DISEÑO DE ZAPATAS AISLADA SIMETRICA EN MUROS PORTANTES

DATOS GENERALES

Area Tributaria : A trib = 25.50 M2

Longitud Tributaria ( X ) : L trib ( X ) = 6.00 Mts.

Longitud Tributaria ( Y ) : L trib ( Y ) = 4.25 Mts.

Atura del Muro : H = 0.00 Mts.

Espesor del Muro : t = 0.00 Mts.

Ancho de Sobrecimiento : a sobrc. = 0.00 Mts.

Atura del Sobrecimiento : H s/c = 0.00 Mts.

Altura de Escavacion : H exc. = 1.00 Mts.

Ancho de Viga ( X ) : A vig. ( X ) = 0.35 Mts.

Altura de Viga ( X ) : H vig. ( X ) = 0.55 Mts.

Ancho de Viga ( Y ) : A vig. ( Y ) = 0.45 Mts.

Altura de Viga ( Y ) : H vig. ( Y ) = 0.35 Mts.

Ancho de Columna : a col. = 0.45 Mts.

Largo o Espesor de Columna : b col. = 0.35 Mts.

Altura Total de Columna : H total. col = 10.60 Mts.

Esfuerzo Admisible del Terreno : τ Adm. Terr. = 3.00 Kg / Cm2.

Peso Especifico del Muro : γ mur = 0.00 Kg / M3.

Peso Especifico del Concr. Zap. : γ concr. Zap. = 2400.00 Kg / M3.

Peso Especifico del Concr. Sobrec. : γ concr Sobrec. = 0.00 Kg / M3.

Peso Especifico del Concr. Vig. : γ concr. Vig. = 2400.00 Kg / M3.

Peso Especifico del Concr. Col. : γ concr. Col. = 2400.00 Kg / M3.

Peso Especifico del Terreno : γ terr. = 1900.00 Kg / M3.

Trabajamos Para una Altura de 1 Mts Lineal B = 1.00 Mts.Peso del Aligerado : P alig. = 0.30 Ton / M3.

Peso del Acabado : P acab. = 0.10 Ton / M3.

Peso del Tabique : P tab. = 0.15 Ton / M3.

Peso del Tabique en Azotea : P tab. Azot = 0.05 Ton / M3.

Sobrecarga Piso Terminado : S / C pis. Ter. = 0.20 Ton / M2.

Sobrecarga Azotea : S / C azot. = 0.10 Ton / M2.

Resistencia del Concreto : F'c = 210.00 Kg / Cm2.

Resistencia a Fluencia del Acero : Fy = 4200.00 Kg / Cm2.

Numero de Pisos de Techo Alig, : Np = 4.00Numero de Pisos de Muros : Np. Mur. = 0.00Numero de Vigas Uniformes : Nvig. = 4.00Factor de Zona : Z = 1.00Factor de Uso : U = 1.00Nivel de Piso Terminado : N. P. T. = 0.20 Mts.

Nivel de Terreno Natural : N. T. N = 0.00 Mts.

Coeficiente de Carga Muerta : Coef C.M = 1.40Coeficiente de Carga Viva : Coef C.V = 1.70

Coeficiente de Corte : Ǿ Corte = 0.85

Coeficiente de Flexión : Ǿ Flexión = 0.90Porcentaje Estimado de Carga : % Est. Carg. = 0.00 %

Recubriminto : Re = 0.075 Mts.

Estimacio de Diam. Acero 1/2 : Ǿ Acero = 0.0127 Mts.

Ancho de Zapatas : Tzap. = 0.00 Mts.

Largo de Zapata : Szap. = 0.00 Mts.

Altura de Zapata : h zap. = 0.00 Mts.

Calculos del Peso Total

P. Los Alg. Pis. Term. Plo.ali.pt = 42.08 Ton. / Mts.

P. Los Alg. Pis. Azot. Plo.ali.az = 11.48 Ton. / Mts.

Peso del Muro Pm = 0.00 Ton. / Mts.

