Esfuezos en una Columna

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COLUMNAS DE DIMENCIONES 30*45 CM 30cm*45cm con un ρ =1% cm 45 30 cm COLUMNA BASE (m) 0,3 ALTURA (m) 0,45 AREA (Ag) 0,135 materiale s psi Mpa kpa ρ cuantía % 0,01 concreto (f´c) 4000 28 28000 Ast (m2) 0,00135 acero (fý) 60000 420 42000 0 A´s(m2) 0,00067 5 d (m) 0,39 (m) 0,06 f´s (KN/m2) 1694,11 76 Ø 0,7 Falla Balanceada cb (m) Øpub (KN) ØMub´ e´ (m) e (m) Ømu Pmáx Pmin 0,2294 974,61 350,5 6 0,36 0,19 189,8 2624 378 Falla por Compresión C Øpub ØMub´ e Ømu fs (Mpa) 0,23 974,61 350,5 6 0,36 0,19 189,8 420 0,24 1037,22 358,6 7 0,35 0,18 187,5 377

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columnas con diferentes dimensiones y su comportamiento graficado, en compresión y tensión por Jhon Felipe Abril Alfonso

Transcript of Esfuezos en una Columna

COLUMNAS DE DIMENCIONES 30*45 CM30cm*45cm con un =1%

cm

45

30

cm

COLUMNA

BASE (m)0,3

ALTURA (m)0,45

AREA (Ag)0,135materialespsiMpa kpa

cuanta %0,01concreto (fc)40002828000

Ast (m2)0,00135acero (f)60000420420000

As(m2)0,000675

d (m)0,39

d (m)0,06

fs (KN/m2)1694,1176

0,7

Falla Balanceada

cb (m)pub (KN)Mube (m)e (m)muPmxPmin

0,2294974,61350,560,360,19189,82624378

Falla por Compresin

CpubMubeemufs (Mpa)

0,23974,61350,560,360,19189,8420

0,241037,22358,670,350,18187,5377

0,251098,22366,410,330,17185,2338

0,261157,79373,790,320,16182,8302

0,271216,10380,810,310,15180,2269

0,281273,27387,470,300,14177,4237

0,291329,42393,770,300,13174,4209

0,301384,67399,700,290,12171,2182

0,311439,08405,280,280,12167,8156

0,321492,76410,490,270,11164,2133

0,331545,75415,350,270,10160,3110

0,341598,12419,840,260,10156,289

0,351649,92423,970,260,09151,770

0,361701,21427,740,250,09147,051

0,371752,02431,150,250,08142,133

0,381802,39434,200,240,08136,817

0,391852,36436,890,240,07131,21

Falla por Traccin

CpubMubeemufs'

0,23985,51354,160,360,19191,6443

0,22943,03344,580,370,20189,0436

0,21900,55334,530,370,21185,9428

0,20858,06324,000,380,21182,4419

0,19815,58312,970,380,22178,4410

0,18773,10301,410,390,22173,8399

0,17730,62289,290,400,23168,7388

0,16688,13276,580,400,24163,0374

0,15645,65263,230,410,24156,7359

0,14603,17249,180,410,25149,7342

0,13560,68234,360,420,25141,8322

0,12518,20218,650,420,26133,1299

0,11475,72201,910,420,26123,4271

0,10433,23183,960,420,26112,5238

0,09390,75164,480,420,26100,0197

30cm*45cm con un =2%

COLUMNA

BASE (m)0,345

ALTURA (m)0,45

AREA (Ag)0,135

cuanta %0,0230

Ast (m2)0,0027

As(m2)0,00135

d (m)0,39

d (m)0,06materialespsiMpa kpa

fs (KN/m2)1694,1176concreto (fc)40002828000

0,7acero (f)60000420420000

Falla balanceada

cb (m)pub (KN)Mube (m)e (m)muPmxPmin

0,2294974,61416,050,430,26255,23020378

Falla por compresin

CpubMubeemufs (Mpa)

0,23974,61416,050,430,26255,2420

0,241057,35424,150,400,24249,7377

0,251136,87431,900,380,21244,3338

0,261213,53439,280,360,20239,0302

0,271287,65446,300,350,18233,8269

0,281359,51452,960,330,17228,6237

0,291429,34459,260,320,16223,4209

0,301497,34465,190,310,15218,1182

0,311563,70470,770,300,14212,8156

0,321628,55475,980,290,13207,3133

0,331692,05480,840,280,12201,6110

0,341754,31485,330,280,11195,989

0,351815,44489,460,270,10189,970

0,361875,53493,230,260,10183,851

0,371934,67496,640,260,09177,433

0,381992,93499,690,250,09170,917

0,392050,38502,380,250,08164,11

Falla por traccin

CpubMubeemufs'

