Analisis estructural parte v
- 2. + , - , . /
, 0
* + , - ./ 012 ,
" # # "
"
# '
!
+ 1 1 2
3 2 4
3 !
4 ( "
5 . 6
. !
2 " #
! # 3 6
. "
. ! ! " . !
7 . 8
9 ! " !
! ! "
. ! ! ( ) #
# " 6
1 , .
!
: $ # ! )
0 ;
$ <7.8" -7.8 " =7.8
- 3. 1$ 5 ( & ; <7.8 -7.8
> ? $
* 6
∆ ? 3 . ! >
. -
<
>
? , . $ . ! > #
> >
. ! > =∆
!
=+∆=∆+∆
3 . ! #
( . '
# .
7&8 . ! 6
54
54
=−=∆
- 9. :
+ , -
( "
! !
1$ 5 ( ? ; >
->? - $
4 ) > "
θ
( > !
θ ? >
#
θ ? ) >
- 10. 0
( . ?, )
> # ->
- . ? ( 6 (
7E8
!
=+θ
) >"
. ->
F # 6 6
>−<−>−<+>−<−=
>−<−>−<+>−<−=
==
=+=
=→=
=→=
∑
∑
44159
44159
90D1A4
0
4A4
897
9
&
&
< , 6 -D
- 13. 4
1$ 5 ( & 3 <7.8 -7.8
B 9 I 5 B 4 > " , ? $
6
3 . ! >
3 . ! 6
6 >
6 ,
?
?$∆
- 14. 44
! ,
=++∆
=++∆
$
$
$ # . # '
.
$$
1
5912
==
−=∆=∆
F - ./
20
==
$ !
2015912
2015912
=++−
=++−
$ # > B 42: 9J= , B 42: 9J=
3 , -
- 15. 45
1$ 5 ( ?
B 1 I 5 B 5
* . B >. B
B 2 I 4 B 4
- B -, B $ 4 K
K
- 16. 42
< 6 .
< 6 - B
< 6 -> B
! ,
'"
" " "!
$
$
$
$
1
?
5
1
87
1
87
@@
44
44
==
==
−
=
−
=
=++
=++
θ
θ
θ
θ
- 18. 41
B 1 I 5 B 5
- " -3" 3. ? $
6
$$#$ 4∆=∆=∆
6 - B
- 19. 4:
6 -> B
6 3. B
! ,
=+++∆
=+++
=+++
#
#
#
# ### ### #
# ### ###$
### #$
θ
θ
- 20. 40
8 2 2 , . 3
1 - 2 -
H - ) ' 0 4" C
- " F # - 9
! '
( ! "
' '
7$ 8 (
#
! G?
• . G .
• 3 !
• . . !
7E8" )
• * ) " .
" # ! "
#
• 3 ' ) " #
! . ! .
8 !
8 '
?∆ ! # 4 . 6
- " -6 ? - # " 6
8 7( 8
- 6 ? -
6
- 21. 4
- 6 " -6 ? ( ) " ' " # 6
8 78 ( . 8
- L
? -
-6
L
? - 6 ! - L
< , 6
B ,
K B -
8 6
-66
L
? - 6 6
- 6
L
? - ! -66
L
6
< , 6 #
8 3 # ∆ 6 !
- 6
L
? - # ∆ .
6
-6
L
? - 6 # ∆ .
ϕ ? C " # 7 ) 8
( !
- B - %
E - L
E - 6
LL
-6 B -6
%
E -6
L
E -66
LL
* 8 ? =Σ
- 24. 54
=∆=∆=∆
==
=
/θθθ
θ
9# 9) * ! ;)$ < " =)>* $ ( /
θ
θθθ
θ
θθθ
9
4
95:
1
2495:
1
24
9
95:
1
4295:
1
42
+−=
∗++∗+−=
∆+++=
+=
∗++∗+=
∆+++=
>,
(
( )
θθ
θθθθ
θθθθ
55
4
51
55
4
5142
1
51
42
1
51
1
42
++−=
++=++=
+++=
∆+++=
9# 9) * ! ?#) )5$) * ! * ! / :
,
7E8 ,
" " ")! "
#
0421
1911
9
11:
555
@555
1:
@$
555511:
5
4
29
5
51
9555511:
55
4
51
9
4
95:
−=
=
−
=
−=+
=+++−
=+Σ
=Σ
=+
=++++−
=+Σ
=Σ
=Σ
θ
θ
θ
θ
θθ
θθ
θθ
θθθ
- 25. 55
$ . !
