ekler

EKLER

Prof. Dr. Ahmet TOPU, Betonarme I, Eskiehir Osmangazi niversitesi, 2011, http://mmf2.ogu.edu.tr/atopcu

192

Ek1:BETON SINIFLARI ve MEKANK ZELLKLER (28 GNLK BETON) Beton Snf fck 2 N/mm Kp silindir (15x15x15) fctk 2 N/mm

cu0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003

k1

Ec Gc 0.4Ec 2 2 N/mm N/mm

c0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20

c1/C

Ek3:Dikdrtgen kesitli kirilerde dengeli donat oranlar S220 S220 S220 S220 S420 S420 S420 S420 S420 S420 S420 S420 S420 S500 S500 S500 S500 S500 S500 S500 S500 S500NOT:

C16/20 C18/22 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60

16 18 20 25 30 35 40 45 50

20 22 25 30 37 45 50 55 60

1.4 1.5 1.6 1.8 1.9 2.1 2.2 2.3 2.5

0.85 0.85 0.85 0.85 0.82 0.79 0.76 0.73 0.70

27000 27789 28534 30250 31800 33227 34555 35802 36981

10800 11116 11414 12100 12720 13291 13822 14321 14792

10-5 10-5 10-5 10-5 10-5 10-5 10-5 10-5 10-5

Ec = 3250 fck + 14000 Bantsndan hesaplanmtr. TS 500/2000 de bu deerleryuvarlatlmtr. Her iki deer de kullanlabilir.

Ek2:ELK SINIFLARI ve NEKANK ZELLKLER fyk elik snf S220a S420a S500a S420b S500bs S500bk BI-a BIII-a BIV-a BIII-b BIV-bs BIV-bk(N/mm2)

Es(N/mm2)

fyd(N/mm2)

sd0.000957 0.001826 0.002174 0.001826 0.002174 0.002174

fsu(N/mm2)

Min. Kopma uzamas su

32 mm0.18 0.12 0.12 0.10 0.08 0.05

32 mm0.18 0.10 0.10 0.10 0.08 0.05

Yzey D N, P N, P N, PHasr

220 420 500 420 500 500

2x105 2x105 2x105 2x105 2x105 2x105

191.30 365.22 434.78 365.22 434.78 434.78

340 500 550 550 550 550

S220 ve S500 elii kiri ve kolonlarda kullanlamaz (Bak: Dep. Yn.-2007, Madde 3.2.5.3). S420b eliinin kullanmndan kanlmaldr. C16/20 ve C18/22 betonlar deprem blgelerinde kullanlamaz (bak: Dep. Yn-2007, Madde 3.2.5.1)193

N, P N, P


Deprem blgelerinde kullanlamaz

C16/20 C18/22 C20/25 C25/30 C16/20 C18/22 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 C16/20 C18/22 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60

Yeni yaplar iin

Eski yaplar iin

elik Beton

mc=1.4 0.0327 0.0368 0.0409 0.0511 0.0141 0.0158 0.0176 0.0220 0.0254 0.0286 0.0314 0.0339 0.0362 0.0110 0.0124 0.0138 0.0172 0.0199 0.0224 0.0246 0.0266 0.0283

mc=1.5 0.0305 0.0382 0.0378 0.0477 0.0131 0.0148 0.0164 0.0205 0.0237 0.0267 0.0293 0.0317 0.0338 0.0103 0.0116 0.0128 0.0161 0.0186 0.0209 0.0230 0.0248 0.0264

mc=1.7 0.0270 0.0303 0.0337 0.0421 0.0116 0.0130 0.0145 0.0181 0.0209 0.0235 0.0259 0.0280 0.0298 0.0091 0.0102 0.0113 0.0142 0.0164 0.0184 0.0203 0.0219 0.0233

Ek4:DONATI UBUKLARI KTLE ve ALANLARI (mm2) ap (mm) Ktle kg/m ubuk says 1 2 3 4 5 6 7 8 9 10 11 12 13 14396 704 1100 1583 2155 2815 3563 4398 5322 6333 6872 7433 8621 9896 11259 17593

15424 754 1178 1696 2309 3016 3817 4712 5702 6786 7363 7964 9236 10603 12064 18850

