probleme rezolvate statica
Post on 05-Apr-2018
293 Views
Preview:
TRANSCRIPT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 1/304
a€i:,::tvL<iua;U;g3Tf
[U
IEuBuflue
J$L
.
1
:
,
-
e1
q
1
-
-
a
:
..
..,
3
1
.
.'1
fgyh
EfF-
ff#3 $ry
l.*H
F41
q
5tz]<Fr<zFz
3.f)<3
IT
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 2/304
:a* a n - I
h"'q//e 'r
Y
.4 .J
,
"-
! L z z cgE
*;Ea
ai?
:E
iAei
*a
gr l;?
ftSr
Ee
fEg;$
F:
=
1
sIE
iE
fgE
1
e*E
?E
iE
i i g EiE
:V
e
xEi;e
Iu
= *
Ei;e*g
g
;E;*
3Fi:g
xFF
3
3tr F
g] x
i*HfF=
:g;
eFE
+
AP+
s;E g
;9
r
F
FrF
i =r+=r
I
I
I
I
rI
I
r
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 3/304
N*MNsN
o
_
+
N
*oF
a
)n-t x
v+
!
dq
-
O
!
6O
g
o.3
".t:a
=!=nr3I
ia
--
I
a
--
r
.
.-
3
S=
v
a
c
=
a
;
)
"
!_
--
:
f-=
s
,€
\=
rJt
:
!=
-
=
s1
i=
n
E
o
=
2
:
,
i
:
5
;r
:;=:-
!
^
L-
(J
i-
=
=
n
-.
?
'-=J
A
i=
.=
.
-
c
F-
.
-3
5
fr
-=
1
*
itsr
rr
.
c=
=
q
+
=
a
=
i
.L
;?
;
a
A
'
=
7
.nF
?=+
:1Y
-
4
.=
o
.9
c
-
F
-
a
Fb
*=
i.=7
-La
'9;=
1
'uO
a
o
:JF
=
;9t
,-
-
h-
i
=i
i.g
a=
Y
r
!
r
+
-
h
i
-
=
a
f
;
^
-
{
uL
:J
-
:
1
o
=_
:
-
z
.a
-
.
:
:
,=
i:
€Fe
'a
.
=
t
-
-
:_
.
-
--
.
!
.=
=-
E-=
'=
=
.=
*
+
t.
I*E
t
'-
==
--
==
=
.
.
.c
?
-
=
-
':a
=
!
=
,2
-
-
'-Y
E
;
;
=
l.a
';=
-"
.7
z
a
-
-=
=-=
cF
a
=
2=
=
=
o
.
-?
=
a
r
'-
r
:=
i7
.u
=
=
_-
,v
a
_
*a
J
;
-4?3
t=-
,
.=
:=
',
za=
S
:7
=
4
=.
r
=
==
a
r
-
:=
L
!4
.
=
e
=
l-
-
.4=
*
E
L
c
=
r=.:
v
"^
i
I
:=
.
"
:
-
=
*
:r
h A=
=-a
-
'=
,,
:_
:
J.
'=,
7
t
?
=
'
,1
a?
o
3*
^
-L=
U
==
=
E
-=;
=
1
a
=f+.
-
'4=
'trZ
r=E
;
:E
-
:e
-=1"E
.?
-
.a
=
j=
.
I
I
o
;
=
r
.
J
.5
;
C
.2
't
i-e
.Jc
4
c
i
,r
n;,
,_
\
\
\n
,,A
<
h NN
h r ^
aL.sG
^t-eoC
i
!=.
!cxct.=
.U
F
t
l-
I
'+
I
r
I
I
I
I
I
I
I
IT
I
r
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 4/304
*Ft
i:s;e
?E;gr;
a+
rs
$;X;F
*u
lg
i;=
;I€;;
l:g i;=
E=
;re
ir i+ :
l;r
!a
.+a
€
=
:=
.7
=
;=
t11
==
:* 1,
:E=
iEi
:1=
!1
E
E
; ;*Ieai
l-
td
*_
/
r
Y\\ \\ q , /
*
-*
dl-lo
7
==
=
"
;4
+
;
:zEs!
"c
-
P
=
-?
-d
-=
-3
t
'N6 .
9?
;
-
i
r
-
;
=
a
T
Ji:
p
Fyr
=
v
4
.1
=L :9
,=
I
;9
!
q
'-
7
. *
=
-o
'
o
c
-
5
i
1
;
f 5
r&
"
E
F
<
?
E
;+
-e=
5
h
;-
\
4rJ
=
*1
=F
i*
-
1
\
\>
:E
irs$ ;
:;nA
;e
+a
*t
;a:
l rg+
+
Fl;
i;F;s ia
F
Er
i c
g+ r€
*
= +
;+;+
;e
;3
._'!
F
-
ca
-_
g=
J*==
:3
H
*
1S
XF
;*-g
i l;eE
;t
€F
E
Ft
E5a E
ra3:
c
>"
!J
;
i-
D
':.=
3
n
6
-
c
5
r
L
=
!
-
{
^
;
-
-
*
:- :AE?Tr
\
;rs
Fa
^
D
-
-^
-
-
F
b2
"3i*
3
=p
4
*_+ ;1
ec
*
=-
'9
.*
5"+
"
=
*5PJI
,$
Ag
$=
.?
-a
G
*a
i
.
!5
=
i-X
*?
-
;W4
ah
G
4
"+
f
Lm=
3o,*
!
E
\c
5
!1
=
rE
I
t
=Ef
!
G
=
E
-
5
-J
c
4
! lB
H
-
:
"^
E3
-
s
=+
=
H
E
=
**
y3z
_
s
n o -- o- z -
-
F
\
,
\
$
*
I
I
I
I
I
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 5/304
ttq
;a
b
!=
:
-
A
>
\
E
.=
i"=
a
.
.
,*
;,
:A
;
:=
EE
J
:1
E
9Ei;
i E
-
E?E
I
f=; r= :,1
E
:F
=
:E
: 5*
;:=F
:
?a
;
i::;=
=
="zz
E
;ei;
i1
;=
iE
:;?=
:
I:
3
E
:
::
:-
tE
3E
E*
*
- ;;=ri E
*=EFa"E
{,
-
O
!
\=
-
O
t
?
!^
!35
=
5
-
!
=
o
.
S';
'E
';*
u
-
a
i
:1_
=
\>
'1
g
._
c
.T
{
-
r=
1
"c
:
!
'd
.^
Y=or
sF
r>
'-
,v
i+=
E
"
;" d
!
F
g
E
*
!
2
:=
'
e
r
h
a-=F*=
*Y
-=
-
u"
Cv
L
=
'"=_
a
'-
!
-
=
1
-
*
'
=
-
3
=+
c
-
r:=
.
!-
l-crF
:
'a
!
E
ii
-
:
r:.
!
!=
-
!
=n
c
=
--
J
:s
:+
c9!
-a
-
/
i
-
!
-
+
7=.--
'
.
=
-L
-
.c
_v
J
to
s4
"c=
-+
L
-
-
c
a
I=
E
-E
e
-
-
.
4
-
4
':7
:aQ
:
+
-
?
jo
r
.
-_p<
|
|
3FE1
a
fq
I
t-
I
\V" )Jt
-
air
:?fE
t
Fi; gi l
:eu
t
=
=
--s
i,
:e
S
!
sf
i
=
r:
,
_=
=
.
:
>
??
t
.1;
;
_
E
;:
5
;€
;t=Zg-
;
E
:
j; E
1
=
==,:e
i =:E
:
1
i; 7
;*t=
::
==
;
i ; =
:rd==
;
=
r:=
r=
:
3;i:
i *
a
-.
i:
Esr3
:z=
:
,;
:
}*=
::;
;=
::E5
1
1;
;:r?:1
+=:.
i;;:*s
t+
*
=;=E
+
E
rE
!==
.E
g
1: iuE
3
:5-uE i:
IIIIIilIII
c
7
8
^
a
>ra
i
I
I
IT
I
I
r
I
n
I
IT
IT
IT
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 6/304
f
+
o
G
;
E
qB
ry
9F
s
F
EE
.trpIgF"
-x
o
s=:
-E-
N
!o
=
3E
-<E*+
eEsqx3.d
!tF58
.-G
.c
co
7
Fa=
;F
EE
Fs!r==
E
I"
9R::
!1
E-
.1
eS
+
33=
X
=
-
'E
Ff
:E=
:3:^
En
d5
=
;
€
a
)=
=
.
i,"
;-
"9
^
l-
'-
=
c3
t=
'=
o33
^
:
?
*E
Js3
I
*s4=*
T
c5
n3
s
5
21
5
i
r1
z=
-u
a
a
a
-
F
-
9
=+
f
=
2
i;
:u
'n
r
:F5
E
T
t
+
.
s
4
cB
'Ja
f
-=
E
?7
F
i.
*74
4
i =
II
f(n t:t1
-_*
a ac o- z o
"sE
--3-*F
;gE$
drFa
E
=3
r-7H
Eig
"7vi =
F
3
FA;
*
F;F
i-
=
s-
,g?NPR*
=
[e
ase
38^e:*
*
e15
=L
E
iIrB
E
?
3d3
l.=
5f=i
'-o
Q
iY
+
a
*4^
:6G
F
frT
"3
=
gB3;-
i$$
?F
*o
o
da5
g- 1-E
I.n
33
*3
s-€
-
83
r?
i-=
GP
o
G
aa
c
aE
;3
Br:
rr
EF
i3cEsg3
:r
F
=z1
=F
+
s
gF;€;
3 i
i
=
:tit
r
ie
E=
i
:
n
;=E
.*E
'i
e
Fl;F
e
lr;$5*
.
.
"L
:
j-
.
=
=rE
rs
;
4=e=
=
-=E
.
-*F
:
, { o o o{ Fo
:>
!
a a 3
.H|A =
c*E
+ s,
s
"3F+
:
F
>
F
c
t
-v
.
i
.
L
+
\L
*
tn1
E
tTa.-
Pp
I
r
!
1
Iu t
-
-
.
H
\1
{L1
r
l
*
l* F
t 4 ;
.c
o
<-
6 4 =H
L
@G
I
E =
T
= O =
<
.
i
2
N
:
a
|
!
u
G
l
l
-
|
|
*H
'a E
?
'
G
-h E!
-
I
X
;5c
I3
--
F=
-
5
*
la
t
-
l
'-n nr
Y
i =
x
s
l
-
i
:
:a
I
:
l
,
o
o
:5
-
l
:C-L c
= ;
-
N+
l
r
e
i-
t
-
o
L
i
--
:w
e
o o
I
I
I
I
I
I
I
I
r
rI
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 7/304
=N
;
"56g
e3g
r
!
Y
)-
-
'
Y7
4
jr36
<ar3
5!
?aL
g
r
!F
-=iF
_C
."F:F
'27
7
"vs
'
Y
sJ
5
Ic
F
:
7'aE2
,_
g
,x
c
e
b
l-
t
\
^ i
\$
F!qU
A^1
.oH
-*
=
'-c1
c
'-
E
dE
o
a
L
.
a
=9
-c
=:
o
E
_
=
E
i
':€
-
*
u
C
i-
=
=
.
c
U
O
C
q
g
F
g
"
q
.
l
1
aq
'9
6
C
4
'-
=
-
F
)
'
-
-
-
e
_
-
T
-L
=r
+
' =
:a
F
I1
.
;
'. -
9
o
j_
i
r
-
i
j-=
a
.
-
-
1
-
o
-
1
'4
l
c
:
,
-3
\
+
,-
=l.--
--X
= +
r+
=i *1
E
E , -:
F
.
a
-
_J*
; *--1"=
i
-z
'3
=
:
't
i=
e
i
.
._-
E
.E
,
E
J
€
,1
9
;
*
P
.
:
f
Y
C
:
-
)
-
=
-
-
-o
g
*f
?
i7
a
6
EcE
E
:
==
q
-EEi
i::=
E
:
EFC
F
!
^
-
-
-
v
d
;=
u9
==
-4
E
E
{
r
LpoFc
I
I
IT
I
I
I
I
r
I
I
I
lrr
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 8/304
F I o o z - co* : - o r o r o cz q
I
I
I
I
I
r
I
I
I
I
I
I
lr
I(
str
I4
3
>Fi O NG
**
E
l"=|}o! t {ob T '-
4
1
G c "
Mk + a i i I a
h o ; -L ln \ I Y
p-
c
rst -L t lr l
g
AE
O
€EF
e
s
€
=
Eq8
5
E
r
p
EF
F
E
I
o
3Fo
i.F
oF
=g
q
3
:x
e1
esT
g
s+
1
-2
t4
F
+g=i
ei
Z2
-
-
*5
.=
o
i \
1
:-
ia9
; -d-r$
_N=
;?
€
=
7*1=
-
.:
q
*=
Ji
.=
7
.1
i=
9
l,5
:
F
!=
3
+
s*=
I
F
b
3+
=F
3qB
s
;rr F
3
S
:
' d
i8
E
tl
.c
I
==5=
;
.u-nI
i
;3rT
5
3
o€
f
;
e
-
=
-=
;J
O
J
=:x
9xoE
P
:U
+
$
IJ
f
A
*G
\F ! dN
\J
F
l
+
M ,}M
:
I
-Y'.-
ua
q
la4
oI
J
la=iFg"C i
-
4s
o
=
l U+.+
ie* I
fs
-$I
-J"=Fh* "+
I I I
=
"HaH H
rE
ls l>
"= , f- I
E
_ q 5 rI
"*
I I
-
L
\ I h \ l t9 r$
i r[- IJ
I
i-
A
INp
IJr
s t N 6 t Ir'"1*o l;
te3=
?
l
g
:
"+
l
;
a-Y
o -q
y
--
"?7
?
hu
@
6
;
-D
, -o *2
\
-1
r
F
H5
:'
c
;+:=
dg
c ! B o ?
t4
'J
v
i<i
l
=
J
:L
-_.
h
; 6
l
- to
N 1 . H
M S!r
;r3F
I
's
?
sc
*
c
t4
c
-M>
i)g
{E
l F
J."M
g"
.YY
* i
**i
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 9/304
r
lq
je= I
4
d
1
r
e
l
r
d
1€
-
'
fY
\
aEa
F
!
:Q
@
z
\
d
H
.*
F+
=g
r
-o4
,
a-a
Ns
pLt
a
i
!
:<:
.
-
J
,5
^
r
i
O
j
N
'a
9-a
a
!
C>
:<
_
v'ht=:N
FzF
l
:
r-q
-
F
r
.
l
'_
fH
.1
q
.!cr
i
\
lr
€
,c=
.
1
l
i
:x-"-*
\
*-h
N
E
.*
v
l
ac
I
I
IT
I
r
I
I
r
I
I
I
l
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 10/304
2
n
O - { c oc I co- : c
IJ fJ
n N
F
u l
=
t9 t9gr
;
tv
i"
d+
'
b
h4
\
-
r
iu4C
I
:
l
'*
iD
-
t1
r
g
t
.1S
=
'cT
\*
t
lr A
.
:
r
\- l 'u
a
a -ci r o z
i I +ls i
w* '- .Hs i
sg i
N
-1
=
+ s2t
t
+
r
**:
:
;a
- i U
}Js .ol I .?
Z
iK
z
tL
z
b
l
l- IL 1
,r
!
L ir
'a
t
Y
'
l
*
,
-*l
i
ts I t
.
--/-,
."
-J
*=
s|
t
ts
I
\\
r
t
l"
|
, .1
I
+_<
-
F--
\
F-
-=--st+ l
*
-L
-
,^
\H#r ,
-
t
/
l*
I
I
I
I
I
I
I
I
rI
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 11/304
=
i:
!
*s
:
:
EE
.8r
,x
)c
60cE
F
v
=
:o
*
_
'q
'g
:a
g
*
E
6
re
E
*
f-
H
:
E
E
io
F
?
E
'.v
-h
_
e?
i €
=
,
a=
E
r
cd
.E
.:+
tLaE'a
=
s
E
s
E
r +T
r*_
E
:E
't
'+
lL
;i
*=
:
--a
=
t
-
.o
="+ z=
+€
E
L
-
!<c
,=
l
Irh
-z
';S
=u
r =E
E
=
aa
6
lE
i
ish
'=
,
*
5-E
+ 3
.=
'-
sE"
-
':-
1
7
l-E
i
i:a5
:a+
:
?r
?
EZi F
E
;E
:
's$
"
';f
E*
i
,=
s
-b=
6
-
f"
c
4
^
-T
:
7
=
E
ts
*
iE
F
E
E
"_
f=E
,E
3
'}€
F;
=
.=
E
I
v
\k_x
L'Z
.E
sE
s
O
-
ec
:ai"
j
E
'E
,- d
s
3
-
=
u
3
' o
;*z} E€
xE'nE
r5
=*€
U
*€
y
!
!"
:
c
:
!;"
?
:
:+
q
,
E
:
sx
{
:E;
*
=
-
o
p
9
P
-9
'
:
-
IIsgE
S
tEe#E
€t
7sa
;E
-5E
;€
H5
s€
;
tJF)(F
tq
;x
+7
|a
-4
i€Ta
O
*a
isc
q
.oY
;
+
O
r
(c
-
1
l
oc<
,
nT
:-F
r
l
l
':E-:"
€=
-T=
=
l(q
:*T
!
i."=
L
!T
lr
-T
d
.r=
S
-1
f
:
n
r
j
:
;
?
:
\
j
.
i
^
i
_
r>
l
H
X
Lr
-
i
L
l
;
E n
L
E
-
nh
4
^
n
r
i*
-a
!1U
(
+
()
F
€
;
.N
=U.
'
'
v
1
-?
,
'-
=
- a
-
'
I
a-
'-c-=
\-,Ql
>
.
;q
t
C
t
i
\
^
-
,
;
L
>
Y
c
F
l
\a-
.
l
:
(a
rFy
l
I
=
t:
.a
;
bD
'sn\
\
r
*
G
V
.-
:
9;"
n
F
i-
la.5
r
I
I
I
r
I
I
r
I
I
I
I
I
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 12/304
$
F
5
+ o
a
o
Q+
3
f**
E E
E
==
E
?
e
E
:
i-
J
e
=H
H
o
-
o
^
!-5F
=
g
-=
^
E
-s
"
1 T
=F
_o
_
:
\?J
- :
-
*
;
"z
ia
o
u
,
|>
*
4
la€
=
-c
a
:*aFE
l:ri =
-c
'
U
a
i
;
I
X
a
=
!
=
"
-
*
=
(
'
:
Z
R
:<
!
I
;s+
lr
l
E=
5=E
:
:
-
5
l
:
"a=
*
"
-0 I
+
:
=
E"s€=
-
-
q=
i
i
ts
b
=P
f
|=
' +=
=:
.:
'"
\=
:
iL
c
r
'fF
E
r
IH-*
:+g
lr-*-
.a 4c7=
-
=
a
O
l
o
iV
j-
r*
'4
;
N
F
a ocr - o F t9
t2-1
-
+
i-2
i
E'v
G
H = 3
-5
-
*J
p
l r e .o a o N
=+ = G
:
t
!l
-o
4
E
f"
I
-
ir
-
te
lr
'
=
:
c
l
ir
l
s
d
t7
t
lc
i-
.a
l
t
u
Hq
=
is
6
J
|
ip
.
\
t
.
a
F
B
*
:
N9
H
.
s
{ d a aoz co :; o
t FO -?ni
*F
n
c
=
w
x
:
c
N
;
h
a
ts$
c
ccc
7
*
w
:
*v+Fs=
-cE
t a -
F
E
(s1
!uh
E
s
?
A
N
N*
6 =
rf
N*
"3A3*
.1ts
lS
i-FO o
_
J ld
+
F
!
:a!=*
^
JP
u-;
D
a
^
,r
;
o
x^^
F
6
E
=
6EtsE
Oc
:s
P
w^@
u=6
2
<
X4
r
i x3
c
e
i
P
l
v
7=
^
5r
E
4
.h
Ed
:
t
=H
F
:5
l i"F
=-
EeP
P
X
ot 5- io@
t
+o
*E S
:a
F
@-
:6
c
sO G
.^ t t
-q
s
I
I
IT
I
I
I
I
I
I
rI
I
IT
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 13/304
\oo
Iu
:N
c
--
E
l
a
^_i
n
,n
NF
.=
i
^^
f:' T
sY
i
"
*-I
irug
,s
;
uF
*€
9?
-
F
r=!
:
;
*-
i
x
#E
3<
"
n:
+
I
z
q
-
!
._
o
-
c
i
;
\-
.
bJ
?
iL
.E
:
l
L
d
'.o
-a
. -
-
':
r
-d
Eb
na
Y
Z
D14
tqn
-
t
CY
's
t
:
*
,
5
i
F
iL
L
-l
F;I
rl
-r^
^
N
s
-:
l-
a_
a
-
*cr
r
,
ia
i
F
;€E
*E
r
ir;;Z
;
;g*1
5E Es
=P
=
=
=
v4
;:
i;=;E:
€;
fr3 aE
i;:
F!U!
*-IF
*€
rcI
m+
r*+
n
lrs
*
',
.
n
:4i
'+
a
s
*
+'
1
F-sF
LH
.
\
,
ry
F
I
IT
I
I
I
I
I
I
I
IT
Ir
IFFUF:J
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 14/304
I4Grc .
r
o
lr
=
c l
4@
!5
o
H
9 -J
F
! '
*a
,
=
.
FN
=s
4
s
t
F (
-c
Ja acz { c a :-c
c a G n O
o n --r o{ -
Fq
F
.YRt=?
-1
!
=
e
I
i P
S
\
N
F\
J
"?
cN
F
q
t
F
iJ
*oYr
-
a
io
^
-J 'o tdi^oo
N
! v
ivI
r
t
^
F
q H - -
-J t e '+ t
6*
.J t
**
- t
o*
.J @* t
.C
'n
i
-
E=
I
Y
la c
=
:
I
!
-<
.
:
qE
t
o
E
H
i"
E
l
F
Q
I
;
X
c
S
^
N
A
-
n
-
l
-
B
:s
=
!
i
Q
:H
{
L
>
-
+
.q
\
l
:
D
-
=
"
:
a
:
,
o
=
r
i
=
;
ss
35
=
r
I
*>
n*
r
e
3
G
b
t
t
l
.
-2
,=
l
q
I
;
;
' c
'
=
:?
i
*
d"
i
'
!
=Fx
I
o
o
:
e
:c
i
l
==-
3
aE *b
s
@ +
6
:
3u oP
Nq6
q
o
I
O
+8+H
E
.
rq"E
E
E
i ESF
F
tJ
ry^
E
6s-r$E
:
+
$
!C
+3a
ic
FoS
c
-
'
K
=
:J
o
:
a
ra
e
=E
6 i:
=
i;
*H*
X
3
E
:-
rFO
:3
3: 5
F
n
g3
L
-
-
a
i
-E
+
:
_
i
=
5
R
E
2
H
g61
:
5
'+9
==
;
5
a"
L
rE
'G
ts++
,u
gJ
r
.e
d
F
c
7
!
:F
-
e
n
F
E=3=
o
c
F
*
t* $
H
<
cg-
o
tod
A
n
.
=V
d
E.5
-
;
3E:#F
FSa
s
c I
I 5 e
! tsl^
C
C
tJ
a$
\-=
E
a
G
X
,
ts
X
=
=
pNN y4
H
L
g "n
*lcu
A
I s t ; l
qs l "
i- q O - ?,
- N* I
t3{
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 15/304
g
:-t€
'
L=
.b
i
:k
h
9+
qI
!
,9:
sa
€
3
j
r
k
a
'Io
|
:s
-
o
;
rL
€
7A
o
'€
.
h
eg
€r
=
et
E
6F
:
r*q
a
"p
a
:
=
"
d6
c
S
c
+
Pe
Q
tc
5.)
Eo-
.
=
x
\
x
8
X
t
-
c
&
:v
,ql
q
^.
4
:
-.
eE
6
*
o
d
l
r
F
j
\
o
i
,
F
s
.
?
I
r
Ju
e
v
A
L
^
o
o
=
c
fH
e$g
-
!q
€6q
g
-E
-7so
j5xeQ
,4@
-b
U.A
P6iRrN
:
I,9oP
i-rr
v
nF
-:
n
+
a
.a^L
q
Eu
l;u
L
F
-a
:Eet€
-
a
.
!=Iq€
:.=-e1>
G
i.
c
Q
o.-.-5
?
!bFJqU
O3
c
'a
'4
a
-oo
J
'Si)
'r;
Z
-@
-d
l9
.
a
d
v
oE
Np
h
"
5E*^
I.
.x
v
=
e
ay
=
o€a
iB
6
t
a
=
E cq
E
bE"
!FLF
T
I
I
rr
I
I
I
rI
IT
I
Ida
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 16/304
R*
,a F
Pc=
6,rpc
'w .
F0
Y
.a :o
'2>
:
i 3
t*Y
=
u
e
a
=
.
o
E
-*4
.FEuEE
-c=
E=
nE:
-J4
'"s
9!39
"F:"9
:"
3
!
$
X
r
t
-=
=
RF
;
*E
r
r
=
:"
r
@l=
G
@
D
!
c
=
C
=
d
@lFg
C
^
a
-
*=
4^
-
a
!
-9nq
P4
4
,=:=G
q
b
F
6
=-
s
5-c
{
_
_F^
5
!
!
.
!
'-
G
P
5-
Ea
oX
a
9
.
i
-
F
J
:
F
n1X
:+
5
F
F
P
r
O
a6
-
s
!
-
\
-^-
o
p-
"
4 v
2
F
as
E
sO-1
V
{ q o ocz o* a
o
==
-412
r*
:
*
^
-=2
=
i;+
=
=
-I
=
=
a=
:3
.1
t
=
j
--
_
.
=
^
2
-
:-
-2
-
-
^
7-
=1
;
-
-
Hc
J
:
!
:==
ra
:4
-
=
-==
=
4=
.=
-
=
:3
7:7
'+
--
'*1
I
-
-
-
-
:=':1
=
:
:
:
=
O
!
"
:2=
:T
v
;2
i-
=
E
=
I
._
:=
-
7
!
-
:
4U
'7
1
-
=
"=-
V
.m
3?=
t
=a
;2
e
-a
-J
i-?
i-*
1
=
-
:
j-=
-3
-
;=
=
=
+
=
i
-
;
i
-
-
=
1-=+r
'=^
-1
'-1t
+^
-
,
"+
4E
=
3
5
't-J
n
_=
-1
t
=
H
z
r-
;-3
i-
=T
;
=
;
:
a
-
:J
;
F==
?
s* I
F,
,
g
-
l i t
0
1
r
a
5
P
X
+
N
o
1
F
C
^
-
!4
=
- i! ).
a
c
-
^
c
!K
-
*F=
a 9
:E
+
-=O
=
E
S
n
-
j-
an
'a
=F@
=
=
a
t
?
o
c
'
-
+
**dF
6
+4
F
,^o
i-pX
o
o
H
o
-
x
!4
F P
a
b
!g ir
I
IT
I
I
I
I
I
I
rI
I
IT
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 17/304
i g u
€* =
: E
=l;e
Z|,E
1
? . z
zI;
zZZ r=
z
=E
;
:;
=
1;=
r:1+ iz
., i !E
i
;? z:
z Z1
:;
Z
;1 i=Ez
= vz=
1= :.z
=-, g
z?
,=r=:
Z,;1
z=;€
i _
:V2
=
::itte- ,z
r;3
i
Z=
1:
?q33=
;, 7
* :1g
* :?
1
z=
=e=s
:1
^
aei *
Z2*;E
;7
=
E
:;;:+
E
;
:ZA :=E
1
+a
vE+,=
u5E
E
;n
F
;Eti E
t!*
ai H
i!E
lz i;:=?
i
E ;Es
;=1i 'i
:z:1=
:
t ai;E
; ri
:;;
iaqC
lEi uEir ,i
ti + :
;
i,uzr?=
F::t
;+i €
g:
:
=E*=z=n
ZE
-
1
u-
i =
nzE
a=
1:=7=
Z:=:
i Z
12:!1
f
t1:7:E
E i
, i ,8=E}e
..=
:r1
z=
EE
=EzE
=
r;;E
,=s
E*-g
E
g
E
Zec
I
T
IT
r
I
tr
IT
I
I
I
n
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 18/304
'r , - o ac . co -
\
!s
0
n*\
!
t4
3
;L
J
:>L.
- I
5
rF ,
IA ! t *
--
\
i
v
l*
=
!
l l Is
l
Tzd
=7i:
E
=
A;e:"=;f
F
7tur
7
="3
=
{=1 ?
=r:=
;
,=-J=
=
=
1
r
j fJ+=
v?-L+*=
=
=
i i i; ;:-=5
*="
f
1E
1E
f*!*
=
-=
=
=
-*
1
;
1F
;
t
:o:cE:
-Na
,
:2
"=
'2
-
r
\
p '
:
-=
7
o
a
i
r
L
r
'
:L
s
;
-
* t-
f;
.
N
-
.^
.
-;E
o=
!
*
7
N
I
e3
"
";*E
F
'
P
*
4
-
:
=2
->
-
-a
!
:=E
d
EE
+s
4
g
.4
:a
;
r*
o
- .. c
a ts
I
I
I
IT
I
I
r
IT
I
II
I
IT
r
+N
a - T
l4 ':1l l :M
\
/I
l- ",N-
I
{
,--
i
i-
l i
t -
_
-
t
*
l*
ts
^
a
I
r
|
-
, t
.c
!
_I -<
'--
a-
'N
:-
==
'-
==
'
a -_
.?
!9
lv
, -
t_
-
*2
'
'
!3 ' -
|
_
r-1
I
ca -
o
i- i
C i{ 5
!
l
i
-T--l1
-1,
-
-1
l,=-
le
i
i-
J
I
-
^*
'c c
i
t
L
- - 3'.r
e :
"c
1
.
;i
s
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 19/304
-*
'
*
I
'
c
J
3
l
Ir*
lg
>
n
.o
I;4
cs
F
^
<
>>"
r=H
^\
^
-
.-o
?c
l^
-
h
> .
3
,L
t
n
\
!>
.
t
.r
>*s
.
=
L-i-
tn
tr5*-
)a
t
?
a.=
d
+:
€
.
;"
2
=
N
."
.a:
:
a:R
-
=&
i
a
3
s
=-4taY
:
9P
-
i+
aD
+
.a
e
A
.=
o
t3)
,_
e
1A
>
L
!os5
saa
l
;
_
r
l
'r1
t
:
iL
r
?C*
L
i
|
-
I
l
-J
.
.st
<
-
t
-
f
-
-
a$E
L-F.F
IF
!
'-<
)1
,$
{a
1?
.
I
-1*t\
I
I
I
1I
I
I
n
I
tr
lr
t
I F D:Uc7
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 20/304
z
H
4 E i -M L
<-
g
l
lC
r
[_-r
=
1
=
q
'.
E
'J
=
:
i-
{
|
r,
:
tr
=
r
: r
=
-
l
t3
r
r
1
rr
l<=
.
+
rlr
HFi
:
L ltr_
a
t9
J +
|"t :
I
-I
\t
*
- , ac q aI = b
, l-
;i3
o - q
L1
t
,
r
l
i" {
-
Nrere
i
l
tJ
P h l
o
=re
J
,{
l -H
^y'a :
* -LH
E c
:1
\
r : I
H 4
,-
l-
fJ
e
t1 IL
q5
\
-
["1.r
: i
b
-
!
4V
eJ*g
x
l
L
i
!
I
i-
s
a
-R
5
3
j
l4
q
q
<
_
;
J
"
1
l"
J
*
*
B
€.
c
ir
l
,""
|
.
i
r
l
q
.^
c
?
;
h
Nlc
\ t
A
"a C :
I l-
Nt*
fT
d
rg
*
T
[b
.
"
..J.-
-En.,n-Q
-t..
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 21/304
so
N
+
rTlltI
."
ltt
t.h.S
$
dP
€^
Y
-
r
.
a
z
rS.N
.J
..z
E
)4:N=
aD(
U+i
t-
!
i
j<!4;=
=
**3
-O
-
-
*a
(J
t
j
G
F
\s
o\-
I
:
-
t
i
-
n
$
e
l
s
\
:
\r+
ts
*I"
=
I
T
I
lr
I
I
-
lr
rIT
IT
I
t
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 22/304
\ '4 , o a c -
s \
$ i
H ! r1 aH :G H x <p
\
i =F
\
i-
=:L
F
i
!
F
\q5
r
.
I
o
$
eS
:
,
+
,d in
d"cN
cP
c
IA C ts
E i t9l9 +
I-
*
;-FM:
IL
s
c
1
l
o
-
-
fL rG: rel J.
.
1
L
^
<
r-
+ =i@
t
N s
' "
t-
5
l$
is
ls
_
<_
o c c
f v
.
ln f
I
IT
I
IT
rr
r
I
I
rI
I
nT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 23/304
),
r
N.ok
J
a-Oi-?Q
^
1
;E#
,
i
,
!
d
n
*
tF
,a
i
r
I
l:4S
a
t
.s
/
-
<
!J>
o
f
5
*HA
!d
.9
l4a
-
€i
F s
-GF
is
l €
:
rc
o
'
\
F
i
o
q€
J
*
l
'
"
.<
9e
s
T
,_L
:aI
a:-T.^i
Hcv
?3
lrtI|
la
-
-.-n
Y.tm
e
,lr
:+
cIF
l
^
Y
.n
>
b
t
.la6=
Yfcs
\1
I
I
I
II
I
I
r
I
r
lr
IT
r
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 24/304
q
a o z - Ci) - o z( n *
: l9
b l
r* I I r I l3I I I I I I t
y
: a
f
:
!
;
:
.
-
lr
I
i
:
'*
b t
L
, f
L,-A
. \-
i
-! s
=
3
E N
ta ,F
i
t4
I
\ + 'uF ;
r
F
,
t
c
i ss
Fq
SI
! t9
LF\ "
,
]A
I
L
!s > + ;*-t i ,
- pl-
r i ] t-
\
\x
'-r
@
'""
'-*I"-|
-
|*l\Ji--Ps
l\+S
i
Y
I i\P|.z
J +
t
I
IT
I
I
r
r
r
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 25/304
j
tal'-
-TTI
"
i*
f
rE
I\<
,
li-
l
i
a
i'a
-1
-
I
Y{
+
i
rTi
'
l
J
"rh
1
3
Et
F6
r
Y
Ir?L
a
'-
I
Fl
;E
A
ri
'
io
4
i
3
"
t
t
F
!o
.Ec
a
ir:\
t1
't',:A
l+
i
le
Y
_Is
=
h+
>
i
rs
.
l"
r
!1
lH
<
c
h
v
l
*
q
*o
-
l
e.
-
:
q
rH
.1
_
6L*
sF
:l\'Yilc)-
ta5
=
<2.
^c
i
.j
i1
Fcf
$
S
-H\L
\
,H {w
r
su-
o
\+'.P$
=
I
I
I
II
I
I
r
rr
I
r
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 26/304
E o& ix
<
@*;u:
H
N ,L H
:l . N
n
7J
iE ;d
5
=
EY
Y5c
=
rd
1
re
rq
i
=oX
i
x+
a
\
5E
6
]e
o
X
^
-A
=
F
3
*
;5
@
M
i
l
:
:
M
L
o
:
\
.4
B
:a
\
L
:
l
I
;
^
N-
o^
=
5
r
3
-
-=
T
;=
i
-
-
qIL
l
;
-u
-@1
:
-6
c
':
i \
=
-
a
c
_
rv
N
.
:
<
c
1
5r*
*
.,-
t
'tL
""
=
*-
+
|
3
Ur
C
l
! a
':*
6 a 6o
F i I t_ *
.
t)
"q
rq l
I
h
4
!
"h
r
l
.
(
,
-
i-
P-
-
t*+
J
rA-
-_
i
$-
E '
iA la
.1
l
IT
'
I
lr
Nr
-:
I
l
l"l
*
l
l
:a
|
l
-
rA
S
q
{ { a7 o o JF z "1
.
r
I
|"
I
II
,1
,
I
lf
1I,
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 27/304
r
i
clr
or'.T'+I
aavOi
,
I-T
L@
t
|*
-C
>c
o
',
I+
-.qT
r
rq1
t{
€I
:
I
-h
la
,Y.n\.!
i
-h
F
qi-;
>
"-1
h1
F(9
I
.
{
t
cra
\
.
-
v
!T=
a
cFFF
II
\_
.-<
'(a
\
I
rr
I
I
rT
r
IT
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 28/304
i*
<
L t
Iq
_P=
- I a o { o- c
- - c
iMf> "l-
4
6
O
1
I
t
i
I a
O
I
'.L
<
l*c
r
, .-
3
l
i
eL
-
i 3
l
R - 6 g ^ 0
l4
+
+
:_
;q
:
te
1
:
/
l
-
_b5
t I
I
r
I
ra
t
/L
L
-E
T
s
l
2
|"v
G
*^r
cF
I
F
-
z -
.
P
'E
:EE
5
*H 6EF
EH
'
t4
Lr
L
g
"
s
t9
iY1
G
:r"e
M
FP
M
-aR
R
-
I-
E
TF
JT
*
I J
l
',o
I
{
c
__
1
I
L
|'
-
-
Prs
-
L
-
."1
o
.-
s
@
,
's
-L
*
+
t_
TN
-
1L
T
TL
i-q
cr
r
tJ+(r
*
t
t9
I
l-
-
5;
rrrc+n$
l-F
q :."
!
*
*1*
-:
l
Y
t3
c
l
t3
l
-<
r
*
l
o3g
*
m q
9
N
I
J
r
IT
I
I
I
r
I
I
t
r
I
-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 29/304
;
\
F
H
E
*
f
-
r*
Yl l =-R
:c1
=
r
l
:+_y
c
s
loO
(c
{
" c
l
i-
'
l
.-
o
!F
.u
;FN
=
-
4
.: 1
\:rr
I
-
.
-
;
^
V
.
:
i
9r{
4
\j
F!
\F-4.n:
-trc
-
l
-q
*
o
c
:
?
z
:
ir
r
l
l-
c
.
o
l-
.
F
.
y
,
t
F l "
l -
l i:
-*
a
i
u
.
= =€F
la
t
!
4
io
.
tJ
p
l
inq
"
u
.
c
u
frc
ta
l
d
d
Q
DjE
L
(i
la"
.P
l-$
-,
.
l
l
.Y
c
+
4
a1R
c
I
1
l_
\
:
-A
>F
€H=
:
F
htta,
ts(cF=FOF'
r
I
I
II
I
I
r
T
r
r
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 30/304
C @ o z , o* -
H g ^
.F-
q
!L i
i H!
Y
z2\
B
i !FHn .a i Hs
a
rT
1
irrq
tI
(
)
|
\-
|\
-_
L
i:
I@i
v
r
[
.sEE J
HF
H
h -"
&
.0
=Gis" i4 .L C
I
:J
l
*
u "
+
-
tgE
l--o
r:
X
l
L
o
"
e
r roL l- \
o
0
lg
<H
\ i
-_
t
l
*J
^
Yi {*H
i+b
4
,2
-T
H
s =aF
t2
F
-+
+
t
f)
I
I
I
I
I
tN
t
I
r
I
l
i
I
-?
r
t* lst l+ t t+
s
.
- {
e
\
rm
m
I
* I
[9
[]-*
I I
A
(
,J
1
H lqE=L
€
r
m
m
L
tH
*
rq
L
U
F
o
*1J*
\
fc o t
L i
fI FO
q
I
TTT
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 31/304
+
(
'
;
-
t
t
+
"K =K :=
t"
t"
?
4
Iqli
|
-a
I
I
u3
(
|
r
.
|
|
L
*L *U
's
E
i-
--J
C
r9
|
|
'
<
L
.
I
I
f
E
i
t
"
9
I
t
<
-
iI
I
.*P
f+^
q
I
'-
'-
r
|
-
!
-
I
r
I
-
+
=
-
N
-4
-lz
-
-N
-
=
U-
-
-5
|
|
t
.
;
tr
Y
:
i
!
l--
ia
l
|
+
a
I
ru
|
|
J
!
I
|
'=
-
.d .
k?
I
i
I
r
I
i*
sc
tI
I
F
lqttI
I
=
^
|
|
1
|
|
-
v
I
I
;=
I
I
P
-s-s
s
\G
t
=
=LC
c
h5O
!GDi4lNu.J-:.
-
q
'+
-1
-E
i,
3
:
l-
-
*_=
-
!
-
!
:
:;
;g,
!
:;
;
;*;j;rrE
; jE -
l-r
E:
: j
; !
J# :E
;
E,1:r; e FI
g
i+E
r
1:;=s
i
:
;=
::i
,
t*=s=
5!
i ;
:
:
-a
:
:
f'
.
-
.
!
;*:
-
:
.12;
:^
5<
-
:
-
-
<:
r
-
dQ
v
i-X:
<
i
.
!n
:3c!UN
I
"4lI
-<ttit*I
-Ft"it'"Fi"II
*4
"n
.hIt-l*Ii<IIq
:J
r
=
:
:-a
ag
:
f
.
=
Fe
4
t=
:
=
'-=
-
N
=
-
-
'E
-
u
"
"
.:
'
i.
,c
-
-
:=
-
r
fj
l
.-
i--
=
.
!
.
=
J
=
i-
':-?
-7
r
J
:
-
:=
:
._1=
:
t=
g
*c
X
€
t
-
-
.
-:
"
'
4
'
-
.
t
tLL=
,E
G
;=
==
z
u
===E
=
J
a
L
L
:-
-=
-
n
-
i
y
c5
v
=
=E
"
z
-=
.*
:=
X
:=€Y
__
U
==
=
-
-=
-=E
d
=,;s=E
5
=
-
t
:=
N
.-=
z
7=
Z
.-=
=_
2
A
'Z
dc=3
(J
;--e
-
1
:
-
I.
n
'
-
!
-i
F
:
-=
t
J
=
:E
V=
-r=
*==
+
-=
,Q
-5
E
*s
.=
==3PZ
':e
=
zN
N
!
.=-p1
-3IN?
v=
=J
i.:
'=
+5
I
I
I
II
I
r
T
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 32/304
- - o o - co- r
MRIUix
;d ; I ! I T t ; l+ t i tdt & I I t !
FC
F
o
n
o
_F
i.F
*F
3
3
-91
b
U
-
T
-nHs
aFr6
{
'
Y9
s s
6
=
!
I
t
I
i
;
'-<
H
|
!
i
cr
i
-^
e<=
*
,n?S
Y
t
l
tri
5
d
'
J
I
+
c
;
:
:d
^
B
4
c
"
6
:
f
N
s
=
<Y
'
:"
-c
F
t
o
X
:o
,
ro
l
u
L
d
r*
r
;
r
---
c
s *
tP
2N o a r 2 ! oc J
0
r
I
T
T
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 33/304
la
.o
€ra
l{
0
'*l c
E
.
I
-l:-RS
M
I
tLr5
\35tc
'-q
!
L
aa
Fh
-a
'r
*
;
f
-
+
=r
.
c
-r
,
i
:n
:
i
"
ts
!
;
iL
lT
=
.
l
>
-e
!Ff
.:-
-
.u
c
i
I
e
H.Y
.
ts
clr.l
l
"
>
'
=.bt-
+
F
N
H
.N
l{
rY
E.9c
-
-<
.
l-1:ts
.
t
;
lJ
F^n
_
6
'r->
t+
'.
(
c
t
\a+
l
i
-r
-
l-
IF*
{
,^rr
.
'
\UL
d9
:
g
--6
.
;9
-
eN
'
la
a
tbH
?
P
.
r>
r
l
,
rc
-
v
*
a!>
-Qo
cO5
P
4
l
.s
.q
oFF
'?-
l**{F
_
I
I
r
I
I
r
I
II
I
,
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 34/304
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 35/304
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 36/304
{ q Ja o i ca -:-
> 1 r ;
iJ :=EF
*t=
!Hf
!
r
=XF
T
t1
M A4
:
r5
iv
-
g
in
A
;
+
{
"
j-
|
-
qI
i
loi
':
-
t
:
;
l
t c
m
r_s
F tH
l"F
F
->r3
z - cz ca 't ac J
[r_--
|-tJ
+
i_ ,"
**
; /1/1^
/_
)
/v/- {_\_
-
r \_\J
v=
-
G
L\ \! t t -t-
-*-
t-LJ\
I{
I
I
I
I
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 37/304
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 38/304
t
?
-
==
=
=?
-*-
=
A
2
-r4
^-
=
!=1
:?
i=r=P
F
;"9
=
c=
c
c=
;=
n
:=
=r
=lr;?:
.
_
E^_
:=
=
_
=u
:=
L
-=
1+
3?7
i:.;*o=
r
*=
2
o
E=
Z
_
.
:>
:
=
-
<-*
E;E
=
io=;(=
7_-
Z
t"
=
=
6
T
=
?=
=
'F
'= t
11
i:
7
:
_
::
1
;:=:?
s
:=
.
=
-
=
,
j -
z
A
=
=
--
'-=
N
=
:
{
-
-1
_
c
=
;-
:
!
:
u
:
:
;33=
=
i
.z
:
=1"
;
:
i
1
-
.=
,rJ7
?r
?
I
$1
_
I
)
I
iF Fj
-
ry '
ra
v
=
F-
:+
,-
+
o
I
*9
dE
<H
( -o
w
.
N
->
o
H
+
:
a
o
'
=o
- ?
Ft
rd
f
ra-:
"F
l< rS
.
)
i
!&
+
a
!
v
!
G
.q|
.
:
!5
l_ t r9
\
:n
J :
a
J .1*
'
F
i
5
4
0-
€
:
^ i tC '-+
C
g#
|gg;;r=
;+
;*1
o
I z = i z - - t { 2 5 o ._
I
I
I
I
I
I
r
I
n
I
r
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 39/304
F
-F1
l-
++i"
-
cJ
l"\+
;
-J
!
l\i ih
=1. \
iLr
i *
-
.
It
h+
Pi
a
v--=
Y
-
I
r
,l
Y
L
'--.=
=
i€
;a
=
>
==
=
._
-
2
-?
ta
;€
3
^r
*
1
=
-
-a
=t.
:"
:e
.
a
-cX
:F
/
!
-
-7
=
=
-
4
A
G
-
7
-
=-=."
=
-
;F
=:1
E
-
:
t
!
!
!
-=
*
q
;=,+e
*
:=r3
:s
,
€
<:u7
?3;*
:E
=1
-
3
:
=-
.;
c
' -:
t
i
r
.rFr13
-E
,o
t2
2
._E
3
ta
:
.E
-+
J=
r*S
f
.2
. pa=
=
I
=
-
*
;
_
i.=
.
€
'=
;;:
=
€
:=!
i
.=a
d
a
-
c
i-
"
?e
== S
Z
*=
i=z
,r=
i5
:>
.r5
=.
+4
E
-e
;€
,
a
.
i
'
=
E
-
3
'=t=
S
ja
-=,
E
E
3S
e
=
.
:
>
=
=E
€
z
+;3erE
€
=
.;"3:E=
EE
S
a
u
-
g
-
r
S
f=E
6
a
tE=
=
=F;
!
\\
|{
.i
€=
q
/n-I
>
f
.*?
r
:
l
^
s
J
e
-
-!.
==:
=
.
€
3€
?E
=
:"==E
==
=
,
:n
=
EE.=E7,=
i:
;
S
=
t-
-
i-
5
!=
-<?=
4
;E
1
=
.
c
H
l
*
e
c
x
E
;E ae
>
F
!
?
==
i1_
=
=
?
.1
i:-5:
1E
"!. :
,
=!t
="ri
!=E
-t=
j
-c
.c
=
l-1
1
!
;L-
:
==
7
J=
:s*3
:=
'-3
6
; 'E=:
;Z
7
rgPV
:=
*
^
E
E
: r=€ i =
?
;E
!€5-gE
;
iE
4rE"3
,6E
1,EE
:
.v=2
4
q
=
g
rtE
,nEE
z
E
-*E
EE
I
I
I
I
I
I
I
I
I
I
I
I
ItL(cFqFts7OF
i
-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 40/304
-J
i 1 ]-.s
.
:
t""
li+
:
I
I
"
l= id;-l
l=" r
t ti
=c * a'i
l*
,
_
I
i
I1
:hg
* - o o co* c
i ."t{*
^
I+
F
! U <-c z. - o , : h . ; s o {€
' O
i =3 i : l I lc
fF: *
1
rI
:-{:+
r
i:
f
;=F
E
o-
1a
IeE
1i
:g:"3
:
l=r
9
F5
:l,L
3
-
'9
"5
?
r
i $-
r+
l==
1==
:r^:E3
F:
a; $= =
,1
: =
i;;;i *:e+
i
;?;
aE*5eE
i
i: =:=
;
:
+
_=7i=z
=
:::
;1
a;
;*;
ir
Y
=
:=
.rr i:t:Fi gE
Ft I I I i I I I f*.X
-h-s
:-F
&
!- : 5 c r
1 ==t_ f D e : 5 5 t
*t
9 !r.
-
TI
{
1
I
I
I
I
II
I
I
I
I
I
I
I
I
'"1s&gm
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 41/304
j-
o^
oF'3aU!I)1::
-o
-
.
