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8/18/2019 Spec.fundiranje - II Deo Zadatka (Winkler)
1/4
2. RESAVANJE ZADATKA PO WINKLER-ovoj HIPOTEZI
a) Proracun sleganja tacke A
koriscenjem uticajnih funkcija
( )2,
1 o A i k i i
io
S q F b E
ν
π
−= × × ×
× ∑
F=64,0 m2
Povrsina prepusta = ,46!6 cm2
"=,46!6#21,6=0,$4
%amenjujuci rostilj
&sa istom povrsinom ali 'e( prepusta)
14
8/18/2019 Spec.fundiranje - II Deo Zadatka (Winkler)
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1 1
1 1
1 1
1
2 2
2
2
povrsina 1
*,+ 1$,$4 4,+*4,+* 6,6 0,$$
2 2 6,6
4,+* 0,141 0
4,+* 6,6
0,6 4,1$60* 0$$ 4,$+64$ 4,21+022
povrsina 2
2,4* 4,++ 1,24!1,24! 2,44 0,!
2 2 2,44
1,2
k
aa m b m
b
x ym n
a b
F
aa m b m
b
xm
a
α
α
= = = = = = =
= = = = = ≈
= × + × =
= = = = = = =
= =
( )
2
2
2
$ $
$ $
$ $
1$ 4
4! $,11 1,$
1,24! 2,44
0, 2,40606 0$ 1,0$+0! 1,**!6!
povrsina $
4,+! 4,++ 2,4$2,4$ 2,44 1
2 2 2,44
!,*+ $,12,! 1,2 1,!
2,4$ 2,44
1,+!+* 1,2+662 1,44*$* 1,124*4 1,4
k
k
yn
b
F
aa m b m
b
x ym n
a b
F
α
= = = ≈
= × + × =
= = = = = = =
= = = = = = ≈
= × + + + =
4 4
4 4
4 4
4
! !
2**62!
povrsina 4
2,4* 4,16 1,24!1,24! 2,0+ 0,62 2 2,0+
1,24! 2,41 1,$2
1,24! 2,0+
0,6+ 2,6+2 0$2 1,2206$ 2,2116
povrsina !
4,+! 4,16 2,4$2,4$ 2,0+ 1,2
2 2 2,0+
k
aa m b mb
x ym n
a b
F
aa m b m
b
xm
α
α
= = = = = = =
= = = = = =
= × + × =
= = = = = = =
=
( )
! !
! !
1! 4
!
, 1 2 ,
2
!,*+ 2,42,! 1,$2 1,!2,4$ 2,0+
1,*$1*1 1,$12+ 1,!44 1,1+462 1,!016*2!
2 2 12,0!62 24,1124
k
k i i k k i i
i
yna b
F
F b F b F b
= = = = = ≈
= × + + + =
× = × × − × = × = ÷
∑ ∑
1!
8/18/2019 Spec.fundiranje - II Deo Zadatka (Winkler)
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( ) ( ) ( ) ( )
( )
( ) ( )
2
2
2 2
,
1 2 1 1 2 0,$ 1 0,$*!00 0!,1
1 1 0,$
1+!00 111* 12+016$,$
12+
1 1 0,$16$,$ 24,1124 0,162 16, 2
0!,1
16,2
-kupna krutost opruga
o S
rostilja
o
A k i i
io
A
A
E M kN m
R Gq kN m
F
S q F b m cm E
S cm
R K
S
ν ν
ν
ν
π π
− × × + − × × += × = × =
− −+ + +
= = =
− −= × × × = × × = =
× ×
=
=
∑
∑ 1+!00 1144+!,00,162
.rutosti poje"inacnih opruga
1144+!,0. +*4,42
12+i i i
kN m
K F F
F
= =
= × = = ×∑∑
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8/18/2019 Spec.fundiranje - II Deo Zadatka (Winkler)
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/ijagrami momenta &pravac)
/ijagrami momenta &pravac)
1*