torre final
DESCRIPTION
TorreTRANSCRIPT
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
ALUMNO: LAURA VARGAS YVAN A. DISEÑO DE ACERO Y MADERA
WD 75 TON COMB1 105 TONWL 6 TON COMB2 99.6 TONWS 10 TON COMB3 99.6 TON
MODIFICAR SOLO SOMBREADO AMARILLO
NUDOS COORD. (m)X Y
1 0 02 450 03 18.75 3004 37.5 6005 56.25 9006 75 12007 375 12008 393.75 9009 412.5 600
10 431.25 300
COORD. INICIAL COORD. FINALX Y X Y0 0 18.75 300
18.75 300 37.5 60037.5 600 56.25 900
56.25 900 75 120075 1200 375 1200
375 1200 393.75 900393.75 900 412.5 600412.5 600 431.25 300
431.25 300 450 00 0 431.25 300
18.75 300 450 018.75 300 431.25 30018.75 300 412.5 60037.5 600 431.25 30037.5 600 412.5 60037.5 600 393.75 900
56.25 900 412.5 60056.25 900 393.75 90056.25 900 375 1200
75 1200 393.75 900
1 2
3 10
4 9
5 8
6 7
l
2
3
4 6
7
8
91110
1413
1716
2019
5
18
15
12
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
ALUMNO: LAURA VARGAS YVAN A. DISEÑO DE ACERO Y MADERA
BARRAS NUDOS PROPIEDADESINICIAL FINAL A (cm2) E (ton/cm2) L (cm) EA/L غ
1 1 3 10 2100 300.585 69.8637 86.4242 3 4 10 2100 300.585 69.8637 86.4243 4 5 10 2100 300.585 69.8637 86.4244 5 6 10 2100 300.585 69.8637 86.4245 6 7 10 2100 300 70 0.0006 7 8 10 2100 300.585 69.8637 -86.4247 8 9 10 2100 300.585 69.8637 -86.4248 9 10 10 2100 300.585 69.8637 -86.4249 10 2 10 2100 300.585 69.8637 -86.424
10 1 10 10 2100 525.335 39.9745 34.82411 3 2 10 2100 525.335 39.9745 -34.82412 3 10 10 2100 412.5 50.9091 0.00013 3 9 10 2100 495.014 42.423 37.30414 4 10 10 2100 495.014 42.423 -37.30415 4 9 10 2100 375 56 0.00016 4 8 10 2100 465.74 45.0895 40.10117 5 9 10 2100 465.74 45.0895 -40.10118 5 8 10 2100 337.5 62.2222 0.00019 5 7 10 2100 437.723 47.9755 43.26420 6 8 10 2100 437.723 47.9755 -43.264
MATRIZ DE FUERZASCOMB- 1 COMB- 2 COMB-3
1.4 WD 1.2WD+1.6WL 1.2WD+1.6WL+1WS
0 U1 0 U1 0 U10 V1 0 V1 0 V10 U2 0 U2 0 U20 V2 0 V2 0 V20 U3 0 U3 0 U30 V3 0 V3 0 V30 U4 0 U4 0 U40 V4 0 V4 0 V40 U5 0 U5 0 U50 V5 0 V5 0 V50 U6 0 U6 10 U6
-52.5 V6 -49.8 V6 -49.8 V60 U7 0 U7 0 U7
-52.5 V7 -49.8 V7 -49.8 V70 U8 0 U8 0 U80 V8 0 V8 0 V80 U9 0 U9 0 U90 V9 0 V9 0 V9
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
ALUMNO: LAURA VARGAS YVAN A. DISEÑO DE ACERO Y MADERA
0 U10 0 U10 0 U100 V10 0 V10 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 1 sea:N inicial 1 COS= C Ø C S C^2 S^2 CSN final 3 SEN= S 86.424 0.06 1.00 0.00 1.00 0.06
U 1 V 1 U 3 V 3 U 1 V 1 U 3 V 3C^2 CS -C^2 -SC 0.004 0.062 -0.004 -0.062 U 1 0.27184 4.349 -0.272 -4.349 U 1
K= EA CS S^2 -CS -S^2 K1-3 = 69.8637 0.062 0.996 -0.062 -0.996 V 1 K1-3 = 4.349 69.592 -4.349 -69.592 V 1L -C^2 -SC C^2 CS -0.004 -0.062 0.004 0.062 U 3 -0.272 -4.349 0.272 4.349 U 3
-CS -S^2 CS S^2 -0.062 -0.996 0.062 0.996 V 3 -4.349 -69.592 4.349 69.592 V 3
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100.272 4.349 0 0 -0.27 -4.35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U14.349 69.592 0 0 -4.35 -69.59 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 2
-0.272 -4.349 0 0 0.27 4.35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 3-4.349 -69.592 0 0 4.35 69.59 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 2 sea:N inicial 3 COS= C Ø C S C^2 S^2 CSN final 4 SEN= S 86.424 0.06 1.00 0.00 1.00 0.06
U 3 V 3 U 4 V 4 U 3 V 3 U 4 V 4C^2 CS -C^2 -SC 0.004 0.062 -0.004 -0.062 U 3 0.272 4.349 -0.272 -4.349 U 3
K= EA CS S^2 -CS -S^2 K3-4 = 69.8637 0.062 0.996 -0.062 -0.996 V 3 K3-4 = 4.349 69.592 -4.349 -69.592 V 3L -C^2 -SC C^2 CS -0.004 -0.062 0.004 0.062 U 4 -0.272 -4.349 0.272 4.349 U 4
-CS -S^2 CS S^2 -0.062 -0.996 0.062 0.996 V 4 -4.349 -69.592 4.349 69.592 V 4
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0.272 4.349 -0.272 -4.349 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 4.349 69.592 -4.349 -69.592 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 -0.272 -4.349 0.272 4.349 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 -4.349 -69.592 4.349 69.592 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 3 sea:N inicial 4 COS= C Ø C S C^2 S^2 CSN final 5 SEN= S 86.424 0.06 1.00 0.00 1.00 0.06
U 4 V 4 U 5 V 5 U 4 V 4 U 5 V 5C^2 CS -C^2 -SC 0.004 0.062 -0.004 -0.062 U 4 0.272 4.349 -0.272 -4.349 U 4
K= EA CS S^2 -CS -S^2 K4-5 = 69.8637 0.062 0.996 -0.062 -0.996 V 4 K4-5 = 4.349 69.592 -4.349 -69.592 V 4L -C^2 -SC C^2 CS -0.004 -0.062 0.004 0.062 U 5 -0.272 -4.349 0.272 4.349 U 5
-CS -S^2 CS S^2 -0.062 -0.996 0.062 0.996 V 5 -4.349 -69.592 4.349 69.592 V 5
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0.272 4.349 -0.272 -4.349 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 4.349 69.592 -4.349 -69.592 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 -0.272 -4.349 0.272 4.349 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 -4.349 -69.592 4.349 69.592 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 4 sea:N inicial 5 COS= C Ø C S C^2 S^2 CSN final 6 SEN= S 86.424 0.06 1.00 0.00 1.00 0.06
U 5 V 5 U 6 V 6 U 5 V 5 U 6 V 6C^2 CS -C^2 -SC 0.004 0.062 -0.004 -0.062 U 5 0.272 4.349 -0.272 -4.349 U 5
K= EA CS S^2 -CS -S^2 K5-6 = 69.8637 0.062 0.996 -0.062 -0.996 V 5 K5-6 = 4.349 69.592 -4.349 -69.592 V 5L -C^2 -SC C^2 CS -0.004 -0.062 0.004 0.062 U 6 -0.272 -4.349 0.272 4.349 U 6
-CS -S^2 CS S^2 -0.062 -0.996 0.062 0.996 V 6 -4.349 -69.592 4.349 69.592 V 6
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0.272 4.349 -0.272 -4.349 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 4.349 69.592 -4.349 -69.592 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 -0.272 -4.349 0.272 4.349 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 -4.349 -69.592 4.349 69.592 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 5 sea:N inicial 6 COS= C Ø C S C^2 S^2 CSN final 7 SEN= S 0.000 1.00 0.00 1.00 0.00 0.00
U 6 V 6 U 7 V 7 U 6 V 6 U 7 V 7C^2 CS -C^2 -SC 1.000 0.000 -1.000 0.000 U 6 70.000 0.000 -70.000 0.000 U 6
K= EA CS S^2 -CS -S^2 K6-7 = 70 0.000 0.000 0.000 0.000 V 6 K6-7 = 0.000 0.000 0.000 0.000 V 6L -C^2 -SC C^2 CS -1.000 0.000 1.000 0.000 U 7 -70.000 0.000 70.000 0.000 U 7
-CS -S^2 CS S^2 0.000 0.000 0.000 0.000 V 7 0.000 0.000 0.000 0.000 V 7
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 70.000 0.000 -70.000 0.000 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0.000 0.000 0.000 0.000 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 -70.000 0.000 70.000 0.000 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0.000 0.000 0.000 0.000 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 6 sea:N inicial 7 COS= C Ø C S C^2 S^2 CSN final 8 SEN= S -86.424 0.06 -1.00 0.00 1.00 -0.06
U 7 V 7 U 8 V 8 U 7 V 7 U 8 V 8C^2 CS -C^2 -SC 0.004 -0.062 -0.004 0.062 U 7 0.272 -4.349 -0.272 4.349 U 7
K= EA CS S^2 -CS -S^2 K7-8 = 69.8637 -0.062 0.996 0.062 -0.996 V 7 K7-8 = -4.349 69.592 4.349 -69.592 V 7L -C^2 -SC C^2 CS -0.004 0.062 0.004 -0.062 U 8 -0.272 4.349 0.272 -4.349 U 8
-CS -S^2 CS S^2 0.062 -0.996 -0.062 0.996 V 8 4.349 -69.592 -4.349 69.592 V 8
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0.272 -4.349 -0.272 4.349 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 -4.349 69.592 4.349 -69.592 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 -0.272 4.349 0.272 -4.349 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 4.349 -69.592 -4.349 69.592 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 7 sea:N inicial 8 COS= C Ø C S C^2 S^2 CSN final 9 SEN= S -86.424 0.06 -1.00 0.00 1.00 -0.06
U 8 V 8 U 9 V 9 U 8 V 8 U 9 V 9C^2 CS -C^2 -SC 0.004 -0.062 -0.004 0.062 U 8 0.272 -4.349 -0.272 4.349 U 8
K= EA CS S^2 -CS -S^2 K8-9 = 69.8637 -0.062 0.996 0.062 -0.996 V 8 K8-9 = -4.349 69.592 4.349 -69.592 V 8L -C^2 -SC C^2 CS -0.004 0.062 0.004 -0.062 U 9 -0.272 4.349 0.272 -4.349 U 9
-CS -S^2 CS S^2 0.062 -0.996 -0.062 0.996 V 9 4.349 -69.592 -4.349 69.592 V 9
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0.272 -4.349 -0.272 4.349 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 -4.349 69.592 4.349 -69.592 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.272 4.349 0.272 -4.349 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 4.349 -69.592 -4.349 69.592 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 8 sea:N inicial 9 COS= C Ø C S C^2 S^2 CSN final 10 SEN= S -86.424 0.06 -1.00 0.00 1.00 -0.06