€=
J
u
;
td
-!>
a
?
r
;
E
-s
?
i l
a -*
n.r*
-1
T
t
:r=j--3"E
a
=
,
' ':=3=
;
t
u
Sj
ts
EE
T
=o?TE
ri-
F
L
:,g3
; \?
is?
f-T..€
r
=E;E
I
I T
Fa
ilt.c
a,
t
=
>a
=
=
*a
;=
a
2
=
-
1
9
=
-
!
=
-
c
=
i=
;:
1
>
=
Y"=
=Y"
.=a
)
*
9F
-
,
!
s
sr g
S
q3
=
.
>
:
c
-
i
.
.
5*
=
':!
i
-
=
=
=
'
:
a
!."
;
.S
-
-5
<
3-=,
:
:F+
2=
I€
Y
r
I
I
I
I
I
I
r
I
II
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 42/304
i.- i I t I t i
:f r-rL
*
!":
I l- I
" l |
;"1
|
i
i
'
5
I g
!
c
:
Si
i
-! '; t-
o*
Ei) ;g -
o|l
d
.J
i- l
-
\d
I
P
l
-aJ
N-
-
l-
-
l
l=
:
,a4'
r3
-
-
F
r
A
/-
-
-
s '
-
tr-
..-t
aa s
lr h
4
t
t
i
'
t rn
ea
slc
o
! Il i - c U iJ ir a
! l( l-
'
l
i
:
? a
1i
I ta s =
i)
D
L
e
lt t
r
IJ O 3 l c 1
'
a --
I a oZ : ( -:A
> s1 lr
l
i-
1
-
z / , n a Z ; c o a
I
I
I
I
I
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 43/304
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 44/304
@6
$J
i>
-gH
: E F z- - a - - a , c z o @\
I
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 45/304
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 46/304
t \o:
{==
f
*e
r
I
l
i
F
{*
l
-
J
t
:"
{+
I
{*
v
;J
*lo
x
I
:
I-
o*
rJ l 1 l { t t 1
- z: .1 2 - 4 - ( 2 ; oo az6 Ca- a
i
t
-
l_
x \
IT
TT
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 47/304
*dlF
oo'nF
*1ls
r+tiniF
*L
-o
|
\
ar6j
.d
*e
€
E
lo
=
l
a
+8
l
.d
L
q
\
o-
6
?F
,*C
-1
S
I
l
'=
-{
-C
1
\
a
.
s-
:
.H
r
c
i
x
re:
€
8
r<.
I
Fo
:3
',gF
<
H
r
e
.Y
F
.>
*x
+
€
5q
!
ga
!C$
9i\}i<
*o^
+r
e+-
?
J
F
t+F
*l
-1lF
-€t
ts'-FgN
az'?
,9
t
>
G
.Da E
v
:
'e
d
F
3
P
U
,,
s
[q
€
s
I
,at
'
I
*=
+
,
to
I
l
:FP
U.F
i6F
lF
*
l
IF
d
>
.
.+
q
=e
+
ia
ra
iS
c
L
i
.s
f
€
i
t
,-
+
!3
T
'.*r
;
,F
l
6
'sN
\T+
S
ls
t
'u
1Hc
s
t
O
{$:-_-rLrF-:r.l$1,*-
F*,-Js-
1*€\*qI
*-
Y'k.:Y*qt
Fqt
ersF\
f *a
i
r
$FC3tF
*s
o-i6
I
I
I
I
I
I
I
I
I
I
I
I
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 48/304
uN!2F tFc5F
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 49/304
h:.F,Pd-
sO:
5
NA,c
(s
a^n
i
*
>h*
.
v
!
-E
!p
:Oa
O
I
\s
o,cI
R?N
>
':>t
c
a
a
caNr
h
\a1
.*
'
r€(a=..
!
;>d
dH'e:AE
d
ca
-
q
:
rA
t-i
$lo-{-
*i
*-
--
\--\-*
*-
I
*-s-
-?
I
I
I
r
T
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 50/304
o7IF;IFosF
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 51/304
la
;i-I
v\
€r\qi
€*
.--
QS
I
-itv'9*
rf
\iL
-I
sN!-<N
)YN
:i*#
E
L*s-o3
4o
;rg;r=E
;E €E
:?E
E E
E
EEe f
;cEs€EE
E EE EI
:i{eEE
ZEE
$E
?E
';?! E
gE
E
:EE:E
Ia*a;
AEE :E
;
z?E,
EF Er
i
E
E3E;3
F
Ea
t ?s
3E
aLit
-
i
tI
'cvt*H
O3:hri+rX:N
T=a
-od@^h\=o
P\Ho
H-)<
'ai-
C
EO-
c
a-
n-H
e
7t
=cE
t:
t
'S*
Pa
rO
Jn
!
tu
-n
9
E=
Er
Ix
-r
-1c
"
,X
a
a5
=
.=
L
F
I9n
-
o
Fa
':1-
c
tJ
i:
s
"o
.7
c
-
o
?
*"
4
-E-cc
'aL
:
$,
E
)
:q
=
Y
Z
O@
dIIrNr$
q++
6
Jl^-
I
q
|
+
,
I
|
\
i
\
g*\i*
\o
I
I
I
I
I
I
r
IT
I
I
I
I
IT
{ a oc 4 cc : a { oc aq x I zo do x ?
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 52/304
=
r=2
=
^
=
i
:
=
i!q
!.+
.
F
-^
.
<
=
PD
E
"q;
s3
3?+
?F
F
I
I
p
-S
-
c
=
i
!
J
cN
4
t
5
55^
; -
3
r
.
o
+
lE
:
=
=4
ic=
=
E
7=
2F-=
a
-
?)
*
-
A<
-
=
z
7-
1
o:
c
5
-,:=
?
=
i_
c==K
-
=
=
=
"=
=
d=
?
E
=
-=
=
'"E
=
iz=
=
=
43-;
i
-
-
=
9
=
:
-
-
n
2
:?E
=
=
-
=
:
-
'
:
\
=
=
-
-
i
*
S
:T
.-=
:__
.
_=
c
=
-
-
b
=
;=:{E
\
e
;
-
-
.
G
a
E
=
=
a =
?=
=
=
a
:
!1
(J
^
==az=
7
=
,
G
"4
2
N
a
;
=
=
=
,=
=
-
Ic
!
t
*-
i=
o
4
=
!
-
-<
:
!1
-a
A
7
:
*
)Ga
r
:
:
-
-^
-
=
:
r
"
5
=
a
-
:v
+
=
a
<
E=
r
4
=
FG EI+
-n. *
aG
.=sx
/
-
:
tc:*
.
i
J
:
a
-
a
!n
'
-
-
:s
-
'=
l
-
: = -a - \
.=o
Xs
"eF
6 =
i-
o
o
-o
-=
:
a
+
o
6
sa a da
(Ds{+
-=
"F3
F
a
r
X
.
4
X
/
P4
'H
,
a
a
r
i 5
.*
;
1^
'
o
)1
ruN
|F
p
!oc
F
\- "E
NHa
':
:a
;
F
+
Ir
t
i
!
'
\
uo
H
l$
;E
F
L
!
:o
3
Ra
5!o o O * e x=
+
-
+
i-
<
I4
r
i
l
s
q
i-
)
S
-i
\
1
=
l
\
-F+ t
'\
-F
<
= \
I rs I +
+l*
N
rs
-@3
?a
4u
Y
_5
6
F
,2E'tc
G
!
- *
-
E
3
4
1
-+4
=
;
a
N i
c
; = AO :
i=
- t
.*
T
l:r:_:_--
l=
==
-.
=
:r
-ltT-T-
l-ooe{4N-
I
lc
ue
cc?e
-
|E
l-
T
*-T
I-
=
l"
---*-1r
l*
-
T
---
l*:E::::t
:
IT
I
I
I
I
r
I
IT
r
I
I
I
I
'?XFUFiFFI
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 53/304
"Fl
*
";l"
*q
dsi
_iF
{^i-F
Nstt
-"
F
F
ct
.+
F
i
.
-
id
Q*F-
F
IF6
-*q
5cX
i
=
:
-
E
lo'$
*
H
r
a
\€.{
i
Hf
\rYO
r
H
l
lr
}€
k
c
6
c?
b
1FE
c
9
=*
f
*1
T
:
i\
Y
+
:
-
-
|
-
^
-
F
;
S
&rY
rHt
G<
T
S
\
--
\Nc
.1
N
:
b
:
N€+
+
!
\
'
I
t
s+b
;
l*-+
h
^M
.LT.+N*J
-si
-
I
.Nro
6
-1Hr
*
6
.
*I#
=
.S
.rO
E
4
-1
-1_
d
+-^
5
*
"
t
R€io\k
=
e
g
3
n
e
t
\s
;€
"
LB
I
's
r
-_
X
5
lg
.
o
"+d
5
s*
,
t
lsd
3HE
B
E
s
i
=
3
F
?
'E
P
F-)
s
-
Ld?
T
S
g
i
E
E
:r
Y
'(oE;
E
i rE
E
j
tg
E
3
s
a
=
i
o I
1
. 5
e
.-
g
|
t
a
3E
E
c
-
-
n
,
,S
T
'
cF
o
r
J
IT
-5=
'1
9T
3.€
F
:J
|:9
.E5
tr
6D
ng*
*;
r,
A
=r
E
,5Ir
K
u"l3
F€
BuE
'5
+
*
;\
FT
i -_-1
-
?
E=
o
3
3
":
*
>
E
R+
l\a
-
E
1 =*
2
'\3
E;"
g
eLv+
s
: -=
g
=E-E
q
.
,
d
'E
=
=^
,
-o
!
E
\cr
En
E
o
+
H
EJ
€
E5
!
E
t
*
a
!3
c
"
A
FEH*
aE
a
E
;
^
EEi u
s
+
E*
*
saEE
o
3
-E
i
€
KEsE
j
eg
3
&
E
eFE
s
'E
€
\I
tF
tr
I
I
r
IT
I
I
IT
I
I
I
IT
T
: q o ao ,J o I c H, C : x - z a o , X {I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 54/304
E +
fiq l. *
1
'NI ,-P
6. 3
T
<
@l-
'
++IN l
:
t
t
t-
=
F*+
F
t*=
i- "
{t t l-*t tB l* I I-
*=l( I +
\
N
s
inF :**E3as
d B
T
i1
=
,".r
\
r
- --
ti 5=
1
l:
-*.*
- Y
!
=
i
.TX
l__
__
_
__
i:E
C
:oa;
-
i
*_
|-
.e
,_
-
:
tr
i=!!
:LA:ax
:€s:
*
--
I
:
=
;==
l:x
I
N :
"
';::t"-
=
,
:
rsi-1-
n "
=
3
Ij
r
r
t-*1
c1r
I
:U e5s
-cA
5
r
I
r
r*
:f
E "I;;U=
- ;
i.=
FF
coNi____
t=
I
s : F
i
lr---11*.-
F
r_
rt_
l
t
lrHgr$e
15
')o
lrse
le
I-
-
-
--
t-
l-
;=.*-**1I
r
l5
-
r-T-T
-*
lL
)*rr-
I
lttr
t
-
Tltt
y
e<*p-
I
I
I
r
&cG
o#+
I
|-
ilc
?$a
lcc
JO
ir
t\{
q
r
rI
I
IT
r
I
I
I
I
I
I
IxF(JzFxFFOFrsI
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 55/304
tL
o
o.6
o
dx
9
q
e
6i
,
F
N
.*5,N
t
P,2.b|
b
F
l
5"
"D
d
cra
=
-
-r
.=
,
-
E
t
q
5
':
I
i
=
E
3
:q
g
E
I
:
:
E
-
*rrsr,
lRL
oE
r
Jt=
L
-
j
J
t
=
f
A
,11
i
l
o
-
l{
r
-
.Lr
l:-
i
E
r
F
l*
:
sT
f
__
9
:!1
.
l s
"?
-
?
.J
+
r
t
d
;
={
i -1
--
a
',
\
.t*
-?
;
|
-*
;
N-
i.r
:.R
\
T
'!
Hv
r+
T
oF
!
Y
*1t
\
lr
R
t
*h
T
\
Yr
\s__
L
\s--
E-T+
\+
T
*
-b
\
-I
h:+
a
_
S
ar
€o
:1
:
=
E
r
;
E
4*
i
*
ro
"H
-nH
rc
:
;
i
,
E
{
" -.s
€ \
>
r
H
c
i
+
i
.
Pq
.
^
-
9
'
-
.os6
*3
*
4
l
l
'
.
.C
6
q
-1
|_
'
I
u
dTo
?3:
E
x
F
t
l-
-
"tT
::
\*
-3
c
-
:J
r
s
;s
.
':
d
*
E
6
"+
l
.
es>-+S
iEb
ef€\5
tE
-\+$
l6-9
=*)
-td
-+n6J
va!x-vt
I
E
!a*
a.
"s
DO
ot
p
Jd
N
I5
I
I
I
-
IT
I
I
IT
Ilr
I
IT
4 -J o ac q co " c I z- c d s x c 7 J =a - X =
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 56/304
E
,- ihEt
E
l
I
i
i=
l
e
|
|>
f
'
i.Hln
F
*
lNlE-
=
*1
I
|
:
to
:
\
au
i
.a
=*
s
t
;
t
s
..
r.
i
I
c
=*
a
:
j
*
i
|
<
t,*i
;
q
lr
-?
-
-
I
+P
-
I_:
!
I
r
I
-
.
tu
-
l
i-
u
u
,
:+1E
rN I*
J
=
I
1
-
:
X
,
=-;=
q
-
-*
i
-
:
:
i*
\
!-
i<
-
{ -*
+
'
l.
S
-
l
-5
i
l9
:
i-v!" i +++G\
a d
- ; g . La .- O
fs .
F
us
',.? !
r
ta
\
=Y
;
l:
*
-l >
l
^b
c
-
:A
F
T€-o
;
rc
lz
i X;
*+
ol->
=
1
1
=
=
,
r
rF
:-
l
'-*
3l
I
l
!
t
:
:*a
+
i
i"
-5
A
==
lwo
=
*
t
q t
r
ia
:=l=
[":
r
"
:r_p
:_+__
i.
;F:.lF:l::,-
i
;!
et{
,=l.==- =
:
1"
is
-r-;
n
#l;5=
-t#-
Ia
*l:
=
r*-" =
;a =
l- -L_
i
{
+
i
rJ
,-
-+a
r__-t< l**
*
l+
G
I*
t
t T1
*
l-**
*
R\
r
r
I
I
I
I
J
I
I
r
IT
I
I
-IIi
Z\lr
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 57/304
:c5+
X;g
er
zE
+"a=
r
y
;E:E
a
?E:=
;
l!
i;z=E
7E
;1-
i
5
3
=Ez
Y
-
-==
!
"c
tc
,:zr=
=EE
ri.
j,
;
{:ize
. t;
*"
3
;;l::=:s
i;€=!
: r1
:
Z=
==E=
; 5;
i-* i.
;#
;:
r -
6 -j
;=?
;
::r
5:
--1
;:;
;a
;
;r=;
*
;;:rr*
s ::E5
;
i=1-
r=E=
:
i:;
g
;
ir=
::€E
: ;=
E
i
*E
;E
=s5
3*-8
€S
!
:-
i :€z=;-.I
I=
i;e
:2
E
7Z
:E
i5:rE
;E;*E;+
5a
H
:
zz!:Z-:;
Zz
:5
z
eE
z
I=E i;z
zz;?
:
=
F::
:
2
t-Z
gz,Z
1i=:
ZZE
t
i
:T
a1,=
;
;
;
!7r =
FZz .
= EEzvZ2Z
i ;Z
i
EZ
E
? E=
;;
:
I
I
I
IT
I
I
T
I
I
I
I
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 58/304
F(:Fts
FFJFuIT
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 59/304
5
:E
!
€
iP
=a*
E
gg
EE
:>,r
5sT
i
d
;
."
:
;
q
3
5
c
'1E
r
r[T
t*;a
;t>
?
=ES
.:
.T
'f
lr \
-'
*
F
;q-
.J
€u
S
S
.*
F
<d
\1\
?
rs
'+=
?"=q.o
l3_
_
.5
l , "
l '
<
h>
j:
:
E
\_T
i
-L
.
r
|
,>
E
!
S
j--+E
S
h
;
'1
rr
r.
asap
sF
Eseqaq
*
*
E<
Z
Z
A
F
S
c F
:ss
(
\
-$
a^aNv
z;<
!
oo
S3E
F
H
>
a
:=
o
6
s
;k
s
aF
a
a!O!d"5;
-
-=-
-
z=
4
=-
,o
-
|.
-g
hD
:=
=
z
dC
!
6
|E=
e
l
a
-hN
AE=
F
i
l
.
"2
c
lJ9tEhnoiT
*
i
t
r
-1
c
a
l{'t
J
t^
fn
r
!
.u
'.-)
f+
;
{
-d i-T
lr
?
^
f*
T
-"
=
'-
ta,Y
r
\
b
:S
T
;
\+
. t
(o
4
&
L
t
qT
.a\q
HJz
'Boc*sie
I
r
r
IT
T
I
I
I
I
IT
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 60/304
eFFU-tI
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 61/304
,s_
-qF
*
+
i.E
.
-J
i
L
S-
3
I?
i *-"-
,5T
=
=
;-
I
_
. I
:=E,rrs-
r_
I
€
>
3
$+-#
_s.=
."
S
-
^1 T
J
*s
-
,-
it
,
:- jr
oc
g
=
j.Er.
b-+s"s":-3+
:
3*\
+
;
i;
:
"+
.
r
. :
|
:
,rNd
';"
;s
-
|
Y
f
=
i
+_
j.
=i .
J
,ts===
t-
*a
_T1
=
i
-
=
-^._=-,
f
. S
i
,s.
*_
>>
E
?.-9
-
.r
-
,,
1
E
-
=
)!r-
=
+
n
fS
i :*
g
Ji - -
+
p
>
:SA
5
r
;
i
:Ev;J 91
t
E
I
d
;37
3
.-
.-
-
-.
a
s
+i
F
ic
:
ia
HE
:
5
:
iE
i-
c
!u
to
@
e*F*
IT
r
;r
I
,
r
f
In
IT
I
,J a o a a b . d a U - z tn
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 62/304
= s -tJ
Cr
:zk L !
I
f IN t iA l -
r
c
l t9
'o
OH F==5F
a
z
.gf*
r:-
{
r
t
*
\
,
L
i
:v
b
M
T
"
!
rh
I
I
.^a
s*Ea
.1
+
! \5str
!A ;
"
3
r,
-
r
f:
s
f
:
f
;
-Y"*tP)
aS
lE
*H
\?
*1
l.-
i E
*fL
|'
r
r<
_
I
i
l
*
x
.
_
;
r<
dr
q
u
'+
? t I < = I h F
?bRa
--
fA Ita
*_
I
'
F a l
3
FR t
s
t1
11
I i
g l"
.\
!n
€ ir
I
- C
.
I
ro
r I
lo{
o
t
l
ls
i
+
r
4
t
qo i
-
*
pg
**
i{
:
=
c
-=:c i<
E
"-d
e
ir9
j
=
-
=
5
Y
lq
tc
a
+
\
L
l
E-2
\
!
'x
^
a
|
'
|
'
\>
lr
I
i"
-
c
7
,
iq
r
=
I
-
l
I
F
+
irLE
t
io
7
=
J
'
e
N
+
'
-o
H
*A-*
\
*A
5
d
$
+L-
-.
-
|
.1
l
.
ITT
T
I--
rT
*FF?)FcnC
lr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 63/304
=Fr
P
r
da
l
.
*
;oc
^
l
H-
n
IF-:
iH
+c)
-F
H
I
l
:
,
'r
sn'::<€$
\/?*ro
$
IJTr*
s
f
II
I
r
IT
I
r
rr
lr
I1
I
H - o , a - -a
'
c 3 { j a - { {I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 64/304
n &
Y
r
td
*c
i
- C
S-
)
yS
=
:s :"1I
,
'3
t .AJ
cRI
t
'
l
H
a ; |<a
*
c i
*1s
a {
! +I I I t l- J*H
7
'a
v
r /
a
r
\
r
\T\
s
9
J
I
rI
I
I
I
rI
r
r
I
lrI
6
:E:q
FFFh(
n
II
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 65/304
-
S
+
l
ls
>
UrdNt<
I
l
i
-
'-
1
^
lrr
-
:
:
rI
i
.,
1
lutr
J=5
>
*rr
lu-,
t
l
Q
-ots
r6
lr1
3
rd
ir
.€*
6
c
c
':
l EM
-
'c
v
!
,?
+
l-
--"
4
-
aY
lH=€
-c
.q
OrE
Nm
FiE
6
.d
nH
A
=
*
Hl:
Y
F
lS
;*c
6+
aeLFJ
-J
z
i
=>
t
^>
-
|
9=
f
l
l
-
i3
=
r
q
l{
l
c
c
s
)
i.
,
i
a
:
$
i
i
i1
=a
u
._
=
;
:_
L
G^
:
-
I
ra
*
l
*
J
:
d
'
i-
I
=ia
-
s-
-
:
S
,r
i,-
r-
6
l
x
d
-
q
-
t
'
r
I
t
'v
cSrE?
ia
r
,1{L
lJ
l
s
E
*E
s
I
\y
T
\v
r\
S
\
€a
(S
I
IT
r
Ir
r
r
t I a o7 { c a
s = H ;^ b E - t f [
1
o o o t z I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 66/304
AQ =3 8
N
-
L
=
b
=
i Y
"g
:> i?':- l
44
--s?F;.Yi
u lhr
I
l
+
;=!+.
-
re_
:"
; l
Bm !e
*
*\
\
o
H
\HcUI I I
;- f
s
t-E
.*ed
o
*
=
-
i.o*
q
i*
r
T
I
I
r
I
I
I
I
I
I
IT
I
FzFFF
.=-rJl".a-:=J^
cJFo
?
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 67/304
F
.
i€
;
!
F
fao:o
'-E
;
I
{
i
-
I
.
t
t
.
ts
=
*
-_
aE
l
J,n
;-
\:"F
d
t
i E
i
i;$ .rEf=
nrl=
jt*
.A-;
o
3a
;g
?
fe
T
s
s
s
r?
s?
.
-
I
I?:
;J:
i
S
,"1
s*--eAce
"\,?e
2T
+
?I,
*J
t
;g
Lg
i?
^=
H1
-
r
.S
E:T
-
n
i s
b
.r
i-
F
.=
l S
-*
?
:-
fz
e
ir
{H
.rnA?
'1l.e
<h
"
1=?
s TE
f.
Sx=
1
EE
=
E
F
E
!>
':N
P
L
*
g=
a
=!I
F
F
L
\JFU
u
N
d?
\
Ir
I
I
I
I
IT
n
I
I
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 68/304
tF
l'-
=ra*75."e
\s *a
3
rh
\id\=\3^
^8
FU
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 69/304
€kC
J
l
l
;l
rH
.
'
\
->
\Y
-J^
6
-
r
I
. F<
+
'*c>
=!
I
E
I
.
lO
I
'
^
-9
J
ltnssn
v
\*
s{
\
\h
I
Fq
*
tw
I
i-
;
.
:
tn
o=
t
:
a5o
=
,
-
v
/4
d
=
2
=a=
t
;
Y
o
o
.=
u
,=
?
.;
E
.c
"
€
a
1
U
^
=
@-
n
:
._
ra
o
\
r
=
=
=
<
';5
';
:-#=
lt
-a=
=
=
r=a
c
:b
-"
-
'-
-
!
-
-JE
9
=
I
e
;
.
?
8?
==
.
:eJ
--
=
=::TE
=
-
=
-
=
,=
>
-4
J
-V
'-=
-.J
-
!
=
-
I
a
?
e
,=
a
Y
t
'-
-
:=
17
i=
.==_e
L
:
1
;
A
=
!
j
7
a
=
t
-
i;;-:
;=*
.,*
t.*;
-
i.=
E
:-:
=ra
<
=Eo
C
'-
-==
(
=_
-L=
.c
-
,p
=
-c
Y
!*
:
r
x
=L<
.=
J=
+
F
!
i
r
@;
q
-
-
-
f
'
-
:c
_
i,
-c
a
6
t
';=:
u
s?
F
vQ
\
r
r+
It?€
I
r+
q
-
t
l*f^?ilF_
\\
t
+
\b-1__
?"
\q
\
i
\=
ro
+
+\_'
.*
3
eP
-r
L.
'
'1
>S
c0
1
.;c
&
.-
F
€
m
r
?
J
+
\
i-l
I
r=
i
'ol
=*N
'
iJ
;7
:
'{
,ai<
.
E
r.
r
.
A
tS
tul=
*
a"e:
l **
*1
H
IE
s
l.a
?;
.Ii
a
I
#
irm
ia
\X\:;c!L
N
{
r
I
-
r
l
l*c
!1
<
f)*
(
-
\L
I
I
I
I
I
I
r
IT
I
T
I
I
l+ ia >- o ocz { C o{ ca - I a .J dr z q
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 70/304
c a s
!7 i
.N
I
I"cL
-
l-+|J
-
:-1-
JL*_ s i=
-
I Js
-
-
-o
:
*ld
a
"F + I ls +j t I
rI
Is
I
I
I
r
r
I
I
I
I
NJaJ{_
FFFi-UiFI
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 71/304
N
=
]-E*
+I"
:
i,,=
3
-
c
TTE
iz
,
: ti;
I
i=
r==S
f+
=T.>=
7
I
II
I
r
I
I
J
I
I
r
I
I
q I o cz a b
J =1 .u ( I t | p
o c . ? q
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 72/304
1 = E
* l : ; I I - I 4 i I I I t
1
*b
ir il r ? rTt .
s:9 Rl* IR \1s* I
-
'
s
;-<
, I t i
E l IA rr
3
R6s
-
1
u
I t : 1 ',1
a
! t lc
*
c
-
v q r
.
|
-
;s-
6_>
\-
Ir
rL
I I
!
t
l:-
r
I
I
I
r
I
r
I
r
HFtsO,q?!Irt1lFllr
-i.51
tltiIri-i
.xvE
F
.
!
-r
t
I
F9 {L
"
-
<
--
F
i
l1lrclTlY
l€lcliTli-Iinij-s
l{i-lzI
:-I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 73/304
T\
-\\
n
,+
fal
III
--1
l*Jl<)I'f
:-
tItl"-tL
L
F{{€i
*1
;=c
-
s-Jo ,*g=
i -"
,l-s^r
K
I
I
F
ra
:
l1
.=
!L
-a:
,
-r
*
:
';
-
+A
-r
rr
id
*
S
+r
.qD
=-t
:
.
t
';ro
-
3
o
"
-l.
a
-
G
-
'"
I
'Y
l>
-
t?
I
1r+
x
^1
_.=
2
!1__
aa
s,r+\
P
-
t5
tPY6
a
i
[
F
S
: .
':ez
iE
r,
I
-':l._l'E;=
rI
I
I
I
-
I
I
T
I
I
I
|} td o oo q on - o - Jo a F z {: sc : : : *n E = ;
I
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 74/304
iFs
: i i; iEi
;i
,E;
E=
= s
i
lx
/
"
"<F
s
F
b
f"+
-
/
,
qS
$
E
*
re
E
-e=
E
S=E
M
!
b
::==5s
i
:-
*
:
l
6
i
c
l
i
I
C
=
G
-?
s
=
-
f
!
r
:rS
l-?
,
r -e
s
l 5 a
=*La
!a
-
J,
-=
:
:
-
"!?
!S'
i =1
;
f
rse
l ; -
ir-Fl r
r
ar5:
I.=
=E
IL
Fo
I-F
l--==
-r=c
,s
.
v
i;'r
';
J3
lsa
-F
L
,1
L
.
i
l
1
-
c
:
-
U
S
<
q =€N
a=.=Nb
F
q
'a s
&
a:
I ls
rI
I
r
I
rI
r
I
I
rI
.-
r<"
f'1c
C,ol-
-N+
:FlN
c qFfOFUr
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 75/304
n=
R
aT.e
z
at
-
q
--r
..i
!
i.*
.e
dA
c
m
ni
--I
-+I?
*g
ic
iH
<5c
9-z
:
"=
:
a
x
*- -u;
E "EI
f
,cb
L
3+
l,
-=r_r;B
{
E^
*_o
i djS
*1
?
TtEq*-
i
-
,=:_ -
=:
.r
*
=_s
=-
=
.=
^
-
Lc
5
+
<
l- 't'ZZ
t-
N
i-
#
\-
1*
I
rI
I
I
I
T
I
I
I
I
I
I
iGloI
q o n q o- r o
r
-
i- i .o + s r 1
**
o - J a - 'C
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 76/304
r
F
Fr1 l
{
iE; lt"d
-
o =
o @
r
"*
4
+
i-
P
I
i-
F
iH
I
I
I
I
I
T
I
I
I
I
r
!=v
-ixo
d'-.
"
\
{
-
-J
-
r
'
>
i-i,7;
-
iq
.
,c_
'-
N>PL
cFpUFI
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 77/304
qS
eE
q!E3s
!c=
.c
-
=
=
-=
r=EF
a&
+E
bq
'5
r
l;*
b8
=
8
i=EE:
tj FE
;=*s
E;5
i;?
:E
€;
::E;
:r4E
a
-
.-
o
o
^
'e
A
;
;=F
+
;U
j
3
V
_
;EqE-5
i,
==
:
A=
Er
i=
a+:1+
l rq-€-Bs
*
I"
:=
-E
"
==i :
ot
EEB3E
-i
€I
!1
=:
i =s3 I
€:
Ei e
€1E
E
i
;
:
*=
=-Ea
=E
r=g
Ei
E
;
:Etr:s1sE
E
i €
spEe
JEE
=1
.=*E
gs
sE
4
;
;gt
E
As
zE
rtn+
I
+H
"
qr
F
N
_
r
l
T
l
,
i
ir
'-
l
-
^
a"s'
=
l
','
+
a
-
-$
\
:i
i
*
I
"ga
p2
'T
-
i4o
J
**
o'r
F
IJH
-=
I
I
I
r
I
I
I
I
I
€ c a j Cc --
i; if iF s + E=
Cc4 c 2
_6 1=
31 =t =
;1a
€I
r3
$
s
-
i+ 3
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 78/304
+
*g
;;.r:rg;E
,zv=
;3;;$
F
a
ai;*;E3
;E
;**a
.*5q3?
?
;ra
F*
*r1
ls
i "1 X
+*€g rg
c1t1 ' ;
*:3:i*+i =z
if
I
;=
u
;;
s3 i Ei 'l;,g
E
iE+
i,- ;1g
is 'E
1af
F€€r
; ;
i Fi :
E
i =
"gi ?+
+
r
?=
".r : !
i=
=
==:_
:=
E-,=
-
i=
;:i;t
zA
=
rI.
-a?
*J
o=D3
iT
2
=z
z 4+
:
=
-=r7
-1
*==
==
=,ZZ1Z
7
=
3 i =-
-a
E+77
T3
=
.;
:=
'E
-
'-==
-a5?
7*+
gIs
+
3;=
;15
1=
I*=!
i;;a
' ,*11s
-
-X
:-
2??=
=E
=q
gE
aasaF
5
?E
a3!L
;Z;*=n
3
"3
-
=gF
C
P
P= a
E?
1
a:E
=
F*
;i d
L
rZ?=
=
-7
i :
- Itz 1
i
;l!f
{ i I i
IFE
$
e;+E:r$i*
a
1
{l:
?:+
:
i: i3
1
3;
E
e
+;? it:l
rI
I
r
I
I
I
I
I
I
I
iJL:F t-r
FI
F?F
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 79/304
\$
3
i
:; !
#f:
Eg iE
1
E
1
z
;;+
E
,
eE*
XE
i;z?
;3
;
if i.+
;
:=3;E
: l1z€E
:1
:g
ra
=Ei=
f i
:
?E
E
z::
=Z;EE
+:;E
=
tft
"1ZA
?:*
E
;r
:l i ;ai i !Er;1
, :i i; :
:E ;
=F;
;t5E;FE
g
*
+
o.
V
-1
.1.
es
-
|"
c V
s\
r*$
e
<
?L
:rts=
d
S
.
!O'r!
,
lo)=
c
er
F
.
v
5
c
r
>:
a
-_
+
!9
-
!
=:
F
!
>
o
=
E*
ra
+
':=
s
7Y
+Oi)
tre
-
\V'd
=
lrqlv
,,
I
I
I
I
I
I
I
I
I
I
I
l* lg l* I I
+a.7
c =
a
-
.J q o o q o* o
- 1ts 1
co+ - o -
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 80/304
l1
3
3*
f
l- \d
t$
f$o
I F : I.
i t
t
; ;
:v { &Ta,
"
|I r
I9 N -vF
ic .-a q t
t9
3o
"
9
'
i
+&lr:
i
.--
'
r
E
FCJ
i
r
v|
.
tx
tLt
ftf
+
ttT v
-.q
, ! i i4 tel
:N
r!
I
-<4
+
^
'
-
iE
I
I
I
I
I
I
I
I
I
I
I
!FFFFc
Ija
-
-
Y
q
I
N
v
dY
r9i
>-
.=E
C
e
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 81/304
{
-+
+
*+1
T
1
t
€F
I
i
l
t;"
s
\+
d
iTs#
r
h
.S
//.$
/-+
**r\
-1aE
t
)6co6s
+
:=U
t
hm
rm
r*
z
=
e
sF
oH
F
r
i
l>
t>
i>
.7
i I
I
I+
P-
i
r
'r
l
l
x
i
F
=
=
r
I
i;
'1
,
de
^-
ia
=
.
-
o
<
-E
l l l l
.*
d
iJ
a
a
f
.c?
r
=
2
d
S
^
-
A
:
'
:<
'
t
(go
-
-
I
jN
r
c
i
j
,;'.--
^+
o
oi
i
=
i
'G
.^d
o
-
*
|
l
_
g
S
='a:d
t?:
-.;
>
o
F
?
t
q=H
-
I
\
:q
+
:J+
+
c4
oC
t
bsg
*3
,]??T
iT
i 11_
6
N
J
L
^n
Ea
d{*d
=
.a
" 4
t$k€i:
a
F
o
c
*
.?
To
t?
.
-J
--
l-
!
r
tI!
>
::5
;
A
1
:
q
* *a
l\*l
o
l
r
i-
r
"
l
ae
I
,*-cF
I
.eE
r$
-
-
c
c
:3
N
?
.
_+
o
a
;oT
_=
=
|
IT
|
|
i
rl
€
TT
d
c__
ca
*
I
<Ktv
|
I
I
I
I
I
I
I
I
I
I
I
I
H a o + N
'g
o
, . . ^I
^ lI
i
o c z - o -c i cnaC i ac !
F i !
4 F\E
L
1 / iY \Y
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 82/304
c =
=
r
R
i
aDi
'
i
-<
ir"
!q
+
:
r*!
'
:
.
cs=
i
-Fry
tJ
-
i
l
. g
.1re
'\"
a
F= ! o n NG cT 1 I
t
ig
E
.F
=
ta
F
i
.1
:J
.
:1
:
T
i\
i
q
r
.,c
l,r1
F
'rN
I
l-L
1J
a
,
,-
u
L
N
,"
a
<
N
:
l
t
.
i=
rv
N +*
a
.
=:
q
:
i+E
r
f-rF
r
.+
F
FY=,+,
l
lrt
qLE
=
N;sc
;==
d
fF
Er=
ts
r
'
.
;
I
2
G
1
T
'
' r l
t
',
tF
I
c ,
J
r
.
=
I
I
I
I
I
I
I
I
I
I
I
I
JFJFF
'r
']u
:
l-
i
r"P
;c
e
#
gdNE
Z
-6N
.E;t
'EE.=
iC
Im
N
FliNot.dldr'
FUFI
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 83/304
N
.
=,>
FTr
4t
\
f c
,$H
d\oi q;*
I6<
aits
od|\
d
3E
a-
.T
=
g
sl
=Orcd
.*9
P
:
IoF'aE.4
i r-
)dOA,ats
sQ
P
-v
aS
'c
;
A
*
S
C
l
N
I
:=P
3Q
-1
e
l
A
d
3
r
o
A
e
q
H
c
r
5
o
l
Ia
I
,uN
.L-N
d
')
*$
l Q
"e
+p+
4.5
't
;
F
-=
H-1=
aaT
-a
l
\
'
i>9c
*
5
T
'O
i-N
bH
r^
4
$
:XH
,
s=
.oF
>
h
>
b
d
g
<
9
d
s€Fcg
ed*
=
o
,1
'*
'c
,
,
t
-
^
iF
lJ
i
_:
=:"
*1
=
-FS
!*
,o
?1^?.H
+
orUoc
' ' *1*
.
* cm
cd
d
--+++
l l
lr
l
l r
r
c6|o * *
i
r u
-d
i:
s$t,Fs5
19o
3e+_
i
1
|?eee
H
.T
,'os
il;q
E
6TL
?9
cr
,
m
E
?Ti{e
f,FF
H
l-
:
J
l r
KJg
;
Elg*s=3
-g 5
--5
cX 6
.?-K
KTI=
**3r . T
.-3.-;1 - :,"1
ss
'>
':
'h
5
I
+
r
j
||
- -
"
:>
a
l
r
tr
i t
a
c
E
:
:
:
F
*
=
T
I=
=
ac
E
tr
1
*j
_- =
1
;5
5
u
i
\<
I
I
I
I
I
I
I
I
I
I
I
I
l=t
= :1
4
:
sl
J
t
I
*
t Ja ac7 q co. E e i d c j a - i {I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 84/304
: : Na :
t
q
Q lrl
!
*1 iq R x
=
_
<
' ieAlr Ir+,Jcn&
t,
Y
Y
O -
-
-<
l
t9 I
I
I
I
I
I
I
I
I
I
I
I
tlF
F
l
l-1-
.
.9vs
$
ct
JFUF(
.s
lasrot
s
=lrY
?
1e
S
S 'c
o
x
=
_
n
-o
lrYLi i
iY"+J-
H*
ot(JDUF
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 85/304
@
:3
F
lc
1
ln
.>
H
+
9r
T
+
irt
r
T
^
|
1
'r
\c
\
-
,N*
e
';
<Z
3
:
t
*
-
Y
t
;
S
.{3 ;
I
i
-:
i
s
\
-tz
,
c
.
\
*
)
C
i
?
i+.
E
.
c
c
3
T=
\X
1
.=uI
j_
F
_
r+X
4 s
f
:=
,d=
cO
AO
-H
F
lc
5"<{
^
3
.*Y
I
-
rJ
,
e
q
.=
\"
E
q
-r
nc
aP
>
Ess
j rr
d
i ?h
*
F+
c
s
E
:q
.Nl6
s
a
<
Y\r'+ul
,
l
tqo-fJit
:
^
o
.
-1
l
s
s
L
f
?ld+a
lJ1
z
';
3
|
+
4
a.c
11*sY*"y
6+^t7
o
t
?!€
- -s
<-
c
sI
,e
?*-l
f
;onul
l
tj
t
!
I
I
I
I
I
I
I
I
I
I
I
I
-J { , o a { -{ b { oJ c " o I r -
\
{r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 86/304
H E E
Mir. =
I *-
N
F itF to
-CvN
i I -
4
V
M<I
l l
I
Jx
|
-
l
=
;r-a
f c
:*
!ciT i t irq I
I
I
r
I
rI
I
I
I
I
I
-Jr
56Fi[3l-F
trTik
t
'O
'L
O
.
h
-
rJbD
o
o
F
E
6aF
LNa9
)
c
O
i.HE
.5
P
:1
'sg
=NE
)&iE
,
*s
F
a
E
Qb
d
I
-=
-99
)Nv
,"*d
i F
s
gE
E
?7
E
d
V
.n
!l-OFF ztsdoFF
q6
h
C
L
"
G
T
cY@
'a
te
tT+
F
:Et*
.=;
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 87/304
'€'ae
G
'
&H
s€
a
€9_
<d
""(o+
F
q
ts5
Ii i
l
'g e,n
i
:;j
*BTT
S*d{
i €
o
|
-
5
11
[
l
.
To
.
r
n
ze koe
f
5
Z
Z
o
.
k
c=
-
H
.4
L
-
.4
L
-
-
X
-
!a
q
's
#
€
'
e
E
<
+
5
€
3
H
sr E
'-A
=
I
a
.
E
.1?
T
i
F
-I
I
o
+
:H?r rZ
-tr
I +
:f\' d
J
lL
6
q"
,r
:
{*
2
}
.e
E
E
R
Z
1
P
r r l z
i Z
,J
s
rr
a
4
!
=
!
9
l
g
l
"3
"
J$
3
d
€
=e
E
ezReee
1
c
*
V
q
O
1
a
E.l-
+
j*
L
6cE
t
'a
N!ofr>s=6
r
iI
'=
b
1
:=
1
S5Frr
rsF
!Fl-
r
Ir
;+
Ttrd
>FlN\
N
€
=
lo
:
lc
N
:
:rh
i6
h
; E
l
5
.
*
c:
YcN+F
t
tt
k
s
-3
q
P
lg
EL
e
c
tc
5R
FRsF
R
5
cd
K
<
rC-
-
.3
.
,
.
i<rt
.
?"r+
r
jrkf**
:JF
lf
F:r
s
: c
=
SFns
+
s6F
:+r
-TH
iLtLt_t
lt
l.E
*TT?r,P'e
^
.d
a
c
t
t
P
-J
e
:+E
eFS
|ss
E
trSFKRF
o
=
+
^q
(
(9
€
o
*Lrrc
FN
F F5
r++
+|+
:6
J
n
i
- ?
ts
'.
:
3
'*
'=
l
i T
" r
'r
t
*Jr
ee
{
iE LP
6C
!
I
I
I
I
I
I
I
I
I
I
I
{ q 'J o cz aa - =-co c a oc- - - z {Ca
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 88/304
U
\_ jh '/
o
lo
.cF
iqT-/
l
!7l, *1sN .S
J
q\l*
-J\
I
I
I
I
I
I
r
I
I
I
II
DF
,*
3)F
nE
i*=:
1
;in
i;in
=:?
f
€
CFOt
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 89/304
c
F,mig
l
i;
rt=
f
Ii+
.+fl[F
i
,
i
!c=E
y
t
d
t
€
O
_
.
4S
:1^
:
*
=
qH
o
d<
,1
\
*
t
>K3-
-
-
:-
t*n
3
s
Ne=
c
L
I
93
.
=-'4LA
36".
€
E
1ie 5
*E
E
E
;
E
=.F=
a
!i: +'
E=:f+i 7
7i )
1
;3E
2
Y
;:EEig
n
v
I
I
I
I
I
I
I
I
I
I
I
{ j 33Z - = " C C = ; z {I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 90/304
?t1 r-
-
-=n; T
=E
Zz
t
:
?
^
<i,
:
l
,
d
a
-
-
I
-
rJ
3
g
d
'
a
x
=
J
J
"
5
g
=?
=
=->)
r
-e
i
;t
c
-
-
-
:
; ;3=
r
I
J I
=
=
e=
a
'-
:
o*
:
'-X =
c
;a
N
^
r =
:5
- :
-=
*_
=
'
a
i
\ o i 6 G {
:
'7
'?
i lt l l
a
:7
i I \ :
0 @
I
I
I
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 91/304
o . q o acZ Cc =q -q Jac 4 2 g
o -c =
N
,3
=-
=
i
Y
E
:
-
\
t
-q
a
=G
c
f
:
t
4
=
c
\
'-
tJ
) .1
1
s
Y
.
l
=
N tc ta
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 92/304
=-e ,p .F;* c -
{
r
rr i
.
:
'r
'r
i
L=irC. f"
-
-
*
a
:
l4
:=
i
{
\
^
i
"
iri
*
!
i
i,L
i;s
f
itr1
=
:4
:J
!r<
\L
!h
'rqc=
=ts
J
=
'
t
k
t
oG
S*rO
lr
==
1
t
-
,
"
sv
3
:A
*s
-
3S
r
E
=
1C
s-
,=a
J
c
i^;
d
;/v,A
f l*FI
D
|cI
F
|1
|s
ts \tJ \F\
n
€
+
i
*=
r
c
-=
D r r- ! I
-aF-
"*
i1
l
-91
c
<.
\
4
:
t
-
-
irg ,
-
Nc
:
!
A l-
"
a -
'6
:
._'
'
.
_
:
.
'
'p
.>
\ q E
I
I
I
I
IT
I
I
I
I
I
I
I
0QF?
-4v
-?\
I
;"
^
_-
i"
:v<-
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 93/304
-*I
t
_
_
?
/,-
-
-
\-s
\\-+_
__
-+
-
"
=,*
*
s
F
tI
:I
6;
'g
.O
r4O
-
,
O
4
3
=
c
re
Z
=
i
-
t
=E
g'
v
c
H
r-
-
-
O
.=S
-gA
!
v
H
-
:=2,c
F1
O
f
.
_
J?I
-
.=
--
'L
*
,
'!1
E
-
L
:-
-
a
"=
=i;=
5
-t=
1
-
-
=
d
-
?
-N
:7
F
S=-
.L
o
+n
;
"N
E;P
*
i,.+
i.-q;
-:J
,
T
.=-
!;-=
,-N
=
;
r=t
rr
.s
;E+
E
=;
1
;
=Z ?*
;: -=
=i
E -sg:
sE?
-
t-r1
?
!
€
=E;
V
'
a
uL=r
:1 .=
Er
*=E;a
=Z
=
=
ik
=:
i,.*z=
.2
-
=
;
= !E==
E-€
t->
tk
^
!
6
6
.=:
!
H
>e
>v4
dO
.
.
'=d
-+
O6
-a-? :*
E
7
z
A?
a
*4
--
.=
"s
?
2
yc
=
O
=
!a
*
e
-=
a
a
=
I
-
:-
=
At
i
EO-
C
3
i*J
.J
a
,=
7E
O
q<=
r
Y
1
-
1
=
q
,8
E
-0
-
==-n
J
.=bDA_
id
ai ?=2"E
-y
'F.'
rya1
:
ti
-
r:
Y
t
!
€s
"=o
--VIJ
+
'ao
;
c
:
.=
-
l
3
=
t
i
v
J
?
!L
L
:
.
4
i
"
E-*
'
,
-
=7=
-
1=
=
iuz?
!=
ra
.-5=
tQ
-
'=
a
E3
:
-
r
i_
:
=
r
:
fG
-
u
=
c
'n
U
N
=
q?
'E
e
:
g
€.
;;
3
:1
:
!=
o
:
n-
!
-=
tN
!
'
-
q
+
J
.€
::?1a
i3
*
€
':.
E
3
1?
{
;S
':
.6l.z-
l.
:E:
i
C
:
={i =1
:q
=
a++=
tE
a
-=
E
.
f
=
iE
,
.=
=
-1
-E
=*€
i:1
=
i :y
-
a
;g:=a
=-=
'.a
:s
E
.?j*
Ps
-
;q
Ii
-:?
E
:
="
:3=
b 3=s,
.J
".
t
.
.^
:
?;
T
:
Ex
E* E
=i
n
*
F1
*3
.=1
EE€I
5
€s
E
,9
-F1
t
;1=rJ6
E
e;=
*?=E
5E
dgrE
E
:E
n
s+
4ztJ)UF3.AJr<FJz
I
I
r
I
lr
Ir
r
I
I
I
IE I,2 :a az i a c : i 7 z q E cc { - z *
|
:a& .^=
E
?Er€dF
+ ^
Xoa=
4
a&e
h
:
E
-3
go
a
4
-
z
-
"a
a
-2
:
ir
=
hG
t
9
4
9
f
, t
7
;=
.q4
== =1-
!a=
€
.
-= -a
-
-="
.*
.3
;
-
4f*
P
-
i
:Tt.-
X
4
*
tr2
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 94/304
=
E
T
*-=
3=
S5=
l?
+:==
-::
4 -e=*
; i! ? I
;
t1
i?= i
i i gu
11?
: if
i 1
;;1i
;+:
t+ 1
=
+
:-+aE
?
r=-
":*3
*
3
i-
-E
^
-
i
E
>
:1
=
r=
.
_
i
s
T
r5
?T
i
, : *
.
i
i =g=ry7"=r :F 7
J *5:-7Or= c I i =t "? J : =
a v l- g , i I
- ;q
i
i
=
=>
a
'=
--
rs
{
r
l=
!
l
=
:
=
!
=
=
.=
\H
iE
i. *ye
{Z.
{E
{
r
!
Et
-
a4
=5
"
:
"E
=
l r
s
a
,
\
a
=
=
lc
;
r
g ;
i.
=
:
6
:
n
r
a
s
@cP
*
l
o 3
E
l
E
a
=
c
vQ
N
F
c
.
2
Qc
\c
.
;-
=
=9
(H
*
j
*
3
H
te
€
U4
=
o
|5 +
Y
p"
S
'
*=
- = -
.=
5
*
!
C;6<
<
A
=
o
ts
l<
F
=J
E
F
t
:
a
ss
a
+
e^aHt-
i1
iF
;?
x
a*
+
1=
=
==
1
€
>*
*
'
S
=-
-
.*
'a::
'r
;r
, =;
4
r
-=
=
^
-4
|
s
-
;3-_
I
.^
-
a
t
a
i
4
P
=
l
-a
c
=
=
'
=
=;
,5E
-
:=
-
a r
N
s-I
=
FN*
-
g
s
'
c
E
;
a
, !=
-^ =a 4 :a
I
I
I
I
I
I
I
I
I
I
lI
azFJF!
-)d&
'"
F
ora"
is
's
d
eq
=4a
f
o
-v
d:YOI
6
L
-
'F
5
:!
