Primer proracuna Prednapregnutog nosača
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Transcript of Primer proracuna Prednapregnutog nosača
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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