≥ 4.5 ES APLICADA LA NORMA

E-020 CARGAS Y SUS DIFERENTES

L2/4 "≥ 5

METRADO DE CARGAS

PROYECTO: LOCAL COMERCIAL CURSO: ANALISIS ESTRUCTURAL IICARRERA: INGENIERIA CIVIL LUGAR: ABANCAYDOCENTE: ING. RAUL MANRIQUE PADILLA CODIGO: 2008147817ALUMNO: WILBER HURTADO TORRES FECHA: NOVIEMBRE - 2010

Q2= 8.86 T/ML 9.00

Q3= 3.95 T/ML 4.00

ALUMNO : WILBER HURTADO TORRESNOTA : SOLO INGRESAR EN LO COLORES AZULES LOS DATOS SEGÚN PIDA

a). ETAPA CROSS SIN DESPLAZAMIENTOS LATERALES

NODO A B C D E L K J IBARRAS AB BA BG BC CB CF CD DC DE ED EF EL LE LM LK KL KF KN KJ JK JG JO JI IJFD 0.000 0.450 0.100 0.450 0.529 0.118 0.353 0.750 0.250 0.209 0.627 0.164 0.207 0.000 0.793 0.362 0.094 0.000 0.543 0.460 0.080 0.000 0.460 0.000M. Empot P. 0.000 0.000 -15.188 0.000 0.000 -15.188 0.000 0.000 -6.750 6.750 0.000 -11.021 11.021 -16.820 0.000 0.000 24.797 -37.845 0.000 0.000 24.797 -37.845 0.000 0.000

-15.188 -15.188 -6.750 -4.271 -5.799 -13.048 -13.0481er. Distrib. 6.834 1.519 6.834 8.040 1.787 5.360 5.063 1.688 0.893 2.679 0.699 1.200 0.000 4.599 4.726 1.233 0.000 7.089 6.002 1.044 0.000 6.0021er. Transp. 3.417 4.020 3.417 2.531 2.680 0.446 0.844 0.600 0.349 2.363 2.300 3.001 3.545 3.001

4.020 5.948 3.127 1.444 2.712 5.301 3.5452da. Distrib. -1.809 -0.402 -1.809 -3.149 -0.700 -2.099 -2.345 -0.782 -0.302 -0.906 -0.236 -0.561 0.000 -2.151 -1.920 -0.501 0.000 -2.880 -1.631 -0.284 0.000 -1.6312da. Transp. -0.905 -1.575 -0.905 -1.172 -1.050 -0.151 -0.391 -0.281 -0.118 -0.960 -1.076 -0.815 -1.440 -0.815


0.550 0.805 0.437 0.262 0.397 0.759 0.5144ta. Distrib. -0.247 -0.055 -0.247 -0.426 -0.095 -0.284 -0.328 -0.109 -0.055 -0.164 -0.043 -0.082 0.000 -0.315 -0.275 -0.072 0.000 -0.412 -0.236 -0.041 0.000 -0.236

M. Totales 2.867 5.486 -13.968 8.482 8.432 -13.951 5.519 5.287 -5.287 8.030 2.030 -10.060 12.087 -16.820 4.733 4.868 25.636 -37.845 7.341 7.416 25.631 -37.845 4.798 2.517

VA ………….

NODO D F G HBARRAS EF FE FC FK FG GF GB GJ GH HGFD 0.627 0.323 0.108 0.084 0.485 0.417 0.093 0.073 0.417 0.000M. Empot P. 0.000 0.000 15.188 -24.797 0.000 0.000 15.188 -24.797 0.000 0.000

-9.609 -9.6091er. Distrib. 2.679 3.106 1.035 0.810 4.658 4.010 0.891 0.697 4.0101er. Transp. 1.339 2.005 2.329 2.005

3.345 2.3292da. Distrib. -0.906 -1.081 -0.360 -0.282 -1.621 -0.972 -0.216 -0.169 -0.9722da. Transp. -0.453 -0.486 -0.811 -0.486


0.380 0.2284ta. Distrib. -0.164 -0.123 -0.041 -0.032 -0.184 -0.095 -0.021 -0.017 -0.095

