Diseño de Losa Nervada

DISEÑO DE UNA LOSA NERVADA ( LOSA - CABEZO ) DISEÑO PARA TRAMOS EXTREMOS Especificacioes b, =

fy = f'c = Ln = b = h = s/c = Acabado = Tuberias = p.e concreo rec =

0.85 4200 210 475 140.0 20.0 750 100 100 2.40 4.00

;/cm2 ;/cm2 cm. cm. cm. ;/cm2 ;/m2 ;/m2 Ton/m< cm.

!" LA! L#!A! $%&A(A! $# )*+,L%$ )#$ LA (%-"$")"#$  )A&A)T%&"!T")A! %!T",*LA(A! A$T%&"#&+%$T% !% ("!% A$T%&"#&+%$T% ("!% A&A$ )#+# "A!  L#!A! L#!A! !%,A&A(A+%$T% !%,A&A(A+%$T% DISE O DE DISE DE LA LA LO LOSA SA ' Ca.c.o 3e. espeso! 3e .a .osa Pa!a T!a"o E#$!e"o h = Ln / 24 24 h = 1.7 h = %&'&&

cm. cm.

DISEÑO PARA TRAMOS EXTERIORES )onsideremos h = %&'&& cm. %' Me$!a3o 3e Ca!as Ca!a Me!$a ,eso eso ,r ,ropio opio .2 .2031. 31.403 4032.4 = Acabado Acabado 10031.40 = Tuberias 10031.40 = C'M

0.7 .72 0.14 0.14 &'*+

Ton/m n/m. Ton/m. Ton/m. Ton/m.

1.05 '&+

Ton/m. Ton/m.

Ca!a Vi,a !obrecara

75031.40 = C'V

Ca!a U.$i"a 6u =

6u = 1.5 3 )+  1.8 3 ). /'/+ Ton/m.

/' Ca.c.o 3e .os Mo"e$os Mo"e$os Nea$i,os ( E#$!e"os )  9 : + = 91 / 10 6u 3 Ln 2  9: + = -0'12 Ton9m. Mo"e$os Posi$i,o ( T!a"o )   : + = 1 / 14 6u3 Ln 2  : + = +'/1 Ton9m. 1' Ca.c.o 3e. Pe!a.$e Efec$i,o d =

d = h 9 rec 4'&& cm.

+' Ca.c.o 3e. Ace!o Ca$ia Mii"a5 ' Se ININVI - 2* r = 0.7 3  f'c :1/2 / fy r = 0.0024

%' Se ACI r = 14 / fy r = 0.00<< /' Po! Te"pe!a$!a 0.0018 r = ,or o ano 0.00<< r = Asmin = r 3 b 3 d As"i 6 0'/*

c"%

Ca$ia Ma#i"a r maE = 0.50 3 rb r b =  0.85 3 FG 3 f'c / fy : 3  000 /  000  fy : : r maE = 0.010 AsmaE = r 3 b 3 d As"a# 6 %/'01

c"%

ACERO EN EL EXTREMO As = +u / f fy  d 9 a / 2 : a = As fy / 0.85 3 f'c 3 b f = -0'12

 9: + =

a = 2.<77 As = 14.14 a= 2.<77 ,or o ano As 6 1'+ ACERO EN EL TRAMO

Ton9m.

cm2

>Asmin

c"%

9 :7

As = +u / f fy  d 9 a / 2 : a = As fy / 0.85 3 f'c 3 b f =  : + = a = As = a= ,or o ano As 6

0.85

+'/1

Ton9m.

1.5 .85 1.57

cm2

>Asmin

*'24

c"%

9 :7

67 O8

3 f 5/8@  < f
0.85

67 O8

4 f 1/2@ < f 5/8@ '? 20.0 cm.

4' Ve!ificacio po! Co!$e Co!$e e e. Apo;o u =

u = 1/2 3 Ln 3 6u 7.87< Ton.

7.87< 'u

)ore a una (isancia @ d @ d = 1.00

cm.

0.1

'u =

'u = u 3  0.50 3 Ln 9 d : / 0.5 3 Ln 7.<4< Ton.

c =

u B f n n = c  s c = 0.5<  f'c : 1/2 3 bD 3 d 17.204 Ton.

por o ano

O8

'u B  n.

NO RE<' ESTRIBOS

Ace!o Mii"o po! Co!$e AC min = <.50 3 bD 3 ! / fy )onsidernado esribos de f 1/2@ 2 &amas: AC = 2.54 cm2 ! =

21.771

cm

:7 %sribos de 1/2@  2 ? 10 G reso ? 20 cm.