0,23996,42423,250,420,26258,8443

0,22953,93412,550,430,27255,2436

0,21911,45401,280,440,28250,9428

0,20868,97389,410,450,28246,0419

0,19826,49376,890,460,29240,5410

0,18784,00363,670,460,30234,3399

0,17741,52349,710,470,31227,4388

0,16699,04334,920,480,31219,6374

0,15656,55319,220,490,32210,9359

0,14614,07302,470,490,33201,2342

0,13571,59284,540,500,33190,2322

0,12529,10265,190,500,34177,9299

0,11486,62244,160,500,34163,9271

0,10444,14221,050,500,33147,8238

0,09401,66195,260,490,32129,0197

0,08359,17165,920,460,30106,7147

30cm*45cm con un =3%

COLUMNA

BASE (m)0,3

ALTURA (m)0,45

AREA (Ag)0,13545

cuanta %0,03

Ast (m2)0,00405

As(m2)0,00202530

d (m)0,39

d (m)0,06

fs (KN/m2)1694,1176materialespsiMpa kpa

0,7concreto (fc)40002828000

acero (f)60000420420000

Falla balanceada

cb (m)pub (KN)Mube (m)e (m)muPmxPmin

0,2294974,61481,540,490,33320,73417378

Falla por compresin

CpubMubeemufs (Mpa)

0,23974,61481,540,490,33320,7420

0,241077,48489,640,450,29311,9377

0,251175,52497,390,420,26303,4338

0,261269,27504,770,400,23295,3302

0,271359,21511,790,380,21287,5269

0,281445,76518,450,360,19279,9237

0,291529,26524,740,340,18272,4209

0,301610,02530,680,330,16265,0182

0,311688,31536,260,320,15257,7156

0,321764,35541,470,310,14250,4133

0,331838,36546,330,300,13243,0110

0,341910,51550,820,290,12235,689

0,351980,96554,950,280,12228,170

0,362049,86558,720,270,11220,551

0,372117,32562,130,270,10212,833

0,382183,47565,180,260,09204,917

0,392248,40567,860,250,09196,91

Falla por traccin

CpubMubeemufs'

0,231007,32492,330,490,32326,1443

0,22964,84480,520,500,33321,3436

0,21922,36468,030,510,34315,8428

0,20879,87454,810,520,35309,6419

0,19837,39440,810,530,36302,6410

0,18794,91425,940,540,37294,8399

0,17752,42410,130,550,38286,0388

0,16709,94393,260,550,39276,1374

0,15667,46375,200,560,40265,1359

0,14624,97355,760,570,40252,6342

0,13582,49334,710,570,41238,6322

0,12540,01311,740,580,41222,6299

0,11497,53286,420,580,41204,3271

0,10455,04258,140,570,40183,1238

0,09412,56226,030,550,38158,0197

0,08370,08188,790,510,35127,7147

COLUMNA

BASE (m)0,3

ALTURA (m)0,45

AREA (Ag)0,135

cuanta %0,0445

Ast (m2)0,0054

As(m2)0,0027

d (m)0,39

d (m)0,0630

fs (KN/m2)1694,117647materialespsiMpa kpa

0,7concreto (fc)40002828000

acero (f)60000420420000

Falla balanceada

cb (m)pub (KN)Mube (m)e (m)muPmxPmin

0,2294974,61547,030,560,40386,23814378

Falla por compresin

CpubMubeemufs (Mpa)

0,23974,61547,030,560,40386,2420

0,241097,62555,130,510,34374,0377

0,251214,16562,870,460,30362,5338

0,261325,00570,260,430,27351,6302

0,271430,77577,280,400,24341,2269

0,281532,00583,930,380,22331,2237

0,291629,17590,230,360,20321,4209

0,301722,69596,170,350,18311,9182

0,311812,92601,750,330,17302,6156

0,321900,15606,960,320,15293,4133

0,331984,67611,810,310,14284,3110

0,342066,70616,310,300,13275,389

0,352146,48620,440,290,12266,370

0,362224,18624,210,280,12257,251

0,372299,97627,620,270,11248,133

0,382374,01630,670,270,10239,017

0,392446,43633,350,260,09229,71

Falla por traccin

CpubMubeemufs'

