Concreto armado Vigas T

UNIVERSIDAD NACIONAL DE HUANCAVELICA FACULTAD DE CIENCIAS DE INGENIERÍA ESCUELA ACADÉMICO PROFESIONAL DE INGENIERÍA INGENIERÍA CIVIL

CONCRETO ARMADO I

ALUMNO: AL UMNO: CHRISTIAN PÉREZ TORO CÓDIGO: 2010151056

ANÁLISIS Y DISEÑOS DE VIGAS T Y L

Con!n"#o VIGAS T..............................................................................2 ANÁLISIS DE VIGAS T..............................................................................3 CÁLCULO DE LA RESISTENCIA DE UNA VIGA$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$% METODO 1$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$% METODO 2$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$& VERIFICACIÓN DE CUANTÍA$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$5

C'(n)( #! *( +",(:$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$5 C'(n)( -)n"-( #! *( +",(:$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$5 C'(n)( -./"-( #! *( +",(:$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$5 EJEMPLO 1.$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ EJEMPLO 2.$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ DISEÑO DE VIGAS T...............................................................................10 MÉTODO 1........................................................................................ .10 MÉTODO 2........................................................................................ .10 EJEMPLO 3.$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$11 EJEMPLO 4.$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$1%

VIGAS L............................................................................. 1


VIGAS T S! *! 3ono3! 3o-o +",( T ( (4'!**( 4'! "!n!n 'n (n3o (#"3"on(* #! *o( !n *( (7! '!7"o7 #!no-"n(#o patín8 *( (7! #! 'n( +",( T #!9(o #! *( *o( ! #!no-"n( alma$ L( +",( '!#! ;o7-(7 L " !* (*-( ! !n3'!n7( !n !* !/7!-o #! *( *o($ Lo !7"9o #!* (*-( ! 7o*on,(n (( *( *o( 3on *o 4'! (<'#(n !* 7(9(o 3on'no #! *( *o( < +",($

E* 3=#",o ACI >$10$2? !(9*!3! (*,'n( 7!7"33"on! (7( !* #"!@o #! !( +",(: •

•

P(7( +",( T "-7"3(: E* (n3o !;!3"+o #!* ()n no #!9! !/3!#!7 B #! *( *' #! *( +",($ E* (n3o #! *( o73"=n +o*(#( ( 3(#( *(#o no #!9! !/3!#!7  +!3! !* !!o7 #! *( *o( o *( -"(# #! *( #"(n3"( *"97! #!* (*-( T (#<(3!n!$ L( +",( T ("*(#(: D!9!n !n!7 'n !!o7 #! ()n no -!no7 4'! *( -"(# #!* (n3o #!* (*-($ E* (n3o !;!3"+o #!* ()n no #!9! !7 -(
E* !! n!'7o #! *( +",( T '!#! 3(!7 !n !* ()n o !n !* (*-($

S" 3(! !n !* ()n on (*"3(9*! *( ;=7-'*( #! *( +",( 7!3(n,'*(7!8 ! 'on! 4'! !* 3on37!o #!9(o #!* !! n!'7o !. (,7"!(#o < ' ;o7-( no "n'
ANÁLISIS Y DISEÑOS DE VIGAS T Y L 3on37!o ( 3o-7!"=n <( no 3on"! !n o*o 'n 7!3.n,'*o < *( ;=7-'*( (7( +",( 7!3(n,'*(7! <( no on (*"3(9*!$

L( +",( T '!#!n !n!7 #"+!7( ;o7-(8 "!-7! 3'(n#o !* 3on37!o ( 3o-7!"=n !n,( *( ;o7-( #! T8 '!o 4'!8 *( ;o7-( o !* (-(@o #!* 3on37!o !n *( on( #! !n"=n8 4'! ! 'on! !. (,7"!(#(8 no "n'
ANÁLISIS DE VIGAS T CÁLCULO DE LA RESISTENCIA DE UNA VIGA METODO 1 A 3on"n'(3"=n ! -'!7( !* 7o3!#"-"!no ( !,'"7 (7( !* 3.*3'*o #! *( 7!"!n3"( #! #"!@o #! *( +",( T8 !,n !* ,7(3o -o7(#o$

1$ C.*3'*o #! T = A s f y $ 2$ C.*3'*o #!* .7!( #!* 3on37!o !n 3o-7!"=n !;o7(#o (

0.85 f

'c $

'

T =C =0.85 f c A c A c =

T '

0.85 f

c

%$ Lo3(*"(3"=n #!* 3!n7o #! ,7(+!#(# #!* .7!( #!* 3on37!o ( 3o-7!"=n A c $

ANÁLISIS Y DISEÑOS DE VIGAS T Y L &$ C.*3'*o #!