M. Totales 2.030 3.303 15.923 -24.222 4.996 5.028 15.917 -24.226 3.282 1.688


a). ETAPA CROSS SIN DESPLAZAMIENTOS LATERALES

NODO D F G HBARRAS EF FE FC FK FG GF GB GJ GH HGFD 0.627 0.323 0.108 0.084 0.485 0.417 0.093 0.073 0.417 0.000M. Empot P. 0.000 0.000 160.313 -261.745 0.000 0.000 158.625 -258.989 0.000 0.000


22.265 24.5972er. Distrib. -0.906 -7.192 -2.405 -1.870 -10.799 -10.257 -2.288 -1.796 -10.2572er. Transp. -0.453 -5.129 -5.399 -5.129


1.336 1.3534er. Distrib. -0.164 -0.432 -0.144 -0.112 -0.648 -0.564 -0.126 -0.099 -0.564

M. Totales 2.030 28.039 169.321 -254.738 57.378 53.833 166.048 -253.163 33.282 16.923

REACCIONES NECESARIAS PARA IMPEDIR LOS DESPLAZAMIENTOS LATERALES

FUERZA 3D E L F3 17.706

5.287 2.030 4.733

3.00 m 3.00 m 3.00 m

5.519 C 3.303 F 4.868 K

7.281 3.979 6.446

FD CD= +=

5.519 + 5.287=

7.281L 3.00

FD FE= +=

3.303 + 2.030=

3.979L 3.00

FD KL= +=

4.868 + 4.733=

6.446L 3.00

F3 = + + = 7.281 + 3.979 + 6.446 = 17.706


C F K F2 10.142

8.432 4.996 7.341

3.00 m 3.00 m 3.00 m

8.482 B 5.028 G 7.416 J

11.292 6.693 9.863

FD BC= +=

8.482 + 8.432=

11.292L 3.00

FD GF= +=

5.028 + 4.996=

6.693L 3.00

FD JK= +=

7.416 + 7.341=

9.863L 3.00

F2 = + + - F3 = 11.292 + 6.693 + 9.863 - 17.706 = 10.142

MC MD

MF ME

MK ML

FCD FFE FKL

MB MC

MG MF

MJ MK

FBC FGF FJK


C F K F2 10.142

B G J F1 17.385

5.486 3.282 4.798

4.00 m 4.00 m 4.00 m

2.867 A 1.688 H 2.517 I

4.239 2.509 3.716

FD AB= +=

2.867 + 5.486=

4.239L 4.00

FD HG= +=

1.688 + 3.282=

2.509L 4.00

FD IJ= +=

2.517 + 4.798=

3.716L 4.00

F1 = + + - F3 - F2 = 4.239 + 2.509 + 3.716 - 17.706 - 10.142 = -17.385

MARCO A RESOLVER CON LAS FUERZAS LATERALES TOTALES

P3 = 8 Tn D E L F3 17.706

P2 = 6 Tn C F K F2 10.142

P1 = 4 Tn B G J F1 17.385

A H I

H3= P3 + F3 = 8 + 17.706 = 25.706 Tn SE TOMA = 10 Tn

H2= P2 + F2 = 6 + 10.142 = 16.142 Tn SE TOMA = 15 Tn

MA MB

MH MG

MI MJ

FAB FHG FIJ

H1= P1 + F1 = 4 + 17.385 = 21.385 Tn SE TOMA = 7.5 Tn


b). CROSS CON IMPOSISCION DE MOMENTOS EN EL NIVEL TRES (3)