U 9 V 9 U 10 V 10 U 9 V 9 U 10 V 10C^2 CS -C^2 -SC 0.004 -0.062 -0.004 0.062 U 9 0.272 -4.349 -0.272 4.349 U 9
K= EA CS S^2 -CS -S^2 K9-10 = 69.8637 -0.062 0.996 0.062 -0.996 V 9 K9-10 = -4.349 69.592 4.349 -69.592 V 9L -C^2 -SC C^2 CS -0.004 0.062 0.004 -0.062 U 10 -0.272 4.349 0.272 -4.349 U 10
-CS -S^2 CS S^2 0.062 -0.996 -0.062 0.996 V 10 4.349 -69.592 -4.349 69.592 V 10
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.272 -4.349 -0.272 4.349 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4.349 69.592 4.349 -69.592 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.272 4.349 0.272 -4.349 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.349 -69.592 -4.349 69.592 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 9 sea:N inicial 10 COS= C Ø C S C^2 S^2 CSN final 2 SEN= S -86.424 0.06 -1.00 0.00 1.00 -0.06
U 10 V 10 U 2 V 2 U 10 V 10 U 2 V 2C^2 CS -C^2 -SC 0.004 -0.062 -0.004 0.062 U 10 0.272 -4.349 -0.272 4.349 U 10
K= EA CS S^2 -CS -S^2 K10-2 = 69.8637 -0.062 0.996 0.062 -0.996 V 10 K10-2 = -4.349 69.592 4.349 -69.592 V 10L -C^2 -SC C^2 CS -0.004 0.062 0.004 -0.062 U 2 -0.272 4.349 0.272 -4.349 U 2
-CS -S^2 CS S^2 0.062 -0.996 -0.062 0.996 V 2 4.349 -69.592 -4.349 69.592 V 2
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0.272 -4.349 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.272 4.349 U 20 0 -4.349 69.592 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4.349 -69.592 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 -0.272 4.349 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.272 -4.349 U100 0 4.349 -69.592 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4.349 69.592 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 10 sea:N inicial 1 COS= C Ø C S C^2 S^2 CSN final 10 SEN= S 34.824 0.82 0.57 0.67 0.33 0.47
U 1 V 1 U 10 V 10 U 1 V 1 U 10 V 10C^2 CS -C^2 -SC 0.674 0.469 -0.674 -0.469 U 1 26.938 18.740 -26.938 -18.740 U 1
K= EA CS S^2 -CS -S^2 K1-10 = 39.9745 0.469 0.326 -0.469 -0.326 V 1 K1-10 = 18.740 13.036 -18.740 -13.036 V 1L -C^2 -SC C^2 CS -0.674 -0.469 0.674 0.469 U 10 -26.938 -18.740 26.938 18.740 U 10
-CS -S^2 CS S^2 -0.469 -0.326 0.469 0.326 V 10 -18.740 -13.036 18.740 13.036 V 10
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V1026.938 18.740 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -26.938 -18.740 U118.740 13.036 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -18.740 -13.036 V1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V9
-26.938 -18.740 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 26.938 18.740 U10-18.740 -13.036 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18.740 13.036 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 11 sea:N inicial 3 COS= C Ø C S C^2 S^2 CSN final 2 SEN= S -34.824 0.82 -0.57 0.67 0.33 -0.47
U 3 V 3 U 2 V 2 U 3 V 3 U 2 V 2C^2 CS -C^2 -SC 0.674 -0.469 -0.674 0.469 U 3 26.938 -18.740 -26.938 18.740 U 3
K= EA CS S^2 -CS -S^2 K3-2 = 39.9745 -0.469 0.326 0.469 -0.326 V 3 K3-2 = -18.740 13.036 18.740 -13.036 V 3L -C^2 -SC C^2 CS -0.674 0.469 0.674 -0.469 U 2 -26.938 18.740 26.938 -18.740 U 2
-CS -S^2 CS S^2 0.469 -0.326 -0.469 0.326 V 2 18.740 -13.036 -18.740 13.036 V 2
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 26.938 -18.740 -26.938 18.740 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 -18.740 13.036 18.740 -13.036 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 -26.938 18.740 26.938 -18.740 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 18.740 -13.036 -18.740 13.036 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 12 sea:N inicial 3 COS= C Ø C S C^2 S^2 CSN final 10 SEN= S 0.000 1.00 0.00 1.00 0.00 0.00
U 3 V 3 U 10 V 10 U 3 V 3 U 10 V 10C^2 CS -C^2 -SC 1.000 0.000 -1.000 0.000 U 3 50.909 0.000 -50.909 0.000 U 3
K= EA CS S^2 -CS -S^2 K3-10 = 50.9091 0.000 0.000 0.000 0.000 V 3 K3-10 = 0.000 0.000 0.000 0.000 V 3L -C^2 -SC C^2 CS -1.000 0.000 1.000 0.000 U 10 -50.909 0.000 50.909 0.000 U 10
-CS -S^2 CS S^2 0.000 0.000 0.000 0.000 V 10 0.000 0.000 0.000 0.000 V 10
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 50.909 0.000 0 0 0 0 0 0 0 0 0 0 0 0 -50.909 0.000 U 30 0 0 0 0.000 0.000 0 0 0 0 0 0 0 0 0 0 0 0 0.000 0.000 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 -50.909 0.000 0 0 0 0 0 0 0 0 0 0 0 0 50.909 0.000 U100 0 0 0 0.000 0.000 0 0 0 0 0 0 0 0 0 0 0 0 0.000 0.000 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 13 sea:N inicial 3 COS= C Ø C S C^2 S^2 CSN final 9 SEN= S 37.304 0.80 0.61 0.63 0.37 0.48
U 3 V 3 U 9 V 9 U 3 V 3 U 9 V 9C^2 CS -C^2 -SC 0.633 0.482 -0.633 -0.482 U 3 26.842 20.451 -26.842 -20.451 U 3
K= EA CS S^2 -CS -S^2 K3-9 = 42.423 0.482 0.367 -0.482 -0.367 V 3 K3-9 = 20.451 15.581 -20.451 -15.581 V 3L -C^2 -SC C^2 CS -0.633 -0.482 0.633 0.482 U 9 -26.842 -20.451 26.842 20.451 U 9
-CS -S^2 CS S^2 -0.482 -0.367 0.482 0.367 V 9 -20.451 -15.581 20.451 15.581 V 9
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 26.842 20.451 0 0 0 0 0 0 0 0 0 0 -26.842 -20.451 0 0 U 30 0 0 0 20.451 15.581 0 0 0 0 0 0 0 0 0 0 -20.451 -15.581 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 -26.842 -20.451 0 0 0 0 0 0 0 0 0 0 26.842 20.451 0 0 U90 0 0 0 -20.451 -15.581 0 0 0 0 0 0 0 0 0 0 20.451 15.581 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 14 sea:N inicial 4 COS= C Ø C S C^2 S^2 CSN final 10 SEN= S -37.304 0.80 -0.61 0.63 0.37 -0.48
U 4 V 4 U 10 V 10 U 4 V 4 U 10 V 10C^2 CS -C^2 -SC 0.633 -0.482 -0.633 0.482 U 4 26.842 -20.451 -26.842 20.451 U 4
K= EA CS S^2 -CS -S^2 K4-10 = 42.423 -0.482 0.367 0.482 -0.367 V 4 K4-10 = -20.451 15.581 20.451 -15.581 V 4L -C^2 -SC C^2 CS -0.633 0.482 0.633 -0.482 U 10 -26.842 20.451 26.842 -20.451 U 10
-CS -S^2 CS S^2 0.482 -0.367 -0.482 0.367 V 10 20.451 -15.581 -20.451 15.581 V 10
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 26.842 -20.451 0 0 0 0 0 0 0 0 0 0 -26.842 20.451 U 40 0 0 0 0 0 -20.451 15.581 0 0 0 0 0 0 0 0 0 0 20.451 -15.581 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 -26.842 20.451 0 0 0 0 0 0 0 0 0 0 26.842 -20.451 U100 0 0 0 0 0 20.451 -15.581 0 0 0 0 0 0 0 0 0 0 -20.451 15.581 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 15 sea:N inicial 4 COS= C Ø C S C^2 S^2 CSN final 9 SEN= S 0.000 1.00 0.00 1.00 0.00 0.00
U 4 V 4 U 9 V 9 U 4 V 4 U 9 V 9C^2 CS -C^2 -SC 1.000 0.000 -1.000 0.000 U 4 56.000 0.000 -56.000 0.000 U 4
K= EA CS S^2 -CS -S^2 K4-9 = 56 0.000 0.000 0.000 0.000 V 4 K4-9 = 0.000 0.000 0.000 0.000 V 4L -C^2 -SC C^2 CS -1.000 0.000 1.000 0.000 U 9 -56.000 0.000 56.000 0.000 U 9
-CS -S^2 CS S^2 0.000 0.000 0.000 0.000 V 9 0.000 0.000 0.000 0.000 V 9
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 56.000 0.000 0 0 0 0 0 0 0 0 -56.000 0.000 0 0 U 40 0 0 0 0 0 0.000 0.000 0 0 0 0 0 0 0 0 0.000 0.000 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 -56.000 0.000 0 0 0 0 0 0 0 0 56.000 0.000 0 0 U90 0 0 0 0 0 0.000 0.000 0 0 0 0 0 0 0 0 0.000 0.000 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 16 sea:N inicial 4 COS= C Ø C S C^2 S^2 CSN final 8 SEN= S 40.101 0.76 0.64 0.59 0.41 0.49
U 4 V 4 U 8 V 8 U 4 V 4 U 8 V 8C^2 CS -C^2 -SC 0.585 0.493 -0.585 -0.493 U 4 26.381 22.216 -26.381 -22.216 U 4
K= EA CS S^2 -CS -S^2 K4-8 = 45.0895 0.493 0.415 -0.493 -0.415 V 4 K4-8 = 22.216 18.708 -22.216 -18.708 V 4L -C^2 -SC C^2 CS -0.585 -0.493 0.585 0.493 U 8 -26.381 -22.216 26.381 22.216 U 8
-CS -S^2 CS S^2 -0.493 -0.415 0.493 0.415 V 8 -22.216 -18.708 22.216 18.708 V 8
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 26.381 22.216 0 0 0 0 0 0 -26.381 -22.216 0 0 0 0 U 40 0 0 0 0 0 22.216 18.708 0 0 0 0 0 0 -22.216 -18.708 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 -26.381 -22.216 0 0 0 0 0 0 26.381 22.216 0 0 0 0 U80 0 0 0 0 0 -22.216 -18.708 0 0 0 0 0 0 22.216 18.708 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 17 sea:N inicial 5 COS= C Ø C S C^2 S^2 CSN final 9 SEN= S -40.101 0.76 -0.64 0.59 0.41 -0.49
