75
coordenadas DESPLAZAMIENTOS (Ud) nudo X Y UX UY UZ A 4 3 u1 u2 u3 B 4 0 0 0 u6 C 0 5 0 0 0 BARRA Ni Nf Dx Dy L 1 B A 0 3 3.00 2 C A 4 -2 4.47 KL 1794842.147 0 0 -1794842.1 0 0 49856.7263 74785.0895 0 -49856.726 1 0 74785.0895 149570.179 0 -74785.089 -1794842.15 0 0 1794842.15 0 0 -49856.726 -74785.089 0 49856.7263 0 74785.0895 74785.0895 0 -74785.089 866892.0348 0 0 -866892.03 0 0 8777.28185 19626.5989 0 -8777.2819 2 0 19626.5989 58515.2123 0 -19626.599 -866892.035 0 0 866892.035 0 0 -8777.2819 -19626.599 0 8777.28185 0 19626.5989 29257.6062 0 -19626.599 C A 80 KN/m 120 kn 2 m 3 m I II

Analisis Matricial-ejemplo Portico-comprobar Sap

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Page 1: Analisis Matricial-ejemplo Portico-comprobar Sap

coordenadas DESPLAZAMIENTOS (Ud) FUERZA EN NUDOnudo X Y UX UY UZ X YA 4 3 u1 u2 u3 120 0

B 4 0 0 0 u6 R4 R5

C 0 5 0 0 0 R7 R8

BARRA Ni Nf Dx Dy L Cosx Cosy1 B A 0 3 3.00 0.000 1.0002 C A 4 -2 4.47 0.894 -0.447

KL

1794842.147 0 0 -1794842.15 0 00 49856.7263 74785.0895 0 -49856.7263 74785.0895

1 0 74785.0895 149570.179 0 -74785.0895 74785.0895-1794842.15 0 0 1794842.15 0 0

0 -49856.7263 -74785.0895 0 49856.7263 -74785.08950 74785.0895 74785.0895 0 -74785.0895 149570.179

866892.0348 0 0 -866892.035 0 00 8777.28185 19626.5989 0 -8777.28185 19626.5989

2 0 19626.5989 58515.2123 0 -19626.5989 29257.6062-866892.035 0 0 866892.035 0 0

0 -8777.28185 -19626.5989 0 8777.28185 -19626.59890 19626.5989 29257.6062 0 -19626.5989 58515.2123

C

A

k0

80 KN/m

120 kn

2 m

3 m I

II

Page 2: Analisis Matricial-ejemplo Portico-comprobar Sap

k0B

k2

4 m

Page 3: Analisis Matricial-ejemplo Portico-comprobar Sap

FUERZA EN NUDO F´C 21 MpZ E 21538105.800 Cargas en barras

R9distribuidad local

b h A I w frx wy0.5 0.5 0.25 0.00520833 00.4 0.45 0.18 0.0030375 80 -143.108351 64

T

0.000 1.000 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0.000 1 00 0 0 -1.000 0 00 0 0 0 0 1

0.894 -0.447 0 0 0 00.447 0.894427191 0 0 0 0

0 0 1 0 0 00 0 0 0.894 -0.4472135955 00 0 0 0.447 0.89442719099992 00 0 0 0 0 1

KG ensamblada ORDENADA1 2 3 6 4 5 7

745125.8105 -343245.901 66007.8076 74785.0895 -49856.726310862 0 -695269.084-343245.901 1975242.38 -17554.5637 0 0 -1794842.15 343245.90166007.80761 -17554.5637 208085.391 74785.0895 -74785.089466293 0 8777.2818574785.08947 0 74785.0895 149570.179 -74785.089466293 0 0-49856.7263 0 -74785.0895 -74785.0895 49856.7263108621 0 0

0 -1794842.15 0 0 0 1794842.15 0-695269.084 343245.9012 8777.28185 0 0 0 695269.084343245.9012 -180400.232 17554.5637 0 0 0 -343245.901-8777.28185 -17554.5637 29257.6062 0 0 0 8777.28185

1 2 3 6

k1

4745125.8105 -343245.901 66007.8076 74785.0895 -49856.7263

Distribuida completa (global)

Page 4: Analisis Matricial-ejemplo Portico-comprobar Sap

-343245.901 1975242.38 -17554.5637 0 k1 066007.80761 -17554.5637 208085.391 74785.0895 -74785.089574785.08947 0 74785.0895 149570.179 -74785.0895

-49856.7263 0 -74785.0895 -74785.0895

k3

49856.72630 -1794842.15 0 0 0

-695269.084 343245.9012 8777.28185 0 0343245.9012 -180400.232 17554.5637 0 0-8777.28185 -17554.5637 29257.6062 0 0

Page 5: Analisis Matricial-ejemplo Portico-comprobar Sap

Cargas en barrasPuntual Fuerzas restrictivas ( fem)

P1 P2 NiValor ubicación Valor ubicación Ai Vi Mi

0 0 0 00 0 0 0 -71.5541753 143.108351 106.666666667

TT

0 -1 0 0 0 0 1 0 0 0 0 00 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1

0.89442719 0.4472136 0 0 0 0-0.4472136 0.89442719 0 0 0 0

0 0 1 0 0 00 0 0 0.89442719 0.4472136 00 0 0 -0.4472136 0.89442719 00 0 0 0 0 1

KG ensamblada ORDENADA ud/uc Fem global8 9

343245.901 -8777.28185 1 u1 0-180400.232 -17554.5637 2 u2 16017554.5637 29257.6062 3 u3 -106.666666667

0 0 6 u6 00 0 4 0 00 0 5 0 0

-343245.901 8777.28185 7 0 0180400.232 17554.5637 8 0 16017554.5637 58515.2123 9 0 106.666666667

5 7 8 90 -695269.084 343245.901 -8777.28185 u1

Page 6: Analisis Matricial-ejemplo Portico-comprobar Sap

-1794842.15 343245.901 -180400.232 -17554.5637 u20 8777.28185 17554.5637 29257.6062 u30 0 0 0 u6

0 0 0 01794842.15 0 0 0

0 695269.084 -343245.901 8777.281850 -343245.901 180400.232 17554.56370 8777.28185 17554.5637 58515.2123

Page 7: Analisis Matricial-ejemplo Portico-comprobar Sap

Fuerzas restrictivas ( fem)Nf

Af Vf Mf

-71.554175279993 143.10835056 -106.666667

KG4 5 6 1 2 3

49856.726310862 0 -74785.0895 -49856.7263 0 -74785.0895 40 1794842.1472 0 0 -1794842.15 0 5

-74785.089466293 0 149570.179 74785.0895 0 74785.0895 6-49856.726310862 0 74785.0895 49856.7263 0 74785.0895 1

0 -1794842.1472 0 0 1794842.15 0 2-74785.089466293 0 74785.0895 74785.0895 0 149570.179 3

7 8 9 1 2 3695269.08421062 -343245.90118 8777.28185 -695269.084 343245.901 8777.28185 7

-343245.90117913 180400.23244 17554.5637 343245.901 -180400.232 17554.5637 8

8777.2818523518 17554.563705 58515.2123 -8777.28185 -17554.5637 29257.6062 9-695269.08421062 343245.90118 -8777.28185 695269.084 -343245.901 -8777.28185 1343245.90117913 -180400.23244 -17554.5637 -343245.901 180400.232 -17554.5637 28777.2818523518 17554.563705 29257.6062 -8777.28185 -17554.5637 58515.2123 3

-fexternas Feq

-120 1200 -1600 106.6666670 = 0

- R4 R4-R5 R5-R7 R7-R8 R8-160-R9 R9-106,66

Ud (m) RESTRICCIONES0.0001186166113 -23.8899099 R4

Y12
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Z31
Usuario: Feq= -(Femglobal+Fexternas)
Page 8: Analisis Matricial-ejemplo Portico-comprobar Sap

-5.506357098E-05 98.830418 R50.0005993561315 -96.1100901 R7

-0.0003589863714 61.169582 221.169582 R80 17.4612112 124.121211 R90000

Page 9: Analisis Matricial-ejemplo Portico-comprobar Sap

Fem local Fem global U globales

0 0 u4 00 0 u5 0

0 0 u6 -0.0003589863710 0 u1 0.00011861661130 0 u2 -5.506357098E-050 0 u3 0.0005993561315

