165702987 Puente Viga Losa 11m Xls

8/16/2019 165702987 Puente Viga Losa 11m Xls

1/41

DISEÑO DE LOS POSTES DE CONCRETO ARMADO

0.2 0.8 0.2

0.15 Q

0.375 0.05 0.375 0.05 0.0754

0.05

0.45 0.475 P/2

0.45 0.45

0.2

0.2

TIPO DE VEHICULO : : HS20 - 44 P = 4.55 Tn W : 75 kg/m

Longit! : " m 0.#0 $% : 4200

0.&5 $' : 2"0

( = 0.5P ) WL = 2*50 kg

Calculo del As del poste

2*50 + 0.475 = """7.2 kg-m , = ".* , = "452.* kg-mV = ( = 2*50 kg V = ".* , = *055.0 kg

= *.#772* ! = "2 'm = 4.7#0##& , = "452*4.7 kg-'m = 4.7#" 1 = 20 'm

3 = ".27= S3 'o6o' 4 φ "/2

Calculo de los estribos

V' = "&4* kg V = "75" 3 = 0.*2

U3mo φ "/4

= S = "&.2** 'm 'm

=

φ "/4 8 'm

φ$63+ion

= kg/'m2

φ'ot3

= kg/'m2

, = ( 9+" =

'm2

Smin =

En 6o Pot3 !3 Con'3to m!o 3 'o6o'n3ti1o 'onit3nt3 3n:

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85 fc .b

Vc=0.53√ f ' c .bW d

Vs=

Vu

φ −Vc

S=2 Av . fy .d

Vs

Smin

=d /2


2/41


3/41

DISEÑO DEL PARAPETO DE CONCRETO ARMADO

0.15 Q 2*50 kg &uer'a Cortante en la (ase0.0754

= 425.0 kg

0.475 P/2 2275 kg )omento &le*ionante en la (ase

= *"#&.4 kg-m

0.45 Anc+o ,-ectio de la losa parapeto en la (ase

= 0.# m

0.2 E = ".# m

Cortante ltima de iseo )omento ltimo de iseo

V = *557 Jg/m , = 240 kg-m/m

Cortente ltimo ue resiste el concreto"

V' = 7&*4 kg/m V' V OJ

Area de re-uer'o ertical reuerida de acero

= 5.747"0 ! = "2 'm = ".*522577 , = 24000 kg-'m/m = ".*5225& 1 = "00 'm

3 = ".27= S3 'o6o' φ "/2 8 "2.7

= 225.75

S3 'o6o' = φ "/2 8 0.20 m

e-uer'o de Acero de epartici!n emperatura

0.0021t 3 = ".27

t = ".*5 = S3 'o6o' 2φ

"/2 3n '! ' = ".72 = S3 'o6o' 2 φ "/2 3n '! '

1 : 0.45 m t : 0."5 m

VL

,L

,L

VL

'm2

t=

'm

2

'm2

Bin6m3nt3 3 'o6o'n * φ "/2; 3n '! ' 6t36 !3 6 6o 3ti'6 !3 P3to 'i3n!o ntot6 !3 φ !3 "/2; oiAont63.

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85 fc .b

E=0.80 X +1.14

Vu=1.3V

L

E Mu=

1 .3 M L

E

Vc=0.53φ √ f ' c .b .d

Ast =0.002.

b.t .

Asr=2/3 Asv


4/41

DISEÑO DE LA LOSA SOLIDA SUPERIOR DEL TABLERO

6 " 2 m u' libre de los tramos apoados,spesor Carpeta Asa-ltica " 0 9TIPO DE VEHICULO : : HS20 - 44 P = *2# kg

t = 0."7 m = t : 0.2 m

Carga permanente actuente sobre la losa superior

P3o Poio !3 6 6o : 0.4&

P3o C3t $6ti' : 0 = 0.48

)omentos &lectores para la carga permanente: por metro

= 0."#2 Tn-m/m

Carga Concentrada de la rueda mas pesada ;e+iculo 1.50

P = ".50 K4P/2 = "0.&&7 Tn

Im'to !3 6 Cg ,oi6 : I = 0.*

PK")I = "4."5* Tn

)omentos &lectores para la carga ia m!il con ?mpacto"

*.0*0# Tn-m/m

)omento ltimo de iseo "