U 5 V 5 U 9 V 9 U 5 V 5 U 9 V 9C^2 CS -C^2 -SC 0.585 -0.493 -0.585 0.493 U 5 26.381 -22.216 -26.381 22.216 U 5
K= EA CS S^2 -CS -S^2 K5-9 = 45.0895 -0.493 0.415 0.493 -0.415 V 5 K5-9 = -22.216 18.708 22.216 -18.708 V 5L -C^2 -SC C^2 CS -0.585 0.493 0.585 -0.493 U 9 -26.381 22.216 26.381 -22.216 U 9
-CS -S^2 CS S^2 0.493 -0.415 -0.493 0.415 V 9 22.216 -18.708 -22.216 18.708 V 9
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 26.381 -22.216 0 0 0 0 0 0 -26.381 22.216 0 0 U 50 0 0 0 0 0 0 0 -22.216 18.708 0 0 0 0 0 0 22.216 -18.708 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 -26.381 22.216 0 0 0 0 0 0 26.381 -22.216 0 0 U90 0 0 0 0 0 0 0 22.216 -18.708 0 0 0 0 0 0 -22.216 18.708 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 18 sea:N inicial 5 COS= C Ø C S C^2 S^2 CSN final 8 SEN= S 0.000 1.00 0.00 1.00 0.00 0.00
U 5 V 5 U 8 V 8 U 5 V 5 U 8 V 8C^2 CS -C^2 -SC 1.000 0.000 -1.000 0.000 U 5 62.222 0.000 -62.222 0.000 U 5
K= EA CS S^2 -CS -S^2 K5-8 = 62.2222 0.000 0.000 0.000 0.000 V 5 K5-8 = 0.000 0.000 0.000 0.000 V 5L -C^2 -SC C^2 CS -1.000 0.000 1.000 0.000 U 8 -62.222 0.000 62.222 0.000 U 8
-CS -S^2 CS S^2 0.000 0.000 0.000 0.000 V 8 0.000 0.000 0.000 0.000 V 8
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 62.222 0.000 0 0 0 0 -62.222 0.000 0 0 0 0 U 50 0 0 0 0 0 0 0 0.000 0.000 0 0 0 0 0.000 0.000 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 -62.222 0.000 0 0 0 0 62.222 0.000 0 0 0 0 U80 0 0 0 0 0 0 0 0.000 0.000 0 0 0 0 0.000 0.000 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 19 sea:N inicial 5 COS= C Ø C S C^2 S^2 CSN final 7 SEN= S 43.264 0.73 0.69 0.53 0.47 0.50
U 5 V 5 U 7 V 7 U 5 V 5 U 7 V 7C^2 CS -C^2 -SC 0.530 0.499 -0.530 -0.499 U 5 25.440 23.944 -25.440 -23.944 U 5
K= EA CS S^2 -CS -S^2 K5-7 = 47.9755 0.499 0.470 -0.499 -0.470 V 5 K5-7 = 23.944 22.535 -23.944 -22.535 V 5L -C^2 -SC C^2 CS -0.530 -0.499 0.530 0.499 U 7 -25.440 -23.944 25.440 23.944 U 7
-CS -S^2 CS S^2 -0.499 -0.470 0.499 0.470 V 7 -23.944 -22.535 23.944 22.535 V 7
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 25.440 23.944 0 0 -25.440 -23.944 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 23.944 22.535 0 0 -23.944 -22.535 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 60 0 0 0 0 0 0 0 -25.440 -23.944 0 0 25.440 23.944 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 -23.944 -22.535 0 0 23.944 22.535 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
BARRA: 20 sea:N inicial 6 COS= C Ø C S C^2 S^2 CSN final 8 SEN= S -43.264 0.73 -0.69 0.53 0.47 -0.50
U 6 V 6 U 8 V 8 U 6 V 6 U 8 V 8C^2 CS -C^2 -SC 0.530 -0.499 -0.530 0.499 U 6 25.440 -23.944 -25.440 23.944 U 6
K= EA CS S^2 -CS -S^2 K6-8 = 47.9755 -0.499 0.470 0.499 -0.470 V 6 K6-8 = -23.944 22.535 23.944 -22.535 V 6L -C^2 -SC C^2 CS -0.530 0.499 0.530 -0.499 U 8 -25.440 23.944 25.440 -23.944 U 8
-CS -S^2 CS S^2 0.499 -0.470 -0.499 0.470 V 8 23.944 -22.535 -23.944 22.535 V 8
U1 V1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U7 V7 U8 V8 U9 V9 U10 V100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V 50 0 0 0 0 0 0 0 0 0 25.440 -23.944 0 0 -25.440 23.944 0 0 0 0 U 60 0 0 0 0 0 0 0 0 0 -23.944 22.535 0 0 23.944 -22.535 0 0 0 0 V 60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V70 0 0 0 0 0 0 0 0 0 -25.440 23.944 0 0 25.440 -23.944 0 0 0 0 U80 0 0 0 0 0 0 0 0 0 23.944 -22.535 0 0 -23.944 22.535 0 0 0 0 V80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
MATRIZ ENSAMBLADAU 1 V 1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10
27.210 23.089 0.000 0.000 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.938 -18.740 U123.089 82.628 0.000 0.000 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -18.740 -13.036 V10.000 0.000 27.210 -23.089 -26.938 18.740 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 U20.000 0.000 -23.089 82.628 18.740 -13.036 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 V2-0.272 -4.349 -26.938 18.740 105.233 10.410 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.842 -20.451 -50.909 0.000 U3-4.349 -69.592 18.740 -13.036 10.410 167.801 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 V30.000 0.000 0.000 0.000 -0.272 -4.349 109.767 10.464 -0.272 -4.349 0.000 0.000 0.000 0.000 -26.381 -22.216 -56.000 0.000 -26.842 20.451 U40.000 0.000 0.000 0.000 -4.349 -69.592 10.464 173.473 -4.349 -69.592 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 20.451 -15.581 V40.000 0.000 0.000 0.000 0.000 0.000 -0.272 -4.349 114.588 10.427 -0.272 -4.349 -25.440 -23.944 -62.222 0.000 -26.381 22.216 0.000 0.000 U50.000 0.000 0.000 0.000 0.000 0.000 -4.349 -69.592 10.427 180.427 -4.349 -69.592 -23.944 -22.535 0.000 0.000 22.216 -18.708 0.000 0.000 V50.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 -4.349 95.712 -19.594 -70.000 0.000 -25.440 23.944 0.000 0.000 0.000 0.000 U60.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -4.349 -69.592 -19.594 92.127 0.000 0.000 23.944 -22.535 0.000 0.000 0.000 0.000 V60.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -25.440 -23.944 -70.000 0.000 95.712 19.594 -0.272 4.349 0.000 0.000 0.000 0.000 U70.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -23.944 -22.535 0.000 0.000 19.594 92.127 4.349 -69.592 0.000 0.000 0.000 0.000 V70.000 0.000 0.000 0.000 0.000 0.000 -26.381 -22.216 -62.222 0.000 -25.440 23.944 -0.272 4.349 114.588 -10.427 -0.272 4.349 0.000 0.000 U80.000 0.000 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 23.944 -22.535 4.349 -69.592 -10.427 180.427 4.349 -69.592 0.000 0.000 V80.000 0.000 0.000 0.000 -26.842 -20.451 -56.000 0.000 -26.381 22.216 0.000 0.000 0.000 0.000 -0.272 4.349 109.767 -10.464 -0.272 4.349 U90.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 22.216 -18.708 0.000 0.000 0.000 0.000 4.349 -69.592 -10.464 173.473 4.349 -69.592 V9
-26.938 -18.740 -0.272 4.349 -50.909 0.000 -26.842 20.451 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 105.233 -10.410 U10-18.740 -13.036 4.349 -69.592 0.000 0.000 20.451 -15.581 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 -10.410 167.801 V10
U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10105.233 10.410 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.842 -20.451 -50.909 0.000 U310.410 167.801 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 V3-0.272 -4.349 109.767 10.464 -0.272 -4.349 0.000 0.000 0.000 0.000 -26.381 -22.216 -56.000 0.000 -26.842 20.451 U4-4.349 -69.592 10.464 173.473 -4.349 -69.592 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 20.451 -15.581 V4
K= 0.000 0.000 -0.272 -4.349 114.588 10.427 -0.272 -4.349 -25.440 -23.944 -62.222 0.000 -26.381 22.216 0.000 0.000 U50.000 0.000 -4.349 -69.592 10.427 180.427 -4.349 -69.592 -23.944 -22.535 0.000 0.000 22.216 -18.708 0.000 0.000 V50.000 0.000 0.000 0.000 -0.272 -4.349 95.712 -19.594 -70.000 0.000 -25.440 23.944 0.000 0.000 0.000 0.000 U60.000 0.000 0.000 0.000 -4.349 -69.592 -19.594 92.127 0.000 0.000 23.944 -22.535 0.000 0.000 0.000 0.000 V60.000 0.000 0.000 0.000 -25.440 -23.944 -70.000 0.000 95.712 19.594 -0.272 4.349 0.000 0.000 0.000 0.000 U70.000 0.000 0.000 0.000 -23.944 -22.535 0.000 0.000 19.594 92.127 4.349 -69.592 0.000 0.000 0.000 0.000 V70.000 0.000 -26.381 -22.216 -62.222 0.000 -25.440 23.944 -0.272 4.349 114.588 -10.427 -0.272 4.349 0.000 0.000 U80.000 0.000 -22.216 -18.708 0.000 0.000 23.944 -22.535 4.349 -69.592 -10.427 180.427 4.349 -69.592 0.000 0.000 V8
-26.842 -20.451 -56.000 0.000 -26.381 22.216 0.000 0.000 0.000 0.000 -0.272 4.349 109.767 -10.464 -0.272 4.349 U9-20.451 -15.581 0.000 0.000 22.216 -18.708 0.000 0.000 0.000 0.000 4.349 -69.592 -10.464 173.473 4.349 -69.592 V9-50.909 0.000 -26.842 20.451 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 105.233 -10.410 U100.000 0.000 20.451 -15.581 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 -10.410 167.801 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
sabemos que:U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10 MATRIZ DE FUERZAS
