DEM_I_151_PP_Eq_Camilo Andrés_Bolivar Acosta.xlsx

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POLEASENGRANAJE RECTO ENGRANAJE HELICOIDALEJE

NOMBRE PARAMETRO VALOR

DIAMETRO POLEA MOTOR DPM 120RELACION TRANSMISION POLEAS X0 4RELACION DE TENSIONES CORREA(LADOS TENSO-FLOJO) RTC 5POTENCIA DE ENTRADA EJE Ne 65POTENCIA DADA A PIÑON RECTO N1 25RELACION DE TRANSMISION PIÑON RECTO X1 2MODULO PIÑON RECTO M1 2NUMERO DE DIENTES PIÑON RECTO Z1 20ANGULO DE PRESION PIÑON RECTO ANPR 20ANCHO DEL PIÑON RECTO F1 30MODULO NORMAL PIÑON HELICOIDAL M2 4NUMERO DE DIENTES PIÑON HELICOIDAL Z2 20ANGULO DE PRESION NORMAL PIÑON HELICOIDAL ANPH 20ANGULO DE HELICE DEL PIÑON HELICOIDAL ANHH 25RELACIÓN DE TRANSMISIÓN DEL PIÑON HELICOIDAL X2 4ANCHO DEL ENGGRANAJE HELICOIDAL F2 40

LONGITUD RODAMIENTO IZQUIERDO L1 30LONGITUD ENTRE RODAMIENTO Y ENG. HELICOIDAL L2 65L0NGITUD ZONA ENG. HELICOIDAL L3 40LONGITUD CENTRO EJE L4 120LONGITUD ZONA ENG. RECTO L5 30LONG ZONA ENTRE ENG. RECTO Y RODA. DERECHO L6 55LONG RODAMIENTO DERECHO L7 30LONGITUD ZONA POLEA L8 30

ANGULO CON LA VERTICAL ENTRE CENTROS POLEAS Y0 45 N DE REVOLUCIONES MOTOR OMG1 500ANGULO CON LA HORIZONTAL ENTRE CENTROS E . HELICOIDALES Y2 45

DIAMETRO POLEA EJE DPE 480DISTANCIA CENTRO POLEAS DCP 1600.3476ANGULO CORREA THT 6.41740418379

N DE REVOLUCIONES EJE OMG2 13.08996939TORQUE DE ENTRADA (POLEA) TEx 4.96563422447TENSION CORREA LADO TENSO TC1 25.8626782524TENSION CORREA LADO FLOJO TC2 5.17253565049POTENCIA EN EL PIÑON HELICOIDAL N2 40TORQUE EN EL PIÑON HELICOIDAL TBx 3.05577490736DIAMETRO ENGRANAJE RECTO DER 40

DIAMETRO ENGRANAJE HELICOIDAL DEH 80TORQUE EN EL PIÑON RECTO TCx 1.9098593171

FUERZA PIÑON HELICOIDAL FPH 89.701528019FUERZA RADIAL HELICOIDAL FRH 30.6797294696

FUERZA TANGENCIAL HELICOIDAL FTH 76.3943726841FUERZA AXIAL HELICOIDAL FAH 35.6232810225

MAGNITUD FUERZA RADIAL TANGENCIAL FCrt 89.734035351FUERZA TANGENCIAL FCT -84.322410853

FUERZA RADIAL FCR -30.690847632REACCION CZ CZ 84.3224108527REACCION CY CY 30.690847632

REACCION EN EJE Y POLEA EY 20.1724794309REACCION EN EJE Z POLEA EZ -16.991301453

REACCION AX AX 35.6232810225REACCION AY AY -1.0445609305REACCION AZ AZ 70.0622500856REACCION BX BX 35.6232810225REACCION BY BY -14.026153855REACCION BZ BZ 75.7128237223REACCION DY DY 37.8817341378REACCION DZ DZ 106.964285942

REACCION MBZ MBZ 1.00757854317

REACCION MBY MBY -1.0075785432

RANGO UNIDADES

mm2 A 4

50 a 80 KW15 a 40 kW

1 A 41,5 A 4 16 A 22

°20 A 40 mm

2 A 617 A 23

°20 A 30 °

2 A 525 a 45 mm

mm 7.550 A 80 mm 16.25

mm 10100 A 140 mm 30

mm 7.540 a 70 mm 13.75

mm 7.5mm 7.5

°r.p.m

°

mmmm

°

rad/sKN.m

KNKNKW

KN.mmmmm

KN.m

KNKNKNKN

KNKNKNKNKN

KNKN

KNKNKNKNKNKNKNKN

KN.m

Calculo Diámetro Chaveta Engranaje Helicoidal

iteración Ctamaño0 0.7826491878095621 0.7468358554201132 0.7456296320065983 0.745587824460994 0.7455863735680345 0.7455863232138626 0.745586321466285

7 0.7455863214056348 0.745586321403529

Calculo para hallar el diámetro d3 Engranaje Helicoidal

iteración Ctamaño0 0.7839075618290261 0.7385520881303442 0.7369747836181933 0.7369195243226174 0.7369175877357155 0.7369175198663726 0.7369175174878327 0.7369175174044748 0.736917517401552

Calculo para hallar el diámetro Anillo de Retención

iteración Ctamaño0 0.7928530107414921 0.7448118490836332 0.7432926274430713 0.7432428858527174 0.7432412553600395 0.7432412019116696 0.7432412001596037 0.7432412001021698 0.743241200100287

D/d 1.2r/d 0.01

VELOCIDAD CRÍTICA

Masa Engranaje HelicoidalMasa Engranaje Recto

Masa Polea

Velocidad Crítica (rad/s)

DEFLEXIONES Y PENDIENTESDeflelxión Máxima [mm] 6.38550561697235E-12Deflexión Engranaje Helicoidal [mm] 5.38125445051903E-13Deflexión en Engranaje Recto [mm] 8.65124977709969E-13

Sector del eje Ajuste

Zona Rodamiento izquierdo h6Zona Rodamiento derecho h6Engranaje helicoidal js5Engranaje recto h6


Se [MPa] rentalla [mm]162.444724043427 1.56507787394767155.011397608423 2.53657129043058154.761036868777 2.57919512068659154.752359398315 2.58068647791382154.752058254572 2.58073825109559154.752047803185 2.58074004793757154.752047440462 2.58074011029825

154.752047427874 2.58074011246252154.752047427437 2.58074011253763


Se [MPa] rentalla [mm]162.705909033483 1.53936998514423153.292039417823 2.84567647808261152.964658005819 2.90909370647555152.953188523501 2.91134339735499152.952786570328 2.91142227339175152.952772483535 2.91142503771237152.952771989851 2.91142513459044

152.95277197255 2.91142513798562152.952771971943 2.9114251381046


Se [MPa] rentalla [mm]164.562604220374 0.1154.591299873815 0.1154.275973998562 0.1154.265649757453 0.1154.265311336437 0.1154.265300242826 0.1154.265299879172 0.1154.265299867251 0.1

154.26529986686 0.1

Diametros Eje mmDeL1 115.532743575745DeL2 138.639292290894DeL3 138.639292290894DeL4 166.367150749073DeL5 138.639292290894DeL6 115.532743575745DeL7 96.2772863131208DeL8 80.2310719276007

VELOCIDAD CRÍTICA

20 Deflexion Helicoidal10 Deflexión Recto10 Deflexión Polea

Velocidad Crítica (rad/s)

DEFLEXIONES Y PENDIENTESPendiente en rodamiento izquierdo [rad] 1.29621624684055E-11Pendiente en rodamiento derecho [rad] 2.692736096679E-12Pendiente en engranaje helicoidal [rad] 5.3617212016271E-12Pendiente en engranaje recto [rad] 3.79952145731386E-12

