Diseño de Sección de Viga

8/18/2019 Diseño de Sección de Viga

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DISEÑO DE SECCIÓN DE VIGA DOBLEMENTE REFORZADA DE LA (V.P-101)

CASO I

Análii ! "i#$% &'' #l PRIMER NIVEL

1. Cuando el MU = 87.96 tn.m

Datos:

F’c = 210 Kg/Cm2

F = !200 Kg/Cm2

MU = 87.96 tn.m


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Mn Mn1 " Mn2

Mn = Mu

∅ =87.96

0.90

*. +'l+,l% "#l %#n% n%in'l Mn1

Mn1 = K.#.d2 $!.%$ & !0 & 702 = 106.$% 'n.m( K

/. +'l+,l% "#l %#n% n%in'l Mn*

Mn2 Mn ) Mn1 = 97.7%% * 106.$% = )8.8 'n.m

. E'l,'+i2n

Mn1 + Mn n% # n#+#i' '+#% ' +%&#i2n !

"i#$'% V.S.A

VIGA SIMPLEMENTE ARMADA

1. C'l+,l% &% i#'+i%n# ,+#i'

As=

Mu

∅ Fy (d−a

2) ( ∅=0.90

Mn = 97.7%

F’c = 210 Kg/Cm2

K= $!.%$

F = !200 Kg/Cm2


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a= As xFy

0.85 f ' c x b

*. P%+#% i#'i%

1, -teac-n asum-mos a=h

5=75

5 a = 1$ cm

uego s = %7.2% cm2

a= 21.90 cm

2, -teac-n asum-mos a= 21.90 cmuego: s = %9.!1cm2

a= 2%.18 cm

%, -teac-n asum-mos a= 2%.18 cmuego: s = %9.8!cm2

a= 2%.!! cm

!, -teac-n asum-mos a= 2%.!! cmuego: s =%9.9%cm2

a= 2%.!9 cm

$, -teac-n asum-mos a= 2%.!9 cmuego: s =%9.9!cm2

a= 2%.!9 cm

6, -teac-n asum-mos a= 2%.!9 cmuego: s =%9.9!cm2

a= 2%.!9 cm

3. C4#5,#% &% +,'n6' 6ni'

ρ min=0.80√ F ' c

Fy = 0.0027

ρ min= 14

Fy = 0.00%%

ρ min=0.0033

s m-n = 0.00%% & !0 & 70 = 9.2! cm2


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s m-n s

39.2! cm24 3%9.9!cm24

S#l#++i%n' '+#% "# l' '7l'

% ∅ 1 %/85 " 2 ∅ 15

CASO IIAnálii ! "i#$% &'' #l PRIMER NIVEL

1. Cuando el MU = 119.90 tn.m

s = %9.9!cm2( s =2

Datos:

F’c = 210 Kg/Cm2

F = !200 Kg/Cm2

MU = 119.90 tn.m


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Mn Mn1 " Mn2

Mn = Mu

∅ =119.90

0.90

*. +'l+,l% "#l %#n% n%in'l Mn1

Mn1 = K.#.d2 $!.%$ & !0 & 702 = 106.$% 'n.m( K

/. +'l+,l% "#l %#n% n%in'l Mn*

Mn2 Mn ) Mn1 = 1%%.22 * 106.$% = 26.69 'n.m

. E'l,'+i2n

Mn1 Mn # n#+#i' '+#% ' +%&#i2n !

"i#$'% V.D.A

VIGA DOBLEMENTE ARMADA

3. C'l+,l% "#l á#' ' +%&#i2n

’s =

M n 2

Fy (d−d ' ) =26.69

4200 x(70−5) = 9.78 Cm2

8. D##in' á#' "# '+#% "# '++i2n &% +,'n6' á9i'

Mn = 1%%.22

F’c = 210 Kg/Cm2

K= $!.%$

F = !200 Kg/Cm2


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ρmin= 14

Fy = 0.00%%

s m-n = 0.00%% & !0 & 70 = 9.%% cm2

s m-n ’s39.%%4 39.784


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DETERMINANDO EL =REA DE LOS ACEROS A COMPRESIÓN > TRACCIÓN

(SEG?NDO NIVEL4

CASO I

Análii ! "i#$% &'' #l SEG?NDO NIVEL

1. Cuando el MU = 78.$0 tn.m


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Mn Mn1 " Mn2

Mn = Mu

∅ =78.50

0.90

*. +'l+,l% "#l %#n% n%in'l Mn1

Mn1 = K.#.d2 $!.%$ & !0 & 702 = 106.$% 'n.m( K

/. +'l+,l% "#l %#n% n%in'l Mn*Mn2 Mn ) Mn1 = 87.22 * 106.$% = )19.%1 'n.m

. E'l,'+i2n

Mn1 + Mn n% # n#+#i' '+#% ' +%&#i2n !