-71.5541753 0 u7 0143.108351 160 u8 0

106.666667 106.6666666667 u9 0-71.5541753 0 u1 0.0001186166113143.108351 160 u2 -5.506357098E-05

-106.666667 -106.666666667 u3 0.0005993561315

Page 10: Analisis Matricial-ejemplo Portico-comprobar Sap

U locales F barras

0 98.8304 axial 40 23.8899 cortante 5

-0.0003589863714 0.0000 momento 6-5.506357098E-05 -98.8304 axial 1-0.0001186166113 -23.8899 cortante 20.0005993561315 71.6697 momento 3

0 -184.8735 axial 70 154.8383 cortante 8

0 124.1279 momento 90.0001307191 41.7652 axial 1

3.7966061133E-06 131.3784 cortante 20.0005993561315 -71.6697 momento 3

Page 11: Analisis Matricial-ejemplo Portico-comprobar Sap

coordenadas DESPLAZAMIENTOS (Ud) FUERZA EN NUDOnudo X Y UX UY UZ XA 0 0 0 0 0 R1B 0 2.8 u4 u5 u6 500C 3.29 2.8 u7 u8 u9 0D 3.29 0 0 0 0 R10

E 8.8 2.8 u13 u14 u15 0

F 8.8 0 0 0 0 R16

BARRA Ni Nf Dx Dy L Cosx1 A B 0 2.8 2.80 0.0002 B C 3.29 0 3.29 1.0003 D C 0 2.8 2.80 0.0004 C E 5.51 0 5.51 1.0005 F E 0 2.8 2.80 0.000

KL

692296.257 0 0 -692296.257 0 00 7947.27846 11126.1898 0 -7947.278457861 11126.1898

1 0 11126.1898 20768.8877 0 -11126.18984101 10384.4439-692296.257 0 0 692296.257 0 0

0 -7947.27846 -11126.1898 0 7947.278457861 -11126.18980 11126.1898 10384.4439 0 -11126.18984101 20768.8877

KL

687386.354 0 0 -687386.354 0 00 7779.38382 12797.0864 0 -7779.383818961 12797.0864

2 0 12797.0864 28068.2761 0 -12797.08638219 14034.1381-687386.354 0 0 687386.354 0 0

0 -7779.38382 -12797.0864 0 7779.383818961 -12797.08640 12797.0864 14034.1381 0 -12797.08638219 28068.2761

KL

692296.257 0 0 -692296.257 0 00 7947.27846 11126.1898 0 -7947.278457861 11126.1898

3 0 11126.1898 20768.8877 0 -11126.18984101 10384.4439-692296.257 0 0 692296.257 0 0

0 -7947.27846 -11126.1898 0 7947.278457861 -11126.18980 11126.1898 10384.4439 0 -11126.18984101 20768.8877

KL

410435.772 0 0 -410435.772 0 0

Page 12: Analisis Matricial-ejemplo Portico-comprobar Sap

0 1656.06774 4562.46662 0 -1656.067737218 4562.466624 0 4562.46662 16759.4607 0 -4562.466616034 8379.73035

-410435.772 0 0 410435.772 0 00 -1656.06774 -4562.46662 0 1656.067737218 -4562.466620 4562.46662 8379.73035 0 -4562.466616034 16759.4607

KL

692296.257 0 0 -692296.257 0 00 7947.27846 11126.1898 0 -7947.278457861 11126.1898

5 0 11126.1898 20768.8877 0 -11126.18984101 10384.4439-692296.257 0 0 692296.257 0 0

0 -7947.27846 -11126.1898 0 7947.278457861 -11126.18980 11126.1898 10384.4439 0 -11126.18984101 20768.8877

KG ensamblada ORDENADA4 5 6 7 8 9

695333.633 0 11126.1898 -687386.354 0 00 700075.641 12797.0864 0 -7779.383818961 12797.0864

11126.1898 12797.0864 48837.1638 0 -12797.08638219 14034.1381-687386.354 0 0 1105769.41 0 11126.1898

0 -7779.38382 -12797.0864 0 701731.7083299 -8234.619770 12797.0864 14034.1381 11126.1898 -8234.619766156 65596.62450 0 0 -410435.772 0 00 0 0 0 -1656.067737218 -4562.466620 0 0 0 4562.466616034 8379.73035

-7947.27846 0 -11126.1898 0 0 00 -692296.257 0 0 0 0

11126.1898 0 10384.4439 0 0 00 0 0 -7947.27846 0 -11126.18980 0 0 0 -692296.2567737 00 0 0 11126.1898 0 10384.44390 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

U4U5U6U7U8

Page 13: Analisis Matricial-ejemplo Portico-comprobar Sap

U9U13U14U15

Page 14: Analisis Matricial-ejemplo Portico-comprobar Sap

FUERZA EN NUDO F´C 21 MpY Z E 21538105.8

R2 R30 00 0

R11 R120 0 Cargas en barras

R17 R18distribuidad local

Cosy b h A I w frx1.000 0.3 0.3 0.09 0.0006750.000 0.3 0.35 0.105 0.001071871.000 0.3 0.3 0.09 0.0006750.000 0.3 0.35 0.105 0.001071871.000 0.3 0.3 0.09 0.000675

T

0.000 1.000 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0.000 1 00 0 0 -1.000 0 00 0 0 0 0 1

T

1.000 0.000 0 0 0 00.000 1.000 0 0 0 0

0 0 1 0 0 00 0 0 1.000 0 00 0 0 0.000 1 00 0 0 0 0 1

T

0.000 1.000 0 0 0 0-1.000 0.000 0 0 0 0

0 0 1 0 0 00 0 0 0.000 1 00 0 0 -1.000 0 00 0 0 0 0 1

T

1.000 0.000 0 0 0 0

Distribuida completa (global)

Page 15: Analisis Matricial-ejemplo Portico-comprobar Sap

0.000 1.000 0 0 0 00 0 1 0 0 00 0 0 1.000 0 00 0 0 0.000 1 00 0 0 0 0 1

T

0.000 1.000 0 0 0 0-1.000 0.000 0 0 0 0

0 0 1 0 0 00 0 0 0.000 1 00 0 0 -1.000 0 00 0 0 0 0 1

KG ensamblada ORDENADA13 14 15 1 2 3 10

0 0 0 -7947.27846 0 11126.1898 00 0 0 0 -692296.257 0 00 0 0 -11126.1898 0 10384.4439 0

-410435.77231592 0 0 0 0 0 -7947.278460 -1656.06774 4562.46662 0 0 0 00 -4562.46662 8379.73035 0 0 0 -11126.1898

418383.050773779 0 11126.1898 0 0 0 00 693952.325 -4562.46662 0 0 0 0

11126.1898410057 -4562.46662 37528.3484 0 0 0 00 0 0 7947.27846 0 -11126.1898 00 0 0 0 692296.257 0 00 0 0 -11126.1898 0 20768.8877 00 0 0 0 0 0 7947.278460 0 0 0 0 0 00 0 0 0 0 0 -11126.1898

-7947.2784578612 0 -11126.1898 0 0 0 00 -692296.257 0 0 0 0 0

11126.1898410057 0 10384.4439 0 0 0 0

Ud (m)0.029024372947840.00015528253651-0.00592102559330.02853670879965-8.6707339522E-05

Page 16: Analisis Matricial-ejemplo Portico-comprobar Sap

-0.00262654903630.0282013384389

-6.8575196986E-05-0.0077722830249

Page 17: Analisis Matricial-ejemplo Portico-comprobar Sap

Cargas en barras

distribuidad local Puntual Fuerzas restrictivas ( fem)P1 P2 Ni

wy Valor ubicación Valor ubicación Ai Vi Mi0 0 0 0

0 0 0 0 0 0 0

TT

0 -1 0 0 0 01 0 0 0 0 00 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1

TT

1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

TT

0 -1 0 0 0 01 0 0 0 0 00 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1

TT

1 0 0 0 0 0

Page 18: Analisis Matricial-ejemplo Portico-comprobar Sap

0 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

TT

0 -1 0 0 0 01 0 0 0 0 00 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1

KG ensamblada ORDENADA11 12 16 17 18 ud/uc

0 0 0 0 0 4 U40 0 0 0 0 5 U50 0 0 0 0 6 U60 11126.1898 0 0 0 7 U7

-692296.257 0 0 0 0 8 U80 10384.4439 0 0 0 9 U90 0 -7947.27846 0 11126.1898 13 U130 0 0 -692296.257 0 14 U140 0 -11126.1898 0 10384.4439 15 X U150 0 0 0 0 1 00 0 0 0 0 2 00 0 0 0 0 3 00 -11126.1898 0 0 0 10 0

