Diseño de Columnas

IV. DISEÑO DE COLUMNA DE CONCRETO ARMADO 4.1. METRADO DE CARGAS CARGAS PARA LA COLUMNA COLUMNA 3-8 Coclumna :

0.60 m x 0.60 m

Viga

0.25 m x 0.50 m

:

CORTE DE LA COLUMNA COLUMNA C-3

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4.1.1. Metrado de Cargas para Cuarto Piso A. Metrado de Carga Muerta (D) ELEMENTOS Peso de la Viga 109 Peso de la Viga 110 Peso de la Viga 107 Peso de la Viga 112 Peso de la columana C-3 Peso de la losa aligerada Peso del muro Peso de acabado de cierlo raso Peso de piso terminado

ANCHO (m) 0.25 0.25 0.25 0.25 0.60 5.75 6.00 6.00 6.00

ESPESOR PESO ESPECIFICO (m) LARGO (m) (Tn/m2 Ó Tn/m3) 0.50 3.20 2.400 0.50 3.20 2.400 0.50 2.70 2.400 0.50 2.70 2.400 0.60 3.20 2.400 -6.75 0.350 -7.00 0.150 -7.00 0.020 -7.00 0.100

SUBTOTAL (Tn) 0.960 0.960 0.810 0.810 2.765 13.584 6.300 0.840 4.200

31.229 B. Metrado de la sobrecarga (L) ELEMENTOS

ANCHO (m)

Sobre carga

6.00

LARGO (m) 7.00

S=

26.98

PESO ESPECIFICO (Tn/m2 Ó Tn/m3)

TOTAL (Tn)

0.200

8.400

C. Carga Sismica Tn

4.1.2. Metrado de Cargas para Tercer Piso A. Metrado de Carga Muerta (D) ELEMENTOS Peso de la Viga 109 Peso de la Viga 110 Peso de la Viga 107 Peso de la Viga 112 Peso de la columana C-3 Peso de la losa aligerada Peso del muro Peso de acabado de cierlo raso Peso de piso terminado

ANCHO (m) 0.25 0.25 0.25 0.25 0.60 5.75 6.00 6.00 6.00

ESPESOR PESO ESPECIFICO (m) LARGO (m) (Tn/m2 Ó Tn/m3) 0.50 3.20 2.400 0.50 3.20 2.400 0.50 2.70 2.400 0.50 2.70 2.400 0.60 3.20 2.400 -6.75 0.350 -7.00 0.150 -7.00 0.020 -7.00 0.100

SUBTOTAL (Tn) 0.960 0.960 0.810 0.810 2.765 13.584 6.300 0.840 4.200

31.229 B. Metrado de la Sobrecarga (L)

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C. Carga Sismica S=

21.72

Tn

4.1.3. Metrado de Cargas para Segundo Piso A. Metrado de Carga Muerta (D) ELEMENTOS Peso de la Viga 109 Peso de la Viga 110 Peso de la Viga 107 Peso de la Viga 112 Peso de la columana C-3 Peso de la losa aligerada Peso del muro Peso de acabado de cierlo raso Peso de piso terminado

ANCHO (m) 0.25 0.25 0.25 0.25 0.60 5.75 6.00 6.00 6.00

ESPESOR PESO ESPECIFICO (m) LARGO (m) (Tn/m2 Ó Tn/m3) 0.50 3.20 2.400 0.50 3.20 2.400 0.50 2.70 2.400 0.50 2.70 2.400 0.60 3.20 2.400 -6.75 0.350 -7.00 0.150 -7.00 0.020 -7.00 0.100

SUBTOTAL (Tn) 0.960 0.960 0.810 0.810 2.765 13.584 6.300 0.840 4.200

31.229 B. Metrado de la Sobrecarga (L) ELEMENTOS

ANCHO (m)

Sobre carga

6.00

LARGO (m) 7.00

S=

14.31

PESO ESPECIFICO (Tn/m2 Ó Tn/m3)

TOTAL (Tn)

0.500

21.000

C. Carga Sismica Tn

4.1.4. Metrado de Cargas para Primer Piso A. Metrado deCarga Muerta (D) ELEMENTOS Peso de la Viga 109 Peso de la Viga 110 Peso de la Viga 107 Peso de la Viga 112 Peso de la losa aligerada Peso del muro Peso de acabado de cierlo raso Peso de piso terminado

ANCHO (m) 0.25 0.25 0.25 0.25 5.75 6.00 6.00 6.00

ESPESOR PESO ESPECIFICO (m) LARGO (m) (Tn/m2 Ó Tn/m3) 0.50 3.20 2.400 0.50 3.20 2.400 0.50 2.70 2.400 0.50 2.70 2.400 -6.75 0.350 -7.00 0.150 -7.00 0.020 -7.00 0.100

SUBTOTAL (Tn) 0.960 0.960 0.810 0.810 13.584 6.300 0.840 4.200

28.464

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B. Metrado de la Sobrecarga (L) ELEMENTOS

ANCHO (m)

Sobre carga

6.00

LARGO (m) 7.00

S=

7.25

C. Carga Sismica Tn

4.1.5. Total de Cargas para la Columna 3-8 Total de carga muerta (PD) (PD) =

122.152 Tn

Total de carga viva (PL)

=

71.400

Tn

Total de Carga Sismica

=

70.260

Tn

4.2. Datos para el Diseño de Columna 3 -8   DATOS b=t=

60

Cm

f´c =

210

Kg/cm2

fy =

4200

Kg/cm2

PESO ESPECIFICO (Tn/m2 Ó Tn/m3)

TOTAL (Tn)

0.500

21.000

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4.3. Determinación de Carga Ultima u = 1.5D + 1.8L -------(1) Pu1 =