.&2#& Tn-m/m

Area del re-uer'o Principal de Acero perpendicular al rnsito

Area de re-uer'o ertical reuerida de acero

= "".55"&4 ! = "7 'm = 2.7"&07#0&05 , = &2#77.25 kg-'m/m = 2.7"&07#0& 1 = "00 'm

3 = ".#&= S3 'o6o' φ 5/& 8 "#7.#*

= "7"".55

S3 'o6o' = φ 5/& 8 0.20 m = "0.00

Cuantia de Acero Principal Cuantia minima de acero principal

ρ = 0.005&& 0.0024"52

T3ni3n!o 3n '3nt 6 363! 'g i mi6 F3 ti3n3 F3 oot 3t 6o 3io !36 t163o 3'oni!3o 'on3ni3nt3 t = 0.20m.

Tn/m2

Tn/m2 @ n/m2

)

)

)

'm2

'm2/m

ρmin

=

t =0.10+S '

30≥0.16 m

M d=1

10 W D S

' 2

M L=0.80( S ' +0.619.75 ) P(1+ I )

M =1.30 ( M D+1.67 M L )

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85 fc .b

!= As

bd !min=0.70√ f ' c

fy


5/41

DISEÑO DE LA LOSA SOLIDA SUPERIOR DEL TABLERO

Cuantia de Acero (alanceada

0.# = 0.0225 = 0.0""*

= M ρ M

Por tanto " = φ 5/& 8 0.20 m 3 'o3'to

Armadura de epartici!n

& N M 7 N

3 = ".27

= 7 N = .70 = S3 'o6o' φ "/2 8 "2.7= "#

.70

Armadura de emperatura

*.0

β1 = ρ

1 = ρ

m+ = 0.50ρ

1

ρmin

ρm+

S3 'o6o' φ 5/&; 8 0.20m 3n 36 t163o 3io 3 in$3io !3 6 6o 3io !36 t163o 3n 3nti!o 33n!i'6 6 tnito.

S>

= S

S

S> = S 'm2/m

S3 'o6o' φ "/2; 8 0.20 m 3n 36 63'o 3io 3 in$3io !3 6 6o 3io !36 t163o 3n 3nti!o 636o 6 tnito.

ST = 'm2/m

En 3t3 'o 'omo 3+it3 3$3Ao !3 '3o 3n m1 !i3''ion3 !3 6 6o 3io !36 t163o K in'i6 % !3 3ti'ion 'oni!3o inn3'3io into!'i 36 '3o !3 t3m3t.

!= As

bd !min=0.70√ f ' c

fy

!b=0.85 . "1 . f ' c

fy ∗

6000

6000+ fy "

1=0.85− f ' c−280

70∗0.05

S } } } %A rSub { size 8{S} }


6/41


7/41

'm


8/41

DISEÑO DE LAS LOSAS EN VOLADIZO DEL TABLERO

0."5

0.2

+ Peso ,speci-ico CBAB0.55 P;1?> 2.4 n/m

0.* Peso (aranda * )etro

0.450.4 0.2 0.05 2.85 n/m

0.27 Area (aranda0.2 " 4.75,D04 m20.27 0.2 Peso ,sp. Carp. As-al.

0.1 n/m0.55 0.5

0.&

0.5

)etrado de Cargas

E63m3nto O3'in P3o AoPot3 !3 Con'3to m!o 0."5 + 0.2 + 0.55 + 2.4 0.040 Tn/m +" "."* 0.045 Tn-m/mLo P3to n! 0.45 + 0."5 + 2.4 0."2 Tn/m +2 "."* 0."&2 Tn-m/mn! T163 !3 '3o 0.0004& + 2.&5 0.00" Tn/m +* "."* 0.002 Tn-m/mLo !3 V33! 0.2 + 0.55 + 2.4 0.24 Tn/m +4 0.#25 0.244 Tn-m/mP3o Vig S!in36 0.225 + 0.27 + 2.4 0."4 Tn/m +5 0.5"25 0.075 Tn-m/m

Lo 3n Vo6!iAo T1. >o!!. 0.5 + 0.2 + 2.4 0.*"2 Tn/m + 0.*25 0."0 Tn-m/m0.#25 Tn/m 0.5 Tn-m/m

Momento Flector para la Carga Permanente : 0.4# Tn-m/m =

Fuerza Cortante para la Carga Permanente : 0.#25 Tn/m =

Carga de la ueda mas Pesada de un e+iculo 1.5 =620 con impacto"