0.024 0.004 0.025 0.005 0.031 0.004 0.036 0.004 0.036 -0.001 0.030 -0.001 0.026 -0.002 0.017 -0.003 U3 0 U30.004 0.013 0.013 0.012 0.023 0.012 0.033 0.011 0.033 0.001 0.023 0.001 0.013 0.000 0.003 -0.001 V3 0 V30.025 0.013 0.069 0.016 0.090 0.016 0.116 0.014 0.116 -0.012 0.091 -0.013 0.062 -0.016 0.026 -0.013 U4 0 U40.005 0.012 0.016 0.025 0.035 0.024 0.055 0.023 0.055 0.003 0.035 0.002 0.016 0.001 0.002 0.000 V4 0 V40.031 0.023 0.090 0.035 0.172 0.037 0.233 0.034 0.234 -0.031 0.166 -0.036 0.091 -0.035 0.030 -0.023 U5 0 U50.004 0.012 0.016 0.024 0.037 0.035 0.065 0.034 0.065 0.005 0.036 0.003 0.013 0.002 0.001 0.001 V5 0 V50.036 0.033 0.116 0.055 0.233 0.065 0.376 0.063 0.370 -0.062 0.234 -0.065 0.116 -0.055 0.036 -0.033 U6 0 U60.004 0.011 0.014 0.023 0.034 0.034 0.063 0.044 0.062 0.006 0.031 0.005 0.012 0.003 0.001 0.001 V6 X F= -52.5 V60.036 0.033 0.116 0.055 0.234 0.065 0.370 0.062 0.376 -0.063 0.233 -0.065 0.116 -0.055 0.036 -0.033 U7 0 U7-0.001 0.001 -0.012 0.003 -0.031 0.005 -0.062 0.006 -0.063 0.044 -0.034 0.034 -0.014 0.023 -0.004 0.011 V7 -52.5 V70.030 0.023 0.091 0.035 0.166 0.036 0.234 0.031 0.233 -0.034 0.172 -0.037 0.090 -0.035 0.031 -0.023 U8 0 U8-0.001 0.001 -0.013 0.002 -0.036 0.003 -0.065 0.005 -0.065 0.034 -0.037 0.035 -0.016 0.024 -0.004 0.012 V8 0 V80.026 0.013 0.062 0.016 0.091 0.013 0.116 0.012 0.116 -0.014 0.090 -0.016 0.069 -0.016 0.025 -0.013 U9 0 U9-0.002 0.000 -0.016 0.001 -0.035 0.002 -0.055 0.003 -0.055 0.023 -0.035 0.024 -0.016 0.025 -0.005 0.012 V9 0 V90.017 0.003 0.026 0.002 0.030 0.001 0.036 0.001 0.036 -0.004 0.031 -0.004 0.025 -0.005 0.024 -0.004 U10 0 U10-0.003 -0.001 -0.013 0.000 -0.023 0.001 -0.033 0.001 -0.033 0.011 -0.023 0.012 -0.013 0.012 -0.004 0.013 V10 0 V10
0.000 U1 m0.000 V1 m0.000 U2 m0.000 V2 m
-0.148 U3 m-0.661 V3 m-0.126 U4 m-1.345 V4 m-0.141 U5 m-2.006 V5 m-0.052 U6 m-2.630 V6 m0.052 U7 m
-2.630 V7 m0.141 U8 m
-2.006 V8 m0.126 U9 m
-1.345 V9 m0.148 U10 m
-0.661 V10 m
D=[K]^-1*[F]
D=
D=
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
Calculamos las reacciones -0.148 U3-0.661 V3-0.126 U4
U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10 -1.345 V4X-1 -0.27 -4.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -26.94 -18.74 -0.141 U5Y-1 = -4.35 -69.59 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -18.74 -13.04 X -2.006 V5X-2 -26.94 18.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.27 4.35 -0.052 U6Y-2 18.74 -13.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.35 -69.59 -2.630 V6
0.052 U7Resultanes: -2.630 V7
X-1 11.32 Ton 0.141 U8Y-1 = 52.50 Ton -2.006 V8X-2 -11.32 Ton 0.126 U9y-2 52.50 Ton -1.345 V9
0.148 U10Calculamos las fuerzas internas: S=EA/L*[cosØ senØ] Uf -Ui -0.661 V10
Vf -Vi
S 1-3 = 69.8636805 0.06 1.00 -0.148 0.000 = -46.7448 C S 9-10 = 69.86368 0.06 -1.00 0.148 0.126 = -47.556638 C-0.661 0.000 -0.661 -1.345
S 3-4 = 69.8636805 0.06 1.00 -0.126 -0.148 = -47.5566 C S 10-2 = 69.86368 0.06 -1.00 0.000 0.148 = -46.745 C-1.345 -0.661 0.000 -0.661
S 4-5 = 69.8636805 0.06 1.00 -0.141 -0.126 = -46.1546 C S 1-10 = 39.974514 0.82 0.57 0.148 0 = -10.237474 C-2.006 -1.345 -0.661 0
S 5-6 = 69.8636805 0.06 1.00 -0.052 -0.141 = -43.139 C S 3-2 = 39.974514 0.82 -0.57 0 -0.148 = -10.237474 C-2.630 -2.006 0 -0.661
S 6-7 = 70 1.00 0.00 0.052 -0.052 = 7.344436 T S 3-10 = 50.909091 1.00 0.00 0.148 -0.148 = 15.064356 T-2.630 -2.630 -0.661 -0.661
S 7-8 = 69.8636805 0.06 -1.00 0.141 0.052 = -43.139 C S 3-9 = 42.423025 0.80 0.61 0.126 -0.148 = -8.3095976 C-2.006 -2.630 -1.345 -0.661
S 8-9 = 69.8636805 0.06 -1.00 0.126 0.141 = -46.1546 C S 4-10 = 42.423025 0.80 -0.61 0.148 -0.126 = -8.3095976 C-1.345 -2.006 -0.661 -1.345
[R]=[K]*[D]
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
S 4-9 = 56 1.00 0.00 0.126 -0.126 = 14.16413 T-1.345 -1.345
S 4-8 = 45.0895022 0.76 0.64 0.141 -0.126 = -9.99053 C-2.006 -1.345
S 5-9 = 45.0895022 0.76 -0.64 0.126 -0.141 = -9.99053 C-1.345 -2.006
S 5-8 = 62.2222222 1.00 0.00 0.141 -0.141 = 17.48912 T-2.006 -2.006
S 5-7 = 47.9755289 0.73 0.69 0.052 -0.141 = -13.7811 C-2.630 -2.006
S 6-8 = 47.9755289 0.73 -0.69 0.141 -0.052 = -13.7811 C-2.006 -2.630
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
MATRIZ ENSAMBLADAU 1 V 1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10
27.210 23.089 0.000 0.000 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.938 -18.740 U123.089 82.628 0.000 0.000 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -18.740 -13.036 V10.000 0.000 27.210 -23.089 -26.938 18.740 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 U20.000 0.000 -23.089 82.628 18.740 -13.036 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 V2-0.272 -4.349 -26.938 18.740 105.233 10.410 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.842 -20.451 -50.909 0.000 U3-4.349 -69.592 18.740 -13.036 10.410 167.801 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 V30.000 0.000 0.000 0.000 -0.272 -4.349 109.767 10.464 -0.272 -4.349 0.000 0.000 0.000 0.000 -26.381 -22.216 -56.000 0.000 -26.842 20.451 U40.000 0.000 0.000 0.000 -4.349 -69.592 10.464 173.473 -4.349 -69.592 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 20.451 -15.581 V40.000 0.000 0.000 0.000 0.000 0.000 -0.272 -4.349 114.588 10.427 -0.272 -4.349 -25.440 -23.944 -62.222 0.000 -26.381 22.216 0.000 0.000 U50.000 0.000 0.000 0.000 0.000 0.000 -4.349 -69.592 10.427 180.427 -4.349 -69.592 -23.944 -22.535 0.000 0.000 22.216 -18.708 0.000 0.000 V50.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 -4.349 95.712 -19.594 -70.000 0.000 -25.440 23.944 0.000 0.000 0.000 0.000 U60.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -4.349 -69.592 -19.594 92.127 0.000 0.000 23.944 -22.535 0.000 0.000 0.000 0.000 V60.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -25.440 -23.944 -70.000 0.000 95.712 19.594 -0.272 4.349 0.000 0.000 0.000 0.000 U70.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -23.944 -22.535 0.000 0.000 19.594 92.127 4.349 -69.592 0.000 0.000 0.000 0.000 V70.000 0.000 0.000 0.000 0.000 0.000 -26.381 -22.216 -62.222 0.000 -25.440 23.944 -0.272 4.349 114.588 -10.427 -0.272 4.349 0.000 0.000 U80.000 0.000 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 23.944 -22.535 4.349 -69.592 -10.427 180.427 4.349 -69.592 0.000 0.000 V80.000 0.000 0.000 0.000 -26.842 -20.451 -56.000 0.000 -26.381 22.216 0.000 0.000 0.000 0.000 -0.272 4.349 109.767 -10.464 -0.272 4.349 U90.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 22.216 -18.708 0.000 0.000 0.000 0.000 4.349 -69.592 -10.464 173.473 4.349 -69.592 V9
-26.938 -18.740 -0.272 4.349 -50.909 0.000 -26.842 20.451 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 105.233 -10.410 U10-18.740 -13.036 4.349 -69.592 0.000 0.000 20.451 -15.581 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 -10.410 167.801 V10
U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10105.233 10.410 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.842 -20.451 -50.909 0.000 U310.410 167.801 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 V3-0.272 -4.349 109.767 10.464 -0.272 -4.349 0.000 0.000 0.000 0.000 -26.381 -22.216 -56.000 0.000 -26.842 20.451 U4-4.349 -69.592 10.464 173.473 -4.349 -69.592 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 20.451 -15.581 V4
K= 0.000 0.000 -0.272 -4.349 114.588 10.427 -0.272 -4.349 -25.440 -23.944 -62.222 0.000 -26.381 22.216 0.000 0.000 U50.000 0.000 -4.349 -69.592 10.427 180.427 -4.349 -69.592 -23.944 -22.535 0.000 0.000 22.216 -18.708 0.000 0.000 V50.000 0.000 0.000 0.000 -0.272 -4.349 95.712 -19.594 -70.000 0.000 -25.440 23.944 0.000 0.000 0.000 0.000 U60.000 0.000 0.000 0.000 -4.349 -69.592 -19.594 92.127 0.000 0.000 23.944 -22.535 0.000 0.000 0.000 0.000 V60.000 0.000 0.000 0.000 -25.440 -23.944 -70.000 0.000 95.712 19.594 -0.272 4.349 0.000 0.000 0.000 0.000 U70.000 0.000 0.000 0.000 -23.944 -22.535 0.000 0.000 19.594 92.127 4.349 -69.592 0.000 0.000 0.000 0.000 V70.000 0.000 -26.381 -22.216 -62.222 0.000 -25.440 23.944 -0.272 4.349 114.588 -10.427 -0.272 4.349 0.000 0.000 U80.000 0.000 -22.216 -18.708 0.000 0.000 23.944 -22.535 4.349 -69.592 -10.427 180.427 4.349 -69.592 0.000 0.000 V8