0550
1911
9
95: =+=
29
0421
A
5
41911
A
5
51
0252
0421
A
5
1911
5
4
51
0252
1911
9
4
95:
=+
−=−++−=
=+
−=−++=
−=+−=
#
(
>
4509A29
12529
29
052050
4
5
. ==
=+−=
=
−
+=
>,
42052
4A4
552
:5:5521A4
552
1
05229
4
1A4
4
. =−=
=−=
=
−
−=
- 26. 52
* ? F # L B4 -* "
> 9
3
B :0:4-*
* $9) " 9 )@
- 28. 51
( )
84@75591: 4
955591: 4
42A
5
4940A:0:4
1
42
55
55
11
##
##
##
###
θθ
θθ
θθ
θθ
+==
−+=
+++=
∆+++=
−
9# 9) * ! ?#) )5$) # /
( )59 41952 2559559
9552 2410 09 4195591: 4
555
5555
=++
=−++++
=+
θθθ
θθθθ
#
9555955952 2
5591: 49552 2410 0
555
5555
=++
=++−+
=+
#
#
#
θθθ
θθθθ
, 7 8748758 728
#
#
M5 5
M1494
M415
M50
9
4199
4199
1: 4559
55955952 2
52 2559559
5591: 4
5
5
5
5
5
−
−
−
−
−=
=
=
−=
−
=
θ
θ
θ
θ
θ
θ
θ
θ
- 29. 5:
$ C . !
# 255 555914941: 4
455951494410 041552 2
20595149452 2415410 0
2059 4194151: 450559
5555
5555
5555
5555
−=−∗+∗=
−=−∗+∗=
−=−∗+∗=
=+∗+−∗=
−−
−−
−−
−−
, 5N
* ? !
B 1:9 . &1 2
# B 0 5 45 . &1 2
L B 4 -*
B :0:4-*
B 0 C*
- 30. 50
C , " 3 θ " #θ "θ
( * ! (' $ () *
##
##
#
914
914
4
95 4
==
=
∗
=−=
=
=
* )9) * ! * ! ' : !
( ) ( )( )*+# =∆=∆=∆
== θθ
9# 9) * ! 2)$ " =)>*
#(* /
( )
( ) θθ
θθ
5
1
5
1
142
5
1:90
04
5
1:90
=
∗
=
=
∗
=
−
−
);
( )
##
##
##
θθ
θθ
θθ
411254014914
411254014914
42
9
450 50
914
55
55
1
5
++−=
++=
+
∗
+=
−
#(* /
( )
##
###
θ
θθ
5
5
1
14
04
5
1:90
=
=
∗
=
−
- 31. 5
);
( )
( )
( )
( ) ( )9144112594014
24
9
450 50
914
4112594014914
42
9
450 50
914
555
11
5
555
1
5
#
##
##
##
=+
+
∗
+−==
++=
+
∗
+=
−
−
θθ
θθ
θθ
θθ
9# 9) * ! ?#) )5$) * ! * ! :
( )
( ) ( )
( )
( ) ( )54112542 4941125
1451125940149149401491441125
49144112594 14
511259401414914
5
5
M
5
5
#
###
###
#
#
#
#
=++
=+++++−
=++
=Σ
−=+
=+++
=+
=Σ
θθθ
θθθθθ
θθ
θθθ
H 7 8 748 758
#
#
M59
M21:
M2:4
914
914
9401441125
4112542 4941125
4112594 14
5
5
5
5
−
−
−
=
−=
−=
−
=
θ
θ
θ
θ
θ
θ
$ . !
- 33. 2
2$ ! )5 $
∆θθ "
* )9) * ! * ! ' : !
< .