E
C
q
(a
tE
i*UFFco
r
I
lr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 95/304
tl;
N
{
a
;
l--
c
\
c
c
4ctE
c
o
\='"
c
a
o
i
S*
s*
l=
u
:-
i
;ry
I-,!i{:1
-R-1
'
<
I
4__
_
I
I
I
I
I
II
lr
I
lr
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 96/304
*i
n.^\\
'+
N4
\c
a
\)
6
:1
+l0
JO(Jo
IT
TT
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 97/304
-/H'
r
i-1
it,
lJ
s
-J
-1Et1t -
-
t
rs
7i.r
!1
_
_nr*n
iIIo
'3g
t
i
7
fI1tYn
tNII
t#1
J
i
d
o i
LB
F
rN !* l*
- d o o F eo{ -
N + c d a
z r c { , oC { - c
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 98/304
SsCb
\
ls
I Y cQ 9 lr s
I " L c N
.
ir
CI G
+ tc
r
s
c
5
fN
F
6
o
C
CCF
RI IN
:6
q
e
ts
F
!
5VF 9= lr
q c
c
;E
r
l
:
H s*s
.-
4
e
c
! ca" a
i*
!s
I YC t
(
c
U
q
g s
C
C
C
lN
lN
a
f{F
g
lN
t
t
a
o
C
Ce
I
.1 H
g
c
l$
a
IN
s
C
ts
iN
a
tsss
CHN
!+
|
C
9
-rsA
r
l
a
c
C
C
f
{
cge
lS
ag
+
-q
$c
l
a
l
C
-
Y
v
9
C
ts
!cS
rs
rs
t9
\
\
F
t
L
lN
ra
$
a
rrFqN
\
rVrN
1 t
LHaq
fN
e
g
c
r
H
tF
rN
rN
C
g
($
oo
o
v **
9
lN
f
ts
C
C5
\C
NN
C
C
C
fq
FrV9
lN
!E
?
+
*-
:-*
I
I
I
I
I
I
I
I
I
lr
I
T
I
l
*
tHJ3zF:<z:Jt
IT
IT
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 99/304
rr,a
..
=-*1
'"
€
!
s
!
.
!
.n'
]
i
'-\
1
-
i
,
:
l
*
L
:
H
C
?
n
E
!
7
*=
:
V
=z
.
-i
o
ro
r
l
I
r
r
IT
r
I
IT
I
I
s i I
o -J -
f
.
g
.-
i
d
-
f
I
=
r
n,
-<
t
*
-
!
;
: -Fa
tD
"
a
0c
F
1
-
r
:
re
r
lr
r1
ta * :J
t l
fp
{ 1 l- i
4 I N 3
i ta+ 1 -si
q** I
Ft rJ
jt-N-d N
r z = r , { F F - o-r F z
* N | l + rs
"* lY
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 100/304
i-q
+
.-
or
F
=
:
*x FEr
1
3F-
=
!
*g
;
r
i
3
l
i
P-
-
s
iJ
*E
5FP
^h
|
<
*@
c
q
3g
tr
-
t .s
:-
F
=
;N
!H
A
E
t oC
pS5
r
t
.
,
g
;,
-=G
-<
-*
H 4 i=
:_ {= \o -or
*5t
t
!-_
l
.J
-E
'
ro
1i .s -
-
t
J
- l
t
-
.
'-
-1
l-
r:
i
q l
* J
:I
r€ .J
*
-q
5
4S
t_
1
*
-
r q r I
r
I
I
I
I
I
I
I
I
lr
I
NN-ENo:-.=al-
III
crFs1tsz-=oFU
I
J
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 101/304
*G
R\s
K
N.p
1S*T
s\
.e
-*=o
i5
ta
-
_1
,
i
-
F
l
:
*
$
o
*T-q\
.l
iSilF,^
+'-
i!
&*!c=_
-
':X
:
-
=-c
,<
'-
:
F:
c
-1
i. '
,
a
!
,
q+o
-
.
-r
.A
a
I
I
aE
=
e
' ie
it
q-
-
s
'3_
-
{--
la
i
c
l
=
-
-si:E
:F
JF
.
-
1
,
€.
_e
.=c
I
-FH
-
*
ts=
=
?^
-
r-?
:
|-9:
'rc
I
yc
i
l
I
-^
i
lli-.
-II
r
I
lt
I
r
I
fr
T
lr
l
I
rl
,*
I
o cZ Cc
a
.Ji i
*Ji * t
*si
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 102/304
r
5i J { t
z
J>
=
s
F=
Ir=
tJ
:.d
rI
-8
1:7? =
=
;31 a
i
=
Ei
E
=E
E
._===
"7
.
Jrt1*7r
1\7
= r=?:
3
;.=i:
=
+
_
i:
:"5 c
*-"I
;;=
IZ=
i
r,4+
?
+
;
1E=7?3
€?=
: =-
Z=1
=
= =
E
e=
aJ==
i-;
i;+
t$+3
a
q
F
1
=
2E:=
?E
i
;*=+
7:7
=
r
r?=
7=n+
i=Z
Z
7
==
n
$r
J
i3{
i.t?S
E
;1
=
if
=
;
j=
=
:=
a
2a
;
-=
z
*=
i =
i,
:a
i
1
3
i:
=
=
m
a*
-c
r r
--.a
==
Xr?
1
rg
=E
a
?
a
e
r
'a
'=
S
=
3
z*
'!
=1
a
=
:=
1
"*s
i5
1
+
?.
?
Z
rF
rc-
;
r
I
I
I
I
I
I
I
I
I
xl
.
<
2
lz
=i
ta
iI\d
-
R a
l!J
h
'-
x
^r,rJ
a
_4
>
j
:
N
f7
d
5
L
y
-
)5s
:
e
zU
LsCQI=6
-!g
-s
';
:
c-c
9a
,
h,
IT
T
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 103/304
:
a
E
EE
'=
E
I
;=Z
?E?
i:
;1rz
1=;
=
=
: z
sa{" E
E
t=
?j t :1+
;l*;7E
a=
I:
;-:?
a=zca
=
i :
t=
t;Z+z
l
=
r
-^-?1
-+,!
=a
vZ
-14
:=
:1:-
r=
E
rr|E
E
:
)u
==1
:
:E
;E
:
':r
E
z3
lE
5i -
;
:
:=i!E
=;L;;
E
=
i-z
t:
Eg
:€;
;
i:=4 aEAgE
*
7
r
I
r;
r
rr
I
I
I
I
\J € { o a z co-
<
g
+
=
=e
Z
9,
j3
."
5
=z
c
; ?
,i,
t;
l
ta
7
,
r
i
I
c
t
8 .G
o q 3o c t z N \
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 104/304
;-<Ls
*
o< =
U
:
.? -+g
- .g
*o*
:
l
l.
lF=
l
r
3
:*
*e
l
l
-
:
i
c
-ce
,Iq
?
!*
t
_
a
i=
t!
!
=
rca
=
ir
l ;
jr
i,iz
!
I
c
'.
I
iu
c
C>
l
-
+
x
,i l:s
e-
1
s
:
r
2
J
-J
:
'
i
t
'
r
=
{
-e
-
d
{_i
:
c
t
ir i€
a I i I ; €
-s€l i :
:
1
l
l t
$ r : l "F t : - ( l1 li+
G I
;
E
P 7E :- N i s - z \ E a = = -
l i h
rS)€
S>
l
h
o
'F
.
c? ?
3?
F?
. 'r I
ogA-=
|
=
-
vG
e€
€
!€6
-r
a
l Iq lt !
.
-^
-
*
-o<
-=
-or*c tL
-H ?
*FouJ
?
l{
3
c
lcd
rc
r
:
\ -€
€
rr
I
I
IT
I
I
I
T
I
I
I
O
^
"d
:r>
td
a
E
f
,
:
3
:Fo
EE
J
n
^
:
- 1
:*
.-b
{s?
e
sg+
6
*
E
H
F
q
':
*io
;
-+qE
:
=
-6
I
E
E
;dE=
:"
l.b
A
1
;risL
?6x
lq
53K
'a
a
lt
i
pF
^n
-2U>
(gFiFhU
\L
t
-=
Zh
>
,
i
=
.-s
i
i 3;
_
1
-
^Y
o
;
',
i-s
.
g
-=
i3E
tr
:
s
+
z
:Os3
T
T,
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 105/304
lal*
* $
:>
:*
i
,
F-$
K-J
i
x
i
|
x
x!e
!
-JJ
aJ
3
n
S
$
+
*S
+
:
a^
Fd
tF
.
>
n.o
!.^
c
n
s
t*5
^
!
:aL
i
:
i
a
,OE
E
>
E€
<
=
i
b
i
!
l
i
t
\
l
!
t
F
+9
$
-
s
'l a
is
l
s
iso
t
*E}y
i
.=
|
|
t
{
*
:
1
:
TH
+
5g+
t
I
I
tL
ri:
.1
'.
-
..
< <
r.
:
:- i
S
- 3=
=-
=
I
!
,
=r
', *-
,
$
!a
:
i-
f
j
i1
9';eO
n
:1'
-rqi
aQ
6
lr
T
I
I
N
ITr
lr
I
r
r
I
F
:N
:
j
i
-
v
\+
rx "
-e
I
7
I
F&N'
l{
7
l>
!*
l
-
lX
A
lzt4 lv
-
tt
_
! ! t?
\ "1
I
"c : '-
S
I
v a
C
O
+
t
-
+
;f
E
-c
|
;
X
:
no -eI
t9
t 9ivg a A
r
\ :-S i
c
lG t \\c H IG
=
r?s=T
q s ? +
.+
n
.-
:
lL
s
N
l
-
.
+
\b
=
b
*
=
ats
2
3
C€
-5
a
$T
N
-*3
1
o .1 { o c {T
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 106/304
€ l a , r J *1
-ei ,5 z tc g i t * -6 r 3 - : !
l ! a\ t '
.
i>r-.1C
5
AEi- r=
t?
Jr€x
wo
I
l
o
l€
E
F
FF
F
T
r=
_
E
+
:
C
l
i
i
gg
d
2
;
t
'.
io
r
+
c=
E
2
"
;
:?
6
,rnz
j
gE
e
f
€
'
-a
-
1
re
=>
i
l
l
c
!
I;
-
,
_
qa
o
_
l
>:
F
EY
eqPqs-g
^_
i.r,L
l!a
l
!
lZ
*
-
lJ
!
*1
;
F
'
'.*
tug
Jo
t
E
T
.
ao
*
i)
N-€
ta
+
-
I
t
'.
-
-
l
r
F
'3
-1
i F
;-
E
j_
i_3
-
i{
;S
"
*
;
a
s
i
o
-a
-q
=
i:-=l l.e
3
:
=
+
:
E
a
;
:
r*
I
t
iJ
-a
!
-*
F
;J
$T
!aq
i-r*
IQ
r
=
;*
d
l
i
/,
-
D
*-
.3
;6B
IG r
3
3
E
\4
=
l
t
a
:
't ;
-X:-
F
E
?
^E5E
-e;sF&
u
- l-5 i
:
ie
s
s
1
.--
I
TI / a i i
.€
€
-$
irlt
l
r
.
!
:*=
1
.n
r=
.=
_
r-*qiY
"s
f1*ri:=
N
U
.
r
-
tr
r
.
fJ ,
n
Ir
I
IT
I
r
r
I
tr
--lp!?H'u:
^
:
TfE
;
"E€
i g
[
E
€Es
tE*
EE
L
I
o
€
su
FJ
S
{:
:,
€eT
?&
Je
'
*?
+
!-
;
.=
E
.
;*
E
f
5et+
R
.
:
€
E
E
Laa
r
a
?T
:=
;3
ir9.u
=E
N
J=
sOo
:
+
{
L
i*
*r
t
I
*
,+
r
5
i ;.1;
-
r
"
l;_-J
;€
H-ro
1
F
;
i:
-
" r
.=
.E
!
T
'a
E
:.1
c
saT
E
'-
$
il
='=
!8:
e
.
rC
-o
,r
<
H
-zd
:
'-C
.
=
;
qu
+
,
E
E
:3
Eg
T
o3
3
*
=
=\
a
g
e<
c
TJN
I
r
h11
FuoF(FFe
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 107/304
ahsc
6
sx
g
av
.6
l
#
5\
e
6H
*\3soG
d
A
q
hocO
i
l
;
\
*
N
.
2
+
i5
.
F
E
rs
Nr=r
-
r
L
l
I
}
q
N
,Y
'a
H=
F.1
.
'
-
X
;
qF
n
E
j
€
;
EE
(g
H
V
Il+i 'q
E
S
3
I
;*
|
+
o
H3
=
Il
sL
"-S^l;
a
L
-
E
F
.E
-*
{n
f
$
;rg
e
?
F
i;r=
"
+
$E
r
.-r
.+
;^
q.=
n
n
d
c
_
P
F
P
z
5
E eE
IO
o&
Fc{P
E
6
ss*o{
u
!
ld*
o-o
L
x
I
.n
;
9
lTN
r
s vd
,B
l<
UA
'<+\T9
=io
F
I
qc
/
v
JT
d
e
pQ
i
2
S
g
$-
l
':u
Q
i
e
[v
ie
.=X
i
xF
I
gs
(c
I
gd
.F
5
F
.H
I
$
=
5Tl:gE
'*tT
l
co
E
i->
PO
i,rp
i g
*
?
-$ g
;E
,
=ug
!
E
tqa:IE
: 13
i t;:*rr
ip6';
E
Ia
fe=E
C:t
1
E
<!
+r
.*
E=
I=
s
s:3
\
lr
.=E
i
:E
S+
n
FE
-E
-*
:F
-I J
L€
Lr
s
s S
-
E
€
fr
;.
t
I
\qI
=
*
1
a
o
Q
F
Q
c
.
>
H
c
u
?
Eq
E
J=
i E
!=
E
5
a
9
;
t
e&
€
i
T
D
I
r
I
Ilr
T
I
IT
A
H
o
F
H =
-
^
l)
E
^o=
n
nR= =
6
c
-
q
e=
r
ro
-
-r,1
q
ld
H
?
'
o
rE.
L
-
'n
ie
;
-
l r=
:
<
9
-*
{1 :
.
n
:
+ A i -
c { o z {
( G+
z
3
Qi
?
t
t
h*<
V
!L<w
o
1
;JLw
c
:
YCr
ERi-o
o
a
L
@
E ;
cc
-
g
r 1 F
q F o a { o t t$ c
I
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 108/304
?o
O
O
6
oH
.
s
*o l*=,D3
t- -x5i-
?
i
E
^
=Di
c=
r
@
t3(2
r
4
t-
a34
N
F:
q
a
l
_
=
.*
:* s^.
:
--
IJa
l
'
l -1 -+g
uA +:-
lr + 3E
O
x
4
A
^
"g
;
.\E JXs*H 6QI 3
t
7
"E>a\o iEc t r
e
*r&ro
=
.
-3
-
t
!
-
F
i-3
- =
=a
<
M
E
_
_
i?.
\
iG
D
F;
I
=
--e
*5
=
".
3
<?
z
c
'!
F
'
I
L
l
!
+
:
-F
i
l *-
r
.?
I
<
':4
' +
-.
u
F1
x
!
E-
;
i
s
o
-
r
*
:
=-
ra
r
<
i <.9
:e
d
r
'-
5
Z
:
J
'
!
L
i
=
-
=
l
'
-
]F>f,-=
g
+
:
-
I
!P
c
c
P
i
a
c
l
E
I
-<
|
i
:=
*
!
*
f
;
i
"?
^
'-
lr
I
I
'!
i
-
-
2
*{
.
^
-c
1
€
i \
c
;
=
-
l
3
lfv
=
^
F
l
-
=
r
l-
1
: o;
*<
{a
i 3
<
:*
I
*
:e
1
tr
w
.;-
:*
€
:
;
;1
"-
'
I
q
,-
.L=
l
iu
l-
U
;
-
- rc
b
B
q
'!= sglo
^
<t io, o 1
rJ<
la 'd, :s l tQ -ec + -a
->FC
7
sq'n
5
t
4
"_
-
c
I
lr
5
N<
N-
=
I
lo
F
t
a
\ '
l+ =
vb
t-
L
H
n
C{N
(
!
r
F
*1
\y 7^Y
l
C
A
=
.T t"
c
!
P
';
g
tx=
t+
-
b
i
*
;
t
f
i
I d
t_
s
-53
I I l($ l I + I i I I
I
r
I
t
r
I
r
l|
r
I\
9
6to,2
bNl-9
a<;
.=
:
*X
a
i--
{
ei.r1
De
';Em<4I-
v
*
:*
t?crtr
q
E
lrH
S
lr,
L
!?C
r
.a
l
H
S
*IF.-;
-
H;*"€
h7E$-
-i:
c
-
\
+
-I
r
+
R
s
t
\t
z+
q
.
-q
.=
SE
Q
r.
g"G
F
,c-;
F
a
-'4
c
C
,
i
F
| -
;x
SHc^
Y
r
FE
t
s6
-;
oE
.e
';
41"c
,=
'
tE
a
i
.Z
I
6
!
+
-c
=
U
.a
"
.o
X
R
;-
H=
i
.
a
TE
d
E
-
EeE
E
E
bR
E
f
JF&s(JOFFa =FFJ
I
tr
T
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 109/304
.
,_
-
'*
=
-S
Ss
-
&
;
I
c:
e
*
-=
{
t9
49o
Cnt
{r
i l
s+
S
Fatr<
€Q
**.
9
d
a
+
l
-
-
j
V
32
,F
o*o
r?
F
c
>
i
.
-
=
=
r?X
9"
J
l
r
.*
6
r
rx*
c
g
E
EE
s
-+
H
i
o
q
a
h
6
lE
E
iJ
-aic
+
o
u
r
T
i
A
t
sc
s
+
i
,n1
'*
S*
jr':
x,
T
t€E
.*
i *-
-Jx
*
V.=
+
g
-
,
*
:
5
:e
;
;r1
"
t! -3
.
a,
e
*
_
r
r
:
,=Z"
z1
7
l
\o
i 3t
hHts
.>E
ft
L=*L
S
EiS+
r
5
s
"?T&*
r*
1+
q*
o
c
T*=
*z
ng
. -
Yl
- "
E
tJE*ES
I STE
E
:
i
.-*T
-.g5
I€
-
i
o
n
i
=l.?
5o\
$SI
o
q
C
9
L€
E
;&
+
l,
.a
<
e
4$
<+
-$
.
c
-
-
"
-
:
';
;
;
;
;r*
{s
I
lr
5
-u
P
l
r
!
i
<
t;
o
$
Ib
S
ir
l T
j
+
&
9
e
$+
a
l t g
o
s
€
€
*
-g
I
b
g
.e
.
,
5
d
o
k
o
3
q
6
|
;A
n
*
o
.
q
i<
a
f
{€Ita
"X
E
)
's
i $unm
I
I
a
4
t-T
r
I
I
J
lr
-
I
t
5
IT
r
t
ie
F
:
H
:
v=
-a
C
r
!
9H
l I
)
-
o
oV
!
-
;
i
=
:$
*
+
\ 'GH
A
'tE
I
l 3
l-
t
.1 t
<
\c
.t
z
lJ ;= -\
Ht
r
--
.
l1
E
d 'E
I
{ o oc - Co FO n d - g E ,J t9
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 110/304
n: 5 ;4| = ; : ' c L
p ' -
']R'
N
ir
\
ix it9
i
-i ti" ".V
i -
$
#"
A
--
i
'- €
-e
:
i
o
^
l-9V
_
uouo
'
frru
*
l
1
o
.
F
=
B
g-
€
p
t t
iL
t"\ l
-66 i
i! s
C
t
-
a :";"?
!
i_g
A-
@
-4
I -Jrn c3 -6I
rclr
z i
s l
o
lr =€ ! 3 -6
t I
l
€
r z iz= t
t !
l s
I
N
; t:
r
I
IT
r
rr
I
T
J
T
'I
q
.
!= =Er
A<
?5
FU
E
+
-O)*
tJ
_c
'-c
-c
na
A1
'=
L
S>
-"cE
-?
T
o
N*5
L
Y
C
O
-
tq
-5
o€
r
i-
\J
)ca<
_
v
H?E
;E
rc
F
i-
z
^
b1
9-
-
o
L.*9
i
N
:=E
5a
r
Y
"+
-a-
g
gE
r=
.
i
U
':
<N
'-
i
>
o
t
i s
S 3
=
r1
L
u
ir
h
a
;
-E
ogL
#
7
9
4
Q
i=
"-
?
.n
X
E
)
a==
o
!
-
+
':8-
t"3
sE
5g
IU
J
A
ao7:zrUZ
rI
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 111/304
!tI
:+E
i E
*:
I
"a
:-
=
i e3
9
';E
,rE
i
<
s
E
1E
,-*
d
.E
sa
F
7
"=
E
'=
3b
:c
= ;+ : ;EE
E":
:g+
r"!i:r=
"
. :t=f .:;E
=:?i
'i :E:
- -g
g:
.-
E:
j *,E
;E
;
i;=:g
;=zT
r
uE c
:=:r
: =
=
;si
i
o:Egt:o
R
=
:
i;ras
r E;;
E
=
E
1;€
"++EE
:=;4
.=
E:13
u€
:E
=x
;x=*€-
; ;:z
* =
1
={
-r s;s
=Ea:
;
:E
.*=
r
:E!
a=E!
' E:eE
:ssE=
E
E
i--{o
-;+o!FL
ll*1-
*tlr
.Eh
x
}
'=
LU
N
=
-
:)4
{
-+
4
l
=
/
|
z
:"
:
i.
'*
ud
#:&
--
-
=
.
t
.
=
'4A
\
'FtF
\
"d\
E
l{
hgE
*
*-
,*<
.X
I
I
I
r
T
lr
l
I
r
I
2
i o a { ca c
n
c F
= c z - r o = - 9 t I z = d o
r
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 112/304
:
l,;
r1
=
r1
1
=
."
-;
=?
€=
=::==r=
'rr )
=
2
a
j
;=:;=
;:1
:-
:
,
1:_=
-;=v=:r
i f;
l =
:{=
=+
:i;=E
+
;--=
;;
r _
.I
i:=
n
l
+
{
;=;J
-
= =
i ==
1="
zi;
\a$
_
._ r ht l i +I I i I
kt I I i I
:G v \3
t2a
ts
:
E
y
Aq=
x
r1
-
:
?Gt=
-O
X jd .s
Os
: +
.
c
:
O
r
E
c
\
cI
F 1 c F
g+
5
-
c
'"
F
$
'g
g
in
Eb"
t .
laC to \ 'e
\J r
t*
-OQ
\{\
-
Av1t
t'\z
-
LA
.4
P
=
>pe
I\$
i \
\/ g
sr
\
_0
_
r=
\
C
D
\
1
\g
q
l*
Cc
-
:
'J
!A
E
inv t
;
t !n19c
!e
l
-
rt-
J
\ Isl r
ts
#
I
7
rI
II
I
I
I
|
I
4
E
"d
lrs
-
c
r/-
J.
4
I
'
i
.
-
X
n
r-
-
.
"
d
€
E
-
x
a
\
<
i S 15c
H+U
aOq;(FJFa
rrr
trrI
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 113/304
i
ro
\ {
,s
q
-sF.
1H[=L
'A
-
.$$
f
gU
tE
=3
€S
=a1
!e
*F
sN
.E
I
>
6H1
C
F
t
X
t1 &
G XgCG p
, o a z , o* -o
:
-
E3
7-
*a=
5
S^
g
=
S
_E+
^
==
"eF
3
?
=
=r
=s*
g
E
_
=
.
"
E
F
; :
N
*
a
=
g
:
c
5
r
|
|
r Fc - o? no0 c 3 { o {
r
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 114/304
gc
F
E
=-
9
3
:=
c
oF
+c
=\x
A
C
!
X
t+J
'rI.u
! d N4-G P
OE t
H q Xa
\>- \ -
=
?
3
d
-{n
"
d
=-
:
1"=-2=
:47
E
E
1
=E1
ir: r
-*;*S
2
a*
7=-5z
?
',a
5 ;
i=
-
=
;=
=
,
F
"1
=
j
-=
:
a iis i i
tl i
=
'i
*-=
L
S
*
fN
fN
f5$
g c -,
{ i9
r
,
s
4
l-T
TI
3
I
I
rtJa
I
I
f
IT
g,
it
g
::
E
*E
66t+UFz;F
I
rn
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 115/304
?a
=
to€;F-.-
XiYsQ
FI
;
E
; :
;
;
i
;
* ;
r
,
*,E
:;Ig,F
I
.;_
,r*g
n
:HE
n
.
E
.-E
*E
Q
I
g
?5
.=
.-1
*€
aE
p
::-
-
i 2=
i, .
E
t
;
'-
Z
= =
3
.=
€fr
:
i i {
z
= ;r=
; E
e
:;+
-
,;
:
{
?t
;=is
E+E
u=
l;z
;*
=$
=
3
g
-i :
:
!=+a
;
:
:
,
;
:E
6
gE
i z
s
*
z
E
_*
:+
+=o
sb
^ sPq
.2
6==
;E
F
g;
H
t::*=
E
o
usEe
=
;
3
AX
-J
Ea-
i
=
ro
x*E==
?F5
;E;P*r
y-;Et7€
P
tTE:*E
a
:4==€
=*,+
$
l,rqE;
sr=
=
E+
r=
g:E
l
i
!
=
S
";*==
4=a
E€E
6
i IJ_
==-
,-=EcsE
H;E
Eo
:s+Ex*FF
-
=-7-T
--=EL*
.=o
a
,E
E
E*Fi*esE
r
(4
4*Ea
;a
"=E
;o:o
c
:E?:=E
=E
Ip€
/
ff
i #
E
lEFE
1
aE
?
X
'=
l
:
=
-
tr
I
I
I
I
Itn
I
T
r
{ o c co . -
!o
rF
:
r
H
I
;
=o
r -
-o
6
-
r
=
-
1
r
=
6
-
!
Eq
-?w
;-a
=
.
E+
G
n
-d
43
l
e
-
=
o --
F = { r -o { j H 2 { oa- 1
; I
E
E
X
;
-a
S
E*X.
H
I
q=
ts@
aR
.+
i R t
*
.P
rs
r - o o
t lN"
is l-R
tg
I
I
7
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 116/304
-
Z
'z
=
=
5
=
.?r=
z
j i
= ;gu
EE
I661=
gEEr
6E
"
i
=
=
=
=
.
=
=3
l
' =
-=
J
==
=
E
_ .=-
=
=
I-=
=c
=
:=
3
E
=
=
r==
:
€
iI
7
i ;
:"a
;={
-
1=
5=
5
^
:
.
.
-
;
' '
7
P
:
*::1?
rr
"==t-4
?
+i;
gl;+=
.F:F*F=l l1
_
i s
:L
i =
-3
i
j" r
Y
. i f
I' -
->
!
|
. F
':i FrF
=
,
b
-F
:
;
|
:i.?
:
t
'
j
t
i
t
I
I
i
:T
ir
*a5
.r_Y
.
=
.F
;"
:
=
E
l
.
.
'-+;
q
r:
E
rL=
:"=
J:
i :
e
,
i
.
iJ
3
:
e
a
J
'
'
{
h
;
'
:
i
i
3
;
.
:d
=
S
*+
;
a
=
=
"c
l
S
;-?
r
=
?J
?
E-J
o
!
3
2
=
=
-=
=
A
x
+
=
=L
=
-F
F
g
-)
a
-=
_
-4
E
€
i3
!
F
':
c
--
:
i
p
-
*
s
i3
3
F
3
.D
3
|
-
n
|
;
.
;
:
-
l"
a
jD
:
3
ru f
+
!
:-@ r
\
h
!
!
lv
i
-d
9
,5
jc
,a
;u
:
'
:
tz
t
r
"T
:
r
S*5$3:
*t-
!
p+
;
",
+
.F
i
=
\
!
E
,
:
2
;e
TD
l
:
-
-
l
|
oA
lJ
=
_
|
I
{
T
i-
,w
F
F-q
F
+
-
ro
6
'"
F
=
E
-
-D
I
d
o
:
,@ =,
a
tgJ
;
-Ec. -1>
+,srAi9
O
. FI
:
I
T
I
I
rI
I
I
{
I
T
-
i
',r
i
z;
:
^
EJ
1-r
€
i "
E
;;
7
=
?:i =1:
: !
FFz5sj!IF1
In
I
-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 117/304
-=
.3E:
Z- E?a
, A:
7?;:5€
;a
i:
ia
€E=
,r.
;"
tn;l:+
gE
i-
::i
, ;***
1 =-c
i
1i!
1
;f 5
.Y
=.=
:;?t=rE
€
+=
t1;
i:*a
=:aEE
';
::
=L
=
==
=
'=EE
":
+
tt
I E;
;a
+ !
ZE
E
;
i?
=Ezz
;=
=i:E=
;?i :
::
Z
=
;
""i;gS
:
i:e
=
:
::
;
;==
tr:;sEFE*
i1tE
rS
e
e
-
\
l
c*
$
=
4
nio
ui
I
c
tN
.0lo
a
:A
/
4
!a
X
j.
^lC
\eNl
I
I
T
r
T
r
3
I
I
n
t9 i o o z { q o J ia
:*z
f
aC
*
t
*
I
G
{
-P
J
Y*9=
i--F
n
#e
r
/
a
-
-< ! rX
-
* ;_
'1
=
l
^
F7
:s q=
2
P
3
q,
i
=
F"
=
*
n
N -La
:-
=
:& -1
i
'a =
=
-
I
1
7=2
LF=-= is
3
5
*R4
s
-$ -F
G
ts .a ,or3
,os*
s
4
*cg-N_
_-
5
NE-?
=
5 ,4
:o N
4
; -
-
'1\st
'-=
'1
4
{*l
\
q E j o .J ; - oc
I
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 118/304
\{
\
J {
z??
==
E"=
=
7
=
aa
*rI
-=
=
*
qP
o
;=
-
+1
5
*
=9
a
4
:
=
==
=7-T
]A=
="?
4 =c
=
a
=
:
=
j
-
=
?*Z
i
}
.
;
f_
=
1"=
o
?*
i{<
3
=F
'r=
i _
,?
^q
4
4
=
'
=
rF
=1)*z=
T
g
,r
^
?
a
i
-
t\
q
o
f-
:
-
=
:
=
FE
:" F l=
-4
:Hx=.
;
;-
-7
=
-!
'!
't
f?
tE
-3
:r
F
,{
-a
+;
i ?r
F
:"4
?
+=a-
:*
i;
s
*-
:?
"2
"G
-
+
t
'=:;
3
3
rc
: zZ
r=
{
E
i=
j
'*
?
.3
:-
5
I
;-
iD
i
I
:=c
,-
-=.
:
:
:F
=
:
!
3
;r
.
=
?
:
r
q
\
*
e
n
t--
I
I
I
I
rlr
T
I
I
I
I
+l0t--
't1(
t
=+3Ohj5
:
oA
=
rH
;
ts
k
)N\g
o
'*
!o
\9
,A
-gA
\c;
o
=
_
dO
C
=P
=a
a
tsF
.p
E
fo:
N
.H
-=
:*
F
.=
-
:F
a
Q
o
i9
5
-
A
-
-E
5
nH
,c
E
q
_L=
.
-
o
)sy
ts
r':NE
X
L
o
Og
.E
€
t
c?
,s
o
L
,a
k
m
9
d
Y
A
tcFUFF
.
c=
?
rs
:
*A
a4
d
-5
_
e?
U
J
-
a
=
tQq
a
r
t
"
,
.=8s
E-E
:-=d*sd?
"q
-
I
6
=
:
=
Xc=
aE
E.;
+
=
Y
S
lV
.
FJFs
Ir
T
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 119/304
=_*_
=
1
5
.
a1vN
tc
i
*
+
{e
,?_E
-
r
X
x
r
-
e
I
q
r
$
?
"J=
T;
'a
c
r o
-
i
l
d
\
-
-*
.
-
,
,
,
lJ
:
-
.
,
R
E
r!
L
i=
i l9
l-=
-*F
.=
t
F
cEE
3f,
.+
"
3:S+E
IgE
E
=
i,5
I
ZE
*
q
s
,.3E
.aE
1_,
E
i-9
=
e
d
i>
d?
-
=w
6t
-e"s
rE
v
d
8B"
l!rF=;F
a=
c
-
"€I-
+:
lsr+';
IE
X
*E=s
=*G
+
-yn
"_
ze9
c
i:_5
=
:E
3t
!
lcE
_
-
*
R
d
;s+
L
Es.E6
s
>
?7?n
oQ:"
F
3+E i*8
+
;.n3
E€
r
Ljr
*€
a
EE{dr
\
a
)+
c
sE
=
!
=
=
E
=
.
au
':
';
'5
-a
i
;
E
:€
E
E3
?=
.,2
=
"=
:
i
I
',E7
:-
1
.i,
I
i"
.*
!,-,
?
-$
't
's
=^.-
.-
-?
-
.4
!
.F
-
!
:
:
:
-
:=3*
_^
|
-d
F
5
^
:
,"
'f
:
i-
*
=
_
'5
!
e
.r,r:
?
=:
.l
=
:€
-E
i u
ab
i=
,7
E
l v
:-
-J_
r
_e
xEt"
u] r
:=
-
E
=
i!+
=Y
z!
hh
'-+ t-{
=
=i"!
';3 . a
i-
':';Y3
t1
fl
;iZ
tH
€=thfr
;a
^,rE5;a
k?
t1
i
i *u
!T
T;Y
1
:
'=4
i
.5E
*
l
rrrc
6
i
,
?E
S
-="? :rE
E€,3
::
K
X
=
-E
s
e:
o
a-
=
=
===
=====
J
-9=
=C
!€Cc
.
-;
=
-c
=cco
oocc
o
t_:E
?2
52
z4
7z
€;dE
dA
E
-
I
RTTtIotl"!L
*lbltl*\
I
I
t
tJ
rr
I
r
r
N @ Jo aoz - q a ! -o
1
-Fs
JJ
: ]
+E
),
= i;F=
2
+I
e3
f
i,e
:=
ZLN
9
a-x
-
: +
=
l
*
-s
"
: r lO
: Z-c"#4
/
lt
J
:?;-
E
1 t
t
i*i
: ';
Z
4|
a
r
==
:
^
*
r
!
€
€
tFEF
rrE
i=v
,"?
=
:
e
x
X
a
*F
=
:-ce"
=
_D
a
g
'
=
-4
=
=
*
=-?
-==-
i-E
i:-
=
2
c=
=
.
Tn
t
o
9FE
r3
e
=E
=a
I
c
F
:
rg
;3
,
f"9
2
=
=;=g
-d
-
_
==
1a
=
:
;-
"
:
j,=
i{ a
E
:34
i E
= =
F
: ;-=E
7(
J?
,t
;F
;;-=E
-=
E
c
s
"=':ci.
* r o . , ocrI
U
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 120/304
ig
-F
!;<Y
+
*=
= =
*r
n
<n
+
7V
T
;rE
;
rd
{
F=::-
i E
s1
=
t ;n-
z€
?
i-3
I
l
-
ak
i
-C
C
;;3
n
i
:!=
r
'a
-
:'a
i
it(
i,
;=
+
a
,
a
\F
i
=
*
-
:
^
'
:1X
=
t0F
,3
l€
r5
;=
-
=-
E
i:L^E
:
=5
,
=
J-a
=
i=;
-
i
i
=
Z
:=
"
:
=
r
7
:
1
.c
+
i
:
o
"
?
+
r
-
':
^
3
"S
r
t
-
=
1
=
71
f
s
=
.
c
=
-
i
r
=
!<-c
.
r
- - __
C
=a cr-a
?x
a eE
o *c;-N = -
N
lr.
L
la ?
rS
.c
6
_r:>
-:
;{A\ {
x
!
s
.
l{*
zop
:F^i
\X
r2b
z=
c
@J
Ca€ 'n
l*
9
=i"
te'rl
rN J l
c&-
b
I
;
I
I
I
I
II
IT
T
I
*2
E';
?-dF=rf_
_
;E
{
.=;s
3
S
;
!3Et**
+.;s
'.-
o=
€
s€rL
E*J s
E
:
:
;E
E
'!t
E
g;;
IF:OF.
ti
-
:J<l-qn
!a
?
+3SlL
SE--
^
-Y
.e
\/F
Ea
^
!
o=:
e^I
F!tpuF
I
J
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 121/304
I
n
3
-
--
-i
?
:
f3
ss+
jt
3
F
5?.-
?+
a1
j=
t j+r
u
f1
-:{
*:3
:
+
+$
:;1
*1
=zt-+
tE
i s
;.
=
1rz€
r*3E
i
;Ef
q,T=
; ;E
1r
ir
;=
=r
;
;;-.;*
fq
= i z+
5
E
:
;5
?
gZ
e=
T+
E"?"
rL
=
:!x?
t_
*?x?+
.
u i;
Z;>
;E
fg
5i:
E
iIEA
.=
=
.
.
r
I
J
I
t
r
I
tr
r
I
.
7
S!
[
aa=1
so
€H==
=;,z=
?
?E
S"=
;="q
=a
:
?
1
:;
3g
=
7
=
=
i
?1
Eg
:
:1r
=
;E
=
g
-1
+E
=
F
=
= E
7;
+
=C
=
f
=
;
"
s=
r=:
=
^
-a
nE
V
I=
i$
c 7N - t a a - aC z - - Cr -cI
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 122/304
'2
1
,3
i s
=
'*i
i=
=.-=
;+
:a :
=J
=;
;=
=r
,-==
:_
^
=
=
t
=-
=
7
I 1
.3?I
+a
,1==a
- =:!
=
|
.=
=
-
:;=
-?-z=
;=
:==
!
=
{
^
*r ;E
;:
i
1== t7
"T
::
-J
,{
r=
!n:
.1
:
=
-c
7
;F
l n
=
*
*=7
=-
i e
':
:
-*g;
.
x
!0
6F
'
^
- ci.
o
BE
EF
v
F
5
X
7
"
E:A
N
:"x5
i5F
=
-E
t*R
t
*F
n"
z
:1
^
-ts+
=
-=
j=
L
F,"
7
n
Iga
X
-=
.=
f)
4Z
?
Ce
-
=
;
=N
i
j
N
(D
6
r
.2
4
E
"s
O
4
-X
v
=
-
i
'-
m
ie
!
z
sE
X
=
;
I
3
:
a^
!Fm -
_
;
:3
:4
d
r
"d
-F
c
:F
Z
-c
=
=
=
f
=
-
a
r
-E+
V
F5
g*s
IA3;n
ira
;9
*
i"*D
'!6+
E39:
P3
*E
^^F€
!-
.
Es=lt€
=
i E
q+E"
E
^
rF
:{g
=
Y
-I=
E
=
;
F=
=I - N I
t
-7V
s
h t - X lr
M "Vm
M!o \x A aD u
Q^ *u .s
Eor4
! 95
\
I-1
tJIHt
IJta I
-i
J
I
I
itrJ
+ :
r +-
.+ - a-
:
q
l
6
-
F
i
\"
{+-
1 aV
G
t
:- - a aG r
;
lr
=
c o :4
;<
H
tH n;
i
l-
N
:
-
-
.\-
c
X
c
3
-
=
=
S
*
.
; n
-+
Eec
i-
g
a
3
-
!
-
a
^
rD=
:
;c
/
b
?6GI
'7
,c
=
=
r
o
F
t
-
1
;
+
1N
-o
-^ -G
e
o
o
t
IF
J
nE *E
=
=
i
a
:
a
-E
x
o
HF
a
€ !2{ I
I
I
I
r
I
IT
I
T
I
I
E
IL,g
i
,
':o--o
I.
e
;-^
o
'
I
1
-
|
Oa*
E
c
Lr
b
:
P
r
s
l-
E
<C:
I
[
]
-
*
.
!=l=a-
l
l
r
N
\v
tFJq
tI
E{
#;-a
=;
Io.<qJF(1
U5;JFQFs
<-s
I
I
a
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 123/304
sX
/t-+t-_l.u-1o
r
1
i-=pt_q_
_
4
I
T
I
I
|
I
-
I
rT
it
{ Ja c7 t a ::
F ,E;- X i" *
aO3 ^ ?
t - t - =a =t '5 $
= ;e- 'z e =
VM
=.
s
5?
=
ts
-
3
*
-
^
,
i
l
|1
; =
a
:
-
r
-
v
+
;1H
^
+
=
;L
!
!
=
=
t*
-
*
.
.-
rv c
-11
:
:G
-I i
lr
-J
o N r o o - o - - - z r r t9 'F
?
i:-
E
E
w
.oFg
3
Hq
lD
-.n^
!
a?
t M
'.h
-1R
6S
L- E
i
\F
?
,?
i
o
* €
I
i"
_
L
r
z
=
E
Y
5
=
\
b
?L
z
'r
:
Y
*
;+
r
:
!
I
I
:
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 124/304
I t I \!R
+
5
5
F
:
3r?
r.;
1-=E
*i.!
a
1
--
;-
-
+
E
?
Cs
*
:=
,
i |
-FtM
N
s
r
r
="
-
N
=
=:
]
i
:;
i
,
"
,{=V
__=
*}q
!
r
==
'>
*:
L
r
=":
I=!+
.?
I
=*
=
4
i-F
,;
rc
c
?
F
!
"
:-3
i x
Pu-
'3"
q5
Fl
e
:E
t
p
i
J
o
i
=
-
l
5g
I
=
r*
Es
;
trT
:
?
i
?
:-
*F
e+
5
=?
E
*
?]r
?
c
=
E
==.a
: luEg
=
Y
EF*Hs
u'r :
\ l
g X -{
,
*
/ ,
\ \
.8
\
+----
-
sCq \ -
,,.
\a
N
r
I
I
t
I
I
T
I
6!sUzo
-
f
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 125/304
_
.F
u=
-:
:e
>=
J=
-=
S
?Z
==
F
'*
:
I
-a
'z
a=
;
a
=._.-
=
-5
-
-
-
F
=
E=
+:+;
:€
sE
<
t
=:
a
1?E
+E
: z::?
;=-=
.z?
2
ts
-
i,=1 -€
E
;j E
a
E=r;
=
]J
E-
<Vr?7
TZ -
=|-
=E=
E;
=
: ?=
?E
.=ZE
;
:
=:
==
:5!1
=
."e-:
--
=
eE
=E
:+
q
;zE
I
-
==Iz
t;-
'4
-
:=
=9)==
-=E
-
t=
a
:=
:?
4
i=-
n
u
-=-=:
€=
+tE
=
Ei :
ai
1n
:
i E
-=
-r*
?
-*
ij
,
7==
=
:-
=
=7
:
r
= g
";a=f
Iti-
ac4EJ
i'
I
.'t
.-1
.s
t
s
b
I
I
T
t
I
I
I
T
I
t
^**
:
-:, l
-l :
{ i O ao z ! ca J b
=
t4
4J
; -
5
.
'J
J
^
-5
= =
F
:vr_
;
a
l
o
a o
'ts
=
-J-=
=
=
X.
-
4
:
o- a a t "= r I
:
: s - z o - ; a - t 7 C i
3
;
=
-
=
7
=
-€F
8
X
=
=
?
=1
.?
*=P
.=
,
i-f
-
=
4
31
772
:
-
4
=
:
;a
)
2
7
=
:r€
-n=
=v
=
.=
=
-
-=^
"t
;
e
?
-
Z=
;;
7
?
]*
i
*?
= - 1$
tI
€
:=
7A
=
^
a
=-
z
;1
=
7
== : ?
=
a4
=
=
t
-
4
-
-F
v=
F
a
tV,
=,2
=
-c
t
1
;
S
E n"7
I- =
!
* r 4 =:
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 126/304
\=l\
1 J ^
-
*:
-
:5
;=
=4
=
==
;-1
?
:
.=
=
=
l =
Z
=
!
;-U
;3
E
F
E
=?
tr
:=
_=
=7
V
7
+
=
1
=
1
-
>
-;'
J
l=
r-=
3'
=
"=
E
_
:
i =i.n
^
7 :-- i t ' = *+I * : i 3 i
G - -p
-Ga?.
.
n
-a
i-3 a =
=:-gE
=
=
=7r
c5d-X
i
-
=5:E
-_|=
2
-Z4
*+ =c-= *B
F
==
-=P:
-g ;F
E
f1
I I I I .J t-. H-
I t*t*TI I I
}<-
ts'tI I
:
ke c x>i< '
Za
r=,
!x
v AG
ta X r 9
=
i-
1@
lr
ir r
-
'
!
i
5
s :3 ; 7 =;3* -al
>
F
={ q
)=
=
=
=
-R
-
=
;
;
-
a
j-
=-
t=
-
O
a
5-
iH
:
*
6
-:=
)F
itr=
:
-q
i
=
13= +gP
5*=
EF
:=
o
{3 "+
-r
=
=
?_
a
E
-
-
-o
-F
r
{
=c
n
-
f==
-
E
$
^
J
-5
-
=
a
3
*=
;
^=
J
=
|
^
-
^
-
t
;=
og
-
Z
-x=,=
-;
F=
-
io
!
:
r1
5
:
r
:
5L
€
u
t? !
c*F
*i:
.yc+
:=
;,
i
f
4
==
=
'3s
\P
G
=
-
I
, f** I I
F
.
- ts
t-
!
I
r
I
f
I
r
I
I
I
I
zar
-
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 127/304
:3
=E1
ag
i, z7
:z
Z
E EE
=
: :, ,
El:z1:
=;g
1r=
a1:?
=-i i3Z
;;
1:7
;
i =;+= =
:,E
L;
:
t;iE
:;z=
F
;g
: I
:Z
=;=
=:1
=?
=:-E
:iE
UJFr<6:JU
7i
ILa-
:
l
I
I
I
I
I
I
I
I
I
Q r I = a u Ca- r C c -aC- - F r J
I
I
I
r
3 i< a cN - G I
=
;
I
r=
F
G
"
6-=a
:7
J
2
^p+=
?=
+
': Fd
"
.F
=
^
"
'
4
=O -
=
.
t
a
-a
l
t
F
:
|
+ rc =-
G
a4
;
=
F
C!-
:1
=^
9
1
-
-P
,;
=
F
l
a
c
aG
^
'
-=
@
ID*
*
G
.q+i'y
a
;
-=+Y.c a
cQ
?=z
)43
:G
=a
=
t
C
+
^=)?P
!^ ;
"c
=
aa
:-4G
:=oi
-c
"
-
v
E
*P
6
Ic
l
G ;
.
tG
Y
at
-o
.u:
1
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 128/304
I
I
r
II
I
I
I
I
I
F
t t -
l ! xr-
t*
: ,
2
-z
z
--'- r
_
'
h
:
;=
E :
Y
E
5-p
a
F
+
, 5Z>
,
L
V
cE
a
-
.=
+
=
Io
-
tJ
:
o
PZ
=
.
F
e€
:
5
=
.
3
.
b
"
uE
i;5
c=
L+
TL3
:
I
;".
r15=
.c
,*z
<
;;S
{
,sd:
'=
:-
r
i
--
i
Ei:
=
.1X
=*
-
!
O
r
:
I>=
:
.:2
=
-
'=='---
-
"s
i i :q
:
=
i*!
i
i!Jil
o+1.I
-1:4
=
o
A
PJ
-
io.
'-
5
\
!P
I
j
H
-J
5
!
=
^
+^
a
ot
N
l
o
iF
\
9
._
l
.Ft=
r
-a
=
-aO--
!
?
a
-
=
-Ic
,
!
d
c
-=
=
L
^
:
-
\a
t
.Y
r
\J
-
d
i
'r
-
6
'-7
^
E
2
-\7l
=
J
z-1=-
=
4
?
-
_J
_
L
L
Y
-
.3
i
^
a
"
g
=
=
t
a
r
u
J
-
:
:
!
P
:x:=
?
'a
A
=
cLO
rI
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 129/304
rc
I
i
,{-
:jJ
*E
;Y=
=:*z';=
=
:t==_-
I.Z+
1".s
6
dI
.+*.,FE
;gS
;5
€5€
'7*5
? :
:"7
,Z*!
1
E
=V
=-
=?=
i5E=
E
s3
;-S
F
,r E5=
ueE:==
sF
:aV
1
-Z-
in,=
=
:+
a;
zza
"i*=E
^=-
4a"g
i q
i.
=*
r
=
_
j ';3
c
i;s1
rS
- EaZ
:E=
=* S
{}i:;:
!=i":
,:-+
gs"€
T
=
=
=i:
z
+=?Ea
tz
=:Z
zs€
'r+s
i t:
iE=
EE
ia
;
;
-3
-€a."1
li-1
*-r
'7
l!t,\
it-L-
J
I
I
I
I
-
I
I
I
I
5
9
-
H
t
'
-e
@:+
-
N
F
sF
;=Pi5iu=o
F=
F
h
P ^e
^
F
O
x5
.
F
;9
rEE
;J
I
F
G
5
:oE5
-_c1
7
s
.
p
4
-a6x
"
5Q
P
5F
c
c^
;TG
=
E
io
IE3E<
-
N
Eg
TGRX
BJ
=
ca
@ '4
"?
iP
"
EaqP
-t
6oS
-
-E;fx
F
F
o-
i
e7
3
x
5
-F
!5
*e3
3F 3
5
?EE
B+
.
"
ls
c
C -
4
'
Fo
rd
p
A
iEq
7E
.\
F
=E
=
t
=
.