Peso del Sobrecimiento Ps/c = 0.00 Ton. / Mts.

Peso de la Zapata Pzap. = 0.00 Ton. / Mts.

Peso de la Viga ( X ) Pvig. ( X ) = 11.09 Ton. / Mts.

Peso de la Viga ( Y ) Pvig. ( Y ) = 6.43 Ton. / Mts.

Peso del Columna Pcol. = 4.01 Ton. / Mts.

Peso SC piso term. Ps/c pt = 15.30 Ton. / Mts.

Peso SC azotea Ps/c az = 2.55 Ton. / Mts.

Peso Parcial Pparc. = 92.92 Ton. / Mts.

Peso Est. del Cimiento Pes.C = 0.00 Ton. / Mts.

Peso Total Wtotal = 92.92 Ton. / Mts.

Calculo de Cargas

Carga Muerta : CM : 75.07 Ton. / Mts.

Carga Viva : CV : 17.85 Ton. / Mts.

Calculo del Esfuerzo Neto

Peso Especifico Promedio γ prom= 2150 Kg / M3.

Esfuerzo Neto τ neto = 27.22 Ton. / M2.

Calculo del Area de Zapata

Area de la Zapata A'zap. = 3.41 M2.

A'zap = 1.85 X

Dimensiones de Zapata az = 1.85 Mts.

Ancho de Zapata T = 1.90 Mts.

Largo de Zapata S = 1.80 Mts.

Ancho de Zapata T = 1.90 Mts.

Largo de Zapata S = 1.80 Mts.

Area Real de Zapata Azap. = 3.42 M2.

Azap = 1.90 XLongitud de Volteo Lv1 = Lv2

Lv1 = 0.73 Mts.

Lv2 = 0.73 Mts. Ok

Lv = 0.73 Mts.

Dimensionamiento de la Altura de la Zapata

Punzonamiento

Carga Repartida Factorizada : Pu = 135.44 Ton .

Carga Repartida Factorizada : qu = 39.60 Ton / M2.

Vu = Pu – qu * m * n

: Bc = 1.29

Bc < = 2

: K = 130.57

+ d - Cte. = 0561.87 240.59 129.21

Vu = ( Pu – qu * ( a + b ) ) – ( qu * ( a + b )) * d - qu * d 2

Bc = a max. col / b min. col

V’c = ( 1.06 * ( F’c ) 0.5 * bo * d ) * 10

K = Ǿ * 1.06 * ( F’c ) 0.5 * 10

( 4 * k + qu ) * d2 + ( ( a + b ) * ( 2 * k + qu ) ) * d – ( Pu – qu * ( a * b ) ) = 0

d2

: d = 0.31 Mts.

Calculo de H zap.

: H zap. = 0.39 Mts.

Asumir : H zap. = 0.50 Mts. Ok

Verificacion por Corte

a’ = Lv1 – d : a' = 0.41 Mts.

Vud = qu * B * a’ : Vud = 16.39 Ton.

: V'ud = 20.31 Ton.

Vud < = Ǿ Vn 16.39 < = 20.31 Ok

Diseño por Flexión

Momento Maximo : M max. = 10.41 Ton - Mts.

As = Mmax. / ( Ǿ * Fy * ( d – a / 2) ) As1 = 9.84

a = ( As * Fy ) / ( 0.85 * F’c * B ) a1 = 0.023 Mts.

As2 = 9.19

a2 = 0.022 Mts.

As3 = 9.17

a3 = 0.022 Mts.

As4 = 9.17

a4 = 0.022 Mts.

Area de Acero : a = 0.022 Mts.As = Mmax. / ( Ǿ * Fy * ( d – a / 2) )

Vud < = Ǿ * 0.53 * ( F’c ) 0.5 * B * d

Cms2

Cms2

Cms2

Cms2

: As = 9.17

Espaciamiento del Acero

1.27

Estimacio de Diam. Acero 1/2 : = 0.0127 Mts.

