1. TEORIA E
KONSTRUKSIONEVE II
2009
*
[Type the company name]
5/5/2009

2. TEORIA E KONSTRUKSIONEVE II 2009
VEDAT RAMADANI 2
4.50m 4.50m 4.50m
13.50m
4.50m 4.50m 4.50m
13.50m
F=120kn F=120kn
F=120kn F=120kn
X1=1kn X2=1kn
YA=120kn YB=120kn
540knm 540knm
M

3. TEORIA E KONSTRUKSIONEVE II 2009
VEDAT RAMADANI 3
X2=1kn
9.00 m 4.50 m
13.50 m
X1=1kn
4.5knm
M1
YA=1.0kn YB=1.0kn
4.5knm
3.00 m 3.00 m
6.00 m
X1=1kn
4.5knm
M2

4. TEORIA E KONSTRUKSIONEVE II 2009
VEDAT RAMADANI 4
EKUACIONI KANONIK
X1δ11+δ10=0
δ10=(- *4.52
*540)*2-4.52
*540=-14580
δ11= 4.53
)*2+4.53
+2*( 4.52
*3+ 4.52
*3)=160.875
X2= =90.62kn X2= X1

5. TEORIA E KONSTRUKSIONEVE II 2009
VEDAT RAMADANI 5
4.50m 4.50m 4.50m
13.50m
F=120kn F=120kn
X1=90.62kn X2=90.62kn
132.167knm 132.167knm
M
29.37kn
29.37kn
Q
YA=29.37kn YB=29.37kn

6. TEORIA E KONSTRUKSIONEVE II 2009
VEDAT RAMADANI 6
3.00m 3.00m
6.00m
X1=90.62kn
132.167knm
M
45.31kn
45.31kn
Q
YA=45.31kn YB=45.31kn

7. TEORIA E KONSTRUKSIONEVE II 2009
VEDAT RAMADANI 7
155.00mm
23.00mm
377.00mm
23.00mm
400.00mm
14.00mm
DIMENSIONIMI I TRAUT 1
Mmax=1.7*132.167=225.539 knm
lej
Wpot= = =0.0014096m3
=1409.6cm3
Hopt= = =37.54cm
Pervetesohet h=400mm
Karakteristikat e profilit
H=400mm
B=155mm
D=14mm
T=23mm
Ix =29210cm4
Wx=1460cm3
G=1949.4kg/m
=154478.76≤ lej=160000 kn/m2
fmax= = =0.000973m
flej= = =0.054m

8. Teoria e Konstruksioneve II Mars2009
VEDAT RAMADANI 1
1.50m 5.00m 5.00m 5.00m 1.50m
18.00m
Nr=P1+P2+P3+P4
Nr=950+1100+1300+1000=4450kn
Nt=0.15*4450+4450=5117.5kn
Mr=P1*7.5+P2*2.5-P3*2.5-P4*7.5=
Mr=950*7.5+1200*2.5-1300*2.5-1000*2.5=625knm
A=B*L=B*18
NR
P1 P2 P3 P4
Mr

9. Teoria e Konstruksioneve II Mars2009
VEDAT RAMADANI 2
At=0.30*0.40+0.60*0.8=1.04m2
t=1.04*25*18=450kn/m2
3*0.5 10*0.5 3*0.510*0.5 10*0.5
K1=0.25*1.30*160000=5200
K2=0.50*1.30*160000=10400

10. Teoria e Konstruksioneve II Mars2009
VEDAT RAMADANI 3
A
A
PRERJAA-A
PARAQITJA3DETHEMELIT

11. Teoria e Konstruksioneve II Mars2009
VEDAT RAMADANI 4
DIAGRAMET TE PUNUARA ME PROGRAMIN STAAD
303.08
383.24
MOMENTETEPERKULJESTETHEMELIT
Mo
DIAGRAMET
TRANZVERZALET
T(Q)
DIAGRAMET
507.69
302.47279.85
407.39
395.75
310.46
516.52
559.89
519.7
569.65
605.77
532.5
335.27