0,231018,23561,420,550,39393,4443

0,22975,74548,500,560,40387,5436

0,21933,26534,780,570,41380,8428

0,20890,78520,220,580,42373,2419

0,19848,29504,730,590,43364,8410

0,18805,81488,210,610,44355,3399

0,17763,33470,550,620,45344,6388

0,16720,84451,610,630,46332,7374

0,15678,36431,190,640,47319,3359

0,14635,88409,050,640,48304,1342

0,13593,40384,890,650,48287,0322

0,12550,91358,290,650,49267,4299

0,11508,43328,670,650,48244,8271

0,10465,95295,230,630,47218,3238

0,09423,46256,810,610,44186,9197

0,08380,98211,660,560,39148,8147

0,07338,50157,050,460,30101,281

DIAGRAMA DE CUANTIAS TOTALES COLUMNA 30*45

COLUMNAS DE DIMENCIONES 45*30 CMPARA COLUMNA DE 45*30 CM CON =1%COLUMNA

BASE (m)0,45

ALTURA (m)0,3

AREA (Ag)0,13530

cuanta %0,01

Ast (m2)0,00135

As(m2)0,000675

d (m)0,2445

d (m)0,06materialespsiMpa kpa

fs (KN/m2)811,764706concreto (fc)40002828000

0,7acero (f)60000420420000

Falla balanceada

cb (m)pub (KN)Mube (m)e (m)muPmxPmin

0,1412899,64197,660,220,13116,72624378

Falla por compresin

CpubMubeemufs (Mpa)

0,14899,64197,660,220,13116,7420

0,15995,24205,030,210,12115,5353

0,161086,89211,870,190,10114,0293

0,171175,28218,160,190,10112,4241

0,181260,94223,910,180,09110,4195

0,191344,31229,120,170,08108,1153

0,201425,73233,790,160,07105,5116

0,211505,47237,910,160,07102,482

0,221583,76241,500,150,0699,051

0,231660,79244,540,150,0695,123

0,241736,72247,040,140,0590,7-3

0,251811,67249,000,140,0586,0-27

0,261885,77250,420,130,0480,7-49

0,271959,10251,300,130,0475,0-69

0,282031,75251,630,120,0368,8-88

0,292103,78251,420,120,0362,1-105

0,302175,27250,670,120,0354,9-122

0,312246,25249,380,110,0247,2-137

0,322316,78247,550,110,0239,0-152

Falla por traccin

CpubMubeemufs'

0,14855,69190,190,220,13113,2343

0,13791,97180,530,230,14109,3323

0,12728,24170,040,230,14104,5300

0,11664,52158,660,240,1598,9273

0,10600,80146,270,240,1592,2240

0,09537,07132,720,250,1684,4200

0,08473,35117,780,250,1675,2150

0,07409,62101,080,250,1664,286

PARA COLUMNA DE 45*30 CM CON =2%COLUMNA

BASE (m)0,45

ALTURA (m)0,3

AREA (Ag)0,13530

cuanta %0,02

Ast (m2)0,0027

As(m2)0,00135

d (m)0,2445

d (m)0,06materialespsiMpa kpa

fs (KN/m2)811,7647059concreto (fc)40002828000

0,7acero (f)60000420420000

Falla balanceada

cb (m)pub (KN)Mube (m)e (m)muPmxPmin

0,1412899,64233,380,260,17152,43020378

Falla por compresin

CpubMubeemufs (Mpa)

0,1412899,64233,380,260,17152,4420

0,151012,57239,910,240,15148,8360

0,161132,99246,810,220,13144,8300

0,171246,75253,170,200,11141,0247

0,181354,94258,980,190,10137,0200

0,191458,45264,260,180,09133,0158

0,201557,99268,990,170,08128,8120

0,211654,11273,180,170,08124,386

0,221747,29276,830,160,07119,655

0,231837,91279,930,150,06114,526

0,241926,29282,500,150,06109,10

0,252012,69284,520,140,05103,4-24

0,262097,35286,000,140,0597,2-46

0,272180,46286,940,130,0490,7-67

0,282262,19287,340,130,0483,7-86

0,292342,67287,200,120,0376,4-103

0,302422,04286,510,120,0368,5-120

0,312500,39285,290,110,0260,3-135

0,322577,83283,520,110,0251,5-150

0,332654,44281,210,110,0242,3-164

0,342730,30278,360,100,0132,6-176

0,352805,46274,960,100,0122,5-189

Falla por traccin

CpubMubeemufs'

0,15882,97229,710,260,17150,2360

0,14819,24219,350,270,18145,6343

0,13755,52208,010,280,19140,0323

0,12691,79195,560,280,19133,3300

0,11628,07181,850,290,20125,3273

0,10564,35166,680,300,21115,9240

0,09500,62149,730,300,21104,7200

0,08436,90130,530,300,2191,2150

0,07373,17108,370,290,2074,886

PARA COLUMNA DE 45*30 CM CON =3%COLUMNA

BASE (m)0,45

ALTURA (m)0,3

AREA (Ag)0,135

cuanta %0,0330

Ast (m2)0,00405

As(m2)0,002025

d (m)0,2445

d (m)0,06materialespsiMpa kpa

fs (KN/m2)811,76471concreto (fc)40002828000

0,7acero (f)60000420420000

Falla balanceada

cb (m)pub (KN)Mube (m)e (m)muPmxPmin

0,1412899,64269,100,300,21188,13417378

Falla por compresin

CpubMubeemufs (Mpa)