NODO A B C D E L K J IBARRAS AB BA BG BC CB CF CD DC DE ED EF EL LE LM LK KL KF KN KJ JK JG JO JI IJFD 0.000 0.450 0.100 0.450 0.529 0.118 0.353 0.750 0.250 0.209 0.627 0.164 0.207 0.000 0.793 0.362 0.094 0.000 0.543 0.460 0.080 0.000 0.460 0.000M. Empot P. 0.000 0.000 0.000 0.000 0.000 0.000 -10.000 -10.000 0.000 0.000 -10.000 0.000 0.000 0.000 -10.000 -10.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 -10.000 -10.000 -10.000 -10.000 -10.000 0.0001er. Distrib. 0.000 0.000 0.000 5.294 1.176 3.529 7.500 2.500 2.091 6.273 1.636 2.069 0.000 7.931 3.622 0.945 0.000 5.433 0.000 0.000 0.000 0.0001er. Transp. 0.000 2.647 0.000 3.750 1.765 1.045 1.250 1.034 0.818 1.811 3.966 0.000 2.717 0.000

2.647 3.750 2.810 2.284 2.629 3.966 2.7172da. Distrib. -1.191 -0.265 -1.191 -1.985 -0.441 -1.324 -2.108 -0.703 -0.478 -1.433 -0.374 -0.544 0.000 -2.085 -1.436 -0.375 0.000 -2.154 -1.250 -0.217 0.000 -1.2502da. Transp. -0.596 -0.993 -0.596 -1.054 -0.662 -0.239 -0.351 -0.272 -0.187 -0.718 -1.043 -0.625 -1.077 -0.625


0.437 0.561 0.356 0.206 0.353 0.607 0.4534ta. Distrib. -0.196 -0.044 -0.196 -0.297 -0.066 -0.198 -0.267 -0.089 -0.043 -0.129 -0.034 -0.073 0.000 -0.280 -0.220 -0.057 0.000 -0.330 -0.208 -0.036 0.000 -0.208

M. Totales -0.372 -0.941 -0.209 1.150 3.513 0.863 -4.376 -2.805 2.805 2.712 -4.899 2.187 2.321 0.000 -2.321 -4.148 0.670 0.000 3.478 1.130 -0.167 0.000 -0.962 -0.377

VA ………….

NODO D F G HBARRAS EF FE FC FK FG GF GB GJ GH HGFD 0.627 0.323 0.108 0.084 0.485 0.417 0.093 0.073 0.417 0.000M. Empot P. -10.000 -10.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

-10.000 0.0001er. Distrib. 6.273 3.232 1.077 0.843 4.848 0.000 0.000 0.000 0.0001er. Transp. 3.136 0.000 2.424 0.000

3.136 2.4242da. Distrib. -1.433 -1.014 -0.338 -0.264 -1.520 -1.012 -0.225 -0.176 -1.0122da. Transp. -0.716 -0.506 -0.760 -0.506


0.354 0.2964ta. Distrib. -0.129 -0.114 -0.038 -0.030 -0.172 -0.124 -0.027 -0.022 -0.124

