betonarme kopru hesabi

8/10/2019 Betonarme Kopru Hesabi

1/23

PLAK MOMENTLERNN HESABI

Yk: 2015 SH cmu 380 = cmv 200 =

kN

F

F AKS

T 602

120

2 ===

1) Zati Yk iin Plak Momentlerinin Hesab:

cmc

hmeyil

48015!02

1120015!0

2===

m664"565462

3101 == m565"56

5462

3#02 == mort 236

2

"56565 =+=

$o%lam Plak &'rl':

(*eme: kN3#3048512520 =

&s+alt: kN32133048511810 =,a%: kN52630485122040 =Me-il .!: kN4#8304851220630 = / $o%lam 6531 k

a

b M2M1


2/23

nol abaktan :

46250430

185===

b

a 048501=M

162185

430===

a

b 008002 =M

( ) ( ) mkNmGMMMa 283316500800200485021 =+=+= ( ) ( ) mkNmGMMMb 161316504850200080012 =+=+=

rekli Plakta abit Ykten (ola- &klk e Mesnet Momentleri:

mkNmM aa 63228380 ==

mkNmM mesa 64128350 ==mkNmM ab "3016180 ==

mkNmM mesb 58016150 ==

Merke7i am-on $ekerle'i 9in Plak Momentleri:

Yk: 1215 SH cmu 380 = cmv 200 =

kNF

F AKST 602

120

2===

( ( ) cmhhuu plakk 2"810120238220 =++=++=( ( ) cmhhvv plakk 28010120220220 =++=++=

46250430

185===

b

a 5210

185

2"8==

a

u 1"60

430

280==

b

v

&bak 8a ;


3/23

&bak #a ;


4/23

PLAK DONATISININ HESABI

Mal7eme 220B20

sa


5/23

mkNmMd 2512=

"#804"301581000

1025122

6

2 ==

=

= zw

m kdb

Mdk

mmmdk

MdA

ydzs 416

1581"1"#80

10213 26

=

=

=

eilen


6/23

m" 6403"13 ==

m" 025221501024 ==m"T 50160102 ==

Zati -k iin konsol momenti

( ) kNAG 5144514002511 === ( ) kNAG 125131022502522 === ( )

kNAG 5""012

206002533 =

==

( ) kNAG #50150202544 ===

[ ] mkNmMk# 31#5410252#506405"051125133#51514 =+++=

( ) m"$% T 352151600102801518015180 =+=+=+=kNm

%

$FM T

k 1284211352

5160=

=

=

mkNmMko!sol 5145)12842A3161)3241A41 =+=

Mesnet (onatsnn Hesab

sa


7/23

"8802#01#01000

1066#2

6

2 ==

=

= zw

m kdb

Mdk

mmmdk

MdA

ydz

s 23#1#01"1"880

1066# 26

=

=

=

23#56540124012 2

=>=+= #ersmevs AmmmA

Dk erek -ok

onsol


8/23

,a%EEEEEEEEEEEEEEEEEE!: mkN 14822040125" =(*emeEEEEEEEEEEEEEEEE!!!: mkN 25462520125" =

Me-il beton EEEEEEEEEEEEE!: mkN08#222

06"50125" =

$retarlarEE: ( ) ( ) mkN3#5#025"012

6020

150450404512 =

+

++ &na kiri*lerEEEEEEEEEE!!!: ( ) mkN #2251602401602 =+

Dnleme kiri*lerEEEEEEEEEE!: ( ) mkN5##442540608513 =orklklar EEEEEEEEEEEEEEEEEEEEEE!: mkN4= / $o%lam mkN# "15233=&na kiri*lerin atalet momentlerinin @esab

(* ana kiri* atalet momenti

( ) 251"01"

2

62225"166 dmA =

+++=

dmy 0511

51"0

15225"3

4216

2

141")

2

216A21"216166

0 =

+

++

=

( ) ( )

( ) ( ) 423

23

23

23

1

453"8"20511162

1"4

12

1"410511161"2

12

1"2

1051116225"12

25"205118166

12

166

dm

&"

=

++

++

++

+=

9 ana kiri* atalet momenti


9/23

210"25"22126 dmA =+= ( )

dmy #4810"

1125"222121260 =

+=

( ) ( ) 423

23

2 15051#4812225"12

25"22#42126

12

126dm&" =

++

+=

Kpr alk ortas mom!tlr"!"! #sa$ %

6"48018

40"340"1 =

=$

( )5642

40"

