DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
I I S O T E R C N O C E D S A R U T C U R T S E
CARRERA DE INGENIERÍA CIVIL - UNAH DISEÑO DE MENSULAS CORTAS CATEDRÁTICO: ING. JUAN CARLOS ARITA YUJA DE INGENIRÍA CIVIL - UNAH ALUMN AL UMNOS: OS: CARL CARLOS OS LUIS LUIS TORRES TORRES FLORES FLORES--------200 -2008100 810019 19 09:00 EMILIANO MOLINA RUÍ!-----------2009101 RUÍ!-----------2009101""19 ""19
CARRERA SECCION SEC CION::
DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
CONTENIDO I INTRODUCCI#N.................... INTRODUCCI#N........................................ ........................................ ....................................... ............................... .................. ...... 2 II JUSTIFICACION................ JUSTIFICACION.................................... ........................................ ........................................ .......................................... ...................... 2 III O$JETIVOS...................... O$JETIVOS......................................... ....................................... ........................................ .......................................... ...................... " IV MARCO MARCO TE#RICO.......................... TE#RICO.............................................. ........................................ ............................................... ........................... 1. M%NSULA M%NSULAS.... S......... ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ............... .............. .... 2. DISEÑO DISEÑO DE M%NSULAS M%NSULAS CORT CORTAS....... AS............ .......... .......... .......... .......... .......... .......... .......... ........... ................ ............ .. 11.9 & D'()*('+'*,( ()+'/( ) ,(3/( 4 +5/(.......................... V EJEM6LO................... EJEM6LO....................................... ........................................ ........................................ ................................................ ............................ 9 VI CONCLUSIONES.......... CONCLUSIONES.............................. ........................................ ....................................... ........................................... ........................ 12 VII $I$LIOGRAFÍA............... $I$LIOGRAFÍA.................................. ....................................... ........................................ ......................................... ..................... 1"
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
I INTRODUCCI#N E(5 E(5 +*,5 +*,5' '* * ',5 ',5* *3+5 3+5*' *'* * '(+35 '(+35 /73, /73,(( /( +*,(' +*,(' +'* +'*,( ,( / / C*'5 "18 , / ++', /*( ;3'('5*( +*,5,'*( , ?@ / +3/ , /,5 ( // / 7/,5* * / 7/,5* / 200>. S B B+B* ,('( , /( )/'++'*,( (* / 5'/ ,3* * ;3 3 '(* ++ / +3/ /*( 3(3'*( )3, ,* (5 '/''*(. A( ( B+, +*,5'*( (* /73 /73,* ,*(( () ()+5 +5*( *( ;3 ;3 4 '( '(5 5, , , ( ('* '*, ,(( ,5 ,5' '* *( ( +*, +*, / , ', ',) ), ,' ' / )( )(, ,5 5 +* +*,5 ,5 '* '* / / +* +*,5 ,5 '* '* /( /( ( ('* '*, ,(( ,5'*(. L*( +*,5'*( ++ ;3'('5*( ()++*( ( B+, , / +)53/* 4 (++', +*()*,',5. E/ )(,5 ',* , 5', / ,/' +*,*+ / /+5* / 5** ) / +/+3/* 4 '(K* (53+53( ,(3/( (5/+'* )* / C'7* H*,3K* / C*,(53++', CHOC 4 / ACI-"18-0> , (3 ,3/ 11.9 +*, / +3/ (5 )* +*,*+ /( '()*('+'*,( / '(* /*( 5**( +/+3/* 4 '(K* +*)K* +*, )/*( '/3(55'*( 4 5//*( (5.
