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vigas tramos AB BC EF
longitud 3.5 4 4
base 30 30 30
altura 60 60 60
diametro
inercia 54.000 54.000 54.000
K = K' 5.4!" 3.500 3.500a #.#4 6.#50 6.#50
columnas tramos A B $
longitud 3.5 3.5 3
base 40 35 35
altura 40 35 35
diametro
inercia !.333 !.505 !.505
K = K' 6.0"5 3.5#3 4.6%
a 3.04% .#%6 !.0%4b !.6! .53 !.0%4
t .4"3 0.%#5 .3%"
momentos de em&otramiento &ar
carga rectangular carga &untual
ramo viga = 4.0 ramo viga = 4.0
base = 30 base = 30
altura = 40 altura = 40
a = a = !.000
b = b = !.000
carga ( = 3.000 F = !
inercia = 6.000 inercia = 6.000
K K' 4.000 K K' 4.000
a !.000 a !.000
caso )carga en toda la viga* caso )a = b *
+, = 4.000 +, = .000
+,' = -4.000 +,' = -.000
Caso ! )valores de a b*
+, = +, = .000
+,' = +,'= -.000
caso 3 ) !a /b = *
+,=
+,'=
momentos de em&otramiento &ara
caso ! )a 1 b*
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rga rectangular carga &untual
ramo viga = 4 ramo viga = 3
base = 30 base = 30
altura = 40 altura = 40
a = a = .500
b = b = .#00
carga ( = 3.000 F = !
inercia = 6.000 inercia = 6.000
K K' 4.000 K K' 5.000
a !.000 a !.500
caso )carga en toda la viga* caso )a = b *
+, = -4.000 +, =
+,' = 4.000 +,' =
Caso ! )valores de a b*+, = +, = -0.%4#
+,' = +,'= 0.#4#
caso 3 ) !a /b = *
+,=
+,'=
rigideces momento em&otramiento &er,ecto
vigas ( llegan al dia,ragma K
K a K'
a
4 .5 0
elemento 2nercia ongitud relacion 2o c ='
viga AB 54.000 3.5 4.3% 0.4"4
viga BC 54.000 4 4.3% 0.43!
iga EF 54.000 4 4.3% 0.43!
columna A !.333 3.5 .#06 0.000#%3 0."5
columna B !.505 3.5 .000 0.000600 0.4
columna E !.505 3 .000 0.000%6 0.33
dia,ragma 6#50.000 3.5 53".##5 0.044063 54.#56
dia,ragma 6#50.000 3 53".##5 0.05""#5 6.5!6
0.43! 6.#50
caso ! )a 1 b*
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0.33 0.00#
0.066 0.000
0.33 0.00#
0.4"4 0.!4# 0.4"4 0.43! 6.#50
0."5 0.00% 0.4 0.005
0.0"# 0.000 0.05# 0.000
0."5 0.00% 0.4 0.005
A B C $ E
K 0.6%% 0.!4# 0.000 0.000 0.000
0.!4# .#! 6.#50 0.000 0.066
0.000 6.#50 #.#46 0.000 0.000
0.000 0.000 0.000 0.000 0.0000.000 0.066 0.000 0.000 0.565
0.000 0.000 !5.54 0.000 6.#50
0.00% 0.005 !.!4% 0.000 0.000
0.000 0.00# !."0! 0.000 0.00#
K- Err750! Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750! Err750!
Err750! A
Err750! B
Err750! C
Err750! $
Err750! E
Err750! F
Err750! 8
Err750! 8!
Err750! Err750! Err750!
Err750! Err750! Err750!
Err750! Err750! Err750!
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0.000 Err750! 0.000 Err750!
Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750!
Err750! Err750!
Err750!Err750!
Err750!
Err750!
0.000
Err750!
Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750!
0.000 0.000 0.000 0.000
0.000 0.000Err750! Err750!
0.000 0.000
Err750! Err750!
Err750! Err750!
0.000 Err750! 0.000 Err750!
Err750! 0.000 Err750! 0.000
Err750! Err750! Err750! Err750!
Err750! Err750! Err750! Err750!
Err750!
Err750!