I
\ q o q o- -o
E
>-1 x
P.
I txSsbNIs p v
a {
e__ R > i
+
r = FE
a t : - ! a
e X :
**
f
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 130/304
-
IO
E;
H
F
-
9
^
.
cAc
6
-D
J
-
E
da
6
!6FS
a
-^
=
a
dX -G
'3
;*
=
X
H
i
-
sX
7
*A
a
v
-
E*
5
3p
E
t
^
^
O
:
?
.=
*
x
P
.a
-
t^ ;V
=A-JA
s
+
oFA$e=E
a :
A
.3"
r
-
F
-
---
l
^
a
-a4
'-
r
bP
G
!
|
t
A
:
_
o'/*
E
i_
-
X o G o OF
.
G
@iN O M*a -c Na
G= l-
:-N
-
n
>-H
:- a
6
,v = cr3
aa I a
f:=g
3*Ey
p
IEgE
P2+
g
€F5
T ;1
=
*S
e
=
=
r=
:r;?
:'F
+"=
9-gE
=
-
=
;rV
V
7e
t
Fa
;F,='7
r=iZi:e+
=
vo
-_
=
_
i?
V2
gF;r:7=zi:
S=Ed
=
E;+
r=
isqE1
+E
E::-
*
F
l=!*
r
_3
=
J
:=
3
;
:v7
;7=1
?
:a
e:st-
=
==
E
ue|
=
*g
P
:$3E
,
€
5;.:
XoE
3
=-
^
r3E
;7
=
k
=
3
-Z
?E
r =
T
C .=
= =
c
=
G
e
ao
.
J
.
-
|
!
'
t\FF Ff
I r1 l--r=L F
-*
t l-
I
i FL^*-
: t --
-
h IA- l
-
-
1
L .I*
s7
V "L
*
HE [?
t
t
{m f it
S r*
s-
I
-- :
'r ^-
rc- t
,1
--
"1
fJ
3*
F +
cn
l
N--
tLo-
l- I -T
a
I
I
I
!
T
I
I
I
I
I
\
J
*=.s
=:
n
?
:
;
t
ry=
!-
!=
=F
=
!
.=
-
*=
3
E,=
:=
{
J=
--
i ==
Fi-r
:
l=-:
=
=
.-=
1
t
-
!-a
:=
=?
5
;=
.s
=
-gA
za=n;
'rE:34
?
7!
:!5
Z=
-
-c G=
";5
X7=c
l:-
i
I:
t t_Z,z
'!
3
=
r
"
:;
z
E t
l*
3
i-
{
-
:
.--
E5a
;7
it F
.E:g
i_
E
r=?E
.
;-=
r?
?
.F=
AV-=
3
-=^
=
-
:3S
+==
z3Z
3
=H
E3
j
d
a
o
-
'
:
h=
:t+
Zc=
.Z
-aY
-
z
:=
a
ic
E
I
.-
*
n
d
I
'g-
Fi=E-
'-=
a"
.*
,===
Qs
;--
e
,
J
ln
i.n
ly
=
ta
!
2
saEzi
.aFzoEE7
.+
=
'A
e
H
i.=a
Ta
f=
tE
z
d
=
E
U
i
F
c
u
a
=z
X
-
dJ
-
*
r
-_
t
.
L
a
i
4*
;-cC
=
^
-g^
a,
;6
Y
=
=
€
t-a
O
!
-1_
'=
=
b-
cU
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 131/304
t4ixL-pqI
J'!
^
!=
Es
i E:
9
=:=.<
-2:
:
EEiE
s:2
,
7
tE==
,r
=1
€
;
-
o
.J
-a
;i:;
;
=-=i:5
=
|
L
:s
=
_E
g
;=
=
-
i
'*c
A
=
I
;:rE
E
;
vE4E
z-r7
Es:,=
€
Ei::a
=
=
;-:=,r;
f
.Y
.=tZr -:-
-
-
,=?=E
;
:
-a7
Er;3
'.
i -
a
9
.
F =Sn
=
s
:
s
!-==
>r
E
z:2
E
--
:2?t-=.5
r
r
=
:-Z
a
N
-rs
.L*
i
nl-i/"
V
f<ii-
*.
|
.
l<
I
I
I
I
I
I
I
I
I
I
N o - z ca a
-
-
3
3
i:s
glg
S
FE
i H
*2
:r;r
;.
? =
:i
;
5t
i3
.
a;
-
i
*
;
:
t
.+
31
g
=
i:^
=
E
=
;
FF.
F
a - I q
,a< t
e
- ;+
3
=2
!
o-
J
-a
^
=
?
G
s
:5
= =
H
*s
o
d
5N
+
7
5 5 *
6
r3
-a o
'-
o@
t
T
*
_JL
u
J-
/+
r1F i J
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 132/304
;"
39
:
;g
"2
l,
g
is.*gS
E
F
3F
+
1E
+;s= l*F
a
=
=
=3
F;=E-_=
:?
iI?
:e:
BBFge
i*
i3 ti ?
E1=77z
;
rTi=?
i t
1:;;
i 1
v=
=
7;?7
?.
t-=-tE
:
?
1=
=
I{
;F:"3
*
;=+
:
=F
=
=
9E
r
:E
=
g!==
1-?=
1 i
:-5;3
=
:"
==
rx
.--:
,-
-
:
=*=
.=
*
-
i s=*?
S;
*
?
3
i?
;?
:a
4
p
'
3A
S
=i?
?-
:
i
i€
=-?
rF
,=
'
:?";
' -
"E
=
-3
-2
5
_
-
=
".
-a
:
7
sg+
a-
3
,?:
?
F
==
i.E
€
{-=
==
; '-V
;s1*g
t
-
-
1
-7
==N4
J
=
=
=
':
IG
:=3
-*
i.
.-
;
s
=
;?
:1
.
-
=
9
;
=
F*4
=
:
-
^
'
N
-
+e"=
tv
.^rA
i
V;
'
=3
'ts
-
^=
=
l
:?c
*
-
l=
;
=
'D:"
1r?
!
=
lq
l
-
=
i
rq;
F
X
J
1
"==
+
D
:
*
;
=
e
i.
€4
-
J
17
="=
:
7
'a
-
!6
=
':
.-=
2F
1
.
a r
o
"
r
3
?
-
5
o
!S
-
a
-
i8
'o
'
ts
oe
'L
r
-
!C
=
'.
;
2
is
=
.+
5c
s
s
3F
l
c
-lv 6 I @ t
\=
F i Fe
€ t\
.T-
u
L-
l>
i
i
*
\q
'J
\
-&"An
oo
P
'
l-t*\
!
'
:_
s t
l
!O lTr
Np
^
n
,+!9
t9
a
rn l
b l i . - a i*
-
\
4
[
\
i
I
c
^e
!
'-p
a
;-
l
I
I
I
I
I
I
I
I
I
I
h3c
;tf
?
cIFJ3.?a
.La
I7t
*i
-
-
-i
..
cI
F.+
-I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 133/304
i=
I
C
;
a
J
'
-
!
'--4-
=
a
l-
I
^
l-
:=laa
.
,*,A
.
€
-
"1
€r
-
-a
;
i
-
.l
-
t
l
.
-
,L
;
rd
:c
.=<
ala1
^1-
-
.
"1
-:-
J
-
'1
*J
x
i
_
:
t<
l*
F
I
=
I"tFL
tt-kF
.*
irF
-l-1r*r1
FnttqA\ttio
lD
+]E11lJ
JHIU
I
l-
]H:H
. r
1Kqq
irf+Eh-
1iH
'JLe\
Inr1r1F-1tl-_\
\
lIL
lIr+
€
_
t
:-+
'+F
At__
-
ri
E
th
t
.
{y
t
1
Ll_ITrtHt
€
i1frH!Elt-
:
1
=i?a
r1rr _tt"f1-JrrrtIJUiI
-3!
z-|l
=
r-
-r-s
|<rl€.
-a-
.
'l
.
\
rr
1:
r-
i't--
**
*r
l*
-r
Fnt
l
l'
I
e
<
4
<-
{:-l
-c
-
-n
l*
j
-r
-*
l
a
\g
? ElH[J
-*
Hh
I
I
I
I
I
I
I
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 134/304
C
\S
=
4
F
1
a
A
'c
6eE
i
aa
)2
&
-
-a" A
a
)v
,*
=
;
tE
Lo
rNi 3?
.s
t
.q
';"4
i
'!
;
f
a
7
i4
:
-
cg
,E&.,c_b
=<
J
I
|^
(1=
>
^
=
i
*r
;;
I
;<.=b
t
3;
!^.q
-
=
a
l"
.
=
q
?
f*
-o
s
;3
-
i.s
I
I
I
r
I
JF
I
ec)
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 135/304
s\rTl sI
\"L
't*>
I
I
I
I
I
I
r
I
I
{ { c o z co< - {
'V2F
E=E
-9=3
+
9
r
E!
*"
a
=E=
-E=X
=
j E
5
1
r
i:g=
=8
a i H
,Ez
F
*
?=
A
Fee
E Ft+
+:xE
=2
=
qE
2?e
=E
a
=
-5R
c=F
?
E
FxE
;1
.=;F
6
1
e
F?F
.1Z
=IF
:
c?
aE--
==
F;u
d
;d,
3"E
P
p
E
E
-
-_
aF
4=
4E=
+
r
6F
gF
E=.E
o>-o c ! r F oI
I
II
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 136/304
s:J= t:3
x
;sfrF " i+j=Ev =
2i11Z
i.5 i:ev * ; =E = i.7i?: =
i l I
! :J
c!u .-
t
lr
Yo
o
.
!
i
l
i
l
r l
t-"
*-
b
s
!
\-
IJ
ilrc
re I
-:N
-t_ lg
:le
crc
g v 7
i
t
"
.
1 ' ;r
* I
!q
tN
\ ro ;
.ui*
-
+t^|
.
1 ,
. -
I
I
I
I
I
I
I
I
I
I
rcIl
sc;,::
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 137/304
-1
\
.1
\
.7*J
e
^5NRla
-**
i-r
lA
I
;5
e
N.1
l
n
l
,k
tFT*1a
tit
-96
:LCerc
X-3
st=J
'2.1
{F
X.Ec{A
OFh
I_
<
(
-
.q
' ?
4<
a
==
S
.
s=
hae
a.J
':
-s
E
a
-
:
a!1-
-
'
G
-
l-
.o
j
a
o
=
';
o
/ ;
E
.
s
lsF
i
-
.Y
-
-
.=
-
a
,J
#
!
l
\-s
f
a<
c
<
EUBor
ihE
6
€E.)
.
4
i
€3s
,e
!@
O,*L
r=E
fN=gE
:ve
i.A"
a
.
?
cG
I
I
I
I
r
I
I
I
I
{IF a i Za C( a
i I
lc .
: : I
!
lN
\
i9
,"*
.^
*i* I
p !N-:
I
*
l"L"-+ ->E --li"
o -aC c -) -c 4 o {
:G
!
?*
D
@
L
-
- -
-e
; J
= -cF
=
G N '+-J --
6
_
F
o
-
^ N= =-o,G > * ,
-
-
,*
-
s
dn
-oC
k
;==
H {
a
2
-i - --"l
:F -- .T
T
r
-,
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 138/304
:1
- = 's=H - =
.
k iJ:)-1
\a
: *
'c
=a -c -
-. =
I
q
q = . / .- c = :
q 7 |
, *
r
r i
lU
:1
l
AI
;i l4 t I
c
i-**lrt
i--
-
l- -- --
I1i.
i - +
l"=
""
i
--
l "i i -
i--
L
ta i
! :1I
/1
l---"
i---t-
i_j-
-*
F
q
i-=; -,
I
I
I
-
J
I_
I
I
!IYr<€
oF
oO)
aQ
;h
Xr
il
..=
+
:
!Y
'e
)
o
LGF
.yh
s
+
-F
C
'-
*
o.r
rD"
II
I-|:*
ilzr
I_Ilt-iIl-I-*Ial*iI_It-l_ l*>
<-
Ei
1* ""-
I-
l-1
|==
i---T
l- =L
l-="= -
i-
I
I.
=-=
=
l==
=.
l_-r-_
i"-*=
lf'X
U,JF|c
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 139/304
la$QiL/xBqOe.a
6
=d
4
-Ni
o-
,
:1
.
-
I
Y
N
t3
€
-q
a
*d
ro
L
d
=
?
-+
9
!
s
!
'td
i
=
,
_a
L
l
b
e
IhfrG4
;N
T9*
,F-
|<i
F/1
r
€
-<
s
t1
c
i
*
t
!;)5Ao.a
ic
N
ok
ie
t
,7
r
-2
-r
=-
.r
\
'
I\
r
!
l
l
.!
,
:
S
rN
4
c
-
.
X=O4t_
l6s-c-T
*n>
--
ld
.*
tv
N
*
.a
e
t
+rrg
-o€
Ne
-nIJ
Cx
sN
/t#tX\ *
_-Ld
fS\
r
**-1
= r_T--
i"=,-l
N
,
-1
_
l"___
-
.==
_-."-=H
!s
*
I
I
I
I
IT
I
I
I
I
{C { .J o o z , cor c ( a o F b - -c r I
=E
F
:
?
:o
n
E;-
F
3
:??2
-
==^
=
q
=
:={t-
3)4
2':C
qE
G
:
a
r
-=?
d
v
i
=
4
=
!
F
==
=
it*
+E
r;cE
=V
"1^
4
-*7
:*=
-
E
i
7n
;%
t=
=
:
.R
a
:
+
ts ^=>
i-=
:
e
r
!
;d
?
:"
F
*=
-J
c
;
*
-
"=
4
=
f
a
_
=
r
?=
;
:
=
d
a
-
ErE
T8
=
=
3^
4
2
=
E
t
3
+>
4J
-
F
:
3
=
;
"
o=
'
^
=
:J
=
-F
Er
p
t=4
_
-
3
c
=
rc
=
oE
E
Ea
9
\c
d
{I
r
TI
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 140/304
c
'
i R loN
rr-
|
H
o
* "
B
C
AIT
--
|
i1
s
-
a
@lN
N* -
I
, \
n
}-
A
!r
I
- a
'
E-
U
.
-
k-<
i
F*
-
+
iriF
'to '
N* :
#* +
;$AF I
I
I
I
I
r
I
I
I
I
r
c*5-
\
I
3
.
r
s
c
i
>
!
is
<-1eto
F
.1
'
I
Y
aa
a!c
=
,s@*
d
>
o
v
!
*a
aL
O-
J
c
L
!
,
c
)L
c
=
:
\
rc
ia
' .x
6
"+
61
=
H
C
lr
5
=
!
i
o
x
1-
'
q
a
@O2=:F'fE,.l:s!I
9a
=
o
i
i=a
E
-
l
=a
\
r7
Ilq|t'
qpx:?f=-F
r
L=
:"
.>
Y
-
-
?A
KIa3
=Ea
r
l
-
i
'-
=
N
dr
'
5
,_
l
= r
.o
!
=4
'
,
t
7tFF
I
trr
IT
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 141/304
N
'c+o
F
s
t-
z
oo
rNr*
9
^l"iea=-
J
-d_
HI
€n
lis
Jra
-
^t_l"s:
d
.J
I
o**IIla
-s:-
\*
-,:
,;hr-
-J-
t
&
=
h
ric
z
m€
--
*
IIi
tb\
i=
f*
I
\-s
'.*
o
-t-*
.s
\*
r
I
I
lr
I
I
r
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 142/304
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 143/304
c - a ac7 i o I ;A
"
E3?
-
-.
T
J
t
-
?
=E"6
?
c-
$
a
1
5=
i
E66r
n
7-
4
?
-N
j
f
=
"=
-
: cE
=
28
zG
=
=E
=
-
1
r$
:?
a*E
=
t
-
I
-
-
;-os
+
: =
4J
-
=
-a
;
J
!P "6
=
*
i
A
D
^-
rZ
f
.u
:
i
-
)
=
3
3a 3E
e
N<
i
!Y
-
,=
:
.
-
;
t
z .J ! a ! - I ! a ! ! D ] I
I s a r
*
- I I ! *
c -Ocr r - I r d o
o o 6 : 6 3o 6 6 : ! o 5 6 : i: 6 ;xo
!
I@{
I
II
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 144/304
I X
7
i=
r=
u*
==
:
;-=
r
^
=
*
q
?o
!
^
=
3
-=
l
-?
L
z
=
c=
n
-
3=
E
=
>;
=
:>
=
=
- *Z
:
i
E ,
=
-
.s!r
-=
$r
r=
7
'.=
^
v
'-
'a
=9n
'-
t I
r
=
-a
^--
-
-
l
2=
|
"
:3
=:-?
=
I
-
^
{=
T
t
-
:
|':
:i;-
=];
:=
lr
=-a=
|
=
i
-
4
l=)
r
I
t
-*
==
=
=
Ia-=
=
=-9=
_
=
=
=
i
t
=
it
;-
':,
Z
+
-
{p
.
_=
'===*
=
{
-
:
!
:
_
==
.
=E
=
=
:
=
'.=
7
-=
F
:
I
l1"a
7-=
j
=
i=
=
i
:<
"
!
t9
7
l.
;=
-!
N
-
'
.
*
:-
:
I
I
i.*
:
i =
i-
;
-:=
;
T
i
.
4
)
-
:
:
:
:
a
i = --=
=
=
."
. - -
:
-
'
=
:1
_
'
t I I i i I
:v {
I I t
' iHt I o l- I I I
lF
i+
*
a+aX
9 x |
7"a
i
P
F*r? -
=
*
'4N 3S
7
d
ssa-F
rt
-i is
l \€
E."3
=
:
i :t
=
:2V
=t
t
:"i!-*-
7
4t
Tn
i"
z :-3 r=
I
-r3
-=
i;
*="
a= a
<;€
!
td
;.
:u1;
1
:
E;"+:-?'=
;:
€!n=-=
l =
E
:=
,-
E =
i;E
:a-
=+
?
EJ
_3_
_
_
:,=
.==:=
:s=7
?
=3
d
;
-3
-
===
=
i.=
=:
.:n
?z
+
;=
=Z
"=E=
;=
=d
=
=
=
=
+
;e+s
=
ot3
;
rgsg
;3 E3;=
5
a=
C
i3_*
?=
i;q
.==
.=l;=
.2
i;
s
=*e
*=5
"=S
1
;
=
: E
i :
=
.=
r
lr
:
+'r
*
-
-=
:
:
i
:
-
.
F
fF
F;=
I
I
I
I
I
I
I
I
IT
I
@!jao
r
I
I
-
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 145/304
}X
_
H
e
€
cc
.
l
.4
f
i.-*
.g
-
l:
i
I
*)
X
\*"
*Ftt*|1
tlt=r
:rsr-gvI
st=t=
rq
FttJYAn[dE
tHN
>s>
IfRtl-H
v
Ff_
\{
'-d
=
c
d
C
L
o
'a
?
-e_
q
\
4
F
r
1
-
-
-
!
-
a
n"
:e{?
d
i=X9
o*
g
<
-<
z
;-
6
*,
.4
*
'uE
E
'*u8
a
hE3E" \
E.
-eP
-?
ua
>
r
l
I
I
IT
r
r
rI
t9 { = ao t ca t
1 --
:olN l
:r
B
8
g
;*s
*
F
;
frFE
:
;==
ir
=E-3F
i
:5E
F
;*
r.z
*-
*a
_
;;
s
:_
E=_
:-tE
S
:*=
;
=5
"1
'=
FI
i
*=E
:
n
=
;
I5g =
+-
:-=.gr
--
c
r -.32c i s ca i
l"l
!
t
\
ta
o ro c r -I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 146/304
qg
g
s
:c
:
;rY5
T5
?E
frsqHE
3
E
;E
=F
E
3s_E
!=P
1A
:
i :
F
#
{=e
e
!-
-
"BE
s
*oF
3
{
;?
esq-
*
s*F
:1
=*=q
:
'
,
' -=
=
.
aF
i,
:
;
:I
e
,:-
1
a
i
.
=i S
==
-:;
;3
.-
:
r_:,
-
'r=
;-E
-v
1V3
i
=" 15
':
*?;
; +[:F
i;rg
"8
:r1;{
'sEaaEs:Fr
1+5
e
i
ir =7
?
1i:
=
i3"1
:=
E3
E
6
"
3
"
3=
=
*"3
?
l
i
E
xg
di sa
gI=
:=i3 9-1
,
'
t
= t=
'
:
=
4
a+
;
i
I
=
-
-
=
av=
"7
_
_
==
't=
-*
|
'
r
. '
rm
rJ
U
Lu
a
s
*g
'8
\*Hrfa H -
TG
=
!)
'
."=
:-
;
a
"
J
:J
S
-=CF -9
'-
-
*
! cw
=
-
:
-
;
"4
c
* -+ *
.
c:N g
w
';
I
I
r
r
IT
I
I
I
I
I
c,d
O
'N=OoE
;rN
=
a
GtA
5
CcQ
9=o5o
d-J
i9
5
E
I
.G
4dA
Ocn
€
aU
6Y'-=lh
6
Q
-^
.=
r#*
o
=*€
A
r
l
4
r
i
-
\
a
\-
=
Q
UFJ5U
'1
.
-F
-k
\i
:
No
!
s
d!
*
dF
-
tsih
r
*3,
nttttlI"
tt1tttitt_nttli
tliti\i\L
J
c
E
:
)
i
N
o
N<
'-:a
d
eJ
-
{E
?
.n
;
:"-
-
.9N'=
-
Jcc
\
i
d
!{
-E
*
)
g
*
d
=
J9
u
c
-A
G
'-
€
O
o
j3
k
(gn
'-
o
J
c
)-
;
eFE4
"t
=
JF
ao
oo5
r
IT
T
IT
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 147/304
c
x
i.o
B
-rF
{
.
*s
'a
la
l
i
lH
'
5
@
-?
T
.=
i
;
\
o
.<Nd
E
-
c
e-
d
d
o
.-
=
=
{
t
-
t
t€
L
s
EO
_
e
^
.EE
:
6
.
t
(
(
o
.
'
9
o
,
L
O
khD
r
oq
\Q
*qrl
q
a\-
i
-
o
!
:o
N61
E
i)s
c
Fg
E
idE
;
;-
4E
\nU
N
4
-
I
a
-i
tJ
L
?
2
?
Y
Y
94
4
^
'
;
e;
.5
I
-
,
a
a
>
i
=
-6A
:
Fcg
-s
+
6l=
;X
:
!H
.
r
.Jn
:
v
.
a.
+
*/"
'Io
XX
I
J
:
=
;m
1E
;q
d
d
r
i-?;
>
-*
=
J
;?
3=
E*
{3oou
i
1L
k
X
;x
=
:
's
5
L)
1
f
=
*
i
i=
-5N
E
:
a
?
-
.
o
=
a
:
ad4c
F
-?
/k
-s
o
.=U
F
Es
"F
:
E
E35
=
=E
F
cF
i
IN!E
.
l*
'*aln
jh
F
i
"c
I+
a
-
\
+o
'-.1l
€sE
;
E
E$
*
.
:g
=
I
;
=
;
.=
|
o
F
N
H
3
*
u
?
-
o
i
'A
t
d
,
z
:
=:s
i
5
F
'q
X
a
-
E
-4
i 5
.
sE
!s
':E
E
*sa
E
€
=
t
F
i E
V
i.
.s
.g
E
s
:r
E i-
*3
E
F
= "
*
?
-
!
F
,
:=
;
-
!
*
5
.=
'=
E
=-
- :-
E
,s
.
5
I*7
=
+
i g
'
Fd
i
e
s?
€
;a
7
'u- €
l +
:
;
I
s
?Z
s-12
:E
' i
=
'=
l-=
<
-
l_
€
:
=
==
is=H
I"*
t:€
t
.=
=
^
-r.-
+
"ls
f
i,
r
;
r
9
*
E
e.1
3
=
t
L
=
+
,
lX
H
l{5
b
2ErF
E*
q
r
'l- I
-
J==
$
>*
=
1
'
c
E
s
E=:rE=
.
F
E
.
d
=
c
;
t*E
z=
= l
;
-
E
E
E
s=
;
"=
4=
-?
'_f"E
.q
=E
;=
:"=P
-
=
3
E
"g=E=-=
z
*
rTI
i
I
r
|lr*tl!
IL
U
I
I
II
r
I
r
I
J
(
2
l
i
.
irl r
}_
"
-^-
:
:
-
-
|-
,
<
* ^ !
\E
-
d
\
l
-
'c
-E:1 \
4t
.
* -
z: =a Ha
-*
a jr - t a a
\:_ d t
a *" "=
r
!
'^
=
:=X
a
; :
-
5T
4 j o cz a I c
.
tA
Y l
-o - - - - c
/ \g
rr
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 148/304
l l_ ==
G
:
c?
-
_
F
4
C
_
--a
-=
=
=
7"7
?
"a>
t^
,1=
::-
-=
- i-
=^
^ *
-_
aa
-Y=a
a
=
ta-+
=r
.
_
-
?
=
- -d
_E
!
;
:"3
=
T=
?
.F !E
o
6
=
=
EY:F*
-s
G
c
F
;J
=
.1
-
o
9n
\" |
=
o
-I
.
r=
N
-!
L
**
'3
'a
i
n
c
B
;
4
Y
sT
i- ,
j
*
:1;
l
"+
/
C
5
E
'
E -'c! ', o : :
H :9
a
A E3H
:=t5s
-oq
A
U
Aca
=
o
'- .6
5
-w
o
I
a
i
arQ"
I
_ c * a ;
t
_
|
!
lv
c
rc
l
t_
i
ir
r
ri_
i
!*
*
"
: o1*l
N b n aI
t \3
*J1t1 ! t
/
l
rs
6nh
I .JI ! I I I
r
I
I
r
I
r
I
IT
IT
I
OJEYXHYIi."
d
3r
a;r;
l
-
'
l
a
C
-
:
-l
-
l
-
*I
,--
f
q
t 5
ncL
.n-aCl
-
-L
{*"
.
N
-
a
'4m
E=a
7ar
3-F
T
Tr
T
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 149/304
€,do
cH
teX"H
.
4^*ka@
XOF
oY:v
.
-
L
qE
F
-
i E
a
.
.
'
.h>
.s.
-
a
tX.Fo
-b
#
^<
3ae
o2
-'
,v
'-€
+rH
X.6
6:s
d
"Y
f
"
a
d
pH
PX-
Ze
rB
o
.
'8
€
,s
:0Y
Oc
o
:1>
d
u
;o
-
od
a=:3
's9
5
s
,=E5F
qe
-
3
E
6
6
-
r-
-
.
-F
-
eY
t
1F
H
)d=
N!F
lc
s
to1
ou
!_Y
d
E
' *
o
rU
->3
:
C
a
f*
Y
5
E€
J
@"
.JF
F
.o
IhqA
&
,G
=-
a
n
ud
-=-
-
;^
7=
-
;
i=
Ho
==a-e
t=
=F
b
5=
E
cE
.?
a
*
E
'S
?
,
E ;
X
r
-=
t
Y
=
'*
o
^=
r
!
v
;
i+
5
n
'rd
F
=
(g
s
.
*=
'=
*b
.=
"
'e
€
?
c
.ta
I
:
-
a
d
,
.==
r
"7
,
:
7u
:
.
a
.
a=5;:t
F=2
u
Ei jEEg
s7
8+=
;:"F
g
:E:
E
EE
E
*=3
+
E1g
:
E
a EZ
; z1
gE
f ;et=
l:;
E
E;+
g
r:€Ei;
EE
ts
;€;+E *g
t
:=
.zE
=xiE
1
Eat5
?a
Es
;
,:
:;;
i1 ;5gE
3E
r=
c
aE
3z
E
i,Er=
.
r--i*
ig*o
*:j-.:_
^*
II^t-*+
r_
4
i
I
I
II
I
I
T
I
IT
g i a 7 = c i c
I
I
I
I
I
-
lo
u
-4-$
-
H
'
!
:
d
*5
-
'"e
c
ld
*c
c
?
A
=
's
gP
-3
s
D
-
F
-
a
^
*
r=
'
9
=
A
lr
r
a
1
15
-
a
h
;
=
4
7
o
=
F
-
=
,+
4
F
=
=
J
=
9
*3
=
.61
=
=
:
-
4
4s7
,^
<-
ta
i
:=
=e
F
N
.
==r
F
!
laQ
i
!
-
a
"
-5
;_
N
=
-+
J
a
d
-
t_
I
o "
*r
s
*
t+
.r
$
I
oA \ l;
- L "\
I
]#
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 150/304
I
I
tr
r
r
I
I
I
I
i=
7
=e
-7€
=
=F
S!=3
4
3
"=1
-4=
-
.S
17-79
.=1^
Z
a
!E
"
=
:
iE
5I
Fa=
F
;Z
=
;q
r1
-=
;-
=3i .=.=
fF=
a:=-!=,1
{==
l;J;=
=
-.
1
;=
=
"l"z. =
7
E
:=
\
nd
"5
i
-
iL
3?
=E
+
=Zz
n
=1i = "=
'77
= =
-=
:
!*
:
Ifs=:
i
;F.
-s7Ea
:
=
=
1
{ l
-=
*
=
=
=
.+
I
==
:r?
:
-
=
=
Y
iL
-
-
t+!
:
=
1
1
:
=
=
=
+
1=
=
+
7
-
-N
*
;
-
a
-
i-
-
:
.
!
T
=S
L
a
I
-
1
jl
?*=
i C1
r$ - I* N
-
oX
c q G ts '3 N
Y
s> t3
E
=F
i;
=
^
:
6
Po
w
'h5
c
ro !^
!
+
i-c
vJ
:33
X*-c
^
N
O
_a
I
'J
't
=<
.
!
=
-x
=
*
!
=
!
e
TU
=
c+
F
-5
.z ,L l ir .
-
; -= x
i;:
!?iE;=
* 3
3
:,. i
i,
e+i:=
;?;
=+
a
* :i#
;
l
i:}
c 7;
1
r
;#
;;J:* .
iEEi;I
i
:t€E
*
; €Ag
:?e!5
ie*e lE
5"isE
E
E
Eg iE
d "2?
? r;-5
."
i ;r
r56
:"r
:r
3
;€
Fts:
aE-€
a
E*€
'i
= ,a3
;
l=E
;
;!E;
:
+ "i
;
t+E u
g
$*: E
E
J
;;
=
e
<
'::
e
e
I
E
lg;i E
g
i:€
tE
oUs7UF
IT
r
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 151/304
N'o+-=.
aFq'm
-
;d;
4
|
-
:
^
;
lrS
a
:
c+
*
-a
n
d
t
;<
€
=
-
.+
C
c
c
s
lro
F
cO
?-
r
C
.H
-a
=
l
.4
l
;
:"
c
.+
co
J
eA
r
E
Iq
a
a
c
-N
a
-
Y
-
,
c
r
o
Y
I
Y
-
;
i*
E^
-
c
T
-;3
u
?T?
I
r-
.r=
l
l
r
I
-
:P
E
U
c
i
iH
!
*
H
i
.
!
d
4-4
6-d-).,7
a
co
r-niJi-1
ia
-
^;
o
.x
ak
I
6o
-
.
i
--a
i-
.
a
.
H
L
e
'a
s
r
{
-Y
F
-1
=
>
do
"=
.
-
>
o'tn
s
+-
g
.d
L
fH
C
o
=-
v
'=
;
+
_E
3HU
'
h
"9t
=
-
t
L
)a
c
Y
I
d
r
r
5X
Tok
'"
.=
j=
a
ta
o
=
!1
X
o
;o=
O
ts5dg
-*=
=
-E
i E
E
sir
.*!
2;sEE
t
lx
9
i(J=
i
h
;q
4
o
-1
o
o
o
?
q)s
A
E
g]q gE
4
:E
a
!3
3
c:€
o
I
J
I
d
e
F
-
s E
?sE
Q
,5"X
=3
:
do
6
:o
P
e
.3A
x
-=
"*
.
._
=
JF
iE
7
4F
-
dE
5H
=
o
i
d
Q=
!=
=
rU+
q
{o
:+
6
;vXG
Y
GeEa
;P
-E
6
I
H
b9"
i
.-=
:
-
yo.2
I
.
rJ(c
3
*
o
:
N
-o
i
F
:
.
-
i-
f-6N
:
r
:a
-
o
a
a
-J
:
&
J
<
D$E
<
rD
*et
/4
Eg
g
=S
3ri E
;
; E
:
*s:;
-
::;
,E1
=
;
'?i:
'z
;i €
i
e
E
-!;:
F:E 1
:;E
uE
Ei
;:-=
p
-X!
l*
"Z: E
;
i::sE
EE
N
o
rs
€.
---
'-
-
k
>
6
'aq
'}
e-
r
I
n
j
I
I
I
I
I
t
4?>
2E
\an:b
+
o
c^5
Q
-
idF
:
a
=
=
>
EF A
c
o a
cE
S
= =
L
I*
l
DF :
F ov o { Co{ r
2c
^
c
-
.s
=o t o i I
! :\ ,o* . *
*I
&F
f=
a i
! N-
ni*, u*
d q
_1l**
J -F
t
t*+
l
.i-
ris
rc* +
*l* ?
."*
!
PN
^
s
s
-
i I I I i l*
a \
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 152/304
I I I1
-
_N
$\_
n
.
t-$
.aS?Aq
q
n
Is
-
F
.-F ts
_G\r
i
H
mems
L
N
.H
5
su
+
J
s+
*
; ', I I_.u-
N
y4
-H
,S
|
ru
f ,
.
x
6
p="6 '-
1
'
r_ FLfY
l\
\{
't+
\+
us
J$%
b
ift
q b $
G
T
F t r6f t1r
1
r FLJ
. \s
r\
_+
_Gq
:
.
s
+
l
F
\
\
ln-T
nP
|v <
6-A
S
$**
\E
\
[q
]
\s
I
I
r
lr
I
IE
I
!fc
i-';c
=l
.g
;
-t
:
E
l-
c
_ Fz!
I
l
,d
i r
'q
I
r1
(
-
-^
l
=;E
l-Ta
:
;
"z=
'-d
1
=^p
FE
r,
ir
t
,{2
_ l.
!
3+=€
lr4X
:TEd
I
r
E
)
i
i ?1
,
€
€
A
V2
T,7
a
Q
"
;A=
i
I
4
:p
'a
EE
EE
;X
.
:
aE
&
6
EE
F
R
F
sqF
&
,ar
JFFJF
r
I
I
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 153/304
;*
7
*
I
1hI
t
h
-
t.F.
l
G
I
t1
.{
T
-L**;':L
-H^S
+
$ei
io
**
.
c
c3
p
Hc
cC
R
+
**
.*r
oo
+
-
:
nms
id
I
j-
*o
c
J
NQ
;IN
i,rc
l\
t:
l
rL
:14
i
*1
-
i "o
:GT
:--:
I
-
:Y
LtC
-
.*-=
;-
-
n
,J-*-
-_Iy
.u. ^
^
+
+
4
r
.
'm
cc
",o*1
,
r
*n
**
j -E_E
lI
"
"
I
I
II
T
I
I
t
-
t i I I I I
- a 332 c c I C {
F-F 53=
V =J
=
F=
;
=5r=:_
*
_
r
=
=
r
'_
Jy
-
7
i
-=
l"
:
t
2>*
-
>
=
=
:
-
-i*
.
^'--
;
7 "=
5-E
-
=
FJ;
:
<
j.#;f
L
"
=
.
i;r
-;
5
;1
^
l=
5
-
r a E u
I
f
I
I
IT
r
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 154/304
q
$
" lE
2i=
+
=
jr_
.r
-c
:;3
'
;
24
"
i,
-u
"
=r
*=
?=
3--
=
[
a_
:
_
=
i ;=
;
tI
,-
=
S
i*J
a=
9=
-
=-=
=
,o*
9
*
J =+
t"*=3
--*-
i_
;
:
-5
; .
i;-
.^
:r
l:=
r:
;
irC
-
sJo
-
?
\e
-3A
-
F
=Nc:F
5?e s
vS
6
?T
rLT--
.-
l
i-
t€
*
=x
irn
J
s_
-
$ W
h
*
I
,o"
I
#F
YL
f"n
- t
rS'rr
F
J
f
I-
r
r
!r
I
rI
I
I
l
+
rO
O
;
N
m
dc
=
-=T
lN.*
4
v4
c
in
'- ?-s
*q1
-
5,
*
1i + Z
rd
n\=a=
I
lrol ;
-
rn
.
c
*
c
c
9
.
$
g
l
+
-r
It
ro
|
.
N
"1
a
'
om
,
$r
.
F
.
ro
l-r1
!o
rN
ro
^
t*dd
-o
:
*
:
*€
'
$
'
lr
'
|1
lH
.
l
i
F
:=
'*
-a
l
;
ir?
ld.4l"
7
F.ga
rla
6
+
r
-
i
€c
n
ir
o
t
a
{
I
,
+
+
l
i
i.x
L
rO
_
Y
I
l
i_
q
-_
T
k
'
=
-2
Y
fs
I
i-
I
i
.
t1
tO
a
4
,-
*3
'.*
;-;
F*+
h
;
-
I
t
l
-r
_:
;4
'!
lr
A
':
|
.-
c
&d.5s
=.=€a
dI;3FtsF
I
T
lr
rr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 155/304
>)
'=
Z;-F
pio
iE
oo
oF
l
!=
d
G
.>5E
I
c+
-
+
;E"r
H
E
-
to
4
/d
d
"
H
k -
E
Ec
j
,=O
a
tE
4
iS
+
!L+"4
,Q
;
q
-2FX
E.
6J
a
:
-
-a
h#
i
4
*
s
Q6
p
,
E
a
A
r
o
"1\
NO
F
,
:-
l*r
1
o
'-
I
r
Y
-
-Hi
c
lo
N
+
=A
rc
+
'/_Q
Ns
.
dn
srE<d
q
d
l
r
N
,
-u
3
-^
l
s
$
-
',
-*
k
.g
e
--
a
I
"
-ta
le
'3n
(
l
l
id
d
laC
6da-q
-AE
<Rs:ki
S
iR
$
tr
s
I
t
rfs
I
I
r
4 c ? o b
i- o 4 - q
.
H
H
r_
- t
:{=
1
-lY
';
E H-N
A
ts *
c c d -c
= a f
,-? t"A 7
.3
t1
j
_
t
3
!"
*2-
2
1s
I
,
a i-
i
r .
+
s=
*
4
-
l
c
'
.
l
-
{
l
eqN
N
rr
IT
n
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 156/304
-;
.gd
iGG
F
Fap'Y
oa:n :
=
E
=
;
^
^
1 f
=
/
,6 j
J
:
x,5
X
5
<
7O
*
a
7
aN
J - = = =
o
{
JpF
7
5
a + =
to-
:" =^
slr
- -
- ( o
a
!
'3
N
GN ;V : ;"2
t
a -a
!L
-=
:J-
!
-=
i :=a x:E a - .a
x
: I R
i:Pg
crc
-
l
,
F= IR R
-
.-
oi- -
- 9
.
.
_
v -
; '
;
IN
:
9
r
I
lN
'
-
c
1 '- . +
RTs
:'"
l
r$t
2t-
l
l
I
i
^
j
:
i-
'
b
-
JU
4
rI
r
I
rD
I-
q
q
b
SS
tc=
".-
=
x
.
i
.=
-FV
!
-
^*
-4
c
C
.9:J
-
t
a=F
5
-
.J
S
a
!<-
-a=
--;
i
-
:
,x
q
?
.<
-J
s
-
==
.
-1
r
Ja
'v
-
-
x
=
-
'
d
o
.S
F
o
j
;
!
:
?a
J
-1
-
=
L
:
!
hB
;Ii
cjii
?4
ia
,
1
l<:a(
l
'r
lc
v'F
:
r
tT
h
L"
\
.
.9
i
l
o
#h
X
;{
l
l
rY
aE:J*
a-oO=
s
;"yE
;r
51-?;>2
€HB
r':"s
i*dS
r qj?
' ^A
-
.E
u
'
o
X
r
i"s-F!p
,;3, 5':
.--
i
XIc
c
)4K
==^
I
-
=
a
.__
iE
EzE"=
Ef $s=;j q5
da
F
?E
j:+z
z$-s5:e-
co
eHca
tiai!
;F\FA
I
n
!
rI
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 157/304
dl
4l
4
6
;r';,
l
o
6
--
\Or
C
r
<
--_
d
d7N
X
.+s
,+
.+<
<
.
+
<
)6toa
!CE,J
'1
;'tE
*-
a
5
!
s
is
I
/
=-
'
H
v
t
l=
l
.a
-+5
-r
-
?.-_.-
t',**
t
:*
&
r
.
r
L
r
, *
h
i
lN^
a
l
a
I
.{I,
l
t<;
"
h
tdc
I
l.
at7'1
<
'1
r1
>
o
ll
o
cAN
e#
*
'D
EnT
I
l
i
r
d
oN
I
I
=
>
f
ia
K
c
-
=
i-
-
l*|
:
'.1a
1O
;
Icat
:
':ai
*@l€;-
--
^
*r
t-LT*c
*"I-1,1j^tJt
.3Y,a':':c;
JI
fci
i
J
{
-1
lr-3r
.1
-=
'? %
e
<*
.
?,y+
E
I
'-
=F
U
-
;
0o
-
d
E
,
j
'4K
5
^^
!
L
|
,
6
1
^
!!dora
t4
-q
*
6
,e
L+t
I
I
,J
IT
I
r
rI
37
C =
"iS=
r
__
?I>
,
;: =Px
+1
n<
$
s
-
-P
o
s
.*
-
r
'e
'P
ro
':=
7*
;R
r
.- ;X
F
sD+!
- ^=
-
"_
4
=
:- -9
=
rc
-
.+
-
!
i
rz
a2F1
'
-
!
i
^
:"d
;
.o
o
.
;
i1
*
.
2{
=
*
=
/
a
-
(+
E-
c
laa
-
EE
4
t 4-
JC
._ lN
a
s
j
N
+
a -c :13
H
l-
1c = = a
I
I
T
rT
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 158/304
f " T ; =
,PY,Y
:
=
'r
'
"
i,
':
l
l
r
i
i
l
:
l-
I
l
l-
>
*
'-
|
I
i
-r
:"
'.
>
7
r
*
;-
X_1
-u*f-
4
(
:
,r*
;
a
lr
:
**Jcr
=
.*,"7
==
?
=.s
1=
"P"
s
- :
|
=;-
i.L
=
:-
?-
: I-
I
r
l
\
-
c
t
l7"11
c-,
,
i
:
l=1
._1
l
\
;
(1
-:
!
\
s '-
J
G
" t
F
l l
t
r \t !
G
I l*l IN
I
r
r
t
r
,F
1
F-
.
a
cr+
;l
=*
cn".
>A
-cl
.-t
ts
l
o
)
:r
?-i
,"
r
ta
i<' k
i
-|
*
l-
(
_I
--'
"
d-
**'
-r
atIl
A
'o*cI
ac**l*
_rl*rL
'-j---
^
F
-
r"
lr
:*
l
*r
a
i
I
rN
rc
t
i
Nn
a
=*
tiri*-
.IiI
la
a-J{
Xrrl
*"*"
-et*
*el,
:^
*-
--
**:l
a
-*-a-+:+---t
'J?.=E*t
q
i
*a
:+J1
lr
'
t
4
6|F
:
-
c
.
t7
t
>
x
'
]
7
l
'-a
i
T
.
tz
'2
n
i
-
?
.d
H
z
3=<
crcF
x
I
T
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 159/304
O
'=
.==
=7
-!
-=
=O
.
-t
-=-
I
=t
-
=
-
-
t
-
A
=<C
iE
"==
;
!
o
a
-
'r=
c
I
-t
=
-
-
'a
=
j
=
r
.
z
<Cu
=
F-
2
-
!
i
=j
==
==O
7.
=
*=
>
i
la4,s=
:=f*
-
;E
3
-=
;"
=^"-
.
3.1
=,
-
-
-v
v
O
=
=E
i=E
|
=
rq
?P
e
:1
*:k
)
'-
J
-.
=
r
t
--
',*
€
a
-
,
6
:-
I
a
r
it
=
I
I
z:
;
L
,1
:
1
-
ca
;
r
F
|
i:
t;
;
l.
l-
L,
,
*
t:
-g
;
:1
i"
t
--
t
!*
:
:
1;
::1
i
.
'-",
.
t
- !
"
r
i,_
,
".
:
i n:
_,
l::
,
-.
: :
o
-
5
*-
-
{
'
z
-
,
-t,-
;.
-r
.7
\1
=
'_
."
.
]
l
-"!--
rE
.
i
'
!r
!
|
,
q
a*^
|
]
1
i
irT
4:
"1
-
=
:Y
t
=
":E
-Z
i
a
r
:-E
^
"
ta
s
T
^
-1
-
1--
r
lL
ar^
-:
;xi
d
I
I
rI
l;
I
I
ttr
l* t" I I II cz I 3 ={c i c 4 = =a
I
r
r
I?;1E
s
::-
*
;i i
:=
=1
I$
=
=E
i *
:!!g
t=
*
_ +?i
F
;=
:=1i :
*3f;s
-3
i!*1
E;==
r:
fE
i
[3
r=
:
=E!7! *
s
;
,e
i:
l;
gs
1E
;*i:
E
i ; :
:=;e
s; =
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 160/304
I
rT
I
I
r
ia;;E ?=Z
e= =
z
I; ;,r *
lzrr 1
i1,
: :
g
it = 1=z
,+
;=
i;1
Ii,;
7
vl,
e
E=
;{l:
1
rzu=
t; i. -
:?l;
3;EE
;r ;
;F i;
i :
i l
?
itc3; I
E;:
rg; 1
:rE I?
g
7
1=;
-=
=
$
z1lt
=t;
i +
-;t
t E
F;
r*E
;:=
F
;
=
:g=r=
,
|E =
=5
:€
E
t?
;;*
tr;f
+
=
'i
;*
l:r
,
? +
;; i:_
l
I;r
1
s-
i;
;;e
*rSi
i 5 2
i*
'
E=
T
E:=
r
u
:
a
:
cl-s
v^
=.
l
a.--
_
:€h
:
-
*F
-
.
1.9
o
=
v
o
^
N
"ag
=
1
'c
3=
E
sF
T
OO
's=
'vE
:
*i
*
v
v
-
t
)t
.1e
;da
,
5
=
ir
sb
=t
*
-D
.
=
ih
rx
-
r
A
+
d
-
Ls
ao
_
!
j
-
r=
":
n
l
rC
i &
r
ec
-1
:
N
N
q1-*.*
e+t-q*":*6
Ii
AFc
ca
ov
c-
O
l'
ln-.
I2
=
.=
;J-aN
'F:Y
!
?!
:1
i=>2
v"s
o
-
k
r
H
<
C
a
q
r
lr
I
l)f
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 161/304
I
taro
I
\
!
-r
;
Ia
c
1
1
I
-:
*
.
F
r
3
<
'I
--
i --F
=
aA
'-
a
r
t
c
F
lr
. I
l*q
r
--
a
dr
,
ca
o
t
-
C
i<
I
*r
i
r
i
&4
IF
iL
N
\ie
=
,*
v
;-ra
/4
r
-
I
5
r
,4
to
,1+,e
Jt.n*xi.
:.
{o6
,*
N
r_c
:
:
|
6
h
,
ra
J
.1T
:
*c
--
*
i
-
I
lc
^T-"+m-
ctn
t1';6
-ji
._la
.-:
l
)
"*
"
/
.
iF
:.
+cl
F
a_
l-i
'-:*"-
-d
*
: *Q
ac
I
IT
Itr
r
lr
r
Ilr
iJ t d ^ i a i =
I
I
-
-
Is Y
l
=
si ;=
t-:
1
i 7
s t3
?*;i
=
i 1
*a
5
*F
:e
t==
F
o
=
F??
F
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 162/304
T
r
I
r
IT
I
T
I
: ,+': -J ; i
.
^ t
::lf
'i;
r;1
i:
€i i
=
z=
l,
*o+E
l
E
i
r;a
Y
ir
;:
!:
=
3
i*
I-
D-
i:
i;
:E
aE
cs
?
+
F
*
J
F
I t
* tcl*
E* \ I
,* I
!
l
*1
G 4 f.4 & 7 3 .q
r.?F.
:r
ra
=
_:
:-l
"*
-l;
::
HtNN
.oc
LQ
f
!
.d
:H{
t"
=
u
!
-
'3
n
th
q
<
d
tod
.ZL
=
ddnl
'
a
i;EF
I
ia
i
;
l3
x
:!
dB
:
:
:
';5
3
:
F
.c
o
I
ir
C
|
Ii
c cq
i=;
i-'r-
.=
1
rtS
,?
,
;H
-- r1"-
l;i
:r
-L:
E*
z "?
ir
;;
$-r-
=
j
:_
=3
l* I
i*F+
i_
-=
*
,g
l-
i
i
r
E"
;.I-:11
iE
.=- r
*1
.rE
-;-=
i--
i=
i-_
i_
,
is
-rl:- -
::!
-- ,
_
_
_
i1
I-' :=
=
|=|
I.
o
=7
n
I
I
-
lE
|
|
i
;"
ErE
__
_
i_
e
_I::_
T
-
IT
A
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 163/304
tr=
|f
t1
- .- j ;-
r .; ==r
+r"r
-
L
-
r
*--**r.
-",**-
-*s1
-*
!-,
r
.-=_
E
ri:L-
-- ---
L-L
" t *t" "t* =." -t",j .
