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GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
1
Zadatak 2.
Za zadani sistem kombinacijom metoda Crossa i Werner-Csonke odrediti MT dijagrame.
E = 3 .
107 kN/m
2, 1510 −−= Ktα ;
grede: b/h = 48/96 [cm];
stupovi: b/h = 48/48 [cm].
Student Zadatak
[m] [m] [m] [m] [kN/m] [kN] [mm]/[m ]/[ C]
31 Vedran Slunjski 2 4.2 6 5.5 5 37.5 50 -18
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
2
109
8765
4321
5,5
5
4,264,2
23
2,75
2,75
-18 C50 kN
50 kN
37,5 kN/m'
OGOS
S
G
EIEIEIEI
kNmEI
kNmEI
8
4,13271012
48,048,0103
2,106168312
96,048,0103
23
7
23
7
=⇒=
=
⋅⋅=
=
⋅⋅=
1 CROSS
OSNOVNI SISTEM
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
3
55,5
4,2 6 4,2
0,99 mm
0,99 mm
6,75,6
9,10
PLAN POMAKA OD SKRAĆENJA ZBOG TEMPERATURE
410,956 10
2,4
9,9 −⋅−
==ψψ
467 10
0,6
9,9 −⋅=ψ
KOEFICJENTI KRUTOSTI ELEMENATA
5,548372615
OIEkkkk
⋅====
5
10,659OIE
kk⋅
==
2,4
87856
OIEkk
⋅==
6
867
OIEk
⋅=
KOEFICJENTI KRUTOSTI ČVOROVA
O
EI,kkkk 2925956155
=++=
O
EIkkkkk 62,35610,667266
=+++=
OEIkkkk 42,37837677 =++=
OEIkkk 09,248788 =+=
OEIkkk 1,210,9599 =+=
OEIkkk 1,210,610,910 =+=
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
4
MOMENTI UPETOSTI
kNmkM
kNmkM
kNmM
kNmM
kNmM
kNmM
kNmkM
kNmkM
kNmkM
kNmkM
kNmM
kNmM
5,3576
5,3576
0,365
3250
0,245
2350
1,5512
2,45,37
1,5512
2,45,37
7,287612
0,65,37
7,62612
0,65,37
5,3576
5,3576
4,348
5,550
4,348
5,550
56569,10
565610,9
2
2
95
2
2
59
2
87
2
78
6767
2
76
6767
2
67
565665
565656
51
15
=−=
=−=
−=⋅⋅−
=
=⋅⋅
=
−=⋅−
=
=⋅
=
−=−⋅−
=
−=−⋅
=
=−=
=−=
−=⋅−
=
=⋅
=
ψ
ψ
ψ
ψ
ψ
ψ
RAZDJELNI KOEFICJENTI
Čvor 5
09,028,20,5
1
83,028,22,4
8
08,028,25,5
1
5
5959
5
5656
5
1551
=⋅
==
=⋅
==
=⋅
==
k
k
k
k
k
k
µ
µ
µ
∑= 1
Čvor 6
37,0
62,30,3
4
05,062,35,5
1
6
6767
6
6262
=⋅
==
=⋅
==
k
k
k
k
µ
µ
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
5
52,0
62,32,4
8
06,062,30,5
1
6
5665
6
10,6
10,6
=⋅
==
=⋅
==
k
k
k
k
µ
µ
∑= 1
Čvor 7
56,042,32,4
8
05,042,35,5
1
39,042,30,3
4
7
7878
7
3773
7
6776
=⋅
==
=⋅
==
=⋅
==
k
k
k
k
k
k
µ
µ
µ
∑= 1
Čvor 8
09,0
09,25,5
1
91,009,22,4
8
8
4884
8
7887
=⋅
==
=⋅
==
k
k
k
k
µ
µ
∑= 1
Čvor 9
91,0
1,22,4
8
09,01,20,5
1
9
10,9
10,9
9
5995
=⋅
==
=⋅
==
k
k
k
k
µ
µ
∑= 1
Čvor 10
91,0
1,22,4
8
09,01,20,5
1
9
10,9
9,10
10
696,10
=⋅
==
=⋅
==
k
k
k
k
µ
µ
∑= 1