-26.842 -20.451 -56.000 0.000 -26.381 22.216 0.000 0.000 0.000 0.000 -0.272 4.349 109.767 -10.464 -0.272 4.349 U9-20.451 -15.581 0.000 0.000 22.216 -18.708 0.000 0.000 0.000 0.000 4.349 -69.592 -10.464 173.473 4.349 -69.592 V9-50.909 0.000 -26.842 20.451 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 105.233 -10.410 U100.000 0.000 20.451 -15.581 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 -10.410 167.801 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
sabemos que:U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10 MATRIZ DE FUERZAS
0.024 0.004 0.025 0.005 0.031 0.004 0.036 0.004 0.036 -0.001 0.030 -0.001 0.026 -0.002 0.017 -0.003 U3 0 U30.004 0.013 0.013 0.012 0.023 0.012 0.033 0.011 0.033 0.001 0.023 0.001 0.013 0.000 0.003 -0.001 V3 0 V30.025 0.013 0.069 0.016 0.090 0.016 0.116 0.014 0.116 -0.012 0.091 -0.013 0.062 -0.016 0.026 -0.013 U4 0 U40.005 0.012 0.016 0.025 0.035 0.024 0.055 0.023 0.055 0.003 0.035 0.002 0.016 0.001 0.002 0.000 V4 0 V40.031 0.023 0.090 0.035 0.172 0.037 0.233 0.034 0.234 -0.031 0.166 -0.036 0.091 -0.035 0.030 -0.023 U5 0 U50.004 0.012 0.016 0.024 0.037 0.035 0.065 0.034 0.065 0.005 0.036 0.003 0.013 0.002 0.001 0.001 V5 0 V50.036 0.033 0.116 0.055 0.233 0.065 0.376 0.063 0.370 -0.062 0.234 -0.065 0.116 -0.055 0.036 -0.033 U6 0 U60.004 0.011 0.014 0.023 0.034 0.034 0.063 0.044 0.062 0.006 0.031 0.005 0.012 0.003 0.001 0.001 V6 X F= -49.8 V60.036 0.033 0.116 0.055 0.234 0.065 0.370 0.062 0.376 -0.063 0.233 -0.065 0.116 -0.055 0.036 -0.033 U7 0 U7-0.001 0.001 -0.012 0.003 -0.031 0.005 -0.062 0.006 -0.063 0.044 -0.034 0.034 -0.014 0.023 -0.004 0.011 V7 -49.8 V70.030 0.023 0.091 0.035 0.166 0.036 0.234 0.031 0.233 -0.034 0.172 -0.037 0.090 -0.035 0.031 -0.023 U8 0 U8-0.001 0.001 -0.013 0.002 -0.036 0.003 -0.065 0.005 -0.065 0.034 -0.037 0.035 -0.016 0.024 -0.004 0.012 V8 0 V80.026 0.013 0.062 0.016 0.091 0.013 0.116 0.012 0.116 -0.014 0.090 -0.016 0.069 -0.016 0.025 -0.013 U9 0 U9-0.002 0.000 -0.016 0.001 -0.035 0.002 -0.055 0.003 -0.055 0.023 -0.035 0.024 -0.016 0.025 -0.005 0.012 V9 0 V90.017 0.003 0.026 0.002 0.030 0.001 0.036 0.001 0.036 -0.004 0.031 -0.004 0.025 -0.005 0.024 -0.004 U10 0 U10-0.003 -0.001 -0.013 0.000 -0.023 0.001 -0.033 0.001 -0.033 0.011 -0.023 0.012 -0.013 0.012 -0.004 0.013 V10 0 V10
0.000 U1 m0.000 V1 m0.000 U2 m0.000 V2 m
-0.140 U3 m-0.627 V3 m-0.120 U4 m-1.275 V4 m-0.133 U5 m-1.902 V5 m-0.050 U6 m-2.495 V6 m0.050 U7 m
-2.495 V7 m0.133 U8 m
-1.902 V8 m0.120 U9 m
-1.275 V9 m0.140 U10 m
-0.627 V10 m
D=[K]^-1*[F]
D=
D=
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
Calculamos las reacciones -0.140 U3-0.627 V3-0.120 U4
U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10 -1.275 V4X-1 -0.27 -4.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -26.94 -18.74 -0.133 U5Y-1 = -4.35 -69.59 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -18.74 -13.04 X -1.902 V5X-2 -26.94 18.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.27 4.35 -0.050 U6Y-2 18.74 -13.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.35 -69.59 -2.495 V6
0.050 U7Resultanes: -2.495 V7
X-1 10.74 Ton 0.133 U8Y-1 = 49.80 Ton -1.902 V8X-2 -10.74 Ton 0.120 U9y-2 49.80 Ton -1.275 V9
0.140 U10Calculamos las fuerzas internas: S=EA/L*[cosØ senØ] Uf -Ui -0.627 V10
Vf -Vi
S 1-3 = 69.8636805 0.06 1.00 -0.140 0.000 = -44.3408 C S 9-10 = 69.86368 0.06 -1.00 0.140 0.120 = -45.1109 C-0.627 0.000 -0.627 -1.275
S 3-4 = 69.8636805 0.06 1.00 -0.120 -0.140 = -45.1109 C S 10-2 = 69.86368 0.06 -1.00 0.000 0.140 = -44.3408 C-1.275 -0.627 0.000 -0.627
S 4-5 = 69.8636805 0.06 1.00 -0.133 -0.120 = -43.781 C S 1-10 = 39.974514 0.82 0.57 0.140 0 = -9.71098 C-1.902 -1.275 -0.627 0
S 5-6 = 69.8636805 0.06 1.00 -0.050 -0.133 = -40.9204 C S 3-2 = 39.974514 0.82 -0.57 0 -0.140 = -9.71098 C-2.495 -1.902 0 -0.627
S 6-7 = 70 1.00 0.00 0.050 -0.050 = 6.966722 T S 3-10 = 50.909091 1.00 0.00 0.140 -0.140 = 14.28962 T-2.495 -2.495 -0.627 -0.627
S 7-8 = 69.8636805 0.06 -1.00 0.133 0.050 = -40.9204 C S 3-9 = 42.423025 0.80 0.61 0.120 -0.140 = -7.88225 C-1.902 -2.495 -1.275 -0.627
S 8-9 = 69.8636805 0.06 -1.00 0.120 0.133 = -43.781 C S 4-10 = 42.423025 0.80 -0.61 0.140 -0.120 = -7.88225 C-1.275 -1.902 -0.627 -1.275
S 4-9 = 56 1.00 0.00 0.120 -0.120 = 13.43569 T-1.275 -1.275
[R]=[K]*[D]
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
S 4-8 = 45.0895022 0.76 0.64 0.133 -0.120 = -9.47673 C-1.902 -1.275
S 5-9 = 45.0895022 0.76 -0.64 0.120 -0.133 = -9.47673 C-1.275 -1.902
S 5-8 = 62.2222222 1.00 0.00 0.133 -0.133 = 16.58968 T-1.902 -1.902
S 5-7 = 47.9755289 0.73 0.69 0.050 -0.133 = -13.0723 C-2.495 -1.902
S 6-8 = 47.9755289 0.73 -0.69 0.133 -0.050 = -13.0723 C-1.902 -2.495
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
MATRIZ ENSAMBLADAU 1 V 1 U 2 V 2 U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10
27.210 23.089 0.000 0.000 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.938 -18.740 U123.089 82.628 0.000 0.000 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -18.740 -13.036 V10.000 0.000 27.210 -23.089 -26.938 18.740 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 U20.000 0.000 -23.089 82.628 18.740 -13.036 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 V2-0.272 -4.349 -26.938 18.740 105.233 10.410 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.842 -20.451 -50.909 0.000 U3-4.349 -69.592 18.740 -13.036 10.410 167.801 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 V30.000 0.000 0.000 0.000 -0.272 -4.349 109.767 10.464 -0.272 -4.349 0.000 0.000 0.000 0.000 -26.381 -22.216 -56.000 0.000 -26.842 20.451 U40.000 0.000 0.000 0.000 -4.349 -69.592 10.464 173.473 -4.349 -69.592 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 20.451 -15.581 V40.000 0.000 0.000 0.000 0.000 0.000 -0.272 -4.349 114.588 10.427 -0.272 -4.349 -25.440 -23.944 -62.222 0.000 -26.381 22.216 0.000 0.000 U50.000 0.000 0.000 0.000 0.000 0.000 -4.349 -69.592 10.427 180.427 -4.349 -69.592 -23.944 -22.535 0.000 0.000 22.216 -18.708 0.000 0.000 V50.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 -4.349 95.712 -19.594 -70.000 0.000 -25.440 23.944 0.000 0.000 0.000 0.000 U60.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -4.349 -69.592 -19.594 92.127 0.000 0.000 23.944 -22.535 0.000 0.000 0.000 0.000 V60.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -25.440 -23.944 -70.000 0.000 95.712 19.594 -0.272 4.349 0.000 0.000 0.000 0.000 U70.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -23.944 -22.535 0.000 0.000 19.594 92.127 4.349 -69.592 0.000 0.000 0.000 0.000 V70.000 0.000 0.000 0.000 0.000 0.000 -26.381 -22.216 -62.222 0.000 -25.440 23.944 -0.272 4.349 114.588 -10.427 -0.272 4.349 0.000 0.000 U80.000 0.000 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 23.944 -22.535 4.349 -69.592 -10.427 180.427 4.349 -69.592 0.000 0.000 V80.000 0.000 0.000 0.000 -26.842 -20.451 -56.000 0.000 -26.381 22.216 0.000 0.000 0.000 0.000 -0.272 4.349 109.767 -10.464 -0.272 4.349 U90.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 22.216 -18.708 0.000 0.000 0.000 0.000 4.349 -69.592 -10.464 173.473 4.349 -69.592 V9
-26.938 -18.740 -0.272 4.349 -50.909 0.000 -26.842 20.451 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 105.233 -10.410 U10-18.740 -13.036 4.349 -69.592 0.000 0.000 20.451 -15.581 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 -10.410 167.801 V10
U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10105.233 10.410 -0.272 -4.349 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -26.842 -20.451 -50.909 0.000 U310.410 167.801 -4.349 -69.592 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -20.451 -15.581 0.000 0.000 V3-0.272 -4.349 109.767 10.464 -0.272 -4.349 0.000 0.000 0.000 0.000 -26.381 -22.216 -56.000 0.000 -26.842 20.451 U4-4.349 -69.592 10.464 173.473 -4.349 -69.592 0.000 0.000 0.000 0.000 -22.216 -18.708 0.000 0.000 20.451 -15.581 V4
