i graficki rad
DESCRIPTION
dasdTRANSCRIPT
Osnove saobraajnica
Teorija povrsinskih nosaa (I grafiki rad) Milan Jovanovi MRG 46/09
Pravougaona ploa
Za datu plou i optereenje sraunati i nacrtati dijagrame:
1. Ugiba w;
2. Presenih sila Mx, My, Mxy, Tx i Ty;
3. Reakcije oslonaca Ax i Ay.
Geometrijske karakteristike ploe:
m
S
x
80
,
1
=
,
80
,
0
=
a
,
40
,
0
=
b
,
25
,
0
=
g
,
m
h
14
,
0
=
,
20
,
0
=
n
.
Optereenje ploe:
2
/
00
,
8
m
kN
p
=
,
m
kN
q
/
00
,
12
=
,
kN
F
00
,
20
=
.
Iz uslova:
=
x
y
S
S
a
=
80
,
1
80
,
0
y
S
m
S
y
44
,
1
80
,
1
80
,
0
=
=
m
S
y
44
,
1
=
m
S
l
x
x
80
,
10
80
,
1
6
6
=
=
=
m
S
l
y
y
76
,
5
44
,
1
6
4
=
=
=
m
l
x
64
,
8
80
,
10
40
,
0
2
2
=
=
b
m
l
y
88
,
2
76
,
5
25
,
0
2
2
=
=
g
p=8 kN/m
q=12 kN/m
61,80=10,80 m
41,44=5,76 m
y
x
F=20 kN
F=20 kN
F=20 kN
F=20 kN
2
20,4010,8=8,64 m
20,255,76=2,88 m
F=20 kN
F=20 kN
q=12 kN/m
p=8 kN/m
2
1
2
3
6
5
4
k
z
w
=
DD
- diferencijalna jednaina pravougaone ploe izloene savijanju
w
- funkcija ugiba
z
- konstanta spoljnog optereenja upravna na srednju ravan ploe
k
- krutost ploe na savijanje
1
2
3
7
9
10
8
6
5
4
11
15
16
17
13
12
14
61,80=10,80 m
41,44=5,76 m
y
x
w
1
w
2
w
3
w
9
w
7
w
1
w
4
w
4
w
15
Konturni uslovi
Iz uslova oslanjanja:
x pravac (slobodno oslanjanje)
y pravac (ukljetenje)
3
9
w
w
-
=
6
10
w
w
-
=
4
15
w
w
=
5
16
w
w
=
6
17
w
w
=
64
,
0
80
,
0
2
=
=
a
a
}
k
x
x
M
S
k
,
2
=
Proraun koeficijenata iz eme:
215
,
21
8
64
,
0
1
64
,
0
6
8
1
6
2
2
=
+
+
=
+
+
a
a
(
)
(
)
560
,
6
64
,
0
1
4
1
4
2
-
=
+
-
=
+
-
a
250
,
10
64
,
0
1
1
4
1
1
4
2
-
=
+
-
=
+
-
a
563
,
1
64
,
0
1
1
2
=
=
a
64
,
0
2
=
a
Proraun slobodnih lanova (od optereenja)
ij
x
ij
oij
k
S
z
w
4
2
=
a
4
2
x
k
o
S
z
kw
=
a
(
)
(
)
833
,
145
7
2
,
0
1
12
14
,
0
10
3
1
12
2
3
7
2
3
=
-
=
-
=
v
h
E
k
Taka 1.
1
p=8 kN/m
2
q=12 kN/m
1,80
1,44
0,72
2
1
1
1
/
667
,
14
44
,
1
80
,
1
44
,
1
12
44
,
1
80
,
1
0
,
8
m
kN
z
z
S
S
S
q
S
S
p
z
y
x
y
y
x
=
+
=
+
=
540
,
98
80
,
1
80
,
0
667
,
14
4
2
1
=
=
o
kw
Taka 2.
2
p=8 kN/m
2
1,80
1,44
0,72
2
2
2
2
/
00
,
8
44
,
1
80
,
1
44
,
1
80
,
1
0
,
8
m
kN
z
z
S
S
S
S
p
z
y
x
y
x
=
=
=
748
,
53
80
,
1
80
,
0
00
,
8
4
2
2
=
=
o
kw
Taka 3.
3
p=8 kN/m
2
1,80
1,44
0,90
0,72
0,72
(
)
2
3
3
3
/
20
,
7
44
,
1
80
,
1
44
,
1
72
,
0
90
,
0
0
,
8
72
,
0
2
m
kN
z
z
S
S
S
S
p
z
y
x
y
x
=
+
=
+
=
373
,
48
80
,
1
80
,
0
20
,
7
4
2
3
=
=
o
kw
Taka 4.
