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8/16/2019 Diseño contratrabe
1/57
Diseño de contratrabe de cimentación 80x120 (propuesta por Felipe)
Datos: Para que A’s fuya:b = 80.00 cmb' = 0.00 cmt = 120.00 cm
h = 120.00 cm Para que se presente la alla balancea a: = 11!.00 cm".00 cm0.00 cm0.00 cm0.00 cm0.00 cm
’ c = !#0.00 $ c = 280.00
% c = 2!8.000.8#
As = 101.&0 20 ars ( 8 ars ) 20101.&0 20 ars ( 8 ars ) 20
0.000.000.00 *b+cac+,n el0.00
y = &/200.00
p = 0.0211! 0.00!12 opma = 0.028!! o
Revisión por fexión
u = &22.00 u = &2/200/000
Estudio de compatibilidad de de ormaciones se!"n las #ipótesis b$sicas de fexi
&aso Flexion 'ura c 3cm4 a 3cm411.#& 5.80 6 6
6 6 6 66 6 0.0011"5&78 2/!#8.5&6 6 0.00! &/200.00
c
1 = cb =
2 =
! = &aso 1 >es+stenc+a a tens+,n pura:& =
# =m;cm 2
m;cm 2 &aso 2 >es+stenc+a a compres+,n pura:
m;cm 2? 1 = P0c = b
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6 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
C> = 0.5> = &05.81 ton
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&aso c 3cm4 a 3cm42#.2" 21.&8 6 6
6 6 6 6
6 6 0.0021785&1 &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso * c 3cm4 a 3cm4
!5.00 !!.1# 6 66 6 6 66 6 0.002&71#"8 &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso + c 3cm4 a 3cm4#2."& &&.8! 6 6
6 6 6 66 6 0.002701"5# &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.00
6 6 0.00! &/200.006 6 6 6
&aso , c - cb c 3cm4 a 3cm477.&" #7.#0 6 6
6 6 6 6
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c
- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24
- c1 = t < b < ''c- c2 = 9a6t < b' < ''c
- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&
- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c
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6 6 0.00278&0"1 &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.00
6 6 6 6
&aso . c 3cm4 a 3cm4"".18 7#.70 6 6
6 6 6 66 6 0.002"2"857 &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso 8 c 3cm4 a 3cm48".88 "&."0 6 6
6 6 6 66 6 0.002"710&& &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso / c 3cm4 a 3cm4
58.#5 8!.80 6 66 6 6 66 6 0.002"8755! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.00
- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s#
s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c-
s1 = A
s1<
s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24
- c1 = t < b < ''c- c2 = 9a6t < b' < ''c
- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s#
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6 6 6 6
&aso 10 c 3cm4 a 3cm4105.25 52.50 6 6
6 6 6 66 6 0.00280"8#8 &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso 11 c - # c 3cm4 a 3cm4120.00 102.00 6 6
6 6 6 66 6 0.00282# &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
Dia!rama de interacción
n Pnton m ton
1 0.00 68#1."72 #.!# 0.00! 7#2.85 &08.5#
& "2#.#! 7!1.22# ""2.2! 8#!.&57 "52.55 10"#."7" "1#.1! 1!52.#08 7&0.02 17"&.285 #71.7# 15!2.#0
10 &"7.!2 21"&.0"11 !81.75 2&0!.12 0.00 !1!7.#7
s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s#
s = A
s<
s
0 100 2006#00
0
#00
1000
1#00
2000
2#00
!000
!#00
'n ton
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Pu = 0.00 tonu = &22.00 ton muy = 0.00 ton m
con re uerEo que no es hel+co+ al
!20.00 ton0."0
22&.00
11#0.00 ton
0."080#.00
!1!7.#7 ton0."0
215#.#5
150.&& ton
0.00 ton
0.00 o
Revisión por cortante
-ortante Flt+mo Gu
Gu = 11#.00 on Gu ma =Gu = 11#/000.00 Gu ma = 2&2/025.01
-ortante que res+ste el concreto Gc>
Gc> = s+ p H 0.01#Gc> =
p = 0.010#7 = 11!.00 cm
C> = 0.80
P> = 1 ; 31;P > 1;P >y 6 1;P>04
Pn =C> =P> =
Pny =
C>y =P>y =
P0c =C>0c =
P>0 =
P> = 1 ; 31;P > 1;P >y 6 1;P>04P> =
Pu =
Pu ; P> =
2 C> b $c1;2 en el caso e c
C> b 90.2 20p $c1;2
0.# C> b $c1;2 s+ p 0.01#
61#00
61000
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Gc> = &5/"7".22
Cactor que a ecta el Gc>
Gc> = Gc>0.8 H = 160.000&9h6"00 H 1.0 s+ h I "00 mm
h = 1/200.00 mm160.000&9h6"00 = 0.80 = 0.80
-omparac+,n Gu .s. Gc>
Gc> = !5/81!.""Gu = 11#/000.00
>e uerEo trans ersal propuesto
con ars ( &b = 1.2" cm
ramas = &A = #.0" cm2
s requer+ a por tens+on +a onal
s =J = 50.00 K
Gs> = Gu 6 Gc>Gs> = "#/187.2!
