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Matriz de Rigidez Lateral de un Marco de 3N-1Crujía
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KL (Wilbur) MATRIZ DE RIGIDEZ LATERAL (MÉTODO DE WILBUR) ANÁLISIS SÍSMICO ESTÁTICO DE EDIFICIOS ELEMNTO SECCIÓN INERCIA LONG ELEMENTO RIGIDEZ ABSOLUTA RIGIDEZ RELATIVA b (cm) h (cm) VIGAS 30 60 540000 500 1080 4.80 E = 218819.788867461 kg/cm2 COLUMNAS 30 30 67500 300 225 Jhonatan Vázquez: Se normaliza respecto al valor más pequeño que es este. 1.00 Σ Kvigas Σ Kcols Rigidez de entrepiso 1080 1080 225 225 450 K3 = 9267.6616461513 1080 1080 225 225 450 K2 = 9313.6230707007 1080 1080 225 225 450 K1 = 10928.7648741626 Peso por nivel de entrepiso Peso y masa concentrada por nivel de entrepiso Nivel 3 : Nivel 3 : Cantidad b (cm) h (cm) L (cm) γ (kg/cm3) P (kg) P = 2808 kg m3 = 2.862 cm*s2/kg Vigas 1 30 60 500 0.0024 2160 Columnas 2 30 30 300 0.0024 1296 3456 Nivel 2 : Nivel 2 : Cantidad b (cm) h (cm) L (cm) γ (kg/cm3) P (kg) P = 3456 kg m2 = 3.523 cm*s2/kg Vigas 1 30 60 500 0.0024 2160 Columnas 2 30 30 300 0.0024 1296 3456 Nivel 1 : Nivel 1 : Cantidad b (cm) h (cm) L (cm) γ (kg/cm3) P (kg) P = 3456 kg m1 = 3.523 cm*s2/kg Vigas 1 30 60 500 0.0024 2160 Columnas 2 30 30 300 0.0024 1296 3456 Periodo Fundamental de Vibración Zona II. Coef. Sísmico = 0.326 V0/WT = 0.057 Q = 4 Q' = 3.6 Jhonatan Vázquez: Jhonatan Vázquez: El valor 0.8 depende de las condiciones de regularidad de la sección 6.1, según 6.4 NTC-Sismo a0 = 0.119 < c/(RQ') = 0.057 R = 1.6 k1 = 0.8 R0 = 2 k2 = 0 CÁLCULO DE LA FUERZA CORTANTE SÍSMICA DIRECTA (kg) NIVEL Wn (kg) hn (cm) Wnhn Coeficiente Fn Vn 3 2808.000 900.00 2527200.00 0.0001 246.61 246.61 2 3456.000 600.00 2073600.00 0.0001 202.34 449.0 1 3456.000 300.00 1036800.00 0.0001 101.17 550.1 0 0.000 0.00 0.00 0.0001 0.00 550.1 WT 9720 5637600 SENTIDO X NIVEL Wn (ton) Fn Vn Kn Vn/Kn Xn WnXn2 FnXn 3 2808.000 246.61 246.6 9267.66 Jhonatan Vázquez: Kn es la suma de las rigideces de todos los marcos en el mismo piso, en este ejemplo solo es un marco por eso la rigidez Kn es igual a la de entrepiso. Jhonatan Vázquez: Jhonatan Vázquez: El valor 0.8 depende de las condiciones de regularidad de la sección 6.1, según 6.4 NTC-Sismo 0.027 0.125 43.9809 30.8631 2 3456.000 202.34 449.0 9313.62 0.048 0.099 33.5590 19.9393 1 3456.000 101.17 550.1 10928.76 0.050 0.050 8.7570 5.0928 0 0.000 0.00 550.1 0 0.000 0.000 0.0000 0.0000 86.2969 55.8952 T = 0.25 s KL (Condensación Estática) MATRIZ DE RIGIDEZ LATERAL (CONDENSACIÓN ESTÁTICA) ANÁLISIS SÍSMICO ESTÁTICO DE EDIFICIOS Las vigas se consideran axialmente rígidas Las columnas no se consideran axialmente rígidas Ensamble de la Matriz de Rigidez Global [KG] GDL C-1 C-2 C-3 C-4 C-5 C-6 V-1 V-2 V-3 1 0 0 1 1 2 2 0 0 0 2 0 0 4 6 8 10 4 8 12 3 0 0 5 7 9 11 5 9 13 4 1 1 2 2 3 3 0 0 0 5 4 6 8 10 12 14 6 10 14 6 5 7 9 11 13 15 7 11 15 C-1 C α = 90 [K]Local = dxA dyA θ A dxB dyB θ B Datos : 0 0 0 1 4 5 EA/L 0 0 -EA/L 0 0 dxA 656459 0 0 -656459 0 0 0 0 12 EI/L3 6 EI/L2 0 -12 EI/L3 6 EI/L2 dyA f'c = 210 kg/cm2 E = 218819.788867461 kg/cm2 0 6565 984689 0 -6565 984689 0 0 6 EI/L2 4 EI/L 0 -6 EI/L2 2 EI/L θ A 0 984689 196937810 