2.215 2.<75

DISEÑO DE UNA LOSA NERVADA ( LOSA - CABEZO ) DISEÑO PARA TRAMOS INTERNOS Especificacioes b, =

0.85

fy = 4200 f'c = 210 Ln = 475 b = 140.0 h = 20.0 s/c = 750 Acabado 100 Tuberias 100 p.e concr 2.40 rec = 4.00


!" LA! L#!A! $%&A(A! $# )*+,L%$ )#$ LA (%-"$")"#$  )A&A)T%&"!T")A! %!T",*LA(A! A$T%&"#&+%$T% !% ("!% A&A$ )#+# "A!  L#!A! !%,A&A(A+%$T% DISE O DE LA LOSA ' Ca.c.o 3e. espeso! 3e .a .osa Pa!a T!a"o I$e!o h = Ln / 28 h = 1. cm. h = 0'&& cm.

DISEÑO PARA TRAMOS INTERIORES )onsideremos h = %&'&& cm. %' Me$!a3o 3e Ca!as Ca!a Me!$a ,eso ,ropio.4032.4 = 0.72 Acabado 0031.40 = 0.14 Tuberias 0031.40 = 0.14 C'M &'*+

Ton/m. Ton/m. Ton/m. Ton/m.


031.40 = C'V

1.05 '&+

Ton/m. Ton/m.

Ca!a U.$i"a 6u =

6u = 1.5 3 )+  1.8 3 ). /'/+ Ton/m.

/' Ca.c.o 3e .os Mo"e$os Mo"e$os Nea$i,os ( E#$!e"os )  9 : + = 91 / 11 6u 3 Ln 2  9 : + = -4'2& Ton9m. Mo"e$os Posi$i,o ( T!a"o )   : + = 1 / 1 6u3 Ln 2   : + = 1'40 Ton9m. 1' Ca.c.o 3e. Pe!a.$e Efec$i,o d =

d = h 9 rec 4'&& cm.


%' Se ACI r = 14 / fy r = 0.00<< /' Po! Te"pe!a$!a r = 0.0018 ,or o ano r = 0.00<< Asmin = r 3 b 3 d As"i 6 0'/* c"% Ca$ia Ma#i"a r maE = 0.50 3 rb r b =  0.85 3 FG 3 f'c / fy : 3  000 /  000  fy : : r maE = 0.010 AsmaE = r 3 b 3 d As"a# 6 %/'01 c"% ACERO EN EL EXTREMO As = +u / f fy  d 9 a / 2 : a = As fy / 0.85 0.85 f = -4'2&

 9: + =

Ton9m.

a = 2.144 As = 12.70 cm2 a = 2.145 ,or o ano As 6 %'04 c"% ACERO EN EL TRAMO

67 O8

>Asmin

9 :7

4 f 5/8@  2 f 3/4@ '? 20.0 cm.

As = +u / f fy  d 9 a / 2 : a = As fy / 0.85 0.85 f =  : + =

1'40

Ton9m.

a = As = a= ,or o ano As 6

1.4< 8.51 1.4<

cm2

>Asmin

2'+4

c"%

9 :7

67 O8

4 f 1/2@  2 f 5/8@ '? 20.0 cm.


u = 1/2 3 Ln 3 6u 7.87< Ton.

7.87< 'u

)ore a una (isancia @ d @ d = 1.00 cm. 'u =

0.1

'u = u 3  0.50 3 Ln 9 d : / 0.5 3 Ln 7.<4< Ton.

u B f n n = c  s c = 0.5<  f'c : 1/2 3 bD 3 d c = 17.204 Ton. por o ano

'u B

O8

NO RE<' ESTRIBOS

Ace!o Mii"o po! Co!$e AC min = <.50 3 bD 3 ! / fy )onsidernado esribos de f 1/2@ 2 &amas: AC = 2.54 cm2 ! = 21.771 cm :7 %sribos de 1/2@  2 ? 10 G reso ? 20 cm.