P = ".50 K4P/2 = "0.&&7 Tn PK")I = "4."5* Tn

Ditn'i !3 6 'g P 6 3''ion 'iti' !3 6 6o 3n o6!iAo !36 t163o:

= ".2 - 0."5 - 0.* = 0.75 m

n'o 3$3'tio !3 6 6o 3n o6!iAo !36 t163o 6 'g i

E = ".74 m

)omento -lector m*imo para la carga ia &uer'a Cortante para la Carga ia

,D Tn-m/m

,D

VD

Poi'ion 'iti' !3 6 'g 'on'3nt! mi6: oi'in 0.*0 m !36 3to !3 1n! KP3i3n!on oi163 in'ion !36 3i'6o 6 33! !36 t163o !36 P3nt3

E=0.80 X +1.14

M L= P

(1

+ I

)∗ X

E V L= P(

1

+ I ) E


9/41

DISEÑO DE LAS LOSAS EN VOLADIZO DEL TABLERO

."005 Tn-m/m &."*4 Tn/m

)omento Eltimo de iseo &uer'a cortante ltima de iseo

&.77*# Tn-m/m "".77 Tn/m

Area de re-uer'o principal reuerida en la secci!n crFtica "

= "5.22 ! = "7 'm = *.5#2"4 , = &77*&5.5 kg-'m/m = *.5#2"4 1 = "00 'm

3 = ".#&= S3 'o6o' φ 5/& 8 "#7.#*

= "*"5.27S3 'o6o' = φ 5/& 8 "2.# m

&uer'a cortante Gltima ue toma el concreto de la losa en oladi'o

""."0 Tn/m

M = "".77 Tn/m

= 4."05# 3 = ".27

= S3 'o6o' φ "/2 8 "2.7= *"4.""

S3 'o6o' = φ "/2 8 0.*0 m 3n m1o 63'o 3io 3 in$3io

,L = V

L =

,U = V

U =

'm2

P 3$oA 6 6o 3n o6!iAo 3 = 0.20 m im63m3nt3 3 o6ong 6 i66 !36 3$3Ao in'i6 !3 6o tmo o%!o !3 6 6o 3io !36 t163o !36 3nt3 'onit3nt3 3n φ 5/&; 80.20m

VC =

VC V

U

En 6 6o 3n o6!iAo !3 33! 3 = 0.20 3 $i'i3nt3 !ion3 '3o mnimo 3n 6o 63'o 3io 3in$3io.

'm2/m

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85

fc.

b

M =1.30 ( M D+ M L) V =1.30 (V D+V L)

V $ =0.53φ√ f ' c .b .d

As MI%

= ! MI%

.bd


10/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

Anc+o de ?n-luencia para las igas interiores" 6 2.4 m L = 11 m

CL

P 4P 4P

4.27 4.27

0.7" 0.7"

KL/2-0.7" KL/2-0.7"

KP

Factor de Impacto

0.*"" 0.* L 0.3

?6,H$ , A6 ?IA6 ?J,?$,6

Factortes de concentracion de carga para S = 2.4 m

Para Fuerzas Cortantes 0.57 ".&* ".22 "."&

P P P

= 0.57 1 = "."&

$ ".72#2 2.4 m 2.4 m

Para Momento Flectores

$m = ".2"2"

,-ectos )a*imos de la Carga Permanente

P3o oio !3 6 6o = 0.2 + 2.4 + 2.4 "."52C3t $6ti' = 0." + 2.4 = 0.24P3o Poio !3 n3io !3 ig = 0.& + 0.5 + 2.4 = 0.#

2.352 n/m

B3A Cotnt3 ,+im : ,om3nto B63'to ,+imo

"2.#* Tn *5.574 Tn-m

,-ectos de la Carga ia )oil

Fuerza Cortante Maxima : ! = 0.# P = 2.72"& Tn = ".5 + ".&"45

4P 4P P

4.27 4.27 >L = 5.#*"& P = "."45 Tn

> " > 2

@

VD = ,

D =

LW V D D

2

"=

2

&

" LW M

D D =

I =15.24

L+38≤0.30

fv=1+a+b

S

fm= S

1.98


11/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

".42

0.# 2.&5 7.25

KP >L VL = *.2#2 Tn

Momento Flector Máximo

Caso 01 : To!o 36 3i'6o !3nto !36 P3nt3

CL

P 4P 4P >L = "0.7 Tn4.27 4.27

,m+ = *#.472 Tn-m

0.7" 0.7"4.7# 4.7#

>L KP,m+

Caso 0 : So6o 6 !o 3! m 3! !3nto !36 P3nt3

CL

4P 4P >L = &.7# Tn4.27

,m+ = *&.&47 Tn-m

".07 ".07

4.4* 4.4*

>" 8P >L,m+

<

L M2.1K8 nDm

M!M"#$! %L$IM! M&'IM! KC3' 6 3''ion '3nt6

181.28 nDm

&rea de re(uerzo principal re)uerida en la sección cr*tica :

