Spregnute Konstrukcije I Graficki Rad

7/25/2019 Spregnute Konstrukcije I Graficki Rad

1/69

[SPREGNUTE KONSTRUKCIJE] 1. grafki rad

10

dp=16

a/3=155 a/2=230

b0x t0

h0x ?0

b3x t3b2x t2b1x t1

l=23.5m

a=4 .8m

=2.8

s=0. 28

MB=40

1. Elementi spregnutog presek

1.1. !eli"ni nos"

Vertikalni limh

0

0

h0=( 115

1

25 )l=1

20l=

1

2023.5=1.175musvojeno :h

0=1180mm

0=8+

l

750=8+

2350

750=11.133mmusvojeno :

0=12mm

Gornji pojas b0t0

b0=min250mmusvojeno:b

0=300mm

t0=min1012mmusvojeno : t

0=14mm

Marko Miloevi MRG 52/0 1


2/69

00


"onji pojas b1t1

b1=

h0

4+100mm=

1180

4+100=395mmusvojeno :b

1=400mm

t1=min20mmusvajam : t

1=25mm

b

2t

2350x 20

b

3t

3300x15

1.#. $rmirno %etonsk plo"

dp=min16cmusvojeno :dp=16cm

1.&. 'o()ni*i

#rvo tre$a da i%ra&namo smi&e sile.

#. 'ero)+ne +eli"ine

#.1. Konstruk*ioni "elik

E=210GPa=2.1108!/cm

2

"a=0.3

#a=7850 $ /m3

%t=1.2105

#.#. ,eton

Eb=9.253

MB+10=9.253

40+10=34.08GPa

"b=0.2

%t=1.2105

#.&. E-ekti+n irin %etonskog presek



3/69


be=be+bn+bep&bstv

hv=10cm

b=a

3b0

2hv=

480

3

30

210=135cm

bn=b0+2hv=30+210=50cm

bp=a

2

b0

2hv=

480

230

210=215cm

'= 1

1+6.4(bl)2=0.979

'p= 1

1+6.4(bpl)2=0.949

be='b=0.979135=132.165cm

bep='pbp=0 .949215=204.035 cm

be=132.165+50+204.035=386.2cm

'a prora&n &%imamo( be#=135+50+215=400cm

&. /e0nisne krkteristi"ni2 presek

Marko Miloevi MRG 52/0 !


4/69


0

0

1

1

2

2

1

1

0

0

L/4=725

3L/8=1087.5

L/2=1450

presek "0" presek "1" presek "2"

?1450 x 12

?300 x 14

?470 x 25

?1450 x 12

?300 x 14

?470 x 25?420 x 20

?1450 x 12

?300 x 14

?470 x 25?420 x 20?370 x 15

3. Krkteristike presek

3.1. $rmirno %etonsk plo"

130.00 50.00 205.00

10

16

10

Y

X

16

30.00 30.00 185.0030.00110.00

385.00

Marko Miloevi MRG 52/0 )


5/69


(te)=

4001681306

214+

23010

2(16+ 103)+3010(16+

10

2)40016

1306

2+23010

2+3010

=57840

6610=8.75 cm

*b=400161306

2+23010

2+3010=6610 cm

2

+b=40016

3

12+400160.75

21306

3

36

1306

25.25

2+2(30103

36+3010

210.50

2)+ 30103

12+301

230

10

1

6

30 30 18530110

155

385

Tb

17.

17 8.

83

4 +reme t=0

upo,ednimodul elastinosti :Ec=Ea"a=1.0

Ec=210GPa=2.1106

da!/cm2

=2.1108

!/cm2

Eb=9.253MB+10=9.25

340+10=34.08GPa=0.340810

6da!/cm

2=0.340810

8!/cm

2

-oe#icijent ,educije: "b=Eb

Ea=

0.3408106

2.1106 =0.1623

*b,="b*b=0.16236610=1072.80 cm2

+b,="b+b=0.1623210864.375=34223.29 cm4

4 +reme t=tn

=2.8

Eb= 2

2+Eb=

2

2+2.834.08=14.20GPa



6/69


"b=Eb

Ea=

14.20

210=0.0676

*b,="b*b=0.06766610=446.96 cm2

+b,=" b+b=0.0676210864.375=14254.43cm4

svojen p,ocenat a,mi,anja:/01*a= 1

100*b=

1

1006610=66.10cm

2

3.#. !eli"ni nos"

