1

Predimensionamiento De

Columnas, Vigas Y Zapatas Datos: Niveles = 6

Cv = 500 kg/m2

Cm = 300 kg/m2

Cvaz = 100 kg/m2

Cp del suelo = 1.03 kg/cm2

del suelo = 1903 kg/m3

S/C = 500 kg/ m2

E. piso = 0.15 m

Fc = 210 kg/cm2

Fy = 4200 kg/cm2

de columna central y lateral =

de columna esquina = 5/8

1. PREDIMENSIONAMIENTO DE COLUMNAS. COLUMNA 1:

At1 = 5x4.25=21.25 m2

PGp=1.2(300)+1.6(500) =1160kg/m2

PGaz = 1.2 (300)+1.6 (100) = 520 kg/m2

Pt = (5x1160x21.25)+ (520x1x21.25)=134300kg

1 piso:

Asc=(1.1)(134300)(0.25)(210) = 2813.90 cm2= (53.05)2= 55x55 cm

2

2 piso:

Asc=(1.1)(109650)(0.25)(210) = 2297.43 cm2= (47.93)2= 50x50 cm

3 piso:

Asc=(1.1)(85000)(0.25)(210) = 1780.95 cm2=(42.20)2 = 45x45 cm

4 piso:

Asc=(1.1)(60350)(0.3)(210) = 1053.73 cm2= (32.46)2= 35x35 cm

5 piso:

Asc=(1.1)(35700)(0.3)(210) = 623.33cm2= (24.97)2= 25x25 cm

6 piso:

Asc=(1.1)(35700)(0.3)(210) = 623.33cm2= (24.97)2= 25x25 cm

COLUMNA 2:

At =5x2.25=11.25 m2

PGp =1.2(300)+1.6(500 )=1160kg/m2

PGaz = 1.2 (300)+1.6 (100) = 520 kg/m2

Pt = (5x1160x11.25)+ (520x11.25) =71100kg

1 piso:

Asc=(1.25)(71100)(0.25)(210) = 1692.86 cm2= (41.14)2= 45x45 cm

2 piso:

Asc=(1.25)(58050)(0.25)(210) = 1382.14 cm2= (37.18)2= 40x40 cm

3

3 piso:

Asc=(1.8)(45000)(0.25)(210) = 1071.43 cm2= (32.71)2= 35x35 cm

4 piso:

Asc=(1.25)(31950)(0.25)(210) = 760.71 cm2= (27.58)2= 30x30 cm

5 piso:

Asc=(1.25)(18900)(0.25)(210) = 450cm2= (21.21)2= 25x25 cm

6 piso:

Asc=(1.25)(18900)(0.25)(210) = 450cm2= (21.21)2= 25x25 cm

COLUMNA 3:

At=4.25x2.5 =10.625 m2

PGp=1.2(300)+1.6(500) =1160kg/m2

PGaz= 1.2 (300)+1.6 (100) = 520 kg/m2

Pt= (5x1160x10.625)+ (520x10.625) = 67150kg

1 piso:

Asc=(1.25)(67150)(0.25)(210) = 1598.81 cm2= (39.99)2= 40x40 cm

2 piso:

Asc=(1.25)(54825)(0.25)(210) = 1305.36 cm2= (36.13)2= 40x40 cm

3 piso:

Asc=(1.25)(42500)(0.25)(210) = 1011.91 cm2= (31.81)2= 35x35 cm

4

4 piso:

Asc=(1.25)(30175)(0.25)(210) = 718.452 cm2= (26.8)2= 30x30 cm

5 piso:

Asc=(1.25)(17850)(0.25)(210) = 425cm2= (20.6)2= 25x25 cm

6 piso:

Asc=(1.25)(17850)(0.25)(210) = 425cm2= (20.6)2= 25x25 cm

COLUMNA 4:

At=2.25x2.5=5.625 m2

PGp=1.2(300)+1.6(500)=1160kg/m2

PGaz= 1.2 (300)+1.6 (100)= 520 kg/m2

Pt= (5x1160x5.625)+ (520x5.625)=35550kg

1 piso:

