Download - Spregnute Konstrukcije I Graficki Rad
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[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
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00
[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
"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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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 !
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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 )
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
(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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
"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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
+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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
+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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
+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.
*
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).!
+lement A e *e ee 1 +a [cm4]
[cm2] [cm] [cm3] [cm] +as +ap
rmat&ra *).!0 0 0 0.)! 0 525-2,.21
elininosa
)1,.50 11.,5 )*.5 2.!2 10*52).!
!5-*-.-,
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
)-1.-0 10!.,, )*.5 10*52).!
--),*.0,
1500)5.)*
I)elni presek9 : +reme t=0
* 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)elni presek9 : +reme t=tn
* 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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
Presek 5#7
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
+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.
*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.,*
+lement A e *e ee 1 +a [cm4]
[cm2] [cm] [cm3] [cm] +as +ap
rmat&ra *).!0 0 0 0.)! 0 525-2,.21elininosa
),!.00 125.51 5!**.)* !5.0- 12,1*,1.,*
5-20*-.,2
5!,.!0 110.) 5!**.)* 12,1*,1.,*
110,-5.2
2!,5*,.*
I)elni presek9 : +reme t=0
* 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
I)elni presek9 : +reme t=tn
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
* 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.,*
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
'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"
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
p=23.50
2470.
44
340.
75
340.
75
M5=2470.44 !m
6a=340.75 !
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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 !
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
>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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
>n?="n( !* i+
M
+i(+(bG ))= 3159046 829964.43(+133.44 )=6.17 !/cm2
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
>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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
. Pror"un spregnute konstruk*ie s pri+remenim oslon*em u l /2
=: I > 'ont( "eli"nog nos"
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RA RBRC
R'A R'BRC
R'A R'B
RC
[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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.!)
Marko Miloevi MRG 52/0 2
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
!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 !!
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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 !)
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
Marko Miloevi MRG 52/0 !5
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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 !,
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
=: 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
nali%a optereenja po jednom nosa&
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
nali%a optereenja po jednom nosa&
Marko Miloevi MRG 52/0 )2
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
!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 )*
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
Marko Miloevi MRG 52/0 50
-
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
Marko Miloevi MRG 52/0 51
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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
[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
Marko Miloevi MRG 52/0 5)
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.
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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
[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
Marko Miloevi MRG 52/0 55
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
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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
[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
Marko Miloevi MRG 52/0 5
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
*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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
=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
9=40.28 cmusvajam:e2=40cm
n3=
3
!dop=
1453.62
197.92=7.34 omusvajam: n
1=8om
e3=
F
n3
=362.5
8=45.31 cmusvajam:e3=45cm
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
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[SPREGNUTE KONSTRUKCIJE] 1. grafki rad
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