9# 9) * ! ;)$ " =)>*
( )
( )
,,
,,
$
$
,,
,
,,
,
#
#
∆+=
∆+=
∆+=
∆+=
++−=++−=
++=++=
∆++−=
∆++−=
∆++=
∆++=
55
55
555
4
555
4
555
555
014
1
2
00
1
4
:42249524
4
4
:42249542
4
4
014:90
1
2
0
00:90
1
4
0
θθ
θθ
θθθθ
θθθθ
θθ
θθ
5 ! θ " ∆θ "
# 5
9# 9) * ! ?#) )5$)
∆=∆=∆
== #θθ
- 34. 24
( )
( ) ( )
( )
( ) ( )449505912:4
01422:4495
940:45912
:422495014:90
5
5
M
5
5
#
=∆++
=∆++++−
=+
=Σ
−=∆++
=+++∆++−
=+
=Σ
θθ
θθθ
θθ
θθθ
! ! " !
)
( )
9
5
=−−
=−−
=Σ
#
#
- 35. 25
( 6 ! ' .
"
5
857
5
:9
8578979
##
#
###
+
=
=−+
=Σ
++
=
=−++
=Σ
5
:9
9:9
55
:9
9
##
##
##
=+++
=++++
=
+
−
++
−
. !
( )
( ) 89@@@7:9542425425
:900014014:9000:90
5
5
=∆++
=∆++∆++∆++−∆++
θθ
θθθθ
H ! 7 8 748 798
5
2
5
5
:504
1 19
41
:9
495
94
542425425
05912:4
0:45912
−
−
−
=∆
=
−=
−
=
∆
θ
θ
θ
θ
$ C . !
- > B 5 0 J=
-> B & 2 0 J=
->, B 2 04J=
-,> B &5 0 J=
- 36. 22
-,3 B 5 0 J=
-3, B 41 :5J=
< > B 7& 2 0 E5 0 E:98D5 B 5 1:J=
<3, B 75 0 E41 :58D5 B 52J=
1 $ )9 ! 9 * 9 #(* ! )*9 )* !
" !
)
∆ " . " !
# ! "
H" ! 6
* ? 3
B 0 C*
B 1 . 1 2
B 40 0 . 1
= 4"
$
7&8 )
∆
−=ϕ
ϕ ?
- 37. 29
3 ?
2$ ! )5 $ & ∆#θθ "
( * ! (' $ () *
, ) . . 6
* )9) * ! ' : : 2)$ * # $ !
- 38. 21
[ ]
[ ] ∆+=∆++=
∆+=∆++=
∆=
∆
=
∆
=
∆=
∆
=
∆
=
∆−=
∆
=−=
∆=
∆
+=+=
∆+=
∆
+=
+=
==
#" "-"!
.
!
##
#
#
50849712
9
52849714
9
@@
2
5
LLL
LLL
2
5
LLL
2
9
L
L9
2
L
49
1
2
5
1
LLL
49
22
L
49
9
2
9
9
L
θθ
θθ
θ
θ
ϕ
ϕ
ϕ
ϕ
θθ
- 39. 2:
[ ]
[ ]
[ ]
84@@711:49555
5:9495511:
8@755211::9
50495511:
@@
495511:
495511:8497142
1
5:9849712
2
5:99849714
2
#
##
##
#
#
#
#
##
###
###
###
$""!
θθ
θθθ
θθ
θθθ
θθ
θθθθ
θθ
θθ
+∆+
=∆++∆−+
=+
=Σ
++∆
=∆++∆−+
=+
=Σ
∆−+=
∆−+=∆−++=
∆+=∆++=
∆+=∆++=
! H
- 41. 2
. !
" "-""" %
#
#
#
#
#
#
#
#
##
25
2
94100:9
2:0
9
9:042:
0::9
00:9
941
2:
2:
9:04
@@@$
245 4
402
04:
05:95245
4911:555
:955521:
8:@705:95245
0:94952410
=
+
=
=
+
=
−=
=
=
−=
=
=
−
+=∆
−=
−=
=
∆
+
+
+
=∆+
=∆++∆++∆++∆+
θ
θ
θ
θ
θθ
θθθθ