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
II JUSTIFICACION
E, / +53/' /*( 5**( +*,(53+5'*( +*,(53+5'*( (*, '(*( 3,*( ( +*,'+*( ;3 *5*( *5*( *5*( *5*( (( )5*( )5*( , +'5 +'5(( +*,' +*,'+'* +'*,( ,( ;3 *5*(. *5*(. E( 7, 7, ')*5,+' ;3 /*( +53/( (53',5( I,7,' C''/ B ',7,'*( , )+5'+ /*( +*,*+'',5*( / I,7,' C''/ +*,*+, + ( (5*( 5**( ;3 /( )'5, /* '(K*( +',5( +*,'+*( 4 (* 5** (73*( 4 , +3)/'',5* /( '7,+'( /*( +'7*( +*,(53++', +*,(53++', 5,5* /*+/( +** ',5,+'*,/( ;3 (', +** +53/'+', ( (5* 5*( ( )* )** *' ', ,* * ( ( / * *+ +' ', , )* )*( ('* '*, ,/ /(( + + (( +)+'5*( ( +',5( 4 ( B+',5( ;3 /, / ,* / I,7,' C''/ 4 /*( )*('*,/( ,3(5* )( , 7,/.
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
III O$JETIVOS
Objetivo General:
D +*,*+ / /+5* /*( 5**( +/+3/* ) /( (53+53( ,(3/ )3(5( , ACI-"18-0> +)53/* 11.9.
Objetivos Específcos: • •
C*,*+ / ',+' ,5 3, */'* 4 3, ,(3/. D5', / ;3' +* 3* ) / '(K* ,(3/ +* )',+')/ +* (5'*( +* 3*
•
(5'*( )* '++', 5+. C*,*+ /( ()+'++'*,( 5+,'+( ) / / +* ,5( 5',*
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
IV MARCO TE#RICO 1. M%N %NSU SULA LAS S U, ménsula ( +3/;3' +3/;3' /,5* /,5* (53+53/ (53+53/ , voladizo. S )3 '(5',73' ,5: M,(3/( +*5(: );3K*( (/',5( ;3 (', (*)*5 ) /7, *5* /,5* +** / ,;3 3, +* /+, * +3'5. M,(3/( /7( * */'*(: /,5*( (53+53/( ;3 )* (3 /*,7'53 B*'*,5/ 3,+'*,, 3,+'*,, +** 3, '7 ( +' ',.
2. DISEÑ DISEÑO O DE M%NSULAS M%NSULAS CORT CORTAS 11.9 & D'()*('+'*,( ()+'/( ) ,(3/( 4 +5/( L( ,(3/( 4 +5/( (*, */'*( ;3 5',, /+', /3 +*5,5 /53( ,*( ;3 / 3,' ;3 5',, +53 +** ++B( (')/( * '7 '7(( 7, 7, /53 /53 (( ;3 ;3 +** +** / /, ,5* 5* ' ', , '( '(K K* *(( ) ) +*5,5. L +5/ ;3 ( 3(5 , / F'7. R11.9.1 )3 // )* +*5,5 /* /7* / ',5+ / +*/3, 4 / +5/ )* 3,+' / 5++', )* )/(5',5* * B,'',5* / )3,5/ +*)(', * '* 3, // /*+/' )/(5',5* * +*5,5 * / )/5', +7. L ,*5+', )/ ( '/3(5 , / F'7. R11.9.2.
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II 11.9.1 PS )3 '(K ,(3/( 4 +5/( 35'/',* / 5** (53' +3,*: ? AQ ,* 4* ;3 1 4 ? C3,* C3,* (5, (*5' (*5'(( 3, 3 3 4* 4* 5++', B*'*,5 B*'*,5/ / N3+ ,* 4* ;3 V 3. S ()+'+ 3, /'5 (3)'* '73/ 3,* ) Q )* *( *,(. 6'* ) /+'*,( /3 +*5,5 /53 Q ;3 +, / 3,' /( (3( '7*,/( 5++', (5, ,*( ',+/',( 4 ,* ( )*)'* / )/* (*/,5 (5'*( B*'*,5/( +** ( 3(5 , / 73 R11.9.2. S73,* / 5** '(K* B ('* /'* )',5/,5 (/* ) Q '73/ / 3,' * ,*(. S ()+'+ 3, /'5 (3)'* ) N 3+ 4 ;3 (5 5** '(K* (/* ( B /'* )',5/,5 ) N 3+ ,* * '73/ V 3 ',+/34,* N3+ '73/ +*.