692296.257 0 0 0 0 11 00 20768.8877 0 0 0 12 00 0 7947.27846 0 -11126.1898 16 00 0 0 692296.257 0 17 00 0 -11126.1898 0 20768.8877 18 0

Page 19: Analisis Matricial-ejemplo Portico-comprobar Sap

Fuerzas restrictivas ( fem)Nf

Af Vf Mf

0 0 0

KG1 2 3 4 5 6

7947.27846 0 -11126.1898 -7947.27846 0 -11126.1898 10 692296.257 0 0 -692296.257 0 2

-11126.1898 0 20768.8877 11126.1898 0 10384.4439 3-7947.27846 0 11126.1898 7947.27846 0 11126.1898 4

0 -692296.257 0 0 692296.257 0 5-11126.1898 0 10384.4439 11126.1898 0 20768.8877 6

KG4 5 6 7 8 9

687386.354 0 0 -687386.354 0 0 40 7779.38382 12797.0864 0 -7779.38382 12797.0864 5

0 12797.0864 28068.2761 0 -12797.0864 14034.1381 6-687386.354 0 0 687386.354 0 0 7

0 -7779.38382 -12797.0864 0 7779.38382 -12797.0864 80 12797.0864 14034.1381 0 -12797.0864 28068.2761 9

KG10 11 12 7 8 9

7947.27846 0 -11126.1898 -7947.27846 0 -11126.1898 100 692296.257 0 0 -692296.257 0 11

-11126.1898 0 20768.8877 11126.1898 0 10384.4439 12-7947.27846 0 11126.1898 7947.27846 0 11126.1898 7

0 -692296.257 0 0 692296.257 0 8-11126.1898 0 10384.4439 11126.1898 0 20768.8877 9

KG7 8 9 13 14 15

410435.772 0 0 -410435.772 0 0 7

Y18
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y27
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y36
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y45
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 20: Analisis Matricial-ejemplo Portico-comprobar Sap

0 1656.06774 4562.46662 0 -1656.06774 4562.46662 8

0 4562.46662 16759.4607 0 -4562.46662 8379.73035 9-410435.772 0 0 410435.772 0 0 13

0 -1656.06774 -4562.46662 0 1656.06774 -4562.46662 140 4562.46662 8379.73035 0 -4562.46662 16759.4607 15

KG16 17 18 13 14 15

7947.27846 0 -11126.1898 -7947.27846 0 -11126.1898 160 692296.257 0 0 -692296.257 0 17

-11126.1898 0 20768.8877 11126.1898 0 10384.4439 18-7947.27846 0 11126.1898 7947.27846 0 11126.1898 13

0 -692296.257 0 0 692296.257 0 14-11126.1898 0 10384.4439 11126.1898 0 20768.8877 15

Fem local -fexternas Feq0 -500 5000 0 00 0 00 0 00 0 00 0 00 0 00 0 0

= 0 0 = 00 -R1 R10 -R2 R20 -R3 R30 -R4 R100 -R5 R110 -R6 R120 -R7 R160 -R8 R170 -R9 R18

Y54
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
AB67
Usuario: Feq= -(Femglobal+Fexternas)
Page 21: Analisis Matricial-ejemplo Portico-comprobar Sap

Fem local

000000

000000

000000

0

Page 22: Analisis Matricial-ejemplo Portico-comprobar Sap

00000

000000

Page 23: Analisis Matricial-ejemplo Portico-comprobar Sap

coordenadas DESPLAZAMIENTOS (Ud) FUERZA EN NUDOnudo X Y UX UY UZ X YA 0 0 0 0 0 R1 R2B 0 2.8 U4 U5 U6 0 0C 2.8 2.8 U7 U8 U9 0 0D 2.8 0 0 0 0 R10 R11E 6.6 2.8 U13 U14 U15 0 0F 6.6 0 0 0 0 R16 R17G 10.25 2.8 U19 U20 U21 0 0H 10.25 0 0 0 0 R22 R23I 11.65 2.8 U25 U26 U27 0 0

BARRA Ni Nf Dx Dy L Cosx Cosy1 A B 0 2.8 2.80 0.000 1.0002 B C 2.8 0 2.80 1.000 0.0003 D C 0 2.8 2.80 0.000 1.0004 C E 3.8 -2.8 4.72 0.805 -0.5935 F E 0 2.8 2.80 0.000 1.0006 E G 3.65 0 3.65 1.000 0.0007 H G 0 2.8 2.80 0.000 1.0008 G I 1.4 0 1.40 1.000 0.000

KL

942292.1273 0 0 -942292.127 0 00 14723.3145 20612.6403 0 -14723.3145 20612.6403

1 0 20612.6403 38476.9285 0 -20612.6403 19238.4643-942292.127 0 0 942292.1273 0 0

0 -14723.3145 -20612.6403 0 14723.3145 -20612.64030 20612.6403 19238.4643 0 -20612.6403 38476.9285

KL

1038444.385 0 0 -1038444.39 0 00 26822.0648 37550.8907 0 -26822.0648 37550.8907

2 0 37550.8907 70094.996 0 -37550.8907 35047.498-1038444.39 0 0 1038444.385 0 0

0 -26822.0648 -37550.8907 0 26822.0648 -37550.89070 37550.8907 35047.498 0 -37550.8907 70094.996

KL

807678.9662 0 0 -807678.966 0 00 9271.82487 12980.5548 0 -9271.82487 12980.5548

Page 24: Analisis Matricial-ejemplo Portico-comprobar Sap

3 0 12980.5548 24230.369 0 -12980.5548 12115.1845-807678.966 0 0 807678.9662 0 0

0 -9271.82487 -12980.5548 0 9271.82487 -12980.55480 12980.5548 12115.1845 0 -12980.5548 24230.369

KL

616004.2103 0 0 -616004.21 0 00 5598.78153 13213.5989 0 -5598.78153 13213.5989

4 0 13213.5989 41580.2842 0 -13213.5989 20790.1421-616004.21 0 0 616004.2103 0 0

0 -5598.78153 -13213.5989 0 5598.78153 -13213.59890 13213.5989 20790.1421 0 -13213.5989 41580.2842

KL

807678.9662 0 0 -807678.966 0 00 9271.82487 12980.5548 0 -9271.82487 12980.5548

5 0 12980.5548 24230.369 0 -12980.5548 12115.1845-807678.966 0 0 807678.9662 0 0

0 -9271.82487 -12980.5548 0 9271.82487 -12980.55480 12980.5548 12115.1845 0 -12980.5548 24230.369

KL

796614.8708 0 0 -796614.871 0 00 12108.4264 22097.8783 0 -12108.4264 22097.8783

6 0 22097.8783 53771.5038 0 -22097.8783 26885.7519-796614.871 0 0 796614.8708 0 0

0 -12108.4264 -22097.8783 0 12108.4264 -22097.87830 22097.8783 26885.7519 0 -22097.8783 53771.5038

KL

942292.1273 0 0 -942292.127 0 00 14723.3145 20612.6403 0 -14723.3145 20612.6403

7 0 20612.6403 38476.9285 0 -20612.6403 19238.4643-942292.127 0 0 942292.1273 0 0

0 -14723.3145 -20612.6403 0 14723.3145 -20612.64030 20612.6403 19238.4643 0 -20612.6403 38476.9285

KL

2076888.77 0 0 -2076888.77 0 00 214576.518 150203.563 0 -214576.518 150203.563

8 0 150203.563 140189.992 0 -150203.563 70094.996-2076888.77 0 0 2076888.77 0 0

Page 25: Analisis Matricial-ejemplo Portico-comprobar Sap

0 -214576.518 -150203.563 0 214576.518 -150203.5630 150203.563 70094.996 0 -150203.563 140189.992

4 5 6 7 8 9 131053167.7 0 20612.6403 -1038444.39 0 0 0

0 969114.192 37550.8907 0 -26822.0648 37550.8907 020612.64028 37550.8907 108571.925 0 -37550.8907 35047.498 0-1038444.39 0 0 1448927.846 -291504.208 20818.849 -401211.636