0.222 28 0.57 085 113 141 170 198 226 254 283 311 339 368 6 0.395 50 1.01 151 201 251 302 352 402 452 503 553 603 653 8 0.617 79 157 236 314 393 471 550 628 707 785 864 942 1021 10 0.888 113 226 339 452 565 679 792 905 1018 1131 1244 1357 1470 12 1.209 154 308 462 616 770 924 1078 1231 1385 1539 1693 1847 2001 14 1.579 201 402 603 804 1005 1206 1407 1608 1810 2011 2212 2413 2614 16 1.998 254 509 763 1018 1272 1527 1781 2036 2290 2545 2799 3054 3308 18 2.467 314 628 942 1257 1571 1885 2199 2513 2827 3142 3456 3770 4084 20 2.985 380 760 1140 1520 1901 2281 2661 3041 3421 3801 4181 4561 4942 22 3.522 452 905 1357 1810 2262 2714 3167 3619 4071 4524 4976 5429 5881 24 3.854 491 982 1473 1963 2454 2945 3436 3927 4418 4909 5399 5890 6381 25 4.169 531 1062 1593 2124 2655 3185 3716 4247 4778 5309 5840 6371 6902 26 4.834 616 1232 1847 2463 3079 3695 4310 4926 5542 6158 6773 7389 8005 28 5.549 707 1414 2121 2827 3534 4241 4948 5655 6362 7069 7775 8482 9189 30 6.315 804 1608 2413 3217 4021 4825 5630 6434 7238 8042 8846 9651 10455 32 9.867 1257 2513 3770 5026 6283 7540 8796 10053 11309 12566 13823 15079 16336 40 10 mm ubuklar kiri ve kolonlarda boyuna donat olarak kullanlmazlar. 6 eski yaplar iindir, yeni yaplarda kullanlmaz.

alanlar

Ek5:Kiri veya kolonlarda bir sraya san ubuk saysbw(mm)

Ek6:14 3 4 5 6 8 9 10 11 12 13 14 16 17 18 19 20 21 16 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 20 18 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ap (mm) 22 24 25 3 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 10 12 12 11 13 13 12 14 13 13 15 14 14 16 15 15 17 16 16 18 17 17

Dili demelerde bir die san ubuk saysbw(mm)

28 30 32 40 2 2 2 2 3 3 3 2 4 4 3 3 5 5 4 3 6 5 5 4 6 6 6 5 7 7 7 5 8 8 7 6 9 9 8 7 10 10 9 7 11 10 10 8 12 11 10 8 12 12 11 9 13 13 12 10 14 14 13 10 15 15 14 11 16 15 14 12 Net beton rts 30 mm, net donat aral 30 mm ve etriye ap 22 iin 8 mm, 24 iin 10 mm alnmtr. 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000bw= 200 mm eski yaplarn kontrol amaldr.

12 3 4 6 7 8 9 10 12 13 14 15 16 17 19 20 21 22

26 2 3 4 5 6 7 8 8 9 10 11 12 13 14 15 16 16

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200

10 12 2 2 2 2 2 2 2 2 3 2 3 3 3 3 3 3 3 3 3 3 4 3 4 4 4 4 4 4 4 4 4 4 5 4 5 4 5 5 5 5 5 5

ap (mm) 14 16 18 20 2 2 2 0 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 3 3 2 2 3 3 3 2 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 4 4 3 3 4 4 3 3 4 4 4 3 4 4 4 3 4 4 4 4 4 4 4 4 5 4 4 4

22 0 0 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4

Net beton rts 15 mm, net donat aral 20 mm ve etriye ap 8 mm alnmtr.


194

Ek7: Uygulamada karlalan demelerin ou 1.Dikdrtgen geometrilidir 2.Dzgn yayl ykle ykldr 3.Drt tarafndan kirilere otururlar.

TS 500-2000 tablolar ile moment hesab

TS 500-2000, Sayfa: 56

Bu koula uyan demelerin momentleri TS 500-2000 izelge 11.1, sayfa 56 da verilen tablo yardmyla ok basit bir yolla hesaplanr. Bu tablonun benzeri aada verilmitir. Tabloda kenarlarn srekli veya sreksiz olmasna bal olarak 7 farkl deme tipi vardr. Demenin ortasndan geen her iki dorultudaki 1 m lik eritlerin aklk ve mesnetlerinde oluan Mxm, Mxe, Mym ve Mye tasarm momentleri

Md =

1 1000

pLd

2 knet

bantsndan hesaplanrlar. Momentin birimi kN.m/m dir.