12. Teoria e Konstruksioneve II Mars2009
VEDAT RAMADANI 5
Mumax=1.7*507.69=863.073knm
Mumax=1.7*407.39=692.563knm
a=ao+øu+ =2.0+1.0+ =9.4cm
hstat=h-a=120-9.4=110.6cm
lart
Kh= = =2.90
Per MB 3O Kz=0.956 Ea/Eb=10/1.4‰
Aa= = =20.51cm2
I 2ø14 me Aa=3.08cm2
II 4ø25 me Aa=19.64cm2
Aa=22.72>20.51cm2
Aamin= min*Ab=0.25/100*60*110.6=16.59cm2
Posht
Kh= = =3.25

13. Teoria e Konstruksioneve II Mars2009
VEDAT RAMADANI 6
Per MB 3O Kz=0.962 Ea/Eb=10/1.2‰
Aa= = =16.27cm2
I 2ø14 me Aa=3.08cm2
II 3ø25 me Aa=14.73cm2
Aa=17.81>16.27cm2
Aa=17.81> Aamin==16.59cm2
Amon=4ø12/30cm
Stafat
eu=2/3 h≤30cm
eu=2/3*120=80>30cm
pervetesohen
st=ø10/20/10cm
Tu=1.7*569.65=968.405kn
τn= = =1.49MPa
Per MB 30 τr=1.1MPa< τn=1.49MPa
Behet caktimi se per cilat nderje behet fjale
τr=1.1MPa< τn=1.49MPa<3 τr=3.3MPa

14. Teoria e Konstruksioneve II Mars2009
VEDAT RAMADANI 7
Ka nevoje te behet sigurimi nga nderjet kryesore te pjerreta me forca te
reduktuara
n τau
τru
λ
500cm
λ= *5.0=1.30m=130cm
forcat tranzverzale qe pranon betoni
τru= Tu-Tbu
Tbu=1/2(3 τr- τn)*b0*z=1/2(3*1.1-1.49)*60*0.962*110.6=586.7kn
Nderjet ne rreshqitje te reduktuara jane
τru= = =0.905MPa
min Au=min u* = =0.6cm2
st=ø10=0.79cm2
>0.6cm2
dmth e ploteson kushtin

15. Teoria e Konstruksioneve II Mars2009
VEDAT RAMADANI 8
132RØ14
132RØ14
144RØ25
11 4RØ12
11 4RØ12
132RØ14
143RØ25
132RØ14
11 4RØ12
11 4RØ12
pRØ10
132RØ14
143RØ25
132RØ14
144RØ25
11 4RØ12
11 4RØ12
pRØ10
132RØ14
132RØ14
144RØ25
11 4RØ12
11 4RØ12
132RØ14
143RØ25
132RØ14
11 4RØ12
11 4RØ12
pRØ10
132RØ14
132RØ14
144RØ25
11 4RØ12
11 4RØ12

16. Teoria e konstruksioneve II 2009
VEDAT RAMADANI 1
д ч 1:д се определ т ре кции и ди гр ми н ст тичките големини Mr,Mt
и угиб w з д ден т рмир но бетонск кружн плоч со примен н
т блиците н Marcus. одул н ел стичност : E=31*106
KN/m2
, =0.2
a=4m
b=2m
q=20kn/m
P=15kn
t=0.16m
Q=1 N=
E*h3
12*(1- 3 )
=
31*106*0.163
12*(1-0.23 )
=16533.33
Mr=0
Mt=
q*a2
8
(1- )=
20*42
8
(1-0.2)=32knm
W’=-
q*a3
8*N*(1+ )
=
20*43
8*16533.33*(1+0.2)
=-0.00806m
Qr=-
q*a
2
*Q=
20*4
2
*1=-40k
P P
q
2b
2a
q
2a

17. Teoria e konstruksioneve II 2009
VEDAT RAMADANI 2
Q=
r
a
=
2.0
4.0
=0.5 N=
E*h3
12*(1- 3 )
=
31*106*0.163
12*(1-0.23 )
=16533.33
φ1=1-Q2
=1-0.52
=0.75 φ0=1-Q4
=1-0.54
=0.937
Mr=
q*a4
16
*(3+ )* φ1=
20*42
16
*(3+0.2)*0.75=48knm
Mt=
q*a2
16
*[2(1- )+(1+3* )* φ1=
20*42
16
*[2(1-0.2)+(1+3*0.2)*0.75]=56 knm
W”=
q*a4
64*N*(1+ )
*[2(3+ )* φ1-(1+ )* φ0=
20*44
64*16533.33*(1+0.2)
*[2(3+0.2)*0.75-
(1+0.2)*0.937=0.01481m
Q=0
Mr= Mt=
q*a2
16
*(3+ )=
20*42
16
*(3+0.2)=64knm
W=
q*a4
64*N
*
(5+ )
(1+ )
=
20*44
64*16533.33
*
(5+0.2)
(1+0.2)
=0.0209m
Qr=-
q*a
2
*Q=
20*4
2
*1=-40kn

