V-1K
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
PR8'
1.)$ Suere+tructur*
<<IM
QS ( 1B$ g/# .)$ RSHTU ( K$$ g/# .>$
+F
*
Terreno J5 ( &1F ] ( 2>F ( 1!$$ 1!$$ g/#^ t
H ( >.$$ #
E+tr,o de gr*ed*d
1.$$
c ( 2&2$ g/#^ ? '
So0uc,1n.- So0uc,1n. --
PREPRE-=IMENSI8NA=8 -=IMENSI8NA=8 P*r* 0* *0tur* H(>.$$#; ro*#o+ un* +ecc,n re0,#,n*r de e+tr,o con7 '( *nc?o de0 c,#,ento ( [H 2/&H ( 2.$$#2.!D# ( 2.B$# "*dot*do% ? ( *0tur* de0 c,#,ento ( H/! H/) ( $.!D#$.B$# ( $.B$# "*dot*do% * ( 0ong,tud de unt* ( H/12 H/! ( $.&$.!D# ( $.&$# "*dot*do% ( 0ong,tud de t*0n ( H/12 H/! ( $.&$.!D# ( $.&$# "*dot*do% N ( $.B$# "*dot*do% N#ín ( $.2 on <(12# "d*to%; H($; S(1).>&F; +e t,ene7 N#ín( 0ong,tud #ín,#* de c*3ue0* "2.11.2; M*nu*0 de =,+e@o de Puente+; MT Per% ( "2$$$.$$1D<$.$$!DH%"1$.$$$12BS% ( "2$$$.$$1D912;$$$%"1$.$$$12B91).>&%## ( $.2.
V-2$
PUENTES
'R ( &$$ g/#
MSc. Ing. Arturo Rodríguez Serquén
*0tur* equ,*0ente de +ue0o or S/
P=( D;$$$ g/# 1.)$ P ( )$$ g/# =Q P ( K;$$$ g/#
S/ or c*rg* ,* "
.)$
.>$ QS ( 1B$ g/# RSHTU ( K$$ g/#
.2B.2B $.B$
= 0o+*
g/#
+(1).>&F &
H ( >.$$ #
2
$.B$
] ( 2>F
.&$
=e+tr
$.K$ EV EV2 &
$.B$
EV1
1
.&$.1D
EH1( $.B 9 &.D# 9 1!)D g/# ( &121 g/#
>
A
* 9 &.D$# 9 1!$$ g/#^ ( 1!)D g/# * 9 $.&$# 9 2&2$ g/#^ ( 1K) g/#
' ( 2.B$ #
* 9 $.)$# 9 1!$$ g/#^ ( &!B g/#
AS8 I ESTRI'8 8N PUENTE A% oe5,c,ente de e#u3e *ct,o "L*% ∅ ( :ngu0o de 5r,cc,n ,ntern* ( &1F δ ( :ngu0o de 5r,cc,n entre e0 +ue0o 4 e0 #uro ( 2>F "T*0* &.11.B.&-1% β ( :ngu0o de0 #*ter,*0 de0 +ue0o con 0* ?or,zont*0 ( $F ( :ngu0o de ,nc0,n*c,n de0 #uro de0 0*do de0 terreno ( K$F
2
+en "φ + δ% +en "φ − β% +en "θ − δ% +en "θ + β%
"&.11.B.&-2%
P*r* β ( $F 4 ( K$F 7 2
+en "φ + δ% +enφ Γ = 1+ = 2.)21 co+ δ
* =
+en2 "θ + φ% Γ [+en2 θ +en "θ − δ%]
P*r* ( K$F 7 * =
co+2 φ = $.2)B Γ co+ δ
"&.11.B.&-1%
V-21
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
'% A0tur* equ,*0ente de +ue0o or S/ Por c*rg*+ e?,cu0*re+ *ctu*ndo +ore e0 terreno; *greg*#o+ un* orc,n equ,*0ente de +ue0o. =e 0* T*0* &.11.!.>-1; or ,ntero0*c,n *r* H ( >.$$ #; ? ( $.)$ #. % Metr*do de *rg*+ "con+,der*ndo 5r*n3*+ de 1.$# de 0ong,tud de e+tr,o% ARAS VERTIA `(
Vo0u#en "#^% 1.21B 1.&B$ 1.DB$ 1.2B$
= _A "#% "g/#% 2;)1K $.K$ &;1&2 1.>B >;$!$ 1.KB 2;K$$ 1.2B 12;K11