L /53 5'/ ( 5', 5', , / + / )*4*. V3 1.2C 1.C '
V u ≤ ∅ Pnb=∅ ( 0.85 f c A v ) ∅
=0.65
=10.1.1?
=9.".2.?
9.".2. & A)/(5',5* , / +*,+5* =+)5* ) ,+/( )*(5,(* 4 */*( )3,5/-5,(*?............................... )3,5/-5,(*?.................................................. ..................... 0.> 11.9.2 P / /53 , / * 5'* / )*4* ,* ( ,* 0.>.
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II S ()+'+ 3, /53 ,' , / * 5'* / )*4* ) '5 / *+3,+' 3, // )53 '* 3, (3 ')*5,5 5++', '7*,/ ;3 ( )*)7 ( * * / )*4* B+' / + 5'* ',+/', / +5/ * / ,(3/. S B, *(* //( )53( )53( (5 5')* , +5/( +*, /53( , / * 5'* / )*4* ,*( ;3 /( ()+'+( , (5 (++', / 7/,5*.
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II 11.9 11.9." ." P / ( (++ ++' ', , , / + + / )*4 )*4* * '( '(K K( ( ) ) ('( ('(5' 5' ('3/5,,5 V3 3, *,5* 4** V 3 N3+=B-?W 4 3, 3 4* 5++', B*'*,5/ N 3+. N3+ 1.XN3+1 M u=V u a + N uc uc ( h− d )
=11.9."."?
11.9.".1 P , 5**( /*( +/+3/*( '(K* 5*( '73/ 0.> 4 ;3 / +*)* +*)*5 5', ',5* 5* +5/ +5/( ( 4 ,(3 ,(3/( /( /* +*,5 +*,5*/ */ )',+ )',+') ')/ /,5 ,5 / +*5,5. 11.9.".2 P / '(K* / 3* +*5,5 )* '++', A ) ) ('(5' V 3 +3)/' +*, 11.. A vf = 11.7.4.3
-
V u
f μ
∅ y y
— El coeficiente de fricción
=11...1?
Z debe ser tomado como:
Para concreto colocado monolíticamente............ monolíticamente..................... .................... .................... .................... .................... ................... .......... 1 4[ Concreto colocado sobre concreto endurecido con la superficie intencionalmente rugosa como se especifica en 11.7.9......................................................................................... 1 0[ Concreto colocado sobre concreto endurecido no intencionalmente 0 6[ rugoso............................................................................................................................. Concreto anclado a acero estructural mediante pernos con cabeza o mediante barras de refuerzo !"ase 11.7.1#$ ................................................................................................. 0 7[ .
.
-
.
-
.
%onde [ 1 0 para concreto normal& #.'( para concreto li!iano con arena de peso normal ) #.7( para concreto li!iano en todos sus componentes. *e permite usar interpolación lineal si se emplea sustitución parcial de arena. .
11.9.".2.1 P ) +*,+5* ,(' ,*/ V , ,* 5*( 4* ;3 / ,* 0.2\ +] * >.>]. '
V n=800 b w d ó 0.2 f c b w d el que que sea sea meno menorr 11.9 1.9 .3.2.1
11.9.".2.2 P ) / +*,+5* /'',* , 5**( (3( +*)*,,5( * +*,+5* /'',* +*, , )(* ,*/ V , ,* 5*( 4* ;3 / ,* =0.2-0.0Q?\+] * =>.>-1.9Q?]. A/73,*( ,(4*( B, *(5* ;3 / ('(5,+' ' / +*5,5 ,(3/( * +5/( B+B( +*,+5* /'',* ( 3,+', 5,5* ^ + +** Q.
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II 11.9."." P / 3* A ) ('(5' / *,5* 4** V 3 N3+=B-?W +/+3/( +3* +*, 10.2 4 10.". =C/+3/* '7( (53'* ,5(? M u=V u a + N uc ( h− d ) A f =
M u 0.75 f y j u d
=
=11.9."."?