Presek 567

Marko Miloevi MRG 52/0 *


7/69


+lement

"imen%ije A e *e ee 1 +a [cm4]

[mm] [mm] [cm2] [cm] [cm3] [cm] +as +ap

b0t

0!00 1) )5 1,.-, ,50.5) -., *.-* !!!,.

**h

0

01)50 12 1,) 1.0, 15-)*.1

-1*.,, 20.-- )-0,.0

5b

1t

1),0 25 11- 1*).-2 1!**.!

55*.- *1.20 !-1552.

* !!) 10,.-) !5*!.0

,

--.) ,,0!,.

)0 ,,0)-*.!)

+lement A e *e ee 1 +a [cm4]

[cm2] [cm] [cm3] [cm] +as +ap

rmat&ra *).!0 0 0 0.)! 0 525-2,.21elininosa

!!).00 10,.-) !5*!.0, 1,.)1 ,,0)-*.!) 10122.*1

!-.!0 0.)! !5*!.0, ,,0)-*.!) *2,05*.-1

1!,5)!.15

8. I)elni presek

I)elni presek9 : +reme t=0

* i0=*a+*b,=398.30+1072.80=1504.26 cm2

(b= *c*i0=35963.07

1504.26=23.912io

(a=c(b=90.4323.91=66.52cm

+i0=+a+*a(a2++b,+*b,(b

2

+i0=1397543.15+398.3066.522+35750.33+1105.9623.91

2

Marko Miloevi MRG 52/0 ,


8/69


+i0=3827999.46cm4

I)elni presek9 : +reme t=tn

* i=*a+*b,=398.30+495.11=893.41 cm2

3b= *c

* i=35963.07

893.41=40.252i

3a=c3b=90.4340.25=50.18 cm

+i=+a+*a3a2++b,+*b,3b

2

+i=1397543.15+398.3050.182+16004.51+495.1140.25

2

+i=3218589.11cm4

Presek 517

Marko Miloevi MRG 52/0 -


9/69


+lement



b0t

0!00 1) )5 1,.-, ,50.5) -., *.-* !!!,.

**h

0

01)50 12 1,) 1.0, 15-)*.1

-1*.,, 20.-- )-0,.0

5b

1t

1),0 25 11- 1*).-2 1!**.!

55*.- *1.20 !-1552.

*

b2t2 )20 20 -) 1*,.0, 1)0!!.--

5.2! 2-.00 2),!5.05

)1- 11.,5 )*.5

11*.) 10*51!2.)5

10*52).!



rmat&ra *).!0 0 0 0.)! 0 525-2,.21

elininosa

)1,.50 11.,5 )*.5 2.!2 10*52).!

!5-*-.-,

Marko Miloevi MRG 52/0


10/69


)-1.-0 10!.,, )*.5 10*52).!

--),*.0,

1500)5.)*


* i0=*a+*b,=481.80+1105.96=1587.76 cm2

(b= *c

*i0=49996.95

1587.76=31.492io

(a=c(b=103.7731.49=72.28 cm

+i0=+a+*a(a2++b,+*b,(b2

+i0=1950045.46+481.8072.282+35750.33+1105.9631.49

2

+i0=5599603.10cm4


* i=*a+*b,=481.80+495.11=976.91cm2

3b= *c* i

=49996.95

976.91=51.182i

3a=c3b=103.7751.18=52.59cm

+i=+a+*a3a2++b,+*b,3b

2

+i=1950045.46+481.8052.592+16004.51+495.1151.18

2

+i=4 595455.50cm4



11/69


Presek 5#7



12/69


+lement



b0t

0!00 1) )5 1,.-, ,50.5) -., *.-* !!!,.

**h

0

01)50 12 1,) 1.0, 15-)*.1

-1*.,, 20.-- )-0,.0

5b

1t

1),0 25 11- 1*).-2 1!**.!