_A.= "g-#/#% 2;B&D >;B>1 D;K1D &;!2B 1);!2$
=e+tr(12;K11 g/#; _ A = 1);!2$ =1.>> # 12;K11
Vo0u#en "#^% $.K!$ $.1B$ $.$>&
EV(1;)>> g/#; _ A
EV _A "g/#% "#% 1;B&! 2.&B$ 2>$ $.1B$ !) $.&BD 1;)>> =
&;!D$ = 1.KK# 1;)>>
_A.EV "g-#/#% &;!1$ &! 2> &;!D$
V-22
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
*rg*+ EH "re+,n 0*ter*0 de0 terreno% Por &.D$ # de terreno7 EH14 ( EH1 +en δ ( &;121g/# "+en 2>F% ( 1;2!K g/# Por 0o+* de *cerc*#,ento7 EH24 ( EH2 +en δ ( D&> g/# "+en 2>F% ( 2KK g/# *rg*+ << "c*rg* ,* de 0* +uere+tructur* de uente% P< ( K;$$$ g/# *rg*+ g/# o#onente ert,c*0 de 0* +orec*rg* or c*rg* ,*7 F% ( B>K g/#
ARA =e+tr =0o+* P= P=Q EV EH14 EH24 P<
Re+u#en *rg*+ Vert,c*0e+ TIP8 TIP8 V "Lg/#% __A "#% "#% MV"g"g-#/#% = 12;K11 1.>> 1);!2$ = 2$K 2.&B >K1 = D;$$$ 1.>B 1$;1B$ =Q )$$ 1.>B 1;1!$ EV 1;)>> 1.KK &;!D$ EH 1;2!K 2.B$ &;1D& EH 2KK 2.B$ D>) << K;$$$ 1.>B 1&;$B$ 2.&B K$2 K 2.B$ 1;&D& &>;2!B B&;&&D
ARAS H8RI68NTAF% ( 2;)B1 g/# Por 0o+* de *cerc*#,ento7 EH29 ( EH2 co+ δ ( D&> g/# "co+ 2>a% ( !D1 g/#
V-2&
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
*rg*+ a% ( 1;2&& g/# *rg*+ QS ",ento +ore 0* e+tructur*% QS ( 1B$ g/# *rg*+ 'R "5uerz* de 5ren*do% 'R ( &$$ g/# *rg*+ R; SH 4 TU "=e5or#*c,n de0 concreto or c*rg* +o+ten,d* en e0 t,e#o; *cort*#,ento or re+5orz*do; 4 te#er*tur* un,5or#e% R SH TU ( K$$ g/# Re+u#en *rg*+ Hor,zont*0e+ ARA TIP8 TIP8 H "g/#% b "#% MH "g "g bbb A "#% "g-#/#% EH19 EH 2;)B1 1.2& &;B$D EH29 EH !D1 1.)B 1;2>1 $ 'R 'R &$$ B.)$ 1;D>$ RSHTU RSHTU K$$ &.!$ &;2>$ !;1$B 12;B>K Σ =% E+t*do+ 0í#,te+ *0,c*0e+ 4 co#,n*c,one+ de c*rg*+ To#*re#o+ en cuent* 0o+ E+t*do+ <í#,te+ de Re+,+tenc,* I 4 III *0,c*0e+ en e+te c*+o 4 con un *0or n(n=nR nI(1. 8+er*#o+ que e9,+ten nu#ero+*+ co#,n*c,one+ de 5*ctore+ de c*rg* γ *r* c*d* e+t*do 0í#,te co#o uede deduc,r+e de 0*+ T*0*+ &.>.1-1 4 &.>.1-2. Inc0u+o en un +o0o e+t*do 0í#,te encontr*#o+ que ueden e+t*0ecer+e nu#ero+*+ co#,n*c,one+ d,+t,nt*+. E0 d,+e@*dor en e+te c*+o *e0*ndo * +u re+on+*,0,d*d 4 uen 3u,c,o dee +e0ecc,on*r 0o+ 5*ctore+ de c*rg* *ro,*do+ en c*d* t,o de c*rg*. P*r* e0 c?equeo de e+t*,0,d*d *0 ue0co 4 de+0,z*#,ento; o+er*ndo en e0 gr:5,co 0*+ c*rg*+ *ctu*nte+; ut,0,z*re#o+ 0o+ 5*ctore+ γ #:9,#o+ *r* 0*+ c*rg*+ ?or,zont*0e+ "de+e+t*,0,z*dor*+% 0*+ cu*0e+ gener*n ue0co *0rededor de0 unto A 4 de+0,z*#,ento en 0* *+e "EH;