-- i,-=
-_
r|:--- t
- t-.-
cn
drIi
4'd
t
.
R
C
-n
-
T
,
l
|
._
^
_i4
'
'a
3
.
=
H-
_
L
:
t+r
E
-
-k-=
.v
5
s
daZ
3
Y
:
i
+
l
+
d=
+
a
a
Y
C
H
e'A
;---
-,- T -
|: :
:
,
:
.3
---_
*-1---1
L
t-
,-= i -
=rr ==
i ==
-1i-
1 !-
i ,-
-1"* r
=
_i_
'1
,."_
i
I
i
i
i
I
1,I.
=
-
= = =
- ,
i.
-= r"
I_
*
-
'__,_
_
-r-o
=- =I-
_
--L
--=
=
/4
.
-
.
{
|
Lr
L,
i
|
|
___
_L
_
-_
__
-_ ;_
L_
-_ :
;r
-
Ir
r
lr
atI
N i a c2 C : c
tg 3SS
+,r:EA'
J
=4i7 5
;
;
-a
g
;-4
\
,
ts
-
'
F
i;;
{
a ==g
:
:
:=9E.a - i i*I-= =3 i;
LTT [-l;--
-"
:__
_
__
LlE
-
[-85
=
-Lr-
--
FtGf
q
--T
E
--
L
f-_."
E
,,_
:*Lr
1o
=T
-=
E =
f- :-*
l-
l_
"
_:
€N
E i q a t${I
r
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 164/304
'!
tE
3O
Ht
i;F
f*Hi
l-a=E1
*f3*)4 =
'$
?^e-6
-:P
v=;
F
NrNrS==
i
;
+
-
Z
=;=
73
ir3*;g
**
;{
;5s
,_
-
*
.
-
-
*
t
{6
-a
-
:
z
t3
=-
',
(v
;q
;
',
..
.
a
?
s
p
?
i,
S
=
=
):
,*E
=*
-;=;
=
>
-
S
-
-)1
;=3
:";:
$ 1
*r
!T
i,
l:
fF :
:
c
3
A
t*
e 4
l--"
i- - i
l-i - l-* [ F
-_
_
_
-
- i:T- ;ir:",
l
i- -
-a-
IF
[-.l-
L_irr --
,[,,*T
*11qEJ
lJ=,
d[r
|;-!gL-L-
-_--
---T
I
=;1
'i*- l
l =
FT
l-
-*
]-
-T-
I
_ r_
_._
l--r
,
lL**1
1
l-
*T
T
l* l--"1
-"
l--
--
l:.l";=
,
l-Tr-
-l-
1
-**1
-*
l-
-T
T
-i-
l- -*q*-"
Is
Iu
I
I
I
l-
; t-
=I
l.Tr
,_T
l-
- r
=rsT
l_
_1',
*
lr,lr
lr;
i--
l-1=
-
i- -1
--
L
I,l:
-
lrF
r
!e
r
I
:
I
q
!
-
I
o
I
l---r -
-
htKLLl\
I
l.
|
\
I
+
+
-1JP
e
Fy
tV&
I}
I_
I.
f
r'-
C
,J€ta
-g
-**€.d?-:
^IEs=
dt9
-
a
-o
'Y
?
._=
I
.
,^
*
,
=
nF
*=;=N
@
OLn*1C
*^
l-_.q
i"
E'-
"
t_?
e,
:Yr
rF
I\1
'+FI
\o
uI
.=
i-
"c
;r
-
a
J
=
5
,n
i"
.E
.-t=9
.=
'xN
=
d
"
O
)
=_c
u
.*.=
i:
4
=
--
E
=
k
-
-
,*o
5
r
.
e
c
Lc
o
-_
c
a
o
5
!
o
d3=
C
*
'nN
',La
=E F
*
!4
b
E
-o
!=
4=
a
'=
46
t
3
*
:*
3
7
=
4
N
=
=
-
d
X
X
i=E
E
-
!
J
3
t
l:
i ?a:
=a
-
i
*
-
-=a
* - ,*
t>
-
?/+yzE
=zE
4
t
N
*
:9-3
FN
.dt=
5zF.=
$;
N.a
u
xe,
r
I
I
J
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 165/304
/&(s
Rt
I-q\.{
-=i"
€:r2.Eqa
u
+=:-
?
L
u
-=
o
=E
-
:
-
NJ
Ea
<
c
c
e.9
=--J
:
=1-cSvJ
s
-
E
:"3:+
.
*54
.4Y
.;*"
eR
€
i
*
+
44
-
-
,
4
e3
.-
x=
Jd
.
-
+
,
36g
z
-=
!6
.3
'-F
=
-
e
> n
7ZE
.4
c
a
aa
-5N
b
+Y
*F
;
N
i
€
o
-OJA.
a
=
tcN
\
fFiF
**
:1
*
S
s=
:=
!
;-
I
.
-
)
4i,?
Z1
I
;t
:
=
;aI
Ir
-J
-q
:
;=
.E
iF=
=
i.e
=
,9
a
:I:
n=
-
-
:
!
ET
:=
t
F:=e4=
v
.
:1
-
:
a
;
?
l
-=
3EsF-=
a
:"<
=
=:=
"
.P-gn
;=
=1
5!Je
;
:;
::;E
-=
EEE
i i
5Ea
"*
?
:E-"E
.=
:5E
3E
!
"EgE
=
*7t
I<
Hl{\
H\E*
LrH
r
r
I
I
r
;
3
I
I
g o { a 7 i aj o
i E;
Sg*
=?
tg
ir;3
g$
;ca+
; 1E
F
g
;
.i i:
;
1! ;
ii
!F
iE
F*;g
;
7, 1:
;
=n
*r;
*
:
e
;a
s*
-q$"1+
;E:
"Ery
,L ig
g
{JJi+;
{ aI
r
r
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 166/304
g
E
r
r
i;3
i
l? i;
1
iI:r
f,t
n,
i re$
ir*
i n
:-+
*ii: i:
r E e'1+
ni o
iE.r
,-:
rrr
.r=
;t"
?
,l;r
r-
5
H
t-
€lE
;t
**3
rE
i
t
+I+
S
1= , *
* =
:
,*
*
'lg
$e+y T
:Fi E :-i-
i ,uH
-. i.+
Tf
i :-Ei
3
.
e
srFs
I
r
r
lr
r
I
I
r
I
: r
>
(
=
-
i
3E;
i,*=
1::-
:s
r.3a-
,u
E
c
:=
E
i=
:T
E
1
n
T*
:;
oiE:
:
;z?>?
:
-r
g
::t:
a
:i.=
:=;
;
=e
;1: :
/
-
.=
g
!r
=
=
FUFD7o
r
I
r
i
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 167/304
a
t
ra
:
.
h<€
:d.t
?
f
E
=E€
;
:d
:
r.
4:
u
i-
'
-
$;rE
€:-
i-
:.:.
;1=-
+;;1
i
€
-
=-
*
:
i ;
l
;"i .
;=18:=
i
s*
E ;j-=
7
E
i
i=tri +
E=
=
E
jFE
*z3EE
-1
J
::
f_
E
;
"_E
i E'i *
Ei.=
=
=
1:
,
:{
=
:1:1si rEs
:+n
!
€-r
i1
+
F
7
;;+E
;
sa
111
5
j
=
=
;
B
e
-
L
r*
aH X
g
/--
t:^-
-
t<
:O
+.
*
i
'v'
i
i-
c1
EE
*
:)*?-\+d
:S
r
<
c
-
i
|
=
a
J
r:r
I
i
l11
!
:1
_-
!
.
-1
I
I
i
x
-
l
iri " I
:
i
:
.
';-:=:{-
=-
!
-vicc
r=
F
:
.
-
J
i
a
*
-
g
4
4-O
L
ld
E
'=
*
i=E
'
>-
?
f*
,
'cF
'
+lei^
,'-aa
FJ
C
aa
5
,
-
>*
-:=
1
,
Lc-h
.
r
I
I
r
I
I
Tn
t r aa ; a =
3
(5
= B=
F
-3.E-Y
.?Xt*
F
-
E
.-;
a
rL :h
:
e
N
* p
O
NG
q
-
Q6
5
E
1
.
D
\
6+
-v
!=f>
J
o 5
$eG
a<
s o
*x
3
i"
Z
o
p
Erc
o
€
. F z ;c z
\=
-*&I-H
,* F
l* Ir._
l-=#-v-
I
f
r
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 168/304
+:x=3E=
F
v
.P:X
t = :N ; .
5
) n
c
.
.;
l
\ j o
io
:
t
lC
F;1
:
y
f
,*
!J
|->
,1
c
:
iJ
'.$ /
7
Y
"T
f
]
:o
k
V
c
p
Jr
Y
L
'*tI A5 0 'f
?
N*
Ns
nC
r
I
tr
tr
I
IT
I
r
-u
'
:
1
i1>,
17
',-
4^-.
i:E,
Y
.|
-
la
i{
i
,
<
i
i
a
t
aJ
;
i
-
lJ
t=
*a
.t=J
xAE
t,::c
f
I
I
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 169/304
.
:li
rr<
€
c.c!
n
T
I
I
r
I
r
II
{ 1 cz o I
:+
5P
q
-o
=
o
-F
q F
A'/
l
9
r
--
-
,?
9
-
-i
l€
.
l
i
i ;;l*
o 7 ) ?7 j 7 a
7 2o
r
re
! A
rI
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 170/304
T cF.-
':
3
{j
-
)
i
<
\aP*5
l
]
l-
l{*
3d
i
J
s
:
:=
- ?
i
':
. z
r
l
i
tJ
_
i
r"i
l
: * l
rc1 i
% I 1 .
A
"a
Jt=
sN
t* tJ t1 tJ
t Hi-L
'\ *
c
IX
r
r
I
I
rIT
.a
i
E
-
c
.E
;
g
"
_
l-
r
j
+
;i =
+
I
l
i
-
|
I
3-=
-
i
-
i
:
=-
5
I
l
-
. 3
*l
e
xd
+
C
1
<
i
J
i
.1
i*
.x
F t
j
{
d * r
i
d
$ 4
o
E
i
5
;d
"
-€
\
q
5
;
iqt
o
o
€
EF
's
r5
i
d
€
E
;
5E
a
3
a
bam
#tttlttlt-F
k
tttl*l-q
*kt*
H!€
,dQv6
a
:
i
+
> 5
tN
rE
'-k
:
4n
3
-c
i
!
:
'cS
t
o
I
.
d
=
rZ
+
q
*
o+-
^
)
'
!
E:
d
o
?
\C
r
'r
ta
d6
'.
i-
1
;d
*-
j
1
=
e
q
-
tL
'
H
d9 X
o
i
+ro
"
'
=
ta
NSu
cc
\-s
F
** o
.{
lr
*k- *k
\
i
t
'*\*
\
s-
i
I
0
I
t
s
i
*k
ki
-1
oN||
I
tB
t\o
i*
ra
I
lr
s
I
l
t*q+q
52JN
r
r
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 171/304
'
i
'osf
.sw
Y
:=
Y
e=
f
'O
)d
:
1
ta
\
ro
a
ua
t
f
t
*4F
i
.
5
.5
;
--o
-c
q
F
T
X
E
"
;
i
"1
I
3
';€
r 5
l
*.
<
:
iC
'd
I
'<
F
,A
Jtr:
=*
tE
=?
;
E
l x=
r. =
.F
\--e
'o
'rL
=
I
5
k
!3
as
3
:J
:
2a
:
l-
c
:*
i
-1
=
-
iz
'
:*=
i I 'h
=
1
€
!
* q
*
)
-a
=
ts.v
1
,a==
=
F
c
..
Z
.
E
i 4
*
E*F
>
o
:
.E
xg=
:"
.
s>
i
e
2
9
E
'-
i"==l€
'eB
ea
E
.
.
=
'
!
;
€
i4u
7
€
5
f
-|
'=
r
,c
;
i.
r,
E
."o
A
:
d
F
----
;
-
^
i{
5
-a
sE
a-
r
;
y
,
?
'
i
-
;
e
r"
E
-
.
€
.=
,
2
't
.
-
5
I{\a
I$
,,E
E?
i
E
rua
,
.
e
f
aS
ry
aN
\o
s
i .o_
.o
t
l
|
c
:
1
3. .;* g
_-_
r
i-
r
/E
g
,
iA
S
3eE
=
,
.1z:
i
AE
4
rY
r<
.
:!"-
2
-5r
i
q
E
E
i
:(
':
i:
sE
r
N
r4
:"
t
--
d
"
E
1
Aa=,
E
;E
€
g
3
fr
"E
E
\>*H
1tJHHfHH-1l-
1
-=LJ
F<Ft
1
CIIIlHFF
s$sE-h\-\J
1HhF
K
I
r
Tn
-
n
r
I
i*
\
N
/ i -r
i -*-*
'a
/-
-7 j
.aa
,
t"
lY, i :
i-
a 2 N aczi c
:n cG!*
?
j-h*
F
:
rnl
+
is
X3
l i
+
:
i
{1
/
\
a
-+-*
a
:
lq
=
1
|n
>
,
a
's=a
i
I
!
-
i
I
)u
i
ra
t-H
;
-
|
l.s
=
I
|
*=
.
}
I*
:
i ;
l -lr
^=
!<
':+
;
l
I
I '*
-
D
's
l
I
JJ
J
1
lr\-
!
l-1
J
I
la
i
ILJN
\
j*s*$
-*
I
-
i
i
:
IH
-
1
IHiF
I
I
i
*
--H
lN
I
t f
=
o 2 i a{
l-
=
?
-
-=
7
-
X
lJ
-
=^
t
^
1
^
,
;"a
Ts
-
-
.F l
aE
tF:?
I
I
I
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 172/304
r:
t
t :1 .=-
; : I
rr
)
lv F
:
P ' >
l*'--
l
7
oA
i
r
' :_
;
-
c
!+
f ,
-
;
*s lv
=3Z-
a
E
=
= =
=
==
t-
^
.
4
-
r 3l
--5
=
Nt
a
a!
L
>
=
*L
ic
5
a
2
-
=_r
-
.
C
=B!
a
=
!
P-*
i
p
.!
**
i
u=z
=
N
. D= =
: i
-
oE
+
.=
=
ia
-
Ets l*r
2 :- J= -
_
=
,
i-
,
F
:
"-
--=
'-1
-1
t=I
i .
t
=
t
- - l
= i
-
r
-_
*
€
I
r
r
T
r
rI
I
I
-
ra<
fc*
'
G
:u-r
*s
S
t
a=
s
\3:w
o'
r
+
=
l
9
I
E
l
*
rO:
t
3
o
o
l
+
-
i
.*
u
-*
*
s-a
c
t-r
O
rs
-
;€
c;
.N
t
,=
:
r
a
7
3
.
C
<
6
c.=
,-.
a
i
x:*
*
-o
:XE
!
-=
=vn;
-5CEc
zFz
rq-
Ll;
i1
X
-5
-1,rcj
rc
1
i
-aI
i-
a+
4
?/
-ri.
ii.L
qFuF
:1
1_
A3
I
-J
n
T
t
T
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 173/304
o
-
1
c
.cD
a
=
-
iJ
I
=;
a
>
N
-
^ '"c
l.-1
x
:;
Ir
.{
.z
i .
=
XF
.
=
a
ttr
._-3
z
Cf"8YO
*a
H
^
d
-
i
^^
N
r
?
r;
x
'9
;*er-
.
i
-l-
r
c
-o
-1?
Fi*€.T;
1
l
*?I
,
t
"
a:
'1
.a*{
I
-F
l
*n-
oo
it
+
;r-
N;x4
d4
.*
o
4
ITI
q
'
!
m
,+'
eE
-
I
.+
F
-
.2
N
.a
,1'
-t!
--1
l,E
l
:ii
{4
tl{+F
I
r
I
T
I
I
I
I
6
E-
t
:--=
P1
:
r>
x=
5
-)
-n
-X
l
\
L
rL
c
' i
r
,
i
I
I
)
-
a
.
i I
I
|
-
J
'
i
I
-
d
I
I'-
i *S
r=r-;
!
i
.
a
i |
|
=
=5
i l-*u
.J
=
-s
t
]
P*
t
.
iH
-
c
t
-
ls
.g
I
I*
.
"3rc
!
=
i
iq
-=
I
Is
-?
I1
"=
-7
|
r
e
i
|
|
i
f
\
lP
P
*
72
,
1
l
-
,
,c
e
'
Y
!_ ;
=aI
-
-
-
: sa
4 ; a z : r
1 \
rs
t t l tt t l1I1
t IFt*t lt t t- t t l=I t l: lr l l: tta tsI
t l t_t |-l+l.=I
I
l: i: l= t_
tF t1 Is1IH.n ln
*E i tF -#
j 1""
-
itii L
i-i it i -*
-
i*t-
ir i
r
ivtA id
I
i\1l\ i t
r
f
l
I_i ls t l_
<
l= i!
?
|
-
o^
I
l*
i i
*Lo_
i l I
o z : a t c \J
- 1 +-- {
* ==;-
- l.-="
I
I
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 174/304
l;-T+1l-=
.
|i\-
TT"T
i i
-l=- E
JJ
i {h
"=
$ i
l-
:
'-
-
-
HE
1
rr{
lra {
rqL
--r=i i_
=
-
'::i=-
;s=
.:===:
-:l
i ==
ru
i =
=r
l---
-
I rr
I
I
:
tI
I
I
FFFa
$
'ru
I
F-1
Ft
sH
\H
c
'-E
-+
f1
\
i: {L
q
1
ir-_lrl
.o
\i L+
J
iL
IN
-I
oC€f
rF-
l
ac
r<
,
ll
'
-<
-*
oo
'i<
U
rJ
-
zcN
F
T
l\I
t[-*i
o-
*-lk
+
r
r
T
T
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 175/304
roiF-o)a.
e
.
G
E=
Y
C
j_ry
=
=
t
o
rr
=
:
i
=
.
i
:
l
I?
q
c€o
o
E
.n
={
R
:
a
.
q
^
=
:
T
F=
'|-;
, '
-rn1
F
l
i
u
7
\
i
++
=
. -
,
?
i :
- F .
-
_
:
_
?:
:
n
€
"
+
>
t_
_
ly_
S
r=
l:
:
l
o
N
9
a
n
*
'r
,
-
Et
;
5
:
>"
i-
i =
E
=
\
.
':
.X
. i=
-
.,-
--
I=
r
-
.
-:
>
"
I
2;
=
:=
=-=
j;=H
r
i :
;F
s€
3
=
'=
'!P
i =
:c
-4
O
-
.
:a
L
=
=
-
c:
;L
-o
7
!
L
|
\.rs
r=
-
:
-+o=i;
':
-
!
-+
E
'a
-=
|
xY
i
E
a-
.-
-- i
;
,o
-a
l-
c-
Y
i
i
F
;
*-E
€
^
'a
.
'
;<
-
o
qC
=
s
,=L
t
T
l
ia
.=
-
E
a"?s
.
=
-
'5"=N
.n
fR.9;
l
'-
'-
/4
o
i
l
I
';" .
5E
*T\
=
:X=
t
.=r
itF2
\-
I!
)+
.7?A
.
!a
@
=
ry
.d
i;>?
>
:EX
P
X:
6
'
G
'-
-
E
=.
€
c
BF-
J=
,
=I
9
'J>z
'r=
7
-
uEr
Ecc9
."e
i."=5
€nI
is\€
s
I
T
I
r
I
I
r
:
(
i+ ls l- i. ii_ i\ i I 4
J
1 J t* I i I TI J
--=i?s=-
=Uc
j -:-= > =
F
;4I3
7 ; =az - ') 3 ; I 7 F
i :7 c
t t tJ.
:
^ t -
G
C r r-
:
*
- E
- ; :
5
"
/
e
-
4
€;N
a
:
gsx
D
=4
b
-
4 ;
:-F
1i *
are
r<s
l
3? !
*
a
"
"
=
\c
r2 l
\
g
+
)
i
J
L
i c D 3 g -
3 p
o zN a J
. ;
rI
I
r
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 176/304
^
e3
F
*z
,E=
ie
rT
:xF
:
=<
_-
cg
X9
F
\
-J
.==
g
X
:3
:1
!=
2
J
.D
=-=
n
=
i
i
;a
:
l
=
.
i
l
:S
-
;
5
iT
,
,
'=3
|
l
j
p-
4"
i
;
i
=
t
t"
S
.-
-1
=<
==
-
-
+
."^
l
-c
[
; *
a
i.
:rrE;?
:r=
Z +-
+-
*i
H
,F
==F
ra
I
I
t-
l
!
oJ
I
r
i
:-
r*
:r
o
b
" :=
!3
I
|
:
':-
-
r- r
i.
*=
=
,-ir-
-..
r
r
l!
}
L2
Z=
t
-.^
+
+
=
t
"-
=
2
>
--
=
rs
r
d
u
A
-i=
-<
s:
r
;
1
l t
ir=
u
:
r
i
I
a
-J
;
'-
|
-
r-
p-
u
58
i_
;iF
5
h
i
!7"
T
j.
i
s
._c_
+
"
7
i_
G
F
c
5
:
=
-
a -
-a
.
:
=
r
:
o
=r
x
q
;
7
:
3
a
^
-
=
3R
1
-
f
F
T
I
r
r
I
I
--
I-
-
-T
zcn:a
I
-lz=>=c:r,:':
I
I
r
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 177/304
"
rF1:I
tl+II
-
F
<
_
,
$
I
I
I
I
I
I
J : z +
T ;- -1 i : j
'1
)
'
? D * I<
=
:-
=
>
-
-
{
*>>
-
N -
-=
-_ - :
-
i
-
7
.
.
t
-
-
:
r
,
.
.
1
'J
:
:
.
:
l
iv
i- , t
.
\ =
j
.1
'-
;"
l : t* =
I l
;r I \- t t \ =
>> i
omg nm gm q = 3 m
mTnm: -
1ccv= ;1
'
V
nr z "m 2 3 .J g
I
I
:r
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 178/304
*E-?
'J;=r
z
i;1
==
,-=
s
=e==
r=
--;=
=
.;s:r_
::
*7;+
n==?
=
=+!
:+:
i *z=uS
a==
,2
a
e;1=2
=
;=
=2
;
i==r:^
( -t=
=
€
: =
?
=
,===
i:=
3
v?;
==
l:
F
-:
?
=
;
7
i:-? ==
=
2av
g: ;7
a
=
i=€=
3
a7
==
:;=
1
= +
=1
E
3
:€-+
F7=
r-;a
:?:=;
:
==
.
:. ;l
;
:?=
;-
=
-
?
-
J
^^
'==
:=
:=
=
?=
=
=(=
;7=
i
:
=
)
]
l=
=z1
:
?
=
==
:
=
n
u
t
-
-
.
'
-
-
-
-
'
-
:
a
:
; I
I
I
I
I
T
I
I
T
*F*
\
/FI
ar
-\
I
{*:
';2
*u
';,
i
o
i
.:
.=
>
lo
"=
'"=
a
-
=
i
-
;3
,z
:d
.=
:o
'e-
t
:-
'
-
-
i
:
e
c
"
.
q=
=
-
:3
!F
/
YX
n
E'1-
i=P
-
i-
9
-
->
Y+=
!=
^aA
!
aY-
!=
c
-
i
a
=Yi6
r
aJ
uL
!
4
o
c
E
t=I
5e
=
t
1
!
^11=
-.
tFF))!
,.-+i.E.a=1+r,rE=1===-t
-7
.
' =i a.=='.=;"?;'::=:r==
_
?;12
I).a
I
I
I
:
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 179/304
=,r=
j +
.eE
=
=
N
:
>
2
=i J
"?
>
;;E
E s=
;1
a
=€E
trE
i" :s
i,rx
-=*
::7E
i E
E
:i? ;
a
E
=
Z
E
3
:vE
1
E
i; ;1
=i:;
! ;*
i:*
:
i;:a
;E;:
: s;
s
!€=
-
1
4
'=
';
'==
I
**'I
N
JN
5 ;+=
.:
J
,-
.-
zi
E
z;a
;
E
=
z=
=
=
6
5
E
'd2
E
't
:=
,
.+
:z
"
7
-
"
-
=
i=
'-
a
-
;
=i ; tZE,t
;=
:r==| .=
J=
j
.
=t
1A
'
=
o?
'=
r
:Z:
:J
=
=
.=
3
:=
-=
;?
=
.
t
=-
.
1 '= Z:=
i
;j.
=
!
=I
1
a=
'-;
. z+:-=2
;Z=;
i
=
2 ==
i.
,n)
z
+=
.1
E
_r
:=V
tZ
j?=
;-z
lrc
i:-
7t
rE
;-==
-
=
a
=g===1-z?
?:=ErE:-
+
a=!€
:a
Z
1'=
=ra
r
a_=J
:==
;E
,:
r
=
2
1i 2
:-
'.1
1
=
==>=
=tZ
-
i_
- -,=E
=
;
=
=
a;-_
"=r:?
=
JN
-=
=
=
:+Z
.r+=
z
=
=5
n
i,1r1
izt
'
+
=
7
a
=
I
I
I
I
-
I
I
I
i-t-
Y
t*
r __
tr_
_z
|
|
F-* $J
r
J
r*
_-
'l
l*]F
j a aj b
i-
\ id
i = ca 7 z g a c C : U
-a ;D
o =
-oC
f
.o '= = - -c
:
= .
JN -
=
;
7
.a
:
=
>
e
:
a
i
-
4=
T=
- :-N
-
:=
s-a
lr
-+
=
.
D
!
-
,
-
-es"
ts
a
;
^
E
-
7
J
.<z7
<
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 180/304
r "r--
j -
I
T / -
2
=
-
i
=
1
-
-=-
=
=
,_-
-
a
'
'
a=
-
i:=,r1
;
c
1
+
'-=
=
=
=
==
-
=
1
.
-
:
, '?
=
=
_
=
a
=-=
a
==
a
"r:"|?
7-
=
4
=
:*
=E^=-
=1
!=
=
!=
-1a
-
=
4==
!
=
-
'=
2=
=
-
=
'
-=
=
=
7
a.
=
J
a
:
L
=
:
=
=^
(
=
_
:
=
-
=
:-
;=
!= =
=
=
==7E,=
77
a
===1=
=
!
=?
-
=
=
:^
7
1
=
-=
'-
7
r:
;
=
/
:
-=
-L
=-
=
:-
- =
^
n
:iS
-r
_^=
=
==
_:
-
TJ
1
=.
t
rZ
=
=
7
=
=12
:
-
-
j
=
^
-
=
-
-
+
a
-
a
=
;
:
t
=
=
:
-
-
=
a
"=
a
j
1=
:
=aa
=
?==
'
?
"A
?
i-
i
.-=;
==3
J
-
=_
.
=
=
-+
s-N .
Gl-
a
js :
a
r
=
2
=G
-
'.
: i-
- -X tN
a :
!
:-
= S
t
!a =
-2
i1
-4
?
<=;
*
H
X
:?bx
I
I
I
T
r
I
,
I
I
r
lr
:Q
-
-1
1
ral{-a
-=
l
*
-a
-1*-Y3
'
:
2
.E:c
'r .->
-FX
l
I
_
|
I
*{
-a
i*
.
.
I
lr
-
O
r
1
:A
z ;a-z=(::=;;J.
II
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 181/304
*
-
*'-
**"
;
._:
-"
.
-
.
:
a
,3
r
I
{
E,S
F
\
(n
-Ti*"1€_a
-
.
*
I
I
r
I
I
I
I
I
s
\
=
-
.L
:
/
: :
;
' t ;
= a C C a z = r c; c t
-
\
*{\-.J
YT
rm
=%
i - a Z : =
{*
f+
N \**
\
t
'
r \
\
$5S
b
=ev
$e
I
I
r
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 182/304
2E<i-v=
* F -- iz v=I,-v
=*
1
I
/
t
!
-
4
-
-
)
i
*
t
-
:
a2
=
=
l
*
-
=
.
-
\J
:<
' zz
-
l
;;
;
-
^
*t
7
.3
-
l
.
c
- 7 : ; :,a a -
l
IJ \-
.1
r i-\ t- a :
-1 =
: I l
rs
a
r t
.-
l,
r-
i
l
!
r
{
.
:
e
\
1
I :
--
:
. r
L
5r
l
'v
|*
l=
a* |
\
0
F!_
F: ! I ) :* ;>2
T ;
IJ
X
= '
l
4
1 l t :-:h
I
I
I
I
I
I
I
I
I
\\
7=
I
-
a=
"=
r
r?
i
=
I
z
t
=t
:
.=
=
I
t
?E
-
E
-
*
t
+
.
:
-
-
9
:
=
-
t
-
:=
i
a
!
,
>
:
=
, =r+
T--72
.=
:
:
t-
i:-
z
.a
;<
.==:
;sr=
t^
;=-=
;
.V
=
.
?
z+
==
,t-
._
.r=
I "
.-
-
-2
a
2
-
=
=1
- '-
=i;
-
E
+E
r
+
Z
._
:
':
:
=
E
'= €E
-
ta
I
F
:
,=
a=
=
=z
=
l=
"
-=t=
o
,-
-=
=
:
:
-=
t
-
|
-
a
,
=
Ez
)E
==
'!=
-t
=.
=.
.
7
-
j
-
-
i
c
_
-
i=;==
tZ
t
'J
=
=
'-
=
'<
-
:
-
-
=
?=
i=
i=-+
?,
==
.
=
I
;T.
-
:-====
J
!-?
I
-
=
-
:
-
-
-
=
.
i!
.
iX
:
.
iiIII
rac3YF7Faa
tt
^
*
-
I
l1
..=
:x-=
'4
.
=
'7ra
,';7
t
-aci
+
O:
\rI-Fri
'-
F
_-_+
lr*
#*l*\-4.
I
em
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 183/304
=
=E
f
.5U
.=
;E:
i
g^
,
.
"J
.'s
{>
5
'-
I,1
4"
,=
P
!
i
=
.j.n:=E
=
2
6=
Eu
E e
:"e
^
5
.?a
>
;
* gE
r
*
!
.
J
J
>C
I
e
=
L=
j
{1
:=
I
:
c
9
a
lzz7=
:
I
T
I
O
!
i
?
-
i-=??-
--=
t?*a
-
':9<=-
,==
EJT
,E!r- I
.
+
-
-
FN
r
:
l=
rn=2
N
-
-=
a
Z
-_
-_
N
3.
=
i:=E
?
'r=2
=;
,
=Z
.A
I-I\
staN
t
qH
ti_|
(F
\
l*-
lrtb_rQ
l
t
-<
Tt\
1
t(ot+<
d
Ifqloa
.-3
'-'v
a
.
d
<
===
:=
-
4
'-F
;
'-
a
J
/
4
:
:=
r
:
c
:.--^
J
'
?
t:-Y
=cp
.
i?
k
FY
OJ
c
O
!L
t.L5
?=
.1
\L
FV
*3
'
-
'cau
.9r1-
c
/=
*
iJ-
!
5
Y
-
5"
trq
l-l€II*"
*$
q-
\>
-.1-:'-|
;
i
:=.
i-X
f,
i,_rt-
ll.ltL*N
1 t
I
I
I
I
I
I
I
I
l ; z
a
*N
)=
;_
s
-a :4 e-=
=<
:-*=_ =
3^^-
- ^
*
j
NI
z \
r
,
ls
F_
1 l" t
I
r
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 184/304
J
Y
Tn}4
rS
F+
E
\_1
H
H
\H
--
Ir
'1 : t
+
**t ls
lhiJ
"\
:-\ $ t i o\ t \ N, ."
,I
}
'
I
I
I
I
I
II
I
x
jpFFF:U::
*
r,t
;
(zJts-
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 185/304
tm*ol
roo
o.
ra
*H
lr
:
1
*q
-
,
tN
I
|
-*
fc
+
*
*c m+
.-
cm,a
l
*
o
'
*N
Ia
F
+
HN
;
i-
l
^1
,
c"
"
I
t
I
-r
'6
-d
'-
t
.
tN
i
,hE
h
E
l
s
_
N
f
t\ *
ts rL
trT
\
,-7
r
I
I
I
I
I
I
r
{ - I o o J caj -a
= a5
--a 'e
-
\3
>
5 |
l E
;7
:
!
r
r
=
I
l
io2
t"
F
t
i
I
:N
iN
=
--
.
\
\
A
l
a"-
s*
:L
/
i
ip
:p
.
|
i
-
-
-
r
i
N
-
s
u
&A
3
1
"=5
l-*
t
l-
5o
*
-
\
;z
a "?
.T
."
c
i
t
=/
i
^
:r
-
I
|
-F
- a
t
I
J
(
i
\J
6n j
\ s
l* -Fl:
l* t
LU
_+
LH
*c 1'=
n
.4
JO i- ic lon cC J r U o Zd J 3 F - o t r \J
[EI
Nc
=
-=
= ,
_
L
-_
9
-
-
N
N
5
=
"==
'-7
a
a
.
4^
^F
-
'
.
s
Y
o
cE
J
-
=
:=
p
eA
:
-?
-
*
4
D
-nrP
rr-Fr
:
=
\9
o
5
a
-=
7E
r
5
=
-
Q
.H
-D
=?
-
"
,
:d
a
?2
!
-g
: -
I
.B
aw
a
a
=
b =F -F q
=
:-E
^
,\\ 'l-
r (JI
-
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 186/304
l* I
t? Elt
.y
t3-
S
I
tJ
<
c
e
i
a
7
E
*
;
-
a
tJ$
-
i
t-
5
lc
2
-
+
c
P
:*
*S
4*
-
-|
-+
-
=v
-
2
*
Y
L
-
:
""
=
*
N
\
i
{P
*=-
tI
E
=
*
i :r
'?
: 9
l
,
F
*
-
|
z
t
i-
;c
l
:
.*
j
:
:
rc
:
!"1
n
*
O
r
-
1
l
t
!
.
:_
i "-
>2
*
;1,
:1
F
-
p
\€
:
\
.
l;1
.
, Jr-
o
ir
:
a
\
:
-
\-
c
3
#N
c
t
HA
t-
r3
lm(" -*
f
.qI
r i = s
3
i
':=-_r ->
f
N-CrB
w
-A
s
S
1k
]
.Y
lr
e
5
;*
-
I
l
t
7
=
--
-?
,
ie
r
<
|
F
:-
;
r
<
c
-
L-
.
-
\
l
I
-1
n
4
Z
I
g
.
ir)
'
N
I
r
-
1
;
I
I
s
L
i-
r
-
:
t
r-
g
i
l
"
;
o
:
u
.*
i
-
.
N
-
t
q
l
;
'
'-
'a
- t
-
*
-3
lD
i
f
so
s**.;
: 1
-'_
:
Z=
€=
z2
5
,
l
;
=
E
,
-a
r
rJ
i
a
; l
I
ir*
,1
=
|
b
+
.
-
11
-J
7
t
!,I
t,
; 6
"
i
!
=
-= f c = N
I
r
I
I
II
I
I
'e-a?-.L
';-
--a
)s
.=
b
i
6
v
Eai-
r
-
t:F:-
i*\
cFr
\\,L
__
:
<
**
i-
tI
\
r
r
$mr
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 187/304
l
.5
1
L
?
-
Il
l-&
-a_
=_
L
(
.
=
-
i
s
r
I
i-
-
I
E
i
h
q-
_
$
-
*
.
L
L
-
r
1
iiit
*
1I
N
t
j-i1r
b
is
-TrF
:*:
nH
\*
n
|s
is
l{<F!+
\
tm
i-ri>
\
.
!
\
lstFt
'
\
fh. r
,t
,
I
\r
-
*
.u-a\
I
8-=
1
I
"
-FQ\
^
\T
T=S
I
I
I
I
I
I
r
I
{A , { a oc { Ca c
- 0 D a 4 =
s \F
E x
$* / i
X< IY cxs Aoo - 3Ho
-c?
-3 - C c= 3-
N P ^
I
Jq
e
F
l\
*
.-$t l*
*
|
\
t t l.
*1 + ls t
:r -
1
q
i
,
-
'
a e.o'; )
Hd
c
c
I
F
y
g Y ^
( I * c*
a u +'4A
**
i
6E
-
I
t
:-r
P i
l
. * o
lc lr lF t IF IL I l t> lr l I In i - a z E { U c { i {
" G t
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 188/304
* ruqQ N =
Eo- =
-ctq
a
:
G
J
'ox i
jF_ e
.<
B f o
.
*
=
Fd
c
=
a=
5
=
Ca
;F
P
fEN
lc
d
+
*
-
n
c
E
-=
?
=
;-l
t
!3
j
l-
.-
4
,
I
e>
x
|*J
^
-
l
":
-a- 4
"
i
.
=
:o
:
i
-
--
:
q
-
-
i;
1
-
;:
g!=
-
tN
|
-
=
a
5
.
+
lo
F
Ig
*
r+*
I
lr-
|
-
=
|
-
l-
-d
r 't
it
t
:
=
i rr
".-.
E
*
=
?
=
3X
I
f
.1,"}=
,*-
l i
'.
-F
*
I
1
ts
""
'- "
I
F
=
:
s"
.*F
-
=
:
:r
-
,
=
o
-
--
c
,
'8"
l
:P
et*
i
J
F
e
=
\^
a
! d + X i"o
I
_-+
L t
*<i€
E.E
,P
!
=
:
.
F"
i
r
L
I
:;
tl
;
-|
:
=
.
t*
t
- tsC
J
N!
ir
lr
o
.-oo5*
,
E
l
;
-
;
M-
:
4-
*
!
,
.*
.
i
:
.a-
g
:
I,
:
;
,
a
-
;
\
t
4
.i
-a-
o
NG
'
O
I$
.
|
r \
I
I
I
I
I
I
I
rcz_iO
l
-N
,
:
_b
*
-^
9
,N
l
r
|
-
|
l
H ad
Tt
c:F
<>
II
I
I
I
I r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 189/304
F
*g
'>q
I
I
I
I
I
I
r
h ++=5F:- E3i
+
"-
E
;
i-
g
rn
'
:
E,
4
=
{
g
o
t
zm
;
gm
E
;
P
v
i1
2
!.a
-
;
r
gta
it;
:#
T
it:3
;=:
;i 1
1(
; 3g;
;i :E7 iTg
: ; i;
F=.
!€= i
a
.-
;=
=
+!3E
r
^
;=
;oE
it
;3f
a t z q F
I
I
I
I
lr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 190/304
g3
3
?
T
-g
7"
'F
I=o
:1
:T
*
z2
?
=2
c3
=
E+Fr
g
'
C=
-
;eD
=ES
-F
x
5*P
a
-
o
?3
-Y
i=
7
l=
:=
t3
t-=
t
j=
l-=E
s
;=
i-
F
=F
=
-
;G
!=
P
:-,
;=
1
2-
:
=
:
i=
=
' =
,
P
v
i-
c
Y
!z
5
-
I
r
az
-
:5
3-
-
-
-=
-aF-=
!
-
=
=
=
:
?=
,E
-
:-
*
:
i1=7
-N
5
+
=O
;
,>
?=
j
t
-
!=r
=
-
;"
?
=
5
g
9
; ;:
i :
=
3
ri =1
::a7
r$
:iarr=n i i;
v:x
^
a r
F
=
'
!
t
Fi-Z ?
>
F
ir
a t
-
=
\-
\1
a l-.
'<
l:
;
l
>
L
t
1
l€
!l-
:
l<
h
1-
^
a
;
F F s
G = o j fc X
sPE a i
r+
L
\1
'
(c E d:"a 'c
-
t ^
>
-*
;-€
I H l l t l I l- I I L l;-
F5 o €
*+
.* I a.* I
x
X
x
rI
I
I
I
I
I
^
:
I
i=
2-7=
I
;
;
€
.=
'a
/
"3.
?
4
3
Xe
=
;
,:-
-F
;+
C
3?
:
*s
5*
-=
+=
;=
72
=
a
i
.
EE
;=
=
|
:
I
'=
=
"E-=
=
V
I
i
-
:
t
"
',
4
5
i.*
i.:E
-
=
r
;
+7r
€
-
,1
:
7
_-{
=
?
-t*-=r
i .=
S
.r,
I
=-
*
__
€7_
:
|
-S
-
o
'
'
i
=
i
i
Y
:
!
:
1
"
<E
= E
i
1
7
EH
c
e
.
Z
r
:_g
4
?
q
-
d
=V
se-
2;
i ;
sL
Er*
6
t
,
.=
*<E
=p
s
5F
.-E
s*E
=-E
'3a
'.
+
+ ,
=
:-
JEl S?
.E;
*<EF;-€+E
>
E
.<
:=
b
=
' €
E
*;E
i
Z':
tE
i::pE
c
€
=
'f
?3
o(cF
.i*
l*
n4
I
I
I
I
I
I€
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 191/304
di
|
F-
R{
;
l
iod
5
.K
>;aa
.?
'asN
!
t)i)N
/cF
/i\-{n
1
h.i
ir-
:{
;
n=
- 5+
LI-
-_
"C
d
-2{€!q
:z
=1
S
€
Ei
=
:*
Z
G
JE
,
T
//ltfttqYlt\\\
J
j
':
-
\1
\r
\
,
iq
r
:I1
-+
=
I
,3
\*=
'
e
+
ll_i
7
I
I
I
I
I
I
r
.F
, i
-_ a + -
l+ i
= *J7o -= E P
NJ F - r
=f Z 4-
> iT
I
't.I X
\
-+ -
g€
F
I*
i
5
r+
s
;?
-_
:
:
3n
gfr
+
i:
;3g
,-
s
;:
*
?
;
1
E
FA:
;5
r .r"=
e
&
)
3F
F
5
,
Qi=
l;
{€
i
=
'=
-
!
?
=
=3
.==
r
x.
!o=
=
:
z
=
-=
5
F
i ; r "+
:
3
t=;"
:E2
*r
g"*
gi
;FE
;
I
i
-
i?
F
=
9 _
i 3
?
4i_
;=
7
EE
t1 i
!5 1 ! :
\1
1 i a q Co. = b
i , :
i t I I I I I I I i> lc l^ , a I =2 -h
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 192/304
l;5i1
|
|
? -
G
-=
J
:-Z
:
'-
i-
?
;zi
;
1
l
:
n
:
;
r*h
I
;-
J
;y
.
rI
:
-
:
-"
:
-5.
i
;5
*
!*
?
A
ier
F
z
F 3
=
=
j : ?
5
S
'4 *
E
i : a 'a a - ; ;
;"1
I
i1
r
!
lr i,-
I
-T
-
l-
-:-
t-
=
-"=
*1
"
--*s
I I
7
t
*r :
7-
-n
_J
f"_"E_1
l;
t+
-
\ * *g_-4s / Y+
I
\ *u*
b
y , .1
i-t
X i-
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 193/304
-- . I-s i
<
-A,
i
\
==:
J
-
i r
s
*i
"
i
I -o'c
n '
J j
€t
-- s ,i a i
G a . - t I - = =oj- I
E 5
\ r
I : ;2t
- -
-*:€< :
-
:
=
!
:o 4 =f
-{
:
l
lb :
'<
:-
-
,
,
a -N
a
5
:c -I*
!*
?
-?
i
r $!=
J
\
=
l
a l
,J I o . -J c c
' - J i{
\
;
' \ 6al I r U
o n o z c i z =
{ *
\ \ I t I
v.s
h LHA
s€-h
FHH v,C\_
-,L/
t
l-1
\
I
:
I
J
i-
' '
\-
I
,
9n1
z
r_
=
/*
J
:
L
,
- \*_\ -c
' <{
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 194/304
I f =O r
f
r
.
J
r:
1
I
I
.
-
-
j
!
c
5
. 3
-==a iq l*r5
n35z
^ i -=- a
2
:4
=p
N '.--i-5--D
z a r
t
.i_ \ ; -
1t l
I b r
,
> !
\- +
.
L
-
'r
l- i t e l
J
-*dt
.
I
'-
'
i
'
t *
l-
'
- :
i:]1 i:7+w'o I t
I
I
I
I
I
lr
I
{
F
H
i
,1
i
F
u
\{
;
;
1
a
l\
i
-
_
\
_
r
-3
=.
"
i
r
13
\
h
,
-1
-c
=
:
.='
*
=
:
i-i\-
L
r
*t
1$
'a.
i
,L
l
":
>
!*.=
i
:
:-
.
i
:-;z
!
AJ-
I
cU
-G
'v-=
d
{;N
-NE.=
:;
'
t
-
i=
-7
t
3
> I
l,v3
!
v
=
=
;=9
F7F
f{H
a"i
I
I
lr
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 195/304
Il
r
I
I
IT
I
I
a a a z d -!o * '{ o zs ,J = , s
I
r
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 196/304
(1=
_
tvh
i i I
- ; 4 :
E
7
I*
a
=?
^
i5 "=
-
a
p
=
;
I
^
'!1
-
"
<:-
d
=
^
r
:1
Z
;
=
{ --*a
i :
=
==
:_
k-
^
-
-
t1C
-
F
=
^
a
-
:<
-=
=
;
=A
=
-L
=
ia
-_
-JC
=
-
-
|
-==
_
-
i
:=-
=
{
;
j
-=
1
=
.
j
:
;
:
'
4
-
d
i
c
^--
i
I
+
>
P
:zN
5
a
-
=
i*F
:
i- N
: :
cOo xq -
v
= lr F
:
;2 i l-+ ,a
R+
<
jo !p <c.o i*
.
: ;
i na+
+
'"G
tra \? \F
.?
:^
N
I
r
I
I
I
I
r
I
i -T-r
-
a
J
=|
:.
tI:::r
+:;
s__
_
___"L_
___
:=
.rJrr:
:r=
l- - -
-L
- t
i:Fer.:E
i;=
3:1
;:=
=it
l--
____J_
:_
_=
j.=
rE;rr:;::-1
i-+
:-_
_
_
J=_
l:=
_
,
rtr:
t
.-
-
,-
.'-
lri=3
=:=:::t:
I =
-=
ol;.r
i; i;
i--
-
.
,
i
=jt
: 3
::1
':
,
=
i
;
i
'
I
:
l
,
|
,
i
i-
-
-
i-
=-:ra-=i
' :
l=
=
:r;
;;
,;
l--*-
-
-
+
' '.-
:==
- j-. r-
-.,.
i:_
_
t
l__
_
_
F;F
*;>i? l-
j-L-
I=
IF
-
e
i =:r-rtr
l._
r___
lr
-
i.r;
;1=
.-
--
=
==
1
=
r1-a
=r1
=
i= :r;=
:
:r,
-
_
.
_,
l
i
i
I; ;
;
=
j;=
=
===
-_
lt,
i., ;i
!z
=
-=
-=
?-
i-r_
_t_
i.i;=t
t*r:r=
lrl--T-T
-
l:--
-=
"-
€
_ I
I
:
-
.
x
:
l
-
>+
l-
'
tJ€
;
i
r1=
-
,
"
,q
l-
--
-
!
-
!
=
X
=
-
E
F:
'=
d
a
=
c.
-
-
I!_
*E
1=
=
-
-.
=
:
-c
'
:
:
=
3
!
*<
i
c
r
?
i
-
'
r=
.
=
a
4
b
.
J(
EE+
o-FF
'I
T
l
I
I
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 197/304
i.T
T
t?
o
@
tlFlrr
r
i.T
;
c
O
ic
$
isFa
1;--
n-
;a
ro
F
a
t€-o
d
c
;
G
anF3
s
+
dtd
.-
.T-%=
O
Ir
ra
-r
a
-
I
:.-1
1
j;.
I
1
:=
=
-
=
i-9
-lL
a
lt
;
;;r
--
l-
itr
;
;j;
-c
-
€
at:
-
TI
t
lr
-
I
l
;
l9
r<
=
i [
tI
--
Ii=-Il_
r_
l,*;
l9r
l c
-
l-;rr-
e
t
i*
t-*-T
t^
t*
{a
t-
;j:
,
I
i
t^
l= 3
tj
-r
ib
i-
l-
3
i-
i-irl-_i+
I
I5-
l
,-
l=i*-
-
t|^
id
l"
-*
i-l-|
1t
r
I
l*X
dt-t
-I
-oa
r
'.ti
_-
T3
-*l;
t?
+=
=
_
, x
= e
t
; : E
i
S
:
o_
_
i
,I.r=
"
- {
i=fs
=
:
I
:
r
-
;-
-
:.
;
:
:="=
,1
aNi1
aI
.L+!=
'd
':
XJ=
.*
x
'r
'G
:
Z
T
r
-=:
=t
=t
=
.Q
!
.
t+
I
I
_
;
z
v
-'
=
-
-
a
(
' -*
t.
.a
J
.=q*
a
Fz=
.sL
t'J
;-
==
=\=
'
\
s
;a
:
s
q
\
;a
:<
-=
i=L
F
=
c
.q
r+
^
,o
i
N
.-1
q
\*1
o-l1
$
f-{\
\
i-
"
$
H
\"
(J
!$_
I
I
r
I
I
I
I
-a:a 7 i z z -I
I
I
I
I
r
-a : i
4 ;E: -
^
1
5
F
a
+.
*
!d
b !
:
.
I
I
--=:_-
A|+r')+o--
*
.+.o = i
Y
it
a
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 198/304
I
I
IT
I
I
I
I
I
r - t !J
"
?
; E *x5i
*a.J
i C .
7 =,
.4N
i
s
-
*
^ :
- -a :" IF c
=L i
-
i - J l t i * =
fz?