55*.- *1.20 !-1552.

*b

2t

2 )20 20 -) 1*,.0,1)0!!.-

-5.2! 2-.00

2),!5.05

b3t

3 !,0 15 5* 1*-.-2 !*.51 *0.- 10.)120*)11.

,

),! 125.515!**.)

*12,.!)

12,15)).)2

12,1*,1.,*



rmat&ra *).!0 0 0 0.)! 0 525-2,.21elininosa

),!.00 125.51 5!**.)* !5.0- 12,1*,1.,*

5-20*-.,2

5!,.!0 110.) 5!**.)* 12,1*,1.,*

110,-5.2

2!,5*,.*


* i0=*a+*b,=537.30+1105.96=1643.26 cm2

(b= *c

*i0=59366.46

1643.26=36.132io

(a=c(b=110.4936.13=74.36 cm

+i0=+a+*a(a2++b,+*b,(b

2

+i0=2379567.69+537.3074.362+35750.33+1105.9636.13

2

+i0=6829964.43cm4




13/69


* i=*a+*b,=537.30+495.11=1032.41cm2

3b= *c

* i=59366.46

1032.41=57.502i

3a=c3b=110.4957.50=52.99 cm

+i=+a+*a3a2++b,+*b,3b

2

+i=2379567.69+537.3052.992+16004.51+495.1157.50

2

+i=5541235.85cm4

Presek 56; 51; 5#;

1450 x 12

300 x 14

470 x 25

1450 x 12

300 x 14

470 x 25

420 x 20

1450 x 12

300 x 14

470 x 25420 x 20

370 x 15

!eli"nipresek

1osa *

[cm2]

!!) )1- ),!

e 1

[cm]10,.-) 11.,5 125.51

+

[cm4

]

,,0 )-*.!) 1 0*5 2).! 1 2,1 *,1.,*

Marko Miloevi MRG 52/0 1!


14/69


1osaiarm

at&ra

*a

cm

[2]

!-.!0 )-1.-0 5!,.!0

c

[cm]0.)! 10!.,, 110.)

+a

[cm4]

1 !, 5)!.15 1 50 0)5.)* 2 !, 5*,.*

Spregn

utipresek

t

* i0

cm

[2]

1 50).2* 1 5-,.,* 1 *)!.2*

( b

[cm]2!.1 !1.) !*.1!

+i0

[cm4]

! -2, .)* 5 5 *0!.10 * -2 *).)!

t

*i

cm

[2]

-!.)1 ,*.1 1 0!2.)1

3b

[cm])0.25 51.1- 5,.50

+i

[cm4]! 21- 5-.11 ) 55 )55.50 5 5)1 2!5.-5

Marko Miloevi MRG 52/0 1)


15/69


'ont( "eli"nog nos"

R R!200

=: I% > ,etonirne kolo+o:ne plo"e

=: II > Spregnuti nos" prim uti*e sopst+ene te(ine=: II% > 'ost optere?en pokretnim optere?enem=: III > Spregnuti presek prim uti*e skupln %eton=: III% > Spregnuti presek prim uti*e te"en %eton=: III* > Spregnuti presek prim uti*e r:li"itog :gre+n plo"e inos"


16/69


p=23.50

2470.

44

340.

75

340.

75

M5=2470.44 !m

6a=340.75 !


17/69


nali%a optereenja po jednom nosa&

pis optereenja *[cm2 ] 4[ !/m3 ] $1[!/m1]

s4alt na kolovo%& 1!,5.00 21.00 2.-Montani 6 vena7 250.00 25.00 0.*2

6eton isp&ne peake sta%e iinstala7ije

!.00

s4alt na peakoj stasi 1*0.00 21.00 0.!)grada 0.)0

8kela i oplata 9!.50

5+=3.75 !/m1

p=3.75

394.22

54.38

54.38

M5=394.22 !m

6a=6b=54.38 !