K= 0.000 0.000 -0.272 -4.349 114.588 10.427 -0.272 -4.349 -25.440 -23.944 -62.222 0.000 -26.381 22.216 0.000 0.000 U50.000 0.000 -4.349 -69.592 10.427 180.427 -4.349 -69.592 -23.944 -22.535 0.000 0.000 22.216 -18.708 0.000 0.000 V50.000 0.000 0.000 0.000 -0.272 -4.349 95.712 -19.594 -70.000 0.000 -25.440 23.944 0.000 0.000 0.000 0.000 U60.000 0.000 0.000 0.000 -4.349 -69.592 -19.594 92.127 0.000 0.000 23.944 -22.535 0.000 0.000 0.000 0.000 V60.000 0.000 0.000 0.000 -25.440 -23.944 -70.000 0.000 95.712 19.594 -0.272 4.349 0.000 0.000 0.000 0.000 U70.000 0.000 0.000 0.000 -23.944 -22.535 0.000 0.000 19.594 92.127 4.349 -69.592 0.000 0.000 0.000 0.000 V70.000 0.000 -26.381 -22.216 -62.222 0.000 -25.440 23.944 -0.272 4.349 114.588 -10.427 -0.272 4.349 0.000 0.000 U80.000 0.000 -22.216 -18.708 0.000 0.000 23.944 -22.535 4.349 -69.592 -10.427 180.427 4.349 -69.592 0.000 0.000 V8
-26.842 -20.451 -56.000 0.000 -26.381 22.216 0.000 0.000 0.000 0.000 -0.272 4.349 109.767 -10.464 -0.272 4.349 U9-20.451 -15.581 0.000 0.000 22.216 -18.708 0.000 0.000 0.000 0.000 4.349 -69.592 -10.464 173.473 4.349 -69.592 V9-50.909 0.000 -26.842 20.451 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.272 4.349 105.233 -10.410 U100.000 0.000 20.451 -15.581 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4.349 -69.592 -10.410 167.801 V10
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
sabemos que:U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10 MATRIZ DE FUERZAS
0.024 0.004 0.025 0.005 0.031 0.004 0.036 0.004 0.036 -0.001 0.030 -0.001 0.026 -0.002 0.017 -0.003 U3 0 U30.004 0.013 0.013 0.012 0.023 0.012 0.033 0.011 0.033 0.001 0.023 0.001 0.013 0.000 0.003 -0.001 V3 0 V30.025 0.013 0.069 0.016 0.090 0.016 0.116 0.014 0.116 -0.012 0.091 -0.013 0.062 -0.016 0.026 -0.013 U4 0 U40.005 0.012 0.016 0.025 0.035 0.024 0.055 0.023 0.055 0.003 0.035 0.002 0.016 0.001 0.002 0.000 V4 0 V40.031 0.023 0.090 0.035 0.172 0.037 0.233 0.034 0.234 -0.031 0.166 -0.036 0.091 -0.035 0.030 -0.023 U5 0 U50.004 0.012 0.016 0.024 0.037 0.035 0.065 0.034 0.065 0.005 0.036 0.003 0.013 0.002 0.001 0.001 V5 0 V50.036 0.033 0.116 0.055 0.233 0.065 0.376 0.063 0.370 -0.062 0.234 -0.065 0.116 -0.055 0.036 -0.033 U6 10 U60.004 0.011 0.014 0.023 0.034 0.034 0.063 0.044 0.062 0.006 0.031 0.005 0.012 0.003 0.001 0.001 V6 X F= -49.8 V60.036 0.033 0.116 0.055 0.234 0.065 0.370 0.062 0.376 -0.063 0.233 -0.065 0.116 -0.055 0.036 -0.033 U7 0 U7-0.001 0.001 -0.012 0.003 -0.031 0.005 -0.062 0.006 -0.063 0.044 -0.034 0.034 -0.014 0.023 -0.004 0.011 V7 -49.8 V70.030 0.023 0.091 0.035 0.166 0.036 0.234 0.031 0.233 -0.034 0.172 -0.037 0.090 -0.035 0.031 -0.023 U8 0 U8-0.001 0.001 -0.013 0.002 -0.036 0.003 -0.065 0.005 -0.065 0.034 -0.037 0.035 -0.016 0.024 -0.004 0.012 V8 0 V80.026 0.013 0.062 0.016 0.091 0.013 0.116 0.012 0.116 -0.014 0.090 -0.016 0.069 -0.016 0.025 -0.013 U9 0 U9-0.002 0.000 -0.016 0.001 -0.035 0.002 -0.055 0.003 -0.055 0.023 -0.035 0.024 -0.016 0.025 -0.005 0.012 V9 0 V90.017 0.003 0.026 0.002 0.030 0.001 0.036 0.001 0.036 -0.004 0.031 -0.004 0.025 -0.005 0.024 -0.004 U10 0 U10-0.003 -0.001 -0.013 0.000 -0.023 0.001 -0.033 0.001 -0.033 0.011 -0.023 0.012 -0.013 0.012 -0.004 0.013 V10 0 V10
0.000 U1 m0.000 V1 m0.000 U2 m0.000 V2 m0.216 U3 m
-0.301 V3 m1.044 U4 m
-0.728 V4 m2.198 U5 m
-1.250 V5 m3.709 U6 m
-1.860 V6 m3.746 U7 m
-3.119 V7 m2.472 U8 m
-2.556 V8 m1.283 U9 m
-1.823 V9 m0.497 U10 m
-0.953 V10 m
D=[K]^-1*[F]
D=
D=
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
Calculamos las reacciones 0.216 U3-0.301 V31.044 U4
U 3 V 3 U 4 V 4 U 5 V 5 U 6 V 6 U 7 V 7 U 8 V 8 U 9 V 9 U 10 V 10 -0.728 V4X-1 -0.27 -4.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -26.94 -18.74 2.198 U5Y-1 = -4.35 -69.59 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -18.74 -13.04 X -1.250 V5X-2 -26.94 18.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.27 4.35 3.709 U6Y-2 18.74 -13.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.35 -69.59 -1.860 V6
3.746 U7Resultanes: -3.119 V7
X-1 5.74 Ton 2.472 U8Y-1 = 23.13 Ton -2.556 V8X-2 -15.74 Ton 1.283 U9y-2 76.47 Ton -1.823 V9
0.497 U10Calculamos las fuerzas internas: S=EA/L*[cosØ senØ] Uf -Ui -0.953 V10
Vf -Vi
S 1-3 = 69.8636805 0.06 1.00 0.216 0.000 = -20.0523 C S 9-10 = 69.86368 0.06 -1.00 0.497 1.283 = -64.0491 C-0.301 0.000 -0.953 -1.823
S 3-4 = 69.8636805 0.06 1.00 1.044 0.216 = -26.1572 C S 10-2 = 69.86368 0.06 -1.00 0.000 0.497 = -68.6317 C-0.728 -0.301 0.000 -0.953
S 4-5 = 69.8636805 0.06 1.00 2.198 1.044 = -31.3724 C S 1-10 = 39.974514 0.82 0.57 0.497 0 = -5.46365 C-1.250 -0.728 -0.953 0
S 5-6 = 69.8636805 0.06 1.00 3.709 2.198 = -35.9283 C S 3-2 = 39.974514 0.82 -0.57 0 0.216 = -13.9539 C-1.860 -1.250 0 -0.301
S 6-7 = 70 1.00 0.00 3.746 3.709 = 2.571837 T S 3-10 = 50.909091 1.00 0.00 0.497 0.216 = 14.29736 T-3.119 -1.860 -0.953 -0.301
S 7-8 = 69.8636805 0.06 -1.00 2.472 3.746 = -44.8346 C S 3-9 = 42.423025 0.80 0.61 1.283 0.216 = -3.09482 C-2.556 -3.119 -1.823 -0.301
S 8-9 = 69.8636805 0.06 -1.00 1.283 2.472 = -56.3099 C S 4-10 = 42.423025 0.80 -0.61 0.497 1.044 = -12.6951 C-1.823 -2.556 -0.953 -0.728
S 4-9 = 56 1.00 0.00 1.283 1.044 = 13.37867 T-1.823 -0.728
[R]=[K]*[D]
UNIVERSIDAD ALAS PERUANAS FILIAL - AYACUCHO
S 4-8 = 45.0895022 0.76 0.64 2.472 1.044 = -3.86355 C-2.556 -0.728
S 5-9 = 45.0895022 0.76 -0.64 1.283 2.198 = -14.9033 C-1.823 -1.250
S 5-8 = 62.2222222 1.00 0.00 2.472 2.198 = 17.05245 T-2.556 -1.250
S 5-7 = 47.9755289 0.73 0.69 3.746 2.198 = -7.37234 C-3.119 -1.250
S 6-8 = 47.9755289 0.73 -0.69 2.472 3.709 = -20.3419 C-2.556 -1.860
COMBINACION 01
BARRAS TRACCIÓN PERFIL LONGITUD As (cm2) Fy Øt Øt*Fy*AS Iy As(min) Iy(min) COMPROBANDO COMPROBANDO
TON KG cm cm cm2 cm RADIO GIRO AREA
S 6-7 = 7.344 7344.436 T IPN 120 300.000 14.2 2500 0.9 31950 1.23 3.264 1.000 CUMPLE CUMPLE!!!S 4-9 = 14.164 14164.128 T IPN 140 375.000 18.3 2500 0.9 41175 1.4 6.295 1.250 CUMPLE CUMPLE!!!S 5-8 = 17.489 17489.122 T IPN 140 337.500 18.3 2500 0.9 41175 1.4 7.773 1.125 CUMPLE CUMPLE!!!
S 3-10 = 15.064 15064.356 T IPN 140 412.500 18.3 2500 0.9 41175 1.4 6.695 1.375 CUMPLE CUMPLE!!!
PERFIL L K r L/r K*L/r ØFcr As(cm2) ØFcr *As Pu/(ØFcr *As)
BARRAS A COMPRESIÓNS 1-3 = -46.745 -46744.774 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.731 CUMPLE!!!S 3-4 = -47.557 -47556.638 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.743 CUMPLE!!!S 4-5 = -46.155 -46154.628 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.721 CUMPLE!!!S 5-6 = -43.139 -43138.956 C HEB 120 300.585 1 3.06 98.23051 98 1309 34 44506 0.969 CUMPLE!!!S 7-8 = -43.139 -43138.956 C HEB 120 300.585 1 3.06 98.23051 98 1309 34 44506 0.969 CUMPLE!!!S 8-9 = -46.155 -46154.628 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.721 CUMPLE!!!S 4-8 = -9.991 -9990.526 C HEB 100 465.740 1 2.53 184.0871 184 456 26 11856 0.843 CUMPLE!!!S 5-9 = -9.991 -9990.526 C HEB 100 465.740 1 2.53 184.0871 184 456 26 11856 0.843 CUMPLE!!!S 5-7 = -13.781 -13781.063 C HEB 120 437.723 1 3.06 143.0468 143 756 34 25704 0.536 CUMPLE!!!S 6-8 = -13.781 -13781.063 C HEB 120 437.723 1 3.06 143.0468 143 756 34 25704 0.536 CUMPLE!!!
S 9-10 = -47.557 -47556.638 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.743 CUMPLE!!!S 1-10 = -10.237 -10237.474 C HEB 120 525.335 1 3.06 171.678 172 522 34 17748 0.577 CUMPLE!!!
S 3-2 = -10.237 -10237.474 C HEB 120 525.335 1 3.06 171.678 172 522 34 17748 0.577 CUMPLE!!!S 3-9 = -8.310 -8309.598 C HEB 100 495.014 1 2.53 195.6578 196 402 26 10452 0.795 CUMPLE!!!
S 4-10 = -8.310 -8309.598 C HEB 100 495.014 1 2.53 195.6578 196 402 26 10452 0.795 CUMPLE!!!S 10-2 = -46.74477 -46744.774 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.731 CUMPLE!!!
COMBINACION 02
BARRAS TRACCIÓN PERFIL LONGITUD As (cm2) Fy Øt Øt*Fy*AS Iy As(min) Iy(min) COMPROBANDO COMPROBANDO
TON KG cm cm cm2 cm RADIO GIRO AREA
S 6-7 = 6.967 6966.722 T IPN 100 300.000 10.6 2500 0.9 23850 1.07 3.096 1.000 CUMPLE CUMPLE!!!S 4-9 = 13.436 13435.687 T IPN 140 375.000 18.3 2500 0.9 41175 1.4 5.971 1.250 CUMPLE CUMPLE!!!S 5-8 = 16.590 16589.682 T IPN 140 337.500 18.3 2500 0.9 41175 1.4 7.373 1.125 CUMPLE CUMPLE!!!