0 -26822.0648 -37550.8907 -291504.208 1054892.39 -26913.2058 291504.2080 37550.8907 35047.498 20818.84896 -26913.2058 135905.649 -7838.294150 0 0 -401211.636 291504.208 -7838.29415 1207098.330 0 0 291504.2084 -220391.356 -10637.6849 -291504.2080 0 0 7838.294149 10637.6849 20790.1421 5142.260670 0 0 0 0 0 -796614.8710 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0

-14723.3145 0 -20612.6403 0 0 0 00 -942292.127 0 0 0 0 0

20612.64028 0 19238.4643 0 0 0 00 0 0 -9271.82487 0 -12980.5548 00 0 0 0 -807678.966 0 00 0 0 12980.55481 0 12115.1845 00 0 0 0 0 0 -9271.824870 0 0 0 0 0 00 0 0 0 0 0 12980.55480 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0

Page 26: Analisis Matricial-ejemplo Portico-comprobar Sap

FUERZA EN NUDO F´C 21 MpZ E 21538105.8

R300

R120

R180

R240

Cargas en barras

distribuidad local PuntualP1

b h A I w frx wy Valor0.35 0.35 0.1225 0.00125052 00.3 0.45 0.135 0.00227813

0.35 0.3 0.105 0.00078750.3 0.45 0.135 0.00227813

0.35 0.3 0.105 0.0007875 00.3 0.45 0.135 0.00227813

0.35 0.35 0.1225 0.001250520.3 0.45 0.135 0.00227813

T

0.000 1.000 0 0 0 0 0-1 0 0 0 0 0 10 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1.000 0 0 00 0 0 0.000 1 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

Distribuida completa (global)

Page 27: Analisis Matricial-ejemplo Portico-comprobar Sap

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

0.805 -0.593 0 0 0 0 0.805055840.593 0.805 0 0 0 0 -0.59319904

0 0 1 0 0 0 00 0 0 0.805 -0.59319904 0 00 0 0 0.593 0.80505584 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1.000 0 0 00 0 0 0.000 1 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1.000 0 0 0

Page 28: Analisis Matricial-ejemplo Portico-comprobar Sap

0 0 0 0.000 1 0 00 0 0 0 0 1 0

14 15 19 20 21 25 26 270 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

291504.208 7838.294149 0 0 0 0 0 0-220391.356 10637.68492 0 0 0 0 0 0-10637.6849 20790.1421 0 0 0 0 0 0-291504.208 5142.260666 -796614.871 0 0 0 0 01040178.75 11460.19335 0 -12108.4264 22097.8783 0 0 011460.1933 119582.157 0 -22097.8783 26885.7519 0 0 0

0 0 2888226.96 0 20612.6403 -2076888.77 0 0-12108.4264 -22097.87827 0 1168977.07 128105.685 0 -214576.518 150203.56322097.8783 26885.75189 20612.6403 128105.685 232438.424 0 -150203.563 70094.996

0 0 -2076888.77 0 0 2076888.77 0 00 0 0 -214576.518 -150203.563 0 214576.518 -150203.5630 0 0 150203.563 70094.996 0 -150203.563 140189.9920 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 -12980.55481 0 0 0 0 0 0

-807678.966 0 0 0 0 0 0 00 12115.18449 0 0 0 0 0 00 0 -14723.3145 0 -20612.6403 0 0 00 0 0 -942292.127 0 0 0 00 0 20612.6403 0 19238.4643 0 0 0

Page 29: Analisis Matricial-ejemplo Portico-comprobar Sap

Cargas en barrasPuntual Fuerzas restrictivas ( fem)

P1 P2 Ni Nfubicación Valor ubicación Ai Vi Mi Af Vf

0 0 0

0 0 0 0 0 0 0 0

TT1 2

-1 0 0 0 0 14723.3145 00 0 0 0 0 0 942292.12730 1 0 0 0 -20612.6403 00 0 0 -1 0 -14723.3145 00 0 1 0 0 0 -942292.12730 0 0 0 1 -20612.6403 0

TT4 5

0 0 0 0 0 1038444.39 01 0 0 0 0 0 26822.06480 1 0 0 0 0 37550.890710 0 1 0 0 -1038444.39 00 0 0 1 0 0 -26822.06480 0 0 0 1 0 37550.89071

TT10 11

-1 0 0 0 0 9271.82487 00 0 0 0 0 0 807678.9662

Page 30: Analisis Matricial-ejemplo Portico-comprobar Sap

0 1 0 0 0 -12980.5548 00 0 0 -1 0 -9271.82487 00 0 1 0 0 0 -807678.96620 0 0 0 1 -12980.5548 0

TT7 8

0.59319904 0 0 0 0 401211.636 -291504.20840.80505584 0 0 0 0 -291504.208 220391.3561

0 1 0 0 0 7838.29415 10637.684920 0 0.80505584 0.59319904 0 -401211.636 291504.20840 0 -0.59319904 0.80505584 0 291504.208 -220391.35610 0 0 0 1 7838.29415 10637.68492

TT16 17

-1 0 0 0 0 9271.82487 00 0 0 0 0 0 807678.96620 1 0 0 0 -12980.5548 00 0 0 -1 0 -9271.82487 00 0 1 0 0 0 -807678.96620 0 0 0 1 -12980.5548 0

TT13 14

0 0 0 0 0 796614.871 01 0 0 0 0 0 12108.426450 1 0 0 0 0 22097.878270 0 1 0 0 -796614.871 00 0 0 1 0 0 -12108.426450 0 0 0 1 0 22097.87827

TT22 23

-1 0 0 0 0 14723.3145 00 0 0 0 0 0 942292.12730 1 0 0 0 -20612.6403 00 0 0 -1 0 -14723.3145 00 0 1 0 0 0 -942292.12730 0 0 0 1 -20612.6403 0

TT19 20

0 0 0 0 0 2076888.77 01 0 0 0 0 0 214576.51840 1 0 0 0 0 150203.56290 0 1 0 0 -2076888.77 0

Page 31: Analisis Matricial-ejemplo Portico-comprobar Sap

0 0 0 1 0 0 -214576.51840 0 0 0 1 0 150203.5629

1 2 3 10 11 12 16 17-14723.3145 0 20612.6403 0 0 0 0 0

0 -942292.127 0 0 0 0 0 0-20612.6403 0 19238.4643 0 0 0 0 0

0 0 0 -9271.82487 0 12980.5548 0 00 0 0 0 -807678.966 0 0 00 0 0 -12980.5548 0 12115.1845 0 00 0 0 0 0 0 -9271.82487 00 0 0 0 0 0 0 -807678.96620 0 0 0 0 0 -12980.5548 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

14723.3145 0 -20612.6403 0 0 0 0 00 942292.127 0 0 0 0 0 0

-20612.6403 0 38476.9285 0 0 0 0 00 0 0 9271.82487 0 -12980.5548 0 00 0 0 0 807678.966 0 0 00 0 0 -12980.5548 0 24230.369 0 00 0 0 0 0 0 9271.82487 00 0 0 0 0 0 0 807678.96620 0 0 0 0 0 -12980.5548 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

UD (M)U4 0.027127187U5 0.000237249U6 -0.004774479U7 0.026454053U8 0.000194752U9 -0.001209342

U13 0.02487811U14 -0.000291535U15 -0.001482425U19 0.024554227

Page 32: Analisis Matricial-ejemplo Portico-comprobar Sap

U20 -0.000154292U21 -0.005021641U25 0.024554227U26 -0.00718459U27 -0.005021641

Page 33: Analisis Matricial-ejemplo Portico-comprobar Sap

Fuerzas restrictivas ( fem)Nf

Mf

0

KG Fem local3 4 5 6

-20612.6403 -14723.3145 0 -20612.6403 1 00 0 -942292.127 0 2 0

38476.9285 20612.6403 0 19238.4643 3 020612.6403 14723.3145 0 20612.6403 4 0

0 0 942292.127 0 5 019238.4643 20612.6403 0 38476.9285 6 0

KG6 7 8 9

0 -1038444.39 0 0 4 037550.8907 0 -26822.0648 37550.8907 5 0

70094.996 0 -37550.8907 35047.498 6 00 1038444.39 0 0 7 0

-37550.8907 0 26822.0648 -37550.8907 8 035047.498 0 -37550.8907 70094.996 9 0

KG12 7 8 9

-12980.5548 -9271.82487 0 -12980.5548 10 00 0 -807678.966 0 11 0

Y27
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y36
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y45
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 34: Analisis Matricial-ejemplo Portico-comprobar Sap