Marko Miloevi MRG 52/0 1,


18/69


19/69


p1

=p

2

+p

17

3-d=5.41+

51.10+0.45

23=17.04 !/m1

p=17.04 p=17.04p=5.41

P=89

.94

P=89

.94

P=89

.94

7.25

6.50

5.75

6.50

5.75

M (L/2)

F1 F2F3

11.50 1.50 1.50 1.50 1.50 11.50

2.00

Ml/2p. o .

=P(31+32+33 )+p1

(71+72 )+p2

7

3=89.94(7.25+6.50+6.50 )+17.04( 5.752 11.50+ 5.752 11

p=17.04p=5.41

P=89.94

P=89.94

P=89.94

1.00

0.95

0.90

0.84

F1F2

Ta

1.50 1.50 1.50 24.50

2.00

2*p . o .

=P(31+32+33 )+p1

7

2+p

2

7

1=89.94(1.00+0.95+0.90 )+

17.040.84

224.50+

5.411+0.84

2



20/69


p=17.04p=5.41

P=89.94

P=89.94

P=89.94

0.50

0.45

0.40

0.34

0.50

F1F2

T (l/2)

14.50 1.50 1.50 1.50 10.00

2.00

2l /2p . o .

=P(31+32+33 )+p1

72+p2

71=89.94(0.50+0.45+0.40 )+

17.040.34

210+

5.410.50+0.34

2


21/69


22/69


>nG=M

+( n

G=

247044

1271671.76(108.34)=21.05 !/cm2

>n?=M

+

(n?=

247044

1271671.7644.06=8.56 !/cm

2

=: II B)o)tno stlno optere?eneD

!=0

M++a=394.22 !m

>bG="b( !*i +

M

+i(( bG ))=0.172394226829964.43(44.96 )=0.045 !/cm2

>b?="b( !* i+

M

+i((bG ))=0.172394226829964.43(18.96 )=0.019 !/cm2

>nG="n( !*i +

M

+i((bG ))= 394226829964.43(18.96 )=0.11!/cm2

>n?="n(!* i

+M+i(+(bG ))=

39422

6 829964.43(+133.44 )=0.77 !/cm2

=: II% Bpokretno optere?eneD

!=0

M++b=3159.04 !m

>bG="b( !*i +

M

+i(( bG ))=0.1723159046829964.43 (44.96 )=0.36 !/cm2

>b?="b( !* i+

M

+i((bG ))=0.1723159046829964.43 (18.96 )=0.15 !/cm2

>nG="n

(

!

*i

+M

+i

((bG )

)=

315904

6829964.43(18.96 )=0.88 !/cm2



23/69


>n?="n( !* i+

M

+i(+(bG ))= 3159046 829964.43(+133.44 )=6.17 !/cm2

Marko Miloevi MRG 52/0 2!


24/69


A.#. Pror"un npon u t=tn

A.#.1.Uti* skupln %eton

Ms=1784.66 !m !s=3103.76 !

>bG="b(!s* i +

Ms

+i(3b

G)) (s)Eb=0.077(3103.761032.41 + 1784665541235.85(66.33 ))(0.0003 )16

>b?="b

(

!s

*i

+Ms

+i

(3b? )

)(s)Eb=0.077

(

3103.76

1032.41+

178466

5541235.85(40.33)

)0.00031609



25/69


>nG=!s

*i+Ms

+i(3n

G)=3103.761032.41

+ 178466

5541235.85(40.33 )=4.30 !/cm2

>n?=!s

* i+Ms

+i3n

?=3103.76

1032.41

+ 178466

5541235.85

112.07=0.60 !/cm2

A.#.#.Uti* te"en %eton

M=469.16 !m !=129.16 !

>bG="b(!* i+

M

+i(3b

G)):>b0G =0.077(129.161032.41 + 469.165541235.85(66.33))0.560.045=0.035

>bG="b(

!

* i+M

+i(3b

? )):>b0? =0.077(129.161032.41+ 469.165541235.85(40.33))0.560.019=0.02

>nG=!