M u
(
0.75 f y 0.9 d
)
E/ 3* ;3'* ) ('(5' *,5*( )3 +/+3/( )/'+,* / 5* 5* *' *', ,' ' ' ', ,.. E/ * *,5 ,5* * 4* 4* * * ( + +/+ /+3/ 3/ (3 (3, ,* * *,5*( /* / 3* ', , / + / )*4*. 11.9.". P / 3* A , ) ('(5' / 3 4* 5++', N 3+ 5 5' ', ,( ( A, 4 _ N3+. L 3 5++', 4* N 3+ ,* 5*( ,* ;3 0.2V 3 ,*( ;3 ( 5*, '()*('+'*,( '()*('+'*,( ()+'/( ) '5 /( 3( 5++',. N 3+ +*,('( +** 3, +7 ' 3, +3,* / 5++', (3/5 (5'++', / 3* )/(5'+* 5++', 5++', * '+', 5)53. A n=
N uc ∅
f y
; N uc ≥ 0.2 V u
=11.9.".1?
D'* ;3 / 7,'53 /( 3( B*'*,5/( ;3 +5, (* +5/( * ,(3 ,(3/( /( 3(3/ 3(3/, ,5 5 ,* )3 )3 5 5', ',( ( +*, 3+B 3+B )+' )+'(' (', , ( ()+'+ ;3 N3+ +*,('( +*,('( +** +7 '. 11.9.".> P / / 3* )',+')/ 5++', A (+ ,* ( ,* ;3 / 4* ,5 =A A,? 4 =2A Q" Q" A,?. L*( ,(4*( ','+, ;3 / +,5' 5*5/ 3* =A (+ AB? ;3 +3 / + / )*4* ( / 4* ,5: =? L (3 A +/+3/ +/+3/ +3* +*, 11.9.".2 4 A , +/+3/ +3* +*, 11.9.".. =? L (3 1.> +( A +/+3/ +3* +*, 11.9."." 4 A , +/+3/ +3* +*, 11.9.".. C3,* +*,5*/ =? A (+ =2A Q" Q" A,? ( ;3' +** 3* )',+')/ 5++', 4 / (5,5 AQ" (3','(5( +** (5'*( +*( )//*( A(+ '(5'3'*( ,5* 2Q" 4+,5 A (+. L (++', 11.9. (5'(+ (5* / ;3' A B 0.>=2A Q"?. Q"?. C3,* =? +*,5*/ A (+ =A A,? ( ;3' +** 3* )',+')/ 5++', 4 / (5,5 A Q2 Q2 (3','(5( +** (5'*( +*( )//*(
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II A(+ 4 '(5' '(5'3 3'( '( ,5 ,5* * 2Q" 2Q" 4+ 4+,5 ,5 A (+ . N3,5 N3,5 11.9. 11.9. (5'(+ (5*( ;3'',5*(. 2
D5', +3/ ( 4*
3
A vf ó A f / 4* ( 5',,5. Y ( 35'/' ,
/ 3/: 2
A sc = A vf + A n 3
T', T ', ( ,+('* ,+('* '+ '+ / 3 3 ,' ,' '
f c ρmn=0.04 ( ) f y
=11.9.>?
A smn = ρ mn bw d ≤ A sc
11.9. P / 5*5/ A B (5'*( +*( * (5'*( )//*( / 3* )',+')/ 5++', ,* ( ,*( ;3 0.>=A (+ P A,?. AB '(5'3'( 3,'* 3,'* ,5 ,5 ,5 ,5* * /*( =2Q"? =2Q"? 4+ 4+,5 ,5(( / 3 3 * * )',+' )',+')/ )/ 5++',. A h= 0.5 ( Asc − A n)
=11.9.?