J
>-
€
"=
4cri4
sLq
r7
acF
h
d
I
!
t
t
I
II
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 199/304
.=€A
-&l>
.,o
.
.
>
:1
74
U
N
L
NA
es
I
I
I
I
IT
I
s*\ssR
RqR
a
- o c { a{
^+ 31;1
=c
-
r
- i
ia+
:
+
=
1
D*
:
;J
-
--
i
f-
=
t
-
-
l
=
i-
4
=
.;
3
:\
:-
.
--
.7
i
5S
=_:
l4
1
f
:
:
/
==3
;
5
,<
b
F
y
=
:
-
=
i
IIT
I
I
tr
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 200/304
*L
g
-
v
^
'
-
:
:<
.=
:
: t
-5
-aY-=
-e
,2
q '= =O
^ -"LN
t
*
=s
-+
a = -
Y
tsq
i = a a C : a a =c a a =; ' : 5
I
i+ * 'J
a
=G
i : =: = : 1 - - t
E*
-G
*
I
a=
t
-
^ .J=
!
'/
E
':\4* =
- \ " G o;
/
,Y
v
r-
,
F
l.
+lt
]-Y
l:
;+
"*
l<
jj-i"at
: : a
t t +
I la
t €q i
H
rs
c
ci
:a I
I
IT
I
I
I
I
I
).
'
>
tr
-
j
*
7--
.
:
z
ta.79.7;.
ts-c
=vFsF
--a
j.L
x
:
I
.
':*
l
k
lrI
I
r
I
ITI
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 201/304
:rI,
=ro.
i--L
I:
:r*,-
t
:r:!=
:=
;
-
:
i
j--:-
i
--L
- i_-
"
:1
i
i
i
I
i
,
l
,j;;;
; jF=
1
.
i=
-;=
4
=':
l=
:
:
l=
I
-i:;F
.tT
,
t
-1
:
.r
:1
' r
!,:I7
{
:r j:r
r-:r
--
l;.=;a-tu
.
,_
:
.
:
rL
_
I
i
i
l
i
!
|
I
i
*
:
|
I_
I
i-_
r
i
I
i-
j-
t
-r
i
t=
_
*
:_
L
=a
:
i-
,
;
.
,
'j
_
:
:-
jr
i
'
i-j-
-
l-
ir
i
.
I
i--
N
j
i--
,
-
,a
!
,
:
,
i
:a
*
,
]
.:
t"-n
-
'1
=
:
.
r
:-
:1
ta
j
;
i-
i---
-
I
I
,
i
i
r
--_
1
,-
j
:i-- -"
-
c 3
\1
)1;N
I
_
I
a4
I
stCq.:au1
7
J
:
--+
:=
=V
r=
7;
-a
=
:N
dvC
L
r
I
J
I
I
IT
I
t I ! i
j z q :
|_
=
rv
j
H
'^
:
-
-;
-
\
-
=
=
*=
4
---
-+?
7
:v
"^
==
==
r
-^+
t
G
=
-
.-
r
.
-
"^
a
r=
=
333
=
=
,1
=
,"?a+
?
4
!
; :-
- *:
;-= :
"-^-=: +5
-
-
a
t
I
r
r
i l-:
i
i =
i
I
* :
:
rz
i
I
r
- Z J z
i_
_
_
:-c-*===
=
:
:
-
--
:
1
r
-
'r
:
r
-
-
1
-
.
:
====
=1
irr_
r
r*
-
r
r
;1
:1
p
-
:
:1
.
|
l1
,1
J=
.
:-=|
-
1
;
-
i
1
|
i
i
!
i
I
i
I
i_
I
_- __
-j_3
i
Ia
,
I I
I
,.,,-..=
=-== *
-=
.-1
:
t
r I
3
+
I
r
I
:
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 202/304
t
!7
:
r3
-=
^
^^
+
.=
l^^ =
a
-
=
=
_=
1
'.
;4
=
=
.
.a
:
-=
=
:===
=
=
-=-_-
=
=
?
.
'
r
=
=
2=t
'
a=
=
"
1
:Ja
==
>
-
-
j
=
-
.a
=
r_
-1
!
;
,
-
=
--
rq
.=
?7
:
.=
^z
-
,
-s
4==_
=
o
l-
=
-==
-
-=
--
a
/
/
':
===
_
=
=
t
"
a
-=
*a
=
-=
.
|
:
-:
-
=
-
--=-=
r
|
',
7
a=
=
:
,=
=
_V
-:=
a
t
"
:a
l1?
-
.Z-
-
:
=
-
l
=
-
"
-
-
L
=
!
=
A
'
-.
=
=
_2 -=
_
=
J
:-7
-
n
I
:=
C
=
-
===
z2:
"
=
-1^
1",7==
:a=
i
=)
-
-
.7
"<
:
':
2
==
=
-
-
a
'--
:
1
-Y
j
'31
-
;
'"=
=
:
=
:z<)
-
-
;
-=
;
=
1a ;;\1.
=
l
L)
sF
r
lLr
3
:
-
r
i
*
\
q
!
1
'
r-$ i : :
I
I
I
lr
I
I
r
IT
\
z
tIir
x;
::
'
F-
t
---- --- -
-
:
trl :
:t:::
:
_
_ i
I
J
*
Ii
I
i
i
i
l-
,
i
i
=
!
J
:
{
|
|
=
.
I
rl
:
I
t--
I
'-
:
lE
r
;
i -_ I
i :
=r:=.5;,_r
:
--::-:
::ir:
:
=+T.-5
5::r
;r
!!=
t
:::=
?-
:
=
ttS
qrr.:
:-;<F
.1
-
=
:-,= : :-:
i+;
=
i _
r-j_ :
-
\,=
i
{|
:
I
I
I
I
ii
i
i
= l-?-r
=
i=
1i t
r=i
,=
--**
i '.
-; l;:
:
':
|
=
1
l:;-
,=
l-
-^
l
:
l=
r==
r=
l-
l
:
.
:
j-
-
;-1
I
:
'
I
t
r
|
I^
r
-
I
i-
|
I
I
Ii
i1
=
i . I
;
i
-
|
rs
-11
--1
-
-
j
i
ir
:
I
i
I
||
|
'=-
r
lrI
lr
F
I
I
-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 203/304
*:
-?d-s
lr
f
i;;
==-
=
,;ri ,=. 1-.J
,
'
|L
l€*=
:
z
i===- - - -.
^
I=-L
-J
i ' ? = ==n
=
-
=;..1
L.
:
:=.1
-
.
-r
-1
-
__t
.
i========
==
-:
,]_
_
,._
1"1
.= -
,=
:=
]-=
ra: i
1il-f -
:
=4
N
1r-
lraT
lz
s
i;,
7/ri€v
t
T
T
7
I
I
I
I
=- U Um r u> F 7
n a
- o o o- a6 cD
?o .=o
i = - +j . = -
2 \
'rI
."1_I
- *+
J
L*f
b *I
w
l-_
I I
+
_4
"r
I #
J*
i i
s*
J
"
I
\N
iS
r i = *
I
IT
I
I
IT
rI
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 204/304
:=
?
;I:
*
:
-
t=
:=
i;
==:
1;?
a
E=
+"
l;1
7
=-
=+
7
-s=E
t_===
7
=
.
2.4
-?V
,_
=
Z
?1
=r
-?
l.-=
:
i=
E
1
=-
-_=
2^-
-*sI
*=
Z=
;z
-?
-==a
;!
=
;1
=
_7
;1
1, -=
-=:F
a=
=
'
i
-
:
:-1-==
=1
:
;
-:-
:=
5=-7:7
:
a==
.===a
f
"
-+
i
-
-
=
t
=
'
:
=
-
1
r
^
1
,T=
=
r:==
=7
7r=i:
==
2--=
1
i1
zs==
^-=
=
=
:=
1.=
==
=::=
;4
=
:-
";=
-11
1
1
-=
:
:
*
?2
=
:
=
t
J
=
r
^
l:
-T
=
:=
=
:?1
:
;r:
=
-
:aZ
:
;=
:7
=
=
'==
=
1
==
=
=
:=i =
=7===
.
:
=-
.*
-:-71=
.
,==
:
a
-S
=
=
-
i
=
t=
.=
=
:=
t
=
=
:
:
.
-
-
j
-
:
=
=
=
'
:
:
J
-
=
:;
?V
==
=
-=
-
=
i:
:
i
:
=
?=
TF =
z1
7
;
--
i:2
?
?
=
:;zF
T
7?
7=
f
=
=:-:
rS
=-1=.=
:=
=
-:*S
;,_
:-
?
=
;:a
=== =
/
:1
=
i.-
F,_-
=-
=-=V
r5
;?=
':1u
rg =
-?-==
{=
e3
*
--;
=-t=
la
;*zE
r=;
i =
; 3-
l3
:
:
"
:
=
=
=
]-
t
I__
t=
:
?2
-
I-=
==
S
=
z=
;=
;5a
>
.==_
-
-=
;
c
{
:
-
p
r
iA
*rr:
=
r
-3
=
=t-=
,=
-^
:7:
-
r
qF
"3{
-t
L
-=1
=+S
7==
?=-
1
^
=
*€
,=
-7
?
9I=
.e
=E
5
ia,"
ir-
^27=
:
aL
=
?
=
-_
;_
=
=
"1;
-
-
a
^
-
-
-
C
-
.-5
=
/==
a
*s
:=
-=
:=
=-
:r3
=
=:
7=
-
!
F
-
;
-
"
a
'=
r
a
'rN
==--
-
-=
,
s=
7
Z
=
'J=
'/
-=
=
-
=
=
=
==
7>=
i=
-
=
-7=
Zz
=
?
;*
- IT
I
tr
I
I
I
IT
-.-^
>
=
,-
-
:
-
z'
=
t
=
-
2.=
=
:
I
+i+
t*
{rI
-Lfr
.1
x
:
i*Z
:
t
t
=
5
t>
ua
t
.
,
La
i-
">
-
c
=
J
:
-
-=
-
=
r
=
-=*_!q
-=
.-?
r
:
l
t
!
F
^
.
!
i
=-
N
-
L
:
-
t
=
;-_
,
F
.
^
/
a
-
j
-
i
a
^
+
:
a
.
-N
I-
J*
--
=
1
,
*!=
'-
:
r
_
--2=
:
-
-
=
-
-
:^
i
i
1
.7
-
7=
JA
-
.
C
r
-?i*s
3
t=
=
-=-=+J
a^
t
t1-d.
!
=
i-L
-
{
--
:-
-=
a
_
!i-=
=i
cj
J=
a
a
!.
l-
t?-
:
L
L7
-
:==
t'-=
-
=
rr
=
:
=
-
:
-
!
_
.""__
2
=-i=:
:
N
:
-
-i
J
r
,E7
1
:
-
'
-_-
.
-
S,=-
i i
=
?=
.
?
-
!
-a"-
=
==-"-
!
=
:
:
-
=
NL=-
-
-
.a
i
r
i
=
:4t
*
=
=
-=
=
:
\
:
-
tJ
:=1
.
=
=
-
'
=-I
t
==
:
-
-
:
-
'- :
/=t
==
-
q
=
=
:
:I=,=:-
-
-=
=
=4
{
=.=
-=
;=
_^
-
=
-
=
!,OcOF
I
IT
I
I
I
Itr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 205/304
*rttttlt
\1ttlll
=z-*?=
!a -
t
-
|
-
:
.
N
!
I
r
i:
:
':=a
-=
-
'
=
:
r+
:
:
"=
')
i=
=
.=
==
I
i
r
-
7*
z,-
S
,=
f
:
=
:
^
-
-
=
-'-
--
=:
-=
-
=
t
=
J
=
=
'-=
-Z=
:Z:
J=
=
=
r
'-
-
:
!
-
J
:
*
:
=
'a
a
=
a
-
1==
_-
j
-
=
:
-
=*-
-
-
t
-
!A
"
.=-=
=:
j-
n
_g
cc
.
-
L
.F
=
=
^
-
=
=
!7
.
=
=
;
3^
i
:
i
<J
==
j-
'.
z
l==
-
-
.=
v
:
:1
-
=
;3
=
-=
=
=
-
-=
:
-
=
-;->
r
-:
-=
_2I
=
-=
=
r
*
5
V
_
=-j
u=
t>
=
=
.4=J
3
.
=L==
'
=
/-lr
==:"::
.:_:I=t
-;
-
-
_t
:
=^
I
I
a
D
l
r
-
l3s
:
a
7
=
-
-
j1
7
s
z
r
:
I
=
:
a
|
=
=
=
-
t
:
14
=
=
;=
=
=
1
=
=
1
._+
=C
i =
:-=
i
=_u=17au72
:
J==::
==
S I
-;
1
-Z
--
:i!
= .:; $:
7
*
---*
-
I>-(
-*1"=
-a=
|=
4z
"=
-2
-
=
-=
:Z=
:_+
?i:
ir
=r
=-1
=
1
7
-?r
1
, =
1
-3
-
-::
r
=--
j.{=1=
>
:
-J:
-^_L=
-r?-
=
=
=
V =21
i-
**7
- = =
>4
-
=
=
-_
:
;-
i=e
r
;1
=
=
:
:=
: i,-
+
:
a
E
=5
{
r72i 5
=
-
d:
l
.?r] aaE=:
=
;
:
r=;;e
=
-L
,-
c
.
i
_=
z
-
:
'-
:
:-
I
=
iX
=
!=E
e
;
i=E
:r
:
- o z J c ! = c; g a
,
,=
.
u?
:-*
':2='
t-
itZ
3
:1
=
-
--
=
e
l.=
*=
-=i
t
i1
1
5
=
z
7;7
n
:
=-
1=
r.
=5-=
+n=
2
__,
:
;r
r;*
s
3
?€
t
-
i
j
rr
1
r: !=
:
-
i;
f:
-
-s
:
:-
1
:
1 ':=
=--
i
;
F??
=
.-E
+
|
?
*
=
;
=
;
;
,
-
=
=
Z?
-
V
=
=
S
r
t
=
I
IT
I
rr
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 206/304
"1:>
-
o
:
^
-
=:-_l=-'a=
1Z-
-
r
=
::?= !-a
.r.; ;
'.
i
i:
?r--=;-
i _
_=.F=
't a-
.-
=
";
tl d*5i i !
o w
'{ \
:L
:
9
ie
-3*^
\1
a
^
+
-ar
:*HgH
.
F
i
S
9
[1r1
7Z2V=
2
': !3Z,7,==
L-
E
zr"==
eI1
;=
;r
E
4
-
=
=
=?
.
i=:
=7
=
F
*
i:,S=
:3
=
n
;=
l=
i -.=
:=
,
i,==;*
-
=
=
i:==
=
=
':1i L
?
1
=
.c;ir
.F
or
1
;
' -1=
'":==
;.
:r
= i r
== 3
?
=
7-
=
:;
=
;g
i:-z7
r
i. l,
=7
q:gE
.
F
;
:3=?
l.,
F
i
i-
=
==
_
:
:t
:
=
=
a
:
,
.__
_
=
!
::
=
-
E
=
1 =
=
1<7
+
t
==
=
=
-
:
-=E
._
?
9
:
)a=
:r
I
IT
I
3
I
I
F
{II
*a:-,<.!-<=I
r4
- \
1
\
1\-E.h
Ff1trsd
FatIt
'-=
-
:*
4
-
:
_=
u
J--=
-
\=
a
=Lq
..
-
-
t
!
.-
-
t
:
-
-
J
-
i
1
,
i-
F
l*
;
:-?
-
t
=
r-
:
+-
i-1
'1
=
-:J-
r
r
-
?=
-
:az
I
t
I
T
I
In
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 207/304
*
fi
-F=i
&
v>
A
/1
.+
>=
.:=i
^ |<
:
i-
lr
IT
tr
-
I
r
F
i$ ls I a a2 -a a b =
t t \
Ri ! s
:"I
rc\-
^
s t
t
.S i
rs
II
I
I
r
r
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 208/304
D
1 'I i
5;1=u=1
=
gi:=
.
-=
=
1
=3
:. v==
o
:=
=
1:
":=
1
T
=r
lr=
:an
?
;1=
::1.r==
.
==
:=
=^
-
-
-1
: :-
i.o
*=
:1
:
E ^=,-:=
i 3]+
?
"7?=
r
i-=:
;=
i-*
t=
:-
*
:
_
=
-
:
!;11
=
-e1
-
=
:a
Ia
=;1
" ;
=
:
n
-=;
',17=
;=7
o
+^*
l +=
a2
-
4
=7
-.
Xi
==
:i,
=;
E=E
4
:"=*
-
=
=
=
<
^
7
_
_
l;=
=+
1=
1
f=
==
-=
; .==
:=
=
:
J
-
:
-
-a
-a
-
:
:
Jv--==-=
a
z=
.a
=
+
IE
t
-=
=
'!"
a
I
IT
I
I
I
r
*=i
r4-
Et
==
F*.2
l --
.
i E"
=?
.
:
;r
€
:
-1
==
;
- -F
;
i*
*
j
,-q-
_
n
lr
*-E
s
*
=-
;
teh
-
+*:
=
:-
:€
's;a
aE
i :
'.Es
;
e=
;
:€
=
tl
3=
-_ia
-:La
.
NF
.
F>Lr
.*
.
g
r1
\
z=
9t-
a*H'I
|,lr
N*J*-$
-
rr
'
tlt'1
G*G-
"C"1-*
\L*
-
$
G*
-
ir-tr
!
O
'-o
=
v
t
:-
41
io:
9+
)
:
:
.*
;
?
a
c=
{
c1
?==
s
F
E
^
st1
I
t
*t
'f1Its>I
-
e@ir
g
iE
J
E
n
E
w
K
I
T
-
I
r
I
J
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 209/304
'a.4
:
-
:
.s6.
q
6uN
7
9
3;
.B
I
E
?
;
1=
!E
=
Z
!
g
,1tv
=
+-
+"
=
i?"
g:i
?=E
;7
:7:s
.2
z,=
it
e
2
:=1
' E
?
"u
Z
';E
E-
tr
?5
:a=;-=
*-
? tc
t=+
=:
-=
^
is?
=
_
=
=
+
??1
=tZ
V
;=
Za;9-"
;-E
=
=
i
'-
r
-
-T
=
z?
;21
;--t=
+
l:,E
-a
:
: -az
?
Z=,j,
;
,eg
a=
= ti.?rsi E
:
=
;=7E
=
Era
.=
-==
":=Z
*
' g
=
1+
E uE
-
g"
.s
.
c=_T
-=Z
,-a-$ e
'*3E
E
aE
=t
E
.-
7
:1-1
:
C-F
;-J
;
--
|
-
r
1
i
=
i a
>
"=o*
l.1
r
t
1
.*
:r
=R
;-
/
:1
z :+
r
:Fr
^;a
I
l
tr
r
I
IT
r
\ t aaz a - : =3
LiD
-a
=F1 : .
=
-a =-*
^ :C
_
.
E
)
:
-a
:^ ; : -
a
/=
z-a
;<
z c J =O s
3
F3
=
3=
r1;
.=r=
=
-=
1
.!=.=
>_:
=
":;
_=
1
=
:)
=
-u
--
11
== =7?
==1
+7=
"3r
=-T
._=
.*
$-=;=
_
C
S
==
l ?
?
=
=_
:_
3
=
7=
_=?,=
!
=-=
\
' 3!
i
=
;
t
=
;:
:=.=
_
?;
=
==2
=
=
=
:=
:-=
)=
;7
+
=
':n
>-=
=
;
-
=E
3=
=
)*
+
':"
F€E
g
z
e
_;
=
:
:=
.;=
:7=
7
7
-
'g
i€
3B
;
a
__:1€
-72
7
=
t1
.2
;
is
=
.-X
?
?
,
|=
=
=
=
.-
=
"F
i-=r;at
1
:r
1=s a
,
=
=
=
S
1
:
:
=
:o
:
;
=
=
;L
:==
;
^
-
'
c
;
l
L
?
:
;
:
--jr it** i, Tt ls I L \*
I
S
\
*
1
l-
)s
-\ -
I
i4
"A\
7 'a :
s
'€
I
t
1
-=
I
-x
I
I
I
I
IT
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 210/304
_;t : , ,'_ ; . *1' _. - =1' ,a - 7 :
I I -
: - :
f f.a
n , I
$
N - .
a
\-; N
1
D
^
^
Ia
-a
D
')
-
a
-a
o q
S
*"i
o=
lJ
;
j
!aF
-
;
HaX E
Z .*
5G
a -
I
I
I
T
IT
r
C
A
6cho
-1
-r .*.u
a
aE;
ea
.4t
-
:S
-
s
,
$E
i F
.
d
t5E
E
-
-&c- :
?.E
$
E
t
_f :
:
{-*
{
x?1
€
E
'r -
is
j --
!*
.=G
S
a .
3
=
4
r?
;-
:3
=;=
,
39
,
+
.=
*1
.=
E
g
$
-a
f*=
EE
-4E
"=[-
'=
;€
:
.EE
5-
=
-
o
.=
T?
a
:-s
i ;i E
$=.;-
j.r
rS
!.E
I
"
tr
i:r
r
E
I
ia
r i?
E :
=
!a
;-
i
lE
e:= :
€ :
!E
EE
:s
EEl:s;=E
€i
=.r
;rX=-?
Z1
!5
;;+E
:;u 1
;#
E= =
Z,
a=
au,7
a
:c* 1=zE;i;=E
:e:1
:E
;
;g
:s
F5ca cF
rI
I
:r
rJ
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 211/304
3
1
i E';
:
J
T
;
g
i N
-
:n
n
^
f:
H
7
+
=
i
_
T
;
;rE
-
{yE
.=
:1t1=_=,
3
E=
'=
=
'a
-t
"3?
=r
.=
r
3E
F! I
*
Z
lr
"a
t
l
E
=
;=
fd=
=
*=
=
=
'-
-
':"=:
".=
.E
T
+=
;*:=
.=
"
::
i;E
;.7
i i
::E
z
:
:a
s$
sd
,E
E
i i e
:==
;
1 :,
i:
; =
1=
s
:*
:i I
Z
E
i
;u 1 Ers
|E
z
:
=
V=
:=F
;?=
E
z:1
;
*ag"E
*8
I
1
J
I
nI
r
+ a 3z d C =a {c -o Ii
-
I
lr
I
r
o l i:L e - c-
a c=
@N c
: ,
_
:_
=- : : c
z
j(1
,
e
-PE
9A
:
=
5
?
+-n9
a
d
=E
r
<
S=
iH i g
;"F
I
I
r
lJ
rlb8
"
ir
o
G
r
-ga
F-
lc
I
-
I-F
)
r#'1
{
,s
I
\
i I
|_
L.$
5 *
*
.
Il
or
xv H
dH
$Q
?
*4i-=l* fE{*
-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 212/304
I
I
r
I
G
I t# a
>qp
FrtP
i
i
r
r
{
{
|3
i
*
I i :L
I
u
g
r
l
G
{s5
+
=
{
-a -9
-
\
t__
.
g*
\
tF
'
a
*eI-
_
i
bF
\_
d \
:
a-D
e
Y
'
*
>
=
N ;=3N7l{_
-F
-
?="!
s
ts
:
F
>
-
-\=
.9
:
F
=
FO la
a
:
a
l=-
=
;2 i
-
i c:e ;4 I c - N
)
*- .
-"---
"
(
-
__
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 213/304
E Ir
-J E
"J : : c - ca- : o
rX - ;-=4n
4atc w
, l
-
i
l4 .-s = v :*N
{ : z a
N
l.
\ \
\
I t$
lr
t
1
I
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 214/304
J l l
=- a -
*
"
I
;--uir
i
- I
=
-
C = s= tg
i
!
t
N
-
\
r
-
-
c
l
--
,
,
N
N
TA
\
I
'-
=
L
:*
t
:
i
o*
a
i
€ c
.T\
I I I - I I IrDi\
- I I I I
-rI I I s
]H+
I ' I
of*'t I I j{ tN
\
'-6
a
Tr
k
e
f lq-
$-
GTi br
\
I
lr:T
I
T
r
"
j
*
NL
F
6
1
.
\
N
<
i
i
'
F:aG
_
.d
5C;F"
l
i
{
-O
d
L
"5
stg
IEi
,+
;--:
rE
a
"
-
J!r
s=
,=s
f
E
;=
*
=
i --E
=r.?
g+
5
i:
i,*7
i.e5F
JEI
+f
C
lr
r
I
I
I
rI
{U(F.&
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 215/304
\\l
€Esg
E
t*
ic
a
C
E
2
l ;:
7
,E
E
E
3q
S
s
.:a+=
' +
z
T
Z
Z}$
<
L*
o j:I
\".
T
X
es,
=- ;E;*r=r
*
=
+=?E
?=
$
.d
Z
€=
3+!E
E
!
+
t?
E
+Z
fr\
a.is
st
.I*\
x
i1*-{:
i:
tt-+f* su
ls
s
tsLx
$:F
.t
I"..s
\F
I
r
T
I
1
r
j ) z c =3
:l
:
ir
,
=
t
tJ
.=\
a
ir-
*r
t1
=
1 i I 1 I
:
ir !
.3
ai
I
i
t t=i
t ! t a
:
::3i
l
:
-
-
.
TT
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 216/304
.a
H
o'J
in
.
c
*
3
-
-
;G
1
;
i=
.+
:c
=
t
-
a
-
':
,
!<
c
-H
| D!
-
'-
tE
u"
e
)
41 -F
=
r
=
:
.q>
=
qS
.,
,
-+-6
u =
f-
^
oi
1
";
1
-- {*
:
:c€
.
i
:a
Y
u
i-
lJ
-
I
.
?
;*=
l=
i
"
x^
r
,
.
_
T
=
39
J
L
:
-
a
a
\
I
4
E
o--
(
-
j
.
\
;
1
\
'-s
:2
3
s€
-
5
7
t2
1
F
*=
S
.-
r
-
Y
4
I i_
1h-
"2t=t:
J
q*
t
o GJC =
16 a h
n
:= ; z
' lr
{*
i z
rlo
l=
\J
I
it
g
*E
(q
+
\
lx
lr
I
t
I
I
r
-=:-
;€,r
==
ir"
:
1
;i z
-r
I
'; _
_
,
:
l+
.
: :
t
*
:
;'*!l
'a
'
I't3Tc
{i,d
\
r-
l
:N
-a
t
lfm
Nl1
t
. -- .L
r-;-
T
l
'a
'
t
:*€!a
aJF-\JF
:4
dk
sa
:3
.€
@.
x-h*
\
\
O.J
R
eRq
i T
X
r
I
i;a
r
3
I
nI
I
I
IJ
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 217/304
r
;*Jg
,E
2
A
g
-n
-
=tz
'=
-
o
a5
f
:
-3€
:==
T
r*
*
.+
€
:E
-
=s
E;E
;
!:.=
-
EjE=
.
€E
,
;:Z
*=
_
'1
-x
===
a *;
:-;=
a
"€
: {J=
;
;*
;"=
==
E
:
"?
1
E
7
1
_
-=S=
E
b
i
.
N
.<=
',
c
.-
'-
=
Io
Ei 3
i -
j
d
e=
'*7
*
Yz:3E
.HF
-
-
L
-
r
,3
T
.*
IJt-
:
=1-
F
5
=
<:
=
:
:5
=
=
:-
2
€
=E
I
i
id
:
:
=
:
L
la
o
-a
i->
i3
la
-
=
'
=
?
:+
;5
=
:
cr_
l
=
:
:
I
I
.*=
i ?
l
t
a
^
=€
L
.d
F d
,n;-=
?
=
)
5
i
:
:=E
t+
!
l:
I
-
_
Y
+
l
.
=--
>
;E
?*$
t
i.VF
l
l l
.r=;rr$
'-
F
;
'c
:*
:
o
s
a
N
c
o
3
t1
'-
i-
=
:
r
+
-
.=
r
a4d
F
f
.
F
,c9
.
co
V
-
d
t
1
l
=
s
n
F
-d
-
L
rq
i
=3l
tlr
l
\
:
L
/
c
3
tus-
f
s
i*
A
"
e
D
a
."
d
=
E
:
H
-
-
s
:4
7^
iL
!*
'*a
st-
Ii
*
s
.E
Ir*g
I
-
m
I
sI
*L
r
.
I
I
-__|*
\
lq
I
! i--1
:
I
:
+
;
1
x*
l-a
-
|
x
t -
I
\
t
:c
|
{ :a o I q 3i a
*
i
t
I
I
zZ-
-==
-
-
:
:
=
io
F
:{
=
n
a
.
eZi
w
-
7
a .=
-
:
=
-
'q
'L
-€
t
a
:
:
I
'
:
rr
-* =
l{
!
tJ
3
-*_
-,_1
i
l
I
T
.-
-
=-^ = -a i
ci=
=
\n i
3 .
r
41
=
i
-
-=
!
-=
n
a
+-
ta
':-=-
=
i==
:^
-
3
,
:
E
-=-^-_
:7aZ1
\---
.-=:a
x
<F-
!Ea--
i
."7
-
-
a
^ =
= G .^ o
55=6$o*
-
)=
1
:$
*
\s*sss-
SB
"
*
-***osE"
*-_
^S
si-
FFJd
i
,
3
IA -s
{
s
a U r Ilr
T
I
I
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 218/304
G
lrr
J
fI
rn
t
\--
,
E
I
t
*
.r
=
l.--^:
1\-
i\r\
;:7":*1\ l
q-T
I
LE.==
l>
-
:
r
Yl
I
L
*
ra
IJ r
"
:
n
r
-
(
{
,E
+
'=?
+
NF
"-
<N
:
|
-a
'q
a
I
i ;
N
i.
r
:
;
"
-
x-k
-
_
x
L
rs
;
23
"n
:
3frX
JtsF F
'. I
N
\
t
is
I
I
I
I
T
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 219/304
f4
q
-
i
.c
/c
=
_
.
;a
.*
g
'o
AF
=
c
q!+
v
E
*
;
'=E
;
F;
-=S
i=
t>=
r
_
,i.=
E+
R.s- t>)
r=
=
d
N
,
i,= 1
=
q
N
i<
r
L
?-
;
'-
.
.=
.o
-^
NN
=7
*)
I
!4
i
i
r
=
Z
i
l,4
\,
I-
.{
i.9
-\
'\
7
'-7
7
*
.=i.
=
;
-
"3
.
:
"E
-
-e
-h
lg
=
-
'
-
=e
*
:t<
_F
t
r
*FF
."_
E
=
:
EE3
i;d€
c
L
-*
:-+
t=c
'+
r
9.*
d
cE
-o
_
P-
=
-
i;aa
=JU
:^-
F
**
1
i
t
*
F
"5
,
l
l
5
e
S
i\-
T
I
rr
J
r
o
*_
h
( I
!a
iJN i
l
i
9
"&
-
>n .u
lv I
r
l
-
?VL
'=
eF
]*
n
J$
s \
i*jJ
$
I i a ocz , a _ I c a Tlr
n
rI
lr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 220/304
3e= =
ih
^r
-J
a
-
O
=
a1 .=
.
c
;
F
: f=
:
d +
x
'o
F H
+
4
-
lr
I
I
,
I
*
Bp
+
_
-
-
rF*
-YO
-
a
:
I
'a
E
.:
)4<
:
L
=
d
t
"N;
X9
;
:
t
:
-
av
,@7
-
!
"G
h
^
-*
r
<
t5c
?
a
-
*
X
o;=
/
=a
e
ir=
i
:a
_
-qo
s
!=
-=^
u
.-
:
-
-
.-
I
I
fT
It
FizL{F
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 221/304
t
r
IT
tC
I
I L
Faf<
7 . i/
zn C a o
d-<
x=
-
*
=
t
p 3G
')
-
*
i
^
J
*
:
E
-
*
:=
=
,I
c
r
-
=
,-
, , V-
-
i"3
i
--
,
I5
,
=
1
g
*
*
-
P
:
1
n
-?
=
'
=
I
-=
'=
,
=
-
:J
:
:-
t
u
|:=
==
:-8*1
;
!
I
C
5
*
42
-?
: *=
=
E
-
:_
-
-
-=
.
-
N^
-5
j-
.-
=
c
i
o
6
-
-
t
;-61
+E
' -
1
=
T
-
!7
.
E
ih ;
*$
9
r
.L't
o
* ,* -*
= a ; O
:
i*
"
S+:.i
+
IJ
+
i
1i
l-
rT-tt
rH HL
A
i" i s
t
\r
J*
b1
r
\
i
i 1
\
lr
F
+
l-
+
h
s
n
I
I
' F-r
l)
L
$
s *-
.,S
1
-
i$
- \
*
l"
\
'Y l* l_
IT
r
T
rT
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 222/304
+
I
-+
J
-
i-
q\
fj.
1
I
I
J
l
in
|
I
_
_
. i >
T
'q
\_
*r
l I _ .n
!r
r
I
,r
7
:=
II
s
Ss
.*=_S
i
c
i
!
:,--
{F\7
*
i*{_
'
I
l*st
I
.
^
e
3
'qSso
'.f>+
\s^',
G
iol
;
t
I
r
:1.
I
:
!
ir
^
t^
+
i
N
l-
I
i
:N
-
=r
;N
a
Y
=
" h
:
\
:5
N
(
F
a
i
-
=r
trn
I
r
T
r
I
oaFFFFs
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 223/304
\I
'-r
$$
-
dt?
^
r
Ls
I
rn
r
I
rI
- { cz d o ^
: i
l i ; - t- c-
I i \
$
,
*. t
I
a
-_;
*= ;1- a : : ,< G : .
N t i : =
\ i- !
t ;
!
J
;J
F
lr -€
=
.
'
. I | : l+ \
l
i-e9
I
i o
I
"
{T
i-_
I \ 1 I
i*_i
h t f+t \
l s
! \
'
rI
I
F
I
-
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 224/304
i_
4
t
\ \
s1-J
i
^
I
ib
-9
1
!
f
ry&
^G
=I-
^
a -
)
N=i
I
-
:-: G -e
'"n
=
:*
!=
=
?
=
'r
I
=3
i
;
{=
3
:;
=
--
-=
=
-t
=
^
r=:
"rd
=
-
-
^:
-=.=
ir
a,4
-
-
iX
t<
T
'-
--
:<
c
=
-
=
=4
8
j
*
'.=
?
frF
:
+
:
ra
',"7=
"
=
i.=
-
'
-
.
i
:
-
-
-
!
:
Sa
1=
l-=
s
\=
a
-
;
JxS
l -
'J
-=
J
-J
.=
::
-
a
*
'
I
r
-
4
.
l-
r
?
a
"
I
=
=
i
rr
NN
$
': =
1
=
:
=t-,
,F
=
=
=
3
=
,
^
r3
-
=
-=<=-
l
.
<
=E=E
r
?-=
':Jz
=
r
l1
-
-
'r
1
-C
-
l-
-
-
r
-
":{
7
:
7
^t
c
=
=
:=
=
-3
.
C
;n
-
-=
-
:':=2
'!
<
F
v.
1=
.r:
3
1F
-?
3
*
A
=
*
;
'r
i
-J
=
-
:
5
?=
t<
'-=
irH
=
I
*
I< -h
:
-
I
7
_*
*
l-1.4
*
l"*
J
:J
lr
"S
q
I
1
\--
;- =
r
I
r
{
I
r
7li*'
\
"
J
I
T
r
T
r
r
r
I
tcC
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 225/304
*-S
.
r
.1,
i
Y
=L
'--4
:
'-
-
l
.
-
t
-^
F
_
\
:4b
5;\
I
r
Q
I
I
r
*
I a x a .Ci
-e t
-:p
-
n-€ t
t
-;o i *
*-€ . .
o
j o oc c - =
:>
)s
I
\u
\ I I I I I
--
r*I
l\
l*
l"a
t- r i*
|$
I
t
+-
-+
i**i+
\
\
I
t
*
y
I4
1
T__
_
- i1
FE
3
=
:Fe =
:"a
F
?+=
*e
:
.
-E
:aE
q
;
=
.
;5
*
;
fg
;E:xd
!=
+
2-2
=
'3
'FE
=
:;
F
H;L
!:
i
r
F=
<
-=
T
".?Z
r*
r*
n
:1
^
z=
=
;+
g
3
i
t1
-_N
-
r
,
3
3t1-
=
:
?g
1=
s
:
I
G
g
,
I
-
i
'
"
E{
N
--
!
=
;TH
'.1.N
r?=
l=
Y
e
S
=J-^
seF
s
*
:
i
F=
=
F
Y
=i I5
l !
=
^
:
lg
7
L -
x-"
i
q
r
.r
,9
,1
!p
S
o
-a
-
lP
S
$
F
e
t
:+ FE
G"
F
;F
E
=a it
'n
E
i
,r
r
J
I
t
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 226/304
d i
F? --
a J
o
* r
\
I
IT
,
I
rF
r
X
,
:1N
;J<O6u
|-ttJ
c
!JF
4E'6
.
#4:
_
€=t>
1
IC€=
r
_
:
rJ
n
r+
J
I
c
;
i
6
h
i
c
in
*
';>
5
I
i
.
.=
2
:
-
*
.€i€
?s
3
5
+
N
-+
E
;
E
=
i
r
rr-F
."*
o
!
e
\
L
;
r3
'r
d
do_
-
,s-1
_
XHE
+e
_
,=
I
I
f
|
2
:
f
,
-
.
+
;i
R
a
y?
N
6
i
:
$
s
^5
c
.F
I
L
4
X
*m
F
a
F
-
L
'
:*=
c
s
Y
f
E
-3
i
o55Q
F
lt
H
gs
Eqx
*
e
=
-
=s
5
:4
=
I*
a
s
*
>
gl
lI
'
tJ
=kIc
ccI
c:
6
[-
--*
-1_
L
\T
Lo=mv
5$A
d
ad
F:q
c
X
r
l
r
x
i
*
r
-v+
=
r
n
sh
iL
r
U7,JUFc<
--_t*
-*
"
l]I
I
F
r
I
I
f
Tr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 227/304
4-o
Fs€I
(o
T
€
*€
--,iu
Hlt**
.
6
n
*$r
Il
G
<
o
.a
r
F
-
i #
>
.g
I"6
:
.N
i
uF6
t
-va
a
-o
AE
F
.O
j
FQJ
6
q?+
l4
q
F -
XqE
v
a
-.h
a^
g
H
o
,=
Ea
,4?
o
?
6
cX k
>.H6
"
'r
.
:
=
E
|
':
a
*
B;
a;
:
n
g
.<
ds
.
4
f
<
rB
E
=
-
G
:
c
:+
t
ta
$EFAhE
\T"(
-^,Ff
/Zk\
+t
I
I
r
I
rr
{ I az - a ; b
-F a
l
I C \
i
:
-
- 7
--
/-; ic\ '
l \ : 5
;la
;1r
: i
f
:?!
:
;7==
I
r=
2 z:=
?;Z
;
?=
==
E==
2
lF
=;s :
n
; =+
eF
Ilr
T
J
I
lt
n
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 228/304
g
Er€
=
:E
3F l;;E
*:"
F;:? A {*=
t
=
+e i i 1=
;=;g
*1F
=
=I
l€+
g-1=1
?=
tP;g
i:1 1:!
;;E
==i+1=
.
5
t?
=
a
' ]
=
qi = ==
z
z=
a
*=
,F1z
1
ig;J
;*7
;r?
tzc
;7,? ;
[ES
gE
F 3
=
i9+
a;ia :
?F
F:i
r
rT
I
I
r
L*K-=->=-?=-a i-'i-!sqL='-j:*
bj !
7L;rEE
1:7
;gt*f 5f
'€
c
-*It
t:Xt-
'J
e;x
t-!
oriFn
;$
zi :s
i}€
E=;
:=
*
=
q
:
Is
E8* 5
,3
!o
qeY
.
{p
G
9a
E
.=
_
;FF
rE;
gF=
gr
o
F
-
*
-
a
c
9
f
:
I
-=*
.
5=.
ir!
f
€E:
EE s#
l:d
:s==
J
"
t;
--sE_
.
sNE
e=,*
,=c
a:
*
sEs=?
?E
is_€e.-=
;
€; g
E
€E=E=
1
r
==
!C
-
9v
:
r
l;
+
-
;
i
E
=
=;;
=
-+
.r
:
l*=
i{
J
=
;*
.
:
a
=
r=II
UQ-cFJJ
7
I
n
I
I
r
t
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 229/304
:e;o"E
i
-d
.J
S
ia;O:o
5Y
O:Q
"5d5
EE
v<-x
O?*
S9
!*-!-
-
€
s
;
,g4*
'.
I
i E
;+
=i
'=
;
;"
=
-
5
.
s
'.
=7J
F
I
:
*=
E
i
!
=:
i
.-+
Z
=
-
*
=L_
r
i
.=
-
7
-
r
:
*a
3A-
5E
-=; :
*
,
:
.
F
,i -
-:-E
j:.i?
=
g
:
=
= E\
=
:-=
2
:
=
;==
E
;
=
*
=z
.3
a
!=
J1X
=
:;E
;
:
cE
-
:
;
=
.=
5
=
6
:E
:
E*
t€
:J
;
iN
c6c
a.F
"*!
'3
ts
-
.Q
.=
!
i
J
.
,?
=
;
bE
.t-
=
;
:
F
'
c
aI
J?
=-g
'2
;=
.
7;
i,*F
=
=
'-a
=
!
=
--=
:
:{
'-
s
=
=
a
.^?
L
=7=
"
e3
:
-
-
;_
-
-2
-3=
iF
a
=
ls 3E
:=RE
:
i-=
=-
i
rh
':
!;4
a
;S
2v=
-
-
L
E
=C
a
=
-
==
1
=
?
=
-
-3
-=
;r*
'.
-^a
t+
E_
-:€-
=
5
Sc
i=E_=Z
-
;
-
=
-
;
-c
4
r
.5
h
c
t=-
-1S
=.2_
K
=EuaE
5
S"S
:-
a
=i
-
if
tE
r
.f:ElE i 3tr
--€
+
*
37
=
.E
=
3
E34
l-C=
l
N
V
r
\III
I
r
rT
r
T
r
F c , a L a J =3 c o c n{c c ; z 4 { oa E h u
r
r
r
rI
T
rE
=
i;;
*
;
5::g;
i:
= : q G r -N r='sE
-
^-5 E X 7
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 230/304
D
I
I
I
I
IF
l:i;1
*u
1
€a
f i
g
;
q.F
f
q
't"F
c
q
b
rJ
€d-
@i
ra
r
o
g
.N
a
c
i t
(D
C
6
FT
sn
rv_
x
<1
I
it
s5S
\sq
.X
-F
o
!
b
-4
;9X
+
o=
r
c
v
€
bh
?
o,=
a
A
3K
a
1
-N
irs
l S
r>
l
ica
F
N
;
!3
*<C
-
1
trl
.
n
l
-$N
N
;x
- $
<
?
J;a
;gJ=-?2
w;i;. ;<
.
i a
!1;i:;E:Ei E3E:?
F
x
s
L1
ls
**+
s
'
l+
uc
a
t
rca
t+*
I=
b
=tc
:1
t-
;k
==:a
_UrrFg
.
-c
-L
+
'
'
4
-l
o
,q
SC
N
=9
-
qO
Yq
-
s
n
-
.
E
"ra
I
s1'
1
tx
.
-c
r
lr
l>
.
<
'-ri
-
\
r
q
t*FcF =*I
uF!iJF3I
c
6
$
T
T
T
I
r
I
I
-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 231/304
' I*-*
r*
'
l
l
-
'L'ho+
.e
XiqX
^
.
'.
t
r
l
rs
l.
q
t
o
i
.
\
d
I
6
^
a
:
d
q
t
a
.=€
+E
;P
q.=
;;
'
\=
5
._
J
==E?;:"€
;E:?
E
g
i J€
€
:eE
+
;*=
Xi r s;
EE
s
tq
':7=:3
F:E
rTE
= e
t
rE
-
J
3=
>
+
L
;
i
t=j;;;rE
E
=
1=
="?
itE;|EE
j.*
nE
*=
:f.5"*
*E=!E
E
:E
E
-dE
!1
;
=,
E
5E
l:!€
3E
33
.a
;
I
-$
F
\
I
*\t-_,*-*
,1I
-
I
n
r
r
I
r
{ i a az ;= : a
r -
" 6oI i
I
t 1?
a
.
F
P
ra
aS"
;o
*
.
T .y ir
E
,1j_ N
t
,1
t-+
-
t
I
( O eP
:
gA
4"
' =
.
€
o
-
-J
GAm
r
i
*
p
A
i
ra
i
E
I
ls
o
f
l
.N
*
l
-
!s
r
_
ie
F
l * IJ
=
bq E
3
ra
l
[F i
.-r
N
lo
,
FI ;s
Ei I i
r
N
.u
.lr
t
i
r L
i
L8
lrlt "-**
r '
i
!L
^
t
o a x 1 o
N f
N I*1 N I ! N t -L \
i
{+H
, , \t
r'
IT
I
rI
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 232/304
JS
*o
a
iP
-v =
-
! :e
:
-cS
N
iS
N
J
I
4
C
?C
ic
.o
F
-
A>
-S
I =
-=
s-
P
iF ;:
I ^
I
r
I
|
-
,^"
'"
"
a
N
r
f:E
E
;*
-
i
j
t
|+
e
i
'
-
X
,
lc
*
3
J
+SJ
! rg : :L
h
rI
I
r
T
vII
'J,Jtsz-FJPiq5<f
I-
=9-G
i"-
oFi
i
I
n
I
I
r
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 233/304
I
I
I
-
I
I
||{
-
ls
"
t
'%
t
N t
4
m
dJ
N rG : r i I A
E :- Eo -=: F ! .
F
*s ax- =x
C
tC
ta
oB v =
i)sD
E
+
+
$[*x
4 d o c z q c a Tc
$J-x"
F
F
@
N
t
: .
n
-?
b
=
J
; i ;
,1+
;
3X
=
FX E!
E !*
&
-O r r= r o ,c X ? * cao ,
i.-:-
'v-v
6
-
f
-
r
=E
=
Y
'JA
-
i9
3
a
x
i
d
FH
+
Xa
'-a
Q
'
F
P
'
P
,EIX
;r
i
+
z
*+t3
sF
=F2
4
o
o
F?
a
l+
a
E
g
c
f5E
:LE^
3-8x V
Ec ;
r
1 a7'O a =
,+
=
j
7
t5
I
I
I
I
I
I
I
E
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 234/304
3
nio
c =:E6RRRR
ag
3ss
^
t
r
l
r
i
!
*-
|
I
I
r
3
re
a
re
s
;Fa
6
O
O
i9
N
f=
=
t
9
N
J
ioG
og
*)=
a??
5
I
I
i
I
A
A
A
A
!-v
rF
r
q
c
G
=
C
O
'€
cro1
3
x
F
F
>
:1
0
6
0
-E a qO
t
R
!> 4X
t6 6 u
$
=+H lD
E
6,
\
+
F
s
F
F
N
.
€
F
l l
t=q
Fra
oA
A
:-"e-"c
.S
c
c
C
c-Jo
{N
O
tJ
o
c
c
o
IF
I
A
rs
;
H
:
cC
c
:
F.E
Y
:"?
-
:
t?
3
5
N
c
r-c
.E
e
x?5
9
r
:
l =EL*
l$
6T3a
P
D
g
;-
ls-v
F
x.
Fs-t
"r
frH
F
3
tP
F!3
aEo
3
F
o
P
@-
=
6
!
-H
^
F
S
- -
*
-
1:=
is
Uc
-
E
!
3
@
F
L-)
s
.
dG
Z
FE
d
-9
Io
a
-*
6
'86-B
-n
^
+
ta
i
:ca
iD
P^
=
-."-
't t
aJ
o
xo
s
4
-+
ts
s
-
U
,s
*G -F
N
bO
-
8
'a
x><=-+
=6
rJ
=
I
I
I
I
I
-5
F
=
E
ER
RgP
I
i +
+
i =
eI
+
,
TEi E
:?I
r ,
* yT
T
= T
H: =
-=-:
=
i -F
;FF
:
r==
r-=*i-n
E
i r{
se
Es
-&
-,s t.-J
t"s:rs E
;--
i Ei r
:$
$
$r
r:
S
s
*+g?L
7
E
?t i:
E
;
#
E
i
E
s
3
;
3
d6c.n@
o
1++
QFzFpts!-Yo
E
.€
+
"so
t
|
o
i
a
ls
:
-
H
5
:
.c
-
,6
I
gE
;
,*5
g
Ee
*=
3*
Fd
E=
.-
r
€
fr*
;
i
*
=EF
FX
F
-
+
-
E
O
5F
h
.es
tr
,
,
i J
a
g
H
3
oE
*=-_*
g
g-
d
E
*
. 'J=*
5
d
S
E-*cE
-
1
r=E
':!L
!E
B
b
a
+
d
, .=
5
'&
-
b9
Er
."g
=
>q
E
e.6
1
lE"
a
I
E
ts>JF.
:{
1
T
!
l
lo
h
;
r
I
.
r
:
oE
'r
:
i**;
i=
S
i*1
d
E€
t r**
:
:=
.=
-
i
:
i
.=
*
=E
cb
o
o
E
.1
i9=
4
=
.
;.
,
iI
.6
?