24230.369 12980.5548 0 12115.1845 12 012980.5548 9271.82487 0 12980.5548 7 0

0 0 807678.966 0 8 012115.1845 12980.5548 0 24230.369 9 0

KG9 13 14 15

7838.29415 -401211.636 291504.208 7838.29415 7 010637.6849 291504.208 -220391.356 10637.6849 8 041580.2842 -7838.29415 -10637.6849 20790.1421 9 0

-7838.29415 401211.636 -291504.208 -7838.29415 13 0-10637.6849 -291504.208 220391.356 -10637.6849 14 020790.1421 -7838.29415 -10637.6849 41580.2842 15 0

KG18 13 14 15

-12980.5548 -9271.82487 0 -12980.5548 16 00 0 -807678.966 0 17 0

24230.369 12980.5548 0 12115.1845 18 012980.5548 9271.82487 0 12980.5548 13 0

0 0 807678.966 0 14 012115.1845 12980.5548 0 24230.369 15 0

KG15 19 20 21

0 -796614.871 0 0 13 022097.8783 0 -12108.4264 22097.8783 14 053771.5038 0 -22097.8783 26885.7519 15 0

0 796614.871 0 0 19 0-22097.8783 0 12108.4264 -22097.8783 20 026885.7519 0 -22097.8783 53771.5038 21 0

KG24 19 20 21

-20612.6403 -14723.3145 0 -20612.6403 22 00 0 -942292.127 0 23 0

38476.9285 20612.6403 0 19238.4643 24 020612.6403 14723.3145 0 20612.6403 19 0

0 0 942292.127 0 20 019238.4643 20612.6403 0 38476.9285 21 0

KG21 25 26 27

0 -2076888.77 0 0 19 0150203.563 0 -214576.518 150203.563 20 0140189.992 0 -150203.563 70094.996 21 0

0 2076888.77 0 0 25 0

Y54
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y63
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y72
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y81
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y90
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 35: Analisis Matricial-ejemplo Portico-comprobar Sap

-150203.563 0 214576.518 -150203.563 26 070094.996 0 -150203.563 140189.992 27 0

18 22 23 24 ud/uc0 0 0 0 4 U40 0 0 0 5 U50 0 0 0 6 U60 0 0 0 7 U70 0 0 0 8 U80 0 0 0 9 U9

12980.5548 0 0 0 13 U130 0 0 0 14 U14

12115.1845 0 0 0 15 U150 -14723.3145 0 20612.6403 19 U190 0 -942292.127 0 20 U200 -20612.6403 0 19238.4643 21 U210 0 0 0 25 U250 0 0 0 26 U26 =0 0 0 0 27 U270 0 0 0 1 00 0 0 0 2 00 0 0 0 3 00 0 0 0 10 00 0 0 0 11 00 0 0 0 12 0

-12980.5548 0 0 0 16 00 0 0 0 17 0

24230.369 0 0 0 18 00 14723.3145 0 -20612.6403 22 00 0 942292.127 0 23 00 -20612.6403 0 38476.9285 24 0

Y99
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y108
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 36: Analisis Matricial-ejemplo Portico-comprobar Sap

femlocal FEXT F EQUIV0 -1000 10000 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 -R1 R10 -R2 R20 -R3 R30 -R10 R100 -R11 R110 -R12 R120 -R16 R160 -R17 R170 -R18 R180 -R22 R220 -R23 R230 -R24 R24

Page 37: Analisis Matricial-ejemplo Portico-comprobar Sap

coordenadas DESPLAZAMIENTOS (Ud) FUERZA EN NUDOnudo X Y UX UY UZ X YA 0 0 0 0 0 R1 R2B 0 3 U4 U5 U6 0 0C 0 5.8 U7 U8 U9 0 0D 4.5 5.8 U10 U11 U12 0 0E 4.5 3 U13 U14 U15 0 0F 4.5 0 0 0 0 R16 R17

BARRA Ni Nf Dx Dy L Cosx Cosy1 A B 0 3 3.00 0.000 1.0002 B C 0 2.8 2.80 0.000 1.0003 C D 4.5 0 4.50 1.000 0.0004 B E 4.5 0 4.50 1.000 0.0005 E D 0 2.8 2.80 0.000 1.0006 F E 0 3 3.00 0.000 1.000

KL

861524.231 0 0 -861524.231 0 00 15315.9863 22973.9795 0 -15315.9863 22973.979484

1 0 22973.9795 45947.959 0 -22973.9795 22973.979484-861524.231 0 0 861524.231 0 0

0 -15315.9863 -22973.9795 0 15315.9863 -22973.979480 22973.9795 22973.9795 0 -22973.9795 45947.958968

KL

923061.676 0 0 -923061.676 0 00 18837.9934 26373.1907 0 -18837.9934 26373.190734

2 0 26373.1907 49229.956 0 -26373.1907 24614.978019-923061.676 0 0 923061.676 0 0

0 -18837.9934 -26373.1907 0 18837.9934 -26373.190730 26373.1907 24614.978 0 -26373.1907 49229.956037

KL

646143.173 0 0 -646143.173 0 00 6461.43173 14538.2214 0 -6461.43173 14538.221392

Page 38: Analisis Matricial-ejemplo Portico-comprobar Sap

3 0 14538.2214 43614.6642 0 -14538.2214 21807.332088-646143.173 0 0 646143.173 0 0

0 -6461.43173 -14538.2214 0 6461.43173 -14538.221390 14538.2214 21807.3321 0 -14538.2214 43614.664177

KL

646143.173 0 0 -646143.173 0 00 6461.43173 14538.2214 0 -6461.43173 14538.221392

4 0 14538.2214 43614.6642 0 -14538.2214 21807.332088-646143.173 0 0 646143.173 0 0

0 -6461.43173 -14538.2214 0 6461.43173 -14538.221390 14538.2214 21807.3321 0 -14538.2214 43614.664177

KL

692296.257 0 0 -692296.257 0 00 7947.27846 11126.1898 0 -7947.27846 11126.189841

5 0 11126.1898 20768.8877 0 -11126.1898 10384.443852-692296.257 0 0 692296.257 0 0

0 -7947.27846 -11126.1898 0 7947.27846 -11126.189840 11126.1898 10384.4439 0 -11126.1898 20768.887703

KL

646143.173 0 0 -646143.173 0 00 6461.43173 9692.14759 0 -6461.43173 9692.1475948

6 0 9692.14759 19384.2952 0 -9692.14759 9692.1475948-646143.173 0 0 646143.173 0 0

0 -6461.43173 -9692.14759 0 6461.43173 -9692.1475950 9692.14759 9692.14759 0 -9692.14759 19384.29519

4 5 6680297.153 0 -3399.21125

0 1791047.3381 14538.2214-3399.21125 14538.221392 138792.579-18837.9934 0 26373.1907

0 -923061.6757 0-26373.1907 0 24614.978

0 0 00 0 00 0 0

-646143.173 0 0

Page 39: Analisis Matricial-ejemplo Portico-comprobar Sap

0 -6461.43173 -14538.22140 14538.221392 21807.3321

Page 40: Analisis Matricial-ejemplo Portico-comprobar Sap

FUERZA EN NUDO F´C 21 Mp CZ E 21538105.8 VIG 30*45

R30 COL30*40 COL30*300 B0 VIG 30*450

R18 COL30*40 COL30*30

A4,5 MTS

Cargas en barras

distribuidad local PuntualP1

b h A I w frx wy Valor0.3 0.4 0.12 0.0016 00.3 0.4 0.12 0.00160.3 0.45 0.135 0.002278130.3 0.45 0.135 0.002278130.3 0.3 0.09 0.000675 00.3 0.3 0.09 0.000675

T

0.000 1.000 0 0 0 0 0-1 0 0 0 0 0 10 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

Distribuida completa (global)

Page 41: Analisis Matricial-ejemplo Portico-comprobar Sap

0 0 1 0 0 0 00 0 0 1.000 0 0 00 0 0 0.000 1 0 00 0 0 0 0 1 0

T

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1.000 0 0 00 0 0 0.000 1 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

7 8 9 10 11 12 13 14-18837.9934 0 -26373.1907 0 0 0 -646143.173 0

0 -923061.676 0 0 0 0 0 -6461.431729926373.1907 0 24614.978 0 0 0 0 -14538.221392664981.166 0 26373.1907 -646143.173 0 0 0 0