0 -984689 98468905 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -EA/L 0 0 EA/L 0 0 dxB b (cm) h (cm) A (cm2) I (cm4) L (cm) α (°) -656459 0 0 656459 0 0 1 1 6565 0 0 0 984689 0 0 0 0 0 0 0 0 0 0 1 0 -12 EI/L3 -6 EI/L2 0 12 EI/L3 -6 EI/L2 dyB Vigas 30 60 1800 540000 500 90 0 -6565 -984689 0 6565 -984689 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 6 EI/L2 2 EI/L 0 -6 EI/L2 4 EI/L θ B Columnas 30 30 900 67500 300 0 0 984689 98468905 0 -984689 196937810 5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 0 0 0 656459 -0 0 0 0 0 0 0 0 0 0 0 4 [T] = dxA dyA θ A dxB dyB θ B 0 0 0 1 4 5 5 984689 0 0 -0 196937810 0 0 0 0 0 0 0 0 0 0 5 cos α sin α 0 0 0 0 dxA AE/L 12 EI/L3 6 EI/L2 4 EI/L 2 EI/L 0 1 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 - sin α cos α 0 0 0 0 dyA C Vigas 787751.239922858 11343.6178548892 2835904.46372229 945301487.907429 472650743.953715 -1 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 1 0 0 0 θ A V Columnas 656459.366602381 6564.5936660238 984689.049903572 196937809.980714 98468904.9903572 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 cos α sin α 0 dxB 0 0 0 0 1 0 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 - sin α cos α 0 dyB 0 0 0 -1 0 0 4 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 1 θ B 0 0 0 0 0 1 5 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 [T]T = dxA dyA θ A dxB dyB θ B 0 0 0 1 4 5 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 cos α - sin α 0 0 0 0 dxA 6565 0 -984689 -6565 -0 -984689 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 sin α cos α 0 0 0 0 dyA 0 656459 0 -0 -656459 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 1 0 0 0 θ A -984689 0 196937810 984689 -0 98468905 0 0 0 0 cos α - sin α 0 dxB -6565 -0 984689 6565 0 984689 1 0 0 0 sin α cos α 0 dyB -0 -656459 -0 0 656459 -0 4 0 0 0 0 0 1 θ B -984689 0 98468905 984689 -0 196937810 5 MATRIZ DE RIGIDEZ GLOBAL [KG] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 C-2 C α = 90 1 26258.4 -13129.2 0.0 0.0 0.0 0.0 0.0 -0.0 -984689.0 -0.0 -984689.0 0.0 0.0 0.0 0.0 1 0 0 0 1 6 7 2 -13129.2 26258.4 -13129.2 -0.0 984689.0 -0.0 984689.0 0.0 0.0 0.0 0.0 -0.0 -984689.0 -0.0 -984689.0 2 656459 0 0 -656459 0 0 0 3 0.0 -13129.2 13129.2 0.0 0.0 0.0 0.0 -0.0 984689.0 -0.0 984689.0 0.0 984689.0 0.0 984689.0 3 0 6565 984689 0 -6565 984689 0 4 0.0 -0.0 0.0 1324262.4 2835904.5 -11343.6 2835904.5 -656459.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4 0 984689 196937810 0 -984689 98468905 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 5 0.0 984689.0 0.0 2835904.5 1339177107.9 -2835904.5 472650744.0 -0.0 98468905.0 0.0 0.0 0.0 0.0 0.0 0.0 5 -656459 0 0 656459 0 0 1 1 6565 0 0 0 0 0 984689 0 0 0 0 0 0 0 0 1 6 0.0 -0.0 0.0 -11343.6 -2835904.5 1324262.4 -2835904.5 0.0 0.0 -656459.4 0.0 0.0 0.0 0.0 0.0 6 0 -6565 -984689 0 6565 -984689 6 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 0.0 984689.0 0.0 2835904.5 472650744.0 -2835904.5 1339177107.9 0.0 0.0 -0.0 98468905.0 0.0 0.0 0.0 0.0 7 0 984689 98468905 0 -984689 196937810 7 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 8 -0.0 0.0 -0.0 -656459.4 -0.0 0.0 0.0 1324262.4 2835904.5 -11343.6 2835904.5 -656459.4 0.0 0.0 0.0 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 9 -984689.0 0.0 984689.0 0.0 98468905.0 0.0 0.0 2835904.5 1339177107.9 -2835904.5 472650744.0 -0.0 98468905.0 0.0 0.0 9 0 0 0 1 6 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 10 -0.0 0.0 -0.0 0.0 0.0 -656459.4 -0.0 -11343.6 -2835904.5 1324262.4 -2835904.5 0.0 0.0 -656459.4 0.0 10 0 1 0 0 0 0 0 6 0 0 0 0 0 656459 -0 0 0 0 0 0 0 0 0 6 11 -984689.0 0.0 984689.0 0.0 0.0 0.0 98468905.0 2835904.5 472650744.0 -2835904.5 1339177107.9 0.0 0.0 -0.0 98468905.0 11 -1 0 0 0 0 0 0 7 984689 0 0 0 0 -0 196937810 0 0 0 0 0 0 0 0 7 12 0.0 -0.0 0.0 0.0 0.0 0.0 0.0 -656459.4 -0.0 0.0 0.0 667803.0 2835904.5 -11343.6 2835904.5 12 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 13 0.0 -984689.0 984689.0 0.0 0.0 0.0 0.0 0.0 98468905.0 0.0 0.0 2835904.5 1142239297.9 -2835904.5 472650744.0 13 0 0 0 0 1 0 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 14 0.0 -0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -656459.4 -0.0 -11343.6 -2835904.5 667803.0 -2835904.5 14 0 0 0 -1 0 0 6 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 15 0.0 -984689.0 984689.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 98468905.0 2835904.5 472650744.0 -2835904.5 1142239297.9 15 0 0 0 0 0 1 7 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 12 0 0 0 00 0 0 0 0 0 0 0 0 0 0 12 MATRIZ DE RIGIDEZ LATERAL [KL] 0 0 0 1 6 7 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 6565 0 -984689 -6565 -0 -984689 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 Condensación estática: 0 656459 0 -0 -656459 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 -984689 0 196937810 984689 -0 98468905 0 [KL] = 25134.051 -13152.254 1111.022 -6565 -0 984689 6565 0 984689 1 -13152.254 23915.515 -11832.228 kg/cm -0 -656459 -0 0 656459 -0 6 1111.022 -11832.228 10727.344 -984689 0 98468905 984689 -0 196937810 7 Peso por nivel de entrepiso Peso y masa concentrada por nivel de entrepiso C-3 C α = 90 1 4 5 2 8 9 Nivel 3 : Nivel 3 : 656459 0 0 -656459 0 0 1 Cantidad b (cm) h (cm) L (cm) γ (kg/cm3) P (kg) 0 6565 984689 0 -6565 984689 4 Vigas 1 30 60 500 0.0024 2160 P = 2808 kg m3 = 2.862 cm*s2/kg 0 984689 196937810 0 -984689 98468905 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Columnas 2 30 30 300 0.0024 1296 -656459 0 0 656459 0 0 2 1 6565 -6565 0 0 -984689 0 0 -0 -984689 0 0 0 0 0 0 1 3456 0 -6565 -984689 0 6565 -984689 8 2 -6565 6565 0 -0 984689 0 0 0 984689 0 0 0 0 0 0 2 0 984689 98468905 0 -984689 196937810 9 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 Nivel 2 : Nivel 2 : 4 0 -0 0 656459 0 0 0 -656459 0 0 0 0 0 0 0 4 Cantidad b (cm) h (cm) L (cm) γ (kg/cm3) P (kg) 1 4 5 2 8 9 5 -984689 984689 0 0 196937810 0 0 -0 98468905 0 0 0 0 0 0 5 Vigas 1 30 60 500 0.0024 2160 P = 3456 kg m2 = 3.523 cm*s2/kg 0 1 0 0 0 0 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 Columnas 2 30 30 300 0.0024 1296 -1 0 0 0 0 0 4 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3456 0 0 1 0 0 0 5 8 -0 0 0 -656459 -0 0 0 656459 -0 0 0 0 0 0 0 8 0 0 0 0 1 0 2 9 -984689 984689 0 0 98468905 0 0 -0 196937810 0 0 0 0 0 0 9 Nivel 1 : Nivel 