"i#$'% V.S.A

VIGA SIMPLEMENTE ARMADA

Datos:

F’c = 210 Kg/Cm2

F = !200 Kg/Cm2

MU = 78.$0 tn.m

Mn = 87.22'n.m

F’c = 210 Kg/Cm2

K= $!.%$

F = !200 Kg/Cm2


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/. C'l+,l% &% i#'+i%n# ,+#i'

As= Mu

∅ Fy (d−a

2) ( ∅=0.90

a= As xFy

0.85 f ' c x b

. P%+#% i#'i%

1, -teac-n asum-mosa=

h

5=75

5 a = 1$ cm

uego s = %%.2% cm2

a= 21.90 cm

2, -teac-n asum-mos a= 21.90 cmuego: s = %9.!1cm2

a= 2%.18 cm

%, -teac-n asum-mos a= 2%.18 cmuego: s = %9.8!cm2

a= 2%.!! cm

!, -teac-n asum-mos a= 2%.!! cmuego: s =%9.9%cm2

a= 2%.!9 cm

$, -teac-n asum-mos a= 2%.!9 cmuego: s =%9.9!cm2

a= 2%.!9 cm


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Análii ! "i#$% &'' #l SEG?NDO NIVEL

1. Cuando el MU = 129.%$ tn.m

Mn Mn1 " Mn2

Mn = Mu

∅ =129.35

0.90

*. +'l+,l% "#l %#n% n%in'l Mn1

Mn1 = K.#.d2 $!.%$ & !0 & 702 = 106.$% 'n.m( K

/. +'l+,l% "#l %#n% n%in'l Mn*

Mn2 Mn ) Mn1 = 1!%.72 * 106.$% = %7.19 'n.m

. E'l,'+i2n

Mn1 Mn # n#+#i' '+#% ' +%&#i2n !"i#$'% V.D.A


Datos:

F’c = 210 Kg/Cm2

F = !200 Kg/Cm2

MU = 129.%$ tn.m

Mn = 1!%.72

F’c = 210 Kg/Cm2

K= $!.%$

F = !200 Kg/Cm2


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3. C'l+,l% "#l á#' ' +%&#i2n

’s =

M n 2

Fy (d−d ' ) =26.69

4200 x(70−5) = 1%.62 Cm2

8. D##in' á#' "# '+#% "# '++i2n &% +,'n6' á9i'

s ) ’s = ρmax

& # & d = 0.01$9

s * 1%.62 = 0.01$9 !0 70

:. C%&%7'n"% +,'n6'

ρ' =

A ´ S

b x d =13.62

40 x70 = 0.00!86!

´ ρ m-n = β1 x0.85 x F

' c

Fy ( 60006000+ Fy )(d'

d )+ ρ ' ´ ρ m-n = 0.006%82

• ρb = 0.0212$

• ´ ρ =

As

b x d =58.14

40 x70 = 0.2076

s = $8.1!


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•´ ρb = ρb " ρ

'

& F

' s

Fy ´ ρb

= 0.0212$ " 0.00!86!4200

4200

´ ρb = 0.02611!

´ ρ ´ ρb Fs = F = !200 Kg/Cm2

• ´ ρ + ´ ρ m-n

30.020764 + 30.006%824

F ' s = F = !200 Kg/Cm2

;. C4#5,#% "# á#' "# '+#% 6ni%

s m-n = ρmin

& # & d

ρmin=0.80√ F ' c

Fy = 0.0027 ρmin = 0.00%%

ρ min= 14

Fy = 0.00%%

s m-n = 0.00%% & !0 & 70 = 9.%% cm2

s m-n ’s39.%%4 31%.624


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DETERMINANDO EL =REA DE LOS ACEROS A COMPRESIÓN > TRACCIÓN

(TERCER NIVEL4


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CASO I

Análii ! "i#$% &'' #l TERCER NIVEL


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1. Cuando el MU = 96.%0 tn.m

Mn Mn1 " Mn2

Mn = Mu

∅ =96.30

0.90

*. +'l+,l% "#l %#n% n%in'l Mn1

Mn1 = K.#.d2 $!.%$ & !0 & 702 = 106.$% 'n.m( K

/. +'l+,l% "#l %#n% n%in'l Mn*

Mn2 Mn ) Mn1 = 107 * 106.$% = 0.!7 'n.m

. E'l,'+i2n

Mn1 Mn # n#+#i' '+#% ' +%&#i2n !