Drt kenarndan kirilere oturan demelerde saylarKsa aklk dorultusunda Uzun aklk dorultusunda (m den bamsz)

m=

Lu Lk

Md : Demenin aklk veya srekli kenarndaki Mxm, Mxe, Mym veya Mye tasarm momentlerinden herhangi biri Pd : Deme stnde dzgn yayl olan tasarm yk Lknet: ksa dorultudaki net aklk (ok geni olmayan kirilerde LknetLk alnabilir)

1.0

1.1-40 +30 -47 +35 -56 +42 -61 +46 000 +53 -65 +49 000 +57

1.2-45 +34 -53 +40 -62 +47 -65 +49 000 +60 -71 +54 000 +62

1.3-50 +38 -57 +43 -66 +50 -69 +51 000 +65 -77 +58 000 +67

1.4-54 +41 -61 +46 -70 +53 -71 +53 000 +68 -81 +61 000 +71

1.5-59 +45 -65 +49 -73 +55 -73 +55 000 +71 -85 +64 000 +75

1.75-70 +53 -75 +56 -82 +62 -77 +58 000 +77 -92 +69 000 +81

2.0-83 +62 -85 +64 -90 +68 -80 +60 000 +80 -98 +74 000 +83 -33 +25 -41 +31 -49 +37 000 +44 -56 +44 -58 +44 000 +50

1 2Deme tipleri

-33 +25

2 3 4 5

-42 +31 -49 +37 -56 +44 000 +44

: Tablodan alnacak katsay. Ksa dorultuda m=Lu/Lk oranna bal olarak deiir, uzun dorultuda m den bamszdr.Lu : Uzun kenar, Lx ve Ly den byk olan. Lk : Ksa kenar, Lx ve Ly den kk olan.195

6 7

6

-58 +44 000 50

saylar

Art deerler aklk momentlerine, eksi deerler mesnet momentlerine ait deeridir. Buradaki saylar TS 500-2000 deerlerinin 1000 katdr.Prof. Dr. Ahmet TOPU, Betonarme I, Eskiehir Osmangazi niversitesi, 2011, http://mmf2.ogu.edu.tr/atopcu

Ek8:

ETMEL tablolar (iki rnek)1Bir kenar bota dzgn yayl ykl plak:K = pd Lx L y , = Ly Lx0.7 15.3 -5.3 29.2

, Md =0.8 15.1 -6.5 26.7

K

0.9 15.4 -7.0 25.4 1.0 16.0 -7.6 24.8

Lx bota kenara paralel kenardr 1.1 16.8 -8.3 24.6 1.2 17.9 -9.0 24.8 1.3 19.0 -9.7 25.1 1.4 20.2 1.5 21.5 saylar

Mxr Ly 1m Mxe1 Mxm Mxe Mym Mye

0.25 0.3 58.3 -10.8 43.3 -8.7

0.4 27.0 -6.8 61.7

0.5 19.5 -6.1 43.3

0.6 16.5 -6.0 34.0

-10.5 -11.2 25.6 26.2

118.0 97.0

-27.6 -22.3 -16.9 -14.2 -12.6 -56.1 -68.5 -183.0 254.0 109.0 -9.0 -8.2 -7.6 -7.7 -8.2

-11.8 -11.3 -11.2 -11.2 -11.4 -11.7 -12.0 -12.4 -12.9 82.0 -8.9 75.4 -9.8 76.2 81.6 90.1 102.0 118.0 138.0 163.0

Mxe

-10.8 -11.9 -13.2 -14.3 -15.6 -17.0 -18.4

Bota kenar dzgn yayl izgisel ykl plak:- Mxe1 + Mxr r 1m m e e1 Pd (kenar boyunca dzgnyayl izgisel yk)