= 5#.&47 ! = #0 'm = 2&."7"52 , = "&"27&&2 kg-'m/m = "#.7&"000 1 = 50 'm

3 = 5.07= S3 'o6o' "2 φ "

Cálculo más a+usrtado de d = , - d.

B B B B 0.075

5 + 0.05 ) 4 + 0."4

> "

> 2

Conto6 36 Segundo Caso/ Po 6o tnto:

)

)

'm2

V L= # L(1+ I ) fv

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85 fc .b

M =1.30 ( M D+ M L )


12/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

B B B B B 0.05

5 ) 4.

L dN 0.10 m % ! = 0.#0 m K! 3to ok

Calculo más a+ustado de &s iga $2


= 54.2&2* ! = #0 'm = 5.*22"7# , = "&"27&&2 kg-'m/m = *.*"72 1 = 240 'm

3 = 5.07= S3 'o6o' "" φ "

L As reuerido 54.2# 'm2As dispuesto 5#.& 'm2 = S3 'o6o' "2 φ "

Cuantia Máxima de re(uerzo longitudinal

0.0"**

$6t

= = * φ "

&cero m*nimo a (lexión:

"0.&# 'm2

L As 5#.& "0.&# !3

Control de &grietamiento:

$6t

$6t

'm2

P MAX

=

3 F3 t3oi'mnt3 no 3 3Fi33 '3o 3n 'om3in 3n 6 t3 3io !3 6 ig int3io33 'o6o'n 3$3Ao :

As MIN

=

As MIN

=

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85 fc .b

! MAX = As

bW d

As MI%

=0.70√ f ' c

fy b

W d

Z =fs . 3√ d$ A


13/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

C!4$$" %L$IM! M5'IM! n !itn'i ! !3 6 ' !3 6o o%o

V = #5.0& Tn

Cortante ultima )ue toma el Concreto

V' = 2#.*7& Tn

Cortante ultima )ue de6e tomar el Concreto

V = &*."02 Tn

Cortante %ltima Máxima )ue pueden tomar los estri6os

"*.#4 Tn

L s 83.102 n # 13M.K4 n !3

Minima Separacion de estri6os : φ = "/2

S = "".524 'm = 2.5* 'm2

Máxima separación de los estri6os en la sección cr*tica

= 7".7*2 M V = &*."02 = = 2* 'm

Máxima Separacion de los estri6os en toda la iga

S = 45 'm

S = 0.&0 'm

#ota :

?6?(C?$J , ,&,O$ $JI??JA ,J ACC?$J

V,

=

s)A

Coni!3n!o 6 3ion !3 6 ig !i$gm !3 0.*0 + 0.&0m 3n 6 Aon !3 o%o !36 ig in'i63 6 3''ion3'ti' !3 'otnt3 3 3n'3ntn 36m3nt3 !itn'i!3 6o 33 !3 o%o 3n 6g !36 6o !3 0.&5m 'oni!3n!o 3n 36 n6ii nt3io.Po3t 6 minim 3'ion !3 6o 3ti1o 3n 6 Aon 'ti' !3 6 ig in'i63 3'oni!3n 'omo "5.0 'm

D3 '3!o 'on 6o !3t663 !36 3$3Ao !3 6 ig in'i63 3 3!3n 3t163'3 6igi3nt3 'oni!3'ion3

E6 3 m+im !3 3$3Ao # "; 3 mnti3n3 "00N 3$3'ti 3n n 6on it! !3 2.*0m 3n 6

Vu=1.30 (V D+1.67V L )

