Soluzioni Esame minutolo

8/17/2019 Soluzioni Esame minutolo

1/9

. C .. . .

=60 =60. = 2 1= 1 .

=60

τ τ .

= 2

1= 1

15/09/2015 / C . 1

A

C

. 2 :

1. 2.

B


2/9

A

C

. 2 :

1. 2. B

3 =3 2*2= 1

B M

AC

B

M 0B ϕ =

F B B B ϕ ϕ ϕ= +

M


3/9

, C (

A

A

C B

23 2 03

30

22 3

D D

A

B

C A

F R L F L R

F R

R

FLM LR

− + = ⇒ =

==

= =

A

.

.


4/9

( )( ) ( ) ( ) ( )

2 30 00 0

2 3

22 6

2 2 2 2 32 6

C C C C

M T v z v z z z z LEI EI

M T v z v z L z L z L L z L

EI EI

ϕ

ϕ

= − − − <

= − − − − − − < <

C

30

0 22

0 18d C

z Ld s

F v z z v EI

v v

ϕ

=

= − − ==

( ) ( ) ( ) ( ) ( )

0 02

2 2 330 0

03

0

6 32 2 23 0 2 8 2 2

18 3 6 180

429

d s C C C C z L

d C

z EI EI F FL FL F v L

v z L L z L z L z LEI EI EI EI

v

FLv L

ϕ ϕ ϕ ϕϕ ϕ

ϕ ϕ

ϕ

=⇒ = + ⇒ = + ⇒ = = = − − − + − − − + − =

= − −⇒ 2

0

2

0

23

29

d C

EI FLEI

FLEI

ϕ ϕ

ϕ

= +

= −

2 2 2

20

26 9 6 18

F F B B

z L

F FL FL FLz

EI EI EI EI ϕ ϕ ϕ

=

= + ⇒ = − + = −


5/9

M

, B

); A

A

B

M

M ∆ = − M

3 03

30

3 23

D D

A

B

s B A

d B A

R L RL

RLR

M R L

M R L

− + = ⇒ =

= −

=

= − =

= − − = −

M M

M

M

M M

A

.

.


6/9

( )( ) ( ) ( ) ( )

2 30 00 0

2 32 6

2 2 2 32 6

B B B B

M T v z v z z z z LEI EI

M T v z v z L z L z L L z L

EI EI

ϕ

ϕ

= − − − <

= − − − − − − < <

C

30

0 0 18d B

z Ld s

v z z v LEI v v

ϕ

=

= − − = =

M

( ) ( ) ( ) ( ) ( )

3

0 0

2 2 3

0 0

02

0

0

18 63 0

18 6 3 180

18

B B d d

d s B B B B z L

d B

d B

z LEI EI L Lv L v z L z L z L z LEI EI EI EI

v

Lv L

EI L

ϕ ϕ ϕ ϕϕ ϕ

ϕ ϕ

ϕ

ϕ ϕ

=⇒ = + ⇒ = + ⇒ = = = − − − + − − − + − =

= − −⇒

= +

M M M M

M

M

0

6

3

EI L

EI ϕ =

M

2

0 6 6 6 3F

B B

z L

z L L LEI L EI EI EI

ϕ ϕ ϕ

=

= + ⇒ = + =M M M M M


7/9

, :

2 00

18 3 6

F

B B

FL L FLEI EI

ϕ ϕ+ =− + = ⇒ =

M

M M

CB6FL

=M

A B A 2;

3 3B C FL FL

M M = =, ,18 9 18s s s B B C

FL FL FLM M M = = − = −

A

B

C

7 ,18 3 18

2 ,9 3 9

2 1118 3 18

s B

s B

s C

FL FL FLM

FL FL FLM

FL FL FLM

= + =

= − + =

= − + =

6FL=M


8/9

=60 =60

. = 2 1= 1 . =60

τ

τ .

= 2

1= 1

A B

C

( )( )( )

( )( )

21

1

2

0

12 2

1 60 2 60 21 60 2 10.775360 2 1 58 2 2

G

G

dx

s h s h s bs dy

bs s h s

cm

= − +

= + = + −

− + ⋅= + = ⋅ + ⋅

( ) ( ) ( )3 33 1 14

3 3 351490.3

G G G

x

b s dy s s h dy b dy

I cm

− ⋅ − −⋅= − + =

=

. , .

.

,


9/9

τ

τ

τ.

:

460000 1.1652751490.3

n

n

T Ncm

I −= =

( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

3 2

2

3

1.16527 586.517586.517 341.724 (uscente da A)2 2 2

1.16527 586.517341.7242

1.16527 11732 1173.03

y x n G zx

x

y x n n zx

x

y x n n n n zx

x

T S Ab s S A s dy cm A Ncm

I s T S B

S B S A B Ncm I s T S C

S C S A S B S A cm C I s

τ

τ

τ

−

−

⋅= − − = − = − = = ⋅

= = − = =

⋅= + = = − = − =

( ) ( ) ( ) ( ) ( )

( ) ( )

2

2

1 3 2

2

.03 1366.91

1.16527 1211.541211.54 1411.762 10 0

G y x n n zx

x

n zx

Ncm

s dy s T S AS D S C cm D Ncm

I s S E E Ncm

τ

τ

−

−

−

=

− ⋅= − = − = − = =

= =

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