4
p=8 kN/m
2
q=12 kN/m
1,80
1,44
0,72
(
)
2
4
4
4
/
333
,
7
44
,
1
80
,
1
72
,
0
12
80
,
1
72
,
0
0
,
8
2
2
m
kN
z
z
S
S
S
q
S
S
p
z
y
x
y
x
y
=
+
=
+
=
269
,
49
80
,
1
80
,
0
333
,
7
4
2
4
=
=
o
kw
Taka 5.
5
p=8 kN/m
2
1,80
1,44
0,72
(
)
2
5
5
5
/
000
,
4
44
,
1
80
,
1
80
,
1
72
,
0
0
,
8
2
m
kN
z
z
S
S
S
S
p
z
y
x
x
y
=
=
=
874
,
26
80
,
1
80
,
0
368
,
10
4
2
5
=
=
o
kw
Taka 6.
6
p=8 kN/m
2
1,80
1,44
0,72
F=20 kN
0,72
0,90
(
)
2
6
6
6
/
316
,
11
44
,
1
80
,
1
20
72
,
0
72
,
0
90
,
0
0
,
8
2
72
,
0
2
m
kN
z
z
S
S
F
S
S
p
z
y
x
y
x
=
+
+
=
+
+
=
026
,
76
80
,
1
80
,
0
316
,
11
4
2
6
=
=
o
kw
540
,
98
80
,
1
80
,
0
667
,
14
4
2
1
=
=
o
kw
748
,
53
80
,
1
80
,
0
00
,
8
4
2
2
=
=
o
kw
373
,
48
80
,
1
80
,
0
20
,
7
4
2
3
=
=
o
kw
269
,
49
80
,
1
80
,
0
333
,
7
4
2
4
=
=
o
kw
874
,
26
80
,
1
80
,
0
368
,
10
4
2
5
=
=
o
kw
026
,
76
80
,
1
80
,
0
316
,
11
4
2
6
=
=
o
kw
Proraun ugiba
Pomou tablice:
w1
w2
w3
w4
w5
w6
kwo
1
21,215
-13,120
1,280
-20,500
8,0
0
98,540
2
-6,560
21,855
-6,560
4,0
-20,500
4,0
53,748
3
0,640
-6,560
20,575
0
4,0
-20,500
48,373
4
-10,250
4,0
0
24,341
-13,120
1,280
49,269
5
2,0
-10,250
2,0
-6,560
24,981
-6,560
26,874
6
0
2,0
-10,250
0,640
-6,560
23,701
76,026
026
,
76
701
,
23
560
,
6
64
,
0
250
,
10
2
0
874
,
26
560
,
6
981
,
24
560
,
6
2
250
,
10
2
269
,
49
280
,
1
120
,
13
341
,
24
0
4
250
,
10
373
,
48
500
,
20
4
0
575
,
20
560
,
6
64
,
0
748
,
53
4
500
,
20
4
560
,
6
855
,
21
560
,
6
540
,
98
0
8
500
,
20
280
,
1
120
,
13
215
,
21
6
5
4
3
2
1
6
5
4
3
2
1
6
5
4
3
2
1
6
5
4
3
2
1
6
5
4
3
2
1
6
5
4
3
2
1
=
+
-
+
-
+
=
-
+
-
+
-
=
+
-
+
+
+
-
=
-
+
+
+
-
=
+
-
+
-
+
-
=
+
+
-
+
-
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
w
5967
,
14
3121
,
18
1367
,
21
9073
,
21
3633
,
30
6196
,
35
6
5
4
3
2
1
=
=
=
=
=
=
kw
kw
kw
kw
kw
kw
2,625
-0,313
-0,313
-1
-1
1
2
3
7
8
6
5
4
11
13
12
14
y
x
1
2
3
4
5
6
35,6196
30,3633
21,9073
21,1367
18,3121
14,5967
21,1367
35,6196
30,3633
18,3121
21,9073
14,5967
1
4
2
5
3
6
Sile u presecima (momenti savijanja)
}
k
y
y
M
S
k
,
2
=
[
]
m
kNm
M
x
/
k
k
x
y
w
x
w
k
M
+
-
=
2
2
2
2
,
n
20
,
0
=
n
,
64
,
0
2
=
a
313
,
0
64
,
0
20
,
0
2
=
=
a
v
(
)
(
)
'
/
032
,
6
240
,
3
3633
,
30
2
6196
,
35
625
,
2
1367
,
21
313
,
0
2
2
625
,
2
313
,
0
2
2
2
1
4
1
,
m
kNm
k
S
k
w
w
w
M
x
x
=
-
+
-
=
=
-
+
-
=
(
)
(
)
'
/
307
,
3
240
,
3
9073
,
21
6196
,
35
3633
,
30
625
,
2
3121
,
18
313
,
0
2
625
,
2
313
,
0
2
2
3
1
2
5
2
,
m
kNm
k
S
k
w
w
w
w
M
x
x
=
-
-
+
-
=
=
-
-
+
-
=
(
)
(
)
'
/
557
,
5
240
,
3
0
3633
,
30
9073
,
21
625
,
2
5967
,
14
313
,
0
2
625
,
2
313
,
0
2
2
7
2
3
6
3
,
m
kNm
k
S
k
w
w
w
w
M
x
x
=
-
-
+
-
=
=
-
-
+
-
=
(
)
(
)
'
/
380
,
2
240
,
3
3121
,
18
2
1367
,
21
625
,
2
6196
,
35
313
,
0
0
313
,
0
2
625
,
2
313
,
0
313
,
0
2
5
4
1
11
4
,
m
kNm
k
S
k
w
w
w
w
M
x
x
=
-
+
-
-
=
=
-
+
-
-
=
(
)
(
)
'
/
874
,
0
240
,
3
1367
,
21
5967
,
14
3121
,
18
625
,
2
3633
,
30
313
,
0
0
313
,
0
625
,
2