M n= T +!3! !* 97(o #! *( (*(n3( #!* 3!n7o"#! #!*

(3!7o (* 3!n7o"#! #! A c $ 5$ C.*3'*o #! M u=∅ M n $ METODO 2 P7"-!7o ! #!!7-"n( !* +(*o7 #! (8 " 7!'*( -!no7 ! 3on"#!7(7. 3o-o 'n( +",( 7!3(n,'*(7$ S" 7!'*( -(
'

Cw =0.85 ∗f c∗a∗bw '

Cf =0.85 ∗f c∗(b −bw )∗hf

P!7o " (;8 ! 7!!-*((7. ; o7 ( Enon3! ! #!!7-"n( !* -o-!no no-"n(* Mn -'*"*"3(n#o C < C; o7 ' 7!!3"+o 97(o8 4'! +(n #! ' 3!n7o"#! (* 3!n7o"#! #!* (3!7o:

Aunque parece ofrecer pocas ventajas en el cálculo de Mn, este método simplica el diseño de vigas T cuando a>hf, pues permite una solucin directa de un pro!lema que de otra manera tendría que ser resuelto con tanteos

( ) (

Mn =Cw d −

a

2

+ Cf d − hf 2

)


VERIFICACIÓN DE CUANTÍA "uantía de la viga# As ρ = b w∗d

"uantía mínima de la viga# ρmin=

ρmin=

14

fy

0.8 √ f

'c

fy

"uantía má$ima de la viga# 6 P(7( *( +!7"3(3"=n #! 3'(n)( 3on"#!7(7!-o ε c = 0.003 ; Es =2∗10 $

D!* ,7.3o: C(*3'*(n#o *( #"(n3"( (* !! n!'7o: c=

c=

0.003

fy 0.003 + Es 6000 6000

+ fy

d

∗

∗d

C(*3'*(n#o *( #"(n3"( (* !! n!'7o #! *( 'n( !33"=n 7(n;o7-(#( a = β 1∗c

C(*3'*(n#o !* .7!( #! 3on37!o ( 3o-7!"=n < *( -(,n"'# #! *( 3o-7!"=n$ '

C =0.85 ∗f c∗ Ac

ANÁLISIS Y DISEÑOS DE VIGAS T Y L Cono TC8 !non3! ! "!n! *( -(,n"'# #! *( !n"=n #! *( +",( !n 'n !(#o 9(*(n3!(#o8 ( (7"7 #!* 3'(* ! 3(*3'*( *( 3'(n)( 9(*(n3!(#( < *( 3'(n)( -./"-( As =

T fy

ρb =

As bw∗d

ρmáx =0.75 ρb


C'(n)( -./"-( #! *( +",(: EJEMPLO 1.

EJEMPLO 2.


CAPACIDAD POR MOMENTO

VERIFICACIÓN POR CUANTÍA: C'(n)( #! *( +",(: C'(n)( -)n"-( #! *( +",(: C'(n)( -./"-( #! *( +",(:

ANÁLISIS Y DISEÑOS DE VIGAS T Y L DISEÑO DE VIGAS T A* #"!@(7 'n( +",( T8 o7 *o ,!n!7(*8 !* ()n ! #"-!n"on( (* #"!@(7 *( *o(8 !* (n3o #!* (*-( ! !*!33"on! 3on 9(! !n !* (n3o 4'! ! !"-! n!3!(7"o (7( (3o,!7 *( 9(77( #! 7!;'!7o o !,n 7!4'""o (74'"!3=n"3o$ Lo ("n! #! *( +",( T on ''(*-!n! (n ,7(n#! 4'! !* !! n!'7o 3(! #!n7o #! !**o8 o7 *o 4'! '!#!n (*"3(7! *( ;=7-'*( #! *( +",( 7!3(n,'*(7!$ S" !* !! n!'7o 3(! !n !* (*-(8 ! '( ( -!n'#o 7o3!#"-"!no #! (n!o (7( !* #"!@o8 !,n !* -o#o 1 #! (n.*"" #! +",(J (-9"n !/"! 'n 7o3!#"-"!no -. #"7!3o (7( !* 3(o 4'! (K;8 !! ! !* 3(o !n 4'! *( +",( ! 'on! '9#"+"#"#( !n (7! 7!3(n,'*(7!8 !,n !* -o#o 2 #!* (n.*"" #! +",($

MÉTODO 1 A 3on"n'(3"=n ! 7!!n( *o 7o3!#"-"!no #!* #"!@o: 1$ E"-(7 'n +(*o7 #!* 97(o #! (*(n3(8 #!* 3!n7o"#! #!* .7!( ( 3o-7!"=n (* 3!n7o"#! #!* (3!7o8 !( 7"-!7( !"-(3"=n ! !* -(
( )

z =0.9 d ó z =d −

hf 2

2$ Con  !"-(#o ! 3(*3'*( !* .7!( #! (3!7o: As =

Mn z fy

%$ I,'(*(n#o TC ! 3(*3'*( !* .7!( #! 3on37!o '

