Problemas Vigas Continuas.docx

7/26/2019 Problemas Vigas Continuas.docx

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UNIVERSIDAD NACIONAL DE TRUJILLO

FACULTAD DE INGENIERIA

ESCUELA DE INGENIERIA MECANICA

CURSO: RESISTENCIA DE MATERIALES II

TEMA: PROBLEMAS RESUELTOS - VIGAS CONTINUAS

DOCENTE: ING. HECTOR AGUADO MERE

INTEGRANTES:

LLERENA GUARNIZ ANTHONY TORRES BERNARDO FRANK VILLALOBOS NUES JUAN


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VIGAS CONTINUAS

PROBLEMA 01. Calcla! l"# $"$%&'"# %& l"# a(")"# %& la *+,a c"&'+&a c"$" #% $%#'!a %& la +,!a.S% #("&% % l"# a(")"# #"& !/,+0"#1 " % 2a3" la acc+4& 0% la# ca!,a# !"0"#

%5(%!+$%&'a& %l $+#$" a#%&'a$+%&'".

SOLUCION:

A(l+ca$"# la %cac+4& 0% l"# '!%# $"$%&'"# a l"# (&'"# #"2!% l"# a(")"#. C"$" l"# '!%# %#'6& al$+#$" &+*%l1 %# 0%c+! la# al'!a# 78) 79#"& &la#1 la %cac+4& 0% l"# '!%# $"$%&'"# #% %#c!+2% 0% la"!$a:

M1L

1+2M

2(L1+L2 )+M3 L2+6 A

1a1

L1+6 A

2a2

L2=0

El $"$%&'" l%5+"&a&'% %& %l a(")" 81 %# (!"0c+0" ("! la ca!,a a la ++%!0a 0% R 81 %# M8; -8.?@; -9==N$1 $+%&'!a# % %& %l a(")" R9 %l $"$%&'" M9 %# &l". El #+,&" $%&"# 0% M8 #% 0%2%$a&'%&%! al ##'+'+! # *al"! %& la %cac+4& 0% l"# '!%# $"$%&'"#.

L"# '!$+&"# 0% la# 6!%a# 0% $"$%&'"# 0% la %cac+4& a&'%!+"! #% "2'+%&%& 0% la# 'a2la# 0% *+,a#

c"&'+&a# 0a0a# %& la '%"!/a. La ca!,a 0%l '!a$" 8 %# la 0%l ca#" 9. P"! l" 'a&'":


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6 A1

a1

L1= 8

60( 800)(33 )=2880 N m2

Pa!a %l '!a$"


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M1L

1+2M

2(L1+L2 )+M3 L2+6 A

1a1

L1+6 A

2a2

L2=0

El $"$%&'" %& R80%2+0" al *"la0+" %#:

M1=( 4001 )1

2=200Nm

A&la&0" '"0"# l"# '!$+&"# % #% !%+%!% al '!a$"


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M2L

2+2M

3(L2+L3 )+M4L3+6 A

2a2

L2+6 A

3a3

L3=0

D% ac%!0" c"& la 0%+&+c+4& 0% $"$%&'" l%5+"&a&'% M8 ) M #"& &l"#1 ("! l" % la# %cac+"&%#a&'%!+"!%# "!$a& & #+#'%$a c"& 0"# +&c4,&+'a# M< ) M9 % (%0%& !%#"l*%!#% #+ #% c"&"c%& l"#*al"!%# 0% AaL ) A2L (a!a ca0a '!a$"1 c"!!%#("&0+%&'%# a la# ca!,a# 0a0a#. U'+l+a&0" la 'a2la 0%ca!,a# (a!a *+,a# c"&'+&a#1 %#'"# *al"!%# #% calcla&:

6 A1

a1

L1=

w b2

4 L(2L2b2 )=400(3

2)4(4)

[2 (42 )(32) ]=5175N m2

6 A2b2

L2=8w L

3

60=8 (800)(33 )

60=2880 N m2

6 A2a2

L2=7w L

3

60=7 (800)(33 )

60=2520 N m2

6 A3

b3

L2= Pb

L (L2b2)

6 A3b3

L2=600(3)

4[(42)(32)]+ 700(2)

4[(42)(22)]

6 A3

b3

L2

=3150+4200=7350N m2

S#'+')%&0" %#'"# *al"!%# calcla0"# %& la# %cac+"&%# a&'%!+"!%# a(l+ca0a# a %& la %cac+4& 0% l"#'!%# $"$%&'"#1 %&'"&c%# '%&%$"#:

2M2(4+3 )+3M

3+5175+2880=0

3 M2+2 M3(3+4 )+2520+7350=0

S+$(l++ca&0":

14 M2+3M

3+8055=0

3 M2+14M

3+9870=0

R%#"l*+%&0" %l #+#'%$a 0% %cac+"&%#1 '%&%$"#:

M2=445NmM

3=610Nm


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PROBLEMA 04. D%'%!$+&a! l"# $"$%&'"# %& l"# a(")"# 0% la *+,a c"&'+&a c"$" #% $%#'!a %& la+,!a1 #+ a$2"# %5'!%$"# %#'6& (%!%c'a$%&'% %$("'!a0"#.

