Ejercicios Biseccion.docx

PROBLEMA: CALCULE LA DISTANCIA EN LA VIGA DONDE EL MOMENTO SEA EL MINIMO, SIN TENER EN CUENTA LOS EXTREMOS DE LA ESTRUCTURA, TENIENDO EN CUENTA UN GRADO DE RIGIDEZ 1.

∑ 𝑓𝑥 = 0

∑ 𝐹𝑦 = 0 = RA + RB - 150 – 300- 100 = RA + RB = 550

RA = 550 – 285

∑ 𝑀𝐴 = 0 = 150 *2 – 300 *4.5 + RB *10 - 100 * 12

RB = 300 + 1350 + 1200 10 RB = 285 N

Corte 1 ( 0 ≤ x ≤ 3 )

∑ 𝐹𝑦 = 265 – 33,3 𝑥 2 - V V = 265 – 16,65 𝑥 2

RA = 265 N

1

∑ 𝑀𝑜 =- 265 X + 16,65 𝑥 2 . - X + M 3 M = 265X - 5,55 𝑋 3

Corte 2

(3<X<6)

∑ 𝑓(𝑦) = 265 – 150 -100 ( x – 3 ) – V V= 265 – 150 – 100 x + 300 V = 415 – 100 x + ∑ 𝑀𝑜 = - 265 X + 150 ( x – 2 ) + 100 ( x – 3 ) ( x – 3 ) + M M = - 50 𝑥 2 + 415 X – 150

Corte 3 (6<X<10)

∑ 𝑓(𝑦) = 0 = 265 - 150 - 300 – V V = - 185 + ∑ 𝑀𝑜 = - 265 * X + 150 (x-2) + 300 (x-4.5) + M M = -185 x + 1650 Corte 4 (10<X<12)

∑ 𝑓(𝑦) = 265 – 150 – 300 + 285 – V V = 100 + ∑ 𝑀𝑜 = -263 X + 150 (x-2) + 300 (x-4.5) – 285 (x-10) + M M= 100X – 1200 Cortante “V”

Momento “M”

Posición = XR Intervalo = 0 m – 12 m XL = 0.0 Ft Xu = 12 Ft Xr = (xl+xu) 2 Error= [XrR nueva – XR antigua] * 100 XR nueva

Momento = 0 Ec = 6 ≤X≤10 𝑓(𝑥) = -185 x + 1650

Funcion: Donde no hay momento (𝑓(𝑥)= -185 X + 1650.015) TABLAS DE PROGRAMACION EN EXCEL

ITERAR XL 1 0 2 6 3 6 4 7.5 5 8.25 6 8.625 7 8.813 8 8.906 9 8.906 10 8.906 11 8.918 12 8.918 13 8.918 14 8.918 15 8.919 16 8.919 17 8.919 18 8.919 19 8.919 20 8.919 21 8.919 22 8.919 23 8.919 24 8.919 25 8.919

XU 12 12 9 9 9 9 9 9 8.953 8.93 8.93 8.924 8.921 8.919 8.919 8.919 8.919 8.919 8.919 8.919 8.919 8.919 8.919 8.919 8.919

F(XL) f(XU) Xr 1650 -569.985 6 540 -569.985 9 540 -14.985 7.5 262.5 -14.985 8.25 123.8 -14.985 8.625 54.39 -14.985 8.8125 19.7 -14.985 8.90625 2.359 -14.985 8.953125 2.359 -6.31312 8.9296875 2.359 -1.97719 8.91796875 0.191 -1.97719 8.923828125 0.191 -0.8932 8.920898438 0.191 -0.35121 8.919433594 0.191 -0.08021 8.918701172 0.055 -0.08021 8.919067383 0.055 -0.01247 8.918884277 0.021 -0.01247 8.91897583 0.004 -0.01247 8.919021606 0.004 -0.004 8.918998718 2E-04 -0.004 8.919010162 2E-04 -0.00188 8.91900444 2E-04 -0.00082 8.919001579 2E-04 -0.00029 8.919000149 2E-04 -2.8E-05 8.918999434 1E-04 -2.8E-05 8.918999791

F(Xr) 540.02 -14.98 262.52 123.77 54.39 19.703 2.3588 -6.313 -1.977 0.1908 -0.893 -0.351 -0.08 0.0553 -0.012 0.0214 0.0045 -0.004 0.0002 -0.002 -8E-04 -3E-04 -3E-05 0.0001 4E-05

F(XL)*F(XR) Ea 891032.85 -8092.12477 33.3333333 141762.038 20 32490.169 9.09090909 6731.57835 4.34782609 1071.61898 2.12765957 46.4732719 1.05263158 -14.8910836 0.52356021 -4.66369102 0.26246719 0.45000527 0.13140604 -0.17040641 0.06565988 -0.06700446 0.03284072 -0.01530349 0.01642306 0.010547 0.0082122 -0.00068915 0.00410593 0.00118354 0.00205301 9.5728E-05 0.00102649 -1.7873E-05 0.00051324 1.0603E-06 0.00025662 -4.458E-07 0.00012831 -1.9479E-07 6.4156E-05 -6.9279E-08 3.2078E-05 -6.5263E-09 1.6039E-05 2.485E-08 8.0195E-06 4.0492E-09 4.0097E-06

Et 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005 0.000005

CONDICION SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA SIGA PARE

GRAFICADOR GEOGEBRA