s = 2#.#5 cm
s ma perm
s ma p = 0.# s ma p = 0.2#
181/#21."7
Gu = 11#/000.00
s ma p = 0.# = .20 cm
s e +seLo
r+ e s = 2#.#5 cm
M ma p para columnas
C> A y 9senJ cosJ ; Gs>
s+ Gc> H Gu N 1.# C> b $c1;2 s+ Gu I 1.# C> b $c 1;2
1.# C> b $c1;2 =
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M1 = 8#0 b lon ;sqr9 y = "&.57 cmM2 = &8 b estr+bo = 70.57 cm
M! = b;2 = &0.00 cm
r+ e M = 2#.#5 cm
usar M = 1!.00 cm
>e uerEo al centro el claro
O(&)1! & ramas
>e +s+on el re uerEo trans ersal propuesto:
A = #.0" cm2A m+n =
A m+n = 1.2& cm2 o
a separac+,n el re uerEo trans ersal en los e tremos e la columna se re uce a la m+ta .
on +tu ’ en los e tremos e la columna en la cual hay que re uc+r la separac+,n el re u
'1 = b col = 80.00 cm'2 = Q col ; 7 = "8.!! cm'! = 700 mm = 70.00 cm
' = 80.00 cm
0.! $c1;2 b s ; y
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2!.!! cm
77.&" cm
68#1/"70.00 = 0.00
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6 6 0.00 670.00 0.006 6 0.00 670.00 0.006 6 0.00 670.00 0.00
0.027!88#88 &/200.00 &2#/880.00 #!.00 22/#"1/7&0.00Pn 3 4 = 0.00 n 3
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Bs C 3 4 b 3cm46 6 6&08/5#2.52 6&5.27 20/1/!0!.016 6 0.00 0.00 0.00
6 6 6&2#/880.00 6#!.00 22/#"1/7&0.006 6 0.00 670.00 0.006 6 0.00 670.00 0.006 6 0.00 670.00 0.006 6 0.00 670.00 0.00
0.010&1#77" &/200.00 &2#/880.00 #!.00 22/#"1/7&0.00Pn 3 4 = &08/5#2.52 n 3
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6 6 6&2#/880.00 6#!.00 22/#"1/7&0.006 6 0.00 670.00 0.006 6 0.00 670.00 0.006 6 0.00 670.00 0.006 6 0.00 670.00 0.00
0.0021 &/200.00 &2#/880.00 #!.00 22/#"1/7&0.00Pn 3 4 = 1/0"#/"70.00 n 3
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0.000&!8#&& 8"".05 88/5!7."# #!.00 &/"1!/7&".5"Pn 3 4 = 1/5!2/&5#.2# n 3
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olumnas
n ton m
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erEo trans ersal.
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Diseño de columna
Datos: Para que A’s fuya:b = 70.00 cmb' = 0.00 cmt = 70.00 cm
h = 70.00 cm Para que se presente la alla balancea a: = ##.00 cm#.00 cm
!0.00 cm0.00 cm0.00 cm0.00 cm
’ c = 2#0.00 $ c = 200.00
0.8# % c = 1"0.00As = 1#.20 ! ars ( 8
1#.20 ! ars ( 810.1! 2 ars ( 80.000.00 *b+cac+,n el0.00
y = &/200.00
p = 0.01127 P m+n = 20; y = 0.00&"7 op ma = 0.07000 o
Revisión por fexocompresión biaxial
Pu = !".00 ton Pu = !"000.00u = 17.00 u = 1700000.00uy = 11.00 uy = 1100000.00
Estudio de compatibilidad de de ormaciones se!"n las #ipótesis b$sicas de fexi
&aso 2 Flexion 'ura c 3cm4 a 3cm48.18 7.5# 6 6
6 6 6 66 6 0.001177&2 2/!!2.8&6 6 60.008001&"5 6&/200.00
c
1 = cb =
2 =
! = &aso 1 >es+stenc+a a tens+,n pura:& =
# =m;cm 2
m;cm 2 &aso 2 >es+stenc+a a compres+,n pura:
? 1 =m;cm 2 P0c = b
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6 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso c 3cm4 a 3cm410.!0 8."7 6 6
6 6 6 66 6 0.001#&&001 !/088.006 6 60.00#"!#55& 6&/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso * c 3cm4 a 3cm412.&2 10.#7 6 6
6 6 6 66 6 0.001"52725 !/#8#.276 6 60.00&2&&22! 6&/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso + c 3cm4 a 3cm41&.## 12.!7 6 6
6 6 6 6
6 6 0.001578"!1 !/5!".&76 6 60.00!18"71" 6&/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2-
s! = A
s!<