ToleranciaValor inferior Valor superior

149,998 105,00094.998 95,000136.62 138.65

139.998 140,000

factor de modificación de la condición superficial ka 0.8832234871factor de modificación del tamaño kb 0.7839075618

factor de modificación de la carga kc 1factor de modificación de la temperatura kd 1

factor de confiabilidad ke 1factor de modificación de efectos varios kf 0.6549

límite de resistencia a la fatiga en viga rotatoria S'e 235Factor de Seguridad Nf 1.8

ACERO 1020 MAQUINADOSut 470 MPaSy 390 MPa

Sutt 68 Kpsi

Coeficiente de acabado Maquinado A 4.51Exponente de acabado Maquinado b -0.265Diametro interior del rodamiento de 30 mm de ancho d 73.303332626Constante de Neuber flexión raizaf 0.097868575Constante de Neuber torsión raizat 0.0735833024Diametro definido por estática dt 64

DIAMETROS PARA FALLA ESTATICA N =1,8 EN SECCIÓN CRITICA PARA CONCENTRADORES Hombro Anillo Chaveta

Dest 73.3033326 65.211079705 74.5275178Esf.Von Mises 216595.931 216566.90042 216547.185F.S.E 1.80058784 1.8008292091 1.80099317


qs Kt Kts Kf0.944449250170097 2.3 3 2.205679280.955838845827765 2.3 3 2.22474010.956189216744294 2.3 3 2.225328690.956201322992022 2.3 3 2.225349030.95620174308324 2.3 3 2.22534974

0.956201757662721 2.3 3 2.225349760.956201758168712 2.3 3 2.22534976

0.956201758186273 2.3 3 2.225349760.956201758186882 2.3 3 2.22534976


qs Kt Kts Kf0.944013176939385 2.64929478 2.2608732494 2.528708880.958203098840687 2.64929478 2.2608732494 2.558855650.958642242535106 2.64929478 2.2608732494 2.55979306

0.95865756412473 2.64929478 2.2608732494 2.559825770.958658100999055 2.64929478 2.2608732494 2.559826920.958658119814179 2.64929478 2.2608732494 2.559826960.958658120473571 2.64929478 2.2608732494 2.55982696

0.95865812049668 2.64929478 2.2608732494 2.559826960.958658120497489 2.64929478 2.2608732494 2.55982696


qs Kt Kts Kf0.811233419487037 5 3 4.05462990.811233419487037 5 3 4.05462990.811233419487037 5 3 4.05462990.811233419487037 5 3 4.05462990.811233419487037 5 3 4.05462990.811233419487037 5 3 4.05462990.811233419487037 5 3 4.05462990.811233419487037 5 3 4.05462990.811233419487037 5 3 4.0546299

nf8.56772650423787 28.88318593.15949097357614 34.65982311.80002361949334 34.65982313.32482793895391 41.59178772.22620230482567 34.65982314.33107261000882 28.88318593.31222291502838 24.06932162.52746630162877 20.057768

VELOCIDAD CRÍTICA

5.38125445051903E-13 1.07625E-11 5.7915799E-248.65124977709969E-13 8.65125E-12 7.4844123E-243.90030120098479E-12 3.9003E-11 1.5212349E-22

5.84168E-11 1.6539949E-22

1861.38494736559

FACTORES DE CONCENTRACIÓN DE ESFUERZOSkf kfs Se [MPa]

Anillo de Retención 4.054629899 2.52731495 154.26529986686Cuñero 2.225349762 2.88515348 154.752047427437Ajuste Prieto 2.6 152.952771971922Hombro 1 2.649294784 2.26087325 155.681831802407Hombro 2 2.649294784 2.26087325 152.952771971922Hombro 3 2.649294784 2.26087325 152.952771971922Hombro 4 2.649294784 2.26087325 150.27155181208Hombro 5 2.649294784 2.26087325 152.952771971922Hombro 6 2.649294784 2.26087325 155.681831802407Hombro 7 2.649294784 2.26087325 158.459584882856


Kfs d[mm] dpredef[mm] Sut [Mpa] 4702.8548912065 120.789109068123 74.52751781 Se* 2352.8842155312 122.81881527079 120.7891091 r/d 0.0212.8851210622 122.88983228161 122.81881532.8851523544 122.892297671219 122.8898323 raizaf 0.09786857495042.8851534403 122.892383235123 122.8922977 raizat 0.07358330243842.885153478 122.892386204679 122.8923832

2.8851534793 122.892386307739 122.8923862

2.8851534793 122.892386311316 122.89238632.8851534793 122.89238631144 122.8923863


Kfs d[mm] dpredef[mm] Sut [Mpa] 4702.1686862476 135.50840371822 73.30333263 Se* 2352.1917332218 138.528271736931 135.5084037 r/d 0.012.1924498671 138.635399874047 138.5282717 D/d 1.52.1924748743 138.639155875797 138.6353999 raizaf 0.09786857495042.1924757506 138.639287510113 138.6391559 raizat 0.07358330243842.1924757813 138.639292123354 138.63928752.1924757824 138.639292285029 138.63929212.1924757824 138.639292290695 138.63929232.1924757824 138.639292290894 138.6392923


Kfs d[mm] dpredef[mm] Sut [Mpa] 4702.5273149494 124.216165402655 65.21107971 Se* 2352.5273149494 126.858593326014 124.2161654 r/t 0.12.5273149494 126.94614659273 126.8585933 a/t 2.52.5273149494 126.949017646113 126.9461466 raizaf 0.09786857495042.5273149494 126.949111761891 126.9490176 raizat 0.07358330243842.5273149494 126.949114847059 126.94911182.5273149494 126.949114948192 126.94911482.5273149494 126.949114951507 126.94911492.5273149494 126.949114951616 126.949115

Ajuste Prietop 607168658sigma 55479610p/sigma 10.9439965l/d 0.21638887

Ndiv 10 x(m) VYX MYX VZX0 0 0 0

0.003 0 0 00.006 0 0 00.009 0 0 00.012 0 0 00.015 -1.04456093 0 70.06225010.018 -1.04456093 -0.00313368 70.06225010.021 -1.04456093 -0.00626737 70.06225010.024 -1.04456093 -0.00940105 70.06225010.027 -1.04456093 -0.01253473 70.0622501

L1 0.03 -1.04456093 -0.01566841 70.06225010.0365 -1.04456093 -0.02245806 70.06225010.043 -1.04456093 -0.02924771 70.0622501

0.0495 -1.04456093 -0.03603735 70.06225010.056 -1.04456093 -0.042827 70.0622501

0.0625 -1.04456093 -0.04961664 70.06225010.069 -1.04456093 -0.05640629 70.0622501

0.0755 -1.04456093 -0.06319594 70.06225010.082 -1.04456093 -0.06998558 70.0622501

0.0885 -1.04456093 -0.07677523 70.0622501L1+L2 0.095 -1.04456093 -0.08356487 70.0622501

0.099 -1.04456093 -0.08774312 70.06225010.103 -1.04456093 -0.09192136 70.06225010.107 -1.04456093 -0.09609961 70.06225010.111 -1.04456093 -0.10027785 70.06225010.115 -1.04456093 -0.10445609 70.06225010.119 12.9815929 -1.06010826 -5.650573640.123 12.9815929 -1.00818189 -5.650573640.127 12.9815929 -0.95625552 -5.650573640.131 12.9815929 -0.90432915 -5.65057364

L1+L2+L3 0.135 12.9815929 -0.85240278 -5.650573640.147 12.9815929 -0.69662366 -5.650573640.159 12.9815929 -0.54084455 -5.650573640.171 12.9815929 -0.38506543 -5.650573640.183 12.9815929 -0.22928632 -5.650573640.195 12.9815929 -0.0735072 -5.650573640.207 12.9815929 0.08227191 -5.650573640.219 12.9815929 0.23805103 -5.650573640.231 12.9815929 0.39383014 -5.650573640.243 12.9815929 0.54960926 -5.65057364