: S' = 0.14 Mts.

Asumir S' = 0.15

1.00 1/2 @ 0.15

Area de AceroMinimo

: As min = 9.00

1.27

Estimacio de Diam. Acero 1/2 : = 0.0127 Mts.

: S' = 0.14 Mts.

Asumir S' = 0.15

1.00 1/2 @ 0.15

As > = As min9.17 > = 9.00 Ok

Diseño Según Libro ACI

Diseño por Flexión T = 1.90 Mts.

Para B = S = 1.80 Mts.

Momento Maximo : M max. = 18.73 Ton - Mts.

As = Mmax. / ( Ǿ * Fy * ( d – a / 2) ) As1 = 17.70

a = ( As * Fy ) / ( 0.85 * F’c * B ) a1 = 0.023 Mts.

Cms2. / Mts.

A Ǿ acer. =

Ǿ acero

S' =A Ǿ acero / As

Ǿ

Cms2. / Mts.

A Ǿ acer. =

Ǿ acero

S' =A Ǿ acero / As

Ǿ

Cms2

As2 = 16.55

a2 = 0.022 Mts.

As3 = 16.51

a3 = 0.022 Mts.

As4 = 16.51

a4 = 0.022 Mts.

Area de Acero : a = 0.022 Mts.As = Mmax. / ( Ǿ * Fy * ( d – a / 2) )

: As = 16.51

Area de AceroMinimo

: As min = 16.20

As > = As min16.51 > = 16.20 Ok

Espaciamiento del Acero

En Direccion " S "

1.27

Estimacio de Diam. Acero 1/2 : = 0.0127 Mts.

: n = 13.03

n = 13.00

S' = ( S - 2 * Re * - Ǿacero ) / ( n - 1 )

S' = 0.14 Mts.

S' = 0.14

13.00 1/2 @ 0.14

Area de AceroMinimo

: As min = 16.20

1.27

Cms2

Cms2

Cms2

Cms2. / Mts.

Cms2. / Mts.

A Ǿ acer. =

Ǿ acero

n =As / A Ǿ acero

Ǿ

Cms2. / Mts.

A Ǿ acer. =

Estimacio de Diam. Acero 1/2 : = 0.0127 Mts.

: n = 12.79

n = 13.00

S' = ( S - 2 * Re * - Ǿacero ) / ( n - 1 )

S' = 0.14 Mts.

S' = 0.15

13.00 1/2 @ 0.15Espaciamiento del Acero

En Direccion " T "Para B = T = 1.90 Mts.

: As T' = 17.42

1.27

Estimacio de Diam. Acero 1/2 : = 0.0127 Mts.

: n = 13.75

n = 14.00

S' = ( T - 2 * Re * - Ǿacero ) / ( n - 1 )

S' = 0.13 Mts.

S' = 0.13

14.00 1/2 @ 0.13

Area de AceroMinimo

: As min = 17.10

1.27

Estimacio de Diam. Acero 1/2 : = 0.0127 Mts.

: n = 13.50

n = 14.00

S' = ( T - 2 * Re * - Ǿacero ) / ( n - 1 )

S' = 0.13 Mts.

S' = 0.15

Ǿ acero

n =As / A Ǿ acero

Ǿ

Cms2. / Mts.

A Ǿ acer. =

Ǿ acero

n =As / A Ǿ acero

Ǿ

Cms2. / Mts.

A Ǿ acer. =

Ǿ acero

n =As / A Ǿ acero

14.00 1/2 @ 0.15Ǿ

γǾτ

25.5Ok τ

0.15

Longitud Mayor de Columna

Longitud Menor de Columna

1800.00

2300.00

2300.00

2400.00

2400.00

1600.00

1.00

0.30

0.10

0.15

0.05

0.20

0.10

10.00

Re = 7.50 Cms.

Ǿ Ace = 1.27 Cms.