* i+M

+i3n

G=129.16

1032.41+

469.16

5541235.85(40.33)=0.13 !/cm2

>n?=!s

* i+Ms

+i3n

G=129.16

1032.41+

469.16

5541235.85112.07=0.12 !/cm

2

A.#.&.Uti* temperturne r:like

t

s=

1.2104

1.5104=0.80

>bG=>bst

s=0.870.80=0.70 !/cm

2

>b?=>bs t

s=0.810.80=0.65 !/cm

2

>nG=>nst

s=4.300.80=3.44 !/cm

2

>n?=>ns t

s=0.600.80=0.48 !/cm

2



26/69


. Pror"un spregnute konstruk*ie s pri+remenim oslon*em u l /2

=: I > 'ont( "eli"nog nos"

Marko Miloevi MRG 52/0 2*


27/69

RA RBRC

R'A R'BRC

R'A R'B

RC


l /2=14.5m l /2=14.5m

=: I% > ,etonirne kolo+o:ne plo"e

l /2=14.5m l /2=14.5m

=: II > Po o"+r?+nu %eton ukln se pri+remeni oslon* nego+urek*iu prim spregnuti nos"

l /2=14.5m

l /2=14.5m

Marko Miloevi MRG 52/0 2,


28/69


29/69


Mmax=347.39 !m

6*=6B=0.3755l

2=0.37523.5014.5=127.78 !

6@=1.255l

2=1.2523.514.5=425.94 !

.1.#.=: II

P=425.94

29.00

3088.06

-212.97

212.97

Mmax=6@l

4=

425.9429

4=3088.06 !m

6*=6B=6@

2= 425.94

2=212.97 !

.1.&.=: II%

. nali%a optereenja po jednom nosa&

pis optereenja *[cm2 ] 4[ !/m3 ] $1[!/m 1]

s4alt na kolovo%& 1!,5.00 21.00 2.-Montani 6 vena7 250.00 25.00 0.*2

6eton isp&ne peake sta%e iinstala7ije !.00

s4alt na peakoj stasi 1*0.00 21.00 0.!)



30/69


31/69


32/69


p=17.04p=5.41

P=89.94

P=89.94

P=89.94

1.00

0.95

0.90

0.84

F1F2

Ta

1.50 1.50 1.50 24.50

2.00

2*p . o .

=P(31+32+33 )+p1

7

2+p

2

7

1=89.94(1.00+0.95+0.90 )+17.04

0.84

224.50+

5.411+0.84

2

.#. =: III > Skuplne %eton

*b=6430 cm2

8=1566.80cm

dm=2*b8

=26430

1566.80=8.21

6elativnavla)nost s,edine=90

s=0.309

t=tn

!s=Eb*b s=160964300.0003=3103.76 !

Ms=!s3b=3103.760.575=1784.662!m

.&. =: III% > Te"ene %eton

:=

2+=

2.5

2+2.5=0.56

M=M++a+M++b=3088.06+394.22=3482.28 !m

Marko Miloevi MRG 52/0 !2


33/69


!b0=M*b,(b,

+i0=

3482281105.9636.136829964.43

=2037.29 !

!=:!b0=0.562037.29=1140.88!

Mb0=M+b,+i0

=3482.2835750.33

6 829964.43=18.23!m

M=M+:(Mb0+!b03b0 )=3482.28+0.56(18.23+2037.290.5750 )=4148.50 !m

.3. =: III* > Temperturn r:lik

; t=10 Uti*e prim "eli"ni nos"

M@+=617.61 !m

!+=0

>nG=M+

+io(n

G= 61761

1271671.76(108.34 )=5.26 !/cm2

>n?=M+

+io(n

?= 61761

1271671.7644.06=2.14 !/cm

2

F.1.#.=: II II% > Uti*e prim spregnuti nos"

Marko Miloevi MRG 52/0 !!