313
,
0
313
,
0
2
4
6
5
2
12
5
,
m
kNm
k
S
k
w
w
w
w
w
M
x
x
=
-
-
+
-
-
=
=
-
-
+
-
-
=
EMBED Equation.3
(
)
(
)
'
/
058
,
4
240
,
3
3121
,
18
0
5967
,
14
625
,
2
9073
,
21
313
,
0
0
313
,
0
625
,
2
313
,
0
313
,
0
2
5
8
6
3
13
6
,
m
kNm
k
S
k
w
w
w
w
w
M
x
x
=
-
-
+
-
-
=
=
-
-
+
-
-
=
(
)
(
)
'
/
084
,
4
240
,
3
0
2
0
625
,
2
1367
,
21
313
,
0
1367
,
21
313
,
0
2
625
,
2
313
,
0
313
,
0
2
12
11
4
15
11
,
m
kNm
k
S
k
w
w
w
w
M
x
x
-
=
-
+
-
-
=
=
-
+
-
-
=
EMBED Equation.3
(
)
(
)
'
/
179
,
3
240
,
3
0
0
0
625
,
2
3121
,
18
313
,
0
5967
,
14
313
,
0
625
,
2
313
,
0
313
,
0
2
13
11
12
5
16
12
,
m
kNm
k
S
k
w
w
w
w
w
M
x
x
-
=
-
-
+
-
-
=
=
-
-
+
-
-
=
EMBED Equation.3
(
)
(
)
'
/
820
,
2
240
,
3
0
0
0
625
,
2
5967
,
14
313
,
0
5967
,
14
313
,
0
625
,
2
313
,
0
313
,
0
2
11
14
13
6
17
13
,
m
kNm
k
S
k
w
w
w
w
w
M
x
x
-
=
-
-
+
-
-
=
=
-
-
+
-
-
=
[
]
m
kw
i
1
2
3
7
8
6
5
4
11
13
12
14
y
x
1
3
6,032
5,557
3,307
2,380
0,874
4,058
4
6
1
4
4,084
3,178
2,820
4,084
3,178
2,820
2
5,557
3,307
5
0,874
4,058
2,380
6,032
2,380
3,307
0,874
0,874
5,557
4,058
4,058
2
5
3
6
Sile u presecima (momenti savijanja)
21,215
-10,250
-10,250
-6,560
-6,560
2,0
2,0
0,640
2,0
0,640
2,0
1,563
1,563
2,256
-1
-0,128
-1
-0,128
k
k
y
y
w
x
w
k
M
+
-
=
2
2
2
2
,
n
20
,
0
=
n
,
64
,
0
2
=
a
128
,
0
64
,
0
20
,
0
2
=
=
a
v
(
)
(
)
'
/
615
,
14
074
,
2
3633
,
30
128
,
0
2
6196
,
35
256
,
2
1367
,
21
2
128
,
0
2
256
,
2
2
2
2
1
4
1
,
m
kNm
k
S
k
w
w
w
M
y
y
=
-
+
-
=
=
-
+
-
=
(
)
(
)
'
/
215
,
16
074
,
2
3121
,
18
2
9073
,
21
128
,
0
3633
,
30
256
,
2
6196
,
35
128
,
0
2
128
,
0
256
,
2
128
,
0
2
5
3
2
1
2
,
m
kNm
k
S
k
w
w
w
w
M
y
y
=
-
-
+
-
=
=
-
-
+
-
=
(
)
(
)
'
/
880
,
7
074
,
2
5967
,
14
2
0
128
,
0
9073
,
21
256
,
2
3633
,
30
128
,
0
2
128
,
0
256
,
2
128
,
0
2
6
7
3
2
3
,
m
kNm
k
S
k
w
w
w
w
M
y
y
=
-
-
+
-
=
=
-
-
+
-
=
(
)
(
)
'
/
557
,
3
074
,
2
0
6196
,
35
1367
,
21
256
,
2
3121
,
18
128
,
0
2
256
,
2
128
,
0
2
2
11
1
4
5
4
,
m
kNm
k
S
k
w
w
w
w
M
y
y
=
-
-
+
-
=
=
-
-
+
-
=
(
)
(
)
'
/
074
,
3
074
,
2
3633
,
30
0
5967
,
14
128
,
0
3121
,
18
256
,
2
1367
,
21
128
,
0
128
,
0
256
,
2
128
,
0
2
2
12
6
5
4
5
,
m
kNm
k
S
k
w
w
w
w
w
M
y
y
=
-
-
-
+
-
=
=
-
-
-
+
-
=
(
)
(
)
'
/
185
,
4
074
,
2
9073
,
21
0
0
128
,
0
5967
,
14
256
,
2
3121
,
18
128
,
0
128
,
0
256
,
2
128
,
0
2
3
13
8
6
5
6
,
m
kNm
k
S
k
w
w
w
w
w
M
y
y
=
-
-
-
+
-
=
=
-
-
-
+
-
=
(
)
(
)
'
/
383
,
20
074
,
2
1367
,
21
2
0
256
,
2
0
128
,
0
2
2
256
,
2
128
,
0
2
2
4
11
12
11
,
m
kNm
k
S
k
w
w
w
M
y
y
-
=
-
+
-
=
=
-
+
-
=
(
)
(
)
'
/
659
,
17
074
,
2
3121
,
18
2
0
128
,
0
0
256
,
2
0
128
,
0
2
128
,
0
256
,
2
128
,
0
2
5
13
12
11
12
,
m
kNm
k
S
k
w
w
w
w
M
y
y
-
=
-
-
+
-
=
=
-
-
+
-
=
(
)
(
)
'
/
076
,
14
074
,
2
5967
,
14
2
0
128
,
0
0
256
,
2
0
128
,
0
2
128
,
0
256
,
2
128
,
0
2
6
14
13
12
13
,
m
kNm
k
S
k
w
w
w
w
M
y
y
-
=
-
-
+
-
=
=
-
-
+
-
=
[
]
m
kNm
M
y
/
1
2
3
7
8
6
5
4
11
13
12
14
y
x
1