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carga3 0
carga! 3
carga 5
longitud 3
dia,ragma a .5
b .5
base 30
altura 300
diametro
inercia 6#50.000
K = K' 4500.000
a !!50.000b 4500.000
t 6000.000
a vigas
carga triangular
ramo viga = 4.0
base =
altura =
a =
b =
carga ( = 4
inercia = 0.000
K K' 0.000
a 0.000
caso )doble *
+, =
+,' =
caso ! ) sim&le derec9a*
+, = !.33
+,' = -3.!00
caso ! ) sim&le i:(uierda*
+, = 3.!00
+,' = -!.33
olumnas
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carga triangular
ramo viga = 3.!
base = 30
altura = 30
a =
b =
carga ( = !
inercia = 6.#50
K K' !.0"
a .055
caso )doble *
+, =
+,' =
caso ! ) sim&le *+, = -0.6%3
+,' = .0!4
caso ! ) sim&le i:(uierda*
+, = .0!4
+,' = -0.6%3
a K'
c b
4 .5
a K' b t
0.!4# 0.4"4
6.#50 .464
6.#50 .464
0.0"# 0.00% 0.0004#6
0.05# 0.005 0.000!#"
0.066 0.00# 0.000443
!3."! !.!4% 0.!%
!5.54 !."0! 0."3
.464
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6.5!6 !."0!
!5.540."3
6.5!6
.464 !."0!
54.#56 !.!4%
!3."! 0.!%
54.#56 !.!4%
F 8 8!
0.000 0.00% 0.000
0.000 0.005 0.00#
!5.54 !.!4% !."0!
0.000 0.000 0.0006.#50 0.000 0.00#
6!.""0 0.000 !."0!
0.000 0.!" 0.000
!."0! 0.000 0."4
Err750! Err750! Err750! ; 0.000
Err750! Err750! Err750! 0.000
Err750! Err750! Err750! 0.000
Err750! Err750! Err750! 0.000
Err750! Err750! Err750! 0.000
Err750! Err750! Err750! 0.000
Err750! Err750! Err750! %
Err750! Err750! Err750! 3
Err750!
Err750!
Err750!
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0.000 Err750!
Err750! Err750!
Err750! Err750!
Err750! Err750!
Err750!
Err750!
Err750!
Err750! Err750!
Err750! Err750! Err750!
Err750! Err750! Err750!
Err750! Err750!
0.000 0.000
0.000Err750! Err750!
0.000
Err750!
Err750!
0.000 Err750!
Err750!0.000
Err750! Err750!
Err750! Err750!
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A
B
C
$
E
F
8
8!
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metodo cross
Err750! Err750! Err750! Err750!Err750! Err750! Err750! Err750!
D Err750! E F
Err750! Err750!
Err750! Err750! Err750!
Err750! Err750! Err750! Err750!
A Err750! B C
Err750!
resistencia de materiales
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Err750!
Err750!
Err750!
Err750!
Err750!
Err750!
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vigas tramos AB BC $E EF
longitud 6 6 6 6
base 30 30 30 30
altura 50 50 50 50
diametro
inercia 3.!50 3.!50 3.!50 3.!50
K = K' 5.!0% 5.!0% 5.!0% 5.!0%a !.604 !.604 !.604 !.604
columnas tramos A B $ E
longitud 3 3 3 3
base 35 40 35 40
altura 35 40 35 40
diametro
inercia !.505 !.333 !.505 !.333
K = K' 4.6% #. 4.6% #.
a !.0%4 3.556 !.0%4 3.556b !.0%4 3.556 !.0%4 3.556
t .3%" !.3#0 .3%" !.3#0
momentos de em&otramiento &ar
carga rectangular carga &untual
ramo viga = 4.0 ramo viga = 4.0
base = 30 base = 30
altura = 40 altura = 40
a = a = !.000
b = b = !.000
carga ( = 3.000 F = !
inercia = 6.000 inercia = 6.000
K K' 4.000 K K' 4.000
a !.000 a !.000
caso )carga en toda la viga* caso )a = b *
+, = 4.000 +, = .000
+,' = -4.000 +,' = -.000
Caso ! )valores de a b*
+, = +, = .000
+,' = +,'= -.000
caso 3 ) !a /b = *
+,=
+,'=
momentos de em&otramiento &ara
caso ! )a 1 b*
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rga rectangular carga &untual
ramo viga = 4 ramo viga = 3
base = 30 base = 30
altura = 40 altura = 40
a = a = .500
b = b = .#00
carga ( = 3.000 F = !
