Losa de Cimentacion

Página 1

DISE DISE O DE DE LOS LOSA A DE DE CIM CIMEN ENTA TACI CI N 1 DATOS: Fć Fy S/C= Df= qa =

210 4200 450 90 1.4

Kg/cm2 Kg/cm2 Kg/m2 cm K/cm2

1700 2400 1 217370.651

γs = γcº =

Ks = E=

Kg/m3 Kg/m3 Kg/cm3 Kg/cm2

CUADRO DE CARGAS Columna 1 2 3 4 5 6 7 8

b (cm) 40 40 40 40 40 40 40 40 40

9

t (cm) 40 40 40 40 40 40 40 40 40

PD (t) 45 60 60 60 100 70 60 70 60 585

PL (t) 25 30 30 30 40 30 30 30 30 275

1.4Pd+1.7pL

105500 135000 135000 135000 208000 149000 135000 149000 135000

S/C(kg/cm2) =

P1

450

P3

P2

Ks (kg/cm3) 1.00

γs (kg/m3)= 1700

Df

90

Y A

B

C

1

D

2

20

3

E

F Y

450

5

4

6

X

980

G

H 8

7

450

9

40

60

J

K

L X

20

540

540

60

1160.00

DEFINIR EL METODO A USAR: Asumiendo t =

50

λ =

3 Ks E x T^3

λ =

0.00324

cm 1/4

1,75 / λ

T = Ks = E = E =

50 cm 1 Kg/cm3 15000 (F'C)^1/2 217370.651 Kg/cm2 =

539.87

>

Lc

usamos metodo rigido

Página 2

1 CALCULO DEL AREA DE LA LOSA Lcx= 540 Lcy= 450 Area Losa= 1136800 Lx= 1160.00 Ly= 980.00

cm2 cm cm

2 CALCULO DE LA PRESON NETA

qn=

qa-γs1 x h1- γs2 x h2 - γi x h i -γcº x hcº - s/c

qn=

1.1670

K/cm2

3 CALCULO DE LAS PRESIONES POR DEBAJO DE LOS PUNTOS PERIMETRALES X' =

Pi x X' i Pi

X´= ex= ex= Entonces :

578.84 X´- B/2 -1.16

q =

Pu A Pu= Ix= Ix= Iy= Iy= Mx= Mx= My= My=

donde q = Tabla PUNTOS A B C D E F G H I J K L

Y' =

Pi x Y' i Pi

Y´ = ey= ey=

494.30 Y´- L/2 4.30

cm cm +/-

My X Iy

1.131685433

+/-

-1.174E-05

Pu/A 1.132 1.132 1.132 1.132 1.132 1.132 1.132 1.132 1.132 1.132 1.132 1.132

X cm -580 -290 250 580 -580 580 -580 580 -580 -290 250 580

(My X)/Iy 0.0068 0.0034 -0.0029 -0.0068 0.0068 -0.0068 0.0068 -0.0068 0.0068 0.0034 -0.0029 -0.0068

cm cm Mx Y Ix

+/-

1286500.00 Kg (B x L^3)/12

90981893333 cm4 (L x B^3)/12

1.27473E+11 cm4 Pu x ex 5534941.86 k-cm Pu x ey -1495930 k-cm X

+/-

Y cm 490 490 490 490 245 245 -205 -205 -490 -490 -490 -490

6.08356E-05

Y

(My Y)/Ix 0.030 0.030 0.030 0.030 0.015 0.015 -0.012 -0.012 -0.030 -0.030 -0.030 -0.030

q (K/cm2) 1.160 1.165 1.159 1.155 1.153 1.140 1.126 1.112 1.109 1.105 1.099 1.095

VERIFICACIÓN qn > q qn > q qn > q qn > q qn > q qn > q qn > q qn > q qn > q qn > q qn > q qn > q

4 CALCULO DEL PERALTE DE LA LOSA , VERIFICANDO EL CORTE POR PUNZONAMIENTO En las columnas de mayor carga y de menor desarrollo de superficie de punzonamiento COLUMNA 5

Vu= Pu - q nu x m x n

pu= m =

Vu=

208000 -1.1670 x (40+d)x(40+d)

ØVc = Ø1.1(Fć)^1/2 b o ØVc =

208000 40+d

14.35 x 4 x (40+d) x d

Kg n =

qnu= 40+d 40+d

1.1670

K/cm2

...................1

bo = 2m +2n .....................

40 40

40+d

OK OK OK OK OK OK OK OK OK OK OK OK

Página 3

Igualando

1=2

d=

44

cm

40

COLUMNA 2

40+d/2 pu= qnu= Igualando

135000 1.1670

Kg K/cm2

40

Vu = ØVc

40+d d=

45

cm

COLUMNA 1

40 pu= qnu= Igualando

105500 1.1670

Kg K/cm2

40+d/2 40

Vu = ØVc d=

55

cm

tomamos el mayor valor de "d" d= d= Tomamos t=

55 57 67

cm cm cm

40+d/2

Verificación de la condición de diseño