2
3
4
5
6
14,615
3,074
7,880
16,215
7,880
3,557
4,185
3,074
4,185
1
4
2
5
3
6
20,383
17,656
14,074
3,557
3,074
4,185
16,215
14,615
16,215
7,880
20,383
17,656
14,074
3,557
3,074
4,185
Sile u presecima (momenti savijanja)
'
/
000
,
0
1
,
m
kNm
M
xy
=
'
/
000
,
0
2
,
m
kNm
M
xy
=
'
/
000
,
0
3
,
m
kNm
M
xy
=
'
/
000
,
0
4
,
m
kNm
M
xy
=
(
)
(
)
(
)
(
)
'
/
599
,
1
80
,
1
80
,
0
4
20
,
0
1
5967
,
14
6196
,
35
4
1
2
2
6
1
5
,
m
kNm
k
S
v
k
w
w
M
x
xy
-
=
-
+
-
=
-
+
-
=
a
(
)
(
)
(
)
(
)
'
/
343
,
2
80
,
1
80
,
0
4
20
,
0
1
0
3633
,
30
4
1
2
2
7
2
6
,
m
kNm
k
S
v
k
w
w
M
x
xy
-
=
-
+
-
=
-
+
-
=
a
'
/
000
,
0
7
,
m
kNm
M
xy
=
(
)
(
)
(
)
(
)
(
)
'
/
381
,
3
80
,
1
80
,
0
4
20
,
0
1
9073
,
21
9073
,
21
4
1
2
2
3
3
8
,
m
kNm
k
S
v
k
w
w
M
x
xy
-
=
-
-
-
=
-
-
+
-
=
a
'
/
000
,
0
11
,
m
kNm
M
xy
=
(
)
(
)
(
)
(
)
(
)
(
)
'
/
000
,
0
80
,
1
80
,
0
4
20
,
0
1
0
4
1
2
2
6
6
4
4
12
,
m
kNm
k
S
v
k
w
w
w
w
M
x
xy
=
-
=
-
-
+
+
+
+
-
=
a
(
)
(
)
(
)
(
)
(
)
'
/
000
,
0
80
,
1
80
,
0
4
20
,
0
1
0
4
1
2
2
5
5
13
,
m
kNm
k
S
v
k
w
w
M
x
xy
=
-
=
-
+
+
-
=
a
[
]
m
kNm
M
xy
/
1
2
3
7
8
6
5
4
11
13
12
14
y
x
1
2
3
4
5
6
7
8
1,599
2,343
3,381
3,381
2,343
1
4
2
5
3
6
1,599
2,343
3,381
2,343
3,381
Sile u presecima (transverzalne sile)
1
2
3
7
9
10
8
6
5
4
11
15
16
17
13
12
14
61,80=10,80 m
41,44=5,76 m
w
1
w
2
w
3
w
9
w
7
w
1
w
4
w
4
w
15
x
18
19
20
21
22
y
w
18
w
20
23
24
25
Konturni uslovi
Iz uslova oslanjanja:
x pravac (slobodno oslanjanje)
y pravac (ukljetenje)
3
9
w
w
-
=
6
10
w
w
-
=
2
18
w
w
-
=
5
19
w
w
-
=
4
15
w
w
=
5
16
w
w
=
6
17
w
w
=
1
20
w
w
=
2
21
w
w
=
3
22
w
w
=
}
k
x
x
T
S
k
,
3
2
=
k
l
5,125
-5,125
1,563
1,563
1
-1,563
-1
-1,563
i
k
k
x
y
x
w
x
w
k
T
+
-
=
2
3
3
3
,
n
64
,
0
2
=
a
563
,
1
/
1
2
=
a
(
)
m
kN
k
S
k
w
w
w
w
w
w
T
x
x
/
000
,
0
664
,
11
)
9073
,
21
9073
,
21
3633
,
30
125
,
5
3633
,
30
125
,
5
3121
,
18
563
,
1
2
3121
,
18
563
,
1
2
(
2
125
,
5
125
,
5
563
,
1
2
563
,
1
2
3
3
3
2
2
5
5
1
,
=
-
-
+
+
-
-
=
=
-
+
+
-
-
=
(
)
(
)
m
kN
k
k
S
k
w
w
w
w
w
w
T
x
x
/
132
,
1
664
,
11
377
,
39
073
,
66
3633
,
30
275
,
112
537
,
182
664
,
11
)
5967
,
14
563
,
1
2
1367
,
21
563
,
1
2
0
3633
,
30
9073
,
21
125
,
5
6196
,
35
125
,
5
(
2
563
,
1
2
563
,
1
2
125
,
5
125
,
5
3
6
4
7
2
3
1
2
,
-
=
-
+
+
+
-
=
=
-
+
-
+
+
-
=
=
-
+
-
+
+
-
=
(
)
(
)
(
)
(
)
m
kN
k
k
S
k
w
w
w
w
w
w
T
x
x
/
501
,
3
664
,
11
0
244
,
57
9073
,
21
6196
,
35
0
612
,
155
664
,
11
)
0
563
,
1
2
3121
,
18
563
,
1
2
9073
,
21
6196
,
35
0
125
,
5
3633
,
30
125
,
5
(
2
563
,
1
2
563
,
1
2
125
,
5
125
,
5
3
8
5
3
1
7
2
3
,
-
=
-
+
+
+
+
-
=
=
-
+
-
-
+
+
-
=
=
-
+
-
-
+
+
-
=
(
)
m
kN
k
S
k
w
w
w
w
w
w
w
w
T
x
x
/
000
,
0
664
,
11
)
3633
,
30
563
,
1
3633
,
30
563
,
1
0
563
,
1
0
563
,
1
5967
,
14
3121
,
18
125
,
5
3121
,
18
125
,
5
5967
,
14
(
2
563
,
1
563
,
1
563
,
1
563
,
1
125
,
5
125
,
5
3
2
2
12
12
6
5
5
6
4
,
=
-
-
+
-
+
-
+
-
=
=
-
+
-
+
-
+
-
=
(
)
(
)
m
kN
k
k
S