inercia = 6.000 inercia = 6.000
K K' 4.000 K K' 5.000
a !.000 a !.500
caso )carga en toda la viga* caso )a = b *
+, = -4.000 +, =
+,' = 4.000 +,' =
Caso ! )valores de a b*+, = +, = -0.%4#
+,' = +,'= 0.#4#
caso 3 ) !a /b = *
+,=
+,'=
rigideces momento em&otramiento &er,ecto
vigas ( llegan al dia,ragma K
K a K'
a
6 ! 0
elemento 2nercia ongitud relacion 2o c ='
viga AB 3.!50 6 !.4"" 0.6#
viga BC 3.!50 6 !.4"" 0.6#
iga $E 3.!50 6 !.4"" 0.6#
iga EF 3.!50 6 !.4"" 0.6#
columna A !.505 3 .000 0.000%6 0.33
columna B !.333 3 .#06 0.00066 0.!!#
columna $ !.505 3 .000 0.000%6 0.33
columna E !.333 3 .#06 0.00066 0.!!#
dia,ragma 6000.000 3 !#".46# 0.066!! 3!.34!
dia,ragma 6000.000 3 !#".46# 0.066!! 3!.34!
0.6# 0.0%3 0.6# 0.6# 0.6#
caso ! )a 1 b*
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0.330.00# 0.!!# 0.0
0.000444 0.3 0.000.066
0.00# 0.!!# 0.0
0.33 0.6# 0.0%3 0.6# 0.6# 0.6#
0.33 0.00# 0.!!# 0.0
0.066 0.000 0.3 0.00
0.33 0.00# 0.!!# 0.0
A B C $ E
K 0.433 0.0%3 0.000 0.066 0.000
0.0%3 0.#%% 0.6# 0.000 0.3
0.000 0.6# !65.0#3 0.000 0.000
0.066 0.000 0.000 0.300 0.0%30.000 0.3 0.000 0.0%3 0.56
0.000 0.000 4#.045 0.000 0.6#
0.00# 0.0 5."%0 0.000 0.000
0.00# 0.0 5."%0 0.00# 0.0
K- !.45%#0"! -0.!#3#"44" 0.0!!46%" -0.5#4330" 0.44%6""!
-0.!#3#"44" .344#354# 0.00#"043" 0.4%5%6 -0.!"00"34
0.0!!46%" 0.00#"043" 0.0!!54"!! 0.00%5 0.003#!05
-0.5#4330" 0.4%5%6 0.00%5 3.6!%6#4"4 -0.564%%!5
0.44%6""! -0.!"00"34 0.003#!05 -0.564%%!5 ."!#"50%
0.05!53! 0.0!6"653 0.0!!534 0.0%43!3% 0.006##%5
-0.!630%"# -0.5%!0" -0.33#653 -0.60#%4!# -0.04"%#63
-0.43%"#6" -0.335"364# -0.66"!433 -0.4%0%!3# -0.!0!30#
-4.35! A
-3.66 B
-6.#!" C
-3.%53 $
-.0#" E
-#.""# F
30.%0! 8
!30.4%# 8!
-0.#3! -0.50 -.5!
-0.0"0 -0.3! -.33!
-0.64! -0.%0 -0.%0
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0.000 -0.0!6 0.000 -0.0!
-0.54 -0.0!" -0.!45 -0.036
-0.!%" 0.0! -0.35% 0.#4
.534 0.04% !.66 0.!6
0.#3! !.03
.##4!.66
-0.!!
-0.#!0
0.000
0.6"%
.534 -0."%" -0.%"0 -.64%
-0.!56 -0.!64 -0.36! -.!