6"425440"32 =

== $$

kNml#

M# 4#102#"8

8018"15233

8

22

=

=

=


10/23

kNmMHS 4"4#56423056421206"4120 =++=

kNmlq

M# 161"18

8018354

8

22

===

(inamik katsa-snn @esab

3126"13#8018

151 =

++=

Yk eksantriklik katsa-snn @esab

41 453"8" dm&$ = 42 1505dm&$ =

&&& == 32

&&&& 6521505

453"8"41 ===

+= iii

i e&&i

21

( ) =+= &&&i 3#126522 ( ) ( ) ( )( ( )( && ii 58#46#5365212251225116#53652

22222 =+++=

1! ana kiri* iin m6#531=


11/23

ee&

&+=

+= 360016#53

58#4

30#11

2! ana kiri* iin m521=

ee&&

+=

+= 11201225158#4

30#

12

Dleri*si7 kam-on *erit sa-snn blnmas e kam-on -klerin


12/23

me 12505462543 ==

( ) 13811250360013#

652313 =+=K

1511

02421"01381

1511

##140

12maG

13

12

11

==

====

KK

K

K

K

12#"138326"115114"4# MmkNKMM iHSi ====

( )

( )

( )

3#510

3#510"01250112013#

13

323806251112013#

12

184"01253112013#

11

23maG

23

22

21

==

=+=

=+=

=+=

KK

K

K

K

23"645026"13#5104"4# MmkNKMM iHSi ====

El&r"'s"( trt)&ar sa*s!! $)l)!mas %

1 $retar


13/23

02=e

( )

( )2#3"0

2#3"0011201

3#

6522

21"10355112013#

6521

F

22

F

maGF

22

F

21

==

=+=

=+=KK

K

K

mkNKMMtrq

=== 3#522#3"0161"122

F

22

+at" *kt! ,ola* a!a k"r"'lr, ol)'a! aklk ortas mom!tlr" % 0=#e

( ) kNm&

M 5"3#314#102#"1

3#

6521 =

=

( ) kNm&

M 214084#102#"1

3#2 =

=

So!) ms!t mom!tlr"!"! ta'ma -.! -r soprpo("s*o!) %

( )triqiHSi#i MMMM 6141 ++=( ) mkNM =++= 1###6305203#"1383615"3#31411

( ) mkNM =++= 812##63#52"64506121408412

A!a k"r"'lr, ol)'a! maks"m)m ms!t raks"*o!) %

11 =$ ( )

##408018

25480182 =

=$

( )54#0

8018

254280183 =

=$

kN'# "521"22

8018"15233=

=

kNm'HS 2"22"54#030##401201120 =++=

kN'tr #"402

8018354

=

= Ms!t raks"*o!lar!! a!a k"r"'lr ,a-tlmas %


14/23

ii K'' =

( ) kN#' 08#"613#

652"521"21 ==

( ) kN#' 413001

3#

1"521"2

2

==

= ii K''

( ) kNHS' "033426"115112"22"1 == ( ) kNHS' 1510"26"13#502"22"2 == ii K'' =

( ) kNq' tr 334306221#"401 ==

( ) kNq' tr 15112#340#"402 == So!) ms!t raks"*o!lar!! ta'ma -.! -r soprpo("s*o!) %

( )triqiHSi#i '''' 6141 ++=

( ) kN' 681#1"3343"3346108#"6411 =++= ( ) kN' 05461315111510"6141300412 =++=

A!a k"r"' Do!at Hsa$ %

K!ar a!a k"r"' ,o!at #sa$ %

Mal7eme B20420 < 160 15 145 ?m

. 1"0/60/"253425 ?m kNmMd #10240= ha= kabl -a%lr

cd hdhbMy 50850 =

( )2050145205342331850 =My cmkNMdcmkNMy == 1###681006#10

MdMy ol


15/23

2

min 1"841450600365

0418080 mmdb

A

yd

ctds ===

eilen mms 120= seil


16/23

Mal7eme B20420 < 120 10 110 ?m. "25/60/"25245 ?m

mkNMd = 812##6 ha= kabl -a%lr

cd hdhbMy 50850 =

( )105010020245331850 =My cmkNMdcmkNMy =>= 2##6814"8550

"3#013111002450

102##6812

4

2 ==

=

= zw

m kdb

Mdk

mmmdk

MdA

ydzs 8120

1100365"3#0

102##681 24

=

=

=

2min 150511006003650418080 mmdb

A

yd

ctds ===

eilen mms 200= seil


17/23

E!lm k"r"' #sa$ %

de!*++,%-G%K

b

bh

h

w

F4!