0

0

0

P lo. ali.( Piso Term.) = ( Palig. + Pacab. + Ptab.de p.ter) * Atrib. * B * ( Np – 1 )P lo. ali. ( Azot.) = ( Palig. + Pacab. + Ptab de azot.) * Atrib. * B Pm = t * H * γ mur. * B * Np. Mur.Ps/c = a sobrec. * Hs/c * γ concr.sobrec * BPzap. = T * S * γ concr. * Hzap.Pvigas (x ) = Avig (x). * Hvig.(x) * γ concr.vig * Ltrib (x) * NvPvigas (Y ) = Avig (y). * Hvig.(y) * γ concr.vig * Ltrib (y) * NvPcol = a col * b col * γ concr.col * H total col.Peso S.C. ( Piso Term.) = S.C. pt * Atrib * B * ( Np –1 )Peso S.C. ( Azotea ) = S.C. az * Atrib * BPparcial = P lo. ali.( Piso Term.) + P lo. ali. ( Azot.) + Pm + Ps/c + Pvigas + Pc + Peso S.C. ( Piso Term.) + Peso S.C. ( Azotea )Pest. Cim = %est. * Pparcial

Wpeso total= Pparcial + Pest. cim

C.M. = P lo. ali.( Piso Term.) + P lo. ali. ( Azot.) + Pm + Ps/c + Pvigas + Pc + Pest. cimC.V = Peso S.C. ( Piso Term.) + Peso S.C. ( Azotea )

γ prom. = 0.5 * ( γ conc.zap. + γ suelo )

τ neto = τ adm. – ( γ cim. * Hc. + γ terr * ( Hexc. – Hc. ) + S/C (p.t)

1.85 A z = az * azA zap = Wpeso total / τ neto

az = Az0.5

T1 = az + 0.5 * ( a-b )S1 = az - 0.5 * ( a-b )

1.80 A z = t * s

Lv1 = Lv2Lv1 = 0.5 * ( T1 – a )Lv2 = 0.5 * ( S1 – a )

Lv2 = 0.5 * ( S1 – a )

Pu = 1.5 * CM + 1.8 * CV

qu = Pu / ( Azap.)

m = a + d n = b + dbo = 2 * m + 2 * n

Ok Bc < = 2

Vc = Ǿ * V’c

A zap = T * S

Vu = ( Pu – qu * ( a + b ) ) – ( qu * ( a + b )) * d - qu * d 2

bo = 2 * ( a +b ) + 4 * d 2

Bc = a max. col / b min. col

V’c = ( 1.06 * ( F’c ) 0.5 * bo * d ) * 10

K = Ǿ * 1.06 * ( F’c ) 0.5 * 10

Vc = ( 2 * k * ( a + b ) ) * d + ( 4 * k ) * d2

( 4 * k + qu ) * d2 + ( ( a + b ) * ( 2 * k + qu ) ) * d – ( Pu – qu * ( a * b ) ) = 0

Warnimg

Hz = > 0.50 Mts.

a’ = Lv1 – d

Vud = qu * B * a’Vud < = Ǿ Vn

Vud < = Ǿ Vn

a = ( As * Fy ) / ( 0.85 * F’c * B )

d = ( - b + ( b2 – 4 * a * c ) 0.5 ) / ( 2*a )

Hz = d + Rec. + Ǿ acer. / 2

Vud < = Ǿ * 0.53 * ( F’c ) 0.5 * B * d

M max. = 0.5 * qu * B * Lv2

As = M max. / ( Ǿ * Fy * ( d – a / 2) )

= 1.27 Cms.

OJO

Mts.

Mts.

As min = 0.0018 * B * Hz

= 1.27 Cms.

OJO

Mts.

Mts.

Mts.

a = ( As * Fy ) / ( 0.85 * F’c * B )

Cms2

Ǿ acero

S' = A Ǿ acero / As

Cms2

Ǿ acero

S' = A Ǿ acero / As

M max. = 0.5 * qu * B * Lv2

As = M max. / ( Ǿ * Fy * ( d – a / 2) )

As min = 0.0018 * B * Hz

= 1.27 Cms.