k
w
w
w
w
w
w
w
w
T
x
x
/
534
,
0
664
,
11
241
,
34
673
,
55
0
0
0
808
,
74
326
,
108
3121
,
18
664
,
11
)
9073
,
21
563
,
1
6196
,
35
563
,
1
0
563
,
1
0
563
,
1
0
5967
,
14
125
,
5
1367
,
21
125
,
5
3121
,
18
(
2
563
,
1
563
,
1
563
,
1
563
,
1
125
,
5
125
,
5
3
3
1
13
11
8
6
4
5
5
,
=
=
-
+
-
+
-
+
-
=
-
-
+
-
+
-
+
-
=
=
-
+
-
+
-
+
-
=
(
)
(
)
(
)
(
)
m
kN
k
k
S
k
w
w
w
w
w
w
w
w
T
x
x
/
914
,
0
664
,
11
458
,
47
0
5967
,
14
0
850
,
93
1367
,
21
664
,
11
)
0
563
,
1
0
563
,
1
3633
,
30
563
,
1
0
563
,
1
5967
,
14
0
125
,
5
3121
,
18
125
,
5
1367
,
21
(
2
563
,
1
563
,
1
563
,
1
563
,
1
125
,
5
125
,
5
3
7
14
2
12
6
8
5
4
6
,
-
=
=
+
+
+
+
-
=
-
-
-
+
+
-
-
+
-
=
=
-
-
+
+
-
-
+
-
=
(
)
(
)
(
)
(
)
(
)
(
)
(
)
m
kN
k
S
k
w
w
w
w
w
w
w
w
T
x
x
/
816
,
3
664
,
11
)
9073
,
21
563
,
1
9073
,
21
563
,
1
0
563
,
1
0
563
,
1
3121
,
18
5967
,
14
125
,
5
5967
,
14
125
,
5
3121
,
18
(
2
563
,
1
563
,
1
563
,
1
563
,
1
125
,
5
125
,
5
3
3
3
24
13
5
6
6
5
9
,
-
=
-
-
+
+
-
+
-
-
-
+
-
=
-
-
+
-
+
-
-
-
+
-
=
(
)
(
)
m
kN
k
S
k
w
w
w
w
w
w
T
x
x
/
000
,
0
664
,
11
3121
,
18
563
,
1
2
3121
,
18
563
,
1
2
0
0
125
,
5
0
125
,
5
0
2
563
,
1
2
563
,
1
2
125
,
5
125
,
5
3
5
5
13
12
12
13
11
,
=
-
+
-
+
-
=
=
-
+
-
+
-
=
(
)
(
)
m
kN
k
S
k
w
w
w
w
w
w
T
x
x
/
757
,
0
664
,
11
3121
,
18
563
,
1
2
1367
,
21
563
,
1
2
0
0
125
,
5
0
125
,
5
0
2
563
,
1
2
563
,
1
2
125
,
5
125
,
5
3
5
4
14
13
11
12
12
,
=
-
+
-
+
-
=
=
-
+
-
+
-
=
(
)
(
)
m
kN
k
S
k
w
w
w
w
w
w
T
x
x
/
908
,
4
664
,
11
0
563
,
1
2
3121
,
18
563
,
1
2
0
0
125
,
5
0
125
,
5
0
2
563
,
1
2
563
,
1
2
125
,
5
125
,
5
3
8
5
24
14
12
11
13
,
=
-
+
-
+
-
=
=
-
+
-
+
-
=
[
]
m
kN
T
x
/
1
2
3
7
8
6
5
4
11
13
12
14
y
x
1
3
4
6
1
4
2
5
2
5
3
6
7
1,132
3,501
10,133
1,132
3,501
10,133
1,132
3,501
8
0,534
0,914
6,956
0,534
0,914
6,956
0,914
0,534
0,914
0,534
11
0,757
0,757
4,908
4,908
Sile u presecima (transverzalne sile)
}
k
y
y
T
S
k
,
3
2
=
k
k+1
k-1
-0,640
0,640
0,640
-0,640
-3,280
3,280
-1
1
k
k
y
y
x
w
y
w
k
T
+
-
=
2
3
3
3
,
n
64
,
0
2
=
a
,
64
,
0
2
-
=
-
a
(
)
280
,
3
1
2
2
=
+
a
(
)
(
)
m
kN
k
S
k
w
w
w
w
w
w
T
y
y
/
000
,
0
972
,
5
3121
,
18
64
,
0
2
3121
,
18
64
,
0
2
0
0
1367
,
21
280
,
3
1367
,
21
280
,
3
2
64
,
0
2
64
,
0
2
280
,
3
280
,
3
3
5
5
11
11
4
4
1
,
=
=
+
-
+
-
+
-
=
=
+
-
+
-
+
-
=
(
)
m
kN
k
S
k
w
w
w
w
w
w
w
w
T
y
y
/
000
,
0
972
,
5
)
0
5967
,
14
64
,
0
1367
,
21
64
,
0
5967
,
14
64
,
0
1367
,
21
64
,
0
3121
,
18
280
,
3
3121
,
18
280
,
3
0
(
2
64
,
0
64
,
0
64
,
0
64
,
0
280
,
3
280
,
3
3
12
6
4
6
4
5
5
12
2
,
=
+
+
+
+
-
-
-
+
=
=
+
+
+
-
-
-
+
-
=
(
)
m
kN
k
S
k
w
w
w
w
w
w
w
w
T
y
y
/
000
,
0
972
,
5
)
0
0
64
,
0
3121
,
18
64
,
0
0
64
,
0
3121
,
18
64
,
0
5967
,
14
280
,
3
5967
,
14
280
,
3
0
(
2
64
,
0
64
,
0
64
,
0
64
,
0
280
,
3
280
,
3
3
13
8
5
8
5
6
6
13
3
,
=
+
+
+
+
-
-
-
+
=
=
+
+
+
-
-
-
+
-
=
(
)
(
)
m
kN
k
S
k
w
w
w
w
w
w
T
y
y
/
000
,
0
972
,
5
3633
,
30
64
,
0