Asc=(1.5)(35550)(0.20)(210) = 1269.64 cm2= (35.6)2= 40x40 cm

2 piso:

Asc=(1.5)(29025)(0.20)(210) = 1036.61 cm2= (32.19)2= 35x35 cm

3 piso:

Asc=(1.5)(22500)(0.20)(210) = 803.57 cm2= (28.3)2= 30x30 cm

4 piso:

Asc=(1.5)(15975)(0.20)(210) = 570.54 cm2= (23.9)2= 25x25 cm

5 piso:

Asc=(1.5)(9450)(0.20)(210)= 337.5 cm2= (18.37)2= 25x25 cm

5

6 piso:

Asc=(1.5)(2925)(0.20)(210)= 104.46 cm2= (10.22)2= 25x25 cm

Resumen de datos

6

2. PREDIMENSIONAMIENTO DE VIGAS:

Principales:

P=()(10)= (5)(10)= 0.5

b=()(20)= (5)(20)=0.25

Vp = 50cm x 25cm

Secundaria:

P=()(12)=(4.5)(12)= 0.375= 40

b=()(20)=(4.5)(20)=0.225= 25

Vs =40 cm x 25cm

3. PREDIMENSIONAMIENTO DE ZAPATAS: Zapata N 1

CVT = (5000(5)+100) (21.25) = 55250Kg = 55.25Tn

CMT = (300) (21.25) (6) =38250Kg = 38.25Tn

Peralte efectivo

d = 0.08 * Ac *

0.004 * A * Fy d = 0.08 * 1.905 *

4200

210 0.004 * 1.905 * 4200 d = 44.17 32

Altura de la zapata ser:

hz = d + r + b = 44.17 + 10 +1.588 = 55.758cm = 60cm = 0.6m

7

El peralte efectivo de diseo ser:

d = 60 10 1.588 = 48.41cm = 0.4841m

Esfuerzo neto del terreno

= 1.03 (1002) 1903(. 6) 500 24008(.15) = 6858.2

2= 6.858/2

rea de zapata

Az = .n

Az = (.+.)./ = 13.6342

Lv1 = Lv2

T = S = 13.634 (..

) = 3.692 3.7

S = 3.7m T = 3.7m

LV1 = LV2 = ..

= 1.575

Reaccin ultima

Wnu = (.)(.)+.(.)(.) = . = 9810/2

verificacin de cortante

vc > Vu (0.53) ()d > Wnu(S)(LV d) 0.75(0.53)210(10)(3.70)(0.4841) > 9.81(3.7)(1.575 0.4841) 103.18 > 39.596

8

corte por punzonamiento

m = d + t1 = 0.4841+0.55 = 1.034m

n = d + t2 = 0.4841+0.55 = 1.034m Vu < Vc

Vu = Pdin Wnu (m) (n)

Vu = 134.3 9.81 (1.034)2 = 123.812Tn

bo = 2m + 2n = 4(1.034) = 4.136m

= 0.550.55 = 1

(0.27)(2 + 4

) Vc (0.27)(

+ 2)

1.1

0.75(0.27) 2 + 41210 (10)(4.136)(0.4841) = 352.53

Vc 0.75(0.27) (40)(.4841)4.136 + 2 210 (10)(4.136)(0.4841) = 392.595

0.75 1.1 210 (10)(4.136)(0.4841) = 239.375 Acero

Mu = 2

(1)2

Mu = 9.812

(1.575)2 (3.7) = 45.02

= 45.02 105/

9

rea del acero

As =

(2

) = As=()(0.85)()()

45.021050.9(4200)(48.41

2) = (0.85)(210)(370)4200

50.021056.6045104 = 48.41 0.52

0.52 48.41 + 75.736 = 0 = 48.41 48.412 4(0.5)(75.736) 1 = 48.41 46.81

= . As1= 45.0105

0.9(4200)(48.411.5912

) = . As2= 1.591(0.85)(210)(370)4200 = . As=25.018

Verificacin de acero mnimo

As> As 25.0188>0.0018 (48.41) (370)

