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indekilerUluslararas Kat lleri..............................................................................................................................................................................................................................3 In - Metrik Sistem Dnm Tablosu / nemli Deerler ........................................................................................................................................................4 Mhendislikte Sk Kullanlan Metrik Birimlerin SI Birimlerine evirme Tablosu / SI Sisteminde Temel Birimler / Temel Birimlerden retilmi Dier Birimler ..................................................................................................................5 Temel Birimlerden retilmi Dier Birimler .......................................................................................................................................................................................6 l Deiim Tablosu.................................................................................................................................................................................................................................7-9 Dzlemsel Geometrik ekillerin zellikleri................................................................................................................................................................................10-12 Arlk Merkezleri ..............................................................................................................................................................................................................................................13 Alan - evre.................................................................................................................................................................................................................................................14-16 Hacimler.................................................................................................................................................................................................................................................................17 Hacimler.........................................................................................................................................................................................................................................................18-20 Alan - Hacim ...............................................................................................................................................................................................................................................21-22 Yap Yaklak Maliyeti Hesab...................................................................................................................................................................................................................23 1 m3 Harta Kullanlacak Malzeme Miktar.......................................................................................................................................................................................24 imento eitleri ..............................................................................................................................................................................................................................................25 Yap Malzemeleri ve Yap Ksmlarnn Birim Hacim Arlklar.....................................................................................................................................26-27 Balca Malzeme Younluklar ................................................................................................................................................................................................................28 atlaklarn Oluum Yerleri ve Biimleri..............................................................................................................................................................................................29 Taze veya Sertlemi Betonda Grlen atlak Tiplerinin Snflandrlmas ..................................................................................................................30 Beton veya Betonarme Yaplarn ve D Etkenlerle Bozulmas ......................................................................................................................................31 Betonun evre Etkileriyle lgili Etki Snflar ...............................................................................................................................................................................32-33 Beton Snflar ve Dayanmlar (TS500) / Donat eliklerinin Mekanik zellikleri (TS500) .................................................................................34 Beton elik ubuklarnn Kesit Alanlar (cm2) / Kirilerin (bo) Genilii (cm) ve (As) Donats (cm2)..........................................................35 Plaklarda 100 cm Genilik in Donat Alanlar (cm2) / Kayma Donats in ift Tesirli Etriye Deerleri (cm2) .....................................36 Kayma Donats in Pilye Fs 2x Fe Deerleri / Kirilerde Kabul Edilebilecek Pilye (Eim-Krm) Boylar .................................................37 Yuvarlak Betonarme elik ubuu (B.A. Demiri) / Nervrl Betonarme elik ubuklar .................................................................................38 Standart elik Hasrlar (TS 4559) / elik Hasr Kesit Tablosu ............................................................................................................................................39 elik Hasr Birim Arln (Kg/m2) / Standart elik Hasr Kesit Tablosu: (R) Tipi ..................................................................................................40 Standart elik Hasr Kesit Tablosu: (Q) Tipi.....................................................................................................................................................................................41 Yap elikleri in Emniyet Gerilmeleri (ekme ve Kayma Emniyet Gerilmeleri) Normal Yap elii le Yaplan Yaplarda Birleim Aralarnn Emniyet Gerilmeleri...............................................................................................42 Kaynak Dikileri in Emniyet Gerilmeleri (Kgf/cm2) / Mesnet ve Mafsallarda Emniyet Gerilmeleri..............................................................43 at rtleri..........................................................................................................................................................................................................................................................44 aty Oluturan Eleman Boyutlar / eitli rt Malzemesine Gre at Eimleri .................................................................................................45 eitli Metallerle ilgili Yardmc Tablolar.....................................................................................................................................................................................46-50 Scak Haddelenmi elik Lamalar(TS 3024)..................................................................................................................................................................................51 Yuvarlak ve Drt Keli elik Arlklar .............................................................................................................................................................................................52 nce Etli Kare ve Dikdrtgen Profilleri (TS 6475)...........................................................................................................................................................................53 Kaln Etli Dikdrtgen Profilleri (TS 5317) ............................................................................................................................................................................................54 Kaln Etli Kare Profilleri (TS 5317) ..........................................................................................................................................................................................................55 elik Profil Tablolar ................................................................................................................................................................................................................................56-74 Ahap in Emniyet Gerilmeleri (Kg/m2) / Ahabn Neme Gre Ortalama Basn Dayanmlar (Kuruluk Derecelerine Gre) .................75 Basit Durumlarda (n Ett in) Zemin Emniyet Gerilmeleri .................................................................................................................................................76 Dey Hareketli Ykler (TS 498) / Dzgn Yayl Hareketli Ykler (at, Deme, Merdiven in) Dzgn Yayl Dey Hareketli Yk Hesap Deerleri ................................................................................................................................................................77 TS 705 Boyutlarnda Yatay Delikli Tayc Yma ve Blok Tula.......................................................................................................................................78 me Suyu Projelerinin Hazrlanmasnda Faydal Bilgiler ........................................................................................................................................................79 me Suyu Projelerinde ebeke Kriterleri..................................................................................................................................................................................80-82 Betonla lgili Standardlar ......................................................................................................................................................................................................................83-84 Binalarla lgili Tespitler Yaplrken Yararlanlabilicek Yzdeler .............................................................................................................................................85
2
ULUSLARARASI KAIT LLERA01
2
3
A1
4
5
A26
A3
7
8
A49
A510
A6 A7 A8 A9 A10
11
12
13
14
A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
841 mm x 1189 mm 594 mm x 841 mm 420 mm x 594 mm 297 mm x 420 mm 210 mm x 297 mm 148 mm x 210 mm 105 mm x 148 mm 74 mm x 105 mm 52 mm x 74 mm 37 mm x 52 mm 26 mm x 37 mm
B0 1000 mm x 1414 mm 707 mm x 1000 mm B1 500 mm x 707 mm B2 353 mm x 500 mm B3 250 mm x 353 mm B4 176 mm x 250 mm B5 125 mm x 176 mm B6 88 mm x 125 mm B7 62 mm x 88 mm B8 44 mm x 62 mm B9 31 mm x 44 mm B10
C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
917 mm x 1297 mm 648 mm x 917 mm 458 mm x 648 mm 324 mm x 458 mm 229 mm x 324 mm 162 mm x 229 mm 114 mm x 162 mm 81 mm x 114 mm 57 mm x 81 mm 40 mm x 57 mm 28 mm x 40 mm
15
16
17
3
18
IN - METRK SSTEM DNM TABLOSU1/16 1/8 in 3/16 eyrek 1/4 in 5/16 3/8 in 7/16 Yarm Parmak 1/2 in 9/16 5/8 in 11/16 in eyrek 3/4 in 13/16 in 7/8 in 15/16 in Bir Parmak 1 2 3 4 5 in in in in in in in in in in 1.5875 3.1750 4.7625 6.3500 7.9375 9.5250 mm mm mm mm mm mm 0.16 0.32 0.48 0.64 0.79 0.95 1.11 1.27 1.43 1.59 1.75 1.91 2.06 2.22 2.38 2.54 5.08 7.62 cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm * * * * * * * * * * * * * * * * * * * * 12 in= 1 foot (ayak) 3 ft = 1 yarda 1760 yds = 1 mile (mil) 6080 ft = 1 deniz mili 1 cm = 0.3937 in. 1 m = 3.28083 ft 1 mil = 1.60935 km 1 deniz mili =1.85325 km 1 kg = 2.20462 Ibs 1 Ib = 0.453592 kg 1 ft-Ib = 0.13826 kg - m 1 kg - m = 7.233 ft - Ib 1 Beygir (metrik) = 0.98632 HP 1 Beygir = 75 kgmsan = 0.746 KW 1 Beygir saat = 632 kilokalori 1 Kilowat = 1.36 Beygir 1 Kilowat - saat = 860 Kilokalori 1 Kg - m = 9.806 Wat-san (jul) 1 Kilokal = 426.9 kg.m = 4185 jul
11.1125 mm 12.7000 mm 14.2875 mm 15.8750 mm 17.4625 mm 19.0500 mm 20.6375 mm 22.2250 mm 23.8125 mm 25.4000 mm 50.8000 mm 76.2000 mm 101.6000 mm 127.0000 mm
10.16 cm 12.70 cm
NEML DEERLERSaysal Deeri 2 :4 2 3
Saysal Deeri 1: 1 : 2 2 22
Saysal Deeri g 2g : g : 2g e2
3.1416 6.2832 0.7854 9.8696 1.7725 1.4646 39.4784 2.4674
0.3183 0.1013 4.4429 2.5066 1.8453 9-81 m/san 96.2361 0.0510
3.1321 4.4294 1.0030 0.7093 2.7183 0.3679 0.1353 1.6487
2 g g2
42 2: 4
1:e 1 : e2 e
1:2g
4
MHENDSLKTE SIK KULLANILAN METRK BRMLERN SI BRMLERNE EVRME TABLOSUMetrik Byklk Birim arlk Boyut FL-3 Birim 1 kgf/cm3 1 gf/cm3 1 tonf/m3 1 kgf 1 gf 1 tonf 1 kgf.m evirme Katsays Katsay 9.81 9.81 9.81 9.81 9.81x10-3 9.81 9.81 Boyut ML -2T -2 SI Birim N/m3 kN/m3 kN/m3 N kN kN N.m (Joule)
Kuvvet
F FL
MLT -2
-Enerji
ML -2T -2 ML -2T -3
G
FLT-1
1 kgf.m/s 1 HP 1 kgf/cm2 1 kgf/cm2 1 kgf/cm2
9.81 746 9.81x10-4 9.81 9.81x10-2
W W N/m2 (Pa) kN/m2 (kPa) kN/m3 (MPa)
Gerilme NOT: 1. Yerekimi ivmesi 2. 1 gramkuvvet (gf) 3. 1 Newton (N) 4. 1 Joule (J) 5. 1 Watt (W) 6. 1 Pascal (Pa) 7. 1 Bar
FL-2
ML -1T -2
= 9.81 m/s2 = 981 din = 105 din = 1 N.m = 1 j/s=1 N.m/s = 1 N/m2 = 1 Atmosfer=98.1 kN/m2=10m H2O
SI SSTEMNDE TEMEL BRMLERByklk Uzunluk Ktle Zaman Elektrik akm iddeti Termodinamik scaklk Madde miktar Ik iddeti Birimi Metre Kilogram Saniye Amper Kelvin Mole Kandela (candela) Sembol (TSE) m kg s A K mol cd
TEMEL BRMLERDEN RETLM DER BRMLERByklk Uzunluk Birimi Santimetre Kilometre Milimetre Alan Metrekare Kilometrekare Milimetrekare Hacim Metrekp Kilometrekp Hektometrekp Sembol (TSE) cm km mm m2 km2 mm2 m3 km3 hm3
5
TEMEL BRMLERDEN RETLM DER BRMLERByklk Hz Birimi Santimetre/saniye Metre/saniye Kilometre/saat Milimetre/saniye vme Younluk (ktle younluu) zgl hacim Ik iddeti Ktle Zaman Metre/saniyekare Kilogram/metrekp Metrekp/kilogram Kandela/metrekare Gram Miligram Dakika Gn Yl Saat Kuvvet Basn Ak (debi) Debi ve Verim ve Enerji Newton Kilonewton Pascal Kilopascal Metrekp/saniye Litre/saniye Metrekp/gn Metrekp/yl Terajoule Megajoule Kilojoule Joule G Megawatt Kilowatt Watt Frekans Megahertz Kilohertz Hertz Vizkozite Dinamik Vizkozite Kinematik Sktrlabilirlik Salamlatrma G momenti Yzey gerilimi Is kapasitesi - Antropy zgl Is kapasitesi - Antropy zgl Enerji Watt/metre kelvin derecesi Enerji younluu Pascal/saniye Metrekare/saniye Milimetrekare/Newton Metrekare/yl Newton metre Newton/metre Joule/kelvin derecesi Joule/kilogram kelvin derecesi Joule/kilogram W/(m.K) Joule/metrekp J/m3 Sembol (TSE) cm/s m/s km/h mm/s m/s2 kg/m3 m3/kg cd/m2 g mg min d.... gn de yazlabilir (m3 /gn gibi) a .....yl da yazlabilir (m3 /yl gibi) h N kN Pa kPa m3 /s l/s m3/d m3/a TJ MJ kJ J MW kW W MHz kHz Hz Pas (Ns/m2) m2/s mm2/N m2/a N.m N/m J/K J/(kg.K) J/kg Termal iletkenlik Terawatt-saat (TWh da kabul edilir). Gigawatt-saat (GWh da kabul edilir). Megawatt-saat (MWh da kabul edilir). Kilowatt-saat (kWh da kabul edilir). m3 /sn yanl 1 Pa=1 N/m2 Aklama
6
L DEM TABLOSUUzunluk 1 santimetre (cm) 1 metre (m) 1 kilometre (km) 1 inch 1 foot (ayak) (ft) 1 yarda 1 kara mili 1 deniz mili cm 1 100 105 2.540 30.48 91.44 m 0.01 1 1000 0.0254 0.3048 0.9144 1609 1852 km 0.001 1 1.609 1.852 inch 0.3937 39.37 39370 1 12 36 63360 72960 ayak 0.0328 3.281 3281 0.833 1 3 5280 6080 yarda 1.094 1094 0.0278 0.3333 1 1760 2027 k.mil 0.6214 1 1.152 d.mil 0.5396 0.8684 1
Alan 1 santimetrekare (cm2) 1 metrekare (m2) 1 ar (a) 1 hektar (ha) 1 kilometrekare (km2) 1 inch kare (in2) 1 foot kare (ft2) 1 yarda2 1 mil2 1 acre
cm2 1 10000 6.452 929 8361 -
m2 0.0001 1 100 10000 0.0929 0.8361 4050
a 0.01 1 100 1000 40.5
ha 0.01 1 100 259 0.405
km2 0.01 1 2.59 -
in2 0.155 1550 144 1296 -
ft2 10.76 1076 1 9 43640
yarda2 1.196 119.6 0.0039 0.111 1 4850
mil2 2.47 0.3861 0.0016
acre 0.0247 247.1 640 1
Arlk 1 gram (gr) 1 kilogram (kg) 1 kental (k) 1 ton (metrik) 1 onz 1 libre (pound) 1 stone 1 kk ton 1 byk ton
gr 1 1000 100000 28.35 453.6 6350 907.190 1016050
kg 0.001 1 100 1000 0.028 0.453 6.35 907.2 1016
k 0.00001 0.01 1 10 0.00028 0.00453 0.0635 9.072 10.16
metrik ton 0.001 0.100 1 0.0064 0.907 1.016
onz 0.0352 35.273 3527 35273 1 16 224 32000 35840
libre pound 2.205 220 2204.6 0.0625 1 14 2000 2240
stone 0.157 15.74 157.47 0.004 0.071 1 142.9 160
kk ton 0.0011 0.11 1.1023 0.007 1 1.120
byk ton 0.00098 0.098 0.9842 0.0063 0.8929 1
Hacim 1 santimetre kp (cm3) 1 desimetre kp (dm3) 1 inch (in3) 1 foot (ayak) kp (ft3) 1 yarda3 1 onz (ABD) 1 onz (ng.) 1 galon (ABD) 1 galon (ng.) 1 pint (ng.)