L1+L2+L3+L4 0.255 12.9815929 0.70538837 -5.650573640.258 12.9815929 0.74433315 -5.650573640.261 12.9815929 0.78327793 -5.650573640.264 12.9815929 0.82222271 -5.650573640.267 12.9815929 0.86116749 -5.650573640.27 12.9815929 0.90011227 -5.65057364

0.273 -17.7092547 0.8469845 -89.97298450.276 -17.7092547 0.79385674 -89.97298450.279 -17.7092547 0.74072897 -89.97298450.282 -17.7092547 0.68760121 -89.9729845

L1+L2+L3+L4+L5 0.285 -17.7092547 0.63447345 -89.97298450.2905 -17.7092547 0.53707255 -89.97298450.296 -17.7092547 0.43967164 -89.9729845

0.3015 -17.7092547 0.34227074 -89.97298450.307 -17.7092547 0.24486984 -89.9729845

0.3125 -17.7092547 0.14746894 -89.97298450.318 -17.7092547 0.05006804 -89.9729845

0.3235 -17.7092547 -0.04733286 -89.97298450.329 -17.7092547 -0.14473376 -89.9729845

0.3345 -17.7092547 -0.24213466 -89.9729845L1+L2+L3+L4+L5+L6 0.34 -17.7092547 -0.33953556 -89.9729845

0.343 -17.7092547 -0.39266333 -89.97298450.346 -17.7092547 -0.44579109 -89.97298450.349 -17.7092547 -0.49891885 -89.97298450.352 -17.7092547 -0.55204662 -89.97298450.355 -17.7092547 -0.60517438 -89.97298450.358 20.1724794 -0.54465694 16.99130150.361 20.1724794 -0.48413951 16.99130150.364 20.1724794 -0.42362207 16.99130150.367 20.1724794 -0.36310463 16.9913015

L1+L2+L3+L4+L5+L6+L7 0.37 20.1724794 -0.30258719 16.99130150.373 20.1724794 -0.24206975 16.99130150.376 20.1724794 -0.18155231 16.99130150.379 20.1724794 -0.12103488 16.99130150.382 20.1724794 -0.06051744 16.99130150.385 0 0 00.388 0 0 00.391 0 0 00.394 0 0 00.397 0 0 0

L1+L2+L3+L4+L5+L6+L7+L8 0.4 0 0 0

MZX MTOTAL VTOTAL0 0 00 0 00 0 00 0 00 0 00 0 70.07003635

0.2101867502567 0.21021011 70.070036350.42037350051341 0.42042022 70.070036350.63056025077011 0.63063033 70.070036350.84074700102681 0.84084044 70.070036351.05093375128352 1.05105055 70.070036351.50633837683971 1.50650578 70.070036351.9617430023959 1.96196102 70.07003635

2.41714762795209 2.41741625 70.070036352.87255225350828 2.87287149 70.070036353.32795687906447 3.32832673 70.070036353.78336150462066 3.78378196 70.070036354.23876613017685 4.2392372 70.070036354.69417075573304 4.69469244 70.070036355.14957538128923 5.15014767 70.070036355.60498000684542 5.60560291 70.070036355.88522900718769 5.88588305 70.070036356.16547800752996 6.1661632 70.070036356.44572700787223 6.44644334 70.070036356.72597600821451 6.72672349 70.070036357.00622500855678 7.00700364 70.070036357.99120125717601 8.06121127 14.158062637.96859896262895 8.03212302 14.158062637.94599666808189 8.00332979 14.158062637.92339437353483 7.97483477 14.158062637.90079207898777 7.94664118 14.158062637.83298519534659 7.86390117 14.158062637.76517831170541 7.78399043 14.158062637.69737142806423 7.70699697 14.158062637.62956454442305 7.63300906 14.158062637.56175766078187 7.56211493 14.158062637.4939507771407 7.49440237 14.15806263

7.42614389349951 7.42995837 14.158062637.35833700985834 7.36886869 14.158062637.29053012621715 7.3112174 14.158062637.22272324257598 7.25708645 14.158062637.20577152166568 7.24411313 14.158062637.18881980075539 7.23136602 14.158062637.17186807984509 7.2188463 14.158062637.1549163589348 7.20655518 14.158062637.1379646380245 7.19449382 14.15806263

6.86804568455608 6.92007473 91.699267396.59812673108766 6.64571177 91.699267396.32820777761924 6.37141217 91.699267396.05828882415083 6.09718451 91.699267395.78836987068241 5.82303892 91.699267395.29351845599031 5.32069399 91.699267394.79866704129821 4.81876712 91.699267394.30381562660611 4.31740411 91.699267393.80896421191401 3.81682717 91.699267393.31411279722191 3.31739216 91.699267392.81926138252981 2.81970593 91.699267392.32440996783771 2.32489185 91.699267391.82955855314561 1.83527446 91.699267391.33470713845351 1.35649266 91.699267390.83985572376141 0.90589295 91.699267390.56993677029299 0.69210722 91.699267390.30001781682457 0.53734569 91.699267390.03009886335615 0.49982593 91.69926739-0.2398200901123 0.60188798 91.69926739-0.5097390435807 0.79124581 91.69926739-0.4587651392226 0.71212123 26.37486022-0.4077912348645 0.63299665 26.37486022-0.3568173305065 0.55387206 26.37486022-0.3058434261484 0.47474748 26.37486022-0.2548695217903 0.3956229 26.37486022-0.2038956174323 0.31649832 26.37486022-0.1529217130742 0.23737374 26.37486022-0.1019478087161 0.15824916 26.37486022-0.0509739043581 0.07912458 26.374860228.4376949872E-15 8.43769E-15 0

0 0 00 0 00 0 00 0 00 0 0

Ndiv 10 x(m) VYX MYX0 0 0

0.003 0 00.006 0 00.009 0 00.012 0 0

A 0.015 -1.04456093 00.018 -1.04456093 -0.003133680.021 -1.04456093 -0.006267370.024 -1.04456093 -0.009401050.027 -1.04456093 -0.01253473

L1 0.03 -1.04456093 -0.015668410.0365 -1.04456093 -0.022458060.043 -1.04456093 -0.02924771

0.0495 -1.04456093 -0.036037350.056 -1.04456093 -0.042827

0.0625 -1.04456093 -0.049616640.069 -1.04456093 -0.05640629

0.0755 -1.04456093 -0.063195940.082 -1.04456093 -0.06998558

0.0885 -1.04456093 -0.07677523L1+L2 0.095 -1.04456093 -0.08356487

0.099 -1.04456093 -0.087743120.103 -1.04456093 -0.091921360.107 -1.04456093 -0.096099610.111 -1.04456093 -0.10027785

B 0.115 -1.04456093 -0.104456090.119 12.9815929 -1.060108260.123 12.9815929 -1.008181890.127 12.9815929 -0.956255520.131 12.9815929 -0.90432915

L1+L2+L3 0.135 12.9815929 -0.852402780.147 12.9815929 -0.696623660.159 12.9815929 -0.540844550.171 12.9815929 -0.385065430.183 12.9815929 -0.229286320.195 12.9815929 -0.07350720.207 12.9815929 0.082271910.219 12.9815929 0.238051030.231 12.9815929 0.393830140.243 12.9815929 0.54960926

L1+L2+L3+L4 0.255 12.9815929 0.705388370.258 12.9815929 0.744333150.261 12.9815929 0.783277930.264 12.9815929 0.822222710.267 12.9815929 0.86116749

C 0.27 12.9815929 0.90011227

0.273 -17.7092547 0.84698450.276 -17.7092547 0.793856740.279 -17.7092547 0.740728970.282 -17.7092547 0.68760121