K = pd L x , =

Ly Lx

, Md =

K

0.9 5.6 -1.8 18.8 1.0 5.5 -1.8 20.9 5.5 -1.8

Lx bota kenara paralel kenardr 1.1 1.2 5.5 -1.8 27.5 1.3 5.5 -1.8 32.2 1.4 5.5 -1.8 38.0 -37.2 -42.2 1.5 5.5 -1.9 45.5 -46.3 -48.2 saylar

Mxr Mxe1 Mxm

0.25 0.3 22.2 -3.9 73.0 16.8 -3.1 50.8

0.4 10.6 -2.3 30.3

0.5 7.8 -2.0 21.3

0.6 6.52 -1.9 18.1

0.7 0.8 6.0 -1.8 17.2 5.7 -1.8 17.5

23.8

e Lx - Mxe +

Mxe Mym Mye

-14.9 -12.8 -11.0 -10.5 -10.7 -11.4 -12.7 -14.5 -17.0 -20.3 -24.5 -30.0 -11.3 -11.4 -12.8 -15.0 -17.4 -19.6 -21.7 -23.9 -26.5 -29.5 -32.9 -37.0 -4.9 -4.7 -4.8 -5.6 -7.1

-9.4 -12.9 -18.4 -26.8 -39.8 -60.6 -93.5 -148.0 -239.0

Mxm-------------------------------------1etmeli,

E., Plaklar, T yayn, No.19, 1987.Prof. Dr. Ahmet TOPU, Betonarme I, Eskiehir Osmangazi niversitesi, 2011, http://mmf2.ogu.edu.tr/atopcu

196

Ek9:100 cm deme genilii iin donat alanlar (mm2) t (cm)6 5.05.5

(mm)8 1005914

10 15711428

12 22622056

14 30792799

16 40213656

18 50894627

20 62835712

22 76036912

24 90408225

565514

6.06.5

472435

838773

13091208

18851740

25662368

33513093

42413915

52364833

63365848

75406960

7.07.5

404377

718670

11221047

16161508

21992052

28732681

36363393

44874188

54305068

64636032

8.08.5

353333

628591

982924

14141331

19241811

25142366

31812994

39263695

47514472

56555322

9.09.5

314298

559529

873827

12571190

17101620

22342117

28282679

34903306

42234001

50274762

10.010.5

283269

503479

785748

11311077

15391466

20111915

25452424

31412991

38013620

45244309

h: plak kalnl(mm) d: faydal ykseklik(mm) : ubuk ap(mm) t: iki ubuk merkezi aras(cm) As: 100 cm plak eridindeki donat alan(mm2)

11.011.5

257246

457437

714683

1028983

13991339

18281749

23142213

28552731

34553305

41133934

As =

12.012.5

236226

419402

654628

942905

12831232

16761609

21212036

26172513

31673041

37703619

100 2 2 = 78.5398 t 4 t

13.013.5

217209

387372

604582

870838

11841140

15471490

19581885

24162327

29242816

34803351

14.014.5

202195

359347

561542

808780

11001062

14361387

18181755

22442166

27152621

32313120

Alanlar=As

15.015.5

189182

335324

524507

754730

1026993

13411297

16971642

20942027

25342452

30162919

16.016.5

177171

314305

491476

707685

962933

12571219

15901542

19641904

23762304

28282741

17.017.5

166162

296287

462449

665645

905880

11831149

14971454

18481795

22362172

26612585

18.018.5

157153

279272

436425

628611

855832

11171087

14141376

17461698

21122055

25132445

Not: 6 eski projelerin kontrol amaldr. Yeni projelerde kullanlmaz. Seilen donatn aral 1.5 h deerini amamaldr! Donat araln 1.5 h ya yakn semek ekonomiktir.