0.85 f

Ac =

c Ac = As fy As fy '

0.85 f

c

&$ Con !* .7!( #! 3on37!o ! 3(*3'*( ' 3!n7o"#! >?$ 5$ Con !! n'!+o +(*o7 #! 8 ! 3(*3'*( !n A8 < " !! no +(7)( -'3o #!* (n!7"o7 ! '( "no ! +'!*+! ( 3(*3'*(  < A$

MÉTODO 2 A*"3(n#o !* -o#o 2 #!* (n.*"" #! +",( T8 ! o"9*! !n3on7(7 #"7!3(-!n! !* +(*o7 #! A$ L( ;'!7( #! 3o-7!"=n '-"n"7(#( o7 *o 7!3.n,'*o #! *o ("n! #!9! !7 !4'"*"97(#( o7 *( ;'!7( #! !n"=n !n 'n( (7! #!* .7!( #! (3!7o A;8 !n (no 4'! *( ;'!7( #! 3o-7!"=n !n !* (*-( ! !4'"*"97(#( o7 *( ;'!7( #! !n"=n 7!(n! A$ P(7( *( o73"on! +o*(#( #!* ()n ! "!n!n:

ANÁLISIS Y DISEÑOS DE VIGAS T Y L '

0.85 f

c ( b −bw ) hf = Asf fy

D! #on#!8 !* .7!( 7!4'!7"#( #! (3!7o A; !: '

Asf =

0.85 f

c ( b −bw ) hf fy

L( 7!"!n3"( !n *o +o*(#o #! *o ("n! !:

(

Muf =∅ Asf fy d −

hf 2

)

S! #!!7-"n( ( 3on"n'(3"=n !* -o-!no 7!(n! 4'! #!9! 7!""7 !* (*-( < !* (3!7o 7!4'!7"#o (7( !4'"*"97(7 !! +(*o7$ Muw = Mu − Muf

E* (3!7o 7!4'!7"#o (7( !4'"*"97(7 !* -o-!no !n !* (*-( 7!3(n,'*(7 ! o9"!n! o7 -!#"o #! *( !/7!"=n ''(* (7( +",( 7!3(n,'*(7!$ S! #!!7-"n( *( 3'(n)( -./"-( < 3on !**o !* .7!( #!* (3!7o 7!(n! >A?$ '

pb=

0.85 f

cβ1 fy d

Asw = ρ bw d As = Asw + Asf

(

6000 6000 + fy

)


EJEMPLO 3.


7!( #! (3!7o:

7!( #! 3on37!o ( 3o-7!"=n C(*3'*(n#o  R!3(*3'*(n#o A R!3(*3'*(n#o  R!3(*3'*(n#o A VERIFICACIÓN POR CUANTÍA: C'(n)( #! *( +",(: C'(n)( -)n"-( #! *( +",(: C'(n)( -./"-( #! *( +",(:


EJEMPLO 4.

ANÁLISIS Y DISEÑOS DE VIGAS T Y L 7!( #! (3!7o: 7!( #! 3on37!o ( 3o-7!"=n C(*3'*(n#o <

R!3(*3'*(n#o A R!3(*3'*(n#o 

R!3(*3'*(n#o A VERIFICACIÓN POR CUANTÍA: C'(n)( #! *( +",(: C'(n)( -)n"-( #! *( +",(:


C'(n)( -./"-( #! *( +",(:

SOLUCIÓN >MÉTODO 2?: P(7( *( o73"on! +o*(#( #!* ()n ! "!n!: L( 7!"!n3"( !n *o +o*(#o #! *o ("n! !: E* -o-!no 7!(n! 4'! #!9! 7!""7 !* (*-($ S! #!!7-"n( *( 3'(n)( < 3on !**o !* .7!( #!* (3!7o 7!(n! >A?$


VIGAS L L( +",( L on 'n "o !!3"(* #! +",( T8 '! on (4'!**( +",( T 4'! ! !n3'!n7(n !n !* 9o7#! 3on ()n !n 'n o*o *(#o8 !* (n.*"" 4'! ! 7!(*"( (7( !! "o #! +",( #!9! !7 !* -"-o (n.*"" 4'! ! 7!(*"= (7( +",( T8 -!#"(n! !* !"#$%$ 1. S! #!7!3"( *( ("-!7)($ S!,n *( no7-( #! ACI >ACI$ $10$%?8 (7( *( +",( L8 !* (n3o !;!3"+o #! ' ()n no #!9! !7 -(

Concreto armado Vigas T

Recommend Documents