2.215 2.<75

co!$a3o 3e ,a!i..as .a!o 3e ac.a=e (.a)

p.'
DIAMETRO c"' 0.525

% D c"' 11.4<

3 c"' 15

.a c"' 15.00

1/2 5/8
1.27 1.5875 1.05

15.24 1.05 22.8

15 15 15

15.00 20.00 25.00

posicio 3e .os p$os 3e co!$a3o I

.a m.:

Li m.:

Li>0 m.:

Li>0-.a m.:

Li>+ m.:

Li>+-.a m.:

Li>/ m.:

Li>4 m.:

1

0.20

4.75

1.00

0.8

0.5

0.75

2.00

1.00

RESUMEN DE CARACTERISTICAS MAXIMA ELEMENTO ESTRUCTURAL5 LOSAS NERVA

fy =

4200

;/cm2

f'c = b =

210 140

;/cm2 cm.

Tn9cm.: ρmax

M+max

Tn9cm.: M-max

ρmax

M+max

S ? MINIMAS DE DISEÑO DAS - LOSA

M-max

,A&A %L )#$)&%T# υu Vu

Asmin

As

DISEÑO DE UNA LOSA NERVADA ( LOSA - PUENTE ) DISEÑO PARA TRAMOS EXTREMOS Especificacioes b, =

fy = f'c = Ln = b = h = s/c = Acabado Tuberias p.e concreo rec =

0.85 4200 210 475 10.0 20.0 750 100 100 2.40 4.00


!" LA! L#!A! $%&A(A! $# )*+,L%$ )#$ LA (%-"$")"#$  )A&A)T%&"!T")A! %!T",*LA(A! A$T%&"#&+%$T% !% ("!% A&A$ )#+# "A!  L#!A! !%,A&A(A+%$T% DISE O DE LA LOSA ' Ca.c.o 3e. espeso! 3e .a .osa Pa!a T!a"o E#$!e"o h = Ln / 24 h = 1.7 h = %&'&&

cm. cm.

DISEÑO PARA TRAMOS EXTERIORES )onsideremos h = %&'&& cm. %' Me$!a3o 3e Ca!as Ca!a Me!$a ,eso ,ropio.2031.4032.4 = Acabado 10031.40 = Tuberias 10031.40 = C'M

0.78 0.1 0.1 '&*


1.2 '%

Ton/m. Ton/m.


75031.40 = C'V

Ca!a U.$i"a 6u =

6u = 1.5 3 )+  1.8 3 ). /'0*+ Ton/m.

/' Ca.c.o 3e .os Mo"e$os Mo"e$os Nea$i,os ( E#$!e"os )  9 : + = 91 / 10 6u 3 Ln 2  9: + = -2'+4 Ton9m. Mo"e$os Posi$i,o ( T!a"o )   : + = 1 / 14 6u3 Ln 2  : + = 4'% Ton9m. 1' Ca.c.o 3e. Pe!a.$e Efec$i,o d =

d = h 9 rec 4'&& cm.

+' Ca.c.o 3e. Ace!o Ca$ia Mii"a5 ' Se ININVI - 2* r = 0.7 3  f'c :1/2 / fy 0.0024 r =

%' Se ACI r = 14 / fy r = 0.00<< /' Po! Te"pe!a$!a 0.0018 r = ,or o ano 0.00<< r = Asmin = r 3 b 3 d As"i 6 2'1+

c"%

Ca$ia Ma#i"a r maE = 0.50 3 rb r b =  0.85 3 FG 3 f'c / fy : 3  000 /  000  fy : : r maE = 0.010 AsmaE = r 3 b 3 d As"a# 6 %0'1

c"%

ACERO EN EL EXTREMO As = +u / f fy  d 9 a / 2 : a = As fy / 0.85 3 f'c 3 b f =  9: + = a = As = a= ,or o ano As 6

-2'+4 2.<81 1.11 2.<81

Ton9m. cm2

>Asmin

4'*

c"%

9 :7

0.85

67 O8

5 f 5/8@  < f
? 1.5 cm.

ACERO EN EL TRAMO As = +u / f fy  d 9 a / 2 : a = As fy / 0.85 3 f'c 3 b f = 4'%

 : + = a = As = a= ,or o ano As 6

0.85

Ton9m.

1.2 11.<01 1.2

cm2

>Asmin

'/&

c"%

9 :7

67 O8

< f 1/2@  4 f 5/8@ ? 20 cm.


u = 1/2 3 Ln 3 6u .01< Ton.

.01< 'u

)ore a una (isancia @ d @ d = 1.00

cm.

0.1

'u =

'u = u 3  0.50 3 Ln 9 d : / 0.5 3 Ln 8.40 Ton.

c =

u B f n n = c  s c = 0.5<  f'c : 1/2 3 bD 3 d 1.2 Ton.

por o ano

O8

'u B  n.