V $ =0.53φ√ f ' c .bW d

Vs=

Vu

φ −Vc

Vs MAX =2.10√ f ' c .bW d

S= Av . fy .d

Vs

V =1.10√ f ' c .bW d S≤d

4

S≤d

2

S≤ Av. fy

3 .5bW


14/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

= *." "2.#* + *." - 2.*52K*." + *." /2

2&.& Tn-mCL P = 2.72"& Tn

4P 4P

4.27 "".402 Tn

*5.*45 Tn-m

55.#5 Tn - m*." 2."4 5.7

>L 8P "5&.4 Tn - m

= 54.2 ! = &5 'm = 25.70*&2 , = "5&*54#7 kg-'m/m = ".04270 1 = 50 'm

3 = 5."0

= S3 'o6o' "0.7" φ " = 54.2"

= 0.* "2.#* + 0.* - 2.*52K0.* + 0.* /2

7.&2# Tn-m

P = 2.72"& Tn4P 4P P

4.27 4.27 ".74 Tn

"0.55 Tn-m

".2 Tn - m0. 2.&5 7.52

>L KP 4." Tn - m

= "4.7# ! = &5 'm

= .#5&2" , = 407#*.5 kg-'m/m = 5.""4"#2 1 = 50 'm3 = 5."0

Aon '3nt6 !3 6 ig.

Con3!om3nt3 3n 6 3''ion3 F3 3 3n'3ntn 1i'! n !itn'i !3 2.40mm3!i! ti !36 '3nto !3 6 ig 36 3 3$3'ti !3 3$3Ao !3 '3o 3 3!'3 !3 # φ ";

7 φ ";

Con3!om3nt3 3n 6 3''ion3 F3 3 3n'3ntn 1i'! n !itn'i !3 0.*mm3!i! ti !3 6o 33 !3 o%o 36 3 3$3'ti !3 3$3Ao !3 '3o 3 3!'3 4 φ ";

'ontin'ion 3 3$3'tn 6 'o3on!i3nt3 3i$i''ion3 !3 6o 'ot3 !3 1 3$3i!nt3iom3nt3

7"4IFIC&CI!# 8" L&S S"CCI!#"S C!# &s = 9 1

,D =

,D =

> L =

,L =

,Lm+ =

,U =

'm2

'm2

7"4IFIC&CI!# 8" L&S S"CCI!#"S C!# &s = ; 1

,D =

,D =

> L =

,L =

,Lm+

=

,U =

'm2

As= Muφ. fy .(d−

a

2)

a= As . fy

0.85 fc .b

As= Mu

φ. fy .(d−a2)

a= As . fy

0.85 fc .b


15/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

= S3 'o6o' 2.#* φ " "5

&LISIS 8" L& S"CCI!# C"#$4&L

P = 2.72"& Tn4P 4P

4.27 .0# Tn

"4.#7* Tn-m

0 Tn-m

5.5 2."*5 *.*5 *2.5" Tn

>L 8P 2#.*& Tn

&.&7 Tn


S = "02.02 'm = 2.5* 'm2

4* 'm


P = 2.72"& Tn4P 4P

4.27 "2."04 Tn

27.2" Tn-m

.4& Tn-m

2.& 2."*5 .""5 7.4& Tn

>L 8P 2#.*& Tn

50.0" Tn


S = "&.0& 'm = 2.5* 'm2

8IS$4I


16/41


17/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

0.* ".&* QQQ

P P P

0 QQQ m


18/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,


19/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

Anc+o de ?n-luencia para las igas interiores" 6 2.4 m L = 11 m

CL

P 4P 4P

4.27 4.27

0.7" 0.7"

KL/2-0.7" KL/2-0.7"

KP

Factor de Impacto

0.*"" 0.* L 0.3

?6,H$ , A6 ?IA6 ,,?$,6

Factortes de concentracion de carga para S = 2.4 m

Para Fuerzas Cortantes 0.*0 ".&* ".22

P P P

= 0.00 1 = 0.7

$ ".27#2 0.4 2.4 m

Para Momento Flectores

$m = ".2"2"


P3o !3 6o S3io 3n o6!iAo = 0.#2475 Tn/mP3o oio !3 6 6o = 0.7& Tn/mC3t $6ti' = 0." Tn/mP3o Poio !3 n3io !3 ig = 0.# Tn/m

2.81275 n/m

B3A Cotnt3 ,+im : ,om3nto B63'to ,+imo

"5.470 Tn 42.54* Tn-m

,-ectos de la Carga ia )oil

Fuerza Cortante Maxima : ! = 0.# P = 2.72"75 Tn = ".5 + ".&"45

4P 4P P

4.27 4.27 >L = 5.#*"&2 P = "."45 Tn

> " > 2

@

VD = ,D = LW V D D

2

"=

2

&

" LW M

D D =

I =15.24

L+38≤0.30

fv=1+a+b

S

#&."