M. Totales -4.899 -4.886 0.833 0.652 3.401 1.142 -0.182 -0.142 -0.818 -0.347

HALLANDO LAS FUERZAS HORIZONTALES DEBIDO AL DESPLAZAMIENTO EN EL NIVEL 3

FUERZA 33D E L F3 -16.752

-2.805 -4.899 -2.321

3.00 m 3.00 m 3.00 m

-4.376 C -4.886 F -4.148 K

-5.311 -6.519 -4.922

FD CD= +=

-4.376 + -2.805=

-5.311L 3.00

FD FE= +=

-4.886 + -4.899=

-6.519L 3.00

FD KL= +=

-4.148 + -2.321=

-4.922L 3.00

F3 = + + = -5.311 + -6.519 + -4.922 = -16.752


C F K F13 -9.866

3.513 3.401 3.478

3.00 m 3.00 m 3.00 m

1.150 B 1.142 G 1.130 J

2.321 2.276 2.289

FD BC= +=

1.150 + 3.513=

2.321L 3.00

FD GF= +=

1.142 + 3.401=

2.276L 3.00

FD JK= +=

1.130 + 3.478=

2.289L 3.00

MC MD

MF ME

MK ML

FCD FFE FKL

MB MC

MG MF

MJ MK

F13 = + + - F3 = 2.321 + 2.276 + 2.289 + -16.752 = -9.866


C F K F13 -9.866

B G J F1 5.109

-0.941 -0.818 -0.962

4.00 m 4.00 m 4.00 m

-0.372 A -0.347 H -0.377 I

-0.607 -0.552 -0.618

FD AB= +=

-0.372 + -0.941=

-0.607L 4.00

FD HG= +=

-0.347 + -0.818=

-0.552L 4.00

FD IJ= +=

-0.377 + -0.962=

-0.618L 4.00

F1 = + + - F3 - F2 = -0.607 + -0.552 + -0.618 - -16.752 + -9.866 = 5.109

FBC FGF FJK

MA MB

MH MG

MI MJ

FAB FHG FIJ


c). CROSS CON IMPOSISCION DE MOMENTOS EN EL NIVEL DOS (2)

NODO A B C D E L K J IBARRAS AB BA BG BC CB CF CD DC DE ED EF EL LE LM LK KL KF KN KJ JK JG JO JI IJFD 0.000 0.450 0.100 0.450 0.529 0.118 0.353 0.750 0.250 0.209 0.627 0.164 0.207 0.000 0.793 0.362 0.094 0.000 0.543 0.460 0.080 0.000 0.460 0.000M. Empot P. 0.000 0.000 0.000 -15.000 -15.000 0.000 10.000 10.000 0.000 0.000 10.000 0.000 0.000 0.000 10.000 10.000 0.000 0.000 -15.000 -15.000 0.000 0.000 0.000 0.000

-15.000 -5.000 10.000 10.000 10.000 -5.000 -15.0001er. Distrib. 6.750 1.500 6.750 2.647 0.588 1.765 -7.500 -2.500 -2.091 -6.273 -1.636 -2.069 0.000 -7.931 1.811 0.472 0.000 2.717 6.900 1.200 0.000 6.9001er. Transp. 3.375 1.324 3.375 -3.750 0.882 -1.045 -1.250 -1.034 -0.818 0.906 -3.966 3.450 1.358 3.450

1.324 -0.375 -0.163 -2.284 0.087 -0.516 1.3582da. Distrib. -0.596 -0.132 -0.596 0.199 0.044 0.132 0.122 0.041 0.478 1.433 0.374 -0.018 0.000 -0.069 0.187 0.049 0.000 0.280 -0.625 -0.109 0.000 -0.6252da. Transp. -0.298 0.099 -0.298 0.061 0.066 0.239 0.020 -0.009 0.187 0.093 -0.035 -0.312 0.140 -0.312

0.099 -0.237 0.305 0.011 0.280 -0.347 0.1403er. Distrib. -0.045 -0.010 -0.045 0.125 0.028 0.084 -0.229 -0.076 -0.002 -0.007 -0.002 -0.058 0.000 -0.222 0.126 0.033 0.000 0.189 -0.064 -0.011 0.000 -0.0643er. Transp. -0.022 0.063 -0.022 -0.114 0.042 -0.001 -0.038 -0.029 -0.001 0.063 -0.111 -0.032 0.094 -0.032

0.063 -0.137 0.041 -0.067 0.062 -0.143 0.0944ta. Distrib. -0.028 -0.006 -0.028 0.072 0.016 0.048 -0.030 -0.010 0.014 0.042 0.011 -0.013 0.000 -0.049 0.052 0.014 0.000 0.078 -0.043 -0.008 0.000 -0.043

M. Totales 3.055 6.082 1.351 -7.433 -8.902 0.676 8.226 3.353 -3.353 -2.869 5.195 -2.326 -2.790 0.000 2.790 8.064 0.567 0.000 -8.632 -7.240 1.073 0.000 6.167 3.105

NODO D F G HBARRAS EF FE FC FK FG GF GB GJ GH HGFD 0.627 0.323 0.108 0.084 0.485 0.417 0.093 0.073 0.417 0.000M. Empot P. 10.000 10.000 0.000 0.000 -15.000 -15.000 0.000 0.000 0.000 0.000

-5.000 -15.0001er. Distrib. -6.273 1.616 0.539 0.422 2.424 6.260 1.391 1.089 6.2601er. Transp. -3.136 3.130 1.212 3.130