0 929523.107 14538.2214 0 -6461.43173 14538.2214 0 026373.1907 14538.2214 92844.6202 0 -14538.2214 21807.3321 0 0

-646143.173 0 0 654090.451 0 11126.1898 -7947.27846 00 -6461.43173 -14538.2214 0 698757.689 -14538.2214 0 -692296.256770 14538.2214 21807.3321 11126.1898 -14538.2214 64383.5519 -11126.1898 00 0 0 -7947.27846 0 -11126.1898 660551.883 0

Page 42: Analisis Matricial-ejemplo Portico-comprobar Sap

0 0 0 0 -692296.257 0 0 1344900.86150 0 0 11126.1898 0 10384.4439 -1434.04225 -14538.221392

UD (M)U4 0.1395067298U5 0.0013624473U6 -0.0368256433U7 0.2431152182U8 0.0017676629U9 -0.0180884362

U10 0.2423468382U11 -0.0023568838U12 -0.0094726677U13 0.1391772905U14 -0.0018165964U15 -0.0195969109

Page 43: Analisis Matricial-ejemplo Portico-comprobar Sap

D

2,8 MTSE

3MTS

F

Cargas en barrasPuntual Fuerzas restrictivas ( fem)

P1 P2 Ni Nfubicación Valor ubicación Ai Vi Mi Af Vf

0 0 0

0 0 0 0 0 0 0 0

TT1 2

-1 0 0 0 0 15315.9863 00 0 0 0 0 0 861524.2310 1 0 0 0 -22973.9795 00 0 0 -1 0 -15315.9863 00 0 1 0 0 0 -861524.2310 0 0 0 1 -22973.9795 0

TT4 5

-1 0 0 0 0 18837.9934 00 0 0 0 0 0 923061.6760 1 0 0 0 -26373.1907 00 0 0 -1 0 -18837.9934 00 0 1 0 0 0 -923061.6760 0 0 0 1 -26373.1907 0

TT7 8

0 0 0 0 0 646143.173 01 0 0 0 0 0 6461.43173

Page 44: Analisis Matricial-ejemplo Portico-comprobar Sap

0 1 0 0 0 0 14538.22140 0 1 0 0 -646143.173 00 0 0 1 0 0 -6461.431730 0 0 0 1 0 14538.2214

TT4 5

0 0 0 0 0 646143.173 01 0 0 0 0 0 6461.431730 1 0 0 0 0 14538.22140 0 1 0 0 -646143.173 00 0 0 1 0 0 -6461.431730 0 0 0 1 0 14538.2214

TT13 14

-1 0 0 0 0 7947.27846 00 0 0 0 0 0 692296.2570 1 0 0 0 -11126.1898 00 0 0 -1 0 -7947.27846 00 0 1 0 0 0 -692296.2570 0 0 0 1 -11126.1898 0

TT16 17

-1 0 0 0 0 6461.43173 00 0 0 0 0 0 646143.1730 1 0 0 0 -9692.14759 00 0 0 -1 0 -6461.43173 00 0 1 0 0 0 -646143.1730 0 0 0 1 -9692.14759 0

15 1 2 3 16 17 180 -15315.9863 0 22973.9795 0 0 0 4

14538.2214 0 -861524.231 0 0 0 0 521807.3321 -22973.9795 0 22973.9795 0 0 0 6

0 0 0 0 0 0 0 70 0 0 0 0 0 0 80 0 0 0 0 0 0 9

11126.1898 0 0 0 0 0 0 100 0 0 0 0 0 0 11

10384.4439 0 0 0 0 0 0 12-1434.04225 0 0 0 -6461.43173 0 9692.14759 13

Page 45: Analisis Matricial-ejemplo Portico-comprobar Sap

-14538.2214 0 0 0 0 -646143.173 0 1483767.8471 0 0 0 -9692.14759 0 9692.14759 15

123

161718

Page 46: Analisis Matricial-ejemplo Portico-comprobar Sap

Fuerzas restrictivas ( fem)Nf

Mf

0

KG3 4 5 6

-22973.9795 -15315.9863 0 -22973.9795 10 0 -861524.231 0 2

45947.959 22973.9795 0 22973.9795 322973.9795 15315.9863 0 22973.9795 4

0 0 861524.231 0 522973.9795 22973.9795 0 45947.959 6

KG6 7 8 9

-26373.1907 -18837.9934 0 -26373.1907 40 0 -923061.676 0 5

49229.956 26373.1907 0 24614.978 626373.1907 18837.9934 0 26373.1907 7

0 0 923061.676 0 824614.978 26373.1907 0 49229.956 9

KG9 10 11 12

0 -646143.173 0 0 714538.2214 0 -6461.43173 14538.2214 8

Y27
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y36
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y45
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 47: Analisis Matricial-ejemplo Portico-comprobar Sap

43614.6642 0 -14538.2214 21807.3321 90 646143.173 0 0 10

-14538.2214 0 6461.43173 -14538.2214 1121807.3321 0 -14538.2214 43614.6642 12

KG6 13 14 15

0 -646143.173 0 0 414538.2214 0 -6461.43173 14538.2214 5

43614.6642 0 -14538.2214 21807.3321 60 646143.173 0 0 13

-14538.2214 0 6461.43173 -14538.2214 1421807.3321 0 -14538.2214 43614.6642 15

KG15 10 11 12

-11126.1898 -7947.27846 0 -11126.1898 130 0 -692296.257 0 14

20768.8877 11126.1898 0 10384.4439 1511126.1898 7947.27846 0 11126.1898 10

0 0 692296.257 0 1110384.4439 11126.1898 0 20768.8877 12

KG18 13 14 15

-9692.14759 -6461.43173 0 -9692.14759 160 0 -646143.173 0 17

19384.2952 9692.14759 0 9692.14759 189692.14759 6461.43173 0 9692.14759 13

0 0 646143.173 0 149692.14759 9692.14759 0 19384.2952 15

ud/uc femlocal FEXTU4 0 -1000U5 0 0U6 0 0U7 0 -1000U8 0 0U9 0 0

U10 0 0U11 0 0U12 0 0U13 0 0

Y54
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y63
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y72
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 48: Analisis Matricial-ejemplo Portico-comprobar Sap

U14 0 0U15 0 0

0 0 -R10 0 -R20 0 -R30 0 -R160 0 -R170 0 -R18

Page 49: Analisis Matricial-ejemplo Portico-comprobar Sap

coordenadas DESPLAZAMIENTOS (Ud) FUERZA EN NUDOnudo X Y UX UY UZ X YA 0 0 0 0 0 R1 R2B 0 3 U4 U5 U6 0 0C 0 5.8 U7 U8 U9 0 0D 4.5 5.8 U10 U11 U12 0 0E 4.5 3 U13 U14 U15 0 0F 4.5 0 0 0 0 R16 R17G 8 0 0 0 0 R19 R20H 8 3 U22 U23 U24 0 0I 8 5.8 U25 U26 U27 0 0

BARRA Ni Nf Dx Dy L Cosx Cosy1 A B 0 3 3.00 0.000 1.0002 B C 0 2.8 2.80 0.000 1.0003 C D 4.5 0 4.50 1.000 0.0004 B E 4.5 0 4.50 1.000 0.0005 E D 0 2.8 2.80 0.000 1.0006 F E 0 3 3.00 0.000 1.0007 D I 3.5 0 3.50 1.000 0.0008 E H 3.5 0 3.50 1.000 0.0009 H I 0 2.8 2.80 0.000 1.000

10 G H 0 3 3.00 0.000 1.000

KL

861524.231 0 0 -861524.231 0 00 15315.9863 22973.9795 0 -15315.9863 22973.9795

1 0 22973.9795 45947.959 0 -22973.9795 22973.9795-861524.231 0 0 861524.231 0 0

0 -15315.9863 -22973.9795 0 15315.9863 -22973.97950 22973.9795 22973.9795 0 -22973.9795 45947.959

KL

923061.676 0 0 -923061.676 0 00 18837.9934 26373.1907 0 -18837.9934 26373.1907

2 0 26373.1907 49229.956 0 -26373.1907 24614.978-923061.676 0 0 923061.676 0 0

0 -18837.9934 -26373.1907 0 18837.9934 -26373.19070 26373.1907 24614.978 0 -26373.1907 49229.956