S fm =


20/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

".42

0.# 2.&5 7.25

KP >L VL = 2.&477 Tn

Momento Flector Máximo

Caso 01 : To!o 36 3i'6o !3nto !36 P3nt3

CL

P 4P 4P >L = "0.& Tn4.27 4.27

,m+ = *#.472 Tn-m

0.7" 0.7"

4.7# 4.7#

>L KP,m+

Caso 0 : So6o 6 !o 3! m 3! !3nto !36 P3nt3

CL

4P 4P >L = &.7& Tn

4.27

,m+ = *&.&47 Tn-m

".07 ".07

4.4* 4.4*

>" 8P >L,m+

<

L M2.1K8 nDm

M!M"#$! %L$IM! M&'IM! KC3' 6 3''ion '3nt6

1K0.34 nDm

&rea de re(uerzo principal re)uerida en la sección cr*tica :

= &.05&7 ! = #0 'm = *2.0275" , = "#0**&*# kg-'m/m = *2.0275 1 = 50 'm

3 = 5.07= S3 'o6o' "* φ "

Cálculo más a+usrtado de d = , - d.

> "

> 2

Conto6 36 Primer Caso/ Po 6o tnto:

)

)

'm2

V L= # L(1+ I ) fv

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85 fc .b

M =1.30 ( M D+ M L )


21/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

BB BB BB BB BB 0.075! =

"" + 0.05 )"0 + 0."4= 0."0"

BB BB BB BB BB 0.05 "")"0

L dN 0.10 m % ! = 0.#0 m K! 3to ok

Calculo más a+ustado de &s iga $2


= 5&.0"02 ! = #0 'm = 5.&7&44# , = "#0**&*# kg-'m/m = .4"*207 1 = 240 'm

3 = 5.07= S3 'o6o' "" φ "

L As reuerido 5&.02 'm2As dispuesto &.0 'm2 = S3 'o6o' "* φ "

= = * φ "

&cero m*nimo a (lexión:

"0.&# 'm2

L As &.0 "0.&# !3

C!4$$" %L$IM! M5'IM! n !itn'i ! !3 6 ' !3 6o o%o

V = 7&.*#7 Tn

Cortante ultima )ue toma el Concreto

V' = 2#.*7& Tn

Cortante ultima )ue de6e tomar el Concreto

V = 2.&55 Tn

Cortante %ltima Máxima )ue pueden tomar los estri6os

"*.#4 Tn

L s M2.855 n # 13M.K4 n !3

'm2

3 F3 t3oi'mnt3 no 3 3Fi33 '3o 3n 'om3in 3n 6 t3 3io !3 6 ig int3io33 'o6o'n 3$3Ao :

As MIN =

As MIN

=

V,

=

s)A

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85 fc .b

As MI%

=0.70√ f ' c

fy b

W d

Vu=1.30 (V D+1.67V L )

V $ =0.53φ√ f ' c .bW d

Vs=Vu

φ −Vc

Vs MAX =2.10√

f ' c.

bW d


22/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,


S = "5.2* 'm = 2.5* 'm2

Máxima separación de los estri6os en la sección cr*tica

= 7".7*2 M V = 2.&55 = = 2* 'm

Máxima Separacion de los estri6os en toda la iga

S = 45 'm

S = 0.&0 'm

#ota :

?6?(C?$J , ,&,O$ $JI??JA ,J ACC?$J

= ".5 "5.470"404*0 + ".5 - 2.&"275*&20"2"K".5

20.04" Tn-mCL P = 2.72"& Tn

4P 4P

4.27 "4.5&& Tn

2".&5*2 Tn-m

*4.4*5* Tn - m".5 2."4 7.*

Coni!3n!o 6 3ion !3 6 ig !i$gm !3 0.*0 + 0.&0m 3n 6 Aon !3 o%o !36 ig in'i63 6 3''ion3'ti' !3 'otnt3 3 3n'3ntn 36m3nt3 !itn'i!3 6o 33 !3 o%o 3n 6g !36 6o !3 0.&5m 'oni!3n!o 3n 36 n6ii nt3io.Po3t 6 minim 3'ion !3 6o 3ti1o 3n 6 Aon 'ti' !3 6 ig in'i63 3'oni!3n 'omo "5.0 'm

D3 '3!o 'on 6o !3t663 !36 3$3Ao !3 6 ig in'i63 3 3!3n 3t163'3 6 igi3nt3

'oni!3'ion3

E6 3 m+im !3 3$3Ao K20 φ "; 3 mnti3n3 "00N 3$3'ti 3n n 6ongit! !3 2.50m 3n6 Aon '3nt6 !3 6 ig.