OJO

Mts.

Mts.

As min = 0.0018 * B * Hz

Cms2

Ǿ acero

S' = A Ǿ acero / As

S' = ( S - 2 * Re * - Ǿacerro ) / ( n - 1 )

Cms2

= 1.27 Cms.

OJO

Mts.

Mts.

As T' = As * T / S

= 1.27 Cms.

OJO

Mts.

Mts.

As min = 0.0018 * B * Hz

= 1.27 Cms.

OJO

Mts.

Ǿ acero

S' = A Ǿ acero / As

S' = ( S - 2 * Re * - Ǿacerro ) / ( n - 1 )

Cms2

Ǿ acero

S' = A Ǿ acero / As

S' = ( S - 2 * Re * - Ǿacerro ) / ( n - 1 )

Cms2

Ǿ acero

S' = A Ǿ acero / As

S' = ( S - 2 * Re * - Ǿacerro ) / ( n - 1 )

Mts.

P lo. ali.( Piso Term.) = ( Palig. + Pacab. + Ptab.de p.ter) * Atrib. * B * ( Np – 1 )

Pparcial = P lo. ali.( Piso Term.) + P lo. ali. ( Azot.) + Pm + Ps/c + Pvigas + Pc + Peso S.C. ( Piso Term.) + Peso S.C. ( Azotea )

C.M. = P lo. ali.( Piso Term.) + P lo. ali. ( Azot.) + Pm + Ps/c + Pvigas + Pc + Pest. cim

+ ( ( a + b ) * ( 2 * k + qu ) ) * d – ( Pu – qu * ( a * b ) ) = 0

INTERPOLACION

Datos Generales

Ingrese 1 Valor X1 = 10.00 Mts. Y1 = 100.00 Mts.Ingrese 2 Valor X2 = 20.00 Mts. Y2 = 200.00 Mts.Ingrese el Valor a Encontrar Xn = 15.00 Mts. Yn = 150.00 Mts.

INTERPOLACION

Datos Generales

Ingrese 1 Valor X1 = 1.00 Mts. Y1 = 4.00 Mts.Ingrese 2 Valor X2 = 2.00 Mts. Y2 = 5.00 Mts.Ingrese el Valor a Encontrar Xn = 3.00 Mts. Yn = 6.00 Mts.

DIMENSIONES DEL ACERO PARA REFUERZO DEL CONCRETOδ conc. = ### Kg / ( Mts * Cm2 )

ACERO GRADO 60 F'y = 4200 Kgs. / Cm2.NORMA ASTM A - 615

BARRA DIAMETRO AREA PESO AREA ( Cm2. )N° Pulg. Cms. ( Cm2. ) Kgs. / Mts. 1 2 3 4 5 6 7 8 9

2 1/4 0.64 0.32 0.26 0.32 0.63 0.95 1.27 1.58 1.90 2.22 2.53 2.853 3/8 0.95 0.71 0.58 0.71 1.43 2.14 2.85 3.56 4.28 4.99 5.70 6.414 1/2 1.27 1.27 1.03 1.27 2.53 3.80 5.07 6.33 7.60 8.87 10.13 11.405 5/8 1.59 1.98 1.61 1.98 3.96 5.94 7.92 9.90 11.88 13.86 15.83 17.816 3/4 1.91 2.85 2.32 2.85 5.70 8.55 11.40 14.25 17.10 19.95 22.80 25.658 1 2.54 5.07 4.12 5.07 10.13 15.20 20.27 25.34 30.40 35.47 40.54 45.609 1 1/8 2.86 6.41 5.22 6.41 12.83 19.24 25.65 32.07 38.48 44.89 51.30 57.72

10 1 1/4 3.18 7.92 6.44 7.92 15.83 23.75 31.67 39.59 47.50 55.42 63.34 71.26

Kg / ( Mts * Cm2 )

10

3.177.13

12.6719.7928.5050.6764.1379.17