NO RE<' ESTRIBOS


1.05

cm


2.215 2.<75

DISEÑO DE UNA LOSA NERVADA ( LOSA - PUENTE ) DISEÑO PARA TRAMOS INTERNOS Especificacioes b, =

0.85

fy = 4200 f'c = 210 Ln = 475 b = 10.0 h = 20.0 s/c = 750 Acabado 100 Tuberias 100 p.e concr 2.40 rec = 4.00


!" LA! L#!A! $%&A(A! $# )*+,L%$ )#$ LA (%-"$")"#$  )A&A)T%&"!T")A! %!T",*LA(A! A$T%&"#&+%$T% !% ("!% A&A$ )#+# "A!  L#!A! !%,A&A(A+%$T% DISE O DE LA LOSA ' Ca.c.o 3e. espeso! 3e .a .osa Pa!a T!a"o I$e!o h = Ln / 28 h = 1. cm. h = %&'&& cm.

DISEÑO PARA TRAMOS INTERIORES )onsideremos h = %&'&& cm. %' Me$!a3o 3e Ca!as Ca!a Me!$a ,eso ,ropio.4032.4 = 0.78 Acabado 0031.40 = 0.1 Tuberias 0031.40 = 0.1 C'M '&*



031.40 = C'V

1.2 '%

Ton/m. Ton/m.

Ca!a U.$i"a 6u =

6u = 1.5 3 )+  1.8 3 ). /'0*+ Ton/m.

/' Ca.c.o 3e .os Mo"e$os Mo"e$os Nea$i,os ( E#$!e"os )  9 : + = 91 / 11 6u 3 Ln 2  9 : + = -0'02 Ton9m. Mo"e$os Posi$i,o ( T!a"o )   : + = 1 / 1 6u3 Ln 2   : + = +'/+ Ton9m. 1' Ca.c.o 3e. Pe!a.$e Efec$i,o d =

d = h 9 rec 4'&& cm.


%' Se ACI r = 14 / fy r = 0.00<< /' Po! Te"pe!a$!a r = 0.0018 ,or o ano r = 0.00<< Asmin = r 3 b 3 d As"i 6 2'1+ c"% Ca$ia Ma#i"a r maE = 0.50 3 rb r b =  0.85 3 FG 3 f'c / fy : 3  000 /  000  fy : : r maE = 0.010 AsmaE = r 3 b 3 d As"a# 6 %0'1 c"% ACERO EN EL EXTREMO As = +u / f fy  d 9 a / 2 : a = As fy / 0.85 f = 0.85  9 : + = -0'02 Ton9m. a = 2.147 As = 14.00 cm2 a = 2.147 ,or o ano As 6 1'4& c"%

67 O8

>Asmin

9 :7

5 f 5/8@  2 f
ACERO EN EL TRAMO As = +u / f fy  d 9 a / 2 : a = As fy / 0.85 f = 0.85  : + =

+'/+

Ton9m.

a = As = a= ,or o ano As 6

1.442 .808 1.442

cm2

>Asmin

*'2

c"%

9 :7

67 O8

4 f 1/2@  < f 5/8@ ? 20 cm.


u = 1/2 3 Ln 3 6u .01< Ton.

.01< 'u

)ore a una (isancia @ d @ d = 1.00 cm. 'u =

0.1

'u = u 3  0.50 3 Ln 9 d : / 0.5 3 Ln 8.40 Ton.

u B f n n = c  s c = 0.5<  f'c :1/2 3 bD 3 d c = 1.2 Ton. por o ano

'u B

O8

NO RE<' ESTRIBOS


1.05

cm


2.215 2.<75

co!$a3o 3e ,a!i..as .a!o 3e ac.a=e (.a)

p.'
DIAMETRO c"' 0.525

% D c"' 11.4<

3 c"' 15

.a c"' 15.00

1/2 5/8
1.27 1.5875 1.05

15.24 1.05 22.8

15 15 15

15.00 20.00 25.00

posicio 3e .os p$os 3e co!$a3o I

.a m.:

Li m.:

Li>0 m.:

Li>0-.a m.:

Li>+ m.:

Li>+-.a m.:

Li>/ m.:

Li>4 m.:

1

0.20

4.75

1.00

0.8

0.5

0.75

2.00

1.00

DISEÑO DE LOSA NERVADA ( NERVADURA@CABEZO ) Especificacioes5 0.85 b, = fy = 4200 ;/cm2 f'c = 210 ;/cm2 0.0 f = Ln = <75.00 cm. h = <5.00 cm. b = 20.00 cm. d = <0.00 cm. d' = 5.00 cm. rec = 5.00 cm. ENERALIDADES Pe!a.$e Efec$i,o d = h 9 rec d = <0.00 cm. d' = 5.00 cm. '- Es ecesa!io !e,isa! .a Capaci3a3 3e .a Seccio co"o si fe!a Si"p.e"e$e Refo!a3a %nconrar

rb 999999999> rmaE = 0.75 rb

Ca$ia Ba.acea3a 5 r b = 0.85 * b1f'c / fy * 6000 / ( 6000 + fy ) r b = 0.02125 Ca$ia Ma#i"a 5 r max = 0.75 * r b r b = 0.85 * b1f'c / fy * 6000 / ( 6000 + fy ) r max=

0.015

A!ea 3e Ace!o Ma#i"o 5 AsmaE = r maE 3 bd AsmaE = .54 cm2 :7 2 f 5/8" + 1 f
.81 cm2

Mo"e$o Ma#i"o para e cua no se necesia acero a compresion -ALLA ,#& T&A))"#$: +maE = f As 3 fy  d 9 a/2 : a = As fy /  0.85 3 f'c 3 b: a = 11.22 +maE = 875<< H9cm. +maE = 2'2 Tn9m. Ca$ia Mii"a 5 r min = 14 / fy 0.00<<< r min = A!ea 3e Ace!o Mii"o Asmin = r min 3 b 3 d Asmin = 1.8 cm2 :7 1 f 1/2" Mo"e$o Mii"o +maE = f As 3 fy  d 9 a / 2 : a = As fy /  0.85 3 f'c 3 b: a = 2.<5 +min = 25052 H9cm. %'+4 +min = Tn9m. APLICACION DEL PROCEDIMIENTO DE DISEÑO A LA ROTURA A LA VIA DISEÑO POR LEXION TRAMO +u = 8.80 Tn9m. Tanear a = 7.48 As = 8.87 cm2 comprobacion a = 10.44 :7 2 f 5/8@  2 f
#benido de (iarama de %nCoCenes 7

As min

O8

. cm2

DISEÑO DE LOSA NERVADA ( NERVADURA@PUENTE ) Especificacioes5 0.85 b, = fy = 4200 ;/cm2 f'c = 210 ;/cm2 0.0 f = Ln = <75.00 cm. h = <5.00 cm. b = 20.00 cm. d = <0.00 cm. d' = 5.00 cm. rec = 5.00 cm. ENERALIDADES Pe!a.$e Efec$i,o d = h 9 rec d = <0.00 cm. d' = 5.00 cm. '- Es ecesa!io !e,isa! .a Capaci3a3 3e .a Seccio co"o si fe!a Si"p.e"e$e Refo!a3a %nconrar

rb 999999999> rmaE = 0.75 rb

Ca$ia Ba.acea3a 5 r b = 0.85 * b1f'c / fy * 6000 / ( 6000 + fy ) r b = 0.02125 Ca$ia Ma#i"a 5 r max = 0.5 * r b r b = 0.85 * b1f'c / fy * 6000 / ( 6000 + fy ) r max=

0.010

A!ea 3e Ace!o Ma#i"o 5 AsmaE = r maE 3 bd AsmaE = .< cm2 :7 2 f 5/8" + 1 f
.81 cm2

Mo"e$o Ma#i"o para e cua no se necesia acero a compresion -ALLA ,#& T&A))"#$: +maE = f As 3 fy  d 9 a/2 : a = As fy /  0.85 3 f'c 3 b: a = 7.48 +maE = <1<11 H9cm. +maE = 4'/ Tn9m. Ca$ia Mii"a 5 r min = 14 / fy 0.00<<< r min = A!ea 3e Ace!o Mii"o Asmin = r min 3 b 3 d Asmin = 1.8 cm2 :7 2 f 1/2@ Mo"e$o Mii"o +maE = f As 3 fy  d 9 a / 2 : a = As fy /  0.85 3 f'c 3 b: a = 2.<5 +min = 25052 H9cm. %'+4 +min = Tn9m. APLICACION DEL PROCEDIMIENTO DE DISEÑO A LA ROTURA A LA VIA DISEÑO POR FLEXION

TRAMO +u a As comprobacion a :7 Tanear

= = = =

.<1 7.48 .<

Tn9m. cm2

#benido de (iarama de %nCoCenes 7

As min

O8

7.48 2 f 5/8@  1 f
.81 cm2

Diseño de Losa Nervada

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