L*( (5'*( +*( )//*( / 3* )',+')/ 5++', ( ,+('5, ) '5 3, // )53 5++', '7*,/ / +5/ * ,(3/. E/ ;3 ;3' ' (5' (5'*( *( + +*( *( A B 0.>= 0.>=A A(+ - A,? 35*5'+ 35*5'+, ,5 5 )*)*+'*, /( +,5'( )*)'( 11.9.> P A(Q ,* ( ,* ;3 0.0=\+Q 4?. S ()+'+ 3, +,5' ,' 3* 3* ) '5 / )*(''/' 3, // ('5 , +(* ;3 / ,(3/ * / +5/ ( (3 * / ++', / *,5* ', 4 / 3 5, 5++', N 3+
( ) '
ρmn =0.04
f c f y
≤
A sc
bw d
=11.9.>?
11.9. P , / + *,5/ 3, ,(3/ * +5/ / 3* )',+')/ 5++', ,+/( +3* +*, 3,* /*( 5**( ('73',5(:
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II ? M',5 M',5 (*/3 (*/3 (53+53 (53+53// 3, 5,(( 5,((/ / )* /* ,*( ,*( / '(*( '5*` / (*/3 '(K( ) (*// 4 / 3* )',+')/ 5++',. ? M' M',5 ,5 */* */* B+' B+' 5( 5( / 3 3* * )',+ )',+') ')// 5++ 5++', ', ) * 3, /* B*'*,5/ * +? M',5 M',5 /7, /7, *5* *5* '* '* ,+/ ,+/ )*('5'* )*('5'*.. D'* ;3 / +*)*,,5 B*'*,5/ / <)3,5/@ ',+/',* +*,+5* , +*), +*),(', (', =( / F'7. R11.9.1? R11.9.1? ( 5,( 5,('* '* / 3 3* * )',+') )',+')/ / 5++', , / 3'++', / +7 5'+/ / 3* )',+')/ 5++', ( (*/'+'5* (,+'/,5 , 3,'* ( / + / )*4* B(5 / )3,5* *, ( )/'+ / +7 5'+/. D )* /* 5,5* (5 ,+/ , (3 5* 5'* 4 , / +*/3, )*4* , ;3 ( +) (*//
(3 ('(5,+' ()+'+ / 3,+' ( / + / )*4* B(5 / +7 5'+ 5'+/. /. 63 63 *5, *5,( ( 3, ,+/ ,+/ (5'( (5'(+ +5* 5*'* '* , / 5 5* * 5 5'* '* */,* /( ( / 3* )',+')/ 5++', , 3, * B*'*,5/ +** ( ()+'+ , =? * (*/,* 3, '5* '73/ * 3, ,73/* 5K* +3* 5( /*( 5*( /( ( / 3* )',+')/ 5++',. L( (*/3( , '(K( ) (*// (*// / ('(5,+' / 3,+' / 3* )',+')/ 5++',. E/ 5// / (*/3 )/ '5*(,5 , /*( ,(4*( +5/( ( 3(5 , / F'7. R11.9.. 11.9. P / )*4* (* 3, ,(3/ * +5/ ,* )*4+5( ( // / )*+', +5 /( ( 3* )',+')/ 5++', ,' )*4+5( ( // / + ','* / 5,((/ ,+/ =+3,* (5 '(5?. L (5'++', (* / 3'++', / )*4* ( ,+(' ) (73 / (*//* / ('(5,+' / 3,+' / 3* ++ / +7.
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II C3,* ( '(K, ,(3/( ) ('(5' 3( B*'*,5/( / )/5', )*4* (5 (*/ / 3* 5++',.
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
V EJEM6LO
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
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DISEÑO DE MENSULAS CORTAS
ESTRUCTURAS DE CONCRETO II
VI $I$LIOGRAFÍA I,(5'535 A. C. =200>?. Requisitos de Reglamento para Concreto Estructural . F',75*, H'//( M'+B'7,: C*'5 ACI "18. 11.9 - D'()*('+'*,( E()+'/( ) M,(3/( 4 C5/(. )7. 18> - 189.
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