-0.5%0 -0.#!5 -0.5!# -0.5!#
0.000 0.000 0.000 0.000
0.000 0.000-0.5%0 -0.#!0
0.000 0.000
0.%# .4%4
0.!"0 0.#64
0.000 -0.0!" 0.000 -0.036
-0.!%" 0.000 -0.35% 0.000
0.%# 0.05% .4%4 0.0""
0.5%! 0.0!" .!# 0.063
!.000
4.000
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carga3 0
carga! 4
carga %
longitud 4
dia,ragma a !
b !
base 30
altura 400
diametro
inercia 6000.000
K = K' %000.000
a 4000.000b 6000.000
t 6000.000
a vigas
carga triangular
ramo viga = 4.0
base =
altura =
a =
b =
carga ( = 4
inercia = 0.000
K K' 0.000
a 0.000
caso )doble *
+, =
+,' =
caso ! ) sim&le derec9a*
+, = !.33
+,' = -3.!00
caso ! ) sim&le i:(uierda*
+, = 3.!00
+,' = -!.33
olumnas
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carga triangular
ramo viga = 3.!
base = 30
altura = 30
a =
b =
carga ( = !
inercia = 6.#50
K K' !.0"
a .055
caso )doble *
+, =
+,' =
caso ! ) sim&le *+, = -0.6%3
+,' = .0!4
caso ! ) sim&le i:(uierda*
+, = .0!4
+,' = -0.6%3
a K'
c b
6 !
a K' b t
0.0%3 0.6#
0.6# 0.3%"
0.0%3 0.6#
0.6# 0.3%"
0.066 0.00# 0.000444
0.3 0.0 0.000#5#
0.066 0.00# 0.000444
0.3 0.0 0.000#5#
4#.045 5."%0 0.3""
4#.045 5."%0 0.3""
0.3%"
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3!.34!5."%0
4#.0450.3""
3!.34!
0.3%" 5."%0
3!.34!5."%0
4#.045 0.3""
3!.34!5."%0
F 8 8!
0.000 0.00# 0.00#
0.000 0.0 0.0
4#.045 5."%0 5."%0
0.000 0.000 0.00#0.6# 0.000 0.0
3!.#3 0.000 5."%0
0.000 0.400 0.000
5."%0 0.000 0.400
0.05!53! -0.!630%"# -0.43%"#6" ; 0.000
0.0!6"653 -0.5%!0" -0.335"364# 0.000
0.0!!534 -0.33#653 -0.66"!433 0.000
0.0%43!3% -0.60#%4!# -0.4%0%!3# 0.000
0.006##%5 -0.04"%#63 -0.!0!30# 0.000
0.044%"53% -0.33%%6"# -.0036504" 0.000
-0.33%%6"# #.55%4%6#4 0.0!4"!!6 !
-.0036504" 0.0!4"!!6 !#.546"6! 4
-3.!%%
-0.%0
-3.0"
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0.000 -4#.%!0
-05%.3#4-40.!35
-36.54#".%%
3#%.!03.%!6
3.!%%
0.000
0.#3!
.4"5 0.000
-3.43 3#%.!0 0.6"%
-0.5!# -3#6.!!# 0.!"0
-!.66 -%"0.4%%
0.000 0.000
0.000-%"0.4%% 0.5%!
0.000
#%!.36
-0%.35!
0.000 -40.!35
-36.54#0.000
#%!.365!.4!
465.5%"."0%
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A
B
C
$
E
F
8
8!
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metodo cross
cum&le 0.000 cum&le 0.000-0.#3! -0.50 -.5! -3.!%%
D !.03 E F
0.000 cum&le
cum&le .##4 0.000
-0."%" -0.%"0 -.64% -3.43
A 0.#64 B C
.!#
resistencia de materiales
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no cum&le
3.!%%
no cum&le
.4"5
-0%.35!