S 3-10 = 14.290 14289.617 T IPN 140 412.500 18.3 2500 0.9 41175 1.4 6.351 1.375 CUMPLE CUMPLE!!!
PERFIL L K r L/r K*L/r ØFcr As(cm2) ØFcr *As Pu/(ØFcr *As)
BARRAS A COMPRESIÓNS 1-3 = -44.341 -44340.757 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.693 CUMPLE!!!S 3-4 = -45.111 -45110.868 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.705 CUMPLE!!!S 4-5 = -43.781 -43780.961 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.684 CUMPLE!!!S 5-6 = -40.920 -40920.381 C HEB 120 300.585 1 3.06 98.23051 98 1309 34 44506 0.919 CUMPLE!!!S 7-8 = -40.920 -40920.381 C HEB 120 300.585 1 3.06 98.23051 98 1309 34 44506 0.919 CUMPLE!!!S 8-9 = -43.781 -43780.961 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.684 CUMPLE!!!S 4-8 = -9.477 -9476.727 C HEB 100 465.740 1 2.53 184.0871 184 456 26 11856 0.799 CUMPLE!!!S 5-9 = -9.477 -9476.727 C HEB 100 465.740 1 2.53 184.0871 184 456 26 11856 0.799 CUMPLE!!!S 5-7 = -13.072 -13072.322 C HEB 120 437.723 1 3.06 143.0468 143 756 34 25704 0.509 CUMPLE!!!S 6-8 = -13.072 -13072.322 C HEB 120 437.723 1 3.06 143.0468 143 756 34 25704 0.509 CUMPLE!!!
S 9-10 = -45.111 -45110.868 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.705 CUMPLE!!!S 1-10 = -9.711 -9710.975 C HEB 120 525.335 1 3.06 171.678 172 522 34 17748 0.547 CUMPLE!!!
S 3-2 = -9.711 -9710.975 C HEB 120 525.335 1 3.06 171.678 172 522 34 17748 0.547 CUMPLE!!!S 3-9 = -7.882 -7882.247 C HEB 100 495.014 1 2.53 195.6578 196 402 26 10452 0.754 CUMPLE!!!
S 4-10 = -7.882 -7882.247 C HEB 100 495.014 1 2.53 195.6578 196 402 26 10452 0.754 CUMPLE!!!S 10-2 = -44.34076 -44340.757 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.693 CUMPLE!!!
COMBINACION 03
BARRAS TRACCIÓN PERFIL LONGITUD As (cm2) Fy Øt Øt*Fy*AS Iy As(min) Iy(min) COMPROBANDO COMPROBANDO
TON KG cm cm cm2 cm RADIO GIRO AREA
S 6-7 = 2.572 2571.837 T IPN 100 300.000 10.6 2500 0.9 23850 1.07 1.143 1.000 CUMPLE CUMPLE!!!S 4-9 = 13.379 13378.671 T IPN 140 375.000 18.3 2500 0.9 41175 1.4 5.946 1.250 CUMPLE CUMPLE!!!S 5-8 = 17.052 17052.446 T IPN 140 337.500 18.3 2500 0.9 41175 1.4 7.579 1.125 CUMPLE CUMPLE!!!
S 3-10 = 14.297 14297.364 T IPN 140 412.500 18.3 2500 0.9 41175 1.4 6.354 1.375 CUMPLE CUMPLE!!!
PERFIL L K r L/r K*L/r ØFcr As(cm2) ØFcr *As Pu/(ØFcr *As)
BARRAS A COMPRESIÓN cm cm
S 1-3 = -20.052 -20052.286 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.313 CUMPLE!!!S 3-4 = -26.157 -26157.165 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.409 CUMPLE!!!S 4-5 = -31.372 -31372.445 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.490 CUMPLE!!!S 5-6 = -35.928 -35928.335 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.562 CUMPLE!!!S 7-8 = -44.835 -44834.568 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.701 CUMPLE!!!S 8-9 = -56.310 -56309.897 C HEB 140 300.585 1 3.58 83.96239 84 1488 43 63984 0.880 CUMPLE!!!S 4-8 = -3.864 -3863.550 C HEB 100 465.740 1 2.53 184.0871 184 456 26 11856 0.326 CUMPLE!!!S 5-9 = -14.903 -14903.321 C HEB 120 465.740 1 3.06 152.2027 152 669 34 22746 0.655 CUMPLE!!!S 5-7 = -7.372 -7372.343 C HEB 120 437.723 1 3.06 143.0468 143 756 34 25704 0.287 CUMPLE!!!S 6-8 = -20.342 -20341.918 C HEB 120 437.723 1 3.06 143.0468 143 756 34 25704 0.791 CUMPLE!!!
S 9-10 = -64.049 -64049.139 C HEB 160 300.585 1 4.05 74.21861 74 1612 54.3 87531.6 0.732 CUMPLE!!!S 1-10 = -5.464 -5463.652 C HEB 120 525.335 1 3.06 171.678 172 522 34 17748 0.308 CUMPLE!!!
S 3-2 = -13.954 -13953.910 C HEB 120 525.335 1 3.06 171.678 172 522 34 17748 0.786 CUMPLE!!!S 3-9 = -3.095 -3094.816 C HEB 100 495.014 1 2.53 195.6578 196 402 26 10452 0.296 CUMPLE!!!
S 4-10 = -12.695 -12695.091 C HEB 120 495.014 1 3.06 161.7693 162 589 34 20026 0.634 CUMPLE!!!S 10-2 = -68.63174 -68631.739 C HEB 160 300.585 1 4.05 74.21861 74 1612 54.3 87531.6 0.784 CUMPLE!!!
PERFIL FUERZA INT.S 6-7 = IPN 100 7344.43574S 4-9 = IPN 140 14164.1275S 5-8 = IPN 140 17489.1224
S 3-10 = IPN 140 15064.3557S 1-3 = HEB 140 -46744.774S 3-4 = HEB 140 -47556.6376S 4-5 = HEB 140 -46154.6278S 5-6 = HEB 120 -43138.9557S 7-8 = HEB 120 -43138.9557S 8-9 = HEB 140 -46154.6278S 4-8 = HEB 100 -9990.5257S 5-9 = HEB 100 -9990.5257S 5-7 = HEB 120 -13781.0629S 6-8 = HEB 120 -13781.0629
S 9-10 = HEB 140 -47556.6376S 1-10 = HEB 120 -10237.4739
S 3-2 = HEB 120 -10237.4739S 3-9 = HEB 100 -8309.59761
S 4-10 = HEB 100 -8309.59761S 10-2 = HEB 140 -46744.774
PERFIL FUERZA INT.S 6-7 = IPN 100 6966.7219S 4-9 = IPN 140 13435.6867S 5-8 = IPN 140 16589.6818
S 3-10 = IPN 140 14289.6174S 1-3 = HEB 140 -44340.757S 3-4 = HEB 140 -45110.8676S 4-5 = HEB 140 -43780.9612S 5-6 = HEB 120 -40920.3809S 7-8 = HEB 120 -40920.3809S 8-9 = HEB 140 -43780.9612S 4-8 = HEB 100 -9476.72723S 5-9 = HEB 100 -9476.72723S 5-7 = HEB 120 -13072.3225S 6-8 = HEB 120 -13072.3225
S 9-10 = HEB 140 -45110.8676S 1-10 = HEB 120 -9710.97523
S 3-2 = HEB 120 -9710.97523S 3-9 = HEB 100 -7882.24688
S 4-10 = HEB 100 -7882.24688S 10-2 = HEB 140 -44340.757
PERFIL FUERZA INT.S 6-7 = IPN 100 2571.837S 4-9 = IPN 140 13378.671S 5-8 = IPN 140 17052.446
S 3-10 = IPN 140 14297.364S 1-3 = HEB 140 -20052.286S 3-4 = HEB 140 -26157.165S 4-5 = HEB 140 -31372.445S 5-6 = HEB 140 -35928.335S 7-8 = HEB 140 -44834.568S 8-9 = HEB 140 -56309.897S 4-8 = HEB 100 -3863.550S 5-9 = HEB 120 -14903.321S 5-7 = HEB 120 -7372.343S 6-8 = HEB 120 -20341.918
S 9-10 = HEB 160 -64049.139S 1-10 = HEB 120 -5463.652
S 3-2 = HEB 120 -13953.910S 3-9 = HEB 100 -3094.816
S 4-10 = HEB 120 -12695.091S 10-2 = HEB 160 -68631.739
Perfil
Dimensiones
A h b e r u A
cm mm mm mm mm mm mm mm cm cm
IPN 80 7.58 0.91 IPE 80 80 46 3.8 5.2 5 60 328 7.64 3.24
IPN 100 10.6 1.07 IPE 100 100 55 4.1 5.7 7 75 400 10.3 4.07
IPN 120 14.2 1.23 IPE 120 120 64 4.4 6.3 7 93 475 13.2 4.9
IPN 140 18.3 1.4 IPE 140 140 73 4.7 6.9 7 112 551 16.4 5.74
IPN 160 22.8 1.55 IPE 160 160 82 5 7.4 9 127 623 20.1 6.58
IPN 180 27.9 1.71 IPE 180 180 91 5.3 8 9 146 698 23.9 7.42
IPN 200 33.5 1.87 IPE 200 200 100 5.6 8.5 12 159 788 28.5 8.26
IPN 220 39.6 2.02 IPE 220 220 110 5.9 9.2 12 178 848 33.4 9.11
IPN 240 46.1 2.2 IPE 240 240 120 6.2 9.8 15 190 922 39.1 9.97
IPN 260 53.4 2.32 IPE 270 270 135 6.6 10.2 15 220 1040 45.9 11.2
IPN 280 61.1 2.45 IPE 300 300 150 7.1 10.7 15 249 1160 53.8 12.5
IPN 300 69.1 2.56 IPE 330 330 160 7.5 11.5 18 271 1250 62.6 13.7
IPN 320 77.8 2.67 IPE 360 360 170 8 12.7 18 299 1350 72.7 15
IPN 340 86.8 2.8 IPE 400 400 180 8.6 13.5 21 331 1470 84.5 16.5
IPN 360 97.1 2.9 IPE 450 450 190 9.4 14.6 21 379 1610 98.8 18.5
IPN 380 107 3.02 IPE 500 500 200 10.2 16 21 426 1740 116 20.4
IPN 400 118 3.13 IPE 550 550 210 11.1 17.2 24 468 1880 134 22.3
IPN 450 147 3.43 IPE 600 600 220 12 19 24 514 2010 155 24.3
IPN 500 180 3.72
IPN 550 213 4.02
IPN 600 254 4.3
IPE 80 7.64 1.05
Perfil
Términos de sección
iy e1 h1 ix
cm2
IPE
IPE 100 10.3 1.24
IPE 120 13.2 1.45
IPE 140 16.4 1.65
IPE 160 20.1 1.84
IPE 180 23.9 2.05
IPE 200 28.5 2.24
IPE 220 33.4 2.48
IPE 240 39.1 2.69
IPE 270 45.9 3.02
IPE 300 53.8 3.35
IPE 330 62.6 3.55
IPE 360 72.7 3.79
IPE 400 84.5 3.95
IPE 450 98.8 4.12
IPE 500 116 4.31
IPE 550 134 4.45
IPE 600 155 4.66
HEB 100 26 2.53
HEB 120 34 3.06
HEB 140 43 3.58
HEB 160 54.3 4.05
HEB 180 65.3 4.57
HEB 200 78.1 5.07
HEB 220 91 5.59
HEB 240 106 6.08
HEB 260 118.4 6.58
HEB 280 131.4 7.09
HEB 300 149.1 7.58
HEB 320 161.3 7.57
HEB 340 170.9 7.53
HEB 360 180.6 7.49
HEB 400 197.8 7.4
HEB 450 218 7.33
HEB 500 238.6 7.27
HEB 550 254.1 7.17
HEB 600 270 7.08
