momenti upetosti

MOMENTI UPETOSTI SIMETRIČNO OPTEREĆENJE JEDNOSTRANO UPETA GREDA

OBOSTRANO UPETA GREDA

SHEMA OPTEREĆENJA

Mki =

3 ⋅P ⋅ l 16

1 Mki =

3 ⋅P ⋅ a ⋅ (l − a )

Mki =

P ⋅l

4

3 ⋅ P1 ⋅ a(l − a ) 2l

Mki =

3 ⋅ P2 ⋅ l 16

M=

15 ⋅ P ⋅ l

3 ⋅ [P1 ⋅ a(l − a ) + P2 ⋅ b(l − b )] 2⋅l

M=

8

l 2 ⋅P ⋅l 9

P1 ⋅ a(l − a ) l

M=

32

5 Mki =

+

P⋅l

P ⋅ a ⋅ (l − a)

M=

3

3

=

M=

2⋅l

2

Mki

M=

+

3 ⋅P ⋅ l 5

7 Mki =

8 Mki =

9 Mki =

10

9 ⋅P ⋅ l 32

57 ⋅ P ⋅ l 144 33 ⋅ P ⋅ l 64

1

8

5 ⋅P ⋅l 16

[P1 ⋅ a(l − a ) + P2 ⋅ b(l − b )] l

6 Mki =

P2 ⋅ l

M=

M=

M=

M=

2 ⋅P ⋅l 5 3 ⋅P ⋅l 16 19 ⋅ P ⋅ l 72 11⋅ P ⋅ l 32

MOMENTI UPETOSTI SIMETRIČNO OPTEREĆENJE JEDNOSTRANO UPETA GREDA

OBOSTRANO UPETA GREDA

SHEMA OPTEREĆENJA

Mki =

q⋅l2

11

q ⋅ c ⋅ l   c 2   3 − 2  Mki = 16   l  

12

Mki =

q⋅ c 2

Mki =

q⋅c 4 ⋅l

2

Mki =

Mki =

18

p ⋅c 8 ⋅l

(6a

19

2

p ⋅c 2 8 ⋅l

2

(2l − c )

6⋅l

2

M=

M=

(3b + 4c )

(6a(l − a) + 3bc + 4c )

M=

(5c + 4a )

+ 12ac + 5c 2 )

q⋅c2

M=

192

8 ⋅l

Mki =

6⋅l

15 ⋅ p ⋅ l 2

p ⋅c 2

17

q⋅c

64

16 Mki =

M=

3 ⋅p ⋅l2

15

Mki =

M=

(6a(l − a) + 3bc + 4c )

12

q ⋅ c ⋅ l   c 2    3 − 2  24   l  

M=

(3b + 4c )

4 ⋅l

13

14

M=

8

q ⋅ l2

p⋅c 12 ⋅ l

96

12 ⋅ l

M=

32

5 ⋅ p ⋅ l2

p ⋅c2

(6a

p ⋅ l2

2

(5c + 4a)

+ 12ac + 5c 2 )

p ⋅c 2 12 ⋅l

(2l − c )

MOMENTI UPETOSTI NESIMETRIČNO OPTEREĆENJE JEDNOSTRANO UPETA GREDA

OBOSTRANO UPETA GREDA

SHEMA OPTEREĆENJA

P⋅a 2 ⋅ l2

20

q⋅ c2

21

(2l

8 ⋅ l2

q⋅c 2 8 ⋅l

22

2

24

30 ⋅ l 2

)

−c

2

(2l − c )

2

2

q⋅c 2

)

12 ⋅ l 2

(6b

+ 4bc + c

2

2

2

)

q⋅ c3

q⋅c 2

(4a + c )

(4b + c )

12 ⋅ l 2

12 ⋅ l

2

(6a

2

+ 4ac + c 2 )