L1+L2+L3+L4+L5 0.285 -17.7092547 0.634473450.2905 -17.7092547 0.537072550.296 -17.7092547 0.43967164

0.3015 -17.7092547 0.342270740.307 -17.7092547 0.24486984

0.3125 -17.7092547 0.147468940.318 -17.7092547 0.05006804

0.3235 -17.7092547 -0.047332860.329 -17.7092547 -0.14473376

0.3345 -17.7092547 -0.24213466L1+L2+L3+L4+L5+L6 0.34 -17.7092547 -0.33953556

0.343 -17.7092547 -0.392663330.346 -17.7092547 -0.445791090.349 -17.7092547 -0.498918850.352 -17.7092547 -0.55204662

D 0.355 -17.7092547 -0.605174380.358 20.1724794 -0.544656940.361 20.1724794 -0.484139510.364 20.1724794 -0.423622070.367 20.1724794 -0.36310463

L1+L2+L3+L4+L5+L6+L7 0.37 20.1724794 -0.302587190.373 20.1724794 -0.242069750.376 20.1724794 -0.181552310.379 20.1724794 -0.121034880.382 20.1724794 -0.06051744

E 0.385 0 00.388 0 00.391 0 00.394 0 00.397 0 0

L1+L2+L3+L4+L5+L6+L7+L8 0.4 0 0

VZX MZX MTOTAL VTOTAL TORQUE0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

70.0622501 0 0 70.0700364 070.0622501 0.2101867503 0.21021011 70.0700364 070.0622501 0.4203735005 0.42042022 70.0700364 070.0622501 0.6305602508 0.63063033 70.0700364 070.0622501 0.840747001 0.84084044 70.0700364 070.0622501 1.0509337513 1.05105055 70.0700364 070.0622501 1.5063383768 1.50650578 70.0700364 070.0622501 1.9617430024 1.96196102 70.0700364 070.0622501 2.417147628 2.41741625 70.0700364 070.0622501 2.8725522535 2.87287149 70.0700364 070.0622501 3.3279568791 3.32832673 70.0700364 070.0622501 3.7833615046 3.78378196 70.0700364 070.0622501 4.2387661302 4.2392372 70.0700364 070.0622501 4.6941707557 4.69469244 70.0700364 070.0622501 5.1495753813 5.15014767 70.0700364 070.0622501 5.6049800068 5.60560291 70.0700364 070.0622501 5.8852290072 5.88588305 70.0700364 070.0622501 6.1654780075 6.1661632 70.0700364 070.0622501 6.4457270079 6.44644334 70.0700364 070.0622501 6.7259760082 6.72672349 70.0700364 070.0622501 7.0062250086 7.00700364 70.0700364 3.05577491-5.65057364 7.9912012572 8.06121127 14.1580626 3.05577491-5.65057364 7.9685989626 8.03212302 14.1580626 3.05577491-5.65057364 7.9459966681 8.00332979 14.1580626 3.05577491-5.65057364 7.9233943735 7.97483477 14.1580626 3.05577491-5.65057364 7.900792079 7.94664118 14.1580626 3.05577491-5.65057364 7.8329851953 7.86390117 14.1580626 3.05577491-5.65057364 7.7651783117 7.78399043 14.1580626 3.05577491-5.65057364 7.6973714281 7.70699697 14.1580626 3.05577491-5.65057364 7.6295645444 7.63300906 14.1580626 3.05577491-5.65057364 7.5617576608 7.56211493 14.1580626 3.05577491-5.65057364 7.4939507771 7.49440237 14.1580626 3.05577491-5.65057364 7.4261438935 7.42995837 14.1580626 3.05577491-5.65057364 7.3583370099 7.36886869 14.1580626 3.05577491-5.65057364 7.2905301262 7.3112174 14.1580626 3.05577491-5.65057364 7.2227232426 7.25708645 14.1580626 3.05577491-5.65057364 7.2057715217 7.24411313 14.1580626 3.05577491-5.65057364 7.1888198008 7.23136602 14.1580626 3.05577491-5.65057364 7.1718680798 7.2188463 14.1580626 3.05577491-5.65057364 7.1549163589 7.20655518 14.1580626 3.05577491-5.65057364 7.137964638 7.19449382 14.1580626 3.05577491

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-20

-15

-10

-5

0

5

10

15

20

25

CORTRANTE VZ - P.XY

VZ - XY

VZ(kN)

X(m)

VZ(kN)

X()

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1.5

-1

-0.5

0

0.5

1

1.5

FLECTOR Z - P.XY

FLECTOR Z - P.XY

MZ(KN.m)

X(m)

-89.9729845 6.8680456846 6.92007473 91.6992674 4.96563422-89.9729845 6.5981267311 6.64571177 91.6992674 4.96563422-89.9729845 6.3282077776 6.37141217 91.6992674 4.96563422-89.9729845 6.0582888242 6.09718451 91.6992674 4.96563422-89.9729845 5.7883698707 5.82303892 91.6992674 4.96563422-89.9729845 5.293518456 5.32069399 91.6992674 4.96563422-89.9729845 4.7986670413 4.81876712 91.6992674 4.96563422-89.9729845 4.3038156266 4.31740411 91.6992674 4.96563422-89.9729845 3.8089642119 3.81682717 91.6992674 4.96563422-89.9729845 3.3141127972 3.31739216 91.6992674 4.96563422-89.9729845 2.8192613825 2.81970593 91.6992674 4.96563422-89.9729845 2.3244099678 2.32489185 91.6992674 4.96563422-89.9729845 1.8295585531 1.83527446 91.6992674 4.96563422-89.9729845 1.3347071385 1.35649266 91.6992674 4.96563422-89.9729845 0.8398557238 0.90589295 91.6992674 4.96563422-89.9729845 0.5699367703 0.69210722 91.6992674 4.96563422-89.9729845 0.3000178168 0.53734569 91.6992674 4.96563422-89.9729845 0.0300988634 0.49982593 91.6992674 4.96563422-89.9729845 -0.23982009 0.60188798 91.6992674 4.96563422-89.9729845 -0.509739044 0.79124581 91.6992674 4.9656342216.9913015 -0.458765139 0.71212123 26.3748602 4.9656342216.9913015 -0.407791235 0.63299665 26.3748602 4.9656342216.9913015 -0.356817331 0.55387206 26.3748602 4.9656342216.9913015 -0.305843426 0.47474748 26.3748602 4.9656342216.9913015 -0.254869522 0.3956229 26.3748602 4.9656342216.9913015 -0.203895617 0.31649832 26.3748602 4.9656342216.9913015 -0.152921713 0.23737374 26.3748602 4.9656342216.9913015 -0.101947809 0.15824916 26.3748602 4.9656342216.9913015 -0.050973904 0.07912458 26.3748602 4.96563422

0 8.437695E-15 8.43769E-15 0 4.965634220 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1.5

-1

-0.5

0

0.5

1

1.5

FLECTOR Z - P.XY

FLECTOR Z - P.XY

MZ(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-20

-15

-10

-5

0

5

10

15

20

25

CORTRANTE VZ - P.XY

VZ - XY

VZ(kN)

X(m)

VZ(kN)

X()

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1.5

-1

-0.5

0

0.5

1

1.5

FLECTOR Z - P.XY

FLECTOR Z - P.XY

MZ(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1.5

-1

-0.5

0

0.5

1

1.5

FLECTOR Z - P.XY

FLECTOR Z - P.XY

MZ(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-20

-15

-10

-5

0

5

10

15

20

25

CORTRANTE VZ - P.XY

VZ - XY

VZ(kN)

X(m)

VZ(kN)

X()