cm3 1 1000 16.39 29.57 28.41 3785 4546 568.2
dm3 litre 0.001 1 0.0164 23.32 764.6 0.0295 0.0284 3.785 4.546 0.5682
in3 0.061 61.02 1 1728 46656 1.805 1.734 231 277.4 34.68
ft3 0.035 1 27 0.1337 0.1603 0.02
yarda3 0.0370 1 -
ABD onz 0.038 33.81 0.5541 957.5 25853 1 0.9607 128 153.7 19.21
ng. onz 0.353 35.3 0.5768 966.6 26909 1.041 1 133.2 160 20
ABD galon 0.2642 7.481 202 1 1.201 0.1501
ng. galon 0.22 6.228 168.2 0.8327 1 0.125
ng. pint 1.76 0.0288 49.83 1345 0.0520 0.05 6.662 8 1
7
Enerji, ve Is 1 9.478x10 3412.14-6
j 2.778x10 1 2.724x10 1 426.939 1.019x10-8 1 2.648x1013 1 1.0139 3.985x10-4 5.120x10-7 3.827x10-5 1 3.930x10-4 5.050x10-7 3.775x10-5 0.9863 2.648x10 1055x107 1.355x107 101.3x10713 -6 -7
kwh 0.1019 3.671x105 859.845 0.00234 9.806x10 4187x107 0.00158 3.777x10-14 3.725x10-4 0.00156 1 2.38x10-11 632.415 7
kgf.m 2.388x10 3.6x1013 1.3596 3.703x10-6 -4
kcal 10 1.3410 3.653x10 0.00929 3.9683 9.478x10-11 2509.62 2544.43 1 0.00128 0.09607
erg 3.777x10-7
psh 3.725x10-4 -4
hph 0.7375
btu
ft.lbf
It atm 0.00986 35528
1 jul (j)=N.m=w.s 3.6x106 9.8066 4186.8 0.00116 2.778x10-14 0.73549 0.7457 2.931x10-4 107.586 0.2519 3.23x10-4 0.0242 0.1382 10.3 3.766x10-7 2.815x10-5 2.737x10 641.186 270.000 10-7 2.648x106 2.644x10 1055.06 1.3558 101.36
1 kilowattsaat (kwh)
2.655x106 7.233 3088.02 7.376x10-8 1.952x106 1.98x106
1 kilogram kuvvet m (kgf.m)
0.0967 41.32 9.869x10 26131 26439 778.168 1 74.74 10.41 0.0133 1
1 kilo kalori (kcal)
1 erg
1 metrik beygirgc.s (phs)
1 beygirgc s (hph)
1 ng. s birimi (btu)
1 foot libre kuvvet (ft.lbf)
8atm 1 14.655 760 735.559 51.714 1 750.062 14.223 1 0.0193 14.503 0.9678 0.0680 1.315x10-3 0.9869 1.0197 1.359x10-3 0.0703 1 1.0332 at kgf/cm2 psi lbf/n2 torr mm Hg bar 1.01325 0.9806 0.0689 1.333x10-3 1
1 litre atmosfer (atm)
Basn
paskal N/m2 101325 98066.5 6895 133.32 105
1 normal atm. 0 Cde
760 mm cvann arl (atm)
1 metrik atmosfer (at)
1 psi
1 torr
1 bar = 102 dyn / cm2
G 1 101.972 426.9 1.020x10-8 1 7.355x109 1 1.0138 0.00184 3.072x10-5 1.4345 0.0239 1.4149 0.0235 3.030x10-5 0.00181 1 550 1 0.0166 778.17 12.97 0.9863 7.457x10 1.356x107 2.259x105 1055x107 1.758x108 9
kgf.m/s 0.00980 1 4.1868 10-10 0.73549 0.7457 0.00135 2.260x10-5 1.0550 0.0175 4.2x10-3
kw 0.00234 0.2388 1 2.388x10-11 0.1756 0.1781 3.238x10-4 5.396x10-6 0.2519 542.476 1.360x10-10 1.341x10-10 7.376x10-8 4187x107 5.692 5.614 3088.05 10 1.3596 1.3410 737.56210
kcal/s 9.807x107 0.0133 4.426x10 185280 4.426x10-6 3.255x104 3.3x10 60 1 4.670x104 778.04 4
erg/s 0.01315 7.2330 433.98
ps
hp
ft.lp/s
ft.lb/dak
btu/s 0.00929 0.9478 3.9683 9.481x10-11 0.6971 0.7067 0.00128 2.141x10-5 1 0.0166
btu/dak 0.557 56.89 238.08 5.689x10-9 41.83 42.41 0.0771 1.285x10-3 60 1
1 kilogram kuvvet m (kgf.m/s)
1 kilowat (kw)
1 kilo kalori/s (Kcal/s)
1 erg/s 75 76.040 0.1382
1 metrik beygirgc (ps)
1 beygirgc (hp)
1 foot libre kuvvet/s (ft.lb/s)
1 foot libre kuvvet/d (ft.lb/dak) 2.305x10-3 107.586 1.793
1 ng. s birimi/s (Btu/s)
9N2
1 ng. s birimi/d. (Btu/d)
Kuvvet 1 105 1 980665 444805 13825 0.4536 0.0141 1 9.80665 4.4480 0.1383 1.019x10-6 2.2046 1 0.0310 105
dn 0.1019 0.2248 2.248x10-6
kgf
lbf
poundal 7233 7.233x10-5 70.93 32.17 1
1 newton (N) = kg.m/s
1 dyn (dn) = gr.cm/s2
1 kilogram kuvvet (kgf)
= kg 9.80665 m/s2
1 libre kuvvet (lbf)
= lb.ft/s2
1 poundal = lb.ft/s2
Geometrik ekil
Alan - Geometrik Merkez A Xc=
Eylemsizlik Momenti Ixc Iyc Ix Iy Ixc Iyc Ix Iy bh3 / 36 hb3 / 36 bh3 / 12 hb3 / 12 bh3 / 36
Dayanm Momenti Wxc bh2 24
y
DKGEN
bh 2 b 3 h 3
= = = =
=
h
=
Wyc
=
b y
x
Yc
=
hb2 24
a
GENh
A Xc
=
bh 2 a+b 3 h 3
=
=
bh (b2 - ab + a2) = 36=
Wxc
=
bh / 12+
3
bh2 24
b
x
Yc
=
bh (b2 - ab + a2) = 12
y
KARE A Xc= =
h2 h 2 h 2
Ixc Ix I
= Ixc = Iy4
= h4 / 12 = h4 / 3 Wxc3 = Wyc = h
h
6
= h / 12
Ych x
=
y
DKDRTGEN
Ixc A Xc= =
= = = = = =
bh3 / 12 hb3 / 12 bh3 / 3 hb3 / 3 hb3 / 3 b3
b.h b 2 h 2
Iyc Ix Iy Iy I
Wxc
=
bh2 6 hb2 6
h
Wyc3
=
b
x
Yc
=
h
6 (b2 + h3)
y
BOLUKLU DKDRTGEN
A Xc
= =
bh - b1 h1 b 2 h 2
Ixc Iyc
=
(bh3- b1 h3) 1 12 (hb3- h1 b3) 1 12
wxc = 1 6 wyc = 1
(
bh3- b1 h3 1 h
) )
h h1
b1
=
Y3b y x
=
6
(
hb3- h1 b3 1 b
A Xc
= =
b(h-h1) b 2 h 2 Ixc Iyc=3 b (h3- h1)
Wxc Wyc
=
ET h h1 DKDRTGENLERb x
3 b (h3- h1)
12=
6h=
b3(h - h1) 12
b2(h - h1) 6
Yc
=
10
Geometrik ekil TRAPEZa h
Alan - Geometrik Merkez
Eylemsizlik Momenti
Dayanm Momenti
y
h (a+b) A = 2 yc = h 3 (2a+b) a+b
Ixc =
h3 (a2+4ab+b2) 36 (a+b) h3 (3a+b) 12
Wxc
=
Ixc h-yc
Ix
=
b
x
y
DARE
2 A = r
Ixc = Ixc = Ix = Iy
r4 4 5 a4 4
Wxc = Wyc
=
r3 4
r
Xc = r Yc = rx
=
BOLUKLU DAREy
A =
(d2-d21) 4 d 2 d 2
Ixc = Iyc =
(d4-d41) 64
Wxc = Wyc =
(d4-d41) 32d
Xc =d d1
Yc =x
YARIM DAREy
2 A = r 2
Ixc Iyc Ix
=
r4 (92-64) 72 r 8 r4 8 5r4 84
Wxc
=
Ixc (r-yc) r3 8
Xc = Yc =
r 4r 3
= = =
Wyc
=
r x
Iy
11
Geometrik ekily
Alan - Geometrik Merkez A=
Eylemsizlik Momenti 16 175 4 15 32 105
Dayanm Momenti 16 105 4 15
PARABOL
4 ab 3
Ixc = Ixc = Ix=
ab ab3 3
3
Wxc = Wyc =
ab ab2
2
Xc = ba
ycb b x
=
2 a 5
ab
y
YARIM PARABOL
A
=
2 ab 3
Ixc = Iyc = Ix= =
8 175 19 480 16 105 2 15 37 2100 1 80
ab ab3 3
3
Wxc = Wyc =
8 105 19 300
ab ab2
2
Xc = 5 b 8 yc=
a
2 a 5
ab ab3
b
x
y
YARIM PARABOL Oyuklu Dikdrtgen
A
=
1 ab 3
Ixc = Iyc =
ab ab3
3
Wxc = Wyc =
37 1470 1 60
ab ab2
2
Xc = 1 b 4a
ycb x
=
7 a 10
y
SEKZGEN
A = 0.8284 d Xc = y c = d 2
2
Ixc = Iyc = 0.055 d
4
Wxc = Wyc = 0.110 d
3
d
d y
x
ALTIGEN
A = 0.866 d Xc = y c = d 2
2
Ixc = Iyc = 0.06
d
4
Wxc = Wyc = 0.120 d
3
d
d
x
eksenler etrafndaki eylemsizlik momentleri Ix1 Iy = alann x, y koordinat eksenleri etrafndaki eylemsizlik momentleri Wxc1 Wyc = alann geometrik merkezden geen ve x, y koordinat eksenlerine paralel olan eksenler etrafndaki dayanm momentleri
A = geometrik eklin alan Xc1 yc = alan geometrik merkezinin x ve y koordinatlar Ixc1 Iyc = alann geometrik merkezden geen ve x, y koordinat eksenlerine paralel olan
12
GENC
n s s p S D c B q
SD =1/3 CD; AD = BD S = 1/3 h S1 = 1/3 (q + 2p) = 1/3 (c + p)
A
DRTGEND C S1 T M A S S2 B S1 ve S2 sra ile A B C ve A C D arlk merkezleri; S1 T = S S2 S Drtgenin arlk merkezidir.
DARE YAYIb S s R a 0 a Yarm Daire OS = R sina a
a0
x
180
Rs b
OS = 2R / = 0.6366 R
Drttebir Daire OS = 2R 2 / = 0.9003 R Altdabir Daire OS = 3R / = 0.9549 R
DARE PARASIb
S a 0 a
s R
F = Alan OS = s3 12F = 2 3 R sin3a xF sinaa cosa
a0 180
PARABOL PARASIS1
0
S
0
S x
y 3 5 3 8
x
OS =
x : SS1 =
Y
PRZMA
st ve alt yzeylerin arlk merkezlerini birletiren dorunun orta noktas Tepe noktasn taban arlk merkezine birletiren doru zerinde tabandan itibaren yksekliin drtte birinde
PRAMT KON
Tepe noktasn taban arlk merkezine birletiren doru zerinde tabandan itibaren yksekliin drtte birinde
13
DARE DLMl
I = Yay boyu, = Merkez As, r = Yarap, A = Alan 2 A= x r x =0.008727 x r2 360 l= 2xxrxa = xrxa 360 180
a
r
= 57.295 x l r = 2 x A = 57.295 x l r I
DARE KESMESl A = Alan, I = Yay boyu, c = Kiri, r = Yarap, c = 2 h (2r - h) c h=rr 1 2 4r2 - c2 I = 0.01745 x r x r = (c2 + 4h2) 8h c(r - h) A= rx1 2 2 = Merkez Asdr
a
= 57.295 x l r
DARE HALKASI
D1 ve D2 = Byk ve kk dairelerin aplar r1 ve r2 = Byk ve kk dairelerin yaraplar = Dairesel halkann alandr. A
r2 D 1 D2
r1
A = (D2 - D2) 1 2 42 2 A = (D1 + D2) (D1 - D2) A = (r1 - r2 ) olur 4
HALKA PARASI
aD2 r2
D1
A = Para Alan, A= 360
= Merkez Asdr.
(r
2 1
2 - r2
)
r1
TARALI ALANA = Alan, c= Kiri boyudur. r c A = r2 -
( ) x r2 4
= 0.125 x r2 =
1 2 r 2
A = 0.1075 x c2
14
DK GEN
a c B C b
A= Alan, a= Hipotens, b ve c = Dik Kenarlar A= bxc 2 a= b2+ c2 c= a2- b2 =a + b + c
A
b= a2- c2
KZKENAR GENA= hxb 2
= b + 2 + a22
a
a h
a=
()b 2
+ h2
h=
a2
()b 2
2
b
b = 4 a2- h2
ETKENAR GEN
A= a h a
axh 2
A= 0.433 x a2
= 3 x a h= a 3 2
a
DARED= ap, r = Yarap, A= Alan, = evre r D2 A= x r2 = x D =0.785398 x D2 4
D= D=
2 A = 1.128379 = 3.141593 x
A
= 1.7724539
= 2 x r = x D= 3.141593 x D
15
ELPSa
A = Alan, a = Byk Yarap, b = Kk Yarap A = x a x b = (a + b) (yaklak) = [ 1.5 (a + b) - ab ] ( daha iyi yaklak)
b
DARENN DIINA ZLEN HERHANG BR OKGENe
d a r
A = Alan, r = Dairenin Yarap, ve a, b,c, d, e = okgenin Kenarlar A = 1/2 (a+b+c+d+e)x r =a+b+c+d+e
c b
SMPSON KADESA Y1 d Y2 d Y3 d Y4 d Y5 d Y6 d
Y0
A, B, C, D, Alan : iki bitiik dilimi snrlayan eri paras bir parabol yay olarak alnabilecek kk d geniliinde eit dilimlere ayrlr ve u forml ile hesaplanr.F = d/3 [ Y0 + Yn + 2 ( Y2 + Y4 + .......) + 4 ( Y1 + Y3 + .......) ]
D
ETKENAR OKGEN ( Kenar Says : n)s r Alan : F Kenar : s D daire Yarap : R s r 3.4641 2.000 1.4531 1.1547 0.8284 0.6498 0.5359 R s 0.5774 0.7071 0.8507 1.000 1.3066 1.6180 1.9319 R r 2.000 1.4142 1.2361 1,1547 1.0824 1.0515 1.0353 daire Yarap : r r R 0.5000 0.7071 0.8090 0.8660 0.9239 0.9511 0.9659 r s 0.2887 0.5000 0.6882 0.8660 1.2071 1.5388 1.8660
Kenar Says R F s 3 4 5 6 8 10 122
R
F R2
F r2
s R 1.7321 1.4142 1.1756 1.000 0.7654 0.6180 0.5176
0.4330 1.000 1.7205 2.5981 4.8284 7.6942 11.196
1.2990 2.0000 2.3776 2.5981 2.8284 2.9389 3.0000
5.1962 4.000 3.6327 3.4641 3.3137 3.2492 3.2154
16
DKDRTGEN PRAMTN HACM (Temel ekil)
h2 h1 a'
b'
b
Alt Taban Alan A1 = a x b Alt Taban Alan A2 = a ' x b' V = A1 x h1 + 1/3 h2 [ A1 + A2+ (A1 x A2 ) ]
a
KUM FGRES VEYA SMEL OBELSKV = h/6 [ a x b + ( a + a1 ) ( b + b1 ) + a1 + b1 ] rnek ; a = 8m, b=6 m, h= 1 m Eim 1:1.5 a1 = 8 - 2 x 1 x 1.5 = 5m b1 = 6 - 2 x 1 x 1.5 = 3m V = 1/6 [ 8 x 6 + ( 8 + 5 ) ( 6 + 3 ) + 5 + 3 ] = 30m3
b1 a1 a b
h
ATI (Kama)a1 h b a
V = h x b ( 2 X a + a1 ) 6
RAMPA1/m h 1/n2 V= h 6
[ 3 x a + 2 n1 x h
m-n m
] ( m - n)
1/n 1/n1 1/m
a
rnek : h= 1.5 m a= 2.5, m= 12, n= n1= 1 2 V = 1.5 (3 x 2.5) + 2 x1 x 1.5 12-1 6 12
[
] ( 12 - 1)
1/n1 1/n
= 42.28 m3
17
TEKNEa b h a1 b1
a, b, a1, b1 Elips yarm eksenleri V= xh 6
[ ( 2 x a + a1 ) b + ( 2a1 + a ) b1 ]
rnek: a = 45 cm, a1 = 40 cm b = 25 cm, b1 = 20 cm, h = 50 cm V= x 50 6 =150.5 litre
[ ( 2 x 45 + 40 ) 25 + ( 2x40 + 45 )x 20 ]
FIIDaire Kesiti V = x 1 ( 2 Dm2 + De2) 12 Parabol Kesitli V = 1 ( 2 Dm2 + Dm 2 x De + 3 De2) 15 rnek: De = 50 cm, Dm = 70cm, I = 100 cm V = x 100 ( 2 x 702 + 502 ) cm3 = 321.91 litre 12
I Dm De
KP
d a
V = Hacim, A= Kpn yzey Alan, d = Kegendir.
