Raices Variables.docx

PROBLEMA. ENCONTRAR EL FACTOR DE SEGURIDAD PARA CADA PROYECCION DE CONCRETO, TENIENDO EN CUENTA QUE ES UN SUELO ARCILLOSO Y CON UNA SATURACION DE 10 %.

Densidad del agua: 9.81 kn/m3 Cohesion: 15 Angulo de friccion: 27° Saturación del suelo: 8% Densidad del suelo seco:3kn/m3 Densidad del suelo húmedo : 4.5 kn/m3 densidad del suelo saturado: 6 kn/m3

  c    tg    

Donde:

 = Resistencia al corte F/A c = Cohesión del suelo F/A  = presión intergranular o esfuerzo normal F/A  = Ángulo de fricción interna, cuyo valor se considera constant

n  OE  OA  AE  3  AD  cos  AD  2  AC  cos  AB  cos  1  3   cos           cos 2  

1

     1      cos2

 1  3  2c  cot  1  3  sen  2c  cot  sen  1  sen  3  sen  1  3  2c  cos   1  sen  3  sen  1  1  sen  3  3  sen  2c  cos 

 1 1 sen   3 1 sen  2c  cos 

2 E mgh  63.5 in kg9.807 m/s 0.762 m = 475Joules = 350 lbpie

q 

2

cN  qN  0.3BN

 qu  0.867cNc  qNq  0.4BN

 0.867cNc  qNq  0.3BN

∑ 𝑓𝑥 = 𝑓𝑥1 + 𝑓𝑥2 + 𝑓𝑥3 + 𝑓𝑥4 + 𝑓𝑥5 + 𝑓𝑥6 ∑ 𝑓𝑦 = 𝑓𝑦1 + 𝑓𝑦2 + 𝑓𝑦3 + 𝑓𝑦4 + 𝑓𝑦5 + 𝑓𝑦6 ∑ 𝑚1 = 𝑓𝑥1(𝑥. 𝑥. 𝑥. 𝑥. 𝑥. 𝑥) + 𝑓𝑥1(𝑥. 𝑥. 𝑥. 𝑥. 𝑥) − 𝑓𝑥3(𝑥. 𝑥. 𝑥. 𝑥) + 𝑓𝑥4(𝑥. 𝑥. 𝑥) + 𝑓𝑥5(𝑥) + 𝑓𝑥6 TRAMO 1= 5X6 TRAMO 2= -160X5 TRAMO 3= 1575X4 TRAMO 4= -4466X3 TRAMO 5= 458X2 TRAMO 6= -799X TRAMO 7= 300

SUMATORIA DE TRAMOS = FACTORES DE SEGURIDAD

F(X)= 5X6-160X5+1575X4-4466X3 +458X2-799X +300

ITERACION 1 2 3 4 5 6 7 8 9

Xi 1 0.1781894 0.27714297 0.29509816 0.29569603 0.29569667 0.29569667 0.29569667 0.29569667

f(xi) -3087 148.4604842 27.70620278 0.922392941 0.000973412 1.08207E-09 0 0 0.336581048

METODO DE RAICES MULTIPLES RAIZ 1 f'(xi) f"(xi) m Xi+1 -7751 -10030 2.06344476 0.178189398 -1026.34175 -3276.61414 0.68408898 0.277142969 -1444.77698 -5125.88056 0.93629733 0.295098158 -1539.52924 -5426.67911 0.99789255 0.295696035 -1542.77666 -5436.51551 0.99999778 0.295696666 -1542.78009 -5436.52589 1 0.295696666 -1542.78009 -5436.52589 1 0.295696666 -1542.78009 -5436.52589 1 0.295696666 -2.22067779 5.97375496 1.68840119 0.551602248

Ea

Et

Condicion

201.633971 26.9367795 6.17253016 0.21052349 0.00022234 2.4716E-10 0 40.7723707

0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005

SIGA SIGA SIGA SIGA SIGA PARE PARE SIGA

ITERACION 1 2 3 4 5 6 7 8 9

Xi 5 4.71502112 4.73710326 4.73730801 4.73730802 4.73730802 4.73730802 4.73730802 4.73730802

f(xi) 12005 -912.281634 -8.45714788 -0.00070173 -1.0232E-10 8.32188E-11 -4.0927E-11 -3.638E-11 8.32188E-11

f'(xi) 50081 40560.6857 41299.5841 41306.4367 41306.4372 41306.4372 41306.4372 41306.4372 41306.4372

RAIZ 2 f"(xi) m 33186 1.18884026 33452.4135 0.98178776 33469.2528 0.99983408 33469.3799 0.99999999 33469.3799 1 33469.3799 1 33469.3799 1 33469.3799 1 33469.3799 1

Xi+1 4.715021119 4.737103264 4.737308006 4.737308022 4.737308022 4.737308022 4.737308022 4.737308022 4.737308022

ITERACION 1 2 3 4 5 6 7 8 9

Xi 13 12.7747584 12.7467109 12.7465187 12.7465187 12.7465187 12.7465187 12.7465187 12.7465187

f(xi) -33747 -4001.75948 -27.4057387 -0.00115774 5.82077E-10 -3.1032E-09 -1.4697E-09 2.14641E-09 -7.0322E-09

f'(xi) -122063 -140785.402 -142597.944 -142609.987 -142609.988 -142609.988 -142609.988 -142609.988 -142609.988

RAIZ 3 f"(xi) m 100418 0.81469967 66580.0623 0.98673581 62679.2557 0.99991553 62652.7613 1 62652.7602 1 62652.7602 1 62652.7602 1 62652.7602 1 62652.7602 1

Xi+1 12.77475837 12.74671086 12.74651869 12.74651868 12.74651868 12.74651868 12.74651868 12.74651868 12.74651868

ITERACION 1 2 3 4 5 6 7 8

Xi 14 14.1940193 14.3860946 14.4638038 14.4705703 14.4706118 14.4706118 14.4706118

RAIZ 4 f(xi) f'(xi) f"(xi) m Xi+1 Ea Et -74782 75137 311772 0.19494029 14.19401926 -54003.3651 140806.127 365945.4 0.50080935 14.38609464 61.0749501 0.00000005 -19856.0609 216623.93 424318.955 0.84778472 14.4638038 40.9272965 0.00000005 -1716.2601 250563.84 449328.42 0.98786588 14.47057028 14.1801803 0.00000005 -10.522097 253611.706 451544.94 0.99992614 14.47061177 1.20611442 0.00000005 -0.00038862 253630.439 451558.549 1 14.47061177 0.00738612 0.00000005 -1.2333E-09 253630.44 451558.549 1 14.47061177 2.728E-07 0.00000005 6.28461E-09 253630.44 451558.549 1 14.47061177 5.2847E-12 0.00000005

Ea

Et

Condicion

21.0893345 1.80493143 0.01659092 1.3765E-06 3.7748E-13 2.6645E-13 2.2204E-14 2.4425E-13

0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005

SIGA SIGA SIGA SIGA PARE PARE PARE PARE

Ea

Et

Condicion

17.4348735 1.31808361 0.00844664 3.5666E-07 1.1324E-12 4.996E-13 1.1213E-12 2.82E-12

0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005 0.00000005

SIGA SIGA SIGA SIGA PARE PARE PARE PARE

*Cada raíz representa el factor de seguridad de cada proyección de concreto.

Condicion SIGA SIGA SIGA SIGA SIGA SIGA PARE