34/69


M++=M++a+M++b=3088.06+394.22=3482.28!m

!++=0

>bG="b

M+

+io(n

G=0.1723482286829964.43

(44.96 )=0.39 !/cm2

>b?="b

M+

+io(n

?=

0.172348228

6829964.43(18.96 )=0.17 !/cm2

>nG=

M++

+io(n

G= 348228

6829964.43(18.96)=0.97 !/cm2

>n?=M++

+io(n

?=

348228

6829964.43133.44=6.80 !/cm

2

F.1.&.=: II* > Pokretno optere?ene

M=3159.04 !m

!=0

>bG="b

M+

+io(n

G=0.172315904

6829964.43(44.96 )=0.36 !/cm2

>b?="b

M+

+io(n

?=

0.172315904

6829964.43(18.96 )=0.15 !/cm2

>nG=

M++

+io(n

G= 315904

6829964.43(18.96)=0.88 !/cm2

>n?=M++

+io(n

?=

315904

6829964.43133.44=6.17 !/cm

2

Marko Miloevi MRG 52/0 !)


35/69


Marko Miloevi MRG 52/0 !5


36/69


37/69


F.#.&.=: III* > Uti* temperturne r:like

t

s=

1.2104

1.5104=0.80

>bG=>

b

s

ts

=0.870.80=0.70 !/cm2

>b?=>bs t

s=0.810.80=0.65 !/cm

2

>nG=>nst

s=4.300.80=3.44 !/cm

2

>n?=>ns t

s=0.600.80=0.48 !/cm

2

:a%eapon

Ies g ;

teenjep

snovno

optereenje

bG 90.-- 90.51 90.!* 91.,5 90.,0 92.)5

>b? 90.-1 90.2) 90.15 91.20 90.*5 91.-5

>nG 5.2* 9).!0 91.1 90.-- 91.-! 9!.)) 95.2,

>n? 92.1) 0.*0 .) *.1, 1).12 0.)- 1).*0

'a elik !.63v=26 !/cm2

Osno+no optere?ene >dop=0,665>v=0,66526=17,29 !/cm2

Marko Miloevi MRG 52/0 !,


38/69


39/69


40/69


=: II > Posle +e:i+n %eton i uklnn oslon*9 spregnuti presek

prim rek*iu 6c+P

R'A R'B

RC+P

=: II% > Spregnuti presek prim uti*e sopst+ene te(ine II -:e=: II* > 'ost optere?en pokretnim optere?enem=: III > Spregnuti presek prem uti*im skupln %eton=: III% > Spregnuti presek prem uti*im te"en %eton=: III* > Spregnuti presek prem uti*im r:li"itog :gre+n kolo+o: i

"eli"nog nos"

16.1. =: I16.1.1. =: I


pis optereenja *[cm2 ] 4[ !/m3 ] $1[!/m 1]

elini nosa )0-.!! ,-.50 3.20

3olovo%na ploa *)!0.00 25.00 16.08

plata i skela 3.50

5+=23.50 !/m1

Marko Miloevi MRG 52/0 )0


41/69


42/69


Pmax29

4=2029.46+617.61

Pmax=194.74 !

Us+m P=50!

M+=5l

2

8+Pl

4=

23.514.52

8+5029

4=980.11 !m

P=50.00

14.50 14.50

-362.50

16.#. =: II16.#.1. =: II

6c+P=425.94+50=475.94 !

P=475.94

14.50 14.50

3450.56

M++a=3450.56 !m

16.#.#. =: II% > /o)tn sopst+en te(in


Marko Miloevi MRG 52/0 )2


43/69


44/69


45/69


46/69


!b0=M*b,(b

+i0=

3799781105.9636.136829964.43

=2223.04!

!=:!b0=0.562223.04=1111.52!

Mb0=M+b,+i0

=3799.7835750.33

6829964.43=19.89 !m

M=M+:(Mb0+!b03b )=3799.78+0.56(19.89+2223.040.5750 )=4526.74 !m

16.&.&. =: III* > Uti* temperturne r:like

; t=10 Uti*e prim "eli"ni nos"

M+=

5( l2 )2

8Pl

4=23.514.5

2

8

5029

4=617.61362.5=980.11!m

>nG=M

+(G=

98011

1271671.76(108.34 )=8.35 !/cm2

>n?=M

+(?=

98011

1271671.76

44.06=3.40 !/cm2

Marko Miloevi MRG 52/0 )*


47/69


48/69


49/69


50/69




51/69




52/69


53/69


54/69

p*1 p*2

P*

P*

P*

10 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19

20

29.00 29.00

F1

F2 F3

p*1


M10=2301.72 !m

3 1 31 32 3 1 1

2.0

0.20

64

0.