.=
:
q
k
:
€
d
e
E
E
-
0
g-^
'-
o
,
1
!*
es
'a
H
-
5r
:q
:=
ZEo
E
x
hr
E
E
E
,6
u
i
*
4
3
jc
o
-6
-a
--4
FF
qA
egN
s
t
*
Lq!a)n*
I
I
I
I
I
Iq's
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 235/304
. 85
:J
P
9
z9_
h
*
oq
.H
e
o
i*
*qF
C
-;-gr
$
Ec
{$Fs
sE
o
;3
lE
-
*
Ri;
;*
?*=
3i: gS
.B
+
3Eg
i;
;Fg€sLA
:
:€E
;
i E j:
;g
;*
sT
E
*.=d
:r
5n
b
r+
s
$;*
*E
$$l=
:Eg
g=s
5
F
tg*Eg
sr;s
$
cY
n
oo
+
roc
.+
r
l-n1
H
rc
O
+O
!
*
+
T
k
CF
5X
r
o
:
o
€krJ
iE|t
sbNtl++
c
1>
'Lno
R
9
n-E
-
9N'
I
I
-
I
I
I
\J
{
g E
b
=
'
N
;
e
c
l
r
6;F*-i_ +
-
rr
=
:
u-
|
c
F
.=N5
=
J
N=
lrv
=$r
tJ
la
-
:
f
vrc:
u
t.1
:o+o s
8
>
t
o
lr
1
Pq
&Aq t
X q ! 5
9 )a
t ,
{ - o aaz " a{ a o -oc-ca r coqc z X 3 " ao
< o
|* Er
l
l-
^
u
E
o**E
S
r
I
i- N
a
N
$ l lY N
^
H
l+
-
F
i l N
N
,Fn
F+\1 1
{
I
I
I
I
I
I
I
n
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 236/304
7F
-
I v
'c
!c
!
5
*-3
e=6w
sN
l
T
ir_
ts: -
=
€=
b
u
-$c-3
1o
-9
3
-
'L
i
r
3
Y
I-r
lD
l
l
tJ
-
l+
+
-
*
fq
*co9
=
;1
i:
f;:
hos3
E
d,8l.
:n
',
l
-
i
3
5
;
gN
q .c
{
5e
o4D
:
=^
I3E
I
I
I
I
I
,
"€ e
sr
f=
:
4E
E
Z
!€
E
;F
i
r
';a
.
:
:
EE
&
€
;
rE
s*
;*
e
;"
;gF
5E
n=:ts
:
l;g
} E
;i .A
=
<
*
-
;
a
-
=
i
=
e
-c=5
*
:.-*
,
't-E€
tl: s
-:g
: =:*
;
=s
E
;€
:ETr"+s?
EFE
gj=
=;5
i#
;;
E=
;F::
;;*
=
2Z1
:
-
*:r5
NaQF)F;qU
s
=
c
=E?
-
q
-a
i,
,F
'
"
i
3
:
d
.
:sI
Eg$
E
f E E4z
Y
:
:F@a
L
-;g
iza
€
-=g,,:
3
s5
;
5=
Z"
Z
=
o
l
_"J
E
nz=
q
c
d
E
z
= 3
=
E
* esS
c
:9
'-
i?
:
-
n
g
F{E
=
F
=
^
!
J
^
r
=E
zZ
i:
"9 *E
-
-
-
i-
irJ-x=
'-
.
:
-=
"
i
=Z*
€
:
=s
;
=
?:=."F
i:
*
*z
?;E
5
i
n
"
=c
4
o
-
==
-c
A
:
=EEE
-
.
=
!
o
==
a=
4
-
E
=
4
=1c_
-9
E.qo
c
:
.a
N:N=
d
O
Jo
;
N
rN
J
t
-cE6
-=
3FUFct-+
t;
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 237/304
$8E
g
ZE
r
+*
s:E
{
;
E
;
FFg
B
=r€
E5
:=
*
r s
E;t
i-
d
r
'
=
;
i!:
.
. H;
?=i
EJS
=
E
EgE_
*
rs
E
;rE +;
E
u
;g
En
6vXO
3
,
o
!s
:*
x
5
:J
aO
I
,o
9,--
5
s
.=
!
-
.
!=
J
.s
4
:
E
3P+
i
!E
-
€
a
.*
-
a
s
;
t
:
'f
Sa
.
EsET
*:X.=
:
r
C
t"
P
f
!5
dH
-
.
F
t
.F
-3
5<
r
i
t
on
b
=
',
h
a
u
-?-d
=
.o
;
J
JG
a
qO
O
A
m3E(
.q
h
ItIIJ
I
I
I
I
I
I
{ * {- o a ca ; a
3
r
r
s
*
ig
I
I
I
|
-7
;
x
""-
f
s
aQ
o2
:
\
6
!
o
:
:
:
;
td
F:
<
P
E
R
P
'
.
F
c
n
-
-_F
5-
lC
6=
EO
.
p
5
+
C
H
;
c
X
Q
'Jdx X=
Q
FX=
*
a
gQ
o
;o^'-o+
a
=
;
F
;
:
-
O
F
I
J
a
F
h
=
\
ug
tr
-
_=
*-83
=e
^6-
=
sE
=
-
s O
-
F
-
I
J
"q
l €
4
rJ
lc
o
-c ^
5N
q + E
\ ^
I
d
r \nr
c o - - { c { a i 2 o 2 coa z F-J
i?
t
=
7
t
7
<
?q
??.,
"
E
;G
=
-"-a
+
=
5
4
-
^"-.-n
i
--
-
=
=
o
c
=
.4
)
5
=
N
-sa
FG
n
=
:
<
-
=
;
==
S
1
=g
r
'?=
+=E=
a
-rIE
r
C
.3
>
fI
|
^v==
""5
5
3E
I*oC=
s
FcP
i
H
F
*3
n5t
:
6
o
I
i
o
-
-
r IE
"
g9
-
3E
rc
o
=
=d
c
=
i
n
?
5S?-*
t=E_
=
;F
^=
=-
==
F
;a*
:
X+
a
o4
' -z.
l3=
1=
'FF
rF
"aq
+
r
-
s
C
3S
;s5=
B
5
a
!
l"
;+
6op9
F
G
o^o
i
FH
5FS?
t i-
1 l{*I i I
^
{*
-
r
s,-l:
'h
=
r
*
==
t
c
c=
!
a
_
t
-
o
*a
-
=
-
I
:
T
'
=
E
a
-a
2
.
* ;c
=
?
7
h"=
-?
=
-
-H
-
a
-v
-
<
-=
s*
;
(4
t
?
3;
=:_
'h'-
-1
=
=
a4
=
^
-
=
A
3
;
r-
\
t
N
=
=
c
L
4
.
--
=
2
-
s
.
*
g
i,
3
_r^
=
=9I
7
s
c
5 i
"1
1
tQ
?4
-
:1
=-
-=
=
I
:
;
s
-
rc
-
+
-
q
I
P
a
-
=
i
^
=
;
;
o
=
=
v
a4a=
=B
:
3
.+ .q
r
-t
ts
s -
S
* =:EFE! +
1
;==r
??i
; -
J-
' L
a=
3=T
;
a :5
s-
x r$
bo s
I
I
I
I
I
I
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 238/304
r? =_ r b -a!1 e ' . :$- ;.+: d-_ a =: ja - 2 3) zP * aa ==^- -
c ==:1) ijF '? '3 :a
_E3F
F
r+
i3T
-
ffg*gi;n
;?
eZ
.e;=
$e1
=
-7
**;
=a
;F
!
g+1i
i :
a
Fi*=
t;;3
a
:E:34+
i?
:
"F
7.s
73,-q
1
-o=
*Ci:t;
8
z;=
p
c_=
-
+
;
i
:
==.
i
1
T
a
'
4
f
E
=
J
"E
=7"
-3
giA =
;
"a
=
=
-
;a
-
)
N
=
F
.J
F
fAE=
=
.r
5
6
F
g55
t g
g
;=
.*1
s
;*a
5lE
r
S
4
.
E
Ys
r E
;1E
r+
iJ+@
l
O
.
Erc
iF
l
'
(
o
3q f
r-+- 1 :
4ur
a rJ
o
a i
:
:1
r t
FE
5A
R:
0
-
;=
-
:1
i=F
,33
r,_
3c
_
f
c5
ea
!^
n"
F
F
BrE
sF=
Ff
S
F"?
-s=
:+
r5
-
dE
a
3
i !
;gF
-
O
5
,
=
3
"V
j,
1=
cA
|
-T=
"
E
=
a
pG
(-
6c7
:r?
=
|J
_
l
t=c
\=
,
I*^E
!
-
l
G
:
:a
=G
=
.^
lp
' ! =q=
-X
5
3X
e3
7=2
=
l
':=
t=
*3$
--
=
53
5G s
T
-*3
;
l-
-F
-=
*
s
=
:
t
a
:
5_-=I
:
:
=
=
-
-
:^^
-
9
R*
+=
;
{58
Y 9E
4
^
*
-p
c?
*=
=
v
a
w
E
op*
.3
:*
**
s=
-rC
J
-n
-=
-
d
o
q
@ i-
E
"
r
J
=
oF
o4
-
<
.-
=
p
=
I
I
I
I
I
5'bE+=
's
9+:d|a,-it
.-
*c
:
T
.
:
E.
,o
n
-2JY
(*L
;L-v".sR
*
+
;4
tr
€E
;=
G
Dc
f_
r
3
e
+
N
"cuo
o
t?
r
=
r
r
:
E
.
a
'
.3
a
:c'Cu
9!r
:t::"X
i"
od
etocc
53LE
E
A!Z
tXU
*
akg(JA
Na.*cX
3r
.d
{s
a
tF
Lt
qan
t$
t
r
iB
i{iOO
I
-
sE
c
:Lo
t"e
c
I
E
-1cO
€
^
a
'=
p3g
E
Hd
-
*
c
?
ro
t
3F;
y
*^.*
.
:
H
'
IH
|
|
-
-
l lJe
l r
-:1
ry
$=
r
r
o
6
F
i
i
t3
|
|
i
E
,xa
s
$
.G
K
g
:-LA
hF
6:rE
z
r(JFE7F,U
RlsL
:I
.
{
*tts
i*s*
:ssR
'
++q|
+
!FOFoJFFN
ry
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 239/304
R-tcc6
C
o
O
D
"O
-
U
,
v
."AC
5
ico
'
c
F
+
n
-
A
d<iv
.
o
.'.sE
-
e^^
99
Y3
-€P
vx
!x
rqX.
-S$
i<
cJe
@6
-eO
o
td
E
e
O
o
p
|
|
H<
|
|
c
r
-o
la
5
ac
rs
-
-
.
d$
l<
.
l
l
l
S
F
o
.
:L
3
&
€
= ;
,a
F
.=
a
,a
\a
<
+u
i
d
ry
c
d
i
ir
J
l
l
'
f
S1
S
'X
s<
ld
&
-
'r
:
'6
n*^
=
Hv
E
5ss$
c
t{
2E
d
fs
INttl"F.D
+$iF
H
lE
*E
H?
I
I
I
I
I
*a
-F
'?<
;a -o ro 5
,H QX
-=
!F
1
?
i =r
"
i€
L
_
s
{
_
_
_
i, .S*: t#
z
i;
?E
=
sa
.-
l
;
-
F
Eo
e
i
F
'*
t-FE3==
=c
$
=
lSq
c- i:3
dTr
=E?
=
:r
;
B
$
e
:
?
N-
=
=
!
a
P
',
3
ER
2
=
r
;L
e-
4
:
o
,
:
D
-a
ra
i
=
-
:
(S
:
c
&
Z
S
+
-
c
H
!
F
=
vE
a
E
F3=
;
3?
3o
?
C r o r F o c r x * oo {F
A -Gos
'3tsE X- :E
J
te!
F
P
A
eE
r
r
r
=N
I
i
|
*O
iP
o
-
--
-J
=
le +
L
H
r
I
r
E
t
-
.
'
G
'n
9-@!c
t *G+. ^
F '+=I X i{
w A :
\Ys
F
a
\
"
$
|
t<
t
*,F
6
EH
;
;E
\S
trF
c
*
.*g
: 5
r
7
^=
i
N{
|
-
;
ik
:-
i
js
;
!
ir
5 F
-
sE
I
t*
!1
1
9';r=,V?
-
:}
i
?-
|
!
i
=
r
=
=
r
aGc
Q
>
.n Uo
*
^2
t+
xO
o\c
- q o o z F (*
I
ts
.$
:
_
EN
a_
I
i :a
q
: lq n t L P
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 240/304
|
|
t
.
F
F
B
;
F
tr
gc
$
,Pt
s
r
ro
tsts
=
i
-=
F>S
lR
L
:
-
-
lS
r
I
r f
,,
:;j:=
+
|
l
:p
*
1
3H1"S
s
I
6
:
l
!
r
t I
H
if
|
|
|
.
=
o
-_
n
l
o]
:=
I
SU
*
^
?a
i
G
.l
i
?
:
5 +
r
-1
l+
q
lo
,*f
9
(4
A
l
l?
'-
:-
i
i=
N
\
c
f:;
H
z
'z=
3
i
dG tF
FF
E
oS
B
?
1
rQ'r-
G
?:
o
;
|
|
,
;
5s
+B
i-*
-
i
|
1
-
.
Y
rrrd
a 49grL
F
a+
a
&
t2 &$l iJ |
-o
I
g
'-Y
g
o
a
[ci
s
+
sJ
N
B
*;
t
l
t
t
r
l
dN!o g
l
3H
,5 FCra :
t+
5
5
i-+ I t
su
.Fr
,
q5
i1" I
I
I
I
I
I
I
qE
it:
:4:
r-
Yl**cs
irlP
t
cA
(JF!tQF!J
6^
.1
!
*
'c
tc
a
N
, +
-
o
a
€
o
a
-wSr
:
o
a
I
3€
rc
.
-
Y
k
:v
=
c
^
=
Y
,
t
!
'r
lr
6
I
i:e3.5F
=
U=
6s
5N
'-a
XXc
q
XXo3.E
*Fa
:TFF
gsFF
F
FFO(JFts
S
l:
q!
#r$-
G
!*
l>-
r
_
fFsp
$I
r
I
I
rI
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 241/304
'.1
t_J=*
Fr*T
hls
Ir **
*
I \
Es
o
**s\-N
s
.
I
I
o=
lt
;
3
€c
<=
.
so
-o
a
-
O
dC
i&
l
o
s
i
Md
{
{
f
a
8
o
s
*
*
i
.1
Vz
;
I=U=E,E
iN
c
I
-
l
.o
l
.
;D6
tE
r
*s
ha
m
.
uT
E
g
l
lc
I
'a
-*
--
*?
cft
s
t
',_
r_
9
'1
6 F
-
=.
\
XX=a'3;dH
XX
Tts
.9H.a
q
p=E
fa
-*
I
I
I
I
I
I
f
is
z
= ooz { . :
i;*
$s
r l :-
c
-
F
i=
;
*y
=
.
=
-v
-
"
F
!
A
r rt:=\
tJ
.
i
; r l:1
=
j l
sS -i R
i I F
1
+
\
N
A
"R
tot>r !o ITL t lr t IE l= z oI = Coo
=d@t
:n o*
=N
-1
" ia
o
s !
a
A = : o R*D o
rn N,*1+
_
\uN
€!
lo
m
s
[FH
!
*
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 242/304
I
,
l:*
Hto t
4 t
s
;
o
3
S
o i ,h
o
:"
+
!
e
*
;
.aX
T
a
D
t
5
a
rJ
*E
?
l
rc
:
:*
*
?
j-
=
n
-
lJ
g
\
-<
4
r
F
_5
rc
:7
i
-
H=
i
J
-
!
.
-
rn
r
\
-
^
Q =!4
id
I
I
I
I
I
s
uFS
e
-f
+
l+
|
S
$c1
s$
cS
UUFq(:td
N
l$FF
I
I
.=
:
4-
!
c
;5
' 3=
' =
-
n
4
<"
=f:
-
?
*=
E
.-
=-
::
;"
=
=di :r
r
T
3r r;
E
st
r
E
:
:
';==
i TT?n7rL
r^
.* :
?E
ir=
=-
=l !
a
l
r
I
-
u
-a
Er
_i :.;=E
:-A
Fs€
i=
i
tFo€yE
Ir
i
-';?
E':
$
',
E
:;a
; E
€
2=,==
o
9
a
=
x=
=
d
-=
9
2
1^
!
4
=
-
=
i
;
=td
f3d
l-
.
=
:
c
t
€
L
o
+Ym
'i"z=l; |,
=:,
,
--
-
l
r:=*s
: *
c
.
x=
=
=
r
i
-
e
'Z
Z
Z
FJUF
liIii1
(ii
-:L
,d
f-p9
;aF
+
I
LL
,v
L
_
ic
r
:-
rs
'l fg
I
I
I
I
Ir
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 243/304
TFf+
^
i
-g$9R:
a
t
i-
A
,
*E_Z-4
1:=;+=:
';r
_
I
3
,Tj
= 3 +
=i
u
' TF
F
E
g;€
f
i=
=
T
,
i
=
,.
-*
2.
de
*I
3!
e
r
E*+
a
i r
4E
a
E
l
:3
:
Ei E
:
zE
^
E
S9
.9
I=e
.
*
i=F
?
=
zssi€
a
I
I
I
I
I
A6
H
J
o o - - od b X
: oo @
{
5
F
i=
Y
n
^
=
a3
X
z
eR
,?
e
6
=
E
5
"F
X
P
^-
cE
o
-n
raY
A
P
2
-
f
d
e
r
-
q
=
6
!E
3
9
35
A
:5
:a
i
=
=
o
v-
E
3
C
-
O
o-=
3
u+
-
!
o
P
i+
;
=
sEt
C
=
+
x5E
6
-
ts
3
9
i^
t
o3
*-
=
_o
!
c
=
i(=
o
T
c
a
a :=
G "5
+
+
-E
w
a@
-=
i,=
it
d
i."5F
'
5
io
^
O
"F
=
-4
!
X F
z t
qF
6 o z { o -
FsFl l
*o
*
\
N
-- l "
i
I .-
|
:
-c
I I
.1q-q
i I - \
F *s d
++F
c4
V
=Y
:1V
4
r
a
-
q
i-
c
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 244/304
AO -=Oo -(D :s
€
"
Ft
a
r
l
:
N
l
;G"xg3"E
r-
p rIr=
h E -=
l
;
3
:
C
-;
: 't
e
Yni
3grr
Fi+
=
l=
lc
l
r
iD
t
O
;
5
O
c
F
r
=E !
=
:
:1=
A
=H=^
*E
-
7;5
=
=3
-= =
:
;
"=J
+s=
^"1
F
=;
€1
+i:
c
5r6-;
=
;
.
-
E3
-- ?q
3
+
=:
"
=
=?=
;=
-
-2
i
"a=
-
-=
:==
a
i:=
i "=q
=
:
;
3
3-1
*
7
=
!P
.+
=_
:$
f; i.
-=
a
rX
^
=
i
a
C
oEl-
-z
V
r=
:^i-
=
**3.F
CJ3
F
,4
+
=
-=-*E
z;al:€
:F
=
*
t7
|7
=
-
l:
Efa
:" =
==
3==
c
:=
;q
r,3
:
I$=
_3
;8
r
<c
9
=
=
i
=
a*
i=n
F
i
a
:=
-
i *F
=g
=
-
Y
I=
= 1
;
es=
FrE
=
:EE
2
=
.
E
I
=
G
i
oT
c
:
=
:L
x r J
I
I
I
I
|lin,**1'3,*ii*i*J
a
n
7o
XO
;Y
I
:K
E
*;€
I
4
-=
d
-JA
:
s5
.
:cR Y
q
-Y6
I
i
j
c
l
I
)LA
i*E F$
"
o,
'-b
I
I
F
-
O
tL
a
<
I9S
o
U
o*A
Y
d
F5 r
<
:"Y
"
'{
rL F
n
=L-
o
H
N
-
n
s
ra
:
:
b
b
a
:
'
.a
ia
9
1
Y
C
r
Y
r
E
ts
I
i
'
Y
t
I
i
7
h
N
-
.
A
k
!
{
-Fx-
J
.
xg
?
H
O
:
€H
.
h3F
KA
ro
c
lit
I
^
*
'-
'
i
ii
ttIH^4
t
lFh"**
t-1
=t
s
atE
S
qR
€)
"
!€
hqqo
Ii;I
ItIr
(Fa=uFfU
F
?H
iZ
.'u
oFFOFFc@
{%
$
-
.AE
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 245/304
.n
s
A.
c
titb
46
i4
Fn
r{
5c
-
-
4
ih
*
'd
.r
lirJ
::LA
.€
H
to
J
X
ls
1
o
.
r<
YH
i
=
F
".
a
E
'
':
i
9E
/ aJ
,
!
l<
g
F
;7
F:9
e
.
4
'6C
-s?3E
L
f r
IFN
?
I
P
O
I
d
H
c
-Fs
3
;EH
c
U
LBaH
c
A
T
I
r
I
I
II
3
5F
i$d=
F,86E
;a
-
i =>
6
x
s
'Alay
L
:TN-
.
,
!
!
A
u
c
i
3*
E-E
Ce
I
, . o a o - o
"x;X
O (D rQ
ac cr . od.c ac t cao
z 6 8E
<
5g
r
o
\
,
S6 =
G
1
X
u
X
Seu '=6"
\
=i
*
I+ i
5
'
+c
."x;* 3X
a
4
3
G -g s "=
r,I
-
;7
.
/)=-s
"=^qD X
.
s
-
Fs
.
.8
usE
1
. X x iP l
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 246/304
a ;
=F F
N
-
te
>
e
-
i5
.n
;
?
o
YF
i* lr N
-" r =
.=
c
:l {
-6- rYn P 3 e i- * T -<
3sH
E
ts
+
'*3=
=
a
F
F
8
b
5
3E;hi8
eE
g!3HEH
aEF=F
}sS=
7E=i-L
q
3
EF
4
=
E
=
"=
i+
Ea
3
E
=
;6
=
g-
a
{
=
Ss3
:3EB
rE"=
3
-
N
i
;
-
--
=
!
Ps3-
3
:
=
1=E3
8
=
$
-=
3
;
=J1
?
i
7=
-
^
ic+
r
+3
=
=
a
"d
2
2--
-
a
a
=3
a
' :t
+
;
3
-6O =E
1
:
.+
o
6
^
=
o
ci
E
=
l =s7Z
F
!
-
9
-
r
-9
ju
=
.
= 7
e
f
|"
-==
:
+a!-a9
,1?-.+X
E
c
cX
R
-: *o
9
d
YrTa
.
.-
RS9
-=
3
:
=oE
;
fSsF*8r=
.
d
=u
E
ts
_
|
3
|
'A V - Eo .P X X
I
I
I
I
I
I
IIl
i1
i=l-s
:3
rt:
: Ill=It
tI
-
3z
sIi
oFt-JFUF6
IT
I
I
rI
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 247/304
'C"
I
i
i
lrn
liNi
z
I
I
I
I
I
I
ca
O -2 J.O
O
==-
!
lo
a
D
.
o 'a{
1 N
G
,5
f
'
t
! I
f*
ti
i
. lA '
e
E t I
N1
a
i I"5
g d o oc - o-
? I 4
z 1 f
a : - g ca C r c 2 c < -1 cao O
)
t
i.-
;11
i t ?F l
'|Ni I
- i3
I
I
I
I
I
r
I
t
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 248/304
z
ttl
BI
*lc
-1
{
9
cs
i l -L \
t
lO
O (.
1
c *s
=
=
l
:
fJ
l=
:
r*
i
i
l7 F *
rn NI
I
I
I
I
i.E
ld
E
gg
:;
A*E
4
g
tE
:^sE:E
:
T Er1
5E
=
i,=
:
_
o*
_
igE
i T
E=
;*
g+
Z:" i
5E
="
;
iC
dEE"r
3
a
i
:€
o=
; '
::=
,rg
:E
gE
;
"8
=
€;
-E:n
-s5
*E
r*E
E
:$;37
rn
.5
*
F.dC(;FX
zDFU
:A=Yr
Tlr'r
r
-a
:
:
-N
=x\alti
:
1
cO
FF
N
FF
HT$T
I
I
I
I
r
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 249/304
S
E
H
r*€EE
:
eAE€
:
:
H
Es=
: !E:
eV =
'r9A
9
-1
j
-
.
-;g
E
i- n2
E€
?,
?s_
:E
>X_ai g
^;-cEs5gE
S*
:+
t
':
g
EE
r
=_
q*n
F
i E
€
se
;F?
?TE
E
J
E.a€
;1
3S
{
c
oc
:
!
E
5
5
"=E
E
'1o
d
t
'>1
Y
-
.Fz
tp
=
I
+
c
.
.=Ar
'-s
'Fac
'-
P
;
*
o
i
=
?
=
r
i
!
nE
:.
'=
-
a
:"L
I
h
c,
=
>
.47
E
g
Fr?
=
=j
:N
?
a
j
-
>
x
=<
7
7
L
=
o
N
X
Q
.
qN
'
7
-7Za
'5E
?
:
:
)=
v
,J
i
t
C
=?=
=
'
s
'J
=
;-
!
a
:
J
ia
-"
!
Lc
>
;
'7
1.
!
.
a
o
-
t
r2
:=
=E
a
2
-H
c
2
=
I
rI
I
I
28
=-s3
*=
E5
IF
Zn
1=EaE; r+
i ;
;E;==
E(+;Ei
? r " ==
=
I =
F= = :=
?e=
" ?=
=
i;=1
=
=
tr
i-=5s
1
3
it 1z?
:;77
i; =+
=
7
F;
7
==-;--
+i:?J;
ria
s
=?
:
1:3 E
=
=
=
1ZC
=
:7
<
z
i L\z=
;=
-F 3
=1
=
?
_i ?
=
=
?a-
!
'
l
:
-
3
=
1
E
E
1=
eeE
E
7 =
===
=
_
-_
;
>
=X
_
iq F tz tx J ,
J
c
G
.N
''J
:
-7
(
3 :
*
J
:1 '= .
':.=
- x
{ i o o - coI a
-4
? 3H gAtu
a i
? c ?@
3
o ro r -odc z c ? t1 oo
G t I : i I { F I I
I :Lt
9
Bi I-
R
5+
.
$Y
-
' {+
$
SI-sSs
i + =
F
F
i
I
I
I
r
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 250/304
z- D
l I
-
o
*t I : e{
El I
** v5
p
=
E
F
;x!
9
-C
'\
$
;E ^
c
1
:^+
:
Ec=c4J
-=
E1
F
3
)' G
+
=a
)
e
-
t6g*
n
-F^
6
fAP
9
t
+
e
;
!o
r_
a
E
cF
A
iE '-H*oF
o
o
ts
E
g
E
F
*g@
=
-
J
=
5
sE
5
.
!
;
,
\
*
;Fu
C
Io
:1
1
.=:
=
ir
O
g
-gN
?
E
re
- $
I
I
I
I
r
IiI
N
NlI
oa!'33
ol!
*u
U
!
9A
@
<
A
L
G
O
"g
s9Eo
Q
hX
i
l
,
l
*+
d
d
o
-
o
o
L:-
a
_'s6H
o1 g.
*;b
Fq
a
v
X
:n
E
E
E3
":E
g
t
.=
aH
:a
.
E
Y
Y
co
f
L
=3 g{3
,
*?
;5E:
i *
iE
,+-
3
;E sLE;
?s ;
E
ixE:
€r*=
EE
;3Ef E
;E
s
H
E
E;T
EEg
E
:E
i,
;-
ErsE
3
E
x,,i *
a
Z:
Vs
1
o
-
o
r
c
>L
;
*E*a
€
E
S::
JF
cF
r?HUuF!F{
qX
I
4E
P3
:
^l
r)
d
Ir
-
,
'a
t
.9
"€,
?
"T
*
*1
l
l
t
-
]
c
-E
-g
-
ro
-
L
*
:?r-o
3
'z
lFL
f'1At&
tltFF
{I
\
tL*
$
$
I
I
r
r
lrI
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 251/304
5
f
.O
aF
tite
ro
l$
-
c
-
IN
Id
J
ll
i
I
-F
-E
-€
{<
Ii
d
r-
ia
q{
Y
-i*:
*?
*T
l-1
l
lN
ilt
p
:
:L
:
-1i-N
:15
c'aXX.-
\Ft
Cd
ra
:
/
aX
o-X
s=
E
d
k
-4
d
J
JEE
;->E
2S
q
.3
g-
;*
=
*
-x
c
oN
F
v-
.P
a
a
J
:JE
,k
i
hA
'-.
.EX9
+
H
*X
E
c
6
F
aDo
.Ac
*s"
Ir
-nI{:L
I
rI
I
I
t3
s
s
aa c { ai o
? x=
;4
-
<FRE
!
r
i
o
--raPH
\-J
HE3
-
s
5
!
a<-
T
=
-
=
.E
!J
.
+
-s
o
"
^
&
5
!3 JF
CG
=vJ
uR
CAO
!
*o
a
S
*
s
s
N
q-s\+-*
s
.**
-* -
-**
s=$$
N
F
s$
o Ta -a- - cF c Fc 2 !
. oo 2
:_
^
rc=
-
!
} ; 3
Y
a
4
o
FA*9H
g
-u
q
"g
A
IY
-
e
; ^+
5
2
;4
Fc
i3
o
D
:3E
E
g
=
:
-
L
:b
-
=
-6
=
f
=
'"L
;
5
=
a
o
4
6
-o
r
=
a
$
*
6*
-
=
E
h
L
l
O
=
F
=
=
-
?
$E
JFc+O_
:
=
E:E
io.n
3 ",
EX
l,
'hF
C
>=
.
a +
; cO
E
A p 1Qcv'a
F
+
*
gT trore
+
"
'
t t F
F r
F al I
uis
t : @
\S
I
I
I
rI
r
I
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 252/304
I
{E
Frt
G
!
t
tF
r1
c
-*c
N
it
I
t L-c
t
F i i
N .
9I I J
? H =
.+
gE
=
FNa ,
i
€
ua5!q
"
=
l
i
tJ l
-
l
r
H
l
-
|
l
.
t lr rs R
I
r
l"
n
Ir
:rg
ggE
i 3ga
i EiE
; -z
iEi;
;iF
: i:
i?::Ez
si r?
r:
: ;E?E :!*
€vl:.
E:
E !7+
t:?E
:;r
"=
=
!1zaE
=+E
:
;
*
S;;A
S
u
ra
roUJzi5
IOr$XL€N
d"5<;
.=
=-El-J
"
-<<
-LO
&
XY=oO^ZA
:F
I
IT
lr
I
ITr
I
IrO
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 253/304
Ea
1+g
,3
i 1
r
i :
;* 3
?
r:
$
g
:;=
:s*
zEuE
: ;
i:E:;$
E
E
ia
II
I
I
a a :z - o ,a J o { oo {I
I
r
I
I
I
I
t -
-+
o ,
.s$Fa
lJ-
o
!Ge
d "-
/1
=
\
(e
v
t xC
a
=
-
r -^
o s
=
G
;
o o O - i
- =I
c :- \a )y
i d !A
i-
V
6Z
i;g=
s
=iee
|
=
=Z;+i =:z:i
-77;I
+
tZ
|1
1
Z ;
]--3
j 3
+
r =
:7
=i
l-=
72
' =
=
=
i
=
==
3
=
:Z
;
9
=
+=?
-=
5
;5E3
s
iFSe +e
a
= i-s
I E -
-
ts
l
-
>
J l r
14
i
\T i-
*3
t f
=
:(
\ 1
t
** I a
l
Ft
i
-! 3
t i 3
<t i 3 t
I 'o IJ
:J -
S
:=:- = a
a
"
*
iJ
*3 !+
^
j
e
?a N i
3i^
l 3
E\
4
l
:
|
g r
.a$ -B
x
;-v4>-
txY
i
wga a
*-+X
3En ;2
I
:
1
;P
-6
r- o
t ;- l
-*
-*" ,
"
l
s F
G -= 6G
I p
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 254/304
r
I
=
A
Rta
+
!3ra;=
F
1;a
,
ra
a
:=
9
1
=
ri;
r+!=,
3
tz=?
==
r
a
=€
I
:a+=
=
=
?
:
=;:*
E
I*
-=
3
=
:
:
1
==
1a
;
=
i =T
=
==
=a
;
:=
J
:"
r?
i *=
=
E3A
FI
?
3: **
')c 2
rc t
2
t E
a's
i
a l
c c-
4
ro\OtFF(J
. *.Ea
E
d
Z
=
,
-
'*
;5
s
?
;
t
,1
I
E
,
l
q
-r
,s
i E
l.
-
;g
.
l,g
=
-
i-
i
i
=
€
r
sg
g
:
o
.=
i:
:4
a
€
l
l
5
I
:
p
5
.5
I:
f
&
rs
$
f i
t
-
;
q
E
+
.1
i " A
l,
'g
E
cc+
-
s
I
i
I
I
|
|
g
,
'a
e
r
i
r
i
l
l F
F
-E**E:H
rrg
as
s
a
; :
;f" =.
=:=;
E
r
|
|
|
|
t
.5
,g
r
t
l
lr
tt"3
E
$
JS
S
$S
.
E
io
{
.d
E
q
E
3
€
€
s
z
=;"3
FFk@a
n7q
I
I
T
I
lr
I
T
I
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 255/304
93o-9
€H
*
iE
{
3
*
kE
Ezx
.E
E
d,J
i;
€
3
AL
.5
X
g
E
o
.
9
p
€
;
^
E
1
EztF
s
9
F
;
-
E
;?
; E
€
Er
,g
,_P
.^3
l
; X
i
=
I
:U
"
;
d
-ss
;*
i6
:
'E
\
o
lL
; d
F
-$
^.=-
*o
t
E
.e
\=-
;
3
r*
E
X
E€
-L
!
lri *
z
?
-Tq
N
n
6
E
sF
F
L
':
;E
x
g=
, *8
F
€EqEc
sE
E
E€E
o€
H
s1
&io
aH
E
€
f€a
E
EF
##3F-H
S
€
E
EE
@q/Yt
T
I
r
I
I
iJ
ahb
d
pq
-
e
=
s= =
E
D x
=
-=
:-^
X
'o
i
:=
I
-F
Y
=
l
.
a
-
- 2
=a
-
L
.
F
c
f
t
{
:
ir
E
-^g
'1
la
a
-
Y
= =
-1a
Z
,-
LJ
?
a =
3r
4o
:-
c
a
=
:
'.--
J
<
- v
2
!N:
+
J
l
F
.F !.
'!
;
=
Q
s
o
"*
'c
F
F
c
o o - - : coI C = = oX =- oo c
*F
r
-^
-N
O:a
F
'3
tFl5 ,
a
6
?
L i
=
A =
= :
JN
:*
-G
|o
i
F t F o =G
J@
F I T .* - - -
* l1
r i I -+*
- -
5 t1 I
-_ 5 *
- I :o :"
l I c
-1 - o oo F co- -
X'c
.
J { I -L
t \ +
-
i
-
F
lN
*
=
: ti
= a 1 a - n = r C $
-i
-- h l i1
a
I
I
rI
r
I
-
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 256/304
o r c /
gF
E3F2
grE,==
j
;=
=€
E
F;
oE
=
.
*
-
6
>^
:
iz:
itz=
:(
?
1
^
"1
=
q
==*
=
t:
E :
=
ir
-
F
-
{;=
t
:
F
f
--
=-
i :
'!F
!=
iTE
*
-=
i1
;,=
i;
7=
==
=
:
=F
t
Gs
-
3
c
G*
-
-
-^
=
E
?
:
II
I
r
I
I
R
ts
I'qF
€
:_L:saE
:{E
,?e
=
=
=1
€
+A
;i ;E
i;n*:5
E
:S5
?!1
E
i;Ez
E
F
75i
,€;
a
;E
#
-=
.
';r
-R
=
l*5s
u
lr
E
s
Hs
N+.2E
;
.
I
i
I
+
l
:J
-p2
r-
!J
-=
|
.=
l
'o
-
-
h
l
'
F
N
Lc
q
I
oI
3
l
fn
+
,=r
,Y
O
U
.4:
11
.
.g
3Z
oE
'I@.N
HN:
;U
oz
*1r\
s"$J
Jh\N\thlIIFr
I
t
IT
I
I:r
t
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 257/304
g
=
.5
5S
E
;5E
E,=E
*EEg
g;E
;
::E
;€
=
sg-E€
)s!k€
*c=b
€
E
!g
IE
i
c
fc
c€
6c
-1
-N
rc
+C
-
-.
;
:e
r
I
r
iX
r
|
1
6
l
lr
l
b
+
#
F
'tn
{<
Pl.E
"
H-E
3
o
=
a
z€
cI
erra
doIi:L
IlxIt
T
I
I
r
I
- :a a3Z . i a
- 6
a4
2-
4
_
!
r
-
G
a
:
!
-
g
3
*3
!
-
1
,__
-
iG
-1
;
=
:=
'-
-4
.g-J
^
v
+
_
e
=
7=
-a.
e
a
-
- _
:
=
4
{ 33.
a
r4
:"5
=
ir- s
=2
l-a
t
-e; ..=
-D -115- =)
-_ *3og -_^g
l !1
F N
{ \
1=
: ;F:7 i
t1
r :
t - i r >
,+
d
-
N
R
1
\ 55
s+
+
-s
$|
JS
W
dds
N
-5
:0tz
-T
\+
l
*'
lF
b
!$
t tNts |b
N
a
I
I
I
t
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 258/304
z =
E: l I
+,-
st t \
,1
-r
1
:
r!J
Er
ir=
1 I -
*
-=27+ =
=
=
!
4
*-x=.o
' th
3E=N
)--
lJ
"
^3
I
E
^
=
X@5
E
j
i=
N
N
"+e
!
r
o
?
'-
\
ry
E
=
\
s
=:-=
\4
"= i
-
5
2
N
.
. X
.?
:
N
>
reg $ f =
\ i-a
"
J
.
\
q
F
3
i
F
t
n
l--
=
t+aO=
=
F
*
1
7
*A
YVY
/
5
ir
t
,
.
-
wa
'-
i5
:
{
I a
Ir
r
a
I
IT
iIAr:^
='ci.
=
L
E=
J
i
i
i
I
t
:!
--
-E
-
-
.
|
|
!
r
!r
.
;o
:
-
_
-a-_=i'-oI:=o:-
-
;i
3
S
E
i
A
.Nl6
^sI{
I
,
l
F
?
-
A
It
6as
Il:L
IH-i
O)fFL5(
oz
\q
q
=
I
l
t
Hc
i
'
f"a
c0
:
+;
-L
\9c
l
JFF
\+q
ra
'Rs
rrrr
rr
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 259/304
hEE';
*o
.
i-
-Q
c
'^
-
3
ET?
t
n
l
' *-
<
o
i
o
=
oo
|
_
$
1
I
5T
-
r*
2
9
=
A
:
:
r
l
N
r
it$
$
-=
H
F
t
\
\
-+Na
'-*
s
a
5
\
'r
,
s
=
;
d
I
^
7=
-
*
i
';
la1
J
c
+
l
c
:
,,
f
;r!;
j Rh
I,:
I
-c
=
r?
;
d
!
*
E'\o
-
3
€g
" F
c
i
=
r
-
i
i
;
r
l
:
N
€
dq
-
h
7
q i c o L = C
ic
E.r
,a
'
;
l
j
,
N
N
i-
"
;<
l
o -cC-c-
Cc c =,
= =c a z
;F D fXi.c
; e
-N 'E= = - =t = X I
L
H
€
*:-
!
-
1
I
iT-sE
a
x-=
:
L=
;-
=
9
^u
."2:
=
:
p
-
;s
=
;a
:o
"
1
ic
E^
sa8
r*
=-
i"
a
=w -
-
5
-az1A
*
J
t
)
n
4
=
t
-F -4
==
-
=
N
x
: =
*h
-Gw
;= G
I
I
n
I
l
IT
I
I
lr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 260/304
I X x
$
-
.,I
tsT
l
sJd
I
I
I
lr
I
n
'n
i
55'5
r
E
.3
t_
.
-
'd
eDl
,^
:F
;
N
to
-
I
a
:*
oX
.
I
-
=
=
:
F
-9
'
.
5
n?
G
d
cJ
-
:
!
i
JV
.
:k
ir
:*
t
d
=
;
+
Oo4
'
€aX
,Tl1+
1
L
;J
J
a
r
=
*
F
a
.3
+
.a
i
.-^
C
L
P
o
.
-
O
T
l+
-
_
$
i
.
_ 9
i"
j
:+E
d
-OJ
5*-=:
O
S
i
p
=
u
ab\
!
FU!
sN
&L
r3
€q
.
a
X!9A
"8
.$E
t*rE
E
n
i;."
l-diL
JL
;€
lNA
c
d
iro
?
.1
a
o
U
'J
;6
i F
*5
:
'
L
n
,rr!"a5
xo
b
-n
5
I=3
3:={9
.
.
'6.5
!=LE
53Cza
R
=n
+
r
(fF?F
?S:;€
T
.o
F
.rTzFE
-
I
G
|
|
|
.
lr
l
!
'
l
'
In
,
r
7
'S
:1
"
.*
l.
-;
!)
-rr
1
I
i
r
l
,
'
':
F
3S3a
!-=
=E.3'-€5!a
'
O
\
o.eE
-
!3z
z
=]$
*1
*
i F
\ 'F
*
,N
lf-J
fs
F
;
r
I
I
I
,t
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 261/304
,+
;
b
a2
gE
?
""
.zi.
.s
oo
R
:J
Er
H
-=
"
,
;
1-*
6l"
rn
l"
g
-5
3
:hq
ii.s
-J
)a:c:
.F
j
i5
E
lvEt
I
^
E
i
=;
x
F
i E
t
i
=a
.Ec
-
r5
s
r
-
-
3
c
a
f
i
l"
'
e
^
-=
l
?
:
d
-;
l
:.8
1
?1
F
'
"
I
J
:
^
'
e
.
1;
l
?
'a
1
.
l
?
=
.
*q
€
-
i
ls
Z
.
I
,
n
,
|
g=
'*
g
l
.
j
7
3
!
';
1
:o2
igE:9€
H
I
IT
IT
-
r
N
*3
*
R dX;-s
rcX
.6
a
^ "F
:
jc
-
:
i
=
=
-3
?
=
E
;
:
F
5F
x=-
=
X
-
-Ef-"a.
*
-
s
!E
:
.
1
1
t
r
=
;
^=*
=
.
i
-
-
zY
:
FP
=
v
_
*S
&
u
-
C
7c
i) rC- :Co C a7 Coc ! 1
l*B
4 - a z j co- -
c
i
T
;E-$
7: z
l* tlra
I; Y
z :
I
n
I
lrI
I
r
-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 262/304
z?-
=
r
:_
-
_
a
_
.
=
=1
\_
_
a
d
_
=
=
I
c
3
-
-
-a
a1;
;:
-
:
:
a
"+
:
d
t
a -
-
A1
a
."
7
'-*
F
:
-
-=
1
n
,
,
-
)
4
-
I
=
|=
r
s*
=
=
'
!
-=
"
a
^
r
l
-o
'
"
'"
t
3
:
I
in
-
F
?=
*
Tcr
\
=
J
:
_,1
l
.
;'
)
'/_
\- :
t a - : a =
s+
?
* ts
\ i-al* -L
f-*i "-
t [:
*
In{-L
q Y Y {
II
I
I
I
IT
Ci
r';
\N
ls
*e'?
N
NNt
(FC
\FR
a
iI
l
i
!
-c
ne
t:rN:-3
n3Z
IJ
-aii
Ut$L
7+
,?$E
o:\L
\*bo
t
,
\$
-
A
|
*1
\-
r
r
I
t
I
,
.
I
r
3
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 263/304
!o
\
n9
E
r_
v
/ +
-
L
;>n
'E
'-*7E
=
i-.
e
-c
sO
.ng
*
Q
_
*F
N
a
;
-
.=
-a
*=
t
'
A
l-
:
o
; =
EFo
v=
FE:=
IE
€
Ise
"E
-
-=
a
!
-c
i-
==E
,=E
(
J
-
io
'
.EF
)
=
-
>
e
-
|
Y
-
=4
=
2;"
=
3
:
t
:
l-.--?
X
5
i
.
c
=
,2
_
=
^
N
q4
'=
Jv
:d:=
t
e
1
_
-=
^
i;7
=E,s
':=
2
=A
=-
t
-
=
r-
.
'
t
ix
.
-
Q
-
F
.
]
:?
-.
.;J;F
.
r
-
J
L
-
{
-
:'
r4
U
=V
-
o
'"J
F
e=
i]+
:-E
::E
xE
-=+-;u
-
r
=
u
;u
u
rai
--
?i
aX
+
o
lr
!
aC*
$
-
:-
"
l
jNN
+
+
N
N
l.
*n
\
-
,
;
i .E
j
r
]
,N
:
I
'!-=rN
4
'-
l
=.
I
tr
'r
J
r
s
{ + r a g c a J b
{
; z -J
I
r
I
l
IT
I
I
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 264/304
) {
A, {
Itr
I
rI
c.
i:H
NL
Fo
--=d-
-+
jr
c
!*
-
*c
'4qGO
-T
4i **
lN
6n
KT
-
dOLv
A
UFFFO
cX
i
X
FFs
F$H
*""
A
r
-
I
sa
I
II
I€O
'e,LO
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 265/304
'
d<
IT
I
lr
r
aa
i a ^ =)1I I i I I i i I I I i I I i I I I i
*T\
\r.
wt<.-\ $\
F*sY
* \b
ia F 7 I
U
B 'D
.9 X * rz
k
F
:
€ Ei
l
.
IU FC"1
o
3
rF
i
9 *LJrc
u}
J
a-
X
=
';<l -
-
C
3
!a
"=
lG i>C
ex = 1 * -
=E
q
F
E
l 1
5
i :
!a-e
e
3
?
;--
a
:-L
t
5
+ =
rF
-E
=
dN
;=
t€a-=
h
?
'N
N
'e
.
*FE
\
z
i:F
I
f
=
j=
-.
y
.
*N
s
-;
4
g
-h
-
=
-5
=-
-=
!=
;
a
X
I
+
Y
a
=
Gd
-
q
=
O
+
+
r- -A
l;
32
N
a- I
i E
I
"
g
*
C cI ca ;1 x -1
rT
I"9**
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 266/304
G / 7
xIT i . iZ r
a x X6{ z i /
,-4
z
:X
-
;-a
:
:
i
i
-
;
JE
.
: ;=
=
=
.
=
t
';=
'.
:=
Z
-
.9
i
*
L
*
:
i :r.E
-
traa
:"a
,o
=
j
i
f
E==
=
?
=
. =#
;E
:>
;
E
_
so
:
=I4
==
.==
|
4.E
*-
=
=
J
a
i-
Zz
E
;3=E
1
.r
zai:r
:
t
-
.
a=
=
.;r
:
E
=
:{E
=:=
ta
-
:+
.a
E_
.-":=
=t
#
I*
:
=
=
E,rs
-:-3
V=
i,7
-
.
_{*?=
'.
=
z
-=
-!a
:
.
:=
-
7=
'--?=
= :a
+1
.E
f=
=:n
i
-
'
.
-
=
!
'
.
\
L
-
-
:
*
' >
-G*.-=
4
"E
e
:=
:g
;1
:=E=;eE
E
.=
=-?
-=
E
T
;
=
-
=if=€
:
=
{=
ei"3
"
1E
--
l-d
-
=
=v g eBN
S
.:=
'=
. Jt
Uh
;"a-
=
ir=
-
on=8=
3
r
-
x-=
^_
E
?
'L
st
rg
Z
8j
+
E
+:
|z.E
g
=
+$E=t?-=r2r o
r=
!1
t_
=
-
€E
4
E
Ec
:
i;7
= {
Gr:
t
:e4
68t
.r:
=
ito
Er€
>z
;
l;
r
Zr=
:
i E
-=
E
= y
;
;
3
:
=
==
"
*
I.1
:
:
i-?;le E
I.
=
:;
l;
;:;r'r
=
:
z
:
a
=a
i, :
.
E
o :"* ?
=
=
.
*
,.
c
!
!
-,,
r
-
.}=
1=J--=
|.,==
:i;
:E
;=7
==a
-=
,==A
r '-1=
=
=.E
._=
=
-
_
*"
=
:
€
7
?=>+
?
:r7
::
1.
=
:r7=
;
!*=
-
:r
a
=
v
=
*=
1=
=
'.=
s
*=IS
.=
-=
';-=
=
E=E
:=
s;
:
r=2
-=
i -_=
;=
-
-
.
=
l
i:t;
:?
a
:
;a_a
.=
7:
!=
;
=
i-=
=I
-
T
r
r
T
T
!
I
r!a5=a7=
-:asaf
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 267/304
-
aF
c;iFi"Nd
=
)4=
41
-
!
'-o@o
od
.
q
4=1
c
E
,=
X
ut
rO
=oA
d
+
r*
4.
Na
o
,
=iH=
'x
UN
,L'A-
L
'
"
-
vdO9
**
An
.
r(
:
z
F
-
1
r
=:?
s
.=
/
-
3
= -
;5
":
l.-:
:=
'r_
:
i
.
1 !=>
E
=En
^
:
:1
=.
*
l-s
;:j
=
p1r
.-
s--
-
, =,
:
.;=
;
a
-q
"a
IT
:
IT
I
lJ i+
FE
crE :r
;F?
r
r=
+
ni=
7
!i:2
-:
,i
=g:7
* =r
rz
=*:
Ei5
i ,r$
t€vE
trtg
i5?z?