1 : 0 0 0 -1 0 0 8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 Cantidad b (cm) h (cm) L (cm) γ (kg/cm3) P (kg) 0 0 0 0 0 1 9 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 Vigas 1 30 60 500 0.0024 2160 P = 3456 kg m1 = 3.523 cm*s2/kg 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 Columnas 2 30 30 300 0.0024 1296 1 4 5 2 8 9 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 3456 6565 0 -984689 -6565 -0 -984689 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 656459 0 -0 -656459 0 4 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 -984689 0 196937810 984689 -0 98468905 5 -6565 -0 984689 6565 0 984689 2 -0 -656459 -0 0 656459 -0 8 wn = 108.5697295566 wn2 = 11787.3861759915 Det = -18493.7198995643 -984689 0 98468905 984689 -0 196937810 9 Matriz de Rigidez Lateral Frecuencias naturales de vibracion C-4 C α = 90 [KL] = 25134.051 -13152.254 1111.022 w1 = 25.1420 rad/s 1 6 7 2 10 11 -13152.254 23915.515 -11832.228 w2 = 72.4646 rad/s 656459 0 0 -656459 0 0 1 1111.022 -11832.228 10727.344 w3 = 108.5697 rad/s 0 6565 984689 0 -6565 984689 6 0 984689 196937810 0 -984689 98468905 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Matriz de Masas Periodos de vibración -656459 0 0 656459 0 0 2 1 6565 -6565 0 0 0 0 -984689 0 0 -0 -984689 0 0 0 0 1 [M] = 3.523 0 0 T1 = 0.250 s 0 -6565 -984689 0 6565 -984689 10 2 -6565 6565 0 0 0 -0 984689 0 0 0 984689 0 0 0 0 2 0 3.523 0 T2 = 0.087 s 0 984689 98468905 0 -984689 196937810 11 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 2.862 T3 = 0.058 s 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 6 7 2 10 11 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 Matriz de Valores Característicos 0 1 0 0 0 0 1 6 0 -0 0 0 0 656459 0 0 0 -656459 0 0 0 0 0 6 [K-wn2M] = -16392.1538837584 -13152.2541247479 1111.022180646 -1 0 0 0 0 0 6 7 -984689 984689 0 0 0 0 196937810 0 0 -0 98468905 0 0 0 0 7 -13152.2541247479 -17610.6892430322 -11832.2280236462 0 0 1 0 0 0 7 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 1111.022180646 -11832.2280236462 -23012.697208635 0 0 0 0 1 0 2 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 -1 0 0 10 10 -0 0 0 0 0 -656459 -0 0 0 656459 -0 0 0 0 0 10 0 0 0 0 0 1 11 11 -984689 984689 0 0 0 0 98468905 0 0 -0 196937810 0 0 0 0 11 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 1 6 7 2 10 11 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 6565 0 -984689 -6565 -0 -984689 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 656459 0 -0 -656459 0 6 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 -984689 0 196937810 984689 -0 98468905 7 -6565 -0 984689 6565 0 984689 2 -0 -656459 -0 0 656459 -0 10 -984689 0 98468905 984689 -0 196937810 11 C-5 C α = 90 2 8 9 3 12 13 656459 0 0 -656459 0 0 2 0 6565 984689 0 -6565 984689 8 0 984689 196937810 0 -984689 98468905 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -656459 0 0 656459 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -6565 -984689 0 6565 -984689 12 2 0 6565 -6565 0 0 0 0 0 -984689 0 0 -0 -984689 0 0 2 0 984689 98468905 0 -984689 196937810 13 3 0 -6565 6565 0 0 0 0 -0 984689 0 0 0 984689 0 0 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 