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-100

-80

-60

-40

-20

0

20

40

60

80

Cortante VY - P.ZX

Cortante ZX

VY(KN)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1

0

1

2

3

4

5

6

7

8

9

FLECTOR Y - P.ZX

FLECTOR Y - P.ZX

MY(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1.5

-1

-0.5

0

0.5

1

1.5

FLECTOR Z - P.XY

FLECTOR Z - P.XY

MZ(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1

0

1

2

3

4

5

6

7

8

9

FLECTOR Y - P.ZX

FLECTOR Y - P.ZX

MY(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1.5

-1

-0.5

0

0.5

1

1.5

FLECTOR Z - P.XY

FLECTOR Z - P.XY

MZ(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-100

-80

-60

-40

-20

0

20

40

60

80

Cortante VY - P.ZX

Cortante ZX

VY(KN)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1

0

1

2

3

4

5

6

7

8

9

FLECTOR Y - P.ZX

FLECTOR Y - P.ZX

MY(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

10

20

30

40

50

60

70

80

90

100

MAGNITUD DE V

MAGNITUD DE V

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

1

2

3

4

5

6

7

8

9

MAGNITUD DE M

MAGNITUD DE M

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-1

0

1

2

3

4

5

6

7

8

9

FLECTOR Y - P.ZX

FLECTOR Y - P.ZX

MY(KN.m)

X(m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

1

2

3

4

5

6

7

8

9

MAGNITUD DE M

MAGNITUD DE M

0 2 4 6 8 10 120

2

4

6

8

10

12

TORQUE

TORQUE

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

10

20

30

40

50

60

70

80

90

100

MAGNITUD DE V

MAGNITUD DE V

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

1

2

3

4

5

6

7

8

9

MAGNITUD DE M

MAGNITUD DE M

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

1

2

3

4

5

6

7

8

9

MAGNITUD DE M

MAGNITUD DE M

0 2 4 6 8 10 120

2

4

6

8

10

12

TORQUE

TORQUE

DIAMETRO VALOR(mm) # INERCIAS(m^4)

D1 120 1 20357.520D2 150 2 49700.978D3 150 3 49700.978D4 180 4 103059.947D5 160 5 64339.818D6 155 6 56666.539D7 120 7 20357.520D8 110 8 14373.768

Ubicación fuerzas a b c d

Valor 0.105 0.273 0.355 0.355

ECUACIONES PLANO Y-X

INTERVALO ECUACIÓN ÁNGULO

0 < X < L1/2 ((AY/2)*X^2+C1)/(E*I1)

L1/2 < X < L2 ((AY/2)*X^2+C3)/(E*I2)

L2 < X < L3 ((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)+C5)/(E*I3)

L3 < X < L4 ((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)+C7)/(E*I4)

L4 < X < L5 ((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)-(CY/2)*(X-(A+B))^2+C9)/(E*I5)

L5 < X < L6 ((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)-(CY/2)*(X-(A+B))^2+C11)/(E*I6)

L6 < X < L7 ((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)-(CY/2)*(X-(A+B))^2+(DY/2)*(X-(A-B-C))^2+C13)/(E*I7)

L7 < X <L8/2 ((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)-(CY/2)*(X-(A+B))^2+(DY/2)*(X-(A-B-C))^2+C15)/(E*I8)

ECUACIONES PLANO Z-X

INTERVALO ECUACIÓN ÁNGULO

0 < X < L1/2 ((AZ/2)*X^2+C1)/(E*I1)

L1/2 < X < L2 ((AZ/2)*X^2+C3)/(E*I2)

L2 < X < L3 ((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)+C5)/(E*I3)

L3 < X < L4 ((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)+C7)/(E*I4)

L4 < X < L5 ((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)-(CZ/2)*(X-(A+B))^2+C9)/(E*I5)

L5 < X < L6 ((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)-(CZ/2)*(X-(A+B))^2+C11)/(E*I6)

L6 < X < L7 ((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)-(CZ/2)*(X-(A+B))^2+(DZ/2)*(X-(A-B-C))^2+C13)/(E*I7)

L7 < X <L8/2 ((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)-(CZ/2)*(X-(A+B))^2+(DZ/2)*(X-(A-B-C))^2+C15)/(E*I8)

Ecua Z-XINTERVALO X(m) Angulo Deflexion

0.015

0 1.2835729E-11 00.003 1.2835798E-11 3.850719E-140.006 1.2836004E-11 7.701438E-140.009 1.2836346E-11 1.155216E-130.012 1.2836826E-11 1.540288E-130.015 1.2837443E-11 1.925359E-13

0.085

0.020 5.279354E-12 1.053562E-130.025 5.2800557E-12 1.317468E-130.030 5.2809134E-12 1.581373E-130.035 5.2819271E-12 1.845279E-130.040 5.2830966E-12 2.109184E-130.045 5.2844221E-12 2.37309E-130.050 5.2859036E-12 2.636995E-130.055 5.287541E-12 2.900901E-130.060 5.2893344E-12 3.164807E-130.065 5.2912837E-12 3.428713E-130.070 5.2933889E-12 3.692619E-130.075 5.2956501E-12 3.956525E-130.080 5.2980672E-12 4.220431E-130.085 5.3006403E-12 4.484338E-13

0.105

0.089 5.302811E-12 4.695463E-130.093 5.3050816E-12 4.906588E-130.097 5.3074519E-12 5.117714E-130.101 5.3099221E-12 5.328839E-130.105 5.312492E-12 5.539965E-13

0.125

0.109 5.3151019E-12 5.764532E-130.113 5.3176927E-12 5.977164E-130.117 5.3202645E-12 6.189884E-130.121 5.3228171E-12 6.40269E-130.125 5.3253506E-12 6.615582E-13

0.255

0.130 3.7345501E-12 3.891885E-130.135 3.73605E-12 4.078585E-130.140 3.7375356E-12 4.265347E-130.145 3.7390067E-12 4.452171E-130.150 3.7404635E-12 4.639057E-130.155 3.7419058E-12 4.826003E-130.160 3.7433338E-12 5.013009E-130.165 3.7447474E-12 5.200074E-130.170 3.7461466E-12 5.387198E-130.175 3.7475315E-12 5.574379E-130.180 3.7489019E-12 5.761617E-130.185 3.750258E-12 5.948911E-130.190 3.7515996E-12 6.136261E-130.195 3.7529269E-12 6.323666E-130.200 3.7542398E-12 6.511125E-13

0.255

0.205 3.7555383E-12 6.698637E-130.210 3.7568224E-12 6.886202E-130.215 3.7580922E-12 7.073819E-130.220 3.7593475E-12 7.261487E-130.225 3.7605885E-12 7.449206E-130.230 3.761815E-12 7.636974E-130.235 3.7630272E-12 7.824791E-130.240 3.764225E-12 8.012657E-130.245 3.7654084E-12 8.200571E-130.250 3.7665775E-12 8.388531E-130.255 3.7677321E-12 8.576537E-13

0.273

0.257 2.9139357E-12 9.542898E-130.258 2.914484E-12 9.586436E-130.260 2.9150302E-12 9.629982E-130.261 2.9155743E-12 9.673534E-130.263 2.9161164E-12 9.717092E-130.264 2.9166564E-12 9.760656E-130.266 2.9171943E-12 9.804227E-130.267 2.9177301E-12 9.847805E-130.269 2.9182639E-12 9.891388E-130.270 2.9187956E-12 9.934978E-130.272 2.9193252E-12 9.978575E-13

0.290

0.274 2.8834977E-12 1.006819E-120.277 2.8855386E-12 1.014896E-120.280 2.8875372E-12 1.022978E-120.283 2.8894933E-12 1.031066E-120.286 2.8914071E-12 1.039159E-120.288 2.8932785E-12 1.047258E-120.291 2.8951074E-12 1.055361E-12

0.34

0.296 2.6540251E-12 1.154227E-120.301 2.6574601E-12 1.167506E-120.306 2.6607415E-12 1.180802E-120.311 2.6638695E-12 1.194113E-120.316 2.6668439E-12 1.20744E-120.321 2.6696649E-12 1.220782E-120.326 2.6723323E-12 1.234137E-120.331 2.6748462E-12 1.247505E-120.336 2.6772066E-12 1.260885E-120.341 2.6794135E-12 1.274276E-12