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
6
0,09
0,080,83
0,090,91
0,91 0,09
0,06
0,05
0,52
0,37
0,05
0,390,56
0,91 0,09
-36,0
-14,3
-15,3
-1,8
1,6
-0,6
0,8
-0,2
0,1
-0,1
-65,8
357,5
-162,7
-144,5
34,7
-17,6
4,9
-5,9
1,5
-2,1
0,5
-0,5
-0,1
0,1
65,8
____
0,1
0,3
-0,1
1,7
-0,3
3,3
-0,9
-30,6
-7,2
24,0
-9,9
-57,0
-34,4
-27,2
2,9
1,5
0,2
357,5
-325,3
-72,2
69,4
-8,8
9,9
-2,9
3,0
-1,0
1,0
-0,2
0,2
30,6
-32,2
-4,1
6,9
-2,1
1,0
-0,4
0,3
-0,1
0,1
-30,6
_____
-0,2
0,1
-0,8
0,5
-4,2
3,4
-8,3
-16,1
-25,6
357,5
-282,1
-35,7
30,4
-18,1
15,2
-3,1
2,7
-0,6
0,5
-0,1
0,1
66,7
____
0,1
0,7
1,5
-13,6
34,4
23,1
____
-0,1
-0,3
-1,7
-3,5
-5,6
7,2
____
0,1
0,5
6,6
____
-0,1
-0,2
-0,9
-1,2
357,5
-141,1
-71,5
15,2
-36,2
7,6
-6,3
1,3
-1,2
0,2
-0,2
125,3
-6,9
-3,5
-0,6
-0,1
-11,1
-62,7
-50,9
51,0
-25,7
4,1
-4,5
0,9
-0,8
0,2
-0,2
-88,6
-287,7
-25,5
102,0
-12,8
8,2
-2,2
1,9
-0,4
0,4
-0,1
0,1
-216,1
13,1
1,1
0,2
14,4
51,5
146,6
-8,2
11,7
-2,6
2,7
-0,6
0,6
-0,1
0,1
201,7
-55,1
73,3
-16,5
5,8
-5,3
1,3
-1,2
0,3
-0,3
2,3
-2,3
-1,7
-0,5
-0,1
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
7
1. ITERACIJA Čvor 10
2,325,35709,0
3,3255,35791,0
5,357
−=⋅−
−=⋅−
=∆M
∑ −= 5,357 Čvor 9
3,148,15809,0
5,1448,15891,0
8,158
367,1625,357
−=⋅−
−=⋅−
=∆
−−=∆
M
M
∑ −= 8,158 Čvor5
2,279,33908,0
1,2829,33983,0
6,309,33909,0
9,339
4,345,357242,7
−=⋅−
−=⋅−
−=⋅−
=∆
−++−=∆
M
M
∑ −= 9,339 Čvor6
5,716,13752,0
9,66,13705,0
9,506,13737,0
3,86,13706,0
6,137
1,167,621,1415,357
−=⋅−
−=⋅−
−=⋅−
−=⋅−
=∆
−−−=∆
M
M
∑ −= 6,137 Čvor 7
0,1027,26139,0
1,137,26105,0
6,1467,26156,0
7,261
5,517,2875,25
=⋅
=⋅
=⋅
−=∆
+−−=∆
M
M
∑= 7,261 Čvor 8
7,12,1809,0
5,162,1891,0
2,181,553,73
−=⋅−
−=⋅−
=−=∆M
∑ −= 2,18
2. ITERACIJA
Čvor 10
9,63,7609,0
4,693,7691,0
3,761,42,72
=⋅
=⋅
−=−−=∆M
∑= 3,76 Čvor 9
8,14,1909,0
6,174,1991,0
4,193,157,34
−=⋅−
−=⋅−
=−=∆M
∑ −= 4,19 Čvor 5
9,26,3608,0
4,306,3683,0
3,36,3609,0
6,367,359,0
=⋅
=⋅
=⋅
−=−−=∆M
∑= 6,36 Čvor 6
2,366,6952,0
5,36,6905,0
7,256,6937,0
2,46,6906,0
6,694,3512,15
−=⋅−
−=⋅−
−=⋅−
−=⋅−
=++=∆M
∑ −= 6,69 Čvor 7
2,82139,0
1,12105,0
7,112156,0
212,88,12
=⋅
=⋅
=⋅
−=−−=∆M
∑= 21 Čvor 8
5,08,509,0
3,58,591,0
8,5
−=⋅−
−=⋅−
=∆M
∑ −= 8,5
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
8
3. ITERACIJA
Čvor 10
0,19,1009,0
9,99,1091,0
9,101,28,8
=⋅
=⋅
−=−−=∆M
∑= 9,10 Čvor 9
6,05,609,0
9,55,691,0
5,66,19,4