V = a3 a = A = 6 x a2
A = 6
v
3
a
d=a3a
DKDRTGENLER PRZMASI
d h b a
V = Hacim, A= Kpn yzey Alan, d = Kegendir. V=axbxh A = 2 x ab + 2 x ah + 2x bh = 2 x (ab + ah + bh) d = a2 + b2 + h2
18
KARE PRZMA
V
= Hacim, S = Taban Alandr, A = Prizmann Yzey Alan
V =Sxh a S a A = 2 x a = 4 x a x h ya da h A = 2a (a + 2 h)2
PRAMTS = Taban Alan, A = Piramitin Tm Yzeyi, V = Hacimdir. V= h h1 axbxh Sxh = 3 3
A = ab + ah1 + bh1
a
b
KESK PRAMTs h1 S h S = Taban Alan, s = st Tabann Alan, h = Piramitin Ykseklii, h1 = Yanal Yzlerin Ykseklii, V = Hacimdir. V= h ( S + s + Ss ) 3
SLNDRS = Taban Alan, A = Silindirin Tm Yzeyi, V = Hacim h = Silindirin Ykseklii, r = Silindir Taban Dairesi Yarap h r V=Sxh2 V = x r x h = x D = 0. 785398 x D2 x h 4 2
A
A =2 x x r + 2 x r x h = 2 r (r + h) = 6.28 x r (r + h)
2
19
SLNDR PARASI
D = Silindirin Taban Dairesi ap h H S = Silindir Parasnn Yanal Yzeyinin Alan r = Taban Dairesi Yarap, V= Hacim, H ve h= Yksekliklerdir. V = 1.5708 x r2 ( H + h ) r D
BO SLNDRR
h
r
S = D Yanal Yzn Alan, S1 = Yanal Yzn Alan, D ve d = Byk ve Kk Silindirlerin aplar, R ve r = Byk ve Kk Silindirlerin Yaraplar V = Hacim V = x R2 x h - x r2 x h = ( R2 - r2 ) .h S = x D x h S1 = x d x h
d D
KON
h1 h r A D
S = Koninin Yanal Yzeyinin Alan, V = Hacimdir. S = x r r2 + h2 = x r x h1 = 1.5708 x D x h12 V = x r x h = 1.0472 x r2 x h = 0.2618 x D2 x h 3
KESK KON
S = Yanal Yzeyin Alan, D ve d = st ve Alt tabanlarn aplar, h1 r h ve h1 = Koni ve Yanal Yzn Ykseklikleri, V = Hacimdir. S = x h1 ( R + r ) = 1.570796 x h1 ( D + d ) V = 1.0472 x h ( R2 + r2 + Rr ) a=R-r olduundan h1 = a2 + h2 = (R - r )2 + h2 olur. D
h
20
SLNDR PARASI
A = Krenin D Yzeyinin Alan, r = Yarap ve V = Hacimdir. r A = 4x x r2 A = 12.566371 x r2 = x D2 V= D 4 x x r3 = 4.188 790 x r3 = D3 = 0.5236 x D3 3 6
BO KRE
R d r
V = Hacim, A = Krenin Tm Alan, D ve d = D ve aplar, R ve r = D ve Yaraplar V= 4 = (R3 - r3) 3
D
V = 4 x (R2 + r2)
KRE PARASIh r x V= R = Krenin Yarap, r = Kre Parasnn Yarap xh = (3 r2 + h2) ya da 6
V = 0.523598 x h (3 r2 + h2) A = 2 x Rh veya A = 2 x x R (R - R2 - r2)
KRESEL BLGEr x r1 h V = x h = [ 3 (r2 + r12) + h2 ] ya da 6 V = 0.5236 x h [ 3 (r2 + r12) + h2 ]
21
KRESEL KAMA
A = Kresel Kamann Alan, V = Kresel Kamann Hacmi r V= A= 360 3603 x 4 x x r = 0.0116 x 3
x r3
x 4 x r2 =
90
x r2 = 0.0348 x x r2
DARESEL KESTL HALKAd r D R A = Halka Yzeyinin Alan, V = Halkann Hacmi V = 4 x 2 x R x r = 19.739 Rr2 A = 4 x 2 x Rr = 39.478418 x Rr
KARE KESTL HALKA
a D R A = Halka Yzeyinin Alan, V = Halkann Hacmi V = 4 x x D x a = 12.566 x D x a V = x D x a2 = 3.1416 x D x a2
ALTIGEN PRZMAA = Yanal Yzeyinin Alan, V = Altgen Prizmann Alandr A = 6 x a b ya da A = 3.46 x h b V = 2.6 x a2b ya da h b a V = 0.866 x h2b
22
Pratik hesaplamaya esas olmak zere yma ve karkas yaplar iin yap birim alanna isabet eden yaklak metraj birim lleri aadadr.MALAT CNS 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Betonarme Betonu Betonarme Demiri Kalp Kalp iskelesi iskelesi Tula Duvar Sva D Sva Tavan Svas Badana (i) Fayans - Seramik Ahap yap + Karkas Ahap Pencere Yal Boya Ahap at, kiremit rt (Toplam naat Alan zerinden) Tek kat ki kat kat Drt kat Be kat 16. Metal rt (Toplam naat Alan zerinden) Tek kat ki kat kat Drt kat Be kat 17. 18. Mozaik Deme Kaplamas Cam 1.33 0.67 0.44 0.34 0.27 0.90 0.10 m2/m2 m /m m /m m /m2 2 2 2
YIMA 0.250 22 1.75 1.90 1.43 0.200 2.40 1.30 0.90 3.00 0.30 0.15 0.12 0.42 m3/m2 kg/m2
BETONARME KARKAS 0.380 34 2.60 2.80 1.43 0.150 2.40 1.30 0.90 3.00 0.30 0.15 0.12 0.42 m3/m2 kg/m2 m2/m2 m3/m2 m2/m2 m3/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2
m3/m2 m3/m2 m /m2 2
m3/m2 m2/m2 m2/m2 m2/m2 m2/m2 m /m m /m m /m2 2 2 2 2
m2/m22
1.25 0.63 0.42 0.33 0.25
m2/m2 m /m m /m m /m2 2 2 2
1.25 0.63 0.42 0.33 0.25 1.33 0.67 0.44 0.34 0.27 0.90 0.10
m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2 m2/m2
m2/m22 2
m2/m22 2
m2/m2 m /m2 2
rnek Olarak 2 Toplam alan Betonarme karkas ve konut olan 1 500 m bir binann metraj olarak hesaplanmas gerekiyor ise; 3 Betonarme Betonu = 0.380 x 1 500 = 570 M Betonarme Demiri = 0.034 x 1 500 = 51 ton Betonarme Kalb = 2.60 x 1 500 = 2 600 m2 Tula Duvar = 0.150 x 1 500 = 150 m3 Projeden metraj karlmas esas olmak zere yaklak pratik kabuller = 7 - 8 m2 kalp Tesviye Tabakas alan = Mozaik deme kaplamas alan 1 m3 Beton Blokaj Alan = Grobeton Alan = Mozaik Alan Demirli Beton Hacmine =70 - 90 kg Demir Kiremit Alan = Ahap at Alan Pencere dorama alannn = %75 - 80 normal dz cam Kiremit Alan = at Yaltm Alan Kap Kanat alannn = %25'i buzlu cam Tavan Svas = Tavan Kire Badana Tm Demirin = %40 - 45 ince Badana Alan = Sva Alan Tm Demirin = %55 - 60 kaln Pencere Yal Boya Alan = Pencere Dorama Alan
23
Younluu
Malzeme Kire harc (la) Snm toz kire
Verimi 1/10 kg yan. kire 1:3 160 200 240 280 1560 500 30 32 133 125 118 111 105 100 1560 1:3
Kartrma Oranlar Kg olarak 1:3.5 138 173 207 241 1575 430 115 108 102 96 91 86 1575 1:3.5 272 306 340 1545 2:1:9 104 130 156 182 156 1520 250 67 63 59 56 53 50 165 1560 1:4 122 153 183 214 1585 380 102 95 90 85 80 76 1585 1:4 240 270 300 1560 2:1:10 96 120 144 168 144 1560 230 62 58 55 52 49 46 150 1590 2:1:11 90 113 136 158 136 1610 210 57 53 50 47 45 43 140 1620 150 1180 135 1200 125 1230 115 1250 140 1120 220 130 1170 200 120 1200 185 113 1240 170 280 260 240 226 1170 2:1:8 1190 2:1:9 1200 2:1:10 2:1:11 390 340 300 1:4.5 109 136 163 190 1600 340 91 85 80 75 72 68 1600 1200 1:3 1210 1:3.5 1220 1:4 1230 1200 400 1210 345 1220 305 1230 272 400 345 305 272 1:3 Lt olarak 1:3.5 1:4 1.4.5
0.4 0.5 0.6 0.7
Kum Kire hamuru
1.3 1.25
Kelle kire veya snmemi toz kire
34 36 38 40
Kum Hidrolik kire harc (lb) Y. hidrolik kire harc h. (II) Hidrolik veya yksek hidrolik kire Kum Kire imento harc (II) Snm Toz Kire imento Kum Kire-imento harc (II) Kire Hamuru
1.3
0.8 0.9 1.0 1.3 0.4 0.5 0.6 0.7 1.2 1.3 1.25 30 32
312 351 390 1520 2:1:8 112 140 168 196 168 1460 275 74 69 65 61 58 55 180 1530
1.5:1:8 1.5:1.9 1.5:1:10 1.5:1:11 1.5:1:18 1.5:1.9 1.5:1:10 1.5:1:11
Kelle kire veya snmemi toz kireci
34 36 38 40
imento Kum
1.2 1.3
I. Grup Hartan II. Grup Har Yaplmas 80 litrelik kartrc Karm Oranlar Hazr Har 1:6 R.T imento, litre Kum, litre 1.5:1:9 80 8 1.5:1:10 70 7 10 150 litrelik kartrc 1.5:1:9 150 14 1.5:1:10 130 12 12
24
Ana Tipler
Genel imento Tipleri K S D2) P
Bileim (ktlece1) % olarak Ana Bileenler Q V W T L LLMinr ilave Bileenler
CEM I
Portlant imentosu
CEM I
95100
0-5 0-5 0-5
Portlant-Curuflu CEM II/A-S imento CEM II/B-S Portlant-Silis Dumanl imento PortlantPuzolanl imento CEM II/A-D
80-94 6-20 65-79 21-35 90-94 6-10
0-5
CEM II/A-P CEM II/B-P CEM II/A-Q CEM II/B-Q CEM II/A-V CEM II/B-V
80-94 65-79 80-94 65-79 80-94 65-79
6-20 21-35 6-20 21-35 6-20 21-35 6-20 21-35 6-20 21-35 6-20 21-35 66-80 81-95 11-35 36-55 18-30 31-50
0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5
CEM II
PortlantUucu Kll imento
CEM II/A-W 80-94 CEM II/B-W 65-79 CEM II/A-T CEM II/B-T CEM II/A-M CEM II/B-M 80-94 65-79 80-94 65-79 35-64 36-65 0-5 20-34 5-19 65-89 45-64 40-64 20-38
Portlant-Pimi istli imento PortlantKompoze imento3) CEM III CEM IV CEM V
CEM III/A Yksek Frn Curuflu imento CEM III/B CEM III/C Puzolanik imento3) Puzolanik imento3) CEM IV/A CEM IV/B CEM V/A CEM V/B
18-30 31-50 -
1) izelgedeki deerler ana ve minr ilave bileenlerin toplam ile ilgilidir. 2) Silis dumannn oran %10la snrlandrlmtr. 3) Portland kompoze imento CEM II/A-M ve CEM II/B-Mde, Puzolanik iment CEM IV/A ve CEM IV/Bde, Kompoze imento CEM V/A ve CEM V/Bde klinkerin yanndaki dier ana bileenler ana bileenler imentoya ait iaretler imentoya ait iaretle beyan edilmelidir. K: Klnker, S: Yksek Frn curufu, D: Silis duman, P: Doal puzolan, Q: Doal kalsine edilmi puzolan, V: Silisli uucu kl, W: Kalkerli uucu kl, T: Pimi ist, L: Toplam organik karbon ierii ktlece %0.50 amayan kalker, LL: Toplam organik karbon ierii ktlece %0.20 amayan kalker.Kaynak: TS EN 197-1 Mart 2002
imentolarn Karakteristik Deerlerle Verilen Mekanik ve Fiziksel zellikleriDayanm Snf 32.5 N 32.5 R 42.5 N 42.5 R 52.5 N 52.5 R 10.0 10.0 20.0 20.0 30.0 2 gnlk Basn Dayanm (Mpa) Erken Dayanm 7 gnlk 16.0 52.5 45 42.5 62.5 60 10 32.5 Standart Dayanm 28 gnlk 52.5 75 Priz balama sresi (dakika) Genleme (mm)
Kaynak: TS EN 197-1 Mart 2002, ICS 91.100.10
25
YAPI MALZEMELER VE YAPI KISIMLARININ BRM HACM AIRLIKLARISIRA NO 1. MALZEME VEYA BLEENN ADI DOAL TALAR a) KRSTAL YAPILI PSKRK VE METAMORFK TALAR Bazalt, melafir, Diyorit, Garbo, Gnayis, istler Diyabaz Granit, Siyanit, Porfir, Mermer Serpantin b) TORTUL, SEDMANTE TALAR Youn kalker, Youn dolomit Grovak, Kumta, Konglomera Kalker, Kalker Konglomeralar, Traverten Gzenekli Pskrk Talar 2. DOAL ZEMNLER Kum, kum-akl Kil, Sk Toprak 3. DKME MALZEMELER Kum, akl, Krmata (mcr) Bims akl (3234) Yksek Frn Crufu Kmr Crufu Gzenekli Doal Ta Mcrlar Genletirilmi perlit agregas (TS 3681) Genletirilmi mantar paracklar Polistren, sert kpk paracklar Testere ve planya tala Saman 4. SIVALAR, APLAR, HARLAR Kire harc, kire-imento harc imento harc Takviyeli har Al harc, kireli al harc Agregasz al sva Al harl ap, imento harl ap Dkme asfalt kaplama 15 Anorganik asll hafif agregalardan yaplm sva harlar Genletirilmi perlit agregasyla yaplan svalar ve har tabakalar 5. BYK BOYUTLU YAPI ELEMANLARI - BETONLAR Normal Beton, (TS 500'e uygun) doal agrega veya mcr kullanlarak yaplm betonlar yaplm betonlar (TS 1114'e uygun agregalarla) Yalnz genletirilmi perlit kullanlarak ve kuvars kumu katlmakszn yaplm betonlar (TS 3649'a uygun) Cruf betonu Gzeneksiz agregalar kullanlarak yaplan hafif betonlar (boluklu) 300-1600 1200 1600-2000 Donatl Donatsz 2400 2200 800 - 2000 1800 2000 1900 1400 1200 2000 2300 800-1000 400 - 800 1800 1000 600 1000 1200-1500 50 - 200 200 15 200 150 1800 2000 2700 2600 2400 600 ve 3000 < 5.5 ve 4.5 > 40 ve 100 > 30 ve 60 > 1000 ve 3000 > 3000 ve 6000 < 4.5 ve 4.0 > 100 den doygun hale gelinceye kadar > 60 ve 100 > 3000 den doygun hale gelinceye kadar
2000 ve > 12000 ve > 3000c ve 3000c) 12000 24000 DIN 4030 - 2 > 200 Uygulamada dikkate alnmaz Baumann Gully Geirgenlii (permeabilite) 10-5 m/sden daha dk olan kil zeminler bir aa snfa geirilebilirler. 2Deney metodunda, SO4 n hidroklorik asitle ekstraksiyonu tarif edilmitir; Alternatif olarak, betonun kullanlaca yerde yaplyorsa, su ile aa karma metodu da kullanlabilir. Islanma kuruma dngleri veya kapiler emme nedeniyle, betonda slfat iyonu birikimi tehlikesi olan yerlerde 3000 mg/kg olan snr 2000 mg/kga indirilir.