19.019.5

149145

265258

413403

595580

810789

10581031

13391305

16541611

20011949

23812320

20.021.0

141135

251239

393374

565539

769733

1005957

12721212

15721496

19011810

22622154

22.023.0

129123

228219

357341

514492

700669

914874

11571106

14281366

17281653

20561967

24.025.0

118113

209201

327314

471452

641616

838804

10601018

13091257

15841521

18851810

26.027.0

109105

193186

302291

435419

592570

773745

979942

12081164

14621408

17401676

28.029.0

101097

180173

280271

404390

550531

718693

909877

11221083

13581311

16161560

30.031.0

094091

168162

262253

377365

513497

670649

848821

10471013

12671226

15081459

32.033.0

088086

157152

245238

353343

481466

628609

795771

982952

11881152

14141371


197

Ek10:

AYDIN/AKGN/TOPU Kolon Tablolar1Kolon donat planlarMydb1

Mydb1 h1

Mydb1 h1

Mydb1

Ast/4

Ast/4

Ast/2

Ast/4

3/8 Ast

Ast/4

NdAst/4 b Ast/4

Mxd

NdAst/2 b

Mxd

Ast/4

NdAst/4 b

Mxd

Nd3/8Ast b

Mxd

h

Donat plan 1

Donat plan 2

h

Donat plan 3

Donat plan 4

n=

Nd b h f cd 100 M xd b h 2 f cd 100 M yd b 2 h f cd f cd bh 100 f yd

Ast toplam donat alandr. n, mx ve my deerlerine ve elik snfna bal olarak deeri tablodan alnr. Varsaymlar: Basn blou modeli: edeer dikdrtgen. cu=0.003 k1=0.85 Elasto-plastik elik: s=Essfyd su=0.10 b1/b=h1/h=0.10

mx = my = A st =

----------------------1Aydn,

M. R., Akgn, . R., Topu, A. Betonarme Kolon Tablolar, Eskiehir, 1991Prof. Dr. Ahmet TOPU, Betonarme I, Eskiehir Osmangazi niversitesi, 2011, http://mmf2.ogu.edu.tr/atopcu

198

AYDIN/AKGN/TOPU Kolon TablolarMydb1

n=Ast/4 Ast/4

Nd b h f cd

elik: S420Ast toplam donat alandr. n, mx ve my deerlerine bal olarak tablodan alnr. Varsaymlar: Basn blou modeli: edeer dikdrtgen. cu=0.003 k1=0.85 Elasto-plastik elik: s=Essfyd su=0.10 b1/b=h1/h=0.10