+
! 1=
$i,t
$;7E
i"-q
;
Esg:Es
F
l1+
i;F
:
e=
7
aA
sEs
F?
gi$
+ + a a { CaJ a
r=oN ;-z
d= G
c 3 7Y!ci9 7 a N
.
z 3
=
z g
2
- a nc- - " c a ==- , = = q a C 4
n
rp
*
: i
. a
c
irrI
S
lr
I
'r
;"*s
i-
|
_
l
' ,
!
=
l;*
-
+
-
l
p
.
=
.
i;
i
,r
=
-
a
r
t
!t
=
V
l
-+
I
*
Y
i i*
J
r
rI
IT
r
r
nI
lr
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 268/304
En
11:
= i; i i ;
ia
;==a
:5i.
=
a
g ;+
€g
i iE
E5
i ir
i
: +i
i;
gFe=
i+ FF€
?
€
#E
z g
FG
O
*--
f f
i,-
l l
i IFs
d
Y y-
'r
l,
$;";
**
t
e
.a
w
_
r
r
l l
t--*-"1
i ';
,
LI
r
r -Oc
;
I
S
-
F
FE
slr
I
I
T
n
'
r
.
'r1
!
.
-,
;
i
-y
=5O^-=
=
F
;N
i.5
g'=?
E.$
.o*
E
S
i=E
=r
DiJ'iiIII
sar;-1
!<-<.:-=cJ,vfr,15,I
:5J
Q
E
f-
iL
i
L
JE
-a
1
)
J
;
i
r
-
i
r
l
:
{1
:Z
air
*
.
F
.
IIi:-tI:
.=I t
ai
*r
r
r
IT
tr
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 269/304
z:xa
*
L^:'=
$
:
'-
t
-
,-
=
:
i
5=
-
t
.==
+
'4
=
.
F^
|
-Y'9=
=
3
*9=
.
;
-
-
!=L
L
:-
1
42
l
-+
+
:
i!=A
-atJ
I
t
_
-
;
-
F
+
,
-
'
,
v
2
:='n
=iJ
i
-9
l-
l=
=
-
-
-
.J
e
=
.=F
:
-q-=
y
.
"Q
L
-
;
.-,n
1=
+
.
:E
:c
=
A
=
r?
J
l-O
<
j
Jo=
=
=
_
i:
I
';
=7
2
=
=
-L
5
.
-v
Q
-
r
\
>
v
t
=
-F
e:
I
-
-
!
e
4
a
;=
.a
O
L
J
L
!
N
t^
.
;
=
:-
dd
:r
=_T*
|
-_
=_
i
J
-
=
j-
*F
3=
;
'
-
r
-
-
'-
-
a
L
i=';Ea
z1E
V
* .E
=t
.
-
\e=
\:
zTa
I
:=
/
oo E
*3
i=
"
J
d
c
L-
=s
r
rJ
-_
7
r=
=E
-!
!F
-
/
1I: s*
srriL
'
I
I
tr
I
a = z a ==:
7
EFE
E
=V
=
=
)
^
-
-
=
7
;r
-=
v7=
=
= -
r+
=
--
FE
*r*1
;F:
=;s
T
=
r=
F
;F
g
;
? I
1r:
rJ
! -
55-i =n ;
Z
ru
5
E
-a
i
=
;
: =
,
;?;
=
,
i .
r.-
=E?
;=
:
5€; I==
i ; =
€
E
E
l;?
,
E
fs
E:S
a
E_E
7+
?:7a=
=
, Z !
g
x
z
-
-
^
*- :
=
-
-)
-
-a
= :-
=*
- =o ::
-
-1:-
a
.l
r
=?
*
-=-
-
=
-H
; .1
,"1
,
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 270/304
i-::
,r;1-
h I
l.
qEsi;=
i
Ji
E;F
FE
!3
5
! p
:
'r-
G6
=
1=
FE
3r
-
F€=
E
5=
=
's?i;E==
a _
',1;-L,
I
(
n
l
1
€/C
v
tJ
.
T
L
__;
\
i3
\
a!
>
.a
a<
s
a
!-
:
o=
!
A\+,
e
<
=
n=
a
q,
_
3=E:
rr
J
\1
!
\.
j
I
\
d
i
-
>
O
a
'-=:=
9
:
f
:
/>J
A
42
tL
=
j^
J_
;
:
-
c=
=
3
.1
=E
A
.
-
-=
'!3=S
I
-
-c
;
-
+=
-
:-
_
l-e
_
,
=
7=
x:=:
-
7
j
i
:
a
Z=
:
|
-=5
r3
=
I
=
-
L
v
=
c
o
c
l 5"?-=
-=
?
'
a
-a
t
a
=
=
|
r-
i "*
ba--
' jr
-"
"=:=
i
r
A
t=
9
?
:
,
-_
tn
i
-*
7
F
sF T
i
<
-1a
=
=x
'a
=
:
c
9
cT
3
-:
?,h
1x-E=!!s'tTN
':
x
S5P>
-
Y-v
lY
.k
i-'ar
:
;
.n
:Data
:
lt>
liE
lc
-
=
|
6
|
-
:
-
f€
t€
:n
|.
;N
id
1
'rJ
rOO
\N
-X
-
E3
'
Q
X=
:Y
;1
I.
-
J
i
ir
Cz€
r
{
I
I
T
rI
I
I
T
!+(-oJF;p!U=
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 271/304
fnL
a
lr
4
€
6
rc
T
**
sH
4
<
t
N
c
lt
g
\
\
E
,<
;
?
a
:
;
_
i
gs
*
i
E
l
_
-T
o
l:R=
-a*aLc
6
C
4
-N
c
i=
5
-cC
3
jrT
o_v
'P
-
=
3R
6
=
L
c
6
H
1Yn
j
a
j
ci
I
I
l
l E
'4
'C
,
-rd
ra
a
-E
rJ
a
i"n
5
=OF
r4
E
I
I
I
r
J
': 7
T
G - -
Di- i ?
N i\ *\
- 3z j J :
\\
C ;Z - I t 1 l j i t I I t?
r3.a ;
t
=M
't4
l=
o i
i,
x
l,?
l
i
i
-
-=
?
3
;3
=
-=
t
^
r
:
L
==
.J-
F
_
=
!
:
-
:J
-=
J7
l
ra
:=
=
! !
*
a*e
S
itttt
l! 3
3 e
g
:g
JJ
3s
-
*4
_-
l l L
c
ir
l
r
I
I
II
rI
IT
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 272/304
I
, tF
IF
:
EEE
S
/?
=
E
E
i
:
h
*
-7.=
.
i-
)<')t1
x2
'4€
:
-J
-
E_O
ois=
O
.
*II
2-
-s
=E
s
is
s
i
F:
iR
sS
n
=
3
q
S
sB
l
iEp
!
L
1
J
0z
gz
h
+
r
R
&
*I
:
I
I
r
lr
nr
IT
I
T
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 273/304
$
L
C
€:
E
\
4_
c
LN
-
g
!
J
=C
!d
;
{4
?
P
>
*=
Nts*
€
1;
e
g
'-
5
v
q
+
*
E
c€
F
-
+
"
9
d
!
=
!
{
z=
:
oo
Y
1.
-qd
ie
.
1
r
rI
I
3+ i { J
;=
1
=
-?
c
==
>
3
:
=
==
=
-
=
1
==
=
:1
=
E
==
;-
+
-i
1
=
-.7
=
==+
=
7
"1=;=
i
i
=
:==rE
-
r;
;=
+
3
;
a
=
-
-
=
]
-
-;=
?7=
-
=
.r
=I
=
=
==
=-=
Es
=
;
=:-
-=-=
,
:
I
-tzr
?=
=+E
3
"
.1,
€i=
t?
=
=
-
,1
.
1
"=
:
l:1
=
-=
*
=
*
.
;?
=L
;
=|=
+
: *_ 3
*
-
=
==
Z
5
; i;;
1;=
l,=
;
1S
J?t .=
==
^-
=
,
t
:
=
:
T
:
.
_
^
._U
;
=
:
=
J
:V
S
+?=
8?
?
+
5 -
Iz
s+;
s,s
a c -C- a { =a z a .
=-
:
'-
;?2=
;
l=
=
=
F
=
r
-Y
==
?
+
a
a
X
iJV
pA
:
;=
-g
:
g
a
-
-
=
-
p>c
N
"=
>
^
v
h
-a-^3=
=
" i
-<
2
=
=
a
>
=
7
\
-C
=- -
a1
:
= Jr
?
'2
<
=
I lN
X X
r
T
I
.rrr
I-T
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 274/304
ri.
t?
.u
=
"=
-5
:
:-4-
-1
,
j :==
l-;:<
r;"
oS;=
=
?
==
=
="=
o
l
l
j=
"=2
=
1
r==+;-
'7
t+
-l
-= ;-!-==
,
l=i =1=
S
=
1S:
':;
.=
=
-^
^a
i
>
zs
ra
i:r
7
-
;r=
=
?
$
,=
-=
o
-
=
=
T
=
.=
:
i-
:
z
?
=
;
i i=
I
i
+
+
lrry I
:
f!
,"
H
?T
$F
N
$
Se
Q
rafzI?
)
tr55
R
$H
Hr*
-s
Firhs
---Jls
f;ryg
N
F
Nr*
qs
I
dr
+
=
0
R*
:
S
+
r
,
I
iE
ES
r+
r
N
s1
=
\=?E!+:S
;
:
t
:
=
{
.r
'+
I
-
=
.$:
,=
:
- i
',=
,i,e
'..
,-:
-r
,l=
=-aaax
<
,
=
i
=
q
l.
=I
t
-
=
I
.
;x
-E
T
Z
-c
=
aa
:?
;;=E
'
!
=
+?
-
.
t
.1=
=i-F
;=
=
=t*
-1
_
if"=
=e
--1=
-
a=r
;
::"'I
1
F
€a
s
;
!R
',T
-
!:€
i;
a E
e
o^
.
;
+
€E1€
t
*s=
F
rFS.a
E
IeF
'f
=
3
3
i:
:x
ze
,
=
i
L
Dr
--
5
=F
i 1
€
'1
=
*a+
==
f
;
9r
-
-=1?a=
,=
.+"
E
_:J=
;=
2e
i,_
.I5*=
_
.=,
-=U
Z
-
i!;
s=:=
v2;
:t=:
-
D'r
;
-
.=-;
rj:-
;,IE=F
a=
\
i1
E.A
i=
>
xs=:=
I-==
*
si"
=!+7
-
.==
> >
:
==:
-
^
:
-
.=
F
!
-
;=
t=?
=
*
=
i ==
F
?
-
':
.
a
,?
'=
z
:="
i;._
dr
;3
=
-
;
a
,YELebz-:1
FFtI
t+
*1
t
ir+
l
t
r
I
I
I
rr
lT
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 275/304
$
4
ir
-
E
.
;t
:5
F
b
=
sX
=
;7
:
i
-r*
.=
:
;
'-
a
=
;
;
2
=
._
-
C
V
i;
-
*
:
-
-
E=
-
.=
._
.=7
?
':
."
.
t
+
rc
t
=
3
:
-
'.;
f-=
8a
-
Z
Z
=
=
E
i+F{
;
-: ;a
:
::-=
=
7:
=z*
-=2
a
i-
z=
1
=
I
,
L
I
Ir
r
Ii cZ i C C
I FgXX1
/
3
Fg
X
1
z
1J!
1
l I ka
2 '/0
iJ
?
/0
I
n
r1
_
_*
:
lt
rn
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 276/304
va .
== =
2a?
5
"
- - Grc5€
i4,"Z
i"t -
t-H
.E
t .J r5
-2+2-2 I
6-tJ
-1-4
!2
,JF
N
'J:0,t7-66,6-3j1 -
J '_5 -2*7
t2 =- -2 -6
,
Fg-X0
)a
OI-!
',$SF
E-***
:" t+
$s*n
ns<**
r+r
H
fT
HtT
TE'+
r
-r
qs
sQ
J
+t
?$
lr$b
*
rr+iee
+
+
aE
+
!_
r+
Fr
r
Lt
I
+I
sIYL
$
;;ry$-=
\
f*sT+
FF
ff\$n
N
,+
r
+
tRLJ
IS*tes=
s=
-s$
1
1T$
^T
E
"
l
FTF
F
l
iT'
r
JiNb
TFF
I
srS
s
S
*
+r
*
;T
;rj
I
t
I
r
rI
I
I
r
I
T
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 277/304
F
H
Rl+
4s
+
T
I
F$Frs
sF
i..q
?qNg'-
3
!1r)a-a'-ogiY
:eY
S
rXoE
I+
F
FF=
:--m
T
rsF
H+
+IwIG
,bTRl
N=T='r
+S
-rF}
+
+
I
I
-
r
uH
E
:
|
|= =>
vF
-
\
{
6Er3F
a
1
;T;
8
+-
-=
'r-<
-7
4n
-^=a
=
=
l
;
--+
:
*
.
=
a
-
F:
-
g1
-
-
*
s
I
3=
:
-(
c
s
-^
i \
=3
'
-
a
iF
E
e
;
s
Cc
"
=
*
-e
t
o
a
\=
L
!
-J
-
.x2
Z"
:e
7S
r-
-_
.^
-a
--
=
-
=
I-=E
;
c
=
"3=J
e
?^
-a-=N
?:" z7
-<7
:
!
^9
6
c1
iJc
a :F
=
:
:
+
c
=E
i
:=tC
*
=
;
-
-
^
c
?<
a
b
-
A
=
97
E
P
-C
'
J
;:
t=
*=
€
i
|
P
Xs>c
-
a
d
=V{
d
"?
=
=
"
*r3
9
zsX'2
\a
x
c
3o
5
:
r
I I
I l=t
p
I tt t-t t l
-
lzl= a a = caa z
a $:
Fg
F:
a
Ei
=F=
c" ;7
r
=;F
;=
1:F
zg
?
E;a
t-
.1
*
=
-
:
-=
G
r1
;i =E
e
Z
?
EE
sr
EF
)=
= Ei
;F
g
=E
=3-=E=
Fe
?
=
*.?=
;
I-*z=
=5
:=
*4
5
^
=
+= i:=
-
=*
=^=
"
=
E
=
=
1
1
:-7
:^
-Z
1
-
:
5
I=
=.
-=I =g=
:1-=
a7
I.=
1
I
i-=
;=
u;
i;=
:=
.
=
1
rT :=
=
=+ E*
4
:=
n:
;
l:=i:
a:;
;1
^==
=
_=+
=
:?=E
=-
/-
iIT
=1
7
==
?
g
=
:=3 a
s
iFF:
+
r
=
-:
j!-
+
; 5=
-=-
_E 3
E-
yT
-?:F
a a z ccJ ^I
f
I
r
I
r
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 278/304
-
lr-r
<
F=+
t_
:
:
T
cc
a *
l-
c
L
i!
^
-
a-
t=: gx
:=
:d*
G
F
€
tg
si;
6
3
S=
*=8
.F
s
ig2
i3
ee
;7
:5
E-
:s€E
:-
r*:3F
"1
:[;
'E =:=
:F
F€==
7
Ea
E
q
r€
:
i=
E
=
i
F
i:
4
F.=
t ic3n;
F 3FF
=
?:
i,9=
=
" =7
fL
=
jri;
-
Sr=
;
F
=
=
+
i=:=
=
:-
:
=
-
=
;
e
-4
=
l, I-
2 ;r::-
;=
i4s=
r?=
)
7A 'i =
.F."
?Z=
4
=
i52
cr
--=
fF";E
F
lE
3:
e
:E=_
€
E
=iE1
s
;
Z
.
,"
=
=:
==
.=t
=
:==.
:=
:1
i
;.=
t
;
:s
s i :-=1=r=
.
i:
=
'i ?
-r =
:-t
=
:=
;
s1
;J
;+"=T
i;
i;:E
t=:1i*:i-?
. i
,s
s
+s
;rE
,
=
E
!i;
2
€
;r=
i5
;;
:E i t;
EE
E
i:;
,e
E
"E
a:*
€S=
*==
'rJtz
h!
2
;€x
rBf
1=
aY
'5L87
z5
u1r
'a
E
.
E
E
ro
,
E
;
E
-E
3
*n
i
!
;E
I
.E
j,
i
€
E
:E
3
.r*
'.
=
,S
.
i,+-"9
t
r
,r
:g
:2j !4
2
=
-i
,:
*=
:€#t-
;;
-*
=--tr*
:{
s
:
Is
?
= i=
=
-1
€
;
€Ej
+*.z_o
7
f i E
"=
1
s
i .
=
;:E
=
s
:g
S
5
:z
=?
,
.
L
<
3
=
'=
-
\
:
iZ
:
$:;3
=
:
=
c
=
:
:E:
1+EfE
:
;
:
:
:
=
?
a
l=
4
!?
7z
i;E
E
;r=
;
i
;a
-c
r
:
=
'!"E
cf
ra
ra
I
IT
I
I
I
I,n
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 279/304
i
=
E:E
a
;e
:
EE
i:;E
-rE
=
n
r.
;
1E
:z
,
"g
=
=E
: .:1
g
EEs5:XTt
It:<
E
E
.€?
Z
;"35
;T
:
lr#
E
5
gE
;E
Z
C
z=
E
;E
:
:=E=
s
:
E
s
tr
xrE
E
-=
]
j
-
;=
t
€E
t
i;
.=
9
f}
E
E
g
EOR
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 280/304
T:gF+
;$$
r
l
**
-i
TTt
:))*;N
+
H-
.1!
<
h
$nm
FS:r*t
Hh*
r+
N-+{h
*
e
1
r r"
-
:1:1
t
;**=_
1
l\
;1+
i+
|
s1
't*
laj
mx
**
F
+m:r5
Y
L
' :
i
=
t
-
t=
:
=
=)
?
77
A-
tr
*E
=
:*E
':
';
:
=:-3
,
=
-
=F
J
=n
r7
:EFl;r +
;
.-l:
;
;':
€
:=
,1
:R
i3
1
:irr
=;=
+
=:
=:5=
:==:1
11
:1
";
E=
=
;=
;
r=
E
e=
1;
Zx
;1
-
?
!=0""=
=
-=;
;u?
;rr E
>i
!.-
=
=
=
Z
>
:
i,
t
;
i:
I
=
E |
.=
!
f_
+I
^ra
I
I
I
I
I
Tn
n
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 281/304
s
N
c
*=
u
vE+
=
;
:=
E
-
i .=
-
--
|
1
===
F
:
S
1
:3
;a
EE
:
!E
=
:1,==
rx*E
==
1qE.=
E
rts
=
g!=
z=E
I
I
I
-
tJ
z2<
l>
g
E
E
LH
\
F Eo
;F
r
C6
=
* hF-
iE
- FNi
I
p
!
+-
i
q
O-
^
+
E
r
-1
rZ
^
r
s
! c
8E
4 ( e 4! 6
z
r
:
|
r
?
g
B
\
ia
\
S -= c - c
N
E
s
-F
I
t
t
3
sN
:N
':
i
B
r
+-
f
\
+
,
;
E
i
q-
|
.
i
*
U *
gg"
*
c
! b
I
I
J , o o { co J r
- \ v
IEF
t>r ; o- 4 z T 1I o
I ;
c
c
,
I
I
I
I
U
I
I
3
r
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 282/304
EfZa
a
I
P
g
|
FE
E
VsE
E
g
X
^
5
a
i
7
iD
F
-X
:
g
<
L
!
f
!oR
;
-E
E
*
ifF
d
D
o
l-
o
o
+C6
qd
F
-
E
B
'"@lr^
d
*N
$P
EssEg
n
;F
E r
E
?
F
;
h
"
*=
vr
E
F
2
{
.;X
;co
F
S
e
Dc€
7od d
-
g E
X
€!F
A
Xr
c
:
\
x
{$
J
3
J
t
x Y q
o
q
I
ra
9
$
te
1
:i
;c9
+
0.
+
/
-
I+*
90+
*
i
.EL
Jf
i1l
:-l-
I
ta
.
rI
l
=z===
aF.k
I
I
I-
n
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 283/304
€
I
I
I
: 4 z ^
O
e
G
r
lD'
"3
l
-ga
E
,
C
ir
\-t
\
5
6
a
E:
5
F
t*
.
"
L
i
=
l
l
-
3
I
;*;S-5r
:>
-
5
-
:-
:1
'1
d> ,-.s
a c i = -a : \
I ( !
I a
( a cG a ;-*=
.
!
i
;*
a
-o
:
i
h
i
l
i l :-
s
a s
-^
*:
.
l ]1
l
;
|
.
-
,e
)
.
s
q
+
t-
sI
i
c
t
i
I
r
i-
'-
t
|
,4
'
:z
.
.r=-
:--;
,F
l
,
:a
l
lr
l
lN
J
=
A
u
la
s
l
r
.+
--
-"
lJ
f
i,
-
;
3J
.
--
=
s
-
:
;1
r"
-r:-
r;-':
1
r Fr
a:
;1
;
l T =
c EL a F a
Z
X
\
Y
-$
:<
a 3z
I
I
I
I
I
n
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 284/304
r.r
I-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 285/304
{ " a a n c {
fY
Y
z=
=
i
z
H
E=P
T
Frs
r
*+
l
l 7
;[E
l E
3+,
=
,n
F
E
t
ri*
s5
3-?
a-
E
;F
,{
*
s
;
:
e
=
Jg
$
t
t
F
xae6
E
i=
"
'iE
=
=
*;
"F5
A
F
6
e
r
i,
r e";=
:
FE
H
s
*
;i I T
F:F
F:
."
qA
&=rgsgo
s
Pi.+
s +E
-
o
^J:-r
t"*E
g?5C
*5
;"+
F
:3
FE
s-H*$Ee
,r=;
|
"D"gS
LFE
i.-g
tg
r
=FsE
s
:F
Fl;$
*
P3a
F&
;=
=
:-
s
C=s
=
:
6
5
rg
4
t
-*3
3z
o
s+
*F
;
=SH
=
I
-_
E:
5
+
3+
i
I
FFF
-
-Y
F
=
=d
'-6
x
-
Io^=
{
6
@
EE3
R
5p- =
F
EsES
^E-
o
6E
I
39
--
o
b
.
5*B :{+
[
':FC
7
3
3
D
QG*A
A
tF x
xJ
i{
E€:
O
iO
H
:
==
A
N
=X
.
'
=
/1
\F =
-=
.
iL
;
-
s
!
(
ts
,
f
E
J
IH a
=
!
o
A
;
:1
p
fa
.
=
*
!N r
.*
Y
F!=
r
tsB
a+
a
e
o,
-c i 4 : o 4 cnar
I
I
I
I
I
I
r
-
-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 286/304
I I C ts
sF
i
lvc
G
i+l
c
{=
E
'^
i
x G
i
q*
2
l-
t
a
rv
C
+
l
l
=
€
ie {gL
'
;
O
a
x
= - t "g
F
F
6
S
:-
z
a
n
N
i
'
E 6 q$
FE
E
!
l, f
i -.
S a
::s-z .
,r ;
IE
i Hg
E
d
+
r
==
*o,
I*
*1-*
!"
FE
.
,rrIr
|5
---
tL
*1
Y
c
^
lF*v
|
:
l1|
+
-
l*
dr1
{
l
Nc
:
\
'
-
I
i-
{s
d
l-
lN
r
Z
-z
i
i
l
I
'
11
'-
a-
.
-
=a
t
i
'-
d
cT
*
;
t
:
rc
.
f1.=
(UcJF7
i;
L
;3I,-
I
.+1
c
*=
6L
r
1
i
ir
ra
=€
-1
i
-
+
'-
lF
y
;
-
.
3
;-r
r:
f
i
,
**
:
-
"1
o
_
_
i;d:
:
!(fUU
z
rJ
z
I
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 287/304
'4
-E
:
:
t
r:
r"
i.
R^3^
*
;
-
:;
q
l
I
r
it
l
,
-
3
H
\
.Y
:E'=
c
;4r
l
c
:*
Ni lr
r1
i
-
-r
lr
-_^
Lr
L
F
c-
=*
r
:
+
lrl
*
l
9
-
!
|
I
I
I
I
|" i*
7 t
! a a a - o
1\
I I I
a \ ts
zs T
.o
ryry
,
^:?
r
r
s
)r
s
F;" #
*Y
EF
*
.;q
" +__r
;-=
s:*=
*
r
*F =
"
$s3
l
,*
a
r L
'
*-s- -
s
5
r
J
ss
* f
sF*
$*"
FrE
b
r
5
r
=
r F
a
:n
F
,1S
"
s
B
H
g
g
z
"-
r
*J ir
^
l
-
tc
qe
l
oN
r
"5 lr IT :- {i
I i t I-c
F i I
ai I
"As i I -e
U v
l$
$
tN
:
lG
"
t
.a j 5 ;4 a I9
t
x3
-
-
-H
=-y
=
:I
a=
:=
r=
=
s
*-:1
-=
F5
i
?5-r
:
';a
t:
'
=
F
J*7
=*c-
-
:
;
-
:?
=
i:9
"
*5
*5
.€
.
i-
J
a
tsH
l ;=3
t
|=3
m
V
-==-
s=
=
S
a^3d
:.>
=
e
\
=
s
=
z
3Er
;
te-
.
-p
o!
-
;"g"=
+
>
Ft3 =
3
p
I
io ;D
I
t IFln IFI l- -O z ! ; oc2 I I I l- l{
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 288/304
Z
o+F
i
?
R
E
i q
j-
;
5
F
IaLTS
N
r
g.r c
qE
I
l{ t IN
t I
NeLe
Ac t I \
SFn
-
D
s
7
^
gd'
.
->
.
i
3
*
l
r
f
I
I
N
s
|
|
'
v*v*
F
N-
s
X
H;$^
l
i
-
,*
.=
r
i
;
r
|
|
-
lt
-9-
3
n
u5
3
r^
-
E
=
3
*
'=
e
-
^
;
^ a3+ag
:
T
-
:T
q1
_r-i;
F
.=-
;
:
-
=
^
:
-
'
=
c
:
;
:
s
-
.=
:
=
=
-
i
=
i
r
i;
:
c
,,"
-
';
5
"La
;n
i==
!
^
._
-
ir
a
-
l
^
-
-
r
i
=
:
,-
-
:==
.
.
-
r;
ir
'7
-Z
c
:a
!=F
r:
r
.-n
=+
:
=
=-r:
l
t
!
=
l
-
:
r-
.
irZ
f
C
F
i
-
:"=
*
,
=
*4
a
!=
L
(L
.=
F
In+
.J=AF
a
-
|
i
>
'f
3
1
i
-
,E
r--
€=
;
=
=
,
N
-
f"€-=
*
.3-3*E
Z
-
E
€3
=
"
.
.e
F
E
uJ
d
c
"J:
.E
-
i-
clailtl-|
)1
IY
i4=-=Ij
*a
) r
iz
"
ter1
ir-h
-N,u
vv
{
-
\A
ra
9
o
c
J
J
4
a+
.9
o
*Ai i,{E
l
9:9
';;
F
r
*u
=
l-
4<
H
=
!
ts
-
/
f
-4*&
.:
-
r
3
C
;-
Y
;
,
-
=
a
x
:x
l_
=
X
2';<-
--
.a
3
a
e
I
'-c
c
;1
€gS t
-
"+E qT
-
e
-
ts
^
=-
-
"T
:
=;o
j,rc
z
!
-*9
fT
-
'
.
-Sl=tc
J
-
?
-o=
:=
;,3
F
--
i i,t
:
i:Fx-$
FS
.?
2c
oN
.
O
+
a
co
n
'.
i
,S
L
l
So
,
-x<
o
-
^-.
e
"-1
*- U
',
,
c
-
I
I
i
i,r
1r12
+
q_
5-I='{
'\
.-+
.t
:=C>P
++
F4;
r
l
5u
4
L
+
i
r€
^
r
FL
F1
l
(J
Is6
d
I
I
I
I
I
I
I
I
I
I
o
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 289/304
.-
'+
!
.
i:
e
q
;
'
" -
'
5
l
z
:
.F
=
:
o
)
, Z
.r
-
A
3
S*
.)
-ad
';
9
i
==
+
i=
B
E
;
f
4
?
:
{
=
:
i!_
:
.
,
E
9
-
l
"=
=
3
.
:
A
^
i
=
"d
:c
+
!
.
:
S
't" Ja
l
;
.
'-,1
-
c
*d
l
i
+
2j€
;
j
.A
R
=
=
-
o
.
3
.5 -*E
;E:q
.
E2
=
E
.
i
f
5
r
I
€
.E
ql
c
3
-
c
^
l <
E
i,
q
q
F
\
N
c
F
.S
.=
;
-
+
=
E
l E
S
=
-T
.
€
iv
O
$
"
';^
'
E
;*E=
I
a
tEF
E
R
-F
.aa
I
II
r
lJ l{ I
- - a a
( H
.-t ;D E
l, =
5E
1=
{C
IE
gv ,"Yv
:Yi
,
-
c
i Er,-?F
a:b
l,-S'
!
X
l+
r
=H
,-x
a
G I tg
3{'eI
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 290/304
V+
5
t+i;i Si:*
it+9ZF
:J';
_E
;1
R
F
:
,
=
z
sE
tm
=
pN
,
i
l s
E
E
';.Yr6
3-q:s:Fq4.rax
!I,II
c=!l1;zvr1i-:FIj
tn?)
i"/
r
I
I
I
I
r
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 291/304
.
5
4
yR€
x
\3Er
_
3
*
*
1
E-_a
q
YI5
3
-
c
o
N
s
\
-
R
l
E
3H
I
Ir
I
€
T
|
=
I8
5
^4
ch
o
a
s
-
'6
c
=
:e
D
a
-C
=
v
r=m':
*?
N
o
t
9
:1
+
<N
4
=
>
'
;p
VV
"
m
!
>
=
c?
t
zr
-
Y
g
oY
*
nL
:C
um
=
v
* :
q a
a
m
-
am
=
-
lmN 4 n
=
=
-=
-
E =v
s=
-
=
=
=
:=
;5
-
=
-
7
t' =
:2
9
E
hn
=
F=
3F
I
l
-
-
-
|
*
L
;
i
5
|<*^o
*T
*E:F
v=
Fsi?
1
IE
cX
c
|
n
r
-
|q
F
=
H=
F=
|
|
2
!;
a
>
=
s? !
=
)d
.
|
>
=
I
i
i
+$ -
3E
?
r
3
=
==
3
_
i
G
* 3
e
|
;
c
I
r =
:=
|
=
q
1
':
-1
{
=
c
\
o
i
F
t
'E
|
:
*
tn u N + I
f O 3 = =
e
<RR<
o
s
Np
g
F
F
sF
-
r rrP
A+
5H
+
s*3r8
F
."
-
tY
r
q
v5
:
"L
.
*?"
'; :
€
Y
.3 ;
= =3
J N 3 4 - r 7 = z r Cz - C c c
3 I
s
c
5.oc+
n
!,
a
*
.S
':
a
-6
c
'(o
I
-nEG
;4
CtJ+
=E
.
=
o
*9
:
N
-e
G
b
=
q
l
l
:p
=
i
k
rc
!
,
;
ic
b
,
=
1
3
I
I
lY
.J
I
i-
l
i
M
r
e
l
=
;
o"
+
-e=
^
-
-J
-1
;€
tc
3
-
e
,
.
'!
L
-
5
.
l
i
t
U
-1
A
n
I
t
n
=
l,:6
i
*
,
.-
-
A
F
F
;
*
5!*
1
"c
c - = g B Y
I
I
r
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 292/304
$| I |
r \ I i |
r^iry
r|^ I
1
I
I
I
I
lbG"-Jlt I Ii
r
|
u |
|
|
|
| II
r
|
@
+H
3
?
g
G
+
q
-
F
*
{
-
&
gEF
E
3
*x
=
-S
=Uxn
^
*^
E
;
se-r
F
=^
F
-
;N
f
*3 s
a
6o
i
s
f
id
4
3
=
S
"
3x:
a
-
E^
E
o
F
=
:
=
IS
f€
t"*
?
-
o
;
;
l .r
;
'x
-c
*
l-s
:5X
9dF
*
R
dr
i o
A
=
e=3E-S (C
N
G
FH
aJi Is a
I
I
I
l\!NIl+
;
,
aA
i
-
=N
=
!
-Y
i
L
-
L
-
=
:n
iX
5
-
_
=
!
i
r
l
.4
11co*1s
'
-
i
-
l
Nr
r
r
s
i<a
j.-,
z:N
r5-=5
==N
-4=
5
o
(o
t
:
-d
i
.a
o
.>
i x
.?
I
I
=
z
t
l
l
r
=
Z
-
,
-
';
*m*
r
-+
:
r
i
,
,*
'
I
I
:
rr <
t
J
=n
'b
i E
=
1
=
-
5_
6
;J
J
I
=
?
'
r=
:
' i.
*
*
'-
-==
;
jF
)
-a
=-
':
v
=_:
ir
!
=
-
t
=
6
+
:
e
i.
7
'r*YUI
"ul\
\+t-
o<
en
l*ttto{NoF
l=*
"
,
\
3
:
!
D
s.':
r
n
im
l$
il
J
i
.b!'-1
\
=
;
:.=_cz
N
Is
FiX
FF
$R
tlGl{9N
HsF
*b=h
' ,+T
Glz0
LC
I
I
I
I
I
I
T
r
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 293/304
E€=tj
=
r
5
g
:
e
E
=
E
=
a
-
;
K
.
*
L
-
ia
l
==
s+r
N
3
c
n
J
E
1
r
d
:
l
l
:3
\
i
n
z
i-X:z
' ==
z=4?
4
:-
=
<
L
a
=<:-
=Et
.di)
-
l
.
,
l
Y
se
'r
=
l
-1
.s
/
?
ra
.
t-
n
-
a
o
.
a
:=
:
o(L
5m
I
I
I
@ c I q c r
Z
2
I
cF
.
:
i
^
e
c
=
;
t
r
!
-9
T
g
E
*
]
F
s
O -c
=
EEF
G
C
+
G
5
e6
-> =^a 7EP
g
=
E
E
T
"P
A
:q
e9r
F
r
t
"t
'|lrc3
F
J
j*J$
|
r
r
I-
"
:
q
-
|
r
I
;-
3
I
t
5
f
l
l
=
rsF
rc
-=
,_
,
c
c
;
,
t
"P
3s=;
=;=! -
"'rN
1
c1
6
N
5,F:
:
-
S="
5E
t,=:
'tS
e
c
.v
v
J
c
ia
:
-
=-
-
]-
L
t -
l;-
En
n.-
=
5r
€
gc
-C
av==c
!
.
v
= N ! =a 1 z I cz + c @{
F
*====
9
5r* :
*
ai 11?
7
:_
g =
i==
1
4E1
a
.
=
=
::-1
r=
FF-
=
?
:==
F Z
1=E
=
i= i E
e
E $
z
?
3F+
: i
;F
- 'l
; :
;F€
€
a5
-:
i^aP
i
a
;r
!-
I
:F
_
v+
r :*s
€
'-?
=
:
Jr
i=
-
-
:
c
-^
Ea
*:
*5=
F
F
-i €
F
l+
=
,--
F
-
-4
:
I
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 294/304
Vo
F
=
v !5*lG
:
(
P= x
N
;
l
-
-a
:
F
.O@,
s
!
6
N
a
@S
i
-
i-
A
q
t
.s>
s
LF
;i
F
-
o
6 P
B
I
XY'c
l
I
-5 I
:
Qy
=
E
)o-
=
x
_
i E=
-
2
-
G
{
X=
+
FDd
:3N
P@c
-
^
F
.5
-rn
F=F
I
F
H
I
i
l
-
l
5
-
o
a
i-
6
^a
-
t-
.
d
/
;
tq*
iE
+
\s.--
=
=d
!F 51=
i:
E
6
t5
F
-a
l
q-*q
!v'
-
l
FEF
'
!
E
{
F(
E
x
'-F
.
1+
.>
5
I
I
I
I
L
q
*
X
.X
4
€
:.gn
a
=
,
t_=
.=
.p'\ 5
=
+
s=
;
3e€
!
,^
'
-=S
?
r
<
,?
*
=
LF
UG
{
"
l=
i
A
a
.
i
5
C
=
-j
-
E
S
-.==
a
N
J
5
:
=
;1
1
.
;1
6b
3lr=
io
=
o
J=
=n
==
j-
.
I
- .=
:
i j ,
q?
*
.r
: =F
3 *
j
!
-J
J3
+=
{C
=
=
)=
+
*a
:
:
:
*?
I
=
x
=
i:i"X
=. -
=
=
-
:
!
Q
_E
=
z58
a
A
r#E
.Y
:r
:5
r
=
4
A
.g
>
x
3.=
:
==
i
=
=
.
=
!
-X
:E
r
'=
-=
'!
:
=-:
:
=
;"
:=
:
!
F
-
=
;
r
i
=
{
k
/
as
!<
o
.
)
:
*
7
\
&
-
\
!
.=
.
;-
-
N
=
=C
;=
<
=
j
-
ca
-=
*
1n
=5
.a
I
e
t
'-
-+=-
.
'
*
L
.
:_
-
{
<
:=
.1
=
,
::
7
.
:Z
J
-=
:
-
.F
'=
?
,
=
-=
i
X
""8
=
v
i=E
a
L
3-
j
-
:
3
:J
!
t-
;
,-
-
<
.
.q
_?
_
a
=
t=
l
-
-
-
-
:
=
U3cq
tiIl:S
tA
Ae
(1
I
t
!
,-
-
'--
i.
^
q
q
a3F
r'
I
I
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 295/304
.q
-
a
.
|
"a
:
r
A
I
l
i
'
ra
'
"
:
des
l--*
v
'*N.ln
*?
4
€
=R
S
.*
!^
.3q
t
'"
c
E
re:d
iFo
€
l
ts
'1
r*a.6
iEi,
*
J
1d
Y+
ia
!
I
I
I
la i- I I
i "1 z - - h
NFi l
F
\*
--
i
iF
l
,
l
Fsa€e
aN
€Y
i
.
6-
i
;
C-=9c
*s
UH
*H
is
E
3
f
'a
;
gi ;
=
=i
_
g 3:{
;-
<=
-
R6
*
t
i 5N*
=
:
i:
!
+
i
r
I=
F
i3
y
:
X
i
N
i
s
* i "
*€
-+ -N F o h I I N < { o :d
o s a4E
F FI
i
tt9
F
N
s"ss*
+q
q
i l (
a
o {a
5&
.*o
g YN i *l;I
i
?
t
-
G;
:
,=irry
ir
'
i= : 5X
I
I
,n
I
,rrL
.
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 296/304
r
-H
l.
Q3
.=
"+
=
t?*Q
?
?-
=
E:
E
F
=
=
E
+
;g
^
P
:aFR
i,
o
X7
F ;H
-;
3FS
5
=
<
:
P
1
9*
T
-
=_
lL
i .*€:
.
a
.a
S
1=!*X
E 7=
G
=
2
Y= l
-
.*5
*1
-
A
r
(1
le
,
i
s
r
,
;
.=
s
:
-c
-
- =
€
-
-
+
F
aa 3
-=
; l3
o-9ie g
EX-
,
5E
=
N
a
4
;
-
?
x3 i
NG ;
==
=
o
I
A+
+,#=
P
7
?
:
x
7
xb
=
:- lv
i
z,a 5 !?
h (s
'
r,.L.I
*'{
1v.l
Eg
sB3
F
*E*gE
€€
ieFg i:€
lnx
a;*c
: €
;s€:s*gE
:e
:,+ u=
+:2
{r
f;
!g
i EE
a;;3
cj $
i
s i
:f
s
EE
=:
;j
E5
gs*x=
s
5;;rE
E
+
tJoo
FF
cF(:F
'<
:
t'
tta
l
'-=t
=
.
-a
c+
!
,2
I
vz
+,
R
i+
r
I
I
I
I
I
I
r
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 297/304
J
a
Li6
A
6
X
.N:F
-
€-
:d
a
.
6
J
4
'
-s
L
E
+
c
-t.
o
:
,
'-
=
t?Sr
€=
\*>
Lg
f-4
:
'IE
1)
5
LTr_--
^
a
r
-
-sj*o
O
.
ia
',o
\
z
'7
I
L
't
-E
v-
\
'.cu
'3
*-
a
-6
l*R
=E
"
k
l,c
E
1
I
-
if
T
\
-
i
l
l
t
i
rY-*
c
**
:
F
=
lr
l
O
Q
*
=
E{<
;
=N
5
iF
i
'a3
I
I
I
xx
x
hs
s
5T
;-
F
hxx
r
-t
*l
f
Z=
l:
3
i !
,i I
:=
*=
;*
;
]$
r
iE
rr-* .= -
sg
sl=;+
*==
?
-*
"
$--
r
"
x:=Fi;
g
-*
:3:3=
7;
=
-
^
=
=
;
: =7
t aE-a
==
**=
3
*?
IF
?=n|
*axr*=
=
"=
z=
)
a:=
=
o1
j= -
1
1
=
=
.
==
Z
t2
+
=
a
^
= r=
't
i 3g; ?
:-
===
"
=
-
=
:
"3="r=-
rgi
3
r*g
t33
1
G
-
.
'
=
-
,
=
T
-
-
-
_z=
=
-=
'a
!)
'=
' i
5
;
E
=
i;-=
:
3=.- a-
:=t=
=
g
2
'I^
=
-
+
-
f
3
.*-
'-2
-2
'=
d
;
".-".
?
e
a
i
$
=:
-Z
:
tS
g
s
#
?aE Ie
6
g
S
g
?
:
3
F
IFIR
I l< td l( t t t t* I t I t?lr l5l=Itv l> l a : ; 0 t
s -C c
=
c
; o
x$
ax
3
.E
-+7
|S@
"7
i
C
;
-
C
:EG;X
-a
h
G+
I
t
\
:E
o
r
\
$c
i-
s
.
n
1*
r {
1r ,\
: -c= E x
g /a
\ iq
: h
ir
I
j
==
:
T
_F
?*:1
l
d
^ ?';
l
' a
:a
=
i
at
l A
-
.
!
"T'";5
J
^L
e
-a i
c
_
i- rlc
P
c
r aqg 3 o
t { o o co -
I
I
r
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 298/304
+r= :eH;aa
7
Hrs?2 ;-=5
?
\
*
--
q*
',*
i " ir
,
-r
3
-;
G;
.G6='
O E
a
O=FoH=
*
\
=
.
/
'aB
-
l
o
[
i
\U
,3
J
:
!O F
i
*Ll_
t
r
F
Ft
€
'
5
'=r-3
0
p $(
oa+.}
Pd
C
H
X
r
l
ry! !
c*
i
3
i ,
t
o
a
B
L
i
- "2 o =o
I
II
I
Ft:$
N)FpNF?t5
B
i
'r
*#
*E
;o
E
E
,
g
E
yEH
.s
dE
E
:$
E
ERsE
*s
5
=
'1
5*
U
i Fy
E
i:
=
3
YZ
r
9=
i s;€E
;E
ErEE*
E
=;
E&,g
; =i:E
ii;g
gE
E
;;E
i1
5E
;}EB
!EE;!rEe
E
E=rA
E
tg-*F
E€E
c1I
*trC
Ia
cil1
a
t
.
.Ii
rdI|It
on-
t+c
Il
nir
It-d
tI
*(
o
*
-F
tcE-
v
O
I
=n
z
oz
/I'q
i
I
I
I
I
I
I
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 299/304
rX
?T
i -1l_+
{
$
#
+
df:#
I
I
I
@
z aQ G c
e s Po :
L o !
1 ih
i
cA
+ ; J l b
t i L{
l x t I
a*
: /:rs
?
G t I t I to j*
z
6 3
*
i
r
: F
Ng
+
uN
o rD
l
a EcX
;
lg = FN l
s
r
t3
,
tJ^
Ni I I \ \
r I a ! & C ^ I
\ i
7 tJ.F
,
r*
l- .- c l \ A I
Bf ir6u
u
: "-Io
t4 t>4 o o o{ r
s
I
I
I
I
I
I
I
0
:
ag
=
-
C
g
-o
E
h l*
x =
!c
;aX
Y
I
o* F
l- IF lN l2lr t> IH td i IF IIJ I ta JT
l>
ld
I2IvFINlo lP ls- l- lolv lF q oq ; a <
O
s
c!
."
i
a
o
I-
;+
'9!X ^
*
.t IasH
+HJr l
I
I
*$1Lu
_-
.x
q
J^=
n
ts
-
X
'oo
"-
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 300/304
*
F
I
IFz ts
ltg i
r
ra
i *
?
s
*1*"1
X
1l L
V
,-
i
.5
5
F
:G:@
€
4,<
^
)<t
i
l<
.
t
n.oY!Q
L
*
I
**
r
taV
rdco
<D
I
Hsr<
,
r\
c
,
l
i€
fS
,-5
-d
D€
-
6m
@
to
sF
r
1IrJ
L
*1
t
L
,
--
N
o.d
-*
o
t&'cAd
+
IJ
7
*n
'.
.=
oO
|
!m
to
s
ic
Et
la
c
a
i
{FtsJN
O!s:
l
gN3
'c
c9
.?Er=
:
r
!o
J=A
lrsF
l-€
:
r
r
:r;
-<
,
c
.
,
a
ir
,
u
!
i
=
r
.
.
6
i
.
i
1
l
'_
I
=
'r
,5
c
1
*1
:
I
,*
-
-, E
:
+
?
o
-
r
-
.
l
co
,
€,rE
= f
'.-',
<
's
Q
rd
!D
5
3KH
rr$
-
=F
l dr-r
gn
iJ
YI
I
i
i:*E
:
S
.4
l
l
.
'=
a
7
:
:
:c
a4:
E-
i ?
5
;*+R
",
;
n
:
r
3*$
a+;
laEJE
s
s
"
F
E
:
1
=
:
oE
.
E
E
.d
:g
g
=
!
fs
.c
.
!
f
cZB
FF
I
TT
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 301/304
goE
It
i<co-L
A
i€lt:*
N
I**I
IcF
XNtH
ILE
6alr
i
9 F
F
:
p
:
:"
s
9
-
n
c
E
!
-
.
rc
irF
.1
tcF
t3=
i
;:
?t
i;
E
i ;;
=
I:=
i--
1"?-_+
!5
.
+rt=
=.=i;
t
=r
:*5*= ;.:
=1=
5$
-r3u
,r1
;:. x
:r
:=
.r :*
+=
:
ir i
;
:=; 3
:rF
+ =.x; *
r
-S;
Ir
;s
:
zi
i.F
F"z-7
: E
;
r
:7
i;FE
;;F:1
7F
i F
F
*n
-*
*n
J*_J
"*
!J*
e
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 302/304
J
9
:1
E
:
i
a
i:_1
t
aa
E;_ F
F
=
s.
3
ri s
-1i
5F
r
€FIE
i
sF
!:
7
z+
i+
;
+
E
1F
*r*F*-
*
tE
rn
\d
7:-
:J.Z
7
.H
/
r1
:<
:e
:4
L!.=-.C=
>-.;
:O
-a
-<'=s
Z
<I
z
+;=
fs
5
v
->5
=
._
;E
:
E
';
:
i
-
-
'!
'=
=
'
3ei ?"
'.E
g
:-E
d
3*
=
F
i E j
E
u."!€
"
5
l?1
q
3
!F
:{=
oJ*
ig=;=*ca
dE
:€
3
_*T
Es:g
'a
=
-
cE"
'*
?
-g=
;- g=$
s
ss
Es!
A
aaD
irJa
S
N
=.pt.e
sp+:i:%s${lsX
t
*
I
I
I
T
I
r
I
I
I
I
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 303/304
'd
X:e
A::v:,
z
I
I
I
-Yf
.c:r
z:
E=q
[E
E
6/?^
^4=
a
a 9<
:
;
z =
:>
=
F7s<4
=
:z
:= E t:
=
"
= r37
z
P :g : = 2pd -Y s 7 B =
r
o
-
\-l_-r
I
e6
I
q
I
lF
i r
a
i*_-"-
lr i
t
t
1
t
I
t6
1
l:
Ii \ --_1
-
a
E
q
:AB*
6
TI*e|
s
?H\
;
iaE
-
it"E
i
e
E
i
$ =
i
s "
-
*
i-
"
'r
sJ ;
-
- l I i, 'l
I I I
-_
f
€a
*_
6
E
€
Yd6
=
**na
tsis
ESos
l *eY
6
I?s*
L H
o z
o =
nnQ
a
+
s
&
o
N
a
P@
*g
A
6
A
5
F
{
=
ts P
+a o"1s ui
r-
=
r
*-
\"-\
\"\"\
iLE
te\r
i\\\\\
i t
#
\F\\=\r
l\\
l- ;
" nT
'\\=
&_11
---*1
I
---
gr
E+
;x-
\r lt F
I t 1-I* l€
*
\g3
\AHiEdiF
F
!s ls \ it
I
I
I
I
I
I
I
I
r
I
8/2/2019 Probleme rezolvate statica
http://slidepdf.com/reader/full/probleme-rezolvate-statica 304/304
I*o *2 ?
laaial5
tq
; : '1 i : ?
,
nr *
<
G
-
;1w
*$x
m
'
9
I
E
Z
sFPs
*o
I
9
^
e
19
t
ireF :
F
-
r>
ts
FFB ! - ' * :
I
rI
I
top related