25.018>32.241 As = 32.241

Nv = 32.241

2= 16.12 17

S = 3702(2.75)1.588

16= 22.09 0.22

Lv =370 2(7.5) = 355 = 3.55

10

17 @ 0.22

Zapata N 2

CVT = (500(5)+100) (11.25) = 29250Kg = 29.25Tn

CMT = (300) (11.25) (6) =20250Kg = 20.25Tn

Peralte efectivo

d = 0.08 * Ac *

0.004 * A * Fy d = 0.08 * 1.905 *

4200

210 0.004 * 1.905 * 4200 d = 44.17 32

Altura de la zapata ser:

hz = d + r + b= 44.17 + 10 +1.588 = 55.758cm = 60cm = 0.6m

El peralte efectivo de diseo ser:

d = 60 10 1.588 = 48.41cm = 0.4841m

Esfuerzo neto del terreno

= 1.03 (1002) 1903(. 6) 500 24008(.15) = 6858.2

2= 6.858/2

rea de zapata

Az = .n

Az = (.+.)./ = 7.222

11

Lv1 = Lv2

S= Lv2 + t2 Lv2 = S- t2

T= 2 Lv1 + t1 Lv1= 12

2AZ=T2-T (t1-2t2)

2(7.22)= T2-T (0.45-2(0.45))

14.44= T2 + 0.45T

0= T2 + 0.45T -14.44

= 0.45 0.452 4(1)(14.44)2 = 3.585

2S2=AZ-S (t1-2t2)

2S2=7.22-S (0.45-2(0.45)) S = 0.450.4524(2)(7.22)4

= 2.015

Lv2 = 2.015-0.45 = 1.565

Lv1 =..

=1.567

Lv2=Lv1=1.60

S=1.6+ (0.45)=2.05 m

T=2(1.6)+ (0.45)= 3.65 m

Reaccin ultima

Wnu = (.)(.)+.(.)(.)(.) = . = 9570/2

m = d + t1 = 0.4841+0.45 = 0.934m

n = d + t2 = 0.4841+0.45 = 0.934m

12

verificacin de cortante EJE x

vc > Vu (0.75) ()d > Wnu(S)(LV d) 0.75(0.53)210(10)(3.65)(0.4841) > 9.57(3.65)(1.6 0.4841) 101.783 > 38.979 EJE y

(0.75) ()d > Wnu(S)(LV d) 0.75(0.53)210(10)(2.05)(0.4841) > 9.57(2.05)(1.6 0.4841) 57.166 > 21.8923

corte por punzonamiento Vu < Vc

Vu = Pdin Wnu (m) (n)

Vu = 71.58 9.57 (0.934)2 = 63.23 Tn

bo = 2m + 2n = 4(0.934) = 3.736m

= 0.450.45 = 1

(0.27)(2 + 4

) Vc (0.27)(

+ 2)

1.1

13

0.75(0.27) 2 + 41210 (10)(3.736)(0.4841) = 318.44

Vc 0.75(0.27) (30)(0.4841)3.736 + 2 210 (10)(3.736)(0.4841) = 312.46

0.75 1.1 210 (10)(3.736)(0.4841) = 216.225 Acero

Mu =

2(1)2

Mu = 9.572

(1.6)2 (3.65) = 44.71 . = 44.71 105/

rea del acero

As =

(2

) = As=()(0.85)()()

44.711050.9(0.85)(210)(365) = 48.41 a 0.5 a2

0.52 48.41 + 76.25 = 0 = 48.41 48.412 4(0.5)(76.25) 1 = 48.41 46.81

= . As1= 44.711050.9(4200)(48.41(0.51.6)) = .