100 M xd mx = b h 2 f cdMxd

NdAst/4 b Ast/4

my = A st =

100 M yd b 2 h f cd f cd bh 100 f yd

Donat plan 1

n=0

n=0.1

saylar


199

Mydb1

AYDIN/AKGN/TOPU Kolon Tablolarn= Nd b h f cd


Ast/4

Ast/4

NdAst/4 b Ast/4

Mxd

100 M xd mx = b h 2 f cd my = A st = 100 M yd b 2 h f cd f cd bh 100 f yd

Donat plan 1

n=0.2

n=0.3


200


n=Ast/4 Ast/4

Nd b h f cd


NdAst/4 b Ast/4

Mxd


Donat plan 1

n=0.4

n=0.5


201


n=Ast/4 Ast/4

Nd b h f cd


NdAst/4 b Ast/4

Mxd


Donat plan 1

n=0.6

n=0.7


202


n=Ast/4 Ast/4

Nd b h f cd


NdAst/4 b Ast/4

Mxd


Donat plan 1

n=0.8

n=0.9


203

AYDIN/AKGN/TOPU Kolon TablolarMydb1 h1

n=

Ast/2

Nd b h f cd


NdAst/2 b

Mxd


h

Donat plan 2

n=0

n=0.1


204


n=

Ast/2

Nd b h f cd


NdAst/2 b

Mxd


h

Donat plan 2

n=0.2

n=0.3


205


n=

Ast/2

Nd b h f cd


NdAst/2 b

Mxd


h

Donat plan 2

n=0.4

n=0.5


206


n=

Ast/2

Nd b h f cd


NdAst/2 b

Mxd


h

Donat plan 2

n=0.6

n=0.7


207


n=

Ast/2

Nd b h f cd


NdAst/2 b

Mxd


h

Donat plan 2

n=0.8

n=0.9


208


n=

Ast/4

Nd b h f cd


Ast/4

Ast/4

NdAst/4 b

Mxd


h

Donat plan 3

n=0

n=0.1


209


n=

Ast/4

Nd b h f cd


Ast/4

Ast/4

NdAst/4 b

Mxd


h

Donat plan 3

n=0.2

n=0.3


210


n=

Ast/4

Nd b h f cd


Ast/4

Ast/4

NdAst/4 b

Mxd


h

Donat plan 3

n=0.4

n=0.5


211


n=

Ast/4

Nd b h f cd


Ast/4

Ast/4

NdAst/4 b

Mxd


h

Donat plan 3

n=0.6

n=0.7


212


n=

Ast/4

Nd b h f cd


Ast/4

Ast/4

NdAst/4 b

Mxd


h

Donat plan 3

n=0.8

n=0.9


213


n=3/8 Ast

Nd b h f cd


Nd3/8Ast b

Mxd


Donat plan 4

n=0

n=0.1


214


n=3/8 Ast

Nd b h f cd


Nd3/8Ast b

Mxd


Donat plan 4

n=0.2

n=0.3


215


n=3/8 Ast

Nd b h f cd


Nd3/8Ast b

Mxd


Donat plan 4

n=0.4

n=0.5


216


n=3/8 Ast

Nd b h f cd


Nd3/8Ast b

Mxd


Donat plan 4

n=0.6

n=0.7


217


n=3/8 Ast

Nd b h f cd


Nd3/8Ast b

Mxd


Donat plan 4

n=0.8

n=0.9


218

Ek11:

Nd A c f cd

m

S220a=1 .

d/h=0.750

U. ERSOY Kolon abaklar11 ERSOY,

0. 9 0. 8 0.7 0. 6

U., v.d., Tama Gc El Kitab, ODT, Ankara, 1980

0. 1

0.4 0.3 0.2

5 0.

As: bir ubuun alan Ast: ubuklarn toplam alan Ac: Brt beton alan : donat oran m=fyd/fcd = Ast/Ac Ac= h2/4

UYARI: S220a snf elik yeni yaplarda boyuna donat olarak kullanlamaz. Bu sayfadaki abaklar eski yaplarn kontrol amacyla verilmitir.

Md A c hf cdNd A c f cdm

=1 .00.9

S220ad/h=0.85

Nd A c f cd

m

0.4 0.3 0.2 0.1

0.8 0.7 0.6 0.5

0. 8 0.7 0. 6

0 0. 9

=1 .

S220ad/h=0.95


0.4 0.3 0.2 0. 1

5 0.


Md A c hf cdProf. Dr. Ahmet TOPU, Betonarme I, Eskiehir Osmangazi niversitesi, 2011, http://mmf2.ogu.edu.tr/atopcu

Md A c hf cd

219

U. ERSOY Abaklar

Nd A c f cd

S420a ve S420bm =1 .2

d/h=0.754

1.

1. 0 0. 9 0. 8 0. 7 0. 65 0. .4 0 3 0. . 2 0 .1 0


m=fyd/fcd t= As/Ac Ac= h2/4

Md A c hf cdNd A c f cdm

=1 .

S420a ve S420b4

d/h=0.85

Nd A c f cd

m

=1 .

4

S420a ve S420bd/h=0.95

1. 2 1. 0 0. 9 0. 8 0. 7 0. 6

1. 2 1. 0 0. 0. 9 8 0. 7 0. 65 0. 0.4

0. 3 0. 2


0.

0. 3 2


5 0. 0.4

1 0.

1 0.


Md A c hf cd220

Nd A c f cd

S220ahi/h=0.6 d/h=0.75

MdAs+

Nd A c f cd

S220a hi/h=0.6 d/h=0.95

MdAs+

Nd

Nd

m

9 0. 0.7 8 0.6 0.4 0.5 0. 0.2 3 0.1

=1 0. .0

hi d h

m

As: bir ubuun alan Ast: ubuklarn toplam alan Ac: Brt beton alan Acn: Net beton alan : donat oran m=fyd/fcd = Ast/Acn Ac= h2/4 Acn= (h2-hi2)/4