1527

1.400.10

0.

0537

2.0

0.20

64

0.1625

1.40 0.10

0.

043"

2.90 :0.0537=1.40:xx=0.025931=0.1527+0.0259=0.1786

2.90 :0.0537=0.10:xx=0.001831=0.15270.0018=0.1509

2.90 :0.0439=1.40:x x=0.02123 2=0.1625+0.0212=0.1837

2.90 :0.0439=0.10:xx=0.001531 1 =0.16250.0212=0.1413


6 6 61 0.

0501

1.)52

# 0.100

-

2.2!

20.150

).!,*1

& 0.152,

).)2-!

0.1,-*

5.1,)

3 0.20*)

5.-5*

0.

1-!,

5.

!2,!

8 0.1*25

).,125

0.1

)1!

).0

,,

< 0.121*

!.52*)

A 0.0-

)!

2.))

),

0.0512

1.)-)-

73

10.*,!,-.*5-15.*,-!.1150.*2

#F.16A

72

2.10*,*.!)5!10.2101.


55/69

p*1p*2

P*

P*

P*

10 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19

20

29.00 29.00

F1

F2


10 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19

20

F1

F2 F3

M10=(P (31+32+33 )+p1 (72+73 )+p271 )=(89.94(5.1794+5.9856+5.3273 )+17.04(18.6710+29.1

0

3 1 31 32 3 1 1

2.0

1.40

1.

00

0.

8753

0.

1247

2.0

0.

8753

0.

7520

1.500.10

0.

1233

2.90:0.1247=1.40:xx=0.060231=0.8753+0.0602=0.9355

2.90:0.1233=2.80:x x=0.119032=0.7520+0.1190=0.8710

2.90:0.1233=1.30:x x=0.055331 1 =0.7520+0.0553=0.8073


6 1

3 0.!55

1 0.-,5!

3 0.-,10

3 0.-0,!

# 0.,520

& 0.*1

!23 0.51*0

8 0.)0*0

< 0.!0)0

A 0.2110

0.12-0

F 0.05,0

16

0

72

1.01!51.,51.*!,!1.!!*1.0250.,)2)0.)1*0.2*-20.0-2*.818

71

1.)51*1.2*,*0.0-,!1.25-,3.6


56/69

p*1p*2

P*

P*

P*

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

20

29.00 29.00

p*1


10 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19

20

F1

F2

0=P

(3 1+31+32 )+p1

7

2+p

2

7

3=89.94(1.0+0.9355+0.8710 )+17.048.5815+5.414.0652=420.

10

3 1 31 32 3 1 1

1.00

2.0

1.40

0.943

0.

057

0.943

2.0

0.872

1.500.10

0.

071

2.90 :0.057=1.40:xx=0.02831=0.943+0.028=0.971

2.90 :0.071=2.80:x x=0.06832=0.872+0.068=0.940

Marko Miloevi MRG 52/0 5*

6 61 0.02

5# 0.0)

-& 0.0*

-3 0.0-

)8 0.0

)< 0.0

*A 0.0-

0.0,

2

F 0.0)!

16

1

31

0.,1

11

0.)!

32

0.)0

3 0.0

)1#

0.-,2

1&

0.,-

13

0.**

18

0.5)

1 Uti* sopst+ene te(ine

M$=2470.34 !m

>bG="b

M$

+io(b

G=0.172247034

6829964.43(44.96)=0.28 !/cm2

>b?

="bM$

+io (b

?