EN 196-2b
TAZE BETON KME SINIFLARI
Snf S1 S2 S3 S4 S5
kme (mm) 10 - 40 50 - 90 100 - 150 160 - 210 220
Kaynak: TS EN 206-1 Nisan 2002, ICS 91.100.30
33
Beton Snf
Karakteristik Silindir (150 mm x 300 mm) Basn Dayanm, fck MPa
Edeer Kp (150 mm x 150 mm) Basn Dayanm, fck MPa 20 22 25 30 37 45 50 55 60
Karekteristik eksenel ekme Dayanm, fctk MPa 1.4 1.5 1.6 1.8 1.9 2.1 2.2 2.3 2.5
28 Gnlk Elastisite Modl Ec MPa 27000 27500 28000 30000 32000 33000 34000 36000 37000
C 16 C 18 C20 C 25 C30 C 35 C 40 C 45 C 50
16 18 20 25 30 35 40 45 50
BETON SINIFI
C 16
C 18
C 20
C 25
C 30
C 35
C 40
C 45
C 50
K1
0.85
0.85
0.85
0.85
0.82
0.79
0.76
0.73
0.70
Donat ubuklar Mekanik zellikler Doal Sertlikte S220a Minimum Akma Dayanm fyk (MPa) 220 S220a 420 S500a 500
Hasr Donat Soukta ilem Grm S420b 420 S500bs 500 S500bk 500
Minimum Kopma Dayanm fsu (MPa) 32 Minumum kopma Uzamas su (%) 32 < 50 Minumum Kopma Uzamas su (%)
340
500
550
550
550
550
18
12
12
10
8
5
18
10
10
10
8
5
34
AP mm 6 8 10 12 14 16 18 20 22 24 25 26 28 30 32 34 36 38 40 45 50
G kg/m 0.222 0.395 0.617 0.888 1.210 1.580 2.000 2.470 2.980 3.550 3.85 4.170 4.830 5.550 6.310 7.130 7.990 8.900 9.870 12.480 15.410
UBUK SAYISI 1 0.28 0.50 0.79 1.13 1.54 2.01 2.54 3.14 3.80 4.52 4.91 5.31 6.16 7.07 8.04 9.08 10.18 11.34 12.57 15.90 19.64 2 0.57 1.01 1.57 2.26 3.08 4.02 5.09 6.28 7.60 9.05 9.82 10.62 12.31 14.14 16.08 18.16 20.36 22.68 25.13 31.81 39.27 3 0.85 1.51 2.36 3.39 4.62 6.03 7.63 9.42 11.40 13.57 14.73 15.93 18.47 21.21 24.13 27.24 30.54 34.02 37.70 47.71 58.91 4 1.13 2.01 3.14 4.52 6.16 8.04 10.18 12.57 15.21 18.10 19.63 21.24 24.63 28.27 32.17 36.32 40.72 45.36 50.26 63.62 78.54 5 1.41 2.51 3.93 5.65 7.70 10.05 12.72 15.71 19.01 22.62 24.54 26.55 30.79 35.34 40.21 45.40 50.90 56.70 62.83 79.52 98.15 6 1.70 3.01 4.71 6.79 9.24 12.06 15.26 18.84 22.81 27.14 29.45 31.86 36.94 42.41 48.26 54.48 61.07 68.04 75.40 95.43 117.81 7 1.98 3.52 5.50 7.92 10.78 14.07 17.81 21.99 26.61 31.67 34.36 37.17 43.10 49.48 56.30 63.56 71.25 79.38 87.96 111.33 137.45 8 2.26 4.02 6.28 9.05 12.32 16.08 20.36 25.14 30.41 36.19 39.27 42.47 49.26 56.55 61.34 72.63 81.43 90.73 100.53 127.23 157.08 9 2.54 4.52 7.07 10.18 13.85 18.10 22.90 28.28 34.21 40.72 44.18 47.78 55.42 63.62 72.38 81.71 91.61 102.07 113.10 143.14 176.72 10 2.83 5.03 7.85 11.31 15.39 20.11 25.45 31.42 38.01 45.24 49.09 53.09 61.58 70.68 80.42 90.79 101.79 113.41 125.66 159.04 196.35
TAIYICI UBUK API (mm) 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
3 UBUK bo 11.8 12.4 13.0 14.0 14.6 15.6 16.6 17.6 19.0 20.0 21.0 22.4 23.4 24.8 25.8 As 3.4 4.6 6.0 7.6 9.4 11.4 13.6 15.9 18.5 21.2 24.1 27.2 30.5 34.0 37.7
4 UBUK bo 15.0 15.8 16.6 17.8 18.6 20.0 21.4 22.8 24.6 26.0 27.4 29.2 30.6 32.4 33.8 As 4.5 6.2 8.0 10.2 12.6 15.2 18.1 21.2 24.6 28.3 32.2 36.3 40.7 45.4 50.3
5 UBUK bo 18.2 19.2 20.2 21.2 22.6 24.4 26.2 28.0 30.2 32.0 33.8 36.0 37.6 40.0 41.8 As 5.7 7.7 10.0 12.7 15.7 19.0 22.6 26.5 30.8 35.3 40.2 45.4 50.9 56.7 62.8
6 UBUK bo 21.4 22.6 23.8 25.4 26.6 28.8 31.0 33.2 35.8 38.0 40.2 42.8 45.0 47.6 49.8 As 6.8 9.2 12.1 15.3 18.8 22.8 27.1 31.9 36.9 42.4 48.3 54.5 61.1 68.0 75.4
7 UBUK bo 24.6 26.0 27.4 29.2 30.6 33.2 35.8 38.4 41.4 44.0 46.6 49.6 52.2 55.2 57.8 As 7.9 10.8 14.1 17.8 22.0 26.6 31.7 37.2 43.1 49.5 56.3 63.6 71.3 79.4 88.0
8 UBUK bo 27.8 29.4 31.0 33.0 34.6 37.6 40.6 43.6 47.0 50.0 53.0 56.4 59.4 62.8 65.8 As 9.1 12.3 16.1 20.4 25.1 30.4 36.2 42.5 49.3 56.5 64.3 72.6 81.4 90.7 100.0
35
UBUK aral (cm) (t) 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0
(mm) OLARAK UBUK API6 4.04 3.77 3.53 3.33 3.14 2.98 2.83 2.69 2.57 2.46 2.36 2.26 2.17 2.09 2.02 1.95 1.89 1.82 1.77 1.71 1.66 1.62 1.57 1.53 1.49 1.45 1.41 1.34 1.28 1.23 1.18 1.13 1.09 1.05 1.01 0.98 0.95 8 7.18 6.70 6.28 5.91 5.59 5.29 5.03 4.79 4.57 4.37 4.19 4.02 3.87 3.72 3.59 3.47 3.35 3.24 3.14 3.05 2.96 2.87 2.79 2.72 2.65 2.58 2.51 2.40 2.29 2.19 2.10 2.01 1.94 1.86 1.80 1.74 1.68 10 11.22 10.47 9.82 9.24 8.73 8.27 7.85 7.48 7.14 6.83 6.54 6.28 6.04 5.82 5.61 5.42 5.24 5.07 4.91 4.76 4.62 4.49 4.36 4.25 4.13 4.03 3.93 3.74 3.57 3.41 3.27 3.14 3.02 2.91 2.81 2.71 2.62 12 16.16 15.08 14.14 13.31 12.57 11.90 11.31 10.77 10.28 9.84 9.42 9.05 8.70 8.38 8.08 7.80 7.54 7.30 7.07 6.85 6.65 6.46 6.28 6.11 5.95 5.80 5.65 5.39 5.13 4.92 4.71 4.53 4.35 4.19 4.04 3.90 3.77 14 21.99 20.52 19.24 18.11 17.10 16.20 15.39 14.66 13.99 13.39 12.83 12.32 11.84 11.40 11.00 10.62 10.26 9.93 9.62 9.33 9.05 8.79 8.55 8.32 8.10 7.89 7.69 7.33 7.00 6.70 6.41 6.16 5.92 5.70 5.50 5.31 5.13 16 28.73 26.81 25.14 23.66 22.34 21.17 20.11 19.15 18.28 17.49 16.76 16.09 15.47 14.90 14.36 13.87 13.41 12.97 12.57 12.19 11.83 11.49 11.17 10.87 10.58 10.31 10.05 9.58 9.14 8.75 8.38 8.05 7.74 7.45 7.18 6.94 6.71 18 36.36 33.93 31.81 29.94 28.28 26.79 25.45 24.24 23.14 22.13 21.21 20.36 19.58 18.85 18.18 17.55 16.97 16.42 15.90 15.42 14.97 14.54 14.14 13.76 13.39 13.05 12.72 12.12 11.57 11.07 10.61 10.18 9.79 9.43 9.09 8.78 8.49 20 44.87 41.88 39.26 36.95 34.90 33.06 31.41 29.91 28.55 27.31 26.17 25.13 24.16 23.27 22.44 21.66 20.94 20.27 19.64 19.04 18.48 17.95 17.46 16.94 16.54 16.11 15.72 14.96 14.28 13.66 13.09 12.57 12.08 11.64 11.22 10.83 10.47 22 54.3 50.81 47.51 44.72 42.23 40.01 38.01 36.20 34.55 33.05 31.67 30.41 29.24 28.16 27.15 26.21 25.34 24.52 23.76 23.04 22.36 21.72 21.12 20.55 20.01 19.49 19.01 18.10 17.27 16.52 15.83 15.21 14.62 14.08 13.58 13.11 12.67 24 64.63 60.32 56.55 53.22 50.27 47.62 45.24 43.09 41.13 39.34 37.70 36.19 34.80 33.51 32.31 31.20 30.16 29.19 28.28 27.41 26.61 25.85 25.13 24.45 23.81 23.20 22.62 21.55 20.57 19.67 18.85 18.10 17.40 16.76 16.16 15.60 15.08
(mt.de) UBUK SAYISI 14.3 13.3 12.5 11.8 11.1 10.5 10.0 9.5 9.1 8.7 8.3 8.0 7.7 7.4 7.1 6.9 6.7 6.5 6.3 6.1 5.9 5.7 5.6 5.4 5.3 5.1 5.0 4.8 4.6 4.4 4.2 4.0 3.8 3.7 3.6 3.4 3.3
AP mm 6 8 10 12 14 16 18 20
ETRYE SAYISI 1 0.56 1.00 1.57 2.26 3.08 4.02 5.09 6.28 2 1.13 2.01 3.14 4.52 6.16 8.04 10.2 12.6 3 1.70 3.02 4.71 6.79 9.24 12.1 15.3 18.8 4 2.26 4.02 6.28 9.05 12.3 16.1 20.4 25.1 5 2.83 5.03 7.85 11.3 15.4 20.1 25.4 31.4 6 3.39 6.03 9.42 13.6 18.5 24.1 30.5 37.7 7 3.96 7.04 11.0 15.8 21.6 28.1 35.6 44.0 8 4.52 8.04 12.6 18.1 24.6 32.2 40.7 50.3 9 5.09 9.05 14.1 20.4 27.7 36.2 45.8 56.5 10 5.65 10.0 15.7 22.6 30.8 40.2 50.9 62.8 11 6.22 11.1 17.3 24.9 33.9 44.2 56.0 69.1 12 6.78 12.1 18.8 27.1 36.9 48.2 61.1 75.4 13 7.35 13.1 20.4 29.4 40.0 52.3 66.2 81.6 14 7.92 14.1 22.0 31.7 43.1 56.3 71.2 87.9
36
AP mm 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
PLYE SAYISI
(kesmeye kar 45 Derece eik ubuk adedi)
1 0.71 1.11 1.60 2.18 2.84 3.60 4.44 5.38 6.40 7.51 8.71 10.0 11.4 12.8 14.4 16.0 17.8 19.6 21.5 23.5 25.6 27.8
2 1.42 2.22 3.20 4.35 5.69 7.20 8.89 10.8 12.8 15.0 17.4 20.0 22.7 25.7 28.8 32.1 35.5 39.2 43.0 47.0 51.2 55.5
3 2.13 3.33 4.80 6.53 8.53 10.8 13.3 16.1 19.2 22.5 26.1 30.0 34.1 38.5 43.2 48.1 53.3 58.8 64.5 70.5 76.8 83.3
4 2.84 4.44 6.40 8.71 11.4 14.4 17.8 21.5 25.6 30.0 34.8 40.0 45.5 51.4 57.6 64.1 71.1 78.4 86.0 94.0 102 111
5 3.55 5.55 8.00 10.9 14.2 18.0 22.2 26.9 32.0 37.5 43.5 50.0 56.9 64.2 72.0 80.2 88.9 98.0 107 117 128 139
6 4.27 6.66 9.60 13.1 17.1 21.6 26.7 32.2 38.4 45.0 52.2 60.0 68.2 77.0 86.4 96.2 107 118 129 141 153 167
7 4.98 7.77 11.2 15.2 19.9 25.2 31.1 37.6 44.8 52.6 61.0 70.0 79.6 89.9 101 112 124 137 150 164 179 194
8 5.69 8.89 12.8 17.4 22.7 28.8 35.5 43.0 51.2 60.1 69.7 80.0 91.0 103 115 128 142 157 172 188 204 222
9 6.4 10.0 14.4 19.6 25.6 32.4 40.0 48.4 57.6 67.6 78.4 90.0 102 116 130 142 160 176 193 211 230 250
10 7.11 11.1 16.0 21.8 28.4 36.0 44.4 53.8 64.0 75.1 87.1 100 114 128 144 160 178 196 215 235 256 278
11 7.82 12.2 17.6 23.9 31.3 39.6 48.9 59.1 70.4 82.6 95.8 110 125 141 158 176 195 215 236 258 281 305
12 8.53 13.3 19.2 26.1 34.1 43.2 53.3 64.5 76.8 90.1 104 120 136 154 173 192 213 235 258 282 307 333
13 9.24 14.4 20.8 28.3 37.0 46.8 57.8 69.9 83.2 97.6 113 130 148 167 187 208 231 255 279 305 333 361
14 9.95 15.5 22.4 30.5 39 8 50.4 62.2 75.3 89.6 105 122 140 159 180 201 224 249 274 301 329 358 389
Not: 60 Derece eik ubuklar iin yukardaki miktarlar 0.966 ile arplacaktr. (DIN 1045)
h cm 20 25 30 35 40 45 50 55 60 65
Derece 45 19 26 33 40 47 54 61 68 75 82 60 27 33 38 44 50 56 61 67
h cm 70 75 80 85 90 95 100 105 110 115
Derece 45 90 97 104 111 118 125 132 139 146 153 60 73 79 84 90 96 102 108 114 120 126
h cm 120 125 130 135 140 145 150 155 160 165
Derece
h 60 132 137 143 149 155 161 166 172 178 184 cm 170 175 180 185 190 195 200
Derece
45 160 167 174 181 188 195 202 209 216 223
45 231 238 245 252 259 266 273
60 190 195 201 207 213 219 224
37
STEEL MATERIAL TS 708 - 1985 la DIN 488 - 1972 Bst 22/34 GU
Standart aplar
Metretul Arl G (Kg/m) 0.222 0.395 0.617 0.888 1.210 1.580 2.000 2.470 2.980 3.550 3.850 4.170 4.830 5.550 6.310
ubuk Alan F (m2) 0.283 0.503 0.785 1.130 1.540 2.010 2.540 3.140 3.800 4.520 4.910 5.310 6.160 7.070 8.040
ubuk Hacmi W (m3) 0.021 0.050 0.098 0.170 0.269 0.402 0.573 0.785 1.050 1.360 1.530 1.730 2.160 2.650 3.220
ubuk evresi U (cm2/m) 189 251 314 377 440 503 565 628 691 754 785 817 880 942 1010
Standart Boy (m) KANGAL KANGAL KANGAL 12.00 m 12.00 m 12.00 m 12.00 m 12.00 m 12.00 m 12.00 m 12.00 m 12.00 m 12.00 m 12.00 m 12.00 m
6 8 10 12 14 16 18 20 22 d 24 25 26 PROPERTIES FOR DESIGNING TS 708 - 1985 DIN 488 - 1972 28 30 32
STEEL MATERIAL TS 708 - 1985 la DIN 488 - 1980 Bst 47/50 RU
Standart aplar 10 12 14 16 18 20 22 24
G (Kg/m) 0.617 0.888 1.210 1.580 2.000 2.470 2.980 3.550 3.850 4.170 4.830 5.550 6.310
F (cm2) 0.785 1.130 1.540 2.010 2.540 3.140 3.800 4.520 4.910 5.310 6.160 7.070 8.040
W (m3) 0.098 0.170 0.269 0.402 0.573 0.785 1.050 1.360 1.530 1.730 2.160 2.650 3.220
U (cm2/m) 314 377 440 503 565 628 691 754 785 817 880 942 1010
Cs
25 26 28 30
YUVARLAK BETONARME ELK UBUUNUN 1 m (birim metre) AIRLIININ PRATK HESAPLANMASI
32
1 METRE NAAT DEMR AIRLIK FORML : 0.00617 x d2 d = Demir ap mm olarak rnek: 8 mm demir iin 0.00617 x 82 = 0.395 kg/m 12mm demir iin 0.00617 x 122 = 0.888 kg/m
TOR ELKTEN DZE - DZDEN TOR ELE s dz = 0.70 x s tor s tor 1900 s dz 1400 = = 1.36 = 0.70 = s tor = 1.36 x s dz s dz 1400 stor 1900 Tordan Dze 8 0.50 cm2 0.50x1.36=0.68 10 10 0.79 cm2 0.79x1.36=1.07 12 12 1.13 cm2 1.13x1.36=1.54 14 14 1.54 cm2 1.54x1.36=2.09 16
Dzden Tora 12 1.13 cm2 1.13 x 0.70=0.79 10 14 1.54 cm2 1.54 x 0.70=1.08 12 16 2.01 cm2 2.01 x 0.70=1.41 14 18 2.54 cm2 2.54 x 0.70=1.78 16
38
TANIMI :
elik Hasr, deme, perde, istinat duvar, temeller, saha betonlar, tnel ve galeriler, kanal ve kanaletlerin donat malzemesidir.