465.5%"
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vigas tramos AB BC $E EF
longitud 5 6 5 6
base 35 35 35 35
altura 50 50 50 50
diametro
inercia 36.45% 36.45% 36.45% 36.45%
K = K' #.!"! 6.0#6 #.!"! 6.0#6a 3.646 3.03% 3.646 3.03%
columnas tramos A B $ E
longitud 4 4 3 3
base 35 40 35 40
altura 35 40 35 40
diametro
inercia !.505 !.333 !.505 !.333
K = K' 3.!6 5.333 4.6% #.
a .563 !.66# !.0%4 3.556b .#! !.000 !.0%4 3.556
t 0.5%6 .000 .3%" !.3#0
momentos de em&otramiento &ar
carga rectangular carga &untual
ramo viga = 4.0 ramo viga = 4.0
base = 30 base = 30
altura = 40 altura = 40
a = a = !.000
b = b = !.000
carga ( = 3.000 F = !
inercia = 6.000 inercia = 6.000
K K' 4.000 K K' 4.000
a !.000 a !.000
caso )carga en toda la viga* caso )a = b *
+, = 4.000 +, = .000
+,' = -4.000 +,' = -.000
Caso ! )valores de a b*
+, = +, = .000
+,' = +,'= -.000
caso 3 ) !a /b = *
+,=
+,'=
momentos de em&otramiento &ara
caso ! )a 1 b*
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rga rectangular carga &untual
ramo viga = 4 ramo viga = 3
base = 30 base = 30
altura = 40 altura = 40
a = a = .500
b = b = .#00
carga ( = 3.000 F = !
inercia = 6.000 inercia = 6.000
K K' 4.000 K K' 5.000
a !.000 a !.500
caso )carga en toda la viga* caso )a = b *
+, = -4.000 +, =
+,' = 4.000 +,' =
Caso ! )valores de a b*+, = +, = -0.%4#
+,' = +,'= 0.#4#
caso 3 ) !a /b = *
+,=
+,'=
rigideces momento em&otramiento &er,ecto
vigas ( llegan al dia,ragma K
K a K'
a
6 ! 0
elemento 2nercia ongitud relacion 2o c ='
viga AB 36.45% 5 !."5 0.!33
viga BC 36.45% 6 !."5 0."4
iga $E 36.45% 5 !."5 0.!33
iga EF 36.45% 6 !."5 0."4
columna A !.505 4 .000 0.00045" 0.00
columna B !.333 4 .#06 0.000600 0.#0
columna $ !.505 3 .000 0.000%6 0.33
columna E !.333 3 .#06 0.00066 0.!!#
dia,ragma %666.66# 4 4"!.# 0.05""#5 !#.60
dia,ragma %666.66# 3 4"!.# 0.066!! 54.3""
0.!33 0.# 0.!33 0."4 0."4
caso ! )a 1 b*
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0.330.00# 0.!!# 0.0
0.000443 0.3 0.000.066
0.00# 0.!!# 0.0
0.33 0.!33 0.# 0.!33 0."4 0."4
0.00 0.004 0.#0 0.006
0.050 0.000 0.0%5 0.000
0.00 0.004 0.#0 0.006
A B C $ E
K 0.466 0.# 0.000 0.066 0.000
0.# 0.%!5 0."4 0.000 0.3
0.000 0."4 !%!.463 0.000 0.000
0.066 0.000 0.000 0.366 0.#0.000 0.3 0.000 0.# 0.654
0.000 0.000 54.%%5 0.000 0."4
0.004 0.006 4.55 0.000 0.000
0.00# 0.0 6."#6 0.00# 0.0
K- !.30333%"# -0.34045""5 0.0#%%3 -0.4553!45# 0.4!%3"5
-0.34045""5 .!"%3!%#5 0.00630!35 0.45#3006 -0.!4%5643#
0.0#%%3 0.00630!35 0.0!554% 0.00#64!! 0.00!653%#
-0.4553!45# 0.45#3006 0.00#64!! !.""%04356 -0.556%#035
0.4!%3"5 -0.!4%5643# 0.00!653%# -0.556%#035 .6#6!0#6
0.03"#6%! 0.00!#56% 0.0!50#%04 0.063!4%5 0.000!65
-0.!63645 -0.56#5#06 -0.50"5!6%" -0.!3%0!6 -0.04%300"
-0.406"!356 -0.!#0#5!6% -0.#5#4%6% -0.43543!3 -0.0#0!60%6
-5."% A
-3.!35 B
-"."0! C
-4.6"4 $
-0."3 E
-.!" F
!50.%0 8
3!6."64 8!
-.!03 -0.#65 -!.36!