18. Teoria e konstruksioneve II 2009
VEDAT RAMADANI 3
q
2a
+
48 48
64
Mt
64 5656
3232
Mr
-0.008
0.0148
0.02
0.0148
-0.008W

19. Teoria e konstruksioneve II 2009
VEDAT RAMADANI 4
β=
b
a
=
2.0
4.0
=0.5
x1=(3+ )*(1- β2
)+2*(1+ )* β2
*ln β =(3+0.2)*(1-0.52
)+2*(1+0.2)*0.52
*ln0.5 =1.98
x2=(1- )*(1- β2
)-2*(1+ )*ln β =(1+0.2)*(1-0.52
)-2*(1+0.2)*ln0.5 =2.26
Mr=Mt=
P*b
4
*x2=
15*2
4.0
*2.26=16.59knm
Qr=0
W=
P*b*a2
8*N*(1+ )
*( x1- x2)+ x2* φ1=
20*2*42
64*16533.33*(1+0.2)
*( 1.98- 2.26)+
2.26*0.75=0.000713
Q=1
Mr=0
Mt=
P*b
4
*(1- )*(1- β2
)=
15*2
4
*(1-0.2)*(1- 0.52
)=4.5knm
P P
2b
2a

20. Teoria e konstruksioneve II 2009
VEDAT RAMADANI 5
+
16.59 16.59
Mt
16.5916.59 4.54.5
Mr
0.00056
7
0.0007
0.00598
0.0007
0.00056
7
W
P P
2b
2a
W’=
P*b*a
8*N*(1+ )
*(1- β2
)=
15*2*4
8*16533.33*(1+0.2)
*(1- 0.52
)=0.000567
Q=0
W=
P*b*a2
8*N*(1+ )
*x1=
15*2*42
8*16533.33*(1+0.2)
*1.98=0.00598m

21. Teoria e konstruksioneve II 2009
VEDAT RAMADANI 6
Ly
д ч 2: се определ т ст тичките големини з д ден т пр во голн
рмир но бетонск плоч ,тов рен со р мномерен тов р п,со примен н
т блиците н rcus. се определи м ксим лен угиб н плоч т .
=31*106
kN/m2
: =0.2
Lx=5m
Ly=6m
P=12kn/m
T=0.16m
λ=
Ly
Lx
=
6
5
=1.2
N=
E*h3
12*(1- 2 )
=
31*106
*0.163
12*(1-0.22
)
= 11022.22
vx=vy= v
з д ден т плоч (вклештен во две стр ни и две стр ни слободни
потпрен ) ги чит ме следниве под тоци
v=1-
15
32
*
λ2
1+λ4
=1-
15
32
∗
1.22
1+1.24
=0.78
px=p*
λ4
1+λ4
=12*
1.24
1+1.24
=8.09kn/m
Lx

22. Teoria e konstruksioneve II 2009
VEDAT RAMADANI 7
py= p*
1
1+λ4
=12*
1
1+1.24
=3.90kn/m
max во долн т зон
Mxmax=
9
128
*px*Lx
2
*v=
9
128
*8.09*5.02
*0.78=11.09knm
Mymax=
9
128
*py*Ly
2
*v=
9
128
*3.90*6.02
*0.78=7.70knm
Muxmax=11.09*1.8=19.96knm
Muymax=7.70*1.8=13.68knm
орн т зон
Mxmin=-
px*Lx2
8
=
8.09*5.02
8
=-25.28knm
Mymin=-
px*Lx2
8
=
3,90*6,02
8
=-17.07knm
Muxmin=1.8*(-25.28)=-45.50knm
Muymin=1.8*(-17.07)=--30.72knm
ресметк н угиб
W=
1
N
*
px*Lx4
720
*(1.064+2.815*v)=
=
1
11022.22
*
8.09*5.04
720
*(1.064+2.815*0.78)=0.00207m