Problemas Vigas Continuas.docx
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Transcript of 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