Con3!om3nt3 3n 6 3''ion3 F3 3 3n'3ntn 1i'! n !itn'i !3 4m m3!i! ti !36 '3nto !3 6 ig 36 3 3$3'ti !3 3$3Ao !3 '3o 3 3!'3 !3 20 φ "; " φ";

Con3!om3nt3 3n 6 3''ion3 F3 3 3n'3ntn 1i'! n !itn'i !3 0.*mm3!i! ti !3 6o 33 !3 o%o 36 3 3$3'ti !3 3$3Ao !3 '3o 3 3!'3 5 φ ";

'ontin'ion 3 3$3'tn 6 'o3on!i3nt3 3i$i''ion3 !3 6o 'ot3 !3 1 3$3i!nt3iom3nt3

7"4IFIC&CI!# 8" L&S S"CCI!#"S C!# &s = 1

,D =

,D =

> L =

,L =

,Lm+

=

S= Av . fy .d

Vs

V =1.10√ f ' c .bW d S≤d

4

S≤d

2

S≤ Av. fy

3.5bW


23/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,

>L 8P "00.& Tn - m

= **. ! = #0 'm = "5.&40"&2 , = "00&"2"# kg-'m/m = 2".5*544 1 = 50 'm

3 = 5."0

= S3 'o6o' 7 φ " = **.

= 0.* "5.470"404*0 + 0.* - 2.&"275*&20"2"K0.

#."&& Tn-mP = 2.72"& Tn

4P 4P P

4.27 4.27 ".742 Tn

"0.550" Tn-m

".2 Tn - m0. 2.&5 7.52

>L KP 4&.0 Tn - m

= "5.77 ! = &5 'm = 7.4"#04 , = 4&0*5#.* kg-'m/m = &.&00000 1 = 50 'm

3 = 5."0

= S3 'o6o' *.0#"5 φ " "


P = 2.72"& Tn4P 4P

4.27 .0& Tn"".075 Tn-m

0 Tn-m

5.5 2."*5 *.*5 24.05 Tn

>L 8P 2#.*& Tn

-".0# Tn


S = -&*2 'm = 2.5* 'm2

45 'm

,U =

'm2

'm2

7"4IFIC&CI!# 8" L&S S"CCI!#"S C!# &s = > 1

,D =

,D =

> L =

,L =

,Lm+

=

,U =

'm2

'm2

?6?(C?$J , ,&,O$ AJ6,6A ;estribos 1/29>

> L =V

L =

VD =

VU =

VC =

VS =

S,

=

As= Mu

φ. fy .(d−a

2)

a= As . fy

0.85 fc .b

As= Mu

φ. fy .(d−a2 )

