# Método de La Matriz Pi

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Metodo de la Matriz Pi.

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ANÁLISIS ESTRUCTURAL II DOCENTE: ING. CARMEN CHILON MUÑOZESTUDIANTE: TORRES SONO JUAN CARLOS SISTEMAS DE MARCOS CON MUROS MÉTODO DE LA COLUMNA ANCHA EQUIVALENTE  APLICANDO EL MÉTODO DE LA MATRIZ π (pi) 1.- Ensamblando la matríz global de rigidezBarras 1 2 3 4 5 6 7a e 7 7 c 7 y0b f 1 3 d 2 1! # 7 7 \$ \$ 7 \$ y01 3 4 6 2 5 22.- %esarrollo de la matríz Elemento 1. a b 70.3 0.6 -0.3%ato& '77# 0.30E( 0.6 1.6 -0.6)17# -0.60E( '* # E( -0.3 -0.6 0.3)((# 1.60E( 0.6 0.\$ -0.6)71# -0.60E(Elemento 2. e f 70.3 0.6 -0.3%ato& '77# 0.30E( 0.6 1.6 -0.6)73# -0.60E( '* # E( -0.3 -0.6 0.3)37# -0.60E( 0.6 0.\$ -0.6)33# 1.60E(Elemento 3.7 1 \$%ato& '77# )\$\$# 0.71E( 0.711 1.067 -0.711)17#)71# 1.07E( 1.067 2.133 -1.067)((#)44# 2.13E( '* # E( -0.711 -1.067 0.711)7\$#)\$7# -0.71E( 1.067 1.067 -1.067)\$1#)1\$# -1.07E()74#)47# 1.07E()14#)41# -1.07E()\$4#)4\$# -1.07E(  Elemento 4. 7 3 \$0.711 1.067 -0.711%ato& '77#)\$\$# 0.71E( 1.067 2.133 -1.067)73#)37# 1.07E( '* # E( -0.711 -1.067 0.711)7\$#)\$7 -0.71E( 1.067 1.067 -1.067)76#)67 1.07E()33#)66# 2.13E()3\$#)\$3# -1.07E()36#)63# 1.07E()\$6#)6\$# -1.07E(Elemento 5. c d 711\$.441 236.\$\$1 -11\$.441%ato& '77# 11\$.44E( 236.\$\$1 1655.013 -236.\$\$1)72# -236.\$\$E( '* # E( -11\$.441 -236.\$\$1 11\$.441)27# -236.\$\$E( 236.\$\$1 -707.4\$7 -236.\$\$1)22# 1655.01E(Elemento 6. 7 2 \$167.73 251.60 -167.73%ato& '77#)\$\$# 167.73E( 251.60 1+52.40 -251.60)72#)27# 251.60E( '* # E( -167.73 -251.60 167.73)7\$#)\$7 -167.73E( 251.60 -11+1.60 -251.60)75#)57 251.60E()22#)55# 1+52.40E()2\$#)\$2# -251.60E()25#)52# -11+1.60E()\$5#)5\$# -251.60E(Elemento 7. y0 1 y00.245\$ 0.3\$4 -0.245\$%ato& '11# 0.\$0E( 0.3\$4 0.\$ -0.3\$4)22# 3.10E( '* # E( -0.245\$ -0.3\$4 0.245\$)12# 1.12E( 0.\$44\$ 1.12 -0.\$44\$)21# 1.12E(Elemento \$. y0 2 y00.245\$ 0.\$44 -0.245\$%ato& '22# 3.10E( 0.\$44\$ 3.10 -0.3\$4  )33# 1.12E( '* # E( -0.245\$ -0.\$44\$ 0.245\$)23# 0.\$0E( 0.3\$2 1.12 -0.3\$4)32# 1.12E(Elemento +. y0 1 y00.245\$ 0.3\$4 -0.245\$%ato& '44# 0.\$0E( 0.3\$4 0.\$ -0.3\$4)55# 3.10E( '* # E( -0.245\$ -0.3\$4 0.245\$)45# 1.12E( 0.\$44\$ 1.12 -0.\$44\$)54# 1.12E(Elemento 10. y0 5 y00.245\$ 0.\$44 -0.245\$%ato& '55# 3.10E( 0.\$44\$ 3.10 -0.3\$4)66# 1.12E( '* # E( -0.245\$ -0.\$44\$ 0.245\$)56# 1.12E( 0.3\$2 1.12 -0.3\$4)65# 1.12E( Elementos !e po#t #\$n l m t#%& 'lo l '11# '11 ,1  '11 ,3  '11 ,7 # 4.533E('12#'21 '12,7 # '21 ,7 # 1.12E('13# '31 # 0 E('14# '41 '14,3 # '41 ,3 # 1.067E('15#'51 # 0 E('16#'61 # 0 E('17#'71 # 0.467E('1\$#'\$1 '1\$,3 # '\$1 ,3 # -1.067E('22# '22,5  '22 ,6 '22,7  '22,\$ # 3613.61\$ E('23#'32 '23,\$ # '32 ,\$ # 1.12E('24#42 # 0 E('25#'52 '25,6 # '52,6 # -11+7.604 E('26#'62 # 0 E('27#'72 '27,5  '27 ,6 # 14.716 E('2\$#'\$2 '2\$,6 # '\$2 ,6 # -251.5+7E('33# '33 ,2  '33 ,4  '33 ,\$ # 4.533E('34#'43 # 0 E('35#'53 # 0 E('36#'63 '36,4 # 1.067E('37#'73 '37,2  '37,4 # 0.467E('3\$#'\$3 '3\$,4 # -1.067E('45#'54 '45,5 # 1.12E(
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