2
0
64
,
0
2
1367
,
21
6196
,
35
280
,
3
0
280
,
3
1367
,
21
2
64
,
0
2
64
,
0
2
280
,
3
280
,
3
3
2
12
4
1
11
15
4
,
=
=
+
-
+
-
+
-
=
=
+
-
+
-
+
-
=
(
)
(
)
m
kN
k
k
S
k
w
w
w
w
w
w
w
w
T
y
y
/
511
,
10
972
,
5
021
,
14
797
,
22
3121
,
18
592
,
99
3121
,
18
972
,
5
)
9073
,
21
64
,
0
6196
,
35
64
,
0
0
64
,
0
0
64
,
0
3121
,
18
3633
,
30
280
,
3
0
280
,
3
3121
,
18
(
2
64
,
0
64
,
0
64
,
0
64
,
0
280
,
3
280
,
3
3
3
1
13
11
5
2
12
5
5
,
-
=
=
+
+
+
-
-
=
+
+
+
-
-
+
-
+
-
=
=
+
+
-
-
+
-
+
-
=
(
)
(
)
m
kN
k
k
S
k
w
w
w
w
w
w
w
w
T
y
y
/
778
,
8
972
,
5
0
433
,
19
0
0
5967
,
14
856
,
71
0
5967
,
14
972
,
5
)
0
64
,
0
3633
,
30
64
,
0
0
64
,
0
0
64
,
0
5967
,
14
9073
,
21
280
,
3
0
280
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3
5967
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14
(
2
64
,
0
64
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0
64
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0
64
,
0
280
,
3
280
,
3
3
7
2
14
12
6
3
13
6
6
,
-
=
+
+
-
-
+
-
+
-
=
+
+
+
-
-
+
-
+
-
=
=
+
+
-
-
+
-
+
-
=
(
)
m
kN
k
S
k
w
w
w
w
w
w
T
y
y
/
000
,
0
972
,
5
)
3121
,
18
640
,
0
2
3121
,
18
640
,
0
2
6196
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35
1367
,
21
280
,
3
1367
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21
280
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3
6196
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35
(
2
640
,
0
2
640
,
0
2
280
,
3
280
,
3
3
5
16
1
4
15
20
11
,
=
+
+
-
+
-
+
-
=
=
+
-
+
-
+
-
=
(
)
m
kN
k
S
k
w
w
w
w
w
w
w
w
T
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000
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0
972
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5
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14
640
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0
1367
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21
640
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0
5967
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14
640
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0
1367
,
21
640
,
0
3633
,
30
3121
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18
280
,
3
3121
,
18
280
,
3
3633
,
30
(
2
640
,
0
640
,
0
640
,
0
640
,
0
280
,
3
280
,
3
3
6
4
17
15
2
5
16
21
12
,
=
+
+
+
-
-
+
-
+
-
=
=
+
+
-
-
+
-
+
-
=
(
)
m
kN
k
S
k
w
w
w
w
w
w
w
w
T
y
y
/
000
,
0
972
,
5
)
0
640
,
0
3121
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18
640
,
0
0
640
,
0
3121
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18
640
,
0
9073
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21
5967
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14
280
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3
5967
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14
280
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3
9073
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21
(
2
640