MALAT :
elik Hasr, souk ekilerek mukavemeti arttrlm ve nervrlendirilmi St IVb ubuklannn birbirlerine elektrik nokta kayna ile birletirilmesi suretiyle imal edilir.
STANDART :
lgili standartlar TS4559, TS 500 Bayndrlk Rayici 04.305/1, 04.305/2 Birim Fiyat No: 23.010 - 23.011
EMNYET GERLMESi : 2400 Kg / cm2 Akma snr 5 000 kg/cm2 Min kopma uzama oran: %5 - 8 STANDART ELK HASIR EBADI : 5.00 x 2.15 m. ebadndadr. HASIR ELK TPLER : (R) Tipleri 15 Adet boy, 20 Adet en ubuklu (Q) Tipleri 15 Adet boy, 33 Adet en ubuklu'dur. * elik Hasrlarn bindirme boyu alan ynde en az 3 gz, tevzi ynnde en az 1 gzldr. * Boy ubuklarn yanndaki "d" harfi ubuklarnn ift olduunu gsterir.
ubuk ap mm 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
ubuk Arl kg/m 0.099 0.125 0.154 0.187 0.222 0.260 0.302 0.347 0.395 0.445 0.499 0.556 0.617 0.680 0.746 0.815 0.888
Tek ubuk Kesit Alan cm2 0.126 0.159 0.196 0.238 0.283 0.332 0.385 0.442 0.503 0.567 0.636 0.709 0.785 0.866 0.950 1.039 1.131 50 100d 2.52 3.19 3.93 4.75 5.65 6.64 7.70 8.84 10.05 11.35 12.72 14.18 15.71 17.32 19.01 20.77 22.62 75 150d 1.68 2.12 2.62 3.17 3.77 4.43 5.13 5.89 6.70 7.57 8.48 9.45 10.47 11.55 12.67 13.85 15.08
ubuk aralarna Gre DONATI KEST ALANI (cm2/m) ubuk Aralklar (mm) 100 1.26 1.59 1.96 2.38 2.82 3.31 3.85 4.42 5.03 5.67 6.36 7.09 7.85 8.66 9.50 10.39 11.31 150 0.84 1.06 1.31 1.58 1.88 2.21 2.57 2.95 3.35 3.78 4.24 4.73 5.24 5.77 6.34 6.92 7.54 200 0.63 0.80 0.98 1.19 1.41 1.65 1.92 2.20 2.51 2.84 3.18 3.54 3.92 4.33 4.74 5.19 5.66 250 0.50 0.64 0.78 0.95 1.13 1.33 1.54 1.77 2.01 2.27 2.54 2.83 3.14 3.46 3.80 4.15 4.52 300 0.42 0.53 0.65 0.79 0.94 1.10 1.28 1.47 1.67 1.89 2.12 2.36 2.61 2.89 3.16 3.45 3.76
39
Hasr tipi okunur. (R) veya (Q) seilen hasr tipi Q221 /188150. 150.6.5.6.0 BURADA: 221 ..........................Boy ubuklarn metretuldeki toplam kesit alan (cm2m) 188 ..........................En ubuklarn metretuldeki toplam kesit alan (cm2m) 150 ..........................Boy ubuklarn aral (mm) 150..........................En ubuklarnn aral (mm) 6.5 ..........................Boy ubuklarn ap (mm) 6.0 ..........................En ubuk ap (mm) Standart elik Hasr Ebad : 5.00 (a) x 2.15 (b) Q tipi boy / en 15 /33 adet ubukludur. 5.00 x 15 x 0.260 = 19.50 Kg 2.15 x 33 x 0.222 = 15.75 Kg W= 35.25 Kg
Buna gre: elik Hasr Birim Arl = W / axb = 35.25 / 5.00 x2.15 = 3.28 kg/m2 bulunur. (Uygulanacak poz. 23.11)
Hasr Tipi
ubuk Aral (mm) BOY/EN 150/250 150/250 150/250 150/250 150/250 150/250 150/250 150/250 150/250 150/250 150/250 150/250 150/250
ubuk ap (mm) BOY/EN 4.5 / 4.5 5.0 / 5.0. 5.5 / 5.0 6.0 / 5.0 6.5 / 5.0 7.0 / 5.0 7.5 / 5.0 5 5d / 5.0 8.0 / 5.0 6.0d / 5.0 6.5d / 5.5 7.0d / 6.0 7.5d / 6.5
Hasr Kesit Alan (cm2/m) BOY/EN 1.06 / 0.64 1.31 / 0.78 1.58 / 0.78 1.88 / 0.78 2.21 / 0.78 2.57 / 0.78 2.95 / 0.78 3.17 / 0.78 3.35 / 0.78 3.77 / 0.78 4.43 / 0.95 5.13 / 1.13 5.89 / 1.33
Hasr Birim Arl
R R 106 R 131 R 158 R 188 R 221 R 257 R 295 R 317 R 335 R 377 R 443 R 513 R 589
kg/m2 1.33 1.65 1.86 2.10 2.36 2.63 2.93 3.11 3.25 3.58 4.22 4.92 5.66
40
HASIR TPi Q Q 106/106 Q 131/131 Q 158/131 Q 158/158 Q 188/131 Q 188/158 Q 188/188 Q 221/131 Q 221/158 Q 221/188 Q 221/221 Q 257/131 Q 257/158 Q 257/188 Q 257/221 Q 257/257 Q 295/131 Q 295/158 Q 295/188 Q 295/221 Q 295/257 Q 295/295 Q 317/131 Q 317/158 Q 317/188 Q 317/221 Q 317/257 Q 317/295 Q 317/131 Q 377/158 Q 377/188 Q 377/221 Q 377/257 Q 377/295 Q 443/158 Q 443/188 Q 443/221 Q 443/257 Q 443/295 Q 513/188 Q 513/221 Q 513/257 Q 513/295 Q 513/221 Q 513/257 Q 513/295
Hasr ubuklarnn ARALIK (mm) BOY 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 EN 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 AP (mm) BOY 4.5 5 5.5 5.5 6.0 6.0 6.0 6.5 6.5 6.5 6.5 7.0 7.0 7.0 7.0 7.0 7.5 7.5 7.5 7.5 7.5 7.5 5.5d 5.5d 5.5d 5.5d 5.5d 5.5d 5.5d 6.0d 6.0d 6.0d 6.0d 6.0d 6.5d 6.5d 6.5d 6.5d 6.5d 7.0d 7.0d 7.0d 7.0d 7.0d 7.0d 7.0d EN 4.5 5 5 5.5 5.5 5.5 6.0 5.0 5.5 6.0 6.5 5.0 5.5 6.0 6.5 7.0 5.0 5.5 6.0 6.5 7.0 7.5 5.0 5.5 6.0 6.5 7.0 7.5 5.0 5.5 6.0 6.5 7.0 7.5 5.5 6.0 6.5 7.0 7.5 6.0 6.5 7.0 7.5 6.5 7.0 7.5
Hasr Kesit Alan (cm2/m) BOY 1.06 1.31 1.58 1.58 1.88 1.88 1.88 2.21 2.21 2.21 EN 1.06 1.31 1.31 1.58 1.31 1.58 1.88 1.31 1.58 1.88 2.21 1.31 1.58 1.88 2.21 2.57 1.31 1.58 1.88 2.21 2.57 2.95 1.31 1.58 1.88 2.21 2.57 2.95 1.31 1.58 1.88 2.21 2.57 2.95 1.58 1.88 2.21 2.57 2.95 1.88 2.21 2.57 2.95 2.21 2.57 2.95
Hasr Birim Arl kg/m2 1.70 2.09 2.32 2.54 2.57 2.78 3.01 2.83 3.05 3.28 3.53 3.12 3.34 3.57 3.82 4.10 3.44 3.66 3.89 4.14 4.41 4.71 2.93 3.15 3.38 3.63 3.91 4.20 3.29 3.51 3.74 3.99 4.26 4.56 3.89 4.13 4.38 4.65 4.95 4.56 4.81 5.08 5.38 5.27 5.54 5.84
2.57 2.57 2.57 2.57 2.57 2.95 2.95 2.95 2.95 2.95 2.95 3.17 3.17 3.17 3.17 3.17 3.17 3.17 3.77 3.77 3.77 3.77 3.77 4.43 4.43 4.43 4.43 4.43 5.13 5.13 5.13 5.13 5.89 5.89 5.89
41
Yap elii
Akma Snr a Kgf/cm2 N/mm2 186 206 235 255 284 294 353
ekme Emniyet Gerilmesi a Kgf/cm2 1140 1360 1440 1560 1740 1800 2160 N/mm2 112 124 141 153 171 177 212
Kayma Emniyet Gerilmesi em Kgf/cm2 658 728 831 900 1005 1039 1247 N/mm2 65 71 82 88 99 102 122
Fe 33 Fe 34 Fe 37 Fe 42 Fe 46 Fe 50 Fe 52
1900 2100 2400 2600 2900 3000 3600
Perinler Ykleme Hali Kayma Tem kgf/cm2 N/mm2 Ezilme ez kgf/cm2
Uygun Civatalar EY 1400 137 2800 275 1120 110 EIY 1600 157 3200 314 1120 110
Kaba Civatalar EY 1120 110 2400 235 1120 110 EIY 1260 124 2700 265 1120 110
Ankraj Civatalar EY 1120 110 EIY 1120 110
EY 1400 137 2800 275 400 47
EIY 1600 157 3200 314 540 53
N/mm2 ekme em kgf/cm2 N/mm2
KAYNAKLAR(1) TS 498, Yap Elemanlarnn Boyutlandrlmasnda Alnacak Yklerin Hesap Deerleri, Kasm 1997 (2) TS 500, Betonarme Yaplarn Hesap ve Yapm Kurallar, ubat 2000 (3) Afet Blgelerinde Yaplacak Yaplar Hakknda Ynetmelik, Eyll 1997 (4) Ersoy, U., Betonarme, Cilt I, Istanbul 1987. (5) zden, K. Altan, M., Aydoan, M., Betonarme Kesitlerin Boyutlandrlmas, stanbul 1987.
42
1 2 3
2 Diki eiti Kt Kaynak
3 Diki Nitelii Muayene edilmi veya edilmemi
4elik Cinsi
Gerilme Basn ve eilme basnc
Fe EY
37 EIY
Fc EY
52 EIY
1400 1600 2400 2700
4
ift tarafl yarm Y tipi ke kayna
atlak, balant ve kk hatas olmad muayene ile saptanm Muayene edilmemi
ekme ve kaynak ynne dik eilme ekmesi
1400 1600 2400 2700
5
Kk kaynatlm yarm Y tipi ke kayna Ke kayna
1100 1250 1700 1900 Muayene edilmi veya edilmemi Basn ve eilme basnc, 1100 1250 1700 1900 ekme ve eilme ekmesi, kyaslama deeri Kayma 1100 1250 1700 1900
6
Yarm Y tipi ke kayna ukur ve yark kayna
7
Btn diki eitleri
EY Yklemesi: esas yklerin toplam (TS 648) EIY Yklemesi: esas ve ilave yklerin toplam (TS 648) (bu standardn kapsam iinde deprem de bir ilave yktr.)
Malzeme EY kgf/mm2 Basn Eilmede ekme Eilmede basn Hertze gre deme basnc 6500 1600
Normal Yap elii ( 37) EIY N/mm2 157 kgf/mm2 1800 N/mm2 177
Ykleme Hali
637
1800
785
kiden fazla rulolu mesnetlerde bu deerler 1000 kgf/cm2 (98 N/mm2) azaltlr.
