Prednapregnuti beton

Prenapregnuti betonSeminarski rad

Univerzitet u Novom SaduGraevinski fakultetSubotica

Profesor: dr Danijel KukarasStudent: ore MihailoviSubotica, januar 2015. godineSadrajSadraj11. Geometrijske karakteristike12. Statiki sistem i uticaji42.1. Stalno optereenje - sopstvena teina nosaa42.2. Dodatno stalno optereenje52.3. Sneg62.4. Vetar73. Prednaprezanje nosaa93.1. Marka betona MB 4093.2. Usvajanje kablova93.3. Materijalne i geometrijske karakteristike114. Naknadno prednaprezanje nosaa134.1. Proraun gubitka sile prednaprezanja134.1.1. Gubitak usled trenja134.1.2. Pad sile pri ukotvljenju ice144.1.3. Gubitak usled elastinog skraenja154.1.4. Gubitak usled relaksacije elika. teenja i skupljanja betona164.2. Presene sile174.2.1. Sopstvena teina konstrukcije174.2.2. Kablovi za prednaprezanje174.2.3. Zbirni uticaji prilikom prednaprezanja t = 0 (sopstvena teina nosaa + kablovi)184.2.4. Dodatno stalno optereenje (trapezasti lim, termoizolacija, sopst. teina ploe)184.2.5. Povremeno optereenje sneg + vetar194.2.6. Pad sile prednaprezanja u kablovima194.2.7. Presene sile u vremenu t = 204.3. Kontrola normalnih napona214.3.1. Normalni napon od prednaprezanja t = 0 (sopstvena teina nosaa + kablovi):224.3.2. Normalni naponi u vremenu t = :224.4. Kontrola glavnih napona zatezanja234.5. Kontrola koeficijenta sigurnosti od loma (presek 10-10)245. Adheziono predraprezanje nosaa275.1. Proraun gubitka sile prednaprezanja275.1.1. Pad sile pri ukotvljenju ice275.1.2. Gubitak usled elastinog skraenja285.1.3. Gubitak usled relaksacije elika. teenja i skupljanja betona:295.2. Presene sile305.2.1. Sopstvena teina konstrukcije305.2.2. Kablovi za prednaprezanje305.2.3. Zbirni uticaji prilikom prednaprezanja t = 0 (sopstvena teina nosaa + kablovi)315.2.4. Dodatno stalno optereenje (trapezasti lim, termoizolacija, sopst. teina ploe)315.2.5. Povremeno optereenje sneg + vetar325.2.6. Pad sile prednaprezanja u kablovima325.2.7. Presene sile u vremenu t = 335.3. Kontrola normalnih napona345.3.1. Normalni napon od prednaprezanja t = 0 (sopstvena teina nosaa + kablovi)355.3.2. Normalni naponi u vremenu t = 355.4. Kontrola glavnih napona zatezanja365.5. Kontrola koeficijenta sigurnosti od loma (presek 10-10)37

Univerzitet u Novom SaduGraevinski fakultetSubotica

Student: ore Mihailovi

Student: ore Mihailovi

Geometrijske karakteristike

Nosa posmatramo u desetinama raspona , ali samo za levu polovinu, zbog simetrije.Na osnovu preporuka za prednapregnuti beton usvojene su sledee geometrijske karakteristike poprenih preseka rigle: Visina na poetku rigle usv. irina gornje flane usv. irina donje flane usv. Usvojen nagib krovne ravni usv. irina rebra usv. Visina gornje flane usv. Visina donje flane usv.

Dimenzije poprenih preseka

Presekx [cm]H=H(x)b1 [cm]b2 [cm]tu [cm]to [cm]br [cm]

00,0085,0070,0050,000,0025,0050,00

150,0090,2970,0050,000,0025,0050,00

2171,50103,1570,0050,000,0025,0050,00

3293,00116,0070,0050,000,0025,0050,00

4366,25123,7570,0050,0025,0025,0035,00

5439,50131,5070,0050,0025,0025,0020,00

6644,60153,2070,0050,0025,0025,0020,00

7849,70174,9070,0050,0025,0025,0020,00

81054,80196,6070,0050,0025,0025,0020,00

91259,90218,3070,0050,0025,0025,0020,00

101465,00240,0070,0050,0025,0025,0020,00

Tabela geometrijskih karakteristikaPresekx [cm]A [cm2]yd=te. [cm]yg [cm]Ix=I1 [m4]Wg [cm3]Wd [m3]kd [m]kg [m]