15

30

20

[5b(2c + b) + 2c ] +

25 2

p⋅c 2 30 ⋅ l 2

[10b

2

+ 5bc + c

2

]

p ⋅ c3 20 ⋅ l 2



p ⋅c 3

p ⋅c 2



60 ⋅ l

60 ⋅ l

a + 4c 

[5a + 2c ] 2

2

[5b + c ]

[10al + 3c ] 2

   2 − 1 2   l  

M ⋅ b   3b  2 −  l   l  

M ⋅ a   3a  2−  l   l  

7 ⋅p ⋅ l2

p ⋅l2

p ⋅l2

120

20

30

27

  40b 2 35 b 7 c + +   c 120 ⋅ l 2   p⋅c3

p⋅c 2

29

l2

12 ⋅ l

M  3a 2

28

l2

p ⋅l2

 60 ⋅ l  c

26

P ⋅ a2 ⋅ b

q⋅ c3

2

2

P ⋅ a ⋅ b2

p ⋅l2

p ⋅ c 3 10a 2

25

−a

2

p ⋅ l2

23 p⋅c2

(l

2

120 ⋅ l 2

[10l

2

− 3c

3

2

]

p ⋅c 3 20 ⋅ l 2

p⋅c 2 60 ⋅ l 2

  10b 2 5 b c + +   c 30 ⋅ l 2   p ⋅c 3

[5b + c ]

[10al + 3c ] 2

p ⋅ c3 60 ⋅ l 2

[5a + 2c ]

MOMENTI UPETOSTI NESIMETRIČNO OPTEREĆENJE JEDNOSTRANO UPETA GREDA

OBOSTRANO UPETA GREDA

SHEMA OPTEREĆENJA

30

31

32

33

34

35

101⋅ p ⋅ l 2

29 ⋅ p ⋅ l 2

p ⋅l2

3240

1620

45

47 ⋅ p ⋅ l 2

p ⋅l2

29 ⋅ p ⋅ l 2

1620

45

1620

17 ⋅ p ⋅ l 2

p ⋅l2

3 ⋅p ⋅l2

480

30

160

41⋅ p ⋅ l 2

3 ⋅p ⋅ l2

p ⋅l2

960

160

30

37 ⋅ p ⋅ l 2

23 ⋅ p ⋅ l 2

7 ⋅p ⋅l2

1920

960

960

53 ⋅ p ⋅ l 2

7 ⋅p ⋅ l2

23 ⋅ p ⋅ l 2

1920

960

960

4

MOMENTI UPETOSTI PRISILNI POMACI ČVOROVA I TEMPERATURA JEDNOSTRANO UPETA GREDA

OBOSTRANO UPETA GREDA

SHEMA OPTEREĆENJA

3 ⋅ k ik

36

*

⋅ ∆v

6 ⋅ k ik

l

3 ⋅ k ik

37

*

38

39

t s ⇒ ∆t s

k ik

*

=

EΙ l

k ik

=

*

⋅ ∆v

6 ⋅ k ik

l

⋅ ∆v

*

⋅ ∆v

6 ⋅ k ik

l

⋅ ∆ϕ

*

⋅ ∆v

l

6 ⋅ k ik

l

3 ⋅ k ik

*

2 ⋅ k ik

*

*

⋅ ∆v

l

⋅ ∆ϕ

4 ⋅ k ik

1,5 ⋅ EΙ ⋅ α t ⋅ ∆t

E Ι ⋅ α t ⋅ ∆t

h

h

*

⋅ ∆ϕ

= α t ⋅ t s ⋅ l - prisilni pomak uslijed jednolike temperature

EΙ E0Ι 0 ⋅l

Mki

Mik

= k ik (4ϕi + 2ϕ k − 6ψ ik ⋅ u) + Mik

Mki

= k ik (4ϕk + 2ϕ i − 6ψ ik ⋅ u) + Mki

= k ik (3ϕk − 3ψ ik ⋅ u) + Mki

5