Mafsal civatalarnda delik kenarnda ezilme
2100
206
2400
235
43
- at rtlerine Alnacak Yklerin Hesap Deerleri 1.7.1Metal Olmayan at rtleri -Asbest-imento Dz Levhalar: Sktrlm Sktrlmam -Asbest-imento Dalgal Levhalar: (Bindirme pay ile beraber) Sktrlm Sktrlmam -Asbest-imento Dalgal Levhalar: (Latalar ile beraber) Sktrlm Sktrlmam - Bitml Karton (Yaptrma malzemesi dahil) - Is izolasyon (Yaptrma malzemesi dahil) - Oluklu Kiremit (Latalar ile beraber) Plak Birim Hesap deeri Hacim Arl (1cm kalnlk iin) kg/dm3 t/m2 (kN/m2) Hafif Beton (Tehizatl) Birim Hacim Arl kg/dm3 1.0 1.80 1.50 0.0190 (0.19) 0.0160 (0.16) 1.2 1.4 1.6 1.8 2.0 1.80 1.50 0.0200 (0.20) 0.0170 (0.17) Hesap deeri t/m3 (kN/m3) 1.150 (11.5) 1.350 (13.5) 1.550 (15.5) 1.750 (17.5) 1.950 (19.5) 2.150 (21.5)
- Normal beton (Sktrlm) (2.7 kg/dm3e kadar birim hacim arlnda agrega kullanlan) Beton Snf Hesap deeri t/m3 (kN/m3) 2.300 (23) 2.400 (24)
1.80 1.50
0.0250 (0.25) 0.0220 (0.22)
C 14den aa C 14 ve yukars
-
0.0150 (0.15)
Tehizatl Normal Beton (Sktrlm) Beton Snf Hesap deeri t/m3 (kN/m3) 2.500 (25)
-
0.00150 (0.015) 0.0500 (0.500)
C 14 ve yukars
1.7.2Metal at rtleri
Hesap deeri t/m2 (kN/m2)
-Metal rtler: Alminyum rt (0.7 mm kalnlk ve 22 mm kaplama tahtas ile beraber) - inko rt (0.63 mm kalnlk ve 22 mm kaplama tahtas ile beraber) - Oluklu sa (0.6 mm kalnlk ve sabitleme malzemesi ile beraber) - Kurun rt (1 mm kalnlk iin) - Bakr rt (1 mm kalnlk iin)
0.0250 (0.25)Duvar ve Sva Harlar Cinsi Hesap deeri t/m3 (kN/m3)
0.0300 (0.30)
- Al Harc (Kumsuz) - Kire harc - Kire + Al Harc - Al + Kum Harc (sva iin) - Anhidrit Harc - Kire + imento Harc - Kire + Tra Harc (Kerpi) - Balk Harc - imento Harc ve imento + Tra Harc
1.200 (12) 1.800 (18) 1.800 (18) 1.800 (18) 1.800 (18) 2.000 (20) 2.000 (20) 2.000 (20) 2.100 (21)
0.0250 (0.25)
0.0120 (0.12)
0.0090 (0.09)
44
Eleman Ad Mertekler Mertekler Mertekler Mertekler Mertekler Mertekler Mertekler Aklar Tabanlar Kuaklar Dikmeler
ki Eleman Aras cm 40-50 50-60 60-75 75-90 2.0-2.5 m 2.5-4.0 m Kk atlarda Byk atlarda Kk atlarda Byk atlarda Umumiyetle
Kesit Boyutu cm 5 x 10 8 x 10 10 x 12 10 x 16 10 x 16 14 x 18 5 x 10 10 x 16 (5 x 10)2 (8 x 16)2 10 x 10
atda ak aralar m 2.0 - 2.5 2.5 - 3.5 3.5 - 4.5 5.0 -
at rts Cinsi
Ykseklik Yar Aklk =tg a 1:2 ila 1:1 1:2.5 1:2 ila 1.75:1 1:3 - 1:1.5 1:6 - 1:5 1.15 - 1:5 1:1 1:1 ila 1.75:1 1:7.5 - 1:5 1:3 - 1:5 1:1.5 - 1:1.25 1:1.75 1:12.5 - 1:10 1:3.5 - 1:1 26 21
Eim (derece olarak) a= 1 2 3 4 ila 45 ve daha ok ve daha ok
Alman arduvaz at ngiliz arduvaz at Makina kiremidi at Oyuk (alaturka) at Basit karton at ift karton at Tahta rtl at Kam ve saman at inko at Dz sa at Dalgal sa at Kurun at Bakr at am at
24 ile 60 18 9 1 2 1 2 - 33 - 11 1 4 2 3 1 4
4 - 11
45 ve daha ok 45 - 60 ve daha ok 7 11 33 29 4 1 2 1 4 2 3 3 4 1 2 - 11 - 18 - 38 1 4 1 2 2 3
- ve daha az -5 2 3
16 - 45 ve daha ok
45
KURUN LEVHALARIN BRM AIRLIKLARIKalnlk (mm) 1.50 1.75 2.00 2.25 2.50 2.75 3.00 Arlk (Kg/m2) 17.10 20.00 22.80 25.60 28.50 31.13 34.20 No 10 11 12 13 14 15 16 17 18 19 20
NKO LEVHALARIN BRM AIRLIKLARIKalnlk (mm) 0.50 0.58 0.66 0.74 0.82 0.95 1.08 1.21 1.34 1.47 1.60 Arlk (Kg/m2) 3.50 4.06 4.62 5.48 5.74 6.65 7.56 8.47 9.38 10.29 11.20
BAKIR LEVHALARIN BRM AIRLIKLARIKalnlk (mm) 0.50 0.56 0.61 0.66 0.72 0.78 0.83 0.94 0.98 1.00 Arlk (Kg/m2) 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00
Not: idarenin yazl msadesi ile Kg/m2 arlklar %1 eksik olabilir.
Not: %0.5 eksik ve tazla olabilir.
GALVANZL (D.K.P.) SACLARIN BRM AIRLIKLARIKalnlk (mm) 0.50 0.60 0.70 0.75 0.90 1.00 1.20 1.50 2.00 2.50 3.00 Arlk (Kg/m2) 3.93 4.71 5.50 5.89 7.07 7.85 9.42 11.78 15.70 19.63 23.55 Kalnlk (mm) 3.50 4.00 5.00 6.00 7.00 8.00 9.00 10.00 12.00 15.00 Arlk (Kg/m2) 27.48 31.40 39.25 47.10 55.00 62.80 70.65 78.50 94.20 117.75
Not: darenin msadesi ile bilumum sac levhalarda Kg/m2 arlklar %5.0 eksik - fazla olabilir.
46
POLRETAN DOLGULU TRAPEZODAL KESTL ALMNYUM LEVHALARIN (m2) AIRLIKLARIKalnlk (mm) 0.50 0.60 0.70 0.90 1.00 1.20 Arlk (Kg/m2) 1.76 2.11 2.46 3.16 3.51 4.22
DZ ALMNYUM LEVHALARIN (m2) AIRLIKLARIKalnlk (mm) 0.50 0.56 0.60 0.70 0.90 1.00 1.20 Arlk (Kg/m2) 1.36 1.51 1.62 1.89 2.43 2.70 3.24
POLRETAN DOLGULU DZ ALMNYUM LEVHALARIN (m2) AIRLIKLARIKalnlk (mm) 0.50 0.60 0.70 0.90 1.00 Arlk (Kg/m2) 1.47 1.76 2.06 2.65 2.95
TRAPEZODAL KESTL ALMNYUM LEVHALARIN (m2) AIRLIKLARIKalnlk (mm) 0.50 0.60 0.70 0.90 1.00 1.20 Arlk (Kg/m2) 1.638 1.965 2.293 2.948 3.276 3.931
YAMUR BORULARI N NKO PARA KESME TABLOSUBoruya isabet eden Standart ldeki Kullanlacak Boru kesiti at sahas yatay izdmde ap (mm) levhadan kesilecek inko inko 2 (m ) paras (mm) No 200 - 300 150 - 200 100 - 150 75 - 100 50 - 75 25 - 50 150 125 100 80 75 70 250 500 400 333 285 200 12 10 - 10 10 - 12 10 10 -
YAMUR BORULARI N NKO PARA KESME TABLOSUOlua isabet eden at sahas yatay izdmde (m2) 200 - 300 150 - 200 100 - 150 75 - 100 50 - 75 25 - 50 Standart ldeki levhadan kesilecek inko parasi (mm) 500 400 333 285 250 200 Oluk kesiti alan (cm2) 250 150 120 80 60 45 Oluk ap (mm) 240 185 155 130 110 90 Para adedi 4 5 6 7 8 10 inko Levha No 14 12 12 12 12 12
47
875 (oluklanmadan nceki alnan genilik 1000dir)
76.2
Kalnlk mm 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 1.00 1.25 1.50 2.0
Dz Oluklu Trapez Stor Arlk Galvanizli Galvanizli Galvanizli Galvanizli Sac Sac Sac Sac kg/m2 mm mm mm mm 2.5 2.75 3.1 3.4 3.8 4.25 4.6 4.95 5.35 5.7 6.1 7.5 8.75 11.0 14.5
adm
875 x 2000 2400 3000
870 x 2000 2400 3000
870 54 204 204 204 102 102 204 102
27.5 TRAPEZ GALVANZL SALAR
2.5
Ak Aral (m) 1.00 1.10 1.20 1.40 1.50 1.80 2.00 2.20 2.40 2.50 2.80 3.00
ET KALINLIINA GRE TAIYABLECE YAYLI YK (Kg/m2) 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 mm mm mm mm mm mm mm mm mm 296 352 400 440 480 530 584 630 680 245 206 152 132 92 74 60 51 47 38 33 290 243 180 155 108 87 71 60 55 45 38 330 276 204 178 124 100 83 69 64 52 44 365 305 225 196 136 110 91 76 70 56 48 400 334 245 213 148 120 100 83 77 61 53 440 370 273 236 164 133 110 91 86 68 59 480 405 300 260 180 146 120 100 94 75 65 520 437 322 280 195 158 130 109 101 80 70 560 470 345 300 210 170 140 118 108 86 75
0.75 mm 724 595 500 366 320 223 181 149 124 116 92 80
0.80 mm 768 630 530 388 340 236 192 158 130 123 98 85
0.85 mm 816 670 565 415 361 252 204 168 140 130 104 90
0.90 mm 864 710 600 443 383 268 216 178 150 138 110 96
1.00 mm 940 775 650 480 419 290 230 192 164 150 120 104
Emniyet gerilmesi 1200 kg/cm2, Hesaplar tek aklkl basit kirie gre yaplmtr.
Ak Aral (m) 1.00 1.10 1.20 1.40 1.50 1.80 2.00 2.20 2.40 2.50 2.80 3.00
ET KALINLIINA GRE TAIYABLECE YAYLI YK (Kg/m2) 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 mm mm mm mm mm mm mm mm mm 165 188 211 231 254 275 296 318 343 136 116 85 74 51 155 131 96 84 58 47 174 146 108 94 65 53 191 160 118 103 71 58 48 210 176 130 113 78 63 52 227 191 140 122 85 69 57 48 245 205 151 132 91 74 61 51 263 221 162 141 98 79 66 55 51 283 238 175 152 106 86 71 60 55 44
0.80 mm 361 298 251 184 160 111 90 75 63 58 46
1.00 mm 452 374 314 230 201 140 113 93 78 72 58 50
1.20 mm 535 442 371 273 238 165 134 110 93 86 68 59
1.50 mm 665 550 462 339 296 205 166 137 115 106 85 74
Emniyet gerilmesi 1200 kg/cm2, Hesaplar tek aklkl basit kirie gre yaplmtr.
48
810 x 2000 2400 3000
OLUKLU GALVANZL SALAR
18
1000 x 2000 2400
TRAPEZ ALMNYUM LEVHALARIN TEKNK ZELLKLER Uzunluk: Min. 1.7 m. - Max: 12.0 m Levha Genilii: 932 mm Faydal Genilik: 888 mm Levha Kalnl (mm) Boy Arl (kg/m) Hesap Arl (kg/m2) Atalet Momenti (cm /m)4
1.20 3.89 4.38 42.0
1.00 3.24 3.65 33.5
0.90 2.92 3.29 29.3
0.70 2.27 2.56 20.8
0.60 1.95 2.20 16.6
0.56 1.81 2.04 14.9
0.50 1.62 1.82 12.4
ARASINDA CAM YN ZOLASYON MALZEMES BULUNAN K KAT ALMNYUM ATI RTSNN ISI LETM KATSAYILARIzolasyon cm Kalnl kcal Is letim Katsays m-C-h 0 2 2.5 3 4 5 6 7 8 9 10 12 12.5 15 20 25
5.2 1.31 1.10 0.95 0.75 0.62
0.52
0.46
0.40 0.36
0.33
0.28
0.27
0.22
0.17
0.14
Hesap forml 1/k=0 193 + 0.28571 e
OLUKLU LEVHALARIN ETL EMLERDEK YZEYLERDE BNDRME PAYLARI VE YARARLI ALANLARIEn az birdirme boyu mmStandart Boy 2500 mm Ak Aras m 1.125 1.15 1.175 Yararl Alan m2 2.36 2.42 2.47 Standart Boy 2000 mm Ak Aras m 0.875 0.90 0.925 Yararl Alan m2 1.84 1.89 1.94 Standart Boy 1600 mm Ak Aras m 1.35 1.40 1.45 Yararl Alan m2 1.42 1.47 1.52 Standart Boy 1250 mm Ak Aras m 1.00 1.05 1.10 Yararl Alan m2 1.05 1.10 1.16
Profil 6
Eim
at
8.5den kk (15%den kk) 8.5 - 15 (15% - 27%) 15den byk (27%den byk) 75 - 90
250 200 150
Cephe
100
1.20
2.52
0.95
2.00
1.50
1.58
1.15
1.21
ELYAFLI MENTODAN OLUKLU LEVHALARStandart Boy mm 2500 12 2000 10 1600 8 1250 6 Standart Genilik mm 1097 6 1097 6 1097 6 1097 6 Bir Levha Alan m2 2.74 2.19 1.76 1.37 Yararl Genilik mm 1050 1050 1050 1050 Bir Levha Alan m2 2.42 1.89 1.47 1.10 Standart Kalnlk mm 6 0.4 6 0.4 6 0.4 6 0.4 Arlk (Yaklak) kg Levha 56.0 29.0 23.0 18.0
49
y b r2 r1 x s x h
PROPERTIES FOR DESIGNING DIN 21541 -1974 PLATNA (GI) Anma ad Gl 110 140 110 140 84 110 10 12 14 19 14 17 5 8 h mm b mm s mm t mm r1 mm r2 mm Kesit Arlk alan G F (Kg/m) 2 (cm ) 31.1 53.0 24.5 41.6
STEEL MATERIAL %33 t b/4 TS 2162-1986 DIN 17100-1980 SFe 37.2 and SFe 44.2 RSt 37.2 and RSt 44.2
PROPERTIES FOR DESIGNING b1 D 9012 STEEL MATERIAL TS 2162 (1986) SFe 37.2 and SFe 44.2 DIN 17100 - (1980) RSt 37.2 and RSt 44.2 OMEGA PROFLLER h h 46 x 83 s b 46 b 83 b1 35 s 5 Arlk Kg/m 5.85Kesit alan (cm2)
7.5
STEEL MATERIAL TS 2162-1986 SFe 37.2 and SFe 44.2 DIN17100-1980 RSt 37.2 and RSt 44.2
y
b
STEEL MATERIAL TS 2162-1986 SFe 37.2 and SFe 44.2 DIN 17100-1980 RSt 37.2 and RSt 44.2 (T) PROFLLER T h h mm 30 b mm 30 35 40 50 s mm 4 4.5 5 6 F cm2 2.26 2.97 3.77 5.66 G Kg/m 1.77 2.33 2.96 4.44 U m2/m 0.114 0.133 0.153 0.191
d s
h 2
y
35 40 50
50
s bGenilik (b) mm.