−=⋅−
−=⋅−
=+=∆M
∑ −= 5,6 Čvor 5
5,14,1808,0
2,154,1883,0
7,14,1809,0
4,181,183,0
=⋅
=⋅
=⋅
−=−−=∆M
∑= 4,18 Čvor 6
3,62,1252,0
6,02,1205,0
5,42,1237,0
8,02,1206,0
2,126,71,45,0
−=⋅−
−=⋅−
−=⋅−
−=⋅−
=++=∆M
∑ −= 2,12 Čvor 7
9,18,439,0
2,08,405,0
7,28,456,0
8,46,22,2
=⋅
=⋅
=⋅
−=−−=∆M
∑= 8,4 Čvor 8
1,03,109,0
2,13,191,0
3,1
−=⋅−
−=⋅−
=∆M
∑ −= 3,1
4. ITERACIJA Čvor 10
3,03,309,0
0,33,391,0
3,34,09,2
=⋅
=⋅
−=−−=∆M
∑= 3,3 Čvor 9
2,03,209,0
1,23,291,0
3,28,05,1
−=⋅−
−=⋅−
=+=∆M
∑ −= 3,2 Čvor 5
2,02,308,0
7,22,383,0
3,02,309,0
2,31,31,0
=⋅
=⋅
=⋅
−=−−=∆M
∑= 2,3 Čvor 6
2,13,252,0
1,03,205,0
8,03,237,0
2,03,206,0
3,23,19,01,0
−=⋅−
−=⋅−
−=⋅−
−=⋅−
=++=∆M
∑ −= 3,2 Čvor 7
4,0139,0
0,0105,0
6,0156,0
0,16,04,0
=⋅
=⋅
=⋅
−=−−=∆M
∑= 1
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
9
H1
M5,9
T9,5
T9,5
M9,5
M6,10
M10,6
T10,6
5
23
50 kN
T8,4T7,3
M8,4M7,3
M4,8M3,7M2,6
T6,2
M6,2
M1,5
T5,1
M5,1
H2
1
5,5
2,75
2,75
50 kN
50 kN
5. ITERACIJA Čvor 10
1,01,109,0
0,11,191,0
1,11,00,1
=⋅
=⋅
−=−−=∆M
∑= 1,1 Čvor 9
1,06,009,0
5,06,091,0
6,01,05,0
−=⋅−
−=⋅−
=+=∆M
∑ −= 6,0 Čvor5
06,008,0
5,06,083,0
1,06,009,0
6,0
=⋅
=⋅
=⋅
−=∆M
∑= 6,0 ODREĐIVANJE REAKCIJA U PRIDRŽANJIMA
kNH
HF
T
M
T
M
x
38,56
24,1114,450
24,115
6,256,30
0
14,455
1509,98,65
0
1
1
6,10
6
95
5
=
+=⇒=
−=−−
=
=
−=−−−
=
=
∑
∑
∑
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
10
II
I
0 79,63
23,25
56,38T
23,25
56,38
MI,0
M0,I
MI,II
79,6356,38
5,55
MII,I
kNHF
kNTM
kNTM
kNTM
kNTM
x 25,2364,093,304,316,315038,560
64,05,5
3,22,10
93,35,5
4,142,70
04,35,5
1,116,50
16,315,5
75,250571,230
2
844
733
622
511
=+−+++−=⇒=
−=−−
=⇒=
=+
=⇒=
−=−−
=⇒=
−=⋅−−
=⇒=
∑
∑
∑
∑
∑
2 WERNER – CSONKA
ZAMJENJUJUĆI POLUOKVIR
kNmMM
kNmMM
II
IIIIII
2192
5,563,79
95,1402
538,56
0,,0
,,
=⋅
==
=⋅
==
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
11
KOEFICJENTI KRUTOSTI ELEMENATA
Stupova:
0,5
2
5,5
4
010,659,
0483726150
EIkkk
EIkkkkk
III
I
=+=
=+++=
Greda:
2,4
324
6,12
8,64444
010,9
0786756
EIkk
EIkkkk
IIG
IG
==
=++=
KOEFICJENTI KRUTOSTI ČVOROVA
0,
0,0
26,233
56,163
EIkkk
EIkkkk
IIIIIGII
IIIIIGI
=+=
=++=
RAZDJELNI KOEFICJENTI
Čvor 1
02,056,160,5
2
93,056,166,12
48,363
05,056,165,5
4
,
,
00
=⋅
==
=⋅
==
=⋅
==
I
III
III
I
IGIG
I
II
k
k
k
k
k
k
µ
µ
µ
∑= 1
Čvor 2
98,026,232,4
3233
02,026,230,5
2
,
,
,
,
=⋅
⋅==
=⋅
==
II
GII
GII
I
III
III
k
k
k
k
µ
µ
∑= 1