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0
640
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0
640
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0
640
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0
280
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3
280
,
3
3
8
5
23
16
3
6
17
22
13
,
=
+
+
+
-
-
+
-
+
-
=
=
+
+
-
-
+
-
+
-
=
[
]
m
kN
T
y
/
1
2
3
7
8
6
5
4
11
13
12
14
y
x
1
2
3
4
5
6
1
4
2
5
3
6
10,511
8,778
10,511
8,778
10,511
10,511
8,778
8,778
Proraun zamenjujuih transverzalnih sila
(
)
(
)
k
k
x
k
xy
x
k
x
y
x
w
k
v
x
w
k
y
x
w
k
v
T
y
M
T
T
-
+
-
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-
+
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2
3
3
3
2
3
,
2
1
64
,
0
80
,
0
2
=
=
a
a
20
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0
=
n
k
l
15,250
-5,625
-5,625
-2
i
(
)
(
)
625
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7
64
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0
20
,
0
2
1
2
2
1
2
2
=
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+
a
v
k
x
x
x
k
A
S
K
K
S
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3
4
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2
64
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0
2
,
0
2
2
2
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-
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-
a
v
(
)
(
)
(
)
(
)
(
)
(
)
m
kN
k
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k
w
w
w
w
w
w
T
x
x
/
355
,
9
664
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11
5967
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14
813
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2
4
9073
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21
625
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7
2
3633
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30
2
2
813
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2
2
813
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2
2
625
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7
625
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7
3
6
6
2
3
3
2
7
,
-
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-
-
+
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-
-
-
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(
)
(
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m
kN
k
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k
w
w
w
w
T
x
x
/
378
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5
664
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813
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2
2
0
813
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2
2
5967
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14
625
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2
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18
2
2
813
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2