-0.0" -0.54# -!.%
-.0"5 -0.!# -0.%
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0.000 -0.03 0.000 -0.0
-0.6!4 -0.035 -0.! -0.03#
-0.345 0.45 -0.366 0.!4#
!.#3 0.0#" 3.#03 0.!00
.!03 3.!6
!.%643.#03
-0.05
-0.#33
0.000
.#0
!.#3 -.5"0 -.36 -!.553
-0.3 -0.3## -0.606 -."!5
-0.6" -.!! -0.#54 -0.6!"
0.000 0.000 0.000 0.000
0.000 0.000-0.5" -0.55
0.000 0.000
0."3" .60
0.4!0 .050
0.000 -0.0" 0.000 -0.0!
-0.!5" 0.000 -0.!#5 0.000
0."3" 0.04# .60 0.0%0
0.6%0 0.0!# .3!6 0.05"
!.000
5.000
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carga3 0
carga! 5
carga #
longitud 4
dia,ragma a !
b !
base 35
altura 400
diametro
inercia %666.66#
K = K' "333.333
a 4666.66#b #000.000
t #000.000
a vigas
carga triangular
ramo viga = 4.0
base =
altura =
a =
b =
carga ( = 4
inercia = 0.000
K K' 0.000
a 0.000
caso )doble *
+, =
+,' =
caso ! ) sim&le derec9a*
+, = !.33
+,' = -3.!00
caso ! ) sim&le i:(uierda*
+, = 3.!00
+,' = -!.33
olumnas
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carga triangular
ramo viga = 3.!
base = 30
altura = 30
a =
b =
carga ( = !
inercia = 6.#50
K K' !.0"
a .055
caso )doble *
+, =
+,' =
caso ! ) sim&le *+, = -0.6%3
+,' = .0!4
caso ! ) sim&le i:(uierda*
+, = .0!4
+,' = -0.6%3
a K'
c b
6 !
a K' b t
0.# 0.!33
0."4 0.454
0.# 0.!33
0."4 0.454
0.050 0.004 0.000%#
0.0%5 0.006 0.0003"
0.066 0.00# 0.000443
0.3 0.0 0.000#55
5!."#4 4.55 0.!!6
54.%%5 6."#6 0.465
0.454
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54.3""6."#6
54.%%50.465
54.3""
0.454 6."#6
!#.604.55
5!."#4 0.!!6
!#.604.55
F 8 8!
0.000 0.004 0.00#
0.000 0.006 0.0
54.%%5 4.55 6."#6
0.000 0.000 0.00#0."4 0.000 0.0
54.%53 0.000 6."#6
0.000 0.!!6 0.000
6."#6 0.000 0.466
0.03"#6%! -0.!63645 -0.406"!356 ; 0.000
0.00!#56% -0.56#5#06 -0.!#0#5!6% 0.000
0.0!50#%04 -0.50"5!6%" -0.#5#4%6% 0.000
0.063!4%5 -0.!3%0!6 -0.43543!3 0.000
0.000!65 -0.04%300" -0.0#0!60%6 0.000
0.0444%"## -0.500"5"54 -.045!04% 0.000
-0.500"5"54 4.5"6663" 5.3003! !
-.045!04% 5.3003! !".0%05%"5 5
-5.!6"
-0.%
-5.0%%
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0.000 -#%.!66
-#3!.!!5-6".0#6
-543.45"5!.064
!!%0."534.#!
5.!6"
0.000
.!03
36.36# 0.000
-5." !!%0."53 .#0
-0.6!" -65.#64 0.4!0
-4.4" -5!%.%!
0.000 0.000
0.000-!63.560 0.6%0
0.000
3!.3!
-3.!4%
0.000 -44.#0!
-5!4.53"0.000
3!.3!56.66
60#.##3."3
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A
B
C
$
E
F
8
8!
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metodo cross
cum&le 0.000 cum&le 0.000-.!03 -0.#65 -!.36! -5.!6"
D 3.!6 E F
0.000 cum&le
cum&le !.%64 0.000
-.5"0 -.36 -!.553 -5."
A .050 B C
.3!6
resistencia de materiales
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no cum&le
5.!6"
cum&le
36.36#
-3.!4%
60#.##3