9 0.8 0.7 0.6 0 0.4.5 0.3 0.2 0.1

=1 0. .0

As: bir ubuun alan/Acn t= As Ast: ubuklarn toplam alan Ac= h2/4 Ac: Brt beton alan 2-h 2)/4 Acn= (h i Acn: Net beton alan : donat oran m=fyd/fcd = Ast/Acn Ac= h2/4 Acn= (h2-hi2)/4

hi d h m=fyd/fcd

Md A c hf cd

Md A c hf cd

Nd A c f cdm

S220ahi/h=0.8 d/h=0.75As+

Md

Nd A c f cdm

S220ahi/h=0.8 d/h=0.95As+

Md

Nd

Nd

0.9 0.8 0.7 0.6 0.4 0. 5 0.3 0.2 0.1

=1 .0

hi d h


0.9 0.8 0.7 0.6 0.4 0.5 0. 0.2 3 0.1

=1 .0

As: bir ubuun salan t= A /Acn Ast: ubuklarn toplam alan Ac= h2/4 Ac: Brt beton (h2-h 2)/4 Acn= alan Acn: Net beton alan i : donat oran m=fyd/fcd = Ast/Acn Ac= h2/4 Acn= (h2-hi2)/4

hi d m=fyd/fcd h

U. ERSOY Abaklar

UYARI: S220a snf elik yeni yaplarda boyuna donat olarak kullanlamaz. Bu sayfadaki abaklar eski yaplarn kontrol amacyla verilmitir.Prof. Dr. Ahmet TOPU, Betonarme I, Eskiehir Osmangazi niversitesi, 2011, http://mmf2.ogu.edu.tr/atopcu

Md A c hf cd

Md A c hf cd221

Nd A c f cdm

S420a ve 420bhi/h=0.6 d/h=0.75As+

Md

Nd A c f cdm

S420a ve 420bhi/h=0.6 d/h=0.95=1 .4hi d h As+

Md

Nd

Nd

=1 .41.2

1.0 0..9 09 0. 0.7 8 0.6 0.4 0.5 0. 0. 3 0.1 2

As: bir alan Ast: ubuklarn toplam alan Ac: Brt beton alan Acn: Net beton alan : donat oran m=fyd/fcd = Ast/Acn Ac= h2/4 Acn= (h2-hi2)/4

hi d h ubuun

1.2 1.0 0.9 0. 0.7 8 0.5 0.6 0.4 0.2 0.3 0.1


Md A c hf cdNd A c f cd

Md A c hf cdNd A c f cd

S420a ve 420b=1 .4

MdAs+

m

hi/h=0.8 d/h=0.75

S420a ve 420b=1 .4

MdAs+

m

hi/h=0.8 d/h=0.95

Nd

Nd

1.2 1.0 0.9 0.8 0.7 0.6 0.4 0.5 0.3 0.2 0.1

1.2

hi d h


1.0 0.9 0.8 0.7 0.6 0.4 0.5 0.3 0.2 0.1

hi d h



Md A c hf cdU. ERSOY Abaklar222

Ek12: EDEER PARABOL - DKDRTGEN GERLME DAILIMININ ZELLKLERGerilmenin tarafsz eksen ile c0 arasnda 20 derece parabol, c0 ile cu arasnda dikdrtgen dald varsaylr. TS 500 /2000 de c0 = 0.002, cu = 0.003, fc = 0.85fcd dir. cu2f 5

fc

0.003

0.85f cd

3f 5

3a 8

cu c 0 c cu

1c 3 c0 fc0.0020.85f cd

a

5a 8

G : Arlk merkezi Paraboln alan = 2 af 3 2 f y(x) = a ( 2x x 2 ) a

c0 c cu

c

c

2c 3

c

c

c = x cu c c0 0 x < cu c arasnda : Parabol ksmn alan = 2 3c ( c ) = f c (2 c0 ) 2 c 2 0

c0 cu

cf c

Dikdrtgen ksmn alan = cu c0 c f c cu ( c ) = f cProf. Dr. Ahmet TOPU, Betonarme I, Eskiehir Osmangazi niversitesi, 2011, http://mmf2.ogu.edu.tr/atopcu

c0 cu

c x c arasnda :

c x c arasnda : Dikdrtgen ksmn alan = 1 c 0.85f cd 3 ( c ) = 0.85f cd2 3

c = x cu c 0 x < 2 c arasnda : 3 4 Parabol ksmn alan = 9 c 0.85f cd 2 c ( c ) = 0.85f cd (2 0.002 c 2 )0.002

223

RNEK: Edeer parabol-dikdrtgen gerilme dalmGenilii 250 mm, ykseklii 600 mm olan dikdrtgen kesitli bir kiriin aklk kesitinde gvenle tamas gereken moment 125 kN.m dir. Malzeme C20/25/S420a, beton rts 40 mm, antiye denetimi iyidir. Edeer parabol-dikdrtgen gerilme dalm varsaym ile gerekli ekme donats alann belirleyiniz.