UPN 80 11 1.33
UPN 100 13.5 1.47
UPN 120 17 1.59
UPN 140 20.4 1.75
UPN 160 24 1.89
UPN 180 28 2.02
UPN 200 32.2 2.14
UPN 220 37.4 2.3
UPN 240 42.3 2.42
UPN 260 48.3 2.56
UPN 280 53.3 2.74
UPN 300 58.8 2.9
KL/r ØFcr1 21252 21253 21244 21235 21226 21217 21208 21189 2116
10 211411 211212 211013 210714 210415 210116 209817 209418 209119 208720 208321 207822 207423 206924 206425 205926 205427 204828 204329 203730 203131 202432 201833 201134 2005
35 199836 199037 198338 197639 196840 196041 195242 194443 193644 192745 191846 191047 190148 189249 188250 187351 186452 185453 184454 183455 182456 181457 180458 179359 178360 177261 176162 175063 173964 172865 171766 170567 169468 168369 167170 165971 164872 163673 162474 161275 160076 158877 157578 156379 1551
80 153881 152682 151383 150184 148885 147686 146387 145088 143789 142590 141291 139992 138693 137394 136095 134796 133497 132198 130999 1296
100 1283101 1270102 1257103 1244104 1231105 1218106 1205107 1192108 1179109 1166110 1154111 1141112 1128113 1115114 1103115 1090116 1077117 1065118 1052119 1040120 1027121 1015122 1002123 990124 978
125 966126 953127 941128 929129 917130 905131 893132 882133 870134 858135 847136 835137 823138 811139 800140 788141 777142 766143 756144 745145 735146 725147 715148 705149 788150 687151 678152 669153 660154 651155 643156 635157 627158 619159 611160 604161 596162 589163 582164 574165 568166 561167 554168 547169 541
170 535171 528172 522173 516174 510175 505176 499177 493178 488179 482180 477181 472182 466183 461184 456185 451186 447187 442188 437189 433190 428191 424192 419193 415194 411195 406196 402197 398198 394199 390200 386
Perfil
Dimensiones Términos de la sección
kp/m h b e r u A
cm mm mm mm mm mm mm mm
1.05 6 HEB 100 100 100 6 10 12 56 567 26 52.1 450
1.24 8.1 HEB 120 120 120 6.5 11 12 74 686 34 82.6 864
1.45 10.4 HEB 140 140 140 7 12 12 92 805 43 123 1509
1.65 12.9 HEB 160 160 160 8 13 15 104 918 54.3 177 2492
1.84 15.8 HEB 180 180 180 8.5 14 15 122 1040 65.3 241 3831
2.05 18.8 HEB 200 200 200 9 15 18 134 1150 78.1 321 5696
2.24 22.4 HEB 220 220 220 9.5 16 18 152 1270 91 414 8091
2.48 26.2 HEB 240 240 240 10 17 21 164 1380 106 527 11259
2.69 30.7 HEB 260 260 260 10 17.5 24 177 1500 118.4 641 14919
3.02 36.1 HEB 280 280 280 10.5 18 24 196 1620 131.4 767 19270
3.35 42.2 HEB 300 300 300 11 19 27 208 1730 149.1 934 25166
3.55 49.1 HEB 320 320 300 11.5 20.5 27 225 1770 161.3 1070 30823
3.79 57.1 HEB 340 340 300 12 21.5 27 243 1810 170.9 1200 36656
3.95 66.3 HEB 360 360 300 12.5 22.5 27 261 1850 180.6 1340 43193
4.12 77.6 HEB 400 400 300 13.5 24 27 298 1930 197.8 1620 57680
4.31 90.7 HEB 450 450 300 14 26 27 344 2030 218 1990 79887
4.45 106 HEB 500 500 300 14.5 28 27 390 2120 238.6 2410 107176
4.66 122 HEB 550 550 300 15 29 27 438 2220 254.1 2800 136691
HEB 600 600 300 15.5 30 27 486 2320 270 3210 171041
iy e1 h1 Sx Ix
cm2 cm3 cm4
A = Area de la de la secciónu = Perímetro de la sección.h1 = Altura de la parte plana del alma.p = Peso por metro.
HEBA
A = Area de la de la secciónSx = Momento estático de media sección, respecto a X.Ix = Momento de inercia de la sección, respecto a X.Wx = 2Ix : h. Módulo resistente de la sección, respecto a X.ix = (Ix : A)1/2 . Radio de giro de la sección, respecto a X.Iy = Momento de inercia de la sección, respecto a Y.Wy = 2Iy : b. Módulo resistente de la sección, respecto a Y.Iy = (Iy : A)1/2 . Radio de giro de la sección, respecto a Y It = Módulo de torsión de la sección.Ia = Módulo de alabeo de la sección.u = Perímetro de la sección.a = Diámetro del agujero del roblón normal.w = Gramil, distancia entre ejes de agujeros.h1 = Altura de la parte plana del alma.p = Peso por metro.
Términos de la sección Agujeros
Peso
Perfil
Dimensionesp
w a kp/m h
cm cm mm mm mm mm
90 4.16 167 33 2.53 9.34 3375 55 - 13 20.4 UPN 80 80
144 5.04 318 53 3.06 14.9 9410 65 - 17 26.7 UPN 100 100
216 5.93 550 79 3.58 22.5 22480 75 - 21 33.7 UPN 120 120
311 6.78 889 111 4.05 33.2 47940 85 - 23 42.6 UPN 140 140
426 7.66 1363 151 4.57 46.5 93750 100 - 25 51.2 UPN 160 160
570 8.54 2003 200 5.07 63.4 171100 110 - 25 61.3 UPN 180 180
736 9.43 2843 258 5.59 84.4 295400 120 - 25 71.5 UPN 200 200
938 10.3 3923 327 6.08 110 486900 90 35 25 83.2 UPN 220 220
1150 11.2 5135 395 6.58 130 753700 100 40 25 93 UPN 240 240
1380 12.1 6595 471 7.09 153 1130000 110 45 25 103 UPN 260 260
1680 13 8563 571 7.58 192 1688000 120 50 25 117 UPN 280 280
1930 13.8 9239 616 7.57 241 2069000 120 50 25 127 UPN 300 300
2160 14.6 9690 646 7.53 278 2454000 120 50 25 134
2400 15.5 10140 676 7.49 320 2883000 120 50 25 142
2880 17.1 10819 721 7.4 394 3817000 120 50 25 155
3550 19.1 11721 781 7.33 500 5258000 120 50 25 171
4290 21.2 12624 842 7.27 625 7018000 120 45 28 187
4970 23.2 13077 872 7.17 701 8856000 120 45 28 199
5700 25.2 13530 902 7.08 783 1.1E+07 120 45 28 212
Wx ix Iy Wy iy It Ia w1
m3 cm4 cm3 cm4 cm6
A = Area de la de la secciónSx = Momento estático de media sección, respecto a X.Ix = Momento de inercia de la sección, respecto a X.Wx = 2Ix : h. Módulo resistente de la sección, respecto a X.ix = (Ix : A)1/2 . Radio de giro de la sección, respecto a X.Iy = Momento de inercia de la sección, respecto a Y.Wy = 2Iy : b. Módulo resistente de la sección, respecto a Y.Iy = (Iy : A)1/2 . Radio de giro de la sección, respecto a Y It = Módulo de torsión de la sección.Ia = Módulo de alabeo de la sección.u = Perímetro de la sección.a = Diámetro del agujero del roblón normal.w = Gramil, distancia entre ejes de agujeros.h1 = Altura de la parte plana del alma.p = Peso por metro. UPN
Dimensiones Términos de la sección
b e u A c
mm mm mm mm mm mm cm cm cm cm
45 6 8 4 46 312 11 15.9 106 26.5 3.1 19.4 6.36 1.33 2.24 1.45
50 6 8.5 4.5 64 372 13.5 24.5 206 41.2 3.91 29.3 8.49 1.47 2.96 1.55
55 7 9 4.5 82 434 17 36.3 364 60.7 4.62 43.2 11.1 1.59 4.3 1.6
60 7 10 5 98 489 20.4 51.4 605 86.4 5.45 62.7 14.8 1.75 6.02 1.75
65 7.5 10.5 5.5 115 546 24 68.8 925 116 6.21 85.3 18.3 1.89 7.81 1.84
70 8 11 5.5 133 611 28 89.6 1350 150 6.95 114 22.4 2.02 9.98 1.92
75 8.5 11.5 6 151 661 32.2 114 1910 191 7.7 148 27 2.14 12.6 2.01
80 9 12.5 6.5 167 718 37.4 146 2690 245 8.48 197 33.6 2.3 17 2.14
85 9.5 13 6.5 184 775 42.3 179 3600 300 9.22 248 39.6 2.42 20.8 2.23
90 10 14 7 200 834 48.3 221 4820 371 9.99 317 47.7 2.56 23.7 2.36
95 10 15 7.5 216 890 53.3 266 6280 448 10.9 399 57.2 2.74 33.2 2.53
100 10 16 8 232 950 58.8 316 8030 535 11.7 495 67.8 2.9 40.6 2.7
e1=r r1 h1 Sx Ix Wx ix Iy Wy iy It
cm3 cm4 cm3 cm4 cm3 cm4
A = Area de la de la secciónSx = Momento estático de media sección, respecto a X.Ix = Momento de inercia de la sección, respecto a X.Wx = 2Ix : h. Módulo resistente de la sección, respecto a X.ix = (Ix : A)1/2 . Radio de giro de la sección, respecto a X.Iy = Momento de inercia de la sección, respecto a Y.Wy = 2Iy : b. Módulo resistente de la sección, respecto a Y.Iy = (Iy : A)1/2 . Radio de giro de la sección, respecto a Y It = Módulo de torsión de la sección.Ia = Módulo de alabeo de la sección.u = Perímetro de la sección.a = Diámetro del agujero del roblón normal.w = Gramil, distancia entre ejes de agujeros.h1 = Altura de la parte plana del alma.p = Peso por metro. UPN
Términos de la sección Agujeros
Peso
p
m w a kp/m
cm mm mm
2.67 25 13 8.64
2.93 30 13 10.6
3.03 30 17 13.4
3.37 35 17 16
3.56 35 21 18.8
3.75 40 21 22
3.94 40 23 25.3
4.2 45 23 29.4
4.39 45 25 33.2
4.66 50 25 37.9
5.02 50 25 41.8
5.41 55 25 46.2