s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c
- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
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&aso , c - cb c 3cm4 a 3cm417.7" 1&.1" 6 6
6 6 6 66 6 0.0021 &/200.00
6 6 60.002& 6&/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso . c 3cm4 a 3cm42#.!! 21.#! 6 6
6 6 6 66 6 0.002&0"85# &/200.006 6 60.000##27!2 61/10#.276 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso 8 c 3cm4 a 3cm4!&.00 28.50 6 6
6 6 6 66 6 0.002##882& &/200.006 6 0.000!#25&1 "0#.886 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.00
6 6 6 6
&aso / c 3cm4 a 3cm4&2.7" !7.2" 6 6
6 6 6 66 6 0.0027&8&!8 &/200.00
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1
- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s#
s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1
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6 6 0.00085072# 1/"81.2#6 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso 10 c 3cm4 a 3cm4#1.!! &!.7! 6 6
6 6 6 66 6 0.002"0""52 &/200.006 6 0.0012&7"#! 2/&5!.#16 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
&aso 11 c - # c 3cm4 a 3cm470.00 #1.00 6 6
6 6 6 66 6 0.002"# &/200.006 6 0.001# !/000.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
Dia!rama de interacción C> = 0.50
> P>ton m ton
1 0.00 61#!.202 !5.2" 0.00! .#2 27.88& #0.#5 #0.2&# #&.87 "1.717 #8.#! 51."7" 77."# 18".70
- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1- s2 = A s2 < s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
Bs+ s+ 3 ;cm24- c1 = t < b < ''c
- c2 = 9a6t < b' < ''c- s1 = A s1 < s1-
s2 = A
s2<
s2- s! = A s! < s!- s& = A s&< s&- s# = A s# < s# s = A s < s
&00
#00
700
"00800
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8 78.25 2"8.#05 #5.80 !82.50
10 &8.71 &"&.8811 !!."2 ##5.8!12 0.00 "0&.00
Pu = !".00 tonu = 17.00 ton muy = 11.00 ton m
1&0.00 ton2!0.00 ton"82.2! ton
5".52 tonPu = !".00 ton
0.!8 o
Revisión por cortante
-ortante Flt+mo Gu
Gu = #.00 on Gu ma =Gu = #/000.00 Gu ma = 8&/00&.25
-ortante que res+ste el concreto Gc>
Gc> = s+ p H 0.01#Gc> =
p = 0.01127 = ##.00 cm
C> = 0.80Gc> = 1#/8"!."0
Cactor que a ecta el Gc>
Gc> = Gc>0.8 H = 160.000&9h6"00 H 1.0 s+ h I "00 mm
h = 700.00 mm
P> = 1 ; 31;P > 1;P >y 6 1;P>04
P> =P>y =P>0 =
P> =
Pu;P> =
2 C> b $c1;2 en el caso e c
C> b 90.2 20p $c1;2
0.# C> b $c1;2 s+ p 0.01#
0 10 20
62006100
0
100
200
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160.000&9h6"00 = 1.0& = 1.00
-omparac+,n Gu .s. Gc>
Gc> = 1#/8"!."0
Gu = #/000.00
>e uerEo trans ersal propuesto
con ars ( !b = 0.5# cm
ramas = &A = 2.8# cm2
s requer+ a por tens+on +a onal
s =J = 50.00 K
Gs> = Gu 6 Gc>Gs> = 0.00
s = s ma perm
s ma perm
s ma p = 0.#
s ma p = 0.2#
#7/002.87Gu = #/000.00
s ma p = 0.# = 2".#0 cm
s e +seLo
r+ e s = 2".#0 cm
M ma p para columnas
M1 = 8#0 b lon ;sqr9 y = !!.!1 cmM2 = &8 b estr+bo = ."2 cm
M! = b;2 = !0.00 cm
r+ e M = 2".#0 cmusar M = 20.00 cm
C> A y 9senJ cosJ ; Gs>
s+ Gc> H Gu N 1.# C> b $c1;2
s+ Gu I 1.# C> b $c1;2
1.# C> b $c1;2 =
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>e uerEo al centro el claro
O(!)20 & ramas
>e +s+on el re uerEo trans ersal propuesto:
A = 2.8# cm2A m+n =A m+n = 1.21 cm2 o
a separac+,n el re uerEo trans ersal en los e tremos e la columna se re uce a la m+ta
on +tu ’ en los e tremos e la columna en la cual hay que re uc+r la separac+,n el re