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
12
1. ITERACIJA
Čvor I
1836005,0
8,33436093,0
2,736002,0
36021995,140
−=⋅−
−=⋅−
−=⋅−
=+=∆M
∑ −= 360
Čvor II
0,32,14802,0
2,1452,14898,0
2,1482,795,140
−=⋅−
−=⋅−
=+=∆M
∑ −= 2,148
2. ITERACIJA
Čvor I
2,0305,0
8,2393,0
0302,0
0,3
−=⋅−
−=⋅−
=⋅−
=∆M
∑ −= 3
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
13
237,2
-337,6
200,8
_____ 0,2 18,0219,0
-334,8 -2,8
219,0 -18,0 -0,2
136,8_____ 3,0 -7,2141,0
-145,2
145,2
141,0 7,2 -3,0
-145,2
0,02
0,050,93
0,02
0,98
kNmMMM
kNmMMMMMMM
kNmMMM
kNmMMM
kNmMMMMM
kNmMMMMM
GII
GI
III
III
I
I
2,145
6,337
2,145
8,136
8,200
5,237
9,1010,9,
877876676556,
6,1095,
10,659,
847362510
483726150
−=+=
−=+++++=
=+=
=+=
=+++=
=+++=
( )( )
( )( )
( )( )
kNmMM
kNmkkk
kMM
kNmkkk
kMM
kNmkkk
kMM
kNmMM
kNmMM
kNmMMMM
kNmMMMM
6,722
2,145
5,626,3372
8,436,3372
5,626,3372
6,722
2,145
4,682
8,136
2,504
8,200
4,594
5,237
9,1010,9
786756
788778
786756
677667
786756
566556
6,1095
10,659
84736251
48372615
−=−
==
−=−⋅++
==
−=−⋅++
==
−=−⋅++
==
===
===
=====
=====
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
___________________________________________________________________________
GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
14
72,5
-72,5
-70,3
0,09
0,080,83
0,090,91
0,91 0,09
0,06
0,05
0,52
0,37
0,05
0,390,56
0,91 0,09
72,6
-2,6
0,2
-0,1
0,1
0,1
70,3
-72,6
2,4
-0,7
0,7
-0,1
____
0,2
-0,3
0,1
-5,1
68,4
63,3
45,7
50,2
-4,5
-0,2
0,2
-72,6
1,2
-1,4
0,3
72,6
0,3
-0,1
-0,3
_____
-0,1
-0,6
0,7
68,4
68,4
-62,5
-46,5
2,8
-2,4
-2,4
2,0
-0,4
0,4
-109
____
0,1
-0,1
-2,3
59,4
57,1
____
-0,1
-0,2
0,3
59,4
59,4
60,9
____
0,1
1,4
59,4
____
-0,2
59,4
59,2
-62,5
-23,2
5,7
-1,2
-4,8
1,0
-0,7
0,2
-0,3
-85,8
50,2
0,5
-0,5
-0,1
50,1
-43,8
4,0
10,5
-3,4
0,5
-0,6
0,3
-0,2
-32,7
-43,8
2,0
21,0
-1,7
1,1
-0,3
0,6
-0,1
-21,2
50,2
2,7
0,1
0,1
53,1
-62,5
30,3
-1,2
1,7
-0,3
0,3
0,1
-31,6
-62,5
15,1
-2,5
0,8
-0,7
0,1
-0,1
-49,8
49,8
50,2
-0,3
-0,1
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
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GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
15
1. ITERACIJA Čvor 5
5,41,5608,0
5,461,5683,0
1,51,5609,0
1,56
2,505,624,68
−=⋅−
−=⋅−
−=⋅−
=∆
+−=∆
M
M
∑ −= 1,56 Čvor 6
7,59,1052,0
5,09,1005,0
0,49,1037,0
7,09,1006,0
9,10
2,235,622,508,434,68
=⋅
=⋅
=⋅
