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Viga con acero a compresion Propiedades de la seccion b 15in := fy 60ksi := ϕest 3 8 in 0.952 cm = := h 22.5in := fc 4000psi := rec 4cm := d h 6cm - 51.15 cm = := Mu 584kip ft := Mn Mu 0.9 := d1 4in := Es 29000ksi := ξy fy Es 2.069 10 3 - × = :=

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### Transcript of Mathcad - Viga Con Acero a Compresion - Copy - 1

Viga con acero a compresion

Propiedades de la seccion

b 15in:= fy 60ksi:= ϕest3

8in 0.952 cm⋅=:=

h 22.5in:= fc 4000psi:=rec 4cm:=

d h 6cm− 51.15 cm⋅=:= Mu 584kip ft⋅:=

MnMu

0.9:=

d1 4in:=Es 29000ksi:=

ξyfy

Es2.069 10

3−×=:=

β1 0.85 fc 4000.001psi<if

0.850.05 fc 4000psi−( )⋅

1000psi−

4000psi fc< 8000psi<if

0.65 fc 7999.99psi>if

0.85=:=

fyfy

psi6 10

4×=:= ρb0.85 β1⋅ fc⋅

fy

87000

87000 fy+

⋅ 0.029=:=

ρmax 0.75ρb 0.021=:= usando el % de ρb % 1:=

ρ % ρmax⋅ 0.021=:= As1 ρ b⋅ d⋅ 6.458 in2⋅=:=

Determinacion momento x acero en tensionresitencia de seccion simplemente reforzada

Mn1 0.9 ρ⋅ b⋅ fy⋅ d2⋅ 1

0.59 ρ⋅ fy⋅( )

fc−

⋅ 474.508 kip ft⋅⋅=:=

Mn2 Mn Mn1−+ 174.381 kip ft⋅⋅=:=

Revision del acero a compresion "fluencia"

aAs1 fy⋅

0.85 fc⋅ b⋅7.598 in⋅=:=

ca

β18.939 in⋅=:=

ξscc d1−

c0.003⋅ 0.00166=:= 0.00166 0.00207< No. O. K

fsc fy ξsc 0.00207>if

ξsc

0.00207

fy⋅ otherwise

48.044 ksi⋅=:=

Area de acero requerida A's

AscMn2

fsc d d1−( )⋅17.413 cm

2⋅=:=

Area de acero requerida a tension As.t

Ast As1 Asc+ 59.078 cm2⋅=:=

Numero de barras a tension "seleccion"

Tension

N3Ast

.713cm2

82.859=:= N4Ast

1.27cm2

46.518=:=

N5Ast

1.98cm2

29.838=:= N6Ast

2.85cm2

20.729=:=

N7Ast

3.88cm2

15.226=:= N8Ast

5.07cm2

11.653=:=

Usar #3 db7

8in:= n 15:= As 0.25 π⋅ db( )

2⋅ n⋅ 58.192 cm2⋅=:=

As max permisible del acero a tension

Asmax 0.75 ρb⋅ b⋅ d⋅ Asc+ 59.078 cm2⋅=:=

Determinacion de espaciamiento de acero longitudina l

smin max db 25mm, ( ) 2.5 cm⋅=:=

sb 2 rec ϕest+( )⋅− db+[ ]

n2.028 cm⋅=:=

fs2

3420⋅ 280=:= Cc 50:=

smax1 380280

fs

⋅ 2.5Cc− 255=:= smax1 smax1 mm⋅ 0.255 m=:=

smax2 300280

fs

⋅ 300=:= smax2 smax2 mm⋅ 0.3 m=:=

smax smax1 smax1 smax2<if

smax2 otherwise

25.5 cm⋅=:=

Compresion

N3Asc

.713cm2

24.422=:= N4Asc

1.27cm2

13.711=:=

N5Asc

1.98cm2

8.794=:= N6Asc

2.85cm2

6.11=:=

N7Asc

3.88cm2

4.488=:= N8Asc

5.07cm2

3.434=:=

Usar #3 db8

8in:= n 1:= As 0.25 π⋅ db( )

2⋅ n⋅ 5.067 cm2⋅=:=

Determinacion de espaciamiento de acero longitudina l a compresion

smin max db 25mm, ( ) 2.54 cm⋅=:=

sb 2 rec ϕest+( )⋅− db+[ ]

n30.735 cm⋅=:=

fs2

3420⋅ 280=:= Cc 50:=

smax1 380280

fs

⋅ 2.5Cc− 255=:= smax1 smax1 mm⋅ 0.255 m=:=

smax2 300280

fs

⋅ 300=:= smax2 smax2 mm⋅ 0.3 m=:=

smax smax1 smax1 smax2<if

smax2 otherwise

25.5 cm⋅=:=

Verificacion de la capacidad a flexion