00,004783,3345,7539,250,030,080,070,160,14

150,005047,8448,5041,790,040,090,070,170,15

2171,505690,5955,1547,990,050,110,100,190,17

3293,006333,3361,7654,240,080,140,120,220,19

4366,255702,0866,6857,070,090,150,130,270,23

5439,504913,3372,0659,440,100,160,140,330,28

6644,605347,3383,6969,510,150,210,180,400,33

7849,705781,3395,1979,710,210,260,220,450,38

81054,806215,33106,6189,990,280,320,270,510,43

91259,906649,33117,95100,350,370,370,320,560,48

101465,007083,33129,23110,770,480,430,370,610,53

Statiki sistem i uticajiStalno optereenje - sopstvena teina nosaa optereenje u preseku 0-0: optereenje u preseku 1-1: optereenje u preseku 2-2: optereenje u preseku 3-3: optereenje u preseku 4-4: optereenje u preseku 5-5: optereenje u preseku 6-6: optereenje u preseku 7-7: optereenje u preseku 8-8: optereenje u preseku 9-9: optereenje u preseku 10-10:

Dodatno stalno optereenje- trapezasti lim: - termoizolacija: - sop. tez. ploce:

Razmak glavnih nosaa je

Sneg- sneg: Razmak glavnih nosaa je

Vetar- Razmak glavnih nosaa je

Tabela presenih silaPresekx (cm)ggdod.gsgw

MgTgMgdTgdMsTsMwTw

00,0000000000

150,00-1,8204,33-0,7180,65-0,3337,64-1,8204,33

2171,50235,79186,7893,0873,7343,4434,41235,79186,78

3293,00452,07169,24178,4566,883,2831,18452,07169,24

4366,25572,17158,66225,8562,63105,429,23572,17158,66

5439,50684,51148,08270,258,45126,0927,28684,51148,08

6644,60957,85118,47378,146,76176,4521,82957,85118,47

7849,701170,4688,85462,0235,07215,6116,371170,4688,85

81054,801322,3159,23521,9723,38243,5810,911322,3159,23

91259,901413,4329,62557,9311,69260,375,461413,4329,62

101465,001443,80569,920265,9601443,80

Prednaprezanje nosaaMarka betona MB 40 - doputeni naponi (u apsolutnim vrednostima):

- zatezanje

(preporuka )Usvajanje kablovaPotrebna sila prednaprezanja Odreujemo iz uslova da se ne prekoarae naponi zatezanja u

Pretpostavljamo (rastojanje od donje ivice preseka do teita kabla), samim tim pretpostavljamo trasu kabla.

Presekx [cm]ak [cm]ek [cm]1. Uslov Nk0 [kN] 2. Uslov

00,0045,700,050,00 Nk0 0

150,0040,218,3018,55 Nk0 -24,264

2171,5026,8528,302987,83 Nk0 1760,648

3293,0013,548,261927,56 Nk0 2265,629

4366,2513,553,182425,54 Nk0 2548,166

5439,5013,558,563079,23 Nk0 2687,892

6644,6013,570,193561,87 Nk0 3154,691

7849,7013,581,693702,10 Nk0 3332,883

81054,8013,593,113628,22 Nk0 3324,164

91259,9013,5104,453412,10 Nk0 3184,32

101465,0013,5115,733096,25 Nk0 2946,72

Usvajanje broja kablovaPresekx [cm]Nk0 [kN]Fpk [kN]0.8* Fpk [kN] n,potrn, usv N [kN]

00,000743594,4063566,4

150,00-24,26743,00594,40-0,0463566,4

2171,501760,65743,00594,402,9663566,4

3293,001927,56743,00594,403,2463566,4

4366,252425,54743,00594,404,0863566,4

5439,502687,89743,00594,404,5263566,4

6644,603154,69743,00594,405,3163566,4

7849,703332,88743,00594,405,6163566,4

81054,803324,16743,00594,405,5963566,4

91259,903184,32743,00594,405,3663566,4

101465,002946,72743,00594,404,9663566,4

Glavni nosa je prednapregnut po sistemu IMS, SPB SUPERUsvajamo kablove od uadi , klase A,Y1770S7, tip kabla A usvojeno

Usvojeno prednaprezanje svih kablova u jednoj fazi.