0.355

0.344 -3.887285E-12 1.688256E-120.347 -3.883958E-12 1.6766E-120.350 -3.880785E-12 1.664952E-120.353 -3.877766E-12 1.653315E-120.356 -3.8749E-12 1.641686E-12

0.37

0.359 3.4102112E-12 3.77012E-120.362 3.4624159E-12 3.780429E-120.365 3.5146353E-12 3.790894E-120.368 3.5668696E-12 3.801517E-12

0.37

0.371 3.6191188E-12 3.812295E-12

0.39

0.376 -8.075511E-12 6.065134E-120.381 -7.952072E-12 6.025065E-120.386 -7.828575E-12 5.985614E-120.391 -7.705019E-12 5.94678E-12

M ELASTICIDAD 205000000000

CONDICIONES DE CONTINUIDAD

VALORES DE X 0.0150

MATRIZ PLANO Y_X

1 21 1 02 0.015 13 0 04 0 05 0 06 0 07 0 08 0 09 0 0

10 0 011 0 012 0 013 0 014 0 015 0 116 0 0

MATRIZ PLANO Z_X

1 21 1 02 0.015 13 0 04 0 05 0 06 0 07 0 08 0 09 0 0

10 0 011 0 012 0 013 0 014 0 015 0 1

16 0 0


ECUACIÓN ÁNGULO ECUACIÓN DE DEFLEXIÓN

((AY/2)*X^2+C1)/(E*I1) ((AY/6)*X^3+C1*X+C2)/(E*I1)

((AY/2)*X^2+C3)/(E*I2) ((AY/6)*X^3+C3*X+C4)/(E*I2)

((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)+C5)/(E*I3) ((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2+C5*X+C6)/(E*I3)

((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)+C7)/(E*I4) ((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2+C7*X+C8)/(E*I4)

((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)-(CY/2)*(X-(A+B))^2+C9)/(E*I5) ((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2-(CY/6)*(X-(A+B))^3+C9*X+C10)/(E*I5)

((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)-(CY/2)*(X-(A+B))^2+C11)/(E*I6) ((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2-(CY/6)*(X-(A+B))^3+C11*X+C12)/(E*I6)

((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)-(CY/2)*(X-(A+B))^2+(DY/2)*(X-(A-B-C))^2+C13)/(E*I7) ((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2-(CY/6)*(X-(A+B))^3+(DY/6)*(X-(A-B-C))^3+C13*X+C14)/(E*I7)

((AY/2)*X^2-(BY/2)*(X-A)^2+MBY(X-A)-(CY/2)*(X-(A+B))^2+(DY/2)*(X-(A-B-C))^2+C15)/(E*I8) ((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2-(CY/6)*(X-(A+B))^3+(DY/6)*(X-(A-B-C))^3+C15*X+C16)/(E*I8)


ECUACIÓN ÁNGULO ECUACIÓN DE DEFLEXIÓN

((AZ/2)*X^2+C1)/(E*I1) ((AZ/6)*X^3+C1*X+C2)/(E*I1)

((AZ/2)*X^2+C3)/(E*I2) ((AY/6)*X^3+C3*X+C4)/(E*I2)

((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)+C5)/(E*I3) ((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBZ/2)*(X-A)^2+C5*X+C6)/(E*I3)

((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)+C7)/(E*I4) ((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBY/2)*(X-A)^2+C7*X+C8)/(E*I4)

((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)-(CZ/2)*(X-(A+B))^2+C9)/(E*I5) ((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBZ/2)*(X-A)^2-(CZ/6)*(X-(A+B))^3+C9*X+C10)/(E*I5)

((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)-(CZ/2)*(X-(A+B))^2+C11)/(E*I6) ((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBZ/2)*(X-A)^2-(CZ/6)*(X-(A+B))^3+C11*X+C12)/(E*I6)

((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)-(CZ/2)*(X-(A+B))^2+(DZ/2)*(X-(A-B-C))^2+C13)/(E*I7) ((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBZ/2)*(X-A)^2-(CZ/6)*(X-(A+B))^3+(DZ/6)*(X-(A-B-C))^3+C13*X+C14)/(E*I7)

((AZ/2)*X^2-(BZ/2)*(X-A)^2-MBZ(X-A)-(CZ/2)*(X-(A+B))^2+(DZ/2)*(X-(A-B-C))^2+C15)/(E*I8) ((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2-(CY/6)*(X-(A+B))^3+(DY/6)*(X-(A-B-C))^3+C15*X+C16)/(E*I8)

Ecua Y-XAngulo Deflexion ÁNGULO TOTAL

-1.80601952E-12 0 1.2962162468406E-11-1.80602442E-12 -5.418063E-15 1.2962231012666E-11-1.80603912E-12 -1.083616E-14 1.2962436645456E-11-1.80606362E-12 -1.625431E-14 1.2962779366808E-11-1.80609793E-12 -2.167255E-14 1.2963259176771E-11-1.80614203E-12 -2.709091E-14 1.2963876075419E-11-7.41307259E-13 -1.481023E-14 5.3311457407009E-12-7.41357439E-13 -1.851689E-14 5.3318476476001E-12

-7.4141877E-13 -2.222382E-14 5.3327055343941E-12-7.41491252E-13 -2.593109E-14 5.3337194014329E-12-7.41574885E-13 -2.963876E-14 5.3348892491297E-12

-7.4166967E-13 -3.334686E-14 5.3362150779607E-12-7.41775605E-13 -3.705547E-14 5.3376968884651E-12-7.41892692E-13 -4.076464E-14 5.3393346812446E-12

-7.4202093E-13 -4.447442E-14 5.3411284569636E-12-7.42160319E-13 -4.818486E-14 5.3430782163482E-12-7.42310858E-13 -5.189604E-14 5.3451839601864E-12

-7.4247255E-13 -5.560799E-14 5.3474456893277E-12-7.42645392E-13 -5.932078E-14 5.3498634046826E-12-7.42829385E-13 -6.303446E-14 5.3524371072222E-12-7.42984608E-13 -6.600609E-14 5.3546083807181E-12-7.43146969E-13 -6.897835E-14 5.3568794872268E-12-7.43316465E-13 -7.195128E-14 5.3592504273284E-12-7.43493099E-13 -7.492489E-14 5.3617212016271E-12-7.43676869E-13 -7.789923E-14 5.364291810751E-12-7.43857159E-13 -8.087509E-14 5.3669015173159E-12-7.44022559E-13 -8.385323E-14 5.3694902581562E-12-7.44173069E-13 -8.683358E-14 5.3720580345819E-12

-7.4430869E-13 -8.981608E-14 5.3746048479822E-12-7.44429421E-13 -9.280067E-14 5.3771306998257E-12-4.92546576E-13 -5.141934E-14 3.7668908273021E-12-4.92598038E-13 -5.388876E-14 3.7683846052759E-12

-4.9263828E-13 -5.63596E-14 3.7698626590888E-12-4.92667303E-13 -5.88318E-14 3.771324989868E-12-4.92685106E-13 -6.130531E-14 3.7727715988075E-12

-4.9269169E-13 -6.378007E-14 3.7742024871672E-12-4.92687054E-13 -6.625603E-14 3.7756176562735E-12-4.92671198E-13 -6.873313E-14 3.7770171075186E-12-4.92644123E-13 -7.121131E-14 3.778400842361E-12-4.92605828E-13 -7.369052E-14 3.7797688623251E-12-4.92556314E-13 -7.61707E-14 3.7811211690013E-12

-4.9249558E-13 -7.865179E-14 3.7824577640458E-12-4.92423627E-13 -8.113375E-14 3.7837786491808E-12-4.92340454E-13 -8.361651E-14 3.7850838261941E-12-4.92246062E-13 -8.610002E-14 3.7863732969393E-12