As2= 1.6(0.85)(210)(365)4200 = . As=24.84

Verificacin de acero mnimo

As> As 24.84>0.0018 (48.41) (365)

14

24.84> 31.811 As =31.81 Nv = 31.81

2= 15.91 16

S = 3652(7.5)1.588

15= 23.22 24 0.24

Lv =205 2(7.5) = 190 cm = 1.9

16 @ 0.24 Ast =

()()

=(31.81)(205)

365= 17.87 cm2

Nv = (17.87)

2= 8.9359

Se= (205)(27.5)(1.588)

8=23.55 cm=0.24 m

Lv=365-(2*7.5)=350=3.5m

9 @ 0.24

Zapata N 3

CVT = (5000(5)+100) = 29.25Tn

CMT = (300) (6) (11.25) = 20.25Tn

Peralte efectivo

d = 0.08 * Ac *

0.004 * A * Fy d = 0.08 * 1.905 *

4200

210 0.004 * 1.905 * 4200 d = 44.17 32

Altura de la zapata ser: hz = d + r + b= 44.17 + 10 +1.588 = 55.758cm = 60cm = 0.6m

15

El peralte efectivo de diseo ser:

d = 60 10 1.588 = 48.41cm = 0.4841m

Esfuerzo neto del terreno

= 1.03 (1002) 1903(. 6) 500 24008(.15) = 6858.2

2= 6.858/2

rea de zapata

Az = .n

Az = (.+.)

./ = 6.8172

Lv1 = Lv2

S = Lv2 + t2 Lv = S t2

T = 2Lv1 + t1 Lv1 = 1

2

2Az = T2 T(t1-2t2)

0 = T2 + 0.40T-13.634

T=0.44(13.634)+0.42

2

T=3.5m

S = 0.4426.817+0.42

4

S = 1.95m

Lv2 = 1.949 0.4 = 1.549

Lv1 = (3.498 0.4)/2 = 1.549

16

Lv2=Lv1=1.55m

S = 1.55 + 0.4 =1.95m

T = 2*1.55 + 0.4 = 3.50m

Reaccin ultima

Wnu = (.)(.)+.(.)

.. = .

verificacin de cortante

Eje X vc > Vu

(0.53) ()d > Wnu(S)(LV d) 0.75(0.53)210(10)(3.5)(0.4841) > 9.839(3.5)(1.55 0.4841) 97.6 > 36.71

Eje Y 0.75(0.53)210(10)(1.95)(0.4841) > 9.839(1.95)(1.55 0.4841) 54.38 > 20.45

verificacin por punzonamiento

m = d + t1 = 0.4841 + 0.4 = 0.884m

n = d + t2 = 0.4841 + 0.4 = 0.884m

V = 67.115 - 9.839(0.884)2 = 59.46Tn

bo = 3(0.884) = 2.652m

= 0.40.4 = 1

17

0.75(0.27) 2 + 41210 (10)(2.652)(. 4841) = 226.04

Vc 0.75(0.27) (30)(.4841)2.802 + 2210 (10)(2.652)(. 4841) = 281.66

0.75 1.1 210 (10)(2.652)(. 4841) = 153.49 rea del acero

As =

(2

) = As=()(0.85)()()

0.9(0.85)() = 0.52

41.371050.9(0.85)(210)(350) = 48.41 0.52

0.52 48.41 + 73.576 = 0 = 48.41 48.412 4(0.5)(73.576) 1 = 48.41 46.81

= . As1= 41.371050.9(4200)(48.410.51.544) = .

As2= 1.544(0.85)(210)(350)4200 = . As = 22.97

Verificacin de acero mnimo

As >Aminimo 22.97 >0.0018 (48.41) (350) 22.97 >30.498 As = 30.498

18

Area del acero longitudinal x

Nv = 30.498

2= 15.249 16

Se = 3502(7.5)1.588

15= 22.23 0.23

Lv = 195 2(7.5) = 180cm = 1.8

16 @ 0.23 rea de acero en la seccin transversal Y

AST=

= 31.84205

365= 17.872

Nv = 16.962

= 8.495 9 Se =

1952(7.5)1.5888

= 22.3 0.23 Lv = 350 2(7.5) = 335cm = 3.5

9 @ 0.23

Zapata N 4

CVT = (500(5)+100) (5.625) = 14625 kg = 14.625Tn

CMT = (300) (5.625) (6) =10125 Kg = 10.125 Tn

Peralte efectivo

d = 0.08 * Ac * 0.004 * A * Fy

d = 0.08 * 1.588 * 4200210 0.004 * 1.588 * 4200

d = 36.82 26.68

Altura de la zapata ser:

19

hz = d + r + b= 36.82 + 10 +1.588 = 48.408cm = 50cm = 0.5m

Por condiciones de diseo la altura de la zapata ser 60 cm

El peralte efectivo de diseo ser:

d = 60 10 1.588 = 48.41cm = 0.4841m

Esfuerzo neto del terreno

= 1.03 (1002) 1903(. 6) 500 24008(.15) = 6858.2

2= 6.858/2

rea de zapata

Az = .n

Az = (.+.)

./ = .P2

Debe cumplir que:

Lv1 = Lv2 S= Lv2 + t2 Lv2 = S- t2

T= Lv1 + t1 Lv1= 1

Az = T2-T (t1-t2)

3.61= T2-T (0.40-0.40)

T=1.9m

Az = S2-S (t1-2t2)

3.61= S2-S (0.40-0.40) S = 1.9 m Lv2=1.9-0.4=1.5 m

20

Reaccin ultima

Wnu = (.)(.)+.(.)(.) = . = 9850/2

m = d + t1 = 0.4841+0.40 = 0.884m

n = d + t2 = 0.4841+0.40 = 0.884m

bo= m+n=1.768 Bc=0.40/0.40 =1

verificacin de cortante

(0.75) ()d > Wnu(S)(LV d) 0.75(0.53)210(10)(1.9)(0.4841) > 9.85(1.9)(1.5 0.4841) 52.98 > 19.01

Corte por punzonamiento Vu < Vc

Vu = Pdin Wnu (m) (n)

Vu = 35.55 9.85 (0.884)2 = 27.85 Tn

(0.27)(2 + 4

) Vc (0.27)(

+ 2)

1.1

0.75(0.27)(2 + 4)210 (10)(1.768)(0.4841) = 150.70 Vc 0.75(0.27) (20)(0.4841)

1.768 + 2 210 (10)(1.768)(0.4841) = 187.77 0.75 1.1 210 (10)(1.768)(0.4841) = 102.325

21

Acero

Mu = 2

(1)2

Mu = 9.852

(1.5)2 (1.9) = 21.05 . = 21.05 105/

rea del acero

As =

(2

) = As=()(0.85)()()

21.051050.9(0.85)(210)(1.90) = 48.41 a 0.5 a2

0.52 48.41 + 68.963 = 0 = 48.41 48.412 4(0.5)(68.963) 1 = 48.41 46.964

= . As1= 21.051050.9(4200)(48.41(0.51.446)) = 11.678 2 As2= 1.446(0.85)(210)(190)4200 = 11.676 2 As=11.678 2

Verificacin de acero mnimo

As> As 11.678>0.0018 (48.41) (190)

11.678> 16.556 As =16.556

22

Nv = 16.556

2= 8.278 9

S = 1902(7.5)1.588

8= 21.67 22 0.22

Lv =190 2(7.5) = 175 cm = 1.75

9 @ 0.22

RESUMEN DE DATOS:

DATOS Z1 Z2 Z3 Z4

hs 0.6m 0.6m 0.6m 0.6m

hz 0.6m 0.6m 0.6m 0.6m

Lv1=Lv2 1.575m 1.6m 1.55m 1.5m

d 0.4841m 0.4841m 0.4841m 0.4841m

Az 13.63m2 7.22m2 6.817m2 3.61m2

S 3.7m 2.05m 1.949m 1.9m

T 3.7m 3.6m 3.498m 1.9m

m 1.034m 0.934m 0.884m 0,884

n 1.034m 0.934m 0.884m 0,884

5/8" 5/8" 5/8" 5/8"

Nv. Long. 17 16 16 9

Sepr. Long. 0,22 0,24 0,23 0,22

Nv. Transv. 17 9 9 9

Sepr. Transv. 0,22 0,24 0,23 0,22