"i#$'% V.D.A


Datos:

F’c = 210 Kg/Cm2

F = !200 Kg/Cm2

MU = 96.%0 tn.m

Mn = 107 'n.m

F’c = 210 Kg/Cm2

K= $!.%$

F = !200 Kg/Cm2


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3. C'l+,l% "#l á#' ' +%&#i2n

’s =

M n 2

Fy (d−d ' ) =0.47

4200 x(70−5) = 0.17 Cm2

8. D##in' á#' "# '+#% "# '++i2n &% +,'n6' á9i'

s ) ’s = ρmax

& # & d = 0.01$9

s * 0.17 = 0.01$9 !0 70

:. C%&%7'n"% +,'n6'

ρ' =

A ´ S

b x d =0.17

40 x70 = 0.00006071

´ ρ m-n = β1 x0.85 x F

' c

Fy ( 60006000+ Fy )(d'

d )+ ρ ' ´ ρ m-n = 0.001!9

• ρb = 0.0212$

• ´ ρ =

As

b x d =44.69

40 x70 = 0.01$96

s = !!.69


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•´ ρb = ρb " ρ

'

& F

' s

Fy ´ ρb

= 0.0212$ " 0.000060714200

4200

´ ρb = 0.021%11

´ ρ ´ ρb Fs = F = !200 Kg/Cm2

• ´ ρ + ´ ρ m-n

30.01$964 + 30.001!94

F ' s = F = !200 Kg/Cm2

;. C4#5,#% "# á#' "# '+#% 6ni%

s m-n = ρ min

& # & d

ρ min=0.80√ F ' c

Fy = 0.0027 ρmin = 0.00%%

ρ min= 14

Fy = 0.00%%

s m-n = 0.00%% & !0 & 70 = 9.%% cm2

s m-n + ’s39.%%4 30.174


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CASO I

Análii ! "i#$% &'' #l TERCER NIVEL

11. Cuando el MU = 111.$% tn.m

Mn Mn1 " Mn2

Mn = Mu

∅ =111.53

0.90

1*. +'l+,l% "#l %#n% n%in'l Mn1

Datos:

F’c = 210 Kg/Cm2

F = !200 Kg/Cm2

MU = 96.%0 tn.m

Mn = 12%.92

F’c = 210 Kg/Cm2

K= $!.%$

F = !200 Kg/Cm2


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Mn1 = K.#.d2 $!.%$ & !0 & 702 = 106.$% 'n.m( K

1/. +'l+,l% "#l %#n% n%in'l Mn*Mn2 Mn ) Mn1 = 12%.92 * 106.$% = 17.%9 'n.m

1. E'l,'+i2n

Mn1 Mn # n#+#i' '+#% ' +%&#i2n !

"i#$'% V.D.A


13. C'l+,l% "#l á#' ' +%&#i2n

’s =

M n 2

Fy (d−d ' ) =17.39

4200 x(70−5) = 6.%7 Cm2

18. D##in' á#' "# '+#% "# '++i2n &% +,'n6' á9i's ) ’s =

ρmax & # & d = 0.01$9

s * 6.%7 = 0.01$9 !0 70

1:. C%&%7'n"% +,'n6's = $0.89


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ρ' =

A ´ S

b x d =6.37

40 x70 = 0.00227$

´ ρ m-n = β1 x0.85 x F '

c Fy ( 6000

6000+ Fy )(d

'

d )+ ρ '

´ ρ m-n = 0.00%70

• ρb = 0.0212$

• ´ ρ =

As

b x d =50.89

40 x70 = 0.01817

•´ ρb

=

ρb

"

ρ'

&

F ' s

Fy

´ ρb

= 0.01817 " 0.00227$4200

4200

´ ρb = 0.020!!$

´ ρ ´ ρb Fs = F = !200 Kg/Cm2

• ´ ρ + ´ ρ m-n

• 30.018174 + 30.00%704

F ' s = F = !200 Kg/Cm2

1;. C4#5,#% "# á#' "# '+#% 6ni%

s m-n = ρ min

& # & d

ρ min=0.80√ F ' c

Fy = 0.0027 ρmin = 0.00%%

ρ min= 14 Fy = 0.00%%

s m-n = 0.00%% & !0 & 70 = 9.%% cm2

s m-n + ’s39.%%4 36.%74

’s = 9.%%


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1


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(PRIMER NIVEL)

APO>O A TRAMO A-B

APO>O B


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(SEG?NDO NIVEL)

APO>O A TRAMO A-B


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APO>O B


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(TERCER NIVEL)

APO>O A TRAMO A-B


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APO>O B


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Diseño de Sección de Viga

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