Materijalne i geometrijske karakteristike Beton: MB 40

Kablovi klase A prema katalogu IMS SPB SUPER i livena podlona ploa.

315.2KotvaS3/16

fpk [N/mm2]1770a [mm]50

Ek [N/mm2]195b [mm]90

Ak [mm2]420c [mm]130

erel, 1000h [%]2.5d [mm]150

Fpk [kN]743e [mm]140

0.8 Fpk [kN]595f [mm]10

0.7 Fpk [kN]558h [mm]70

l [mm]4i [mm]48

[1/rad]0.22a [mm] minimalnoosno rastojanje kablova170

k [rad/m]3x10-3b [mm] min. osnoodstojanje kabla od ivice betona100

Predvieno je da se svi kablovi uteu u jednoj fazi sa obe strane. Predvieno je da se nosai uteu sa po est kabla na sledei nain: 6 poligonalna kabla sa

Naknadno prednaprezanje nosaaProraun gubitka sile prednaprezanjaUsvojena poetna sila od po kablu, odnosno maksimalna zbirna sila .Gubitak usled trenja

koeficijent trenja dna materijala

ugao nagiba kablova u radijanima (ukupan ugao skretanja od mesta hvatanja kabla presom do preseka u kome se trai pad nap ona)

koeficijent gubitka po jedinici duine

Presekx [cm]Nko [kN]Nko(x) [kN]

00.000,003566,40

11.181,183565,22

24.034,033562,37

3l6.896,893559,51

3d91.5891,583474,82

493.2693,263473,14

594.9494,943471,46

699.6499,643466,76

7104.33104,333462,07

8109.01109,013457,39

9113.69113,693452,71

10118.36118,363448,04

Pad sile pri ukotvljenju iceDuina rasprostiranja gubitka:

Gubitak sile na mestu prese:

poputanje klina napon u kablu na mestu prese

Presekx [cm]Nko [kN]Nko(x) [kN]

00,00233,1203333,280

150,00222,4213342,802

2171,50196,4223365,944

3l293,00170,4233389,087

3d293,00170,4233304,395

4366,25154,7483318,390

5439,50139,0743332,385

6644,6095,1863371,578

7849,7051,2983410,776

81054,807,4103449,981

91259,900,0003452,714

101465,000,0003448,043

Gubitak usled elastinog skraenja

promena napona u betonu u nivou rezultujuceg kabla sila prednaprezanja rezultujueg kabla nakon gubitaka usled trenja i ukotvljenja ekcentricitet rezultujueg kabla u odnosu na teite

Presekx [cm]ek [cm]ib2[m2]Mg[kNm]Nko(x)*ebk[kN/cm2]NkoN [kN]

00,000,050,0630,0001,6700,34852,6823280,598

150,008,300,071-1,610277,4260,36354,9533287,849

2171,5028,300,093264,640952,6360,47972,4383293,506

3l293,0048,260,119508,8801635,5710,63095,1963293,891

3d293,0048,260,119508,8801594,6990,62594,5633209,832

4366,2553,180,152644,7001764,6060,63295,6063222,784

5439,5058,560,199772,3301951,6000,689104,2333228,152

6644,6070,190,2751089,2302366,4160,61292,6103278,968

7849,7081,690,3621343,6602786,3910,57086,1913324,585

81054,8093,110,4581531,0503212,2300,54682,5733367,408

91259,90104,450,5641646,8203606,3510,53280,4643372,249

101465,00115,730,6791686,4303990,4450,52178,8443369,199

Gubitak usled relaksacije elika. teenja i skupljanja betona

koeficijent teenja betona: skupljanje betona u vremenu t:

procenjeni pad napona u eliku kablova usled relaksacije napona: dilatacija usled relaksacije (za jedan kabl)

sila posle gubitka usled elastinih deformacija. gubitka pri ukotvljenju i gubitka usled trenja

koeficijent starenja betona: promena napona rezultujueg kabla

koeficijent efikasnostiPresekx[cm]ek[cm]Nko[kN]M[kNm]Mg[kNm]bk0 [MPa]k0[MPa]rel [MPa]k(t)[MPa]Nkt[kN]