SOLUCION:

L"# %$("'!a$+%&'"# %+*al%& a l"# '!a$"# +$a,+&a!+"# = ) 9. E&'"&c%# %#c!+2+$"# la %cac+4& 0% l"#'!%# $"$%&'"# (a!a l"# '!a$"# = ) 81 (a!a 8 ) < ) (a!a < ) 9:

M0L

0+2 M

1 (L0+L1 )+M2L1+6 A

0a0

L0+6 A

1a1

L1=0

M1L

1+2M

2(L1+L2 )+M3 L2+6 A

1a1

L1+6 A

2a2

L2=0

M2L

2+2M

3(L2+L3 )+M4L3+6 A

2a2

L2+6 A

3a3

L3=0

Al ##'+'+! %#'"# *al"!%# a&la!%$"# l"# '!$+&"# 0% %#'"# '!a$"# +$a,+&a!+"#. E& la 'a2la 0% ca!,a#(a!a *+,a# c"&'+&a#1 #% '+%&% %#'"# *al"!%#:

6 A1b1

L1=Pb

L(L2b2 )=4002

4(164 )=2400 N m2

6 A1b1

L1=Pa

L(L2a2 )=4002

4(164 )=2400 N m2

6 A2

a2

L2=6 A

2b2

L2=

w L3

4=600(33)

4=4050 N m2

S#'+')%&0" %& la %cac+4& 0% l"# '!%# $"$%&'"#:

8 M1+4M

2+2400=0

4 M1+14M

2+3 M

3+6450=0

3 M2+6 M

3+4050=0


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R%#"l*+%&0" %l #+#'%$a1 "2'%&%$"#:

M1=147Nm

M2=307Nm

M3=522Nm

PROBLEMA 05. Halla! l"# $"$%&'"# %& l"# (&'"# 0% la# !%acc+"&%#1 c"$" #% $%#'!a %& la +,!a

SOLUCION:

P"! %l '%"!%$a 0% l"# 9 $"$%&'"# %& l"# '!a$"# 8-< )


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D"&0%: M8; ->9@>8@< ; -8== N.$ >8@ ; -== N.$ >9@

E& %l '!a$" 8 < '%&%$"# %l #+,+%&'% 0+a,!a$a 0% ca!,a#:

E#'% 0+a,!a$a %# %& !%al+0a0 la #(%!("#+c+4& 0% 0"# ca!,a#:


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Pa!a la (!+$%!a (a!'% '%&%$"# %& %l ca#" 9 #%,& la 'a2la 0% $"$%&'"#1 0"&0%:

Aa L ; L9 =

Pa!a %l (!"2l%$a: L ;=@ >


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Ll%*a&0" l"# !%#l'a0"# >9@1 >@ ) >?@ a la %cac+4& >8@:

-8==@ 8-8?8-8@

El $"$%&'" l%5+"&a&'% %& %l a(")" >8@:


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D"&0%: M8 ; -5 >5


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8-


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E& %l cla!" >8-@

>9@1 >@ &"# 0a %l #+#'%$a:

8 Q@ML


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M1

L1+2M

2(L1+L2 )+M3 L2+6 A

1a1

L1

+6 A

2a2

L2

=6 EI( h1L1

+h3

L2)

C"$" %l '!a$" 8 %#'a l+2!% 0% ca!,a#. A8a8L8%# c%!". Pa!a %l '!a$" < #% a(l+ca %l ca#" ? 0% la 'a2la 0%ca!,a# (a!a *+,a# c"&'+&a#1 %# 0%c+!:

6 A2a2

L2=w d

2

4L(2L2d2)=900(2

2)4 (3)

[2 (32 )(22)]=4200 N m2

T"$a&0" l"# $"$%&'"# !%#(%c'" 0% R


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E& la *+,a $"#'!a0a 0%'%!$+&a!%$"# l"# $"$%&'"# 0% c"&'+&+0a0. El (&'" = 0% la %l6#'+ca %# a7"!a %l

(&'" 81 ("! l" % 7=; ) 7

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