=⋅
−=∆
−−+−=∆
M
M
∑= 9,10 Čvor 7
1,211,5439,0
7,21,5405,0
3,301,5456,0
1,54
5,622,5028,43
=⋅
=⋅
=⋅
−=∆
−++−=∆
M
M
∑= 1,54 Čvor 8
3,08,209,0
5,28,291,0
8,22,501,155,62
−=⋅−
−=⋅−
=++−=∆M
∑ −= 8,2 Čvor 9
2,06,209,0
4,26,291,0
6,2
=⋅
=⋅
−=∆M
∑= 6,2 Čvor 10
1,05,109,0
4,15,191,0
5,13,02,1
−=⋅−
−=⋅−
=+=∆M
∑ −= 5,1
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
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GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
16
2. ITERACIJA
Čvor 5
2,09,208,0
4,29,283,0
3,09,209,0
9,28,21,0
−=⋅−
−=⋅−
−=⋅−
=+=∆M
∑ −= 9,2 Čvor 6
8,43,952,0
5,03,905,0
4,33,937,0
6,03,906,0
3,92,15,10
−=⋅−
−=⋅−
−=⋅−
−=⋅−
=−=∆M
∑ −= 3,9 Čvor 7
1,19,239,0
1,09,205,0
7,19,256,0
9,22,17,1
=⋅
=⋅
=⋅
−=−−=∆M
∑= 9,2 Čvor 8
1,08,009,0
7,08,091,0
8,0
−=⋅−
−=⋅−
=∆M
∑ −= 8,0 Čvor 9
1,08,009,0
7,08,091,0
8,07,01,0
=⋅
=⋅
−=−−=∆M
∑= 8,0
3. ITERACIJA Čvor 5
2,04,208,0
0,24,283,0
2,04,209,0
4,2
=⋅
=⋅
=⋅
−=∆M
∑= 4,2 Čvor 6
7,05,152,0
1,05,105,0
6,05,137,0
1,05,106,0
5,15,00,1
−=⋅−
−=⋅−
−=⋅−
−=⋅−
=+=∆M
∑ −= 5,1 Čvor 7
2,05,039,0
1,05,005,0
3,05,056,0
6,0
=⋅
=⋅
=⋅
−=∆M
∑= 6,0
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
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GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
17
POPREČNE SILE – nakon 2 Cross-a
9,542,287,26'
2,285
4,685,72'
7,265
3,633,70'
,
6,10
95
=+=
=+
=
=+
=
IIIT
kNT
kNT
kNT
kNT
kNT
kNT
kNT
I 1,798,197,209,197,18'
8,195,5
8,492,59'
7,205,5
9,601,53'
9,195,5
4,591,50'
7,185,5
1,577,45'
0,
84
73
2,6
51
=+++=
=+
=
=+
=
=+
=
=+
=
( )
( ) ( )++=−=∆
+=−=∆
suobjeTTT
TTT
III
IIIIIIIII
5,0'
5,1'
0,0,0,
,,,
KOEFICJENT α
01,15,51,790,59,54
5,56,790,54,56
'' ,0,,,
0,0,,,=
⋅+⋅
⋅+⋅=
⋅+⋅
⋅+⋅=
IIIIIIIIII
IIIIIIII
hThT
hThTα
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
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GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
18
KONAČNI MOMENTI
21 CRCR MMM α+=
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
2,53,7001,18,65
,5403,6301,19,9
0,488,4901,13,2
6,582,5901,12,1
0,681,5301,14,14
7,689,6001,12,7
5,391,5001,11,11
4,544,5901,16,5
8,107,4501,10,57
8,801,5701,11,23
95
59
84
48
73
37
62
26
51
15
=⋅+−=
=⋅+−=
=⋅+−=
=⋅+−=
=⋅+=
=⋅+=
=⋅+−=
=⋅+−=
−=⋅+−=
=⋅+=
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
kNmM
6,425,7201,16,30