00,000,053280,5981,6700,0006,8581301,82497,637287,4082556,3290,779

150,008,303287,849277,426-1,6107,1601304,70297,853290,2352556,4570,778

2171,5028,303293,506952,636264,6409,4541306,94798,021308,5022516,0800,764

3l293,0048,263293,8911635,571508,88012,4421307,10098,032330,4772461,0890,747

3d293,0048,263209,8321594,699508,88012,0461273,74395,531322,8772396,1810,747

4366,2553,183222,7841764,606644,70012,5321278,88295,916326,9782398,7980,744

5439,5058,563228,1521951,600772,33013,6331281,01396,076337,6992377,1520,736

6644,6070,193278,9682366,4161089,23012,2211301,17897,588322,6162465,9760,752

7849,7081,693324,5852786,3911343,66011,3841319,28098,946314,8912531,0580,761

81054,8093,113367,4083212,2301531,05010,9151336,273100,220311,8462581,5570,767

91259,90104,453372,2493606,3511646,82010,5311338,194100,365308,7642594,1640,769

101465,00115,733369,1993990,4451686,43010,3041336,984100,274307,4502594,4240,770

Presene sileSopstvena teina konstrukcijePresekx [cm]Ng [kN]Tg [kN]Mg [kNm]

00,000,0000,0000,000

150,000,000227,530-1,610

2171,500,000210,400264,640

3l293,000,000191,320508,880

3d293,000,000191,320508,880

4366,250,000179,660644,700

5439,500,000169,000772,330

6644,600,000139,6501089,230

7849,700,000108,0801343,660

81054,800,00074,2801531,050

91259,900,00038,2501646,820

101465,000,0000,0001686,430

Kablovi za prednaprezanjePresekx [cm]Nk0 [kN]Tk0 [kN]Mk0 [kNm]

00,00-3260,965-358,372-1,634

150,00-3268,173-359,164-271,232

2171,50-3273,795-359,782-926,556

3l293,00-3274,178-359,824-1580,117

3d293,00-3209,8320,000-1549,063

4366,25-3222,7840,000-1713,766

5439,50-3228,1520,000-1890,556

6644,60-3278,9680,000-2301,415

7849,70-3324,5850,000-2715,978

81054,80-3367,4080,000-3135,348

91259,90-3372,2490,000-3522,307

101465,00-3369,1990,000-3899,198

Zbirni uticaji prilikom prednaprezanja t = 0 (sopstvena teina nosaa + kablovi)Presekx [cm]Nt=0 [kN]Tt=0 [kN]Mt=0 [kNm]

00,00-3260,965-358,372-1,634

150,00-3268,173-131,634-272,842

2171,50-3273,795-149,382-661,916

3l293,00-3274,178-168,504-1071,237

3d293,00-3209,832191,320-1040,183

4366,25-3222,784179,660-1069,066

5439,50-3228,152169,000-1118,226

6644,60-3278,968139,650-1212,185

7849,70-3324,585108,080-1372,318

81054,80-3367,40874,280-1604,298

91259,90-3372,24938,250-1875,487

101465,00-3369,1990,000-2212,768

Dodatno stalno optereenje (trapezasti lim, termoizolacija, sopst. teina ploe)Presekx [cm]Ngd [kN]Tgd [kN]Mgd [kNm]

00,0000,0000,0000,000

10,000204,330-1,8000,000

20,000186,780235,7900,000

3l0,000169,240452,0700,000

3d0,000169,240452,0700,000

40,000158,660572,1700,000

50,000148,080684,5100,000

60,000118,470957,8500,000

70,00088,8501170,4600,000

80,00059,2301322,3100,000

90,00029,6201413,4300,000

100,0000,0001443,8000,000

Povremeno optereenje sneg + vetarPresekx [cm]Np [kN]Tp [kN]Mp [kNm]

00,000,0000,0000,000

150,000,000118,290-1,040

2171,500,000108,140136,520

3l293,000,00097,980261,730

3d293,000,00097,980261,730

4366,250,00091,860331,250

5439,500,00085,730396,290

6644,600,00068,580554,550

7849,700,00051,440677,630

81054,800,00034,290765,550

91259,900,00017,150818,300

101465,000,0000,000835,880

Pad sile prednaprezanja u kablovimaPresekx [cm]Nko [kN]Tko [kN]Mko [kNm]