Malzeme bilgileri : f cd = 20 / 1.5 = 13.33 N/mm 2 , f ctd = 1.6 / 1.5 = 1.07 N/mm 2

c0 = 0.002, cu = 0.003, k1 = 0.85, b = 0.0164f yd = 420 / 1.15 = 365.22 N/mm 2 , yd = 0.0018261c 3

1c 61c 6 1c 45 c 12

Kuvvetler : Fc1 = 1 c0.85 f cd bw = 1 c0.85 13.33 250 = 944.21c 3 34 4 Fc 2 = 9 c0.85 f cd bw = 9 c0.85 13.33 250 = 1258.94c

2c 3

Fs = As f yd = As 365.22 Tarafsz eksen :5 Fc1 (d 1 c) + Fc 2 (d c + 12 c) = M d 6 7 944.21c(560 1 c) + 1258.94c(560 12 c) = 125 106 6

c 2 1278.51c + 139664.80 = 0 c1 = 110.1mm, c2 = 1268 mm c = 110.1 mm Donat alan : Fc1 + Fc 2 = Fs 944.21c + 1258.94c = As 365.22 944.21110.1 + 1258.94 110.1 = As 365.22 As = 664 mm 2 Kontrol : =664 260560

= 0.0047 < 0.85 b = 0.85 0.0164 = 0.01394 < 0.02 > 0.08 fctd = ydf 1.07 365.22

= 0.0023224


RNEK: Edeer dikdrtgen gerilme dalmGenilii 250 mm, ykseklii 600 mm olan dikdrtgen kesitli bir kiriin aklk kesitinde gvenle tamas gereken moment 125 kN.m dir. Malzeme C2025/S420a, beton rts 40 mm, antiye denetimi iyidir. Edeer dikdrtgen gerilme dalm varsaym ile gerekli ekme donats alann belirleyiniz.

Malzeme bilgileri : f cd = 20 / 1.5 = 13.33 N/mm 2 , f ctd = 1.6 / 1.5 = 1.07 N/mm 2

c0 = 0.002, cu = 0.003, k1 = 0.85, b = 0.01640.003 0.85fcd

f yd = 420 / 1.15 = 365.22 N/mm 2 , yd = 0.001826Fc

Kuvvetler : Fc = 0.85c0.85 f cd bw = 0.85 0.85 13.33 250c = 2407.73c Fs = As f yd = As 365.22 Tarafsz eksen : Fc (d 0.425c) = M d 2407.73c(560 0.425c) = 125 106 c 2 1320.27c + 122399.02 = 0 c1 = 100.3 mm, c2 = 1219.9 mm c = 100.3 mm

Md=125 kN.m

Tarafsz eksen

As

As

Fs Gerilme dalm

Donat alan : Fc = Fs 2407.73c = As 365.22 2407.73 100.3 = As 365.22 As = 661 mm 2 Kontrol : =661 260560

bw=250

Deformasyon

= 0.0047 < 0.85 b = 0.85 0.0164 = 0.01394 < 0.02 > 0.08 ffctd = yd1.07 365.22

= 0.0023

Edeer dikdrtgen gerilme dalm modeli kullanlarak As=661 mm2, edeer parabol-dikdrtgen gerilme dalm modelli kullanlarak As=664 mm2 bulundu. Grld gibi aralarndaki fark nemsenmeyecek kadar azdr.Prof. Dr. Ahmet TOPU, Betonarme I, Eskiehir Osmangazi niversitesi, 2011, http://mmf2.ogu.edu.tr/atopcu

225

Ek13: EMATK YAPIM HATALARI

Betonarme yaplarn inasnda yaplan hatalarn ematik gsterimi (biraz deitirilmi).Mehmet Ali TADEMR ve dierleri, Betonun Performansna Gre Tasarmnda Yeni Gelimeler, THBB.


226

ekler

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