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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!

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Err750! A

Err750! B

Err750! C

Err750! $

Err750! E

Err750! F

Err750! 8

Err750! 8!

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0.000 Err750! 0.000 Err750!

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0.000

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0.000 0.000 0.000 0.000

0.000 0.000Err750! Err750!

0.000 0.000

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0.000 Err750! 0.000 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

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Err750!

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0.000 Err750!

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Err750!

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0.000 0.000

0.000Err750! 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