Page 50: Analisis Matricial-ejemplo Portico-comprobar Sap

KL

646143.173 0 0 -646143.173 0 00 6461.43173 14538.2214 0 -6461.43173 14538.2214

3 0 14538.2214 43614.6642 0 -14538.2214 21807.3321-646143.173 0 0 646143.173 0 0

0 -6461.43173 -14538.2214 0 6461.43173 -14538.22140 14538.2214 21807.3321 0 -14538.2214 43614.6642

KL

646143.173 0 0 -646143.173 0 00 6461.43173 14538.2214 0 -6461.43173 14538.2214

4 0 14538.2214 43614.6642 0 -14538.2214 21807.3321-646143.173 0 0 646143.173 0 0

0 -6461.43173 -14538.2214 0 6461.43173 -14538.22140 14538.2214 21807.3321 0 -14538.2214 43614.6642

KL

692296.257 0 0 -692296.257 0 00 7947.27846 11126.1898 0 -7947.27846 11126.1898

5 0 11126.1898 20768.8877 0 -11126.1898 10384.4439-692296.257 0 0 692296.257 0 0

0 -7947.27846 -11126.1898 0 7947.27846 -11126.18980 11126.1898 10384.4439 0 -11126.1898 20768.8877

KL

646143.173 0 0 -646143.173 0 00 6461.43173 9692.14759 0 -6461.43173 9692.14759

6 0 9692.14759 19384.2952 0 -9692.14759 9692.14759-646143.173 0 0 646143.173 0 0

0 -6461.43173 -9692.14759 0 6461.43173 -9692.147590 9692.14759 9692.14759 0 -9692.14759 19384.2952

KL

830755.508 0 0 -830755.508 0 00 13732.8972 24032.5701 0 -13732.8972 24032.5701

7 0 24032.5701 56075.9968 0 -24032.5701 28037.9984-830755.508 0 0 830755.508 0 0

0 -13732.8972 -24032.5701 0 13732.8972 -24032.57010 24032.5701 28037.9984 0 -24032.5701 56075.9968

KL

Page 51: Analisis Matricial-ejemplo Portico-comprobar Sap

830755.508 0 0 -830755.508 0 00 13732.8972 24032.5701 0 -13732.8972 24032.5701

8 0 24032.5701 56075.9968 0 -24032.5701 28037.9984-830755.508 0 0 830755.508 0 0

0 -13732.8972 -24032.5701 0 13732.8972 -24032.57010 24032.5701 28037.9984 0 -24032.5701 56075.9968

KL

923061.676 0 0 -923061.676 0 00 18837.9934 26373.1907 0 -18837.9934 26373.1907

9 0 26373.1907 49229.956 0 -26373.1907 24614.978-923061.676 0 0 923061.676 0 0

0 -18837.9934 -26373.1907 0 18837.9934 -26373.19070 26373.1907 24614.978 0 -26373.1907 49229.956

KL

861524.231 0 0 -861524.231 0 00 15315.9863 22973.9795 0 -15315.9863 22973.9795

10 0 22973.9795 45947.959 0 -22973.9795 22973.9795-861524.231 0 0 861524.231 0 0

0 -15315.9863 -22973.9795 0 15315.9863 -22973.97950 22973.9795 22973.9795 0 -22973.9795 45947.959

4 5 6 7680297.153 0 -3399.21125 -18837.9934

0 1791047.34 14538.2214 0-3399.21125 14538.2214 138792.579 26373.1907-18837.9934 0 26373.1907 664981.166

0 -923061.676 0 0-26373.1907 0 24614.978 26373.1907

0 0 0 -646143.1730 0 0 00 0 0 0

-646143.173 0 0 00 -6461.43173 -14538.2214 00 14538.2214 21807.3321 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

Page 52: Analisis Matricial-ejemplo Portico-comprobar Sap

FUERZA EN NUDO F´C 21 Mp CZ E 21538105.8 VIG 30*45 3

R3 50 COL30*40 2 COL30*300 B 40 VIG 30*450

R18 COL30*40 COL30*30R21 1 6

0 A0 4,5 MTS

Cargas en barras

distribuidad local PuntualP1

b h A I w frx wy Valor0.3 0.4 0.12 0.0016 00.3 0.4 0.12 0.00160.3 0.45 0.135 0.002278130.3 0.45 0.135 0.002278130.3 0.3 0.09 0.000675 00.3 0.3 0.09 0.0006750.3 0.45 0.135 0.002278130.3 0.45 0.135 0.002278130.3 0.4 0.12 0.00160.3 0.4 0.12 0.0016

T

0.000 1.000 0 0 0 0 0-1 0 0 0 0 0 10 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

Distribuida completa (global)

Page 53: Analisis Matricial-ejemplo Portico-comprobar Sap

T

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1.000 0 0 00 0 0 0.000 1 0 00 0 0 0 0 1 0

T

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1.000 0 0 00 0 0 0.000 1 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1.000 0 0 00 0 0 0.000 1 0 00 0 0 0 0 1 0

T

Page 54: Analisis Matricial-ejemplo Portico-comprobar Sap

1.000 0.000 0 0 0 0 10.000 1.000 0 0 0 0 0

0 0 1 0 0 0 00 0 0 1.000 0 0 00 0 0 0.000 1 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

T

0.000 1.000 0 0 0 0 0-1.000 0.000 0 0 0 0 1

0 0 1 0 0 0 00 0 0 0.000 1 0 00 0 0 -1.000 0 0 00 0 0 0 0 1 0

8 9 10 11 12 13 14 150 -26373.1907 0 0 0 -646143.173 0 0

-923061.676 0 0 0 0 0 -6461.43173 14538.22140 24614.978 0 0 0 0 -14538.2214 21807.33210 26373.1907 -646143.173 0 0 0 0 0

929523.107 14538.2214 0 -6461.43173 14538.2214 0 0 014538.2214 92844.6202 0 -14538.2214 21807.3321 0 0 0

0 0 1484845.96 0 11126.1898 -7947.27846 0 11126.1898-6461.43173 -14538.2214 0 712490.586 9494.34866 0 -692296.257 014538.2214 21807.3321 11126.1898 9494.34866 120459.549 -11126.1898 0 10384.4439

0 0 -7947.27846 0 -11126.1898 1491307.39 0 -1434.042250 0 0 -692296.257 0 0 1358633.76 9494.348660 0 11126.1898 0 10384.4439 -1434.04225 9494.34866 139843.8440 0 0 0 0 -830755.508 0 00 0 0 0 0 0 -13732.8972 -24032.57010 0 0 0 0 0 24032.5701 28037.99840 0 -830755.508 0 0 0 0 00 0 0 -13732.8972 -24032.5701 0 0 00 0 0 24032.5701 28037.9984 0 0 0

Page 55: Analisis Matricial-ejemplo Portico-comprobar Sap

D I7

COL30*40 92,8 MTS

8 H

10COL30*40 3MTS

F G3,5MTS

Cargas en barrasPuntual Fuerzas restrictivas ( fem)

P1 P2 Ni Nfubicación Valor ubicación Ai Vi Mi Af Vf

0 0 0

0 0 0 0 0 0 0 0

TT1 2

-1 0 0 0 0 15315.9863 00 0 0 0 0 0 861524.2310 1 0 0 0 -22973.9795 00 0 0 -1 0 -15315.9863 00 0 1 0 0 0 -861524.2310 0 0 0 1 -22973.9795 0

TT4 5

-1 0 0 0 0 18837.9934 00 0 0 0 0 0 923061.6760 1 0 0 0 -26373.1907 00 0 0 -1 0 -18837.9934 00 0 1 0 0 0 -923061.6760 0 0 0 1 -26373.1907 0

Page 56: Analisis Matricial-ejemplo Portico-comprobar Sap

TT7 8

0 0 0 0 0 646143.173 01 0 0 0 0 0 6461.431730 1 0 0 0 0 14538.22140 0 1 0 0 -646143.173 00 0 0 1 0 0 -6461.431730 0 0 0 1 0 14538.2214

TT4 5

0 0 0 0 0 646143.173 01 0 0 0 0 0 6461.431730 1 0 0 0 0 14538.22140 0 1 0 0 -646143.173 00 0 0 1 0 0 -6461.431730 0 0 0 1 0 14538.2214