V-2>
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
AT8RES =E ARA UTI
γ=
γ=Q
γEV
γ<<IM
γ
γEH
γ
γQS
γ'R
γRSHTU
Re+,+tenc,* I*
$.K$
$.!B
1.$$
$
$
1.B$
1.DB
$
1.DB
$.B
Re+,+tenc,* I
1.2B
1.B$
1.&B
1.DB
1.DB
1.B$
1.DB
$
1.DB
$.B
Re+,+tenc,* III*
$.K$
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$
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Re+,+tenc,* III
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A0,c*c,n =e+0,z*#,ento 4 ue0co Pre+,one+ 4 re+,+tenc,* =e+0,z*#,ento 4 ue0co Pre+,one+ 4 re+,+tenc,*
V-2B
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
E% HEUE8 =E ESTA'I
Vue0co *0rededor de0 unto A
( MHU
9o
MVU
Vu A
e('/2-9o
E+t*0e +,7 e '/& "5und*c,n en +ue0o% e $.>B' "5und*c,n en +ue0o roco+o%
Vu A
'(2.B$#
Vu "Lg/#%
Mu "Lg-#/#%
22;)2> >);BD> 22;)2> &1;1K1
&!;!>$ DB;KD1 &!;!>$ >K;1B2
E+t*do Re+,+tenc,* I* Re+,+tenc,* I Re+,+tenc,* III* Re+,+tenc,* III
<
'/2
M?u "Lg-#/#%
'/2
' −9 2 o
"#%
"#%
e#*9('/& "#%
$.K1> 1.2&K 1.1)K 1.2D1
$.&&! $.$11 $.$!1 -$.$21
$.)&& 8Lf $.)&& 8Lf $.)&& 8Lf $.)&& 8Lf
9o =
1B;DDK 1B;DDK K;>K) K;>K)
Mu − M?u Vu
e=
% =e+0,z*#,ento =e+0,z*#,ento en *+e de0 e+tr,o
Hu Vu
E+t*0e +,7 Hu 5
5 ("JVu %
on7 ( tgd ( tg 2>F ( $.>B "T*0* &.11.B.&-1% Jτ ( 1.$$ "T*0* 11.B.D-1% E+t*do+ Re+,+tenc,* I* Re+,+tenc,* I Re+,+tenc,* III* Re+,+tenc,* III
Vu "Lg/#% 22;)2> >);BD> 22;)2> &1;1K1
RESISTENTE "Lg/#%
5 ( "JτVu% 1$;2D1 21;)B) 1$;2D1 1>;&$!
ATUANTE "Lg/#%
Hu );>1! 8Lf );>1! 8Lf B;K>& 8Lf B;K>& 8Lf
V-2!
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
c% Pre+,one+ *ctu*nte+ en 0* *+e de0 e+tr,o
(
< 9o
MHU Vu
Vu
M VU A
e('/2-9o
A
'(2.B$#
q #ín
q #:9
'/2
'/2 q
R #:9
q
'-2e
E+t*do Re+,+tenc,* I* Re+,+tenc,* I Re+,+tenc,* III* Re+,+tenc,* III
Vu "Lg/#%
Mu "Lg-#/#%
22;)2> >);BD> 22;)2> &1;1K1
&!;!>$ DB;KD1 &!;!>$ >K;1B2
M?u "Lg-#/#% 1B;DDK 1B;DDK K;>K) K;>K)
9o =
und*c,n en roc* E+t*0e +,7 q q
Mu − M?u Vu
und*c,n en +ue0o E+t*0e +,7 q q R
e=
' −9 2 o
"#%
"#%
$.K1> 1.2&K 1.1)K 1.2D1
$.&&! $.$11 $.$!1 -$.$21
q =
VU ' − 2e
"g/c#2% 1.2B 1.K! $.K! 1.2B
q R
"g/c#2% 2 8Lf 2 8Lf 2 8Lf 2 8Lf