8 9 3 12 13 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1 0 0 0 0 2 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 -1 0 0 0 0 0 8 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 1 0 0 0 9 8 0 0 -0 0 0 0 0 656459 0 0 0 -656459 0 0 0 8 0 0 0 0 1 0 3 9 0 -984689 984689 0 0 0 0 0 196937810 0 0 -0 98468905 0 0 9 0 0 0 -1 0 0 12 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 1 13 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 12 0 -0 0 0 0 0 0 -656459 -0 0 0 656459 -0 0 0 12 2 8 9 3 12 13 13 0 -984689 984689 0 0 0 0 0 98468905 0 0 -0 196937810 0 0 13 6565 0 -984689 -6565 -0 -984689 2 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 656459 0 -0 -656459 0 8 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 -984689 0 196937810 984689 -0 98468905 9 -6565 -0 984689 6565 0 984689 3 -0 -656459 -0 0 656459 -0 12 -984689 0 98468905 984689 -0 196937810 13 C-6 C α = 90 2 10 11 3 14 15 656459 0 0 -656459 0 0 2 0 6565 984689 0 -6565 984689 10 0 984689 196937810 0 -984689 98468905 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -656459 0 0 656459 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -6565 -984689 0 6565 -984689 14 2 0 6565 -6565 0 0 0 0 0 0 0 -984689 0 0 -0 -984689 2 0 984689 98468905 0 -984689 196937810 15 3 0 -6565 6565 0 0 0 0 0 0 -0 984689 0 0 0 984689 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 10 11 3 14 15 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1 0 0 0 0 2 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 -1 0 0 0 0 0 10 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 1 0 0 0 11 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 1 0 3 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 -1 0 0 14 10 0 0 -0 0 0 0 0 0 0 656459 0 0 0 -656459 0 10 0 0 0 0 0 1 15 11 0 -984689 984689 0 0 0 0 0 0 0 196937810 0 0 -0 98468905 1112 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 2 10 11 3 14 15 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 6565 0 -984689 -6565 -0 -984689 2 14 0 -0 0 0 0 0 0 0 0 -656459 -0 0 0 656459 -0 14 0 656459 0 -0 -656459 0 10 15 0 -984689 984689 0 0 0 0 0 0 0 98468905 0 0 -0 196937810 15 -984689 0 196937810 984689 -0 98468905 11 -6565 -0 984689 6565 0 984689 3 -0 -656459 -0 0 656459 -0 14 -984689 0 98468905 984689 -0 196937810 15 V-1 V α = 0 0 4 5 0 6 7 787751 0 0 -787751 0 0 0 0 11344 2835904 0 -11344 2835904 4 0 2835904 945301488 0 -2835904 472650744 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -787751 0 0 787751 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -11344 -2835904 0 11344 -2835904 6 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2835904 472650744 0 -2835904 945301488 7 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 0 0 0 11344 2835904 -11344 2835904 0 0 0 0 0 0 0 0 4 0 4 5 0 6 7 5 0 0 0 2835904 945301488 -2835904 472650744 0 0 0 0 0 0 0 0 5 1 0 0 0 0 0 0 6 0 0 0 -11344 -2835904 11344 -2835904 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0 4 7 0 0 0 2835904 472650744 -2835904 945301488 0 0 0 0 0 0 0 0 7 0 0 1 0 0 0 5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 1 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 