cros de tres niveles wilhurto1111
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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
PROYECTO: LOCAL COMERCIAL CURSO: ANALISIS ESTRUCTURAL IICARRERA: INGENIERIA CIVIL LUGAR: ABANCAYDOCENTE: ING. RAUL MANRIQUE PADILLA CODIGO: 2008147812ALUMNO: ERWIN BALLON SAAVEDRA FECHA: NOVIEMBRE - 2010
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
PROYECTO: LOCAL COMERCIAL CURSO: ANALISIS ESTRUCTURAL IICARRERA: INGENIERIA CIVIL LUGAR: ABANCAYDOCENTE: ING. RAUL MANRIQUE PADILLA CODIGO: 2008147812ALUMNO: ERWIN BALLON SAAVEDRA FECHA: NOVIEMBRE - 2010
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
PROYECTO: LOCAL COMERCIAL CURSO: ANALISIS ESTRUCTURAL IICARRERA: INGENIERIA CIVIL LUGAR: ABANCAYDOCENTE: ING. RAUL MANRIQUE PADILLA CODIGO: 2008147812ALUMNO: ERWIN BALLON SAAVEDRA FECHA: NOVIEMBRE - 2010
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
PROYECTO: LOCAL COMERCIAL CURSO: ANALISIS ESTRUCTURAL IICARRERA: INGENIERIA CIVIL LUGAR: ABANCAYDOCENTE: ING. RAUL MANRIQUE PADILLA CODIGO: 2008147812ALUMNO: ERWIN BALLON SAAVEDRA FECHA: NOVIEMBRE - 2010
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
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 8.50
6 SOBRE CARGAS : CARGA VIVA (C.V.) T/M2 0.10 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 (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
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 3.58
6 SOBRE CARGAS : CARGA VIVA (C.V.) T/M2 0.10 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 3.95
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
-1.575 -2.077 -1.201 -0.671 -1.078 -1.891 -1.4403er. Distrib. 0.709 0.157 0.709 1.100 0.244 0.733 0.900 0.300 0.140 0.421 0.110 0.223 0.000 0.855 0.685 0.179 0.000 1.027 0.662 0.115 0.000 0.6623er. Transp. 0.354 0.550 0.354 0.450 0.367 0.070 0.150 0.112 0.055 0.342 0.428 0.331 0.514 0.331
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
-0.939 -0.8113er. Distrib. 0.421 0.303 0.101 0.079 0.455 0.338 0.075 0.059 0.3383er. Transp. 0.211 0.169 0.228 0.169
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
ALUMNO : WILBER HURTADO TORRESNOTA : SOLO INGRESAR EN LO COLORES AZULES LOS DATOS SEGÚN PIDA
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
-101.432 -100.3641er. Distrib. 2.679 32.763 10.955 8.520 49.195 41.852 9.334 7.327 41.8521er. Transp. 1.339 20.926 24.597 20.926
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
-5.581 -5.3993er. Distrib. 0.421 1.803 0.603 0.469 2.707 2.252 0.502 0.394 2.2523er. Transp. 0.211 1.126 1.353 1.126
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
FUERZA 2D E L F3 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
FUERZA 1D E L F3 17.706
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
ALUMNO : WILBER HURTADO TORRESNOTA : SOLO INGRESAR EN LO COLORES AZULES LOS DATOS SEGÚN PIDA
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
-0.993 -1.649 -0.901 -0.623 -0.905 -1.667 -1.0773er. Distrib. 0.447 0.099 0.447 0.873 0.194 0.582 0.675 0.225 0.130 0.391 0.102 0.187 0.000 0.718 0.604 0.158 0.000 0.906 0.496 0.086 0.000 0.4963er. Transp. 0.223 0.437 0.223 0.338 0.291 0.065 0.113 0.094 0.051 0.302 0.359 0.248 0.453 0.248
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
-1.222 -0.7603er. Distrib. 0.391 0.395 0.132 0.103 0.593 0.317 0.071 0.055 0.3173er. Transp. 0.195 0.159 0.296 0.159
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
FUERZA 23D E L F3 -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
FUERZA 13D E L F3 -16.752
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
ALUMNO : WILBER HURTADO TORRESNOTA : SOLO INGRESAR EN LO COLORES AZULES LOS DATOS SEGÚN PIDA
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
REACCIONES NECESARIAS PARA IMPEDIR LOS DESPLAZAMIENTOS LATERALES
FUERZA 23D E L F3 29.115
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
FUERZA 23D E L F3 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
FUERZA 13D E L F3 29.115
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
ALUMNO : WILBER HURTADO TORRESNOTA : SOLO INGRESAR EN LO COLORES AZULES LOS DATOS SEGÚN PIDA
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
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
FUERZA 2D E L F3 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
FUERZA 1D E L F3 17.706
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
ALUMNO : WILBER HURTADO TORRESNOTA : SOLO INGRESAR EN LO COLORES AZULES LOS DATOS SEGÚN PIDA
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
REACCIONES NECESARIAS PARA IMPEDIR LOS DESPLAZAMIENTOS LATERALES
D E L #REF! 0.000
C F K 0 0.000
B G J 0 0.000
A H I
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