00,00719,93479,1190,361

150,00727,01579,89760,336

2171,50772,77384,926218,712

3l293,00827,81890,975399,505

3d293,00813,6510,000392,668

4366,25823,9860,000438,167

5439,50851,0000,000498,385

6644,60812,9920,000570,616

7849,70793,5270,000648,262

81054,80785,8510,000731,695

91259,90778,0850,000812,708

101465,00774,7750,000896,652

Presene sile u vremenu t = Presekx [cm]Nt= [kN]Tt= [kN]Mt= [kNm]

00,00-2541,03-279,253-1,273

150,00-2541,16270,883-215,346

2171,50-2501,02230,464-70,894

3l293,00-2446,36189,69142,068

3d293,00-2396,18458,54066,284

4366,25-2398,80430,180272,521

5439,50-2377,15402,810460,960

6644,60-2465,98326,700870,831

7849,70-2531,06248,3701124,033

81054,80-2581,56167,8001215,257

91259,90-2594,1685,0201168,951

101465,00-2594,420,000963,564

Kontrola normalnih napona

Normalni naponi na gornjoj ivici preseka:

Normalni naponi na donjoj ivici preseka:

Doputeni normalni naponi u betonu: faza prethodnog naprezanja MB40: - zatezanje (preporuka )

Normalni napon od prednaprezanja t = 0 (sopstvena teina nosaa + kablovi):Presekx [m]Nt=0 [kN]Mt=0 [kNm]A [cm2]Wg [m3]Wd [m3]g [kN/cm2]d [kN/cm2]

00,00-3260,96-1,634783,330,080,07-0,680-0,684

150,00-3268,17-272,845047,840,090,07-0,329-0,966

2171,50-3273,80-661,925690,590,110,100,023-1,173

3l293,00-3274,18-1071,246333,330,140,120,257-1,291

3d293,00-3209,83-1040,186333,330,140,120,245-1,258

4366,25-3222,78-1069,075702,080,150,130,140-1,270

5439,50-3228,15-1118,234913,330,160,140,023-1,337

6644,60-3278,97-1212,195347,330,210,18-0,041-1,186

7849,70-3324,58-1372,325781,330,260,22-0,052-1,098

81054,80-3367,41-1604,306215,330,320,27-0,035-1,049

91259,90-3372,25-1875,496649,330,370,32-0,005-1,009

101465,00-3369,20-2212,777083,330,430,370,034-0,986

Normalni naponi u vremenu t = :Presekx [m]Nt= [kN]Mt= [kNm]A [cm2]Wg [m3]Wd [m3]g [kN/cm2]d [kN/cm2]

00,00-2541,03-1,274783,330,080,07-0,530-0,533

150,00-2541,16-215,355047,840,090,07-0,252-0,755

2171,50-2501,02-70,895690,590,110,10-0,375-0,504

3l293,00-2446,3642,076333,330,140,12-0,417-0,356

3d293,00-2396,1866,286333,330,140,12-0,426-0,330

4366,25-2398,80272,525702,080,150,13-0,600-0,241

5439,50-2377,15460,964913,330,160,14-0,764-0,204

6644,60-2465,98870,835347,330,210,18-0,872-0,050

7849,70-2531,061124,035781,330,260,22-0,866-0,010

81054,80-2581,561215,266215,330,320,27-0,799-0,031

91259,90-2594,161168,956649,330,370,32-0,703-0,077

101465,00-2594,42963,567083,330,430,37-0,588-0,144

Kontrola glavnih napona zatezanja u zoni oslonca (presek 1-1):

Statiki moment gornje povrine preseka od teita:

Napon smicanja:

Glavni naponi zatezanja: za fazu eksploatacije

Kontrola koeficijenta sigurnosti od loma (presek 10-10)********* GRESKA, treba merodavan presek, 7 ili 8 u zavisnosti gde je maxM Odstojanje rezultantne sile predhodnog naprezanja od donje ivice preseka

Ekcentricitet rezultantne sile predhodnog naprezanja u odnosu na teite preseka betona

Trajni napon uadi Povrina jednog ueta

Ukupna povrina uadi

Dilatacija uadi za predhodno naprezanje

Dodatna dilatacija zbog dekompresije preseka

Dilatacija do dekompresije

Ukupna poetna dilatacija uadi:

Razlika do granice velikih izduenja

Raunski podaci za pritisnutu povrinu betona

za za Odreivanje poloaja neutralne linije x pri lomu Uslov ravnotee normalnih sila u preseku

U sluaju da je neutralna linija u rebru nosaa:

U sluaju da je neutralna linija u gornjoj flani:

(visina flane) Ukupna dilatacija elika Napon u eliku

Sila zatezanja kablova

Sila pritiska u betonu Kapacitet nosivosti preseka moment loma preseka

Udeo sile u bonim stranama flane.