TT13 14

-1 0 0 0 0 7947.27846 00 0 0 0 0 0 692296.2570 1 0 0 0 -11126.1898 00 0 0 -1 0 -7947.27846 00 0 1 0 0 0 -692296.2570 0 0 0 1 -11126.1898 0

TT16 17

-1 0 0 0 0 6461.43173 00 0 0 0 0 0 646143.1730 1 0 0 0 -9692.14759 00 0 0 -1 0 -6461.43173 00 0 1 0 0 0 -646143.1730 0 0 0 1 -9692.14759 0

TT10 11

0 0 0 0 0 830755.508 01 0 0 0 0 0 13732.89720 1 0 0 0 0 24032.57010 0 1 0 0 -830755.508 00 0 0 1 0 0 -13732.89720 0 0 0 1 0 24032.5701

TT13 14

Page 57: Analisis Matricial-ejemplo Portico-comprobar Sap

0 0 0 0 0 830755.508 01 0 0 0 0 0 13732.89720 1 0 0 0 0 24032.57010 0 1 0 0 -830755.508 00 0 0 1 0 0 -13732.89720 0 0 0 1 0 24032.5701

TT22 23

-1 0 0 0 0 18837.9934 00 0 0 0 0 0 923061.6760 1 0 0 0 -26373.1907 00 0 0 -1 0 -18837.9934 00 0 1 0 0 0 -923061.6760 0 0 0 1 -26373.1907 0

TT19 20

-1 0 0 0 0 15315.9863 00 0 0 0 0 0 861524.2310 1 0 0 0 -22973.9795 00 0 0 -1 0 -15315.9863 00 0 1 0 0 0 -861524.2310 0 0 0 1 -22973.9795 0

22 23 24 25 26 27 1 20 0 0 0 0 0 -15315.9863 00 0 0 0 0 0 0 -861524.2310 0 0 0 0 0 -22973.9795 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 -830755.508 0 0 0 00 0 0 0 -13732.8972 24032.570057 0 00 0 0 0 -24032.5701 28037.998399 0 0

-830755.508 0 0 0 0 0 0 00 -13732.8972 24032.5701 0 0 0 0 00 -24032.5701 28037.9984 0 0 0 0 0

864909.488 0 -3399.21125 -18837.9934 0 -26373.190734 0 00 1798318.8 -24032.5701 0 -923061.676 0 0 0

-3399.21125 -24032.5701 151253.912 26373.1907 0 24614.978019 0 0-18837.9934 0 26373.1907 849593.502 0 26373.190734 0 0

0 -923061.676 0 0 936794.573 -24032.570057 0 0-26373.1907 0 24614.978 26373.1907 -24032.5701 105305.95284 0 0

Page 58: Analisis Matricial-ejemplo Portico-comprobar Sap

UD (M)U4 0.0823722209U5 0.0006350245U6 -0.022781406U7 0.1429180703U8 0.0008253815U9 -0.0108950246

U10 0.1417610626U11 0.0005165931U12 -0.0013283717U13 0.0815764605U14 0.0004016515U15 -0.0028672417U22 0.0810390139U23 -0.0009362632U24 -0.0208381697U25 0.1413807221U26 -0.0012128264U27

Page 59: Analisis Matricial-ejemplo Portico-comprobar Sap

Fuerzas restrictivas ( fem)Nf

Mf

0

KG3 4 5 6

-22973.9795 -15315.9863 0 -22973.9795 10 0 -861524.231 0 2

45947.959 22973.9795 0 22973.9795 322973.9795 15315.9863 0 22973.9795 4

0 0 861524.231 0 522973.9795 22973.9795 0 45947.959 6

KG6 7 8 9

-26373.1907 -18837.9934 0 -26373.1907 40 0 -923061.676 0 5

49229.956 26373.1907 0 24614.978 626373.1907 18837.9934 0 26373.1907 7

0 0 923061.676 0 824614.978 26373.1907 0 49229.956 9

Y31
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y40
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 60: Analisis Matricial-ejemplo Portico-comprobar Sap

KG9 10 11 12

0 -646143.173 0 0 714538.2214 0 -6461.43173 14538.2214 8

43614.6642 0 -14538.2214 21807.3321 90 646143.173 0 0 10

-14538.2214 0 6461.43173 -14538.2214 1121807.3321 0 -14538.2214 43614.6642 12

KG6 13 14 15

0 -646143.173 0 0 414538.2214 0 -6461.43173 14538.2214 5

43614.6642 0 -14538.2214 21807.3321 60 646143.173 0 0 13

-14538.2214 0 6461.43173 -14538.2214 1421807.3321 0 -14538.2214 43614.6642 15

KG15 10 11 12

-11126.1898 -7947.27846 0 -11126.1898 130 0 -692296.257 0 14

20768.8877 11126.1898 0 10384.4439 1511126.1898 7947.27846 0 11126.1898 10

0 0 692296.257 0 1110384.4439 11126.1898 0 20768.8877 12

KG18 13 14 15

-9692.14759 -6461.43173 0 -9692.14759 160 0 -646143.173 0 17

19384.2952 9692.14759 0 9692.14759 189692.14759 6461.43173 0 9692.14759 13

0 0 646143.173 0 149692.14759 9692.14759 0 19384.2952 15

KG12 25 26 27

0 -830755.508 0 0 1024032.5701 0 -13732.8972 24032.5701 11

56075.9968 0 -24032.5701 28037.9984 120 830755.508 0 0 25

-24032.5701 0 13732.8972 -24032.5701 2628037.9984 0 -24032.5701 56075.9968 27

KG15 22 23 24

Y49
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y58
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y67
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y76
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y85
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y94
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 61: Analisis Matricial-ejemplo Portico-comprobar Sap

0 -830755.508 0 0 1324032.5701 0 -13732.8972 24032.5701 14

56075.9968 0 -24032.5701 28037.9984 150 830755.508 0 0 22

-24032.5701 0 13732.8972 -24032.5701 2328037.9984 0 -24032.5701 56075.9968 24

KG24 25 26 27

-26373.1907 -18837.9934 0 -26373.1907 220 0 -923061.676 0 23

49229.956 26373.1907 0 24614.978 2426373.1907 18837.9934 0 26373.1907 25

0 0 923061.676 0 2624614.978 26373.1907 0 49229.956 27

KG21 22 23 24

-22973.9795 -15315.9863 0 -22973.9795 190 0 -861524.231 0 20

45947.959 22973.9795 0 22973.9795 2122973.9795 15315.9863 0 22973.9795 22

0 0 861524.231 0 2322973.9795 22973.9795 0 45947.959 24

3 16 17 18 19 20 2122973.9795 0 0 0 0 0 0 4

0 0 0 0 0 0 0 522973.9795 0 0 0 0 0 0 6

0 0 0 0 0 0 0 70 0 0 0 0 0 0 80 0 0 0 0 0 0 90 0 0 0 0 0 0 100 0 0 0 0 0 0 110 0 0 0 0 0 0 120 -6461.43173 0 9692.14759 0 0 0 130 0 -646143.173 0 0 0 0 140 -9692.14759 0 9692.14759 0 0 0 150 0 0 0 -15315.9863 0 22973.9795 220 0 0 0 0 -861524.231 0 230 0 0 0 -22973.9795 0 22973.9795 240 0 0 0 0 0 0 250 0 0 0 0 0 0 260 0 0 0 0 0 0 27

1

Y103
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Y112
Usuario: kg = TT*(KL*T) EN EXCELL: =MMULT(TT;MMULT(KL;T))
Page 62: Analisis Matricial-ejemplo Portico-comprobar Sap

23

161718192021

Page 63: Analisis Matricial-ejemplo Portico-comprobar Sap

ud/uc femlocal FEXT FEQUIU4 0 -1000 1000U5 0 0 0U6 0 0 0U7 0 -1000 1000U8 0 0 0U9 0 0 0

U10 0 0 0U11 0 0 0U12 0 0 0U13 0 0 0U14 0 0 0U15 0 0 0U22 0 0 0U23 0 0 0U24 0 0 0U25 0 0 0U26 0 0 0U27 0 0 0

0 0 -R1 R1

Page 64: Analisis Matricial-ejemplo Portico-comprobar Sap

0 0 -R2 R20 0 -R3 R30 0 -R16 R160 0 -R17 R170 0 -R18 R180 0 -R19 R190 0 -R20 R200 0 -R21 R21