-4.9214045E-13 -8.858421E-14 3.7876470633358E-12-4.92023619E-13 -9.106904E-14 3.7889051273687E-12-4.91895568E-13 -9.355445E-14 3.7901474910885E-12-4.91756297E-13 -9.604039E-14 3.7913741566117E-12-4.91605807E-13 -9.852679E-14 3.7925851261202E-12-4.91444098E-13 -1.010136E-13 3.7937804018615E-12-4.91271169E-13 -1.035008E-13 3.7949599861487E-12

-4.9108702E-13 -1.059882E-13 3.7961238813604E-12-4.90891652E-13 -1.084759E-13 3.7972720899411E-12-4.90685064E-13 -1.109638E-13 3.7984046144004E-12-4.90467257E-13 -1.134518E-13 3.7995214573139E-12-3.71308653E-13 -1.353177E-13 2.9374974600881E-12-3.71198865E-13 -1.35892E-13 2.9380274738917E-12-3.71087461E-13 -1.364663E-13 2.9385552367906E-12-3.70974438E-13 -1.370406E-13 2.9390807490247E-12-3.70859798E-13 -1.376149E-13 2.9396040108359E-12-3.70743541E-13 -1.381892E-13 2.9401250224679E-12-3.70625667E-13 -1.387636E-13 2.9406437841659E-12-3.70506175E-13 -1.393379E-13 2.9411602961769E-12-3.70385065E-13 -1.399122E-13 2.9416745587497E-12-3.70262338E-13 -1.404865E-13 2.9421865721347E-12-3.70137994E-13 -1.410607E-13 2.9426963365841E-12-3.91517113E-13 -1.418335E-13 2.9099561095664E-12

-3.9102328E-13 -1.429291E-13 2.9119121634596E-12-3.90536613E-13 -1.440233E-13 2.9138273604538E-12-3.90057112E-13 -1.451161E-13 2.9157016902833E-12-3.89584777E-13 -1.462076E-13 2.9175351428931E-12-3.89119608E-13 -1.472978E-13 2.9193277084369E-12-3.88661605E-13 -1.483867E-13 2.9210793772749E-12-2.95110389E-13 -1.378299E-13 2.6703818520048E-12-2.94227962E-13 -1.393033E-13 2.673698574233E-12

-2.9337148E-13 -1.407723E-13 2.6768661411016E-12-2.92540944E-13 -1.42237E-13 2.6798844927099E-12-2.91736353E-13 -1.436977E-13 2.6827535716409E-12-2.90957707E-13 -1.451544E-13 2.6854733229156E-12-2.90205007E-13 -1.466073E-13 2.6880436939491E-12-2.89478251E-13 -1.480565E-13 2.6904646345096E-12-2.88777442E-13 -1.495022E-13 2.692736096679E-12-2.88102577E-13 -1.509444E-13 2.6948580348162E-123.06742486E-13 -1.369927E-13 3.8993685609025E-12

3.0780894E-13 -1.360708E-13 3.8961361175936E-123.08849394E-13 -1.351458E-13 3.8930554102198E-123.09863848E-13 -1.342178E-13 3.8901264019855E-123.10852304E-13 -1.332867E-13 3.8873490570061E-123.80553438E-12 8.9433507E-13 5.1099542427551E-123.83028887E-12 9.057888E-13 5.1632776820463E-123.85509828E-12 9.1731686E-13 5.2167465241778E-123.87996261E-12 9.2891944E-13 5.2703575598661E-12

3.90488184E-12 9.4059669E-13 5.3241076993477E-127.58536401E-13 1.9972055E-12 8.11105711902E-128.17746991E-13 2.0011462E-12 7.9940074759613E-128.77173619E-13 2.0053834E-12 7.8775640463698E-129.36816286E-13 2.0099182E-12 7.7617618599591E-12

205000000000

CONDICIONES DE CONTINUIDAD

0.0150 0.0850 0.1250 0.2550

MATRIZ PLANO Y_X

3 4 5 6 7 8 9-1 0 0 0 0 0 0

-0.015 -1 0 0 0 0 01 0 -1 0 0 0 0

0.085 1 -0.085 -1 0 0 00 0 1 0 -1 0 00 0 0.125 1 -0.125 -1 00 0 0 0 1 0 -10 0 0 0 0.255 1 -0.2550 0 0 0 0 0 10 0 0 0 0 0 0.290 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0

MATRIZ PLANO Z_X

3 4 5 6 7 8 9-1 0 0 0 0 0 0

-0.015 -1 0 0 0 0 01 0 -1 0 0 0 0

0.085 1 -0.085 -1 0 0 00 0 1 0 -1 0 00 0 0.125 1 -0.125 -1 00 0 0 0 1 0 -10 0 0 0 0.255 1 -0.2550 0 0 0 0 0 10 0 0 0 0 0 0.290 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0

0 0 0 0 0 0 0


ECUACIÓN DE DEFLEXIÓN

((AY/6)*X^3+C1*X+C2)/(E*I1)

((AY/6)*X^3+C3*X+C4)/(E*I2)

((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2+C5*X+C6)/(E*I3)

((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2+C7*X+C8)/(E*I4)

((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2-(CY/6)*(X-(A+B))^3+C9*X+C10)/(E*I5)

((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2-(CY/6)*(X-(A+B))^3+C11*X+C12)/(E*I6)

((AY/6)*X^3-(BY/6)*(X-A)^3+(MBY/2)*(X-A)^2-(CY/6)*(X-(A+B))^3+(DY/6)*(X-(A-B-C))^3+C13*X+C14)/(E*I7)



ECUACIÓN DE DEFLEXIÓN

((AZ/6)*X^3+C1*X+C2)/(E*I1)

((AY/6)*X^3+C3*X+C4)/(E*I2)

((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBZ/2)*(X-A)^2+C5*X+C6)/(E*I3)

((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBY/2)*(X-A)^2+C7*X+C8)/(E*I4)

((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBZ/2)*(X-A)^2-(CZ/6)*(X-(A+B))^3+C9*X+C10)/(E*I5)

((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBZ/2)*(X-A)^2-(CZ/6)*(X-(A+B))^3+C11*X+C12)/(E*I6)

((AZ/6)*X^3-(BZ/6)*(X-A)^3-(MBZ/2)*(X-A)^2-(CZ/6)*(X-(A+B))^3+(DZ/6)*(X-(A-B-C))^3+C13*X+C14)/(E*I7)


DEFLEXION TOTAL0

3.888648815585E-147.7772980815509E-141.1665948248282E-13

1.555459976617E-131.9443253085618E-131.0639208663413E-131.3304166271201E-131.5969128149543E-131.8634095148663E-132.1299068120228E-132.3964047916631E-132.6629035390714E-13

2.929403139565E-133.1959036784895E-133.4624052412173E-133.7289079131473E-133.9954117797055E-134.2619169263462E-134.5284234385534E-134.7416296889923E-134.9548369119218E-135.1680451511548E-13

5.381254450519E-135.5944648538572E-135.8209880921534E-13

6.035695797931E-136.2504931738556E-136.4653793806701E-136.6803535791915E-133.9257056686542E-134.1140312499054E-134.3024208771123E-134.4908737637361E-13

4.679389123228E-134.8679661690268E-135.0566041145563E-135.2453021732245E-135.4340595584232E-135.6228754835278E-135.8117491618979E-136.0006798068777E-136.1896666317971E-136.3787088499726E-136.5678056747087E-13

6.7569563192992E-136.9461599970281E-137.1354159211721E-137.3247233050012E-137.5140813617806E-137.7034893047728E-137.8929463472384E-138.0824517024387E-138.2720045836369E-138.4616042040997E-138.6512497770997E-139.6383598606966E-139.6822738095592E-139.7261942125846E-139.7701210354263E-13

9.814054243744E-139.8579938032032E-139.9019396794752E-139.9458918382372E-139.9898502451719E-131.0033814865967E-121.0077785666317E-121.0167600769682E-121.0249105956489E-121.0330665247141E-121.0412277496272E-121.0493941558513E-12