Udeo sile pritiska u rebru

Moment loma preseka

Globalni koeficijent sigurnosti

Dobili smo veliki globalni koeficijent sigurnosti jer smo hteli da nam u eksploatacionoj fazi ceo presek bude pritisnut, a samim tim nemamo ni pojavu prslina i elik u nosau je zatieniji od korozije.

Adheziono predraprezanje nosaa na adhezionoj stazi se prednapreu 4 krovna nosaa duine l=29.3 mProraun gubitka sile prednaprezanjaUsled adhezionog prednaprezanja gubici usled trenja su zanemarljivo male veliine.Pad sile pri ukotvljenju ice Gubitak se rasprostire na celoj duini kabla izmeu oporaca. Gubitak sile usled uvlaenja klina iznosi poputanje klina

Presekx [cm]Nko [kN]Nko(x) [kN]

00,0016,7713549,629

150,0016,7713549,629

2171,5016,7713549,629

3l293,0016,7713549,629

3d293,0016,7713549,629

4366,2516,7713549,629

5439,5016,7713549,629

6644,6016,7713549,629

7849,7016,7713549,629

81054,8016,7713549,629

91259,9016,7713549,629

101465,0016,7713549,629

Gubitak usled elastinog skraenja

promena napona u betonu u nivou rezultujuceg kabla sila prednaprezanja rezultujueg kabla nakon gubitaka usled trenja i ukotvljenja ekcentricitet rezultujueg kabla u odnosu na teite

Presekx [cm]ek [cm]ib2[m2]Mg[kNm]Nko(x)*ebk[kN/cm2]NkoN [kN]

00,000,050,0630,0001,7780,742112,2033437,425

150,008,300,071-1,610294,5900,772116,7033432,926

2171,5028,300,093264,6401004,6231,018153,9463395,683

3l293,0048,260,119508,8801713,0491,334201,7543347,875

3d293,0048,260,119508,8801713,0491,334201,7543347,875

4366,2553,180,152644,7001887,5711,482224,0893325,540

5439,5058,560,199772,3302078,8271,609243,2193306,409

6644,6070,190,2751089,2302491,3851,383209,0843340,544

7849,7081,690,3621343,6602899,8251,232186,3193363,310

81054,8093,110,4581531,0503305,0111,136171,8173377,812

91259,90104,450,5641646,8203707,5791,076162,6943386,935

101465,00115,730,6791686,4304108,0111,040157,2603392,369

Gubitak usled relaksacije elika. teenja i skupljanja betona:

koeficijent teenja betona: skupljanje betona u vremenu t:

procenjeni pad napona u eliku kablova usled relaksacije napona: dilatacija usled relaksacije (za jedan kabl)

sila posle gubitka usled elastinih deformacija. gubitka pri ukotvljenju i gubitka usled trenja

koeficijent starenja betona: promena napona rezultujueg kabla

koeficijent efikasnostiPresekx[cm]ek[cm]Nko[kN]M[kNm]Mg[kNm]bk0 [MPa]k0[MPa]rel [MPa]k(t)[MPa]Nkt[kN]

00,000,053437,431,780,007,191364,06102,30297,082688,780,78

150,008,303432,93294,59-1,617,491362,27102,17299,492678,210,78

2171,5028,303395,681004,62264,649,911347,49101,06318,002594,310,76

3l293,0048,263347,871713,05508,8813,021328,5299,64339,912491,310,74

3d293,0048,263347,871713,05508,8813,021328,5299,64339,912491,310,74

4366,2553,183325,541887,57644,7013,471319,6698,97342,382462,740,74

5439,5058,563306,412078,83772,3314,551312,0798,41352,102419,130,73

6644,6070,193340,542491,381089,2312,931325,6199,42333,852499,240,75

7849,7081,693363,312899,831343,6611,891334,65100,10322,882549,660,76

81054,8093,113377,813305,011531,0511,241340,40100,53316,542580,120,76

91259,90104,453386,933707,581646,8210,831344,02100,80313,382597,220,77

101465,00115,733392,374108,011686,4310,621346,18100,96312,482604,920,77

Presene sileSopstvena teina konstrukcijePresekx [cm]Ng [kN]Tg [kN]Mg [kNm]