=

0.172247034

6829964.43 (18.96)=0.12 !/cm2

>nG=M$

+io(n

G= 247034

6829964.43(18.96 )=0.68!/cm2

>n?=

M$

+io(n

?=247034

6829964.43133.44=4.83 !/cm

2

1&.1.#. =: II > Uti* pokretnog optere?en

Mp=2301.72!m

>bG="b

Mp

+io(b

G=

0.172230172

6829964.43(44.96)=0.26 !/cm2

>b?="b

Mp

+io(b

?=0.172230172

6829964.43(18.96)=0.11!/cm2

>nG=Mp

+io( n

G=230172

6829964.43(18.96 )=0.64 !/cm2

>n?=Mp

+io(n

?=230172

6829964.43133.44=4.50 !/cm

2



60/69


61/69


62/69


Ms=892.79 !m

>bG="b(!s* i +

Ms

+i3

G)sEb=0.077(3103.761032.41 + 892795541235.85(66.33))+0.00031609=0.33 !

>b?="b(!s*i +

Ms

+i3

?)sEb=0.077(3103.761032.41 + 892795541235.85(40.33 ))+0.00031609=0.30

>nG=!s

*i+Ms

+i3n

G=3103.76

1032.41+ 89279

5541235.85(40.33 )=2.36 !/cm2

>n?

=

!s

* i +

Ms

+i 3n?

=

3103.76

1032.41 +

89279

5541235.85112.07

=4.81

!/cm

2

Marko Miloevi MRG 52/0 *2


63/69


64/69


T1 T2 T3

4.98

3.43

&1 &2 &3 &4

3.625 3.625 3.625 3.625

7.25

14.50

14.50 7.25

14.50

21=4.59 !/cm

22=4.20 !/cm

23=3.82 !/cm

1=

20+2

1

2F=

4.98+4.59

2362.5=1734.56!

2=

21+222

F=4.59+4.20

2362.5=1593.19!

3=

22+2

3

2F=

4.20+3.82

2362.5=1453.62 !

4=2

3+2

4

2F=

3.82+3.43

2362.5=1314.06 !

13.1.#. Pror"un nosi+osti mo()nik

I +rint > Kom%ino+ni mo()ni*i Bkruti si)roD

!d=6?E+Da

6?E=*13'6B

Da=/*a>a

Marko Miloevi MRG 52/0 *)

h

1'

2

3

10

13

26

m

10

10

10

10

30


65/69


*1=103=30cm2

*2=b0(dp+hv )=28(16+10)=728cm2

3=*

2

*1

=728

30=4.93>33=3

'6B=0.6'b (28)=0.65.0=3.0!/cm2

6?E=3033.0=270!

/=0.7Aa Aatvo,enasid,a

>a=140MPa=14 !/cm2

*a=,2

4=

1.02

4=0.785 cm

2

Da=0.70.78514=7.69 !

Da 1=0.707Da=0.7077.69=5.43 !

!d=270+7.69=277.69 !

II +rint > Elsti"ni mo()ni*i B"ep s gl+omD

Marko Miloevi MRG 52/0 *5


66/69


67/69


68/69


=svajam ra%mak modanika od e=50cm to &% raspon od l=29m daje &k&pan $roj

kr&ti> modanika 8 kom.

II +rint

n1= 1!dop

=1734.56197.92

=8.76 omusvajam :n1=9 om

e1=

F

n1

=362.5

9=40.28 cmusvajam:e1=40cm

n2=

2

!dop=1593.19

197.92=8.05 omusvajam : n

1=9om

e2=

F

n2

=362.5


n3=

3

!dop=

1453.62

197.92=7.34 omusvajam: n

1=8om

e3=

F

n3

=362.5


n4=

4

!dop=

1314.06

197.92=6.64 omusvajam : n

1=7om

e3=F

n3

=362.5

7=51.79cmusvajam: e

4=50cm

=svajam ra%mak modanika od e=40cm to &% raspon od l=29m daje &k&pan $roj

kr&ti> modanika A& kom.

Rekpitul*i

I +rint

Pr+ i :)n "et+rtin

n=725

50=14.50usvojeno:n=15om

/rug i tre? "et+rtin

Marko Miloevi MRG 52/0 *-


69/69


n=725

60=12.08usvojeno:n=13om

Ukupno

n=56om

II +rint

Pr+ i :)n "et+rtin

n=725

40=18.12usvojeno :n=19om

/rug i tre? "et+rtin

n=72545

=16.11usvojeno: n=17om

Ukupno

n=72om

Documents

Spregnute Konstrukcije I Graficki Rad