2
813
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2
2
625
,
7
2
2
3
3
13
6
5
8
,
-
=
+
+
-
=
=
+
+
-
=
(
)
(
)
m
kN
k
S
k
w
w
w
T
x
x
/
081
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14
664
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11
5967
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14
813
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2
4
0
625
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7
2
0
2
2
813
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2
4
625
,
7
2
2
3
6
13
12
14
,
=
+
-
=
=
+
-
=
Reakcije oslonaca slobodno oslonjena ivica
(
)
+
-
-
-
+
+
=
+
-
-
1
1
2
1
2
4
3
,
2
2
2
1
4
2
i
i
k
x
k
x
k
x
w
w
v
w
v
K
S
Z
S
K
A
a
a
64
,
0
80
,
0
2
=
=
a
a
20
,
0
=
n
k
y
y
y
k
A
S
K
K
S
Z
,
3
4
2
=
+
k
k+1
k-1
-2,560
-2,560
13,120
-2
250
,
15
64
,
0
20
,
0
2
1
4
2
1
4
2
=
-
+
=
-
+
a
v
625
,
5
64
,
0
20
,
0
2
2
2
2
2
-
=
-
-
=
-
-
a
v
(
)
(
)
kN
K
K
w
w
w
S
K
A
x
x
358
,
9
147
,
109
664
,
11
3633
,
30
2
5967
,
14
625
,
5
2
9073
,
21
250
,
15
664
,
11
2
625
,
5
2
250
,
15
2
2
6
3
3
7
,
=
=
-
-
=
=
-
-
=
(
)
(
)
kN
K
K
w
w
w
w
S
K
A
x
x
380
,
5
747
,
62
664
,
11
3121
,
18
2
9073
,
21
625
,
5
0
625
,
5
5967
,
14
250
,
15
664
,
11
2
625
,
5
625
,
5
250
,
15
2
5
3
13
6
3
8
,
=
=
=
-
-
-
=
=
-
-
-
=
(
)
(
)
(
)
kN
K
K
w
w
w
S
K
A
x
x
079
,
14
214
,
164
664
,
11
0
2
5967
,
14
625
,
5
2
0
250
,
15
664
,
11
2
625
,
5
2
250
,
15
2
12
6
13
3
14
,
-
=
-
=
-
-
=
=
-
-
=
Reakcije oslonaca ukljetena ivica
(
)
(
)
+
-
-
+
+
-
=
+
-
1
1
2
2
4
3
,
4
2
1
8
2
i
i
h
i
y
k
y
k
y
w
w
w
w
K
S
Z
S
K
A
a
a
64
,
0
80
,
0
2
=
=
a
a
20
,
0
=
n
}
k
y
y
T
S
k
,
3
2
=
(
)
(
)
120
,
13
64
,
0
1
8
1
8
2
=
+
=
+
a
k
7,625
-7,625
2,813
2,813
1
-2,813
-1
-2,813
560
,
2
64
,
0
4
4
2
-
=
-
=
-
a
(
)
(
)
kN
K
K
w
w
w
S
K
A
y
y
807
,
18
316
,
112
972
,
5
6196
,
35
2
3121
,
18
560
,
2
2
1367
,
21
120
,
13
972
,
5
2
560
,
2
2
120
,
13
2
1
5
4
3
11
,
=
=
-
-
=
=
-
-
=
(
)
(
)
kN
K
K
w
w
w
w
S
K
A
y
y
411
,
7
261
,
44
972
,
5
3633
,
30
2
5967
,
14
560
,
2
1367
,
21
560
,
2
3121
,
18
120
,
13
972
,
5
2
560
,
2
560
,
2
120
,
13
2
2
6
4
5
3
12
,
=
=
=
-
-
-
=
=
-
-
-
=
(
)
(
)
kN
K
K
w
w
w
w
S
K
A
y
y
881
,
16
815
,
100
972
,
5
9073
,
21
2
0
.
560
,
2
3121
,
18
560
,
2
5967
,
14
120
,
13
972
,
5
2
560
,
2
560
,
2
120
,
13
2
3
8
5
6
3
13
,
=
=
=
-
-
-
=
=
-
-
-
=
(
)
(
)
(
)
(
)
kN
K
K
w
w
w
w
S
K
A
y
y
000
,
0
000
,
0
972
,
5
0
2
5967
,
14
560
,
2
5967
,
14
560
,
2
0
120
,
13
972
,
5
2
560
,
2
560
,
2
120
,
13
2
7
6
6
8
3
14
,
=
=
-
-
-
-
=
=
-
-
-
-
=
1np
EMBED Equation.3
EMBED Equation.3
Dijagrami momenata savijanja
EMBED Equation.3
EMBED Equation.3
- ema
Diagrami momenata savijanja
EMBED Equation.3
Dijagram momenata savijanja
EMBED Equation.3
EMBED Equation.3
Dijagram transverzalnih sila
EMBED Equation.3
EMBED Equation.3
Dijagram transverzalnih sila
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
PAGE
16 | Strana