a= As . fy

0.85 fc .b

S= Av . fy .d

Vs


24/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,


P = 2.72"& Tn4P 4P

4.27 "2."044 Tn

20."2&5 Tn-m

7.7*507 Tn-m

2.& 2."*5 .""5 5*.75 Tn

>L 8P 2#.*& Tn

**.& Tn


S = 2.7" 'm = 2.5* 'm2

8IS$4I


25/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,


26/41

?6,H$ , A6 ?IA6 P?JC?PA,6 , A(,$ , P,J,


27/41


28/41


29/41


30/41

".5


31/41

* +


32/41


33/41


34/41


35/41

?6,H$ , A6 ?IA6 ?A&AI)A , A(,$

S = 2.4 m L = 11 m S = 2 P = "0.&&7 Tn = ".5 + ".&"45

1 = 0.* ! = 0.7


P3o oio !3 6 ig !i$gm = 0.57 Tn/m

0.57M n/mFactor de Impacto

0.*"" 0.* L 0.3

"(ectos de cargas Permanentes

B3A Cotnt3 ,+im 0.57 Tn

,om3nto B63'to3 ,+imo 0.2*04 Tn - m

"(ectos de la carga 7ia

".&* B3A Cotnt3 ,+im K'on3!om3nt3P P

#."##5 Tn

2.4 m ,om3nto B63'to3 ,+imo K'on3!om3nt3

7.07 Tn - m

Fuerza Cortante ?ltima 20.72" Tn

Cortante %ltima )ue toma el Concreto "".75" Tn

Cortante ?ltimo )ue toman los φ = */& "2.27 Tn

S = 2&.44 'm S = *0 'm

S = 57 'm = ".4* 'm2

S3 'o6o' φ = */& 8 0.* m

Momento Flector %ltimo

"5.* Tn -m


S3 !ion!n 3n tot6 t3 ig !i$gm !3 'on'3to m!o !3 0.*0 + 0.&0 m !3 3''iontn36: !oig n !i3t 3n 6o 3+t3mo !36 t163o !36 3nt3 % 6 t3'3 1i'! 3n 6

3''in '3nt6

@

VD =

,D =

VL =

,L =

VU =

VC =

VS =

,U =

I =15.24

L+38≤0.30

V L= P(1+ I ) & S ' −0.70

S '

M L= PS '

4(1+ I )

S= Av . fy .d

VsS≤d

2

S≤ Av. fy

3.5bW

As= Mu

φ. fy .(d−a

2)

a= As . fy


36/41

?6,H$ , A6 ?IA6 ?A&AI)A , A(,$

= 7.24#45 ! = 0 'm = 5.&5&4*5 , = "527" kg-'m/m = 5.&5&4* 1 = *0 'm

3 = 2.&5= S3 'o6o' * φ */4

min= 5.4 = 2 φ */4

'm2

S3 'o6o' * φ */4; tnto 'omo 3$3Ao mom3nto oitio 'omo mom3nto n3gtio

As= Mu

φ. fy .(d−a

2)

a= As . fy0.85 fc .b


37/41

?6,H$ , A6 ?IA6 ?A&AI)A , A(,$


38/41

DISEÑO DE LOS DISPOSITIVOS DE APOYO: PLACAS DE NEOPRENO

>3''in tot6 3n 6o o%o !3 6 t13 m! !3 '3o:

>T = >D ) >L>T = 42.*2 Tn

50 'm >D = "5.47>L = 2.&4&

40 0.* ".2

0.*

".2

4.&0.*

0.* ".2

eri-icacin del area de la super-icie +ori'ontal

= &0090.07 = 5 Jg/'m2 KP6' !3 R3o3no

= 42*"& = 755.75 'm25

= 50940 = 2000 'm2 .==== Ok

E$3Ao !3 6tmi3nto !mii163 3n 36 'on'3to

$' = 2"0 Jg/'m2 KEti1o

$'= 0.25$ ' = 0.2592"0 = 52.5 Jg/'m2 = 5 Jg/'m2

Conto6 !3 6' !3 n3o3no .====== Ok

eri-icaci!n del acortamiento ertical de las placas de neopreno

B'to !3 Bom B = 40950 B= #.25#*29".2K40)50

= 42.*"& = 2"."5# Jg/'m2 = *02."5 Pi2000

'otmi3nto V3ti'6 K1'o g!o 0 = *.0 N

'otmi3nto V3ti'6 M 7 N ===== Ok

eri-icaci!n del es-uer'o e-ectio de las placas de neopreno

*9".2 = *.0 Cm

= 40 = & 'm .====== Ok 5

= K29!i6t'in tmi' !3 6 ig !3 '3o

L = "" m

3 0.7# 'm ====== Ok

L3go !3 io tnt3o 3 !3'i!o ti6iA 6 igi3nt3 6'3$oA! !3 n3o3no !3 !3A 0

!i3t 3F3i!

3 =

A r(= # T σ adm

σ adm=800 )s*

σ adm

σ adm

+ = L∗W 2 t ( L+W )

σ = #

T

A

σ

'= A,c-.

5

≥2∗/ ∗ 0T ∗ L

/ =12∗10−6 $ −1 0T =30$


39/41

DISEÑO DE LOS DISPOSITIVOS DE APOYO: PLACAS DE NEOPRENO

Po tnto 6 6' !3 n3o3no o3t on ti$'toi


40/41

"#4*.52&0.752#.


41/41

165702987 Puente Viga Losa 11m Xls

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