-0.006 1.2122da. Distrib. 1.433 0.002 0.001 0.001 0.003 -0.506 -0.112 -0.088 -0.5062da. Transp. 0.716 -0.253 0.002 -0.253

0.464 0.0023er. Distrib. -0.007 -0.150 -0.050 -0.039 -0.225 -0.001 0.000 0.000 -0.0013er. Transp. -0.004 0.000 -0.112 0.000

-0.004 -0.1124ta. Distrib. 0.042 0.001 0.000 0.000 0.002 0.047 0.010 0.008 0.047

M. Totales 5.195 9.046 0.490 0.383 -9.919 -8.098 1.289 1.009 5.801 2.877



3.353 5.195 2.790

3.00 m 3.00 m 3.00 m

8.226 C 9.046 F 8.064 K

9.343 10.778 8.994

FD CD= +=

8.226 + 3.353=

9.343L 3.00

FD FE= +=

9.046 + 5.195=

10.778L 3.00

FD KL= +=

8.064 + 2.790=

8.994L 3.00

F3 = + + = 9.343 + 10.778 + 8.994 = 29.115


C F K F2 -2.807

-8.902 -9.919 -8.632

3.00 m 3.00 m 3.00 m

-7.433 B -8.098 G -7.240 J

-10.400 -11.405 -10.117

FD BC= +=

-7.433 + -8.902=

-10.400L 3.00

FD GF= +=

-8.098 + -9.919=

-11.405L 3.00

FD JK= +=

-7.240 + -8.632=

-10.117L 3.00

F2 = + + - F3 = -10.400 + -11.405 + -10.117 + 29.115 = -2.807

MC MD

MF ME

MK ML

FCD FFE FKL

MB MC

MG MF

MJ MK

FBC FGF FJK


C F K F2 -2.807

B G J F1 9.835

6.082 5.801 6.167

4.00 m 4.00 m 4.00 m

3.055 A 5.801 H 3.105 I

4.575 7.251 4.647

FD AB= +=

3.055 + 6.082=

4.575L 4.00

FD HG= +=

5.801 + 5.801=

7.251L 4.00

FD IJ= +=

3.105 + 6.167=

4.647L 4.00

F1 = + + - F3 - F2 = 4.575 + 7.251 + 4.647 - 29.115 - -2.807 = -9.835

MA MB

MH MG

MI MJ

FAB FHG FIJ


c). CROSS CON IMPOSISCION DE MOMENTOS EN EL NIVEL UNO (1)

NODO A B C D E L K J IBARRAS AB BA BG BC CB CF CD DC DE ED EF EL LE LM LK KL KF KN KJ JK JG JO JI IJFD 0.000 0.450 0.100 0.450 0.529 0.118 0.353 0.750 0.250 0.209 0.627 0.164 0.207 0.000 0.793 0.362 0.094 0.000 0.543 0.460 0.080 0.000 0.460 0.000M. Empot P. 0.000 0.000 0.000 -15.000 -15.000 0.000 10.000 10.000 0.000 0.000 10.000 0.000 0.000 0.000 10.000 10.000 0.000 0.000 -15.000 -15.000 0.000 0.000 0.000 0.000

-15.000 -5.000 10.000 10.000 10.000 -5.000 -15.0001er. Distrib. 6.750 1.500 6.750 2.647 0.588 1.765 -7.500 -2.500 -2.091 -6.273 -1.636 -2.069 0.000 -7.931 1.811 0.472 0.000 2.717 6.900 1.200 0.000 6.9001er. Transp. 3.375 1.324 3.375 -3.750 0.882 -1.045 -1.250 -1.034 -0.818 0.906 -3.966 3.450 1.358 3.450

1.324 -0.375 -0.163 -2.284 0.087 -0.516 1.3582da. Distrib. -0.596 -0.132 -0.596 0.199 0.044 0.132 0.122 0.041 0.478 1.433 0.374 -0.018 0.000 -0.069 0.187 0.049 0.000 0.280 -0.625 -0.109 0.000 -0.6252da. Transp. -0.298 0.099 -0.298 0.061 0.066 0.239 0.020 -0.009 0.187 0.093 -0.035 -0.312 0.140 -0.312