311.748

U = 0.75(1.5D + 1.8L +1.25S)---------(2)

Tn

Pu2 =

4.4. Determinación de Momentos Ultimos A) Momento de Carga Muerta Muerta (DMD) MD8 =

13.35

Tn. m

MD3 =

7.22

Tn. m

Mmáx(D) =

13.35

Tn. m

B) Momento de Carga Viva (DML) MD8 =

6.47

Tn. m

MD3 =

6.03

Tn. m

Mmáx(L) =

6.47

Tn. m

C) Momento de Sismo MD8 =

7.13

Tn. m

MD3 =

49.93

Tn. m

Mmáx(S) =

49.93

Tn. m

299.680 Tn

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D) Determinación del Mu u = 1.5D + 1.8L -------(1)

U = 0.75(1.5D + 1.8L +1.25S)---------(2)

Mu8 =

31.671

Tn. m

Mu8 =

Mu3 =

21.684

Tn. m

Mu3 =

U = 0.75(1.5D + 1.8L )---M2b =

16.263

M2s=

30.438

Tn.m

63.072 Tn.m 63.072

Tn.m

Tn. m

4.5. Determinación del Factor ( ɣ) ɣ=

t - d´- dc t

=

60 - 6 - 6 60

=

0.80

=

7.7

4.6. Determinacion de Factor de Logitud Efectiva 4.6.1. Calculo de factor de Resisistencia Rotacional ( ᴪ7) ᴪ=

(Ec *Ic/Lc) (Eg *Ig/Lg)

ᴪ8 =

(60 * 60^3)/(12*325) (35 * 50^3)/(12*700)

ᴪ3 =

0.00

4.6.2. Estimacion de Valor de k Apartir de la Monograma de Jackson y Moreland Moreland

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K= 1.615 4.6.3. Determinación de la Longitud Efectiva Lu =

375

ɭe =

K * lu

Cm =

1.615 * 375 =

605.625

4.7. Determinación de Grado de Esbeltes de la Columna E =

K * lu r

Donde:

=

 

Ic =

60 * 60^3 60^3 12

=

Ac =

60*60

=

=

E =

1080 108000 000 0 Cm Cm4 4

3600

Cm2

  1080000 3600 r=

17.321

Cm

605.625 17.321

=

34.966

>

22

Evaluamos E 34.966

Entoces la columna es esbelta consideramos el Mu el mayor mayor

Cm

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a). Calculo de βd

 =

 =

   .    .    .  .  

  . ∗. ∗. .

0.632

βd =

b). Calculo de EI

EI = EI =

  .∗ .∗ ∗ + 

  .4 .4 ∗   ∗ (

EI =

 ∗ ∗ ) 

 + . . 5.75E+10 Kg.cm2

c). Calculo de Pc

   = () Pc =  Pc  Pc =

π ∗ 5.75 5.75 ∗ 10 (605.625) 1548.038 Tn

 = δns1 =

   .

−. ∗9. ∗9. 1.367

4.9. Determinacion del Factor de Magnificación del Momento Lateral (U=0.75 (1.5D + 1.8L +1.25S)

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1.348

δns2 =

4.10. Determinación del Momento Momento Ultimo de Diseño Muc =

δns1 * Mu1 + δns2 * Mu2

Muc =

1.367 * 16.263 + 1.348 * 63.072

Mu c =

107.249

Tn. m

4.11. Solicitaciones de Finales deDiseño (S.F.D) Mu c =

107.249

Tn. m

Pu =

299.680

Tn

4.12. Determinacion de Excentrecidad Muc e = Pu e =

107.249 299.680

=

0.358

=

0.60

m

4.13. Determinacion del factor e/t e/t =

0.358 0.6

4.14. Determinación de los Valores de K y K e/t K=

Pu f'c * b * t

K=

0.40

K e/t =

Pu * e

=

299.680 * 10^3 210 * 60 * 60

299.680 * 1000 * 0.358 * 100

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Luego

ρc =

=

0.050 23.529

=

0.00213

0.01

≤

ρc

≤

0.08

ρc =

0.01

ρtm

m

4.16. Determinación y Selección de Area de Acero Longitudinal Ast =

ρc * Ac

Ast =

0.01*60*60

=

36.00

cm2

Usaremos el acero longitudinal para la columna columna 3-8 4 Ø 1'' + 8 Ø 5/8''

Ast =

36.40

cm2

Seccion de la columna 3-7

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4.18. Diseño por fuerza cortante 4.18.1. Recistencia de concreto a la l a fuerza cortante Ѵ = .   ′  b*d Ѵc = 0.50 0.50 210 210 * 60 60 * 54 Ѵc =

23.476

Tn Ø=

ØVc =

ØѴc

ØV c =

0.85 * 23.47

=

19.955

ØVc

<

Vu

0.85

Tn

Evaluacion

19.955

24.936 Nesita estribos

4.18.2. Resistencia de acero de la l a fuerza cortante Ѵ = .   ′  b*d Ѵ = 2.1 2.1 210 210 * 60 * 54 Ѵs =

98.599

ØVs =

Vu - ØVc

ØVs =

Evaluacion

Tn

18.074 - 19.955

=

4.981

Tn

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4.18.4. Determinacion del espaciamiento

S=

b/2 = b/2 = 10

60/2 = 60/2 =

30 30

cm cm

10

cm

cm S=

4.18.5. Deerminacion de espaciamiento por confinamiento b Sconf. =

=

60

cm

16ØL =

16*1.587 =

25.392

cm

48Øe =

48*0.953 =

45.744

cm

Sconf. =

25

cm

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4.19. Croquis del diseño de la columna 3-8

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