1.057565628848E-121.0657420540772E-121.1624276399385E-121.1757874427507E-121.1891634143443E-121.2025548093577E-121.2159608823709E-121.2293808878974E-12

1.242814080378E-121.2562597141746E-121.2697170435654E-121.2831853227404E-121.6938053183922E-121.6821121241176E-121.6704283923967E-121.6587536694193E-121.6470875014029E-123.8747436169019E-123.8874277280409E-123.9003012009848E-123.9133641629691E-12

3.9266167375317E-126.3855056169724E-12

6.348700340182E-126.3126168540606E-126.2772571888593E-12

CONDICIONES DE CONTINUIDAD VALORES DE FRONTERA

0.2900 0.3400 0.3700X Y0 0

0.7325 0

MATRIZ PLANO Y_XVECTOR C

10 11 12 13 14 15 160 0 0 0 0 0 0 C10 0 0 0 0 0 0 C20 0 0 0 0 0 0 C30 0 0 0 0 0 0 C40 0 0 0 0 0 0 C50 0 0 0 0 0 0 C60 0 0 0 0 0 0 C7-1 0 0 0 0 0 0 C80 -1 0 0 0 0 0 C91 -0.29 -1 0 0 0 0 C100 1 0 -1 0 0 0 C110 0.34 1 -0.34 -1 0 0 C120 0 0 1 0 -1 0 C130 0 0 0.37 1 -0.37 -1 C140 0 0 0 0 0 0 C150 0 0 0.7325 1 0 0 C16

MATRIZ PLANO Z_XVECTOR C

10 11 12 13 14 15 160 0 0 0 0 0 0 C10 0 0 0 0 0 0 C20 0 0 0 0 0 0 C30 0 0 0 0 0 0 C40 0 0 0 0 0 0 C50 0 0 0 0 0 0 C60 0 0 0 0 0 0 C7-1 0 0 0 0 0 0 C80 -1 0 0 0 0 0 C91 -0.29 -1 0 0 0 0 C100 1 0 -1 0 0 0 C110 0.34 1 -0.34 -1 0 0 C120 0 0 1 0 -1 0 C130 0 0 0.37 1 -0.37 -1 C140 0 0 0 0 0 0 C15

0 0 0 0.7325 1 0 0 C16

VALORES DE FRONTERA

Z00

VECTOR SOLUCION SOLUCIONESMATRIS INVERSA Y-X

1 2 3 415.0023951 C1= -7537.04624 0.97952218 1.36518771 0.88395904 1.365187710.07501198 C2= 0 0 0 0 0

0 C3= -7552.04864 -0.02047782 1.36518771 0.88395904 1.365187710 C4= 0.15002395 0.015 -1 0 0

2820.08131 C5= -7552.04864 -0.02047782 1.36518771 -0.11604096 1.3651877188.6922122 C6= 0.15002395 0.015 -1 0.085 -1-5463.38096 C7= -10372.1299 -0.02047782 1.36518771 -0.11604096 1.36518771-619.710481 C8= 263.967975 0.015 -1 0.085 -1-1687.57192 C9= -4908.74898 -0.02047782 1.36518771 -0.11604096 1.36518771-371.360242 C10= -509.48369 0.015 -1 0.085 -1-4622.3508 C11= -3221.17706 -0.02047782 1.36518771 -0.11604096 1.36518771

-1172.83787 C12= -627.519304 0.015 -1 0.085 -114234.9252 C13= 1401.17374 -0.02047782 1.36518771 -0.11604096 1.36518771-1964.54401 C14= -1026.28071 0.015 -1 0.085 -1

0 C15= -12833.7514 -0.02047782 1.36518771 -0.11604096 1.365187710.07905469 C16= 6205.18562 0.015 -1 0.085 -1

VECTOR SOLUCION SOLUCIONESMATRIS INVERSA Z-X

1 2 3 4-209.802332 C1= 53567.2427 0.97952218 1.36518771 0.88395904 1.36518771-1.04901166 C2= 0 0 0 0 0

0 C3= 53777.0451 -0.02047782 1.36518771 0.88395904 1.365187710 C4= -2.09802332 0.015 -1 0 0

-24610.5241 C5= 53777.0451 -0.02047782 1.36518771 -0.11604096 1.36518771-1087.76834 C6= -2.09802332 0.015 -1 0.085 -141175.3959 C7= 78387.5692 -0.02047782 1.36518771 -0.11604096 1.365187715590.55594 C8= -1990.6452 0.015 -1 0.085 -17396.32108 C9= 37212.1733 -0.02047782 1.36518771 -0.11604096 1.36518771657.529706 C10= 2918.52481 0.015 -1 0.085 -147363.0832 C11= 29815.8522 -0.02047782 1.36518771 -0.11604096 1.365187717656.43545 C12= 4405.92822 0.015 -1 0.085 -139262.6745 C13= -17547.231 -0.02047782 1.36518771 -0.11604096 1.36518771-2124.91478 C14= 12852.9411 0.015 -1 0.085 -1

0 C15= -56809.9055 -0.02047782 1.36518771 -0.11604096 1.36518771

-0.40563552 C16= 29505.0454 0.015 -1 0.085 -1

MATRIS INVERSA Y-X

5 6 7 8 9 10 11 120.82935154 1.36518771 0.65187713 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0 0 0 0 0 0 0 00.82935154 1.36518771 0.65187713 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0 0 0 0 0 0 0 00.82935154 1.36518771 0.65187713 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0 0 0 0 0 0 0 0-0.17064846 1.36518771 0.65187713 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0.125 -1 0 0 0 0 0 0-0.17064846 1.36518771 -0.34812287 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0.125 -1 0.255 -1 0 0 0 0-0.17064846 1.36518771 -0.34812287 1.36518771 -0.39590444 1.36518771 0.53583618 1.36518771

0.125 -1 0.255 -1 0.29 -1 0 0-0.17064846 1.36518771 -0.34812287 1.36518771 -0.39590444 1.36518771 -0.46416382 1.36518771

0.125 -1 0.255 -1 0.29 -1 0.34 -1-0.17064846 1.36518771 -0.34812287 1.36518771 -0.39590444 1.36518771 -0.46416382 1.36518771

0.125 -1 0.255 -1 0.29 -1 0.34 -1

MATRIS INVERSA Z-X

5 6 7 8 9 10 11 120.82935154 1.36518771 0.65187713 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0 0 0 0 0 0 0 00.82935154 1.36518771 0.65187713 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0 0 0 0 0 0 0 00.82935154 1.36518771 0.65187713 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0 0 0 0 0 0 0 0-0.17064846 1.36518771 0.65187713 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0.125 -1 0 0 0 0 0 0-0.17064846 1.36518771 -0.34812287 1.36518771 0.60409556 1.36518771 0.53583618 1.36518771

0.125 -1 0.255 -1 0 0 0 0-0.17064846 1.36518771 -0.34812287 1.36518771 -0.39590444 1.36518771 0.53583618 1.36518771

0.125 -1 0.255 -1 0.29 -1 0 0-0.17064846 1.36518771 -0.34812287 1.36518771 -0.39590444 1.36518771 -0.46416382 1.36518771

0.125 -1 0.255 -1 0.29 -1 0.34 -1-0.17064846 1.36518771 -0.34812287 1.36518771 -0.39590444 1.36518771 -0.46416382 1.36518771

0.125 -1 0.255 -1 0.29 -1 0.34 -1

MATRIS INVERSA Y-X

13 14 15 160 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 0

-1 0 -1.36518771 1.365187710.37 -1 1 0

MATRIS INVERSA Z-X

13 14 15 160 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 00 0 -1.36518771 1.365187710 0 1 0

-1 0 -1.36518771 1.36518771

0.37 -1 1 0

DEM_I_151_PP_Eq_Camilo Andrés_Bolivar Acosta.xlsx

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