0.099 -0.237 0.305 0.011 0.280 -0.347 0.1403er. Distrib. -0.045 -0.010 -0.045 0.125 0.028 0.084 -0.229 -0.076 -0.002 -0.007 -0.002 -0.058 0.000 -0.222 0.126 0.033 0.000 0.189 -0.064 -0.011 0.000 -0.0643er. Transp. -0.022 0.063 -0.022 -0.114 0.042 -0.001 -0.038 -0.029 -0.001 0.063 -0.111 -0.032 0.094 -0.032

0.063 -0.137 0.041 -0.067 0.062 -0.143 0.0944ta. Distrib. -0.028 -0.006 -0.028 0.072 0.016 0.048 -0.030 -0.010 0.014 0.042 0.011 -0.013 0.000 -0.049 0.052 0.014 0.000 0.078 -0.043 -0.008 0.000 -0.043

M. Totales 3.055 6.082 1.351 -7.433 -8.902 0.676 8.226 3.353 -3.353 -2.869 5.195 -2.326 -2.790 0.000 2.790 8.064 0.567 0.000 -8.632 -7.240 1.073 0.000 6.167 3.105

NODO D F G HBARRAS EF FE FC FK FG GF GB GJ GH HGFD 0.627 0.323 0.108 0.084 0.485 0.417 0.093 0.073 0.417 0.000M. Empot P. 10.000 10.000 0.000 0.000 -15.000 -15.000 0.000 0.000 0.000 0.000

-5.000 -15.0001er. Distrib. -6.273 1.616 0.539 0.422 2.424 6.260 1.391 1.089 6.2601er. Transp. -3.136 3.130 1.212 3.130

-0.006 1.2122da. Distrib. 1.433 0.002 0.001 0.001 0.003 -0.506 -0.112 -0.088 -0.5062da. Transp. 0.716 -0.253 0.002 -0.253

0.464 0.0023er. Distrib. -0.007 -0.150 -0.050 -0.039 -0.225 -0.001 0.000 0.000 -0.0013er. Transp. -0.004 0.000 -0.112 0.000

-0.004 -0.1124ta. Distrib. 0.042 0.001 0.000 0.000 0.002 0.047 0.010 0.008 0.047

M. Totales 5.195 9.046 0.490 0.383 -9.919 -8.098 1.289 1.009 5.801 2.877



5.287 2.030 4.733

3.00 m 3.00 m 3.00 m

5.519 C 3.303 F 4.868 K

7.281 3.979 6.446

FD CD= +=

5.519 + 5.287=

7.281L 3.00

FD FE= +=

3.303 + 2.030=

3.979L 3.00

FD KL= +=

4.868 + 4.733=

6.446L 3.00

F3 = + + = 7.281 + 3.979 + 6.446 = 17.706


C F K F2 9.863

8.432 4.996 7.341

3.00 m 3.00 m 3.00 m

8.482 B 5.028 G 7.416 J

11.292 6.693 9.863

FD BC= +=

8.482 + 8.432=

11.292L 3.00

FD GF= +=

5.028 + 4.996=

6.693L 3.00

FD JK= +=

7.416 + 7.341=

9.863L 3.00

F2 = + + - F3 = 11.292 + 6.693 + 9.863 - 17.706 = 10.142

MC MD

MF ME

MK ML

FCD FFE FKL

MB MC

MG MF

MJ MK

FBC FGF FJK


C F K F2 9.863

B G J F1 17.106

5.486 3.282 4.798

4.00 m 4.00 m 4.00 m

2.867 A 1.688 H 2.517 I

4.239 2.509 3.716

FD AB= +=

2.867 + 5.486=

4.239L 4.00

FD HG= +=

1.688 + 3.282=

2.509L 4.00

FD IJ= +=

2.517 + 4.798=

3.716L 4.00

F1 = + + - F3 - F2 = 4.239 + 2.509 + 3.716 - 17.706 - 9.863 = -17.106

MA MB

MH MG

MI MJ

FAB FHG FIJ


e). CALCULO DE LOS MOMENTOS FINALES

NODO A B C D E L K J IBARRAS AB BA BG BC CB CF CD DC DE ED EF EL LE LM LK KL KF KM KJ JK JG JO JI IJM.F. Nivel 1 3.055 6.082 1.351 -7.433 -8.902 0.676 8.226 3.353 -3.353 -2.869 5.195 -2.326 -2.790 0.000 2.790 8.064 0.567 0.000 -8.632 -7.240 1.073 0.000 6.167 3.105