00,0000,0000,0000,000

150,0000,000227,530-1,610

2171,5000,000210,400264,640

3l293,0000,000191,320508,880

3d293,0000,000191,320508,880

4366,2500,000179,660644,700

5439,5000,000169,000772,330

6644,6000,000139,6501089,230

7849,7000,000108,0801343,660

81054,8000,00074,2801531,050

91259,9000,00038,2501646,820

101465,0000,0000,0001686,430

Kablovi za prednaprezanjePresekx [cm]Nk0 [kN]Tk0 [kN]Mk0 [kNm]

00,000-3416,854-375,504-1,712

150,000-3412,381-375,013-283,200

2171,500-3375,361-370,944-955,301

3l293,000-3327,839-365,722-1606,013

3d293,000-3347,8750,000-1615,682

4366,250-3325,5400,000-1768,408

5439,500-3306,4090,000-1936,387

6644,600-3340,5440,000-2344,634

7849,700-3363,3100,000-2747,614

81054,800-3377,8120,000-3145,034

91259,900-3386,9350,000-3537,645

101465,000-3392,3690,000-3926,013

Zbirni uticaji prilikom prednaprezanja t = 0 (sopstvena teina nosaa + kablovi)Presekx [cm]Nt=0 [kN]Tt=0 [kN]Mt=0 [kNm]

00,00-3416,854-375,504-1,712

150,00-3412,381-147,483-284,810

2171,50-3375,361-160,544-690,661

3l293,00-3327,839-174,402-1097,133

3d293,00-3347,875191,320-1106,802

4366,25-3325,540179,660-1123,708

5439,50-3306,409169,000-1164,057

6644,60-3340,544139,650-1255,404

7849,70-3363,310108,080-1403,954

81054,80-3377,81274,280-1613,984

91259,90-3386,93538,250-1890,825

101465,00-3392,3690,000-2239,583

Dodatno stalno optereenje (trapezasti lim, termoizolacija, sopst. teina ploe)Presekx [cm]Ngd [kN]Tgd [kN]Mgd [kNm]

00,000,0000,0000,000

150,000,000204,330-1,800

2171,500,000186,780235,790

3l293,000,000169,240452,070

3d293,000,000169,240452,070

4366,250,000158,660572,170

5439,500,000148,080684,510

6644,600,000118,470957,850

7849,700,00088,8501170,460

81054,800,00059,2301322,310

91259,900,00029,6201413,430

101465,000,0000,0001443,800

Povremeno optereenje sneg + vetarPresekx [cm]Np [kN]Tp [kN]Mp [kNm]

00,000,0000,0000,000

150,000,000118,290-1,040

2171,500,000108,140136,520

3l293,000,00097,980261,730

3d293,000,00097,980261,730

4366,250,00091,860331,250

5439,500,00085,730396,290

6644,600,00068,580554,550

7849,700,00051,440677,630

81054,800,00034,290765,550

91259,900,00017,150818,300

101465,000,0000,000835,880

Pad sile prednaprezanja u kablovimaPresekx [cm]Nko [kN]Tko [kN]Mko [kNm]

00,00744,16581,7820,373

150,00750,20082,44562,261

2171,50796,57287,541225,447

3l293,00851,44293,571410,906

3d293,00856,5680,000413,379

4366,25862,8010,000458,808

5439,50887,2840,000519,635

6644,60841,3060,000590,489

7849,70813,6540,000664,705

81054,80797,6900,000742,718

91259,90789,7190,000824,860

101465,00787,4460,000911,317

Presene sile u vremenu t = Presekx [cm]Nt= [kN]Tt= [kN]Mt= [kNm]

00,00-2672,69-293,722-1,339

150,00-2662,18257,583-225,389

2171,50-2578,79221,917-92,904

3l293,00-2476,40186,39027,572

3d293,00-2491,31458,54020,377

4366,25-2462,74430,180238,520

5439,50-2419,13402,810436,378

6644,60-2499,24326,700847,485

7849,70-2549,66248,3701108,841

81054,80-2580,12167,8001216,594

91259,90-2597,2285,0201165,764

101465,00-2604,920,000951,414

Kontrola normalnih napona

Normalni naponi na gornjoj ivici preseka:

Normalni naponi na donjoj ivici preseka:

Doputeni normalni naponi u betonu: faza prethodnog naprezanja MB40: - zatezanje (preporuka )

Normalni napon od prednaprezanja t = 0 (sopstvena teina nosaa + kablovi)Presekx [m]Nt=0 [kN]Mt=0 [kNm]A [cm2]Wg [m3]Wd [m3]g [kN/cm2]d [kN/cm2]

00,00-3416,85-1,714783,330,080,07-0,712-0,717

150,00-3412,38-284,815047,840,090,07-0,344-1,008

2171,50-3375,36-690,665690,590,110,100,031-1,217

3l293,00-3327,84-1097,136333,330,140,120,267019-1,318

3d293,00-3347,87-1106,806333,330,140,120,271-1,328

4366,25-3325,54-1123,715702,080,150,130,158-1,324

5439,50-3306,41-1164,064913,330,160,140,035-1,381

6644,60-3340,54-1255,405347,330,210,18-0,032-1,217

7849,70-3363,31-1403,955781,330,260,22-0,047-1,117

81054,80-3377,81-1613,986215,330,320,27-0,033-1,054

91259,90-3386,93-1890,836649,330,370,32-0,003-1,015

101465,00-3392,37-2239,587083,330,430,370,037-0,995

Normalni naponi u vremenu t = Presekx [m]Nt= [kN]Mt= [kNm]A [cm2]Wg [m3]Wd [m3]g [kN/cm2]d [kN/cm2]

00,00-2672,69-1,344783,330,080,07-0,557-0,561

150,00-2662,18-225,395047,840,090,07-0,264-0,790

2171,50-2578,79-92,905690,590,110,10-0,369-0,537

3l293,00-2476,4027,576333,330,140,12-0,411-0,371

3d293,00-2491,3120,386333,330,140,12-0,408-0,379

4366,25-2462,74238,525702,080,150,13-0,589-0,275

5439,50-2419,13436,384913,330,160,14-0,758-0,227

6644,60-2499,24847,485347,330,210,18-0,868-0,067

7849,70-2549,661108,845781,330,260,22-0,863-0,019

81054,80-2580,121216,596215,330,320,27-0,800-0,031

91259,90-2597,221165,766649,330,370,32-0,703-0,079

101465,00-2604,92951,417083,330,430,37-0,587-0,149

Kontrola glavnih napona zatezanja u zoni oslonca (presek 1-1):

Statiki moment gornje povrine preseka od teita:

Napon smicanja:

Glavni naponi zatezanja: za fazu eksploatacije

Kontrola koeficijenta sigurnosti od loma (presek 10-10)******** GRESKA, treba merodavan presek, 7 ili 8 u zavisnosti gde je maxM Odstojanje rezultantne sile predhodnog naprezanja od donje ivice preseka

Ekcentricitet rezultantne sile predhodnog naprezanja u odnosu na teite preseka betona

Trajni napon uadi Povrina jednog ueta

Ukupna povrina uadi

Dilatacija uadi za predhodno naprezanje

Dodatna dilatacija zbog dekompresije preseka

Dilatacija do dekompresije

Ukupna poetna dilatacija uadi:

Razlika do granice velikih izduenja

Raunski podaci za pritisnutu povrinu betona

za za Odreivanje poloaja neutralne linije x pri lomu Uslov ravnotee normalnih sila u preseku

U sluaju da je neutralna linija u rebru nosaa

U sluaju da je neutralna linija u gornjoj flani

(visina flane) Ukupna dilatacija elika Napon u eliku

Sila zatezanja kablova

Sila pritiska u betonu Kapacitet nosivosti preseka moment loma preseka

Udeo sile u bonim stranama flane.

Udeo sile pritiska u rebru

Moment loma preseka

Globalni koeficijent sigurnosti

Dobili smo veliki globalni koeficijent sigurnosti jer smo hteli da nam u eksploatacionoj fazi ceo presek bude pritisnut, a samim tim nemamo ni pojavu prslina i elik u nosau je zatieniji od korozije.

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