Kg/mt6.5 7 8 9 10 11 12 13 14 15 16 17 20 22 24 27 30 32 34
Kalnlk (s) mm43 48 53
5
6
21.5 23.5 26.5 31.5 33.5 36.5 41.5 45 46.5 48 50 51.5 55 56.5 57 61.5 65 70 72 75 80 82 85 92 102 122
-
-
(4.34) -
1.73 2.01 2.28 2.56 2.83 3.10 3.38 -
1.35 4.52 -
1.87 2.23 2.58 2.93 3.79 3.64 3.99 4.34 -
1.69 1.84 2.63 5.65 6.44 7.22 (9.58)
1.86 2.29 2.72 3.15 3.58 4.02 4.45 4.88 -
2.03 2.21 3.16 5.79 6.78 7.72 8.67 9.61 (11.5)
2.19 2.36 2.40 2.91 4.01 4.56 (5.11) 5.66 6.21 6.76 7.91 9.01 10.1 11.2 (13.4)
2.77 6.71 -
3.33 -
4.20
-
4.58 -
-
7.74
-
-
-
20.0 -
(24.3) -
-
1.24 1.48 1.72 1.95 2.19 2.43 2.90 -
4.47 5.26 5.79 4.87 5.54 6.21 6.87 7.54 8.21 9.61 10.9 12.3 13.6 7.54 6.30
7.17 7.82 8.80 8.03 8.89 9.76 10.6 12.4 14.2 15.9 17.6 (21.1) 9.54 9.85 -
10.4 11.1 12.6 12.4 -
10.8 (12.1) 12.9 (13.7) 13.0 15.3 (15.9) (17.0) 17.4 (18.0) 19.5 21.6 (25.9) 15.4 18.1 20.6 25.6 (30.6) 14.7 15.2 (17.3) 18.7 (20.0) (21.4) (22.7) -
4.51 5.15 5.78 (7.66)
27.7 34.1 -
(34.4) (42.4) -
- (16.3)
* Parantez iindeki ller zorunluk olmadka kullanlmamaldr.
51
Arlk 7.85 daN/dm Kalnlk d mm
3
Younluk 7.85 kg/dm Arlk kg / m Kalnlkd
3
Arlk kg / md d
Kalnlk d mmd
Arlk kg / md
d
d mm
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 34 36 38 40 42 44 46 48
0.196 0.283 0.385 0.502 0.636 0.785 0.950 1.130 1.327 1.539 1.766 2.010 2.269 2.543 2.834 3.140 3.462 3.799 4.153 4.522 4.906 5.307 5.723 6.154 6.601 7.065 8.038 9.075 10174 11335 12560 13847 15198 16611 18086
0.154 0.222 0.302 0.395 0.499 0.617 0.746 0.888 1.042 1.208 1.387 1.578 1.782 1.988 2.226 2.719 2.984 3.261 3.551 3.853 3.853 4.168 4.495 4.834 5.185 5.549 6.313 7.127 7.990 8.903 9.865 10876 11936 13046 14205
50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175
19.625 21.226 22.891 24.618 26.407 28.260 30.175 32.154 34.195 36.298 38.465 40.465 42.987 45.342 47.759 50.240 56.716 63.585 70.846 78.500 84.546 94.985 103.816 113.040 122.656 132.665 143.066 153.860 165.045 176.625 188.596 200.960 213.716 226.865 240.406
15.414 16.671 17.978 19.335 20.740 22.195 23.700 25.253 26.856 28.509 30.210 31.961 33.762 35.611 37.510 39.459 44.545 49.940 55.643 61.654 67.974 74.601 81.537 88.782 96.334 104.195 112.364 120.842 129.628 138.722 148.12 157.834 168.853 178.180 188.815
180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350
254.340 268.666 283.385 298.496 314.000 329.896 346.185 361.866 379.940 397.406 415.265 433.516 452.160 471.196 490.625 510.446 530.666 551.266 572.265 593.656 615.440 637.616 660.185 683.146 706.500 730.246 754.385 778.916 803.840 829.156 854.865 880.966 907.460 934.346 061.625
199.759 211.011 222.571 234.439 246.616 259.101 271.984 284.996 298.405 312.125 326.150 340.484 355.127 370.078 385.338 400.905 416.781 432.965 449.448 466.258 483.367 500.785 518.510 536.544 554.886 573.536 592.495 611.762 631.337 351.220 671.412 691.912 712.720 733.837 755.262
52
b
h e
NCE ETL KARE VE DKDRTGEN PROFLLER (TS 6475)
KENAR UZUNLUU h Anma Boyutu 15 18 20 25 30 34 35 36 40 45 50 b Anma Boyutu 15 18 10 15 20 15 25 10 15 20 30 20 34 20 25 35 11 20 25 30 40 45 20 25 30 34 40 50 34 20 30 40 50 60 40 70 20 30 40 50 60 80 90 40 50 60 80 100 40 60 h ve b iin toleranslar 0.20 0.20 0.20 0.25 0.25 0.25 0.25 0.25 0.30 0.30 0.30
Birim Arlklar (kg/m) 1 0.438 0.532 0.438 0.516 0.595 0.595 0.752 0.595 0.673 0.752 0.909 0.815 1.03 0.830 0.909 1.07 0.705 1.25 0.537 0.655 0.537 0.635 0.733 0.733 0.930 0.733 0.831 0.930 1.13 1.01 1.28 1.03 1.13 1.32 0.871 1.5 0.632 0.773 0.632 0.750 0.868 0.868 1.10 0.868 0.985 1.10 1.34 1.20 1.53 1.22 1.34 1.57 1.03 1.34 1.46 1.57 1.81 2.05 1.57 1.69 1.81 1.90 2.05 2.28 2.02 2 0.810 0.998 0.810 0.967 1.12 1.12 1.44 1.12 1.28 1.44 1.75 1.56 2.00 1.59 1.75 2.07 1.34 1.75 1.91 2.07 2.38 2.69 2.07 2.22 2.38 2.51 2.69 3.01 2.66 2.38 2.69 3.01 3.32 3.64 3.32 4.26 3.01 3.32 3.64 3.95 4.26 4.89 5.52 4.26 4.58 4.89 5.52 6.15 4.89 5.52 2.5 3 4
55 60 70
0.40 0.40 0.50
80
0.60
90 100 120
0.75 0.80 0.80
2.15 2.46 1.95 2.15 2.54 2.15 2.34 2.54 2.93 3.33 2.54 2.74 2.93 3.09 3.33 3.72 3.29 2.93 3.33 3.72 4.11 4.50 4.11 5.29 3.72 4.11 4.50 4.90 5.29 6.07 6.86 5.29 5.68 6.07 6.86 7.64 6.07 6.86
2.39 2.77 2.39 2.86 2.39 2.63 2.86 3.33 3.80 2.86 3.10 3.33 3.52 3.80 4.28 3.76 3.33 3.80 4.28 4.75 5.22 4.75 6.16 4.28 4.75 5.22 5.69 6.16 7.10 8.04 6.16 6.63 7.10 8.04 8.99 7.10 8.04
4.25 4.88 4,25 4.50 4.88 5.51 4.82 4.88 5.51 6.14 6.76 6.14 8.02 6.76 7.39 8.02 9.28 10.5 8.02 8.65 9.28 10.5 11.8 9.28 10.5
-
-
8.13 9.70 8.13 8.91 9.70 11.3 12.8 9.70 10.5 11.3 12.8 14.4 11.3 12.8
53
b
h e
Boyutlar axb mm 40x20
Kalnl e mm 1.2 1.6 2 2.6 1.2 1.6 2 2.6 3.2 4 1.6 2 2.6 3.2 4 5 1.6 2 2.6 3.2 4 5 1.6 2 2.6 3.2 4 5 2 2.6 3,2 4 5 2 2.6 3.2 4 5 6.3 2.6 3.2 4 5 6.3 7.1 3.2 4 5 6.3 7.1
Arlk kg/m 1.05 1.36 1.65 2.05 1.42 1.86 2.28 2.87 3.42 4.09 2.36 2.91 3.69 4.43 5.35 6.39 2.87 3.53 4.50 5.43 6.60 7.96 3.37 4.16 5.32 6.44 7.86 9.53 4.79 6.14 7.44 9.11 11.1 5.42 6.95 8.45 10.4 12.7 15.5 7.77 9.45 11.6 14.2 17.5 19.4 11.00 13.5 16.6 20.4 22.7
Kesit Alan A cm2 1.33 1.73 2.10 2.62 1.81 2.37 2.90 3.66 4.36 5.21 3.01 3.70 4.70 5.64 6.81 8.14 3.65 4.50 5.74 6.92 8.41 10.1 4.29 5.30 6.78 8.20 10.0 12.1 6.10 7.82 9.48 11.6 14.1 6.90 8.86 10.8 13.2 16.1 19.7 9.90 12.0 14.8 18.1 22.2 24.7 14.0 17.2 21.1 26.0 28.9
Boyutlar axb mm 150x100
Et Kalnl e mm 3.2 4 5 6.3 7.1 8 10 3.2 4 5 6.3 7.1 8 10 3.2 4 5 6.3 7.1 8 10 4 5 6.3 7.1 8 10 4 5 6.3 7.1 8 10 4 5 6.3 7.1 8 10 12.5
Arlk kg/m 12.0 14.8 18.2 22.4 24.9 27.7 33.4 11.5 14.1 17.4 21.4 23.8 26.4 31.8 13.5 16.7 20.5 25.4 28.3 31.4 38.1 17.9 22.1 27.4 30.5 33.9 41.3 21.7 26.8 33.3 37.2 41.5 50.7 24.2 29.9 37.2 41.6 46.5 57.0 69.4
Kesit Alan A cm2 15.2 18.8 23.1 28.5 31.8 35.2 42.6 14.6 18.0 22.1 27.3 30.3 33.6 40.6 17.2 21.2 26.1 32.3 36.0 40.0 48.6 22.8 28.1 34.8 38.9 43.2 52.6 21.7 26.8 33.3 37.2 41.5 50.7 30.8 38.1 47.4 53.1 59.2 72.6 88.4
50x30
160x80
60x40
80x40
180x100
90x50
200x100
100x60
120x60
220 x 120
120x80
250x150
140x90
54
a
a e
Boyutlar axb mm 20 x 20 30 x 30
Et Kalnl e mm 1.2 1.6 2 1.2 1.6 2 2.6 1.2 1.6 2 2.6 3.2 4 1.6 2 2.6 3.2 4 5 1.6 2 2.6 3.2 4 5 1.6 2 2.6 3.2 4 5 2 2.6 3.2 4 5 2 2.6 3.2 4 5 6.3 2.6 3.2 4 5 6.3 7.1
Arlk
Kesit Alan A cm2 0.853 1.09 1.30 1.33 1.73 2.10 2.62 1.81 2.37 2.90 3.66 4.36 5.21 3.01 3.70 4.70 5.64 6.81 8.14 3.65 4.50 5.74 6.92 8.41 10.1 4.29 5.30 6.78 8.20 10.0 12.1 6.10 7.82 9.48 11.6 14.1 6.90 8.96 10.8 13.2 16.1 19.7 9.90 12.0 14.8 18.1 22.2 24.7
Boyutlar axb mm 115 x 115
Et Kalnl e mm 2.6 3.2 4 5 6.3 7.1 3.2 4 5 6.3 7.1 8 10 3.2 4 5 6.3 7.1 8 10 4 5 6.3 7.1 8 10 4 5 6.3 7.1 8 10 4 5 6.3 7.1 8 10 4 5 6.3 7.1 8 10 4 5 6.3 7.1 8 10 12.5
Arlk
Kesit Alan A cm2 11.5 14.0 17.2 21.1 26.0 28.9 14.6 18.0 22.1 27.3 30.3 33.6 40.6 16.5 20.4 25.1 31.1 34.6 38.4 46.6 21.2 26.1 32.3 36.0 40.0 48.6 22.8 28.1 34.8 38.9 43.2 52.6 24.4 30.1 37.4 41.7 46.4 56.6 26.8 33.1 41.1 46.0 51.2 62.6 27.6 34.1 42.4 47.4 52.8 64.6 78.4
kg/m 0.670 0.855 1.02 1.05 1.36 1.65 2.05 1.42 1.86 2.28 2.87 3.42 4.09 2.36 2.91 3.69 4.43 5.35 6.39 2.87 3.53 4.50 5.43 6.60 7.96 3.37 4.16 5.32 6.44 7.86 9.53 4.79 6.14 7.44 9.11 11.10 5.42 6.95 8.45 10.4 12.7 15.5 7.77 9.45 11.6 14.2 17.5 19.4
kg/m 8.99 11.0 13.5 16.6 20.4 22.7 11.5 14.1 17.4 21.4 23.8 26.4 31.8 13.0 16.0 19.7 24.4 27.2 30.2 36.6 16.7 20.5 25.4 28.3 31.4 38.1 17.9 22.1 27.4 30.5 33.9 41.3 19.2 23.7 29.3 32.7 36.5 44.4 21.0 26.0 32.3 36.1 40.2 49.1 21.7 26.8 33.3 37.2 41.5 50.7 61.5
120 x 120
40 x 40
50 x 50
135 x 135
60 x 60
140 x 140
70 x 70
150 x 150
80 x 80
160 x 160
90 x 90
175 x 175
100 x 100
180 x 180
55
y nw
b
a 14 x Cx Cy y
w
F G U J Wx
= enkesit alan = arlk = 1 mt iin evre yzeyi = atalet momenti = mukavemet momenti = J F = atalet yarap
r2
}
ait olduu eilme eksenine izafe
=
b
a
r1 yarm veya tam say mmye yuvarlatlm eksenine a ortaydr 2
n
Profil L 20 x 3 4 a
Boyutlar mm s r1 r2 2 2
F
G
U
Eksenler iinx-x=y-y iin
Eilme Ekseni iinh-h iin J cm4 I cm4 Jh Wh Ih=I1
cm
3
kg/m
m /m
2
ex=ey cm
W cm
V1 cm
V2 cm
Jx=Jy cm4
Wx=Wy Lx=Ly cm4 cm4
20 25
3 3.5 4 3 4 3.5 5 3 4 5 3 4 5 6 3 4 5 6 4 5 6 7 4 5 6 7 8 9 5 6 8 10 5 6 8 10 6 7 8 11 5
1.12 0.88 0.60 0.077 1.45 1.14 0.64 1.42 1.12 0.73 1.85 1.45 0.097 0.76 2.26 1.77 0.80
1.41 1.77
0.85 0.90 1.03 1.08 1.13 1.18 1 24 1.30 1.36 1.41 1.47 1.53 1.52 1.58 1.64 1.70 1.75 1.81 1.87 1.92 1.92 1.98 2.04 2.11 2.16 2.21 2.15 2.21 2.32 2.43 2.32 2.39 2.50 2.62 2.55 2.62 2.67 2.73 2.83
0.70 0.71 0.87 0.89 0.91 1.04 1.05 1.07 1.23 1.24 1.25 1.27 1.40 1.40 1.42 1.43 1.57 1.58 1.59 1.61 1.75 1.76 1.77 1.78 1.80 1.82 1.93 1.94 1.97 2.00 2.11 2.11 2.14 2.17 2.28 2.29 2.31 2.32 2.36
0.39 0.48 0.79 1.01 1.18 1.41 1.81 2.16 2.29 2.96 3.56 4.14 3.45 4.48 5.43 6.33 6.43 7.83 9.16 10.4 8.97 11.0 12.8 14.6 16.3 17.9 14.7 17.3 22.1 26.3 19.4 22.8 29.1 34.9 29.2 33.4 37.5 41.3 48.8
0.28 0.35 0.45 0.58 0.69 0.65 0.86 1.04 0.90 1.18 1.45 1.71 1.18 1.56 1.91 2.26 1.97 2.43 2.88 3.31 2.97 3.05 3.61 4.15 4.68 5.20 2.70 4.40 5.72 6.97 4.45 5.29 6.88 8.41 6.21 7.18 8.13 9.04 10.8
0.59 0.58 0.75 0.74 0.72 0.90 0.89 0.88 1.06 1.05 1.04 1.04 1.21 1.21 1.20 1.19 1.36 1.35 1.34 1.35 1.52 1.51 1.50 1.49 1.48 1.47 1.66 1.66 1.64 1.62 1.82 1.82 1.80 1.78 1.97 1.96 1.95 1.94 1.91