Not*.- u*ndo 0* e9centr,c,d*d e+ neg*t,*; u+*r e0 *nc?o re*0 ' en e0 c:0cu0o de re+,one+. AS8 IIII ESTRI'8 SIN SIN PUENTE E+t*do+ 0í#,te+ *0,c*0e+ 4 co#,n*c,one+ de c*rg*+
V-2D
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
HEUE8 =E ESTA'I
Vu "Lg/#%
Mu "Lg-#/#%
1!;$$> 22;)D> 1!;$$> 21;2>1
2!;DB1 &);D$! 2!;DB1 &>;D2B
M?u "Lg-#/#%
MVu − MHu Vu
' −9 2 o
"#%
"#%
e#:9('/& "#%
$.KDD 1.2$! 1.22D 1.2KK
$.2D& $.$>> $.$2& -$.$>K
$.)&& 8Lf $.)&& 8Lf $.)&& 8Lf $.)&& 8Lf
9o =
11;11> 11;11> D;122 D;122
e=
% =e+0,z*#,ento en *+e de0 e+tr,o on7 ( tgd ( tg 2>F ( $.>>B "T*0* &.11.B.&-1% Jτ ( 1.$$ "T*0* 11.B.D-1% E+t*do+
Vu "Lg/#%
Re+,+tenc,* I* Re+,+tenc,* I Re+,+tenc,* III* Re+,+tenc,* III
1!;$$> 22;)D> 1!;$$> 21;2>1
RESISTENTE "Lg/#%
5 ( "JτVu% D;2$2 1$;2K& D;2$2 K;BBK
ATUANTE "Lg/#%
Hu D;>>1 N.S. D;>>1 8Lf B;2)& 8Lf B;2)& 8Lf
V-2)
PUENTES
MSc. Ing. Arturo Rodríguez Serquén
E0 e+t*do 0í#,te de Re+,+tenc,* I* no e+ +*t,+5*ctor,o or 0o que co0oc*#o+ un d,ente de concreto de +ecc,n $.&$#9$.&$#. en 0* *+e t*0 co#o +e #ue+tr* en 0* 5,gur* con+,der*#o+ *de#:+ 0* re+,+tenc,* *+,* de0 +ue0o +0o en e0 :#,to de0 d,ente.
$.B $.&$
$.B
91!$$91.$$(K;D!$g Re(&;&!Dg $.& 91!$$91.&$(12;!))g =e 0* ,gur* &.11.B.>-1; e0 coe5,c,ente de e#u3e *+,o e+ (D "con J5(&1F 4 Ө(K$F%. A+í #,+#o e0 5*ctor de reducc,n ?*00*do or ,ntero0*c,n e+ R($.>>! "con ]/J5($; *r* e0 +ue0o u,c*do en 0* zon* de 0* unt* de0 e+tr,o%. >!"D% ( &.122 <* re+,+tenc,* *+,* e+7 R e(["K;D!$g/#12;!))g/#% 9 $.&$# ( &;&!Dg P*r* e0 e+t*do 0í#,te de Re+,+tenc,* I*; *greg*ndo e0 d,ente de concreto +e t,ene7 R R ( JτR τ JeR e
on7
"1$.!.&.&-1%
JτR τ ( D;2$2g Je ( $.B$ "T*0* 1$.B.B.2.2-1% R e ( &;&!Dg R R ( D;2$2g $.B$"&;&!Dg%();))! );))!g );))!g D;>>1g 8Lf c% Pre+,one+ *ctu*nte+ en 0* *+e de0 e+tr,o E+t*do Re+,+tenc,* I Re+,+tenc,* I* Re+,+tenc,* III Re+,+tenc,* III*
Vu "Lg/#%
MVu "Lg-#/#%
MHu "Lg-#/#%
1!;$$> 22;)D> 1!;$$> 21;2>1
2!;DB1 &);D$! 2!;DB1 &>;D2B
11;11> 11;11> D;122 D;122
9o =
MVu − MHu Vu
e=
' −9 2 o
"#%
"#%
$.KDD 1.2$! 1.22D 1.2KK
$.2D& $.$>> $.$2& -$.$>K
q =
VU ' − 2e 2
"g/c# % $.)2 $.KB $.!B $.)B
q
R
"g/c#2% 2 2 2 2
8Lf 8Lf 8Lf 8Lf
Not*.- u*ndo 0* e9centr,c,d*d e+ neg*t,*; u+*r e0 *nc?o re*0 ' en e0 c:0cu0o de re+,one+.