'1 = b col = 70.00 cm
'2 = h col ; 7 = 10.00 cm'! = 700 mm = 70.00 cm
' = 70.00 cm
0.! $c1;2 b s ; y
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17.7" cm
!2.!# cm
61"0/227.00 = 0.00
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6 6 0.00 6!0.00 0.006 6 0.00 6!0.00 0.006 6 0.00 6!0.00 0.00
0.01"175!"8 &/200.00 7!/8&0.00 2#.00 1/#57/000.00Pn 3 4 = 0.00 n 3
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Bs C 3 4 b 3cm46 6 61&&/#00.00 622.52 !/!11/.!!6 6 0.00 0.00 0.006 6 67!/8&0.00 62#.00 1/#57/000.00
6 6 &2/#&7.00 0.00 0.006 6 0.00 6!0.00 0.006 6 0.00 6!0.00 0.006 6 0.00 6!0.00 0.00
0.0075 &/200.00 7!/8&0.00 2#.00 1/#57/000.00Pn 3 4 = 101/5#&.00 n 3
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6 6 618/0&&.07 0.00 0.006 6 0.00 6!0.00 0.006 6 0.00 6!0.00 0.006 6 0.00 6!0.00 0.00
0.00087"188 1/"!&.!8 27/!72.#0 2#.00 7#5/072.#0
Pn 3 4 = &2#/&&1.#7 n 3
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olumnas
!0 &0 #0 70 "0 80
R ton m
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.
erEo trans ersal.
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para tomar mas lechos e acero
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-alculo el acero e re uerEo lon +tu +nal :Gar+llas t+po 1 Gar+llas t+po 2
( Gars. & ( Gars.12 7
Rrea e acero propuestaAs = .70!7"!1
! ars el ( 8.##0788"12 ars el ( 10.1!&1&57! ars el ( 1#.20122&&
S Gar. 3+n;84 S Gar. 3+n;84
3cm24
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Gar+llas t+po !( Gars. 0
0
&0 8 202 cas+&0 10 !17!2 10 2#!20 12 228
S Gar. 3+n;84
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Diseño de trabe
Datos: Para que A’s fuya:b = 70.00 3cm4b' = 0.00 3cm4 17.7"t = 70.00 3cm4
h = 70.00 3cm4 Para que se presente la alla balancea = ##.00 3cm4#.00 3cm4 !2.!#!0.00 3cm40.00 3cm40.00 3cm40.00 3cm4 =
’ c = 2#0.00 $ c = 200.00
0.8# % c = 1"0.00As = 11.&0 & ars ( 7
11.&0 & ars ( 72.#! 2 ars ( &0.000.000.00
y = &/200.00
>e +s+,n por fe +,n
u = 5.0#u = 50#000.00
&aso Flexión 'ura c 3cm4 a 3cm4#."& &.88 6 6
6 6 6 66 6 0.000!8&5 "75."56 6 60.01275072 6&/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 0.00! &/200.006 6 6 6
C> = 0.50
1 =
2 =
! = &aso 1 >es+stenc+a a tens+,n pura:& =
# =3 m;cm243 m;cm24 &aso 12 >es+stenc+a a compres+,n pu
? 1 =3 m;cm243cm24
As1 = 3cm24As2 = 3cm24As! = 3cm24As& = 3cm24As# = 3cm24
3 m;cm24
ton
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> = 2#.08u = 5.0#
>e +s+,n por cortante
Gu = #/"50.00
p = 0.00"0&
= !0.00 cmGc> = s+ p H 0.01#Gc> =
C> = 0.80Gc> = 7/5!8."0
Gc> = Gc>0.8 H = 160.000&9h6"00 H 1.0 s+ h I "00 mm
h = 700.00 mm160.000&9h6"00 = 1.0&
= 1.00Gc> = 7/5!8."0
>e uerEo trans ersal propuesto:con ars ( !
b = 0.5# cmramas = 2
A = 1.&! cm2
s requer+ a:s =J = 50.00 K
Gs> = Gu 6 Gc>Gs> = 0.00
s = s ma perm
s ma perm: s1 = + a ; & = 1!."# cms2 = 8 b = 1#.2& cm
s! = 2& b estr+bo = 22.87 cms& = !00mm = !0.00 cm
r+ e s = 1!."# cmusar s = 20.00 cm
ton b $c1;2 s+ p 0.01#
C> A y 9senJ cosJ ; Gs>
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>e +s+on el re uerEo trans ersal propuesto:A m+n =A m+n = 1.21 cm2 o
Ontonces usar:O (!)20 en los e tremos
O (!)2" al centro el claro
0.! $c1;2 b s ; y
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3cm4
a:
3cm4
6107/!87.000.00
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