"

2

180

404

1

80

20

==

==82822=

4433

04040#240382822

816mdm

hb&

e!leme

==

=

=

4

!! 15050 m& kira!i = m452=

$ekerlek -kten


18/23

43

!4

3

!4

12

4

48

4 %

+A

%

+A

% .-

.

b-.%

.%b

.%

Kb

=

=

=

( )m.-

.

%

+A

122"3#0040408018452

1505012124

3

4

3

!

=

=

=

kNF 60= ( ) ( )""eF

"M "

sin?os4

=

= 01" ( ) ( ) mkNe"M == 3"65650sin0?os

22"3#04

60 01

= m" 812

( ) ( ) ( )( ) mkNe"M =

= 413#128122"3#0sin8122"3#0?os22"3#04

60 8122"3#02

= m" 33 ( ) ( ) ( )( ) mkNe"M == 51444322"3#0sin322"3#0?os

22"3#0460 322"3#0

3

= m" 844

( ) ( ) ( )( ) mkNe"M =

= 24#568422"3#0sin8422"3#0?os22"3#04

60 8422"3#04

= m" 215

( ) ( ) ( )( ) mkNe"M =

= 6314482122"3#0sin2122"3#0?os22"3#04

60 2122"3#05

= m" 36 ( ) ( ) ( )( ) mkNe"M == 51444322"3#0sin322"3#0?os

22"3#04

60 322"3#06

mkNM.S =+++++= 3"##15"514446314824#5651444413#123"6565

Zati -kten


19/23

kNb

GF 55#

4

851

85134

3165

2

22

2 =

=

=

kNFFF 352555#225102 21 =+=+=

= 01" ( ) ( ) mkNe"M == 8"41160sin0?os22"3#043525 0

1

= m" 4522

( ) ( ) ( )( ) mkNe"M =

= 0181345222"3#0sin45222"3#0?os22"3#04

3525 45222"3#02

mkNM #o =+= "303220181328"4116)A

mkNMMM HSoo#o =+=+= #43553"##15"26"161"30322416141

Dnleme


20/23

mh 80= mh 85126012555451 =+++= mt 65154 =+= mcb 151225"45122 =+=+=

kN''/'' traaHSa#A 112#33#"4022"22"3"521"22 =++=++=

kN'F A0 82112#33030030 === Arlol mesnet srtnme keri)

kNG #4#446183511315121 ==


21/23

kNG 1042602535"5115122 ==

kNG 5#2"6125515615123 ==

kNG 2614#618545115124 ==

kNGi

6#161442614#65#2"61104260#4#446 =+++=

kNF0T 8""438#8188##50 ==

enar a-a'a etki-en akti+ e %asi+ to%rak itkilerinin blnmas

21 8048018330 mkNhe taa === 2

1 "081)808512A18330)A mkNhhe taa =+=+=

kNdhe% aa 5#4"1512851280411 ===

( ) kNdh

ee%aaa

#260182

15128512)84"81A

2122

=

=

=

kNdt

e% pp 81180"

2

15126324

2

===

K!ar a*ak ta#k"klr" %

D&r"lm ta#k"k" %

kuvvetiddeti

(kN)momentkolu (m) M(kNm)

V(A) 2733,11 2,25 6149,50

G1 7446,46 4,50 33509,07

G2 4260,1 2,25 9585,225

G3 2961,57 3 8884,71

G4 1476,26 0,75 1107,2

! 11809,8 6"3 23619,6

30687,56 to!l#m 82855,305

#1 749,5 12,85"2 4815,54

kN'G' Aii #8188##112#336#16144 =+=+=

23246183 mkNte tpp ===


22/23

#2 6018,72 12,85"3 25780,184

$% 82 11,25 922,5

6850,22 to!l#m 31518,224

L noktasna >re ===

1evire!

1ire!e!1 M

Ms ol


23/23

! 11809,8 '6"3 '23619,6

G1 7446,8 '1,5 '11170,1

to!l#m 5295,03

2

1 58331

"#2

0352"5

"#2

#8188##mkN

2

M

A

'=+=+=

2

2 33186"#2

0352"5

"#2

#8188##mkN

2

M

A

'==+=

3

221

20 400"52582

331865833133186

2mkNmkN emz =

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