2.706 5.388 1.197 -6.585 -7.887 0.599 7.287 2.971 -2.971 -2.542 4.603 -2.061 -2.472 0.000 2.472 7.144 0.503 0.000 -7.647 -6.414 0.950 0.000 5.464 2.751M.F. Nivel 2 3.055 6.082 1.351 -7.433 -8.902 0.676 8.226 3.353 -3.353 -2.869 5.195 -2.326 -2.790 0.000 2.790 8.064 0.567 0.000 -8.632 -7.240 1.073 0.000 6.167 3.105

0.600 1.194 0.265 -1.459 -1.748 0.133 1.615 0.658 -0.658 -0.563 1.020 -0.457 -0.548 0.000 0.548 1.583 0.111 0.000 -1.695 -1.421 0.211 0.000 1.211 0.610M.F. Nivel 3 -0.372 -0.941 -0.209 1.150 3.513 0.863 -4.376 -2.805 2.805 2.712 -4.899 2.187 2.321 0.000 -2.321 -4.148 0.670 0.000 3.478 1.130 -0.167 0.000 -0.962 -0.377

-0.860 -2.175 -0.483 2.658 8.120 1.996 -10.116 -6.485 6.485 6.269 -11.324 5.055 5.366 0.000 -5.366 -9.589 1.550 0.000 8.039 2.612 -0.387 0.000 -2.225 -0.872Cross Sin Desp. 2.867 5.486 -13.968 8.482 8.432 -13.951 5.519 5.287 -5.287 8.030 2.030 -10.060 12.087 -16.820 4.733 4.868 25.636 -37.845 7.341 7.416 25.631 -37.845 4.798 2.517M. FINALES 5.313 9.893 -12.989 3.096 6.918 -11.223 4.306 2.432 -2.432 11.193 -3.671 -7.522 14.433 -16.820 2.387 4.006 27.800 -37.845 6.039 2.192 26.405 -37.845 9.248 5.006

NODO D F G HBARRAS EF FE FC FK FG GF GB GJ GH HGM.F. Nivel 1 5.195 9.046 0.490 0.383 -9.919 -8.098 1.289 1.009 5.801 2.877

4.603 8.014 0.434 0.340 -8.788 -7.175 1.142 0.894 5.139 2.549M.F. Nivel 2 5.195 9.046 0.490 0.383 -9.919 -8.098 1.289 1.009 5.801 2.877

1.020 1.776 0.096 0.075 -1.947 -1.590 0.253 0.198 1.139 0.565M.F. Nivel 3 -4.899 -4.886 0.833 0.652 3.401 1.142 -0.182 -0.142 -0.818 -0.347

-11.324 -11.294 1.925 1.507 7.862 2.640 -0.420 -0.329 -1.891 -0.802Cross Sin Desp. 2.030 3.303 15.923 -24.222 4.996 5.028 15.917 -24.226 3.282 1.688M. FINALES -3.671 1.799 18.378 -22.300 2.123 -1.097 16.892 -23.463 7.669 3.999

F1 F2 F3 H1 MATRIZ INVERSA MULTIPLO RESULT.12.333 130.438 9.411 58.290 -0.008 0.008 0.013 0.886 X1-40.665 -40.655 29.681 24.602 0.008 -0.004 -0.002 0.196 X2110.15 110.15 -11.697 92.174 0.000 0.039 0.015 2.312 X3


D E L #REF! 0.000

C F K 0 0.000

B G J 0 0.000

A H I

cros de tres niveles wilhurto1111

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