2,53,7001,18,65
0,488,4901,13,2
8,1696,3101,17,201
5,2372,2101,11,216
6,1217,3201,16,88
6,388,8501,13,125
4,4310901,17,66
6,425,7201,16,30
5,434,6801,16,25
9,10
10,9
87
78
76
67
65
56
6,10
10,6
−=⋅−=
−=⋅−=
−=⋅−=
=⋅−=
−=⋅−−=
−=⋅−−=
=⋅−=
−=⋅−=
=⋅+−=
=⋅+−=
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
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GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
19
48,0
169,8
237,5
121,6
38,6
43,4
42,6
43,5
5,2
41,5
54,048,0
58,668,7
68,039,5
54,4
10,8
23,0
80,8
M
49,7
107,8
172,3
52,7
11,4
1,1
17,218,2
31,8
37,7
12,3
17,1 24,9 19,4
T
DIJAGRAMI
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
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GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
20
RJEŠENJE U DIM-u
Nodal displacements: nd u_i v_i phi_i -------------------------------------------------------- 1: 0 0 0 2: 0 0 0 3: 0 0 0 4: 0 0 0 5: 0.00223916 2.75924e-10 -0.000324548 6: 0.00223916 -0.000990001 -0.000159187 7: 0.00223916 -5.12222e-09 0.000146206 8: 0.00223916 -9.40413e-10 -7.01765e-05 9: 0.00474139 4.52698e-10 -0.000213801 10: 0.00474139 -0.000990001 -0.000287 Element end forces: el N_ij T_ij M_ij N_ji T_ji M_ji ------------------------------------------------------------------------------------------------ 1: -15.0504 37.89 77.6536 15.0504 12.11 -6.7586 2: 66.8612 17.2428 51.2586 -66.8612 -17.2428 43.5765 3: 279.394 25.2815 65.9963 -279.394 -25.2815 73.052 4: 51.2953 19.5857 55.5541 -51.2953 -19.5857 52.1675 5: -10.6064 32.3323 57.8912 10.6064 17.6677 3.77019 6: 10.6064 17.6677 47.5617 -10.6064 -17.6677 40.7769 7: 44.4423 -4.44398 -51.1326 -44.4423 4.44398 32.4679 8: 44.8673 51.8107 -123.606 -44.8673 173.189 -240.529 9: 19.5857 106.205 167.477 -19.5857 51.2953 -52.1675 10: 17.6677 -10.6064 -3.77019 -17.6677 10.6064 -40.7769 Reactions: nd R_x R_y M -------------------------------------------------------- 1: -37.89 -15.0504 77.6536 2: -17.2428 66.8612 51.2586 3: -25.2815 279.394 65.9963 4: -19.5857 51.2953 55.5541
GRAĐEVNA STATIKA II ____________________________________________________________________________________________________________
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GRAĐEVNA STATIKA II VEDRAN SLUNJSKI, 5228 ak.god.2006/07
21
M DIJAGRAM
T DIJAGRAM