1 0 6 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 1 7 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 4 5 0 6 7 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 787751 0 0 -787751 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 11344 2835904 0 -11344 2835904 4 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 2835904 945301488 0 -2835904 472650744 5 -787751 0 0 787751 0 0 0 0 -11344 -2835904 0 11344 -2835904 6 0 2835904 472650744 0 -2835904 945301488 7 V-2 V α = 0 0 8 9 0 10 11 787751 0 0 -787751 0 0 0 0 11344 2835904 0 -11344 2835904 8 0 2835904 945301488 0 -2835904 472650744 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -787751 0 0 787751 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -11344 -2835904 0 11344 -2835904 10 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2835904 472650744 0 -2835904 945301488 11 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 8 9 0 10 11 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0 8 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 1 0 0 0 9 8 0 0 0 0 0 0 0 11344 2835904 -11344 2835904 0 0 0 0 8 0 0 0 1 0 0 0 9 0 0 0 0 0 0 0 2835904 945301488 -2835904 472650744 0 0 0 0 9 0 0 0 0 1 0 10 10 0 0 0 0 0 0 0 -11344 -2835904 11344 -2835904 0 0 0 0 10 0 0 0 0 0 1 11 11 0 0 0 0 0 0 0 2835904 472650744 -2835904 945301488 0 0 0 0 11 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 8 9 0 10 11 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 787751 0 0 -787751 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 11344 2835904 0 -11344 2835904 8 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 2835904 945301488 0 -2835904 472650744 9 -787751 0 0 787751 0 0 0 0 -11344 -2835904 0 11344 -2835904 10 0 2835904 472650744 0 -2835904 945301488 11 V-3 V α = 0 0 12 13 0 14 15 787751 0 0 -787751 0 0 0 0 11344 2835904 0 -11344 2835904 12 0 2835904 945301488 0 -2835904 472650744 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -787751 0 0 787751 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -11344 -2835904 0 11344 -2835904 14 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2835904 472650744 0 -2835904 945301488 15 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 12 13 0 14 15 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0 12 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 1 0 0 0 13 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 1 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 1 0 14 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 1 15 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 12 0 0 0 0 0 0 0 0 0 0 0 11344 2835904 -11344 2835904 12 0 12 13 0 14 15 13 0 0 0 0 0 0 0 0 0 0 0 2835904 945301488 -2835904 472650744 13 787751 0 0 -787751 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 -11344 -2835904 11344 -2835904 14 0 11344 2835904 0 -11344 2835904 12 15 0 0 0 0 0 0 0 0 0 0 0 2835904 472650744 -2835904 945301488 15 0 2835904 945301488 0 -2835904 472650744 13 -787751 0 0 787751 0 0 0 0 -11344 -2835904 0 11344 -2835904 14 0 2835904 472650744 0 -2835904 945301488 15 KL (ETABS 16) KL (Python)
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