0,1412899,64269,100,300,21188,1420

0,151040,92275,630,260,17182,0360

0,161189,69282,530,240,15175,5300

0,171328,46288,890,220,13169,3247

0,181458,89294,700,200,11163,4200

0,191582,30299,980,190,10157,6158

0,201699,74304,710,180,09151,7120

0,211812,06308,900,170,08145,886

0,221919,97312,550,160,07139,755

0,232024,04315,650,160,07133,526

0,242124,74318,220,150,06127,00

0,252222,48320,240,140,05120,2-24

0,262317,61321,720,140,05113,1-46

0,272410,41322,660,130,04105,7-67

0,282501,14323,060,130,0498,0-86

0,292590,00322,920,120,0389,8-103

0,302677,19322,230,120,0381,3-120

0,312762,86321,010,120,0372,3-135

0,322847,16319,240,110,0263,0-150

0,332930,21316,930,110,0253,2-164

0,343012,13314,080,100,0143,0-176

0,353093,01310,680,100,0132,3-189

0,363172,93306,750,100,0121,2-200

Falla por traccin

CpubMubeemufs'

0,1500846,52260,330,310,22184,1360

0,14782,79248,510,320,23178,1343

0,13719,07235,480,330,24170,8323

0,12655,34221,070,340,25162,1300

0,11591,62205,050,350,26151,8273

0,10527,90187,090,350,26139,6240

0,09464,17166,740,360,27125,0200

0,08400,45143,290,360,27107,3150

0,07336,72115,660,340,2585,486

PARA COLUMNA DE 45*30 CM CON =4%COLUMNA

BASE (m)0,45

ALTURA (m)0,3

AREA (Ag)0,135

cuanta %0,0430

Ast (m2)0,0054

As(m2)0,0027

d (m)0,2445

d (m)0,06materialespsiMpa kpa

fs (KN/m2)811,76471concreto (fc)40002828000

0,7acero (f)60000420420000

Falla balanceada

cb (m)pub (KN)Mube (m)e (m)muPmxPmin

0,1412899,64304,820,340,25223,93814378

Falla por compresin

CpubMubeemufs (Mpa)

0,14899,64304,820,340,25223,9420

0,151069,27311,360,290,20215,1360

0,161246,39318,250,260,17206,1300

0,171410,18324,610,230,14197,7247

0,181562,84330,430,210,12189,8200

0,191706,14335,700,200,11182,1158

0,201841,49340,430,180,09174,7120

0,211970,01344,620,170,08167,386

0,222092,65348,270,170,08159,955

0,232210,16351,370,160,07152,526

0,242323,19353,940,150,06144,90

0,252432,27355,960,150,06137,1-24

0,262537,87357,440,140,05129,0-46

0,272640,36358,380,140,05120,8-67

0,282740,09358,780,130,04112,2-86

0,292837,33358,640,130,04103,3-103

0,302932,34357,950,120,0394,0-120

0,313025,32356,730,120,0384,4-135

0,323116,48354,960,110,0274,5-150

0,333205,98352,650,110,0264,1-164

0,343293,96349,800,110,0253,3-176

Falla por traccin

CpubMubeemufs'

0,1600899,64302,940,340,25223,9375

0,15842,47290,940,350,26215,1360

0,14778,74277,670,360,27207,6343

0,13715,02262,960,370,28198,6323

0,12651,29246,590,380,29188,0300

0,11587,57228,240,390,30175,4273

0,10523,85207,500,400,31160,4240

0,09460,12183,750,400,31142,3200

0,08396,40156,050,390,30120,4150

0,07332,67122,950,370,2893,086

DIAGRAMA DE CUANTIAS TOTALES

INTRODUCCIONEn este informe determinaremos el comportamiento de una columna de 30*45 Centmetros y 45*30 cm, el rea de refuerzo longitudinal de la columna son de 1%, 2%,3%y 4% del rea total Ag de la seccin y una tabla resumen al final de cada columna para mostrar las diferencias de momento y la resistencia de diseo a fuerza axial de los elementos sometidos a compresin teniendo tambin en cuenta la excentricidad de la carga medida desde el centro del refuerzo en traccin, dndonos as diferentes resultados.

Conclusiones El diseo de una seccin de cualquier columna de concreto reforzado, se puede establecer un diagrama de interaccin calculando los puntos correspondientes Pub, Mu para si establecer el funcionamiento de dicha seccin. Los diagramas de compreion-flexion se pueden tomar como ayuda para diseos de estructuras teniendo en cuenta las condiciones de equilibrio y compatibilidad de deformaciones que aparecen el el reglamento colombiano.

DISEO DE COLUMNAS COLUMNAS 30*45 Y 45*30 CM

JHON FELIPE ABRIL ALFONSO

UNIVERSIDAD SANTO TOMAS TUNJA - BOYACA2014