0.62 0.74 0.15 0.18 0.37 0.77 0.75 0.19 0.21 0.36 1.27 0.95 0.31 0.30 0.47 1.61 0.93 0.40 0.37 0.47 1.87 0.91 0.50 0.44 0.47 2.24 1.14 0.57 0.48 0.57 3.85 1.12 0.76 0.61 0.58 3.41 1.11 0.91 0.70 0.57 3.63 4.68 5.63 6.50 5.45 7.09 8.64 9.98 10.2 12.4 14.5 16.4 14.2 17.4 20.4 23.1 25.7 28.1 25.3 27.4 34.8 41.4 30.7 36.1 46.1 55.1 46.3 53.0 59.4 55.4 76.8 1.34 1.33 1.31 1.30 1.52 1.52 1.51 1.49 1.71 1.70 1.69 1.67 1.91 1.90 1.89 1.88 1.86 1.85 2.09 2.08 2.06 2.02 2.30 2.79 2.26 2.23 2.48 2.47 2.46 2.44 2.42 0.95 1.24 1.49 1.77 1.44 1.86 2.22 2.67 2.68 3.25 3.83 4.39 3.73 4.59 5.24 6.02 6.87 7.67 6.11 7.24 9.35 11.3 8.03 9.43 12.1 14.6 12.1 13.8 15.6 17.2 20.7 0.70 0.88 1.10 1.16 0.95 1.18 1.35 1.57 1.53 1.80 2.05 2.29 1.94 2.32 2.57 2.85 3.19 3.47 2.84 3.28 4.03 4.65 3.46 3.95 4.84 5.57 4.74 5.27 5.84 6.30 7.31 0.68 0.68 0.67 0.68 0.78 0.78 0.77 0.77 0.88 0.87 0.87 0.87 0.98 0.98 0.96 0.96 0.96 0.96 1.07 1.07 1.07 1.06 1.17 1.17 1.16 1.15 1.27 1.26 1.26 1.25 1.25
3 25 x 4 5 3 30 x 4 5 3 4 35 x 5 6 3 4 5 6 4 45 x 5 6 7 40 x 4 5 6 50 x 7 8 9 55 x 5 6 8 10 5 6 8 10
30
1.74 1.36 0.84 2.5 2 27 1 78 0.116 0 89 2.78 2.18 0.92 2.04 2.67 2.5 3.28 3.87 2.35 3.08 3.79 4.48 3.49 3.5 4.30 5.09 5.86 3 3.89 4.80 5.69 3.5 6.56 7.41 8.24 4 5.32 6.31 8.23 10.1 5.82 6.91 9.03 11.1 1.60 0.96 2.10 1.00 0.136 2.57 1.04 3.04 1.08 1.84 1.07 2.42 1.12 0.155 2.97 1.16 3.52 1.20 2.74 1.23 3.38 0.174 1.28 4.00 1.32 4.60 1.36 3.06 1.36 3.77 1.40 4.47 1.45 0.194 5.15 1.49 5.82 1.52 6.47 1.56 4.18 1.52 4.95 1.56 0.213 6.46 1.64 7.90 1.72 4.57 1.64 5.42 1.69 0.223 7.09 1.77 8.69 1.85 5.91 1.80 6.83 1.85 7.73 0.252 1.89 8.62 1.93 10.3 2.00
2.12
35
5
2.47
40
6
2.83
45
7
3.18
50
7
3.54
55
8
3.89
60 x
60
8
4
4.24
6 7 65 x 8 11
65
7.53 8.70 9 4.5 9.85 11.0 13.2
4.60
56
Profil
Boyutlar mm a s r1 r2
F
G
U
Eksenler iin
Eilme Ekseni iinx-x=y-y iin I cm4
L
cm
3
kg/m
m /m
2
ex=ey cm
W cm
V1 cm
V2 cm
Jx=Jy Wx=Wy Lx=Ly cm4 cm4 cm4
J cm4
Jh
Wh
Ih=I1
70 x
6 8.13 6.38 1.93 2.73 6 7 9.40 7.38 1.97 2.79 7 70 9 9 4.5 11.9 9.34 0.272 2.05 4.95 2.90 9 11 14.3 11.2 2.13 3.01 11 8.75 10.1 11.4 14.1 16.7 10.8 12.3 15.1 17.9 20.6 6.87 2.04 2.89 7.94 2.09 2.95 9.03 0.291 2.13 5.30 3.01 11.1 2.21 3.12 13.1 2.29 3.24 8.49 2.21 3.13 9.66 2.26 3.20 11.9 0.311 2.34 5.66 3.31 14.1 2.41 3.41 16.1 2.48 3.51
2.46 2.47 2.50 2.53 2.63 2.63 2.65 2.68 2.71 2.82 2.82 2.85 2.89 2.93 3.17 3.18 3.21 3.24 3.29 3 52 3.54 3.57 3.60 3.63 3.71 3.89 3.93 3.98 4.24 4.26 4.27 4.31 4.60 4.63 4.86 4.96 4.99
36.9 42.4 52.6 61.8 45.6 52.4 58.9 71.4 82.4 64.2 72.3 87.5 102 115 104 116 138 158 186 145 177 207 235 262 311 239 280 319 341 368 394 446 472 540 605 638 723
7.27 8.43 10.6 12.7 8.35 9.67 11.0 13.5 15.8 11.1 12.6 15.5 18.2 20.8 16.1 18.0 21.6 25.1 30.1 19.9 24.7 29.2 33.5 37.7 45.7 30.1 35.7 41.0 39.5 42.7 46.0 52.0 50.4 58.2 65.8 63.3 72.3 67.7 78.2 83.5 88.7 99.3 109
2.13 2.12 2.10 2.08 2.28 2.28 2.26 2.25 2.22 2.44 2.42 2.41 2.39 2.36 2.74 2.74 2.72 2.69 2.66 3.06 3.04 3.02 3.00 2.97 2.93 3.36 3.34 3.32 3.66 3.65 3.64 3.63
58.5 67.1 83.1 97.6 72.2 83.6 93.3 113 130 102 115 139 161 181 166 184 218 250 294 230 280 328 372 413 487 379 444 505 541 584 625 705
2.68 2.67 2.64 2.61 2.87 2.88 2.85 2.83 2.79 3.07 3.06 3.03 3.00 2.96 3.45 3.45 3.41 3.39 3.34 3.85 3.82 3.80 3.77 3.74 3.67
15.3 17.6 22.0 26.0 18.9 21.1 24.4 29.8 34.7 26.5 29.6 35.9 43.0 48.6 43.1 47.8 57.1 65.9 79.1 59.9 73.3 86.2 98.3 111 135
5.60 6.31 7.59 8.64 6.54 7.15 8.11 9.55 10.7 8.48 9.25 10.9 12.6 13.9 12.2 13.3 15.4 17.3 19.9 15.5 18.4 21.0 23.4 25.6 29.8
1.37 1.37 1.36 1.35 1.47 1.45 1.46 1.45 1.44 1.57 1.55 1.54 1.53 1.54 1.76 1.76 1.75 1.74 1.73 1.96 1.95 1.95 1.94 1.93 1.93 2.16 2.15 2.14 2.35 2.35 2.34 2.34 2.54 2.53 2.52 2.74 2.73 2.95 2.94 2.93 2.93 2.93 2.91 3.14 3.13 3.12 3.50 3.49 3.49 3.50 3.91 3.90 3.89 3.90 3.89
6 6 7 7 75 x 8 75 8 10 10 10 12 12 7 7 8 8 80 x 10 80 10 10 12 12 14 14
5
5
8 13.9 10.9 2.50 3.53 8 9 15.5 12.2 2.54 3.59 9 90 x 11 90 11 11 5.5 18.7 14.7 0.351 2.62 6.36 3.70 13 21.8 17.1 2.70 3.81 13 16 26.4 20.7 2.81 3.97 16 8 8 10 10 12 12 100 x 12 100 14 14 16 16 20 20 10 10 110 x 12 110 12 12 14 14 120 x 15.5 19.2 27.7 26.2 29.6 36.2 12.2 2.74 3.87 15.1 2.82 3.99 17.8 2.90 4.10 0.390 7.07 20.6 2.98 4.21 23.2 3.06 4.32 28.4 3.20 4.53
6
6
21.2 16.6 3.07 4.34 25.1 19.7 0.430 3.15 7.78 4.45 29.0 22.8 3.21 4.54
4.23 98.6 22.7 4.21 116 26.1 4.18 133 29.3 4.62 4.60 4.59 4.56 140 152 162 186 194 223 251 262 298 29.5 31.6 33.3 37.5 37.7 42.4 46.7 47.3 52.7
11 25.4 19.9 3.36 4.75 11 12 27.5 21.6 3.40 4.80 12 13 6.5 0.469 120 8.49 13 29.7 23.3 3.44 4.86 13 15 33.9 26.6 3.51 4.96 15 23.6 3.64 5.15 27.2 0.508 3.72 9.19 5.26 30.9 3.80 5.37 27.5 3.92 5.54 0.547 9.90 31.4 4.00 5.66 27.3 4.12 5.83 31.6 4.21 5.95 33.8 4.25 6.01 0.586 10.6 35.9 4.29 6.07 40.1 4.36 6.17 44.2 4.44 6.28
12 30.0 12 130 x 14 130 14 14 7 34.7 16 39.3 16 13 35.0 13 140 x 15 7.5 140 15 40.0 15 12 12 14 14 15 15 150 x 16 150 16 16 18 18 20 20 34.8 40.3 43.0 45.7 51.0 56.3
3.97 750 5.00 3.94 857 4.97 3.92 959 4.94 4.27 1010 5.38 4.25 1150 5.36 4.60 4.58 4.57 4.56 4.54 4.51 1170 1340 1430 1510 1670 1820
8
5.29 737 5.31 845 5.33 898 5.34 949 5.38 1050 5.41 1150
5.80 303 52.0 5.77 347 58.3 5.76 370 61.6 5.74 391 64.4 5.70 4.38 71.0 5.68 477 76.0 453 506 558 679 757 830 918 943 1050 1160 1380 1580 71.3 78.5 84.8 95.5 105 113 123 121 133 144 167 186
15 46.1 36.2 4.49 6.35 15 160 x 17 160 17 17 8.5 51.8 40.7 0.625 4.57 11.3 6.46 19 57.5 45.1 4.65 6.58 19 170 x 16 16 18 18 18 170 20 20 22 22 9 55.4 61.9 68.4 74.7 61.8 69.1 76.4 90.6 105 43.5 5.02 7.11 48.6 5.10 7.22 0.705 12.7 53.7 5.18 7.33 58.6 5.25 7.44 48.5 5.52 7.80 54.3 0.785 5.60 14.1 7.92 59.9 5.68 8.04 71.1 5.84 8.26 82.0 5.99 8.47
5.67 1100 95.6 5.70 1230 108 5.73 1350 118 6.39 6.41 6.44 6.47 7.09 7.12 7.15 7.21 7.28 1680 1870 2040 2210 2340 2600 2850 3330 3780 130 145 160 174 162 181 199 235 270
4.88 1760 6.15 4.86 1950 6.13 4.84 2140 6.10 5.51 5.49 5.47 5.44 6.15 6.13 6.11 6.06 6.02 2690 2970 3260 3510 3740 4150 4540 5280 5990 6.96 6.93 6.90 6.86 7.78 7.75 7.72 7.64 7.57
16 16 180 x 18 180 18 18 20 20 24 14 28 28
9
57
y
b 4
r1
r2
F G U J Sx Sx
= enkesit alan = arlk = 1 mt iin evre dzeyi = atalet momenti = J = atalet yarap F
sx
h
x s
x
}
ait olduu eilme eksenine izafe
= yarm I- enkesitinin statik momenti = Jx Sx ekme ve basn merkezleri mesafesi
r1 r2 y 14%
Profil
Boyutlar mmh b s=r1 t r3
F
G
U
Eilme Ekseni iinx-x iin Jx Wx cm3 Ix cm Jx cm4 y-y iin Wy cm3 Iy-I1 cm Sx cm3 Sx cm
I 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 425 450 475 500 550 600
cm
3
kg/m
m /m
2
cm4
80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 425 450 475 500 550 600
42 50 58 66 74 82 90 98 106 113 119 125 131 127 143 149 155 163 170 178 185 200 215
3.9 4.5 5.1 5.7 6.3 6.9 7.5 8.1 8.7 9.4 10.1 10.8 11.5 12.2 13.0 13.7 144 15.3 16.2 17.1 18.0 19.0 21.6
5.9 6.8 7.7 8.6 9.5 10.4 11.3 12.2 13.1 14.1 15.2 16.2 17.3 18.3 19.5 20.5 21.6
2.3 2.7 3.1 3.4 3.8 4.1 4.5 4.9 5.2 5.6 6.1 6.5 6.9 7.3 7.8 8.2 8.6
7.57 10.6 14.2 18.3 22.8 27.9 33.5 39.6 46.1 53.4 61.1 69.1 77.8 86.8 97.1 107 118 132 147 163 180 213 254
5.95 8.32 11.2 14.4 17.9 21.9 26.3 31.1 36.2 41.9 48.0 54.2 61.1 68.1 76.2 84.0 92.6 104 115 128 141 167 199
0.304 0.370 0.439 0.502 0.575 0.640 0.709 0.775 0.844 0.906 0.966 1.030 1.09 1.15 1.21 1.27 1.33 1.41 1.48 1.55 1.63 1.80 1.92
77.8 171 328 573 935 1450 2140 3060 4250 5740 7590 9800 12510 15700 19610 24010 29210 36970 45850 56480 68740 99180 139000
19.5 34.2 54.7 81.9 117 161 214 278 354 442 542 653 782 923 1090 1260 1460 1740 2040 2380 2 750 3610 4630
3.20 4.01 4.81 5.61 6.40 7.20 8.00 8.80 9.59 10.4 11.1 11.9 12.7 13.5 14.2 15.0 15.7 16.7 17.7 18.6 19.6 21.6 23.4
6.29 12.2 21.5 36.2 54.7 81.3 117 162 221 288 364 451 555 674 818 975 1160 1440 1730 2090 2480 3490 4670
3.00 4.88 7.41 10.7 14.8 19.3 26.0 33.1 41.7 51.0 61.2 72.2 84.7 99.4 114 131 149 176 203 235 268 349 434
0.91 1.07 1.23 1.40 1.55 1.71 1.87 2.02 2.20 2.32 2.45 2.56 2.67 2.80 2.90 3.02 3.13 3.30 3.43 3.60 3.72 4.02 4.30
11.4 19.9 31.8 47.7 68.0 93.4 125 162 206 257 316 381 457 540 638 741 857 1020 1200 1400 1620 2120 2730
6.84 8.57 10.3 12.0 13.7 15.5 17.2 18.9 20.6 22.3 24.0 25.7 27.4 29.1 30.7 32.4 34.1 36.2 38.3 40.4 42.4 46.8 50.9
23.0 9.2 24.3 9.7 25.6 10.3 27.0 10.8 30.0 11.9 32.4 13.0
58
y W4 W1 W4 t1
d
h-2c
x
x
max sK a
= Bir l- basn ubuu iin mmkn olan en byk ubuk burkulma boyu; max 250. = Her iki eksene gre ayn atalet momentine malik iki L- eksenleri arasndaki ift sayya yuvarlatlm uzakl (=y - eksenleri arasndaki mesafe); J=2J
d a
y
burulma mukavemeti
Profil
DIN 997e gre Flan delikleri W1 mm d mm h-2c mm W4 mm
max
eksene uzakl e=Inn ykseklii h olan il iin a mm Jy cm Iy cm
I 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 425 450 475 500 550 600
t1 mm
K8m
Wx G
J
cm
P 4
22 28 32 34 40 44 48 52 56 60 62 64 70 74 76 82 86 88 94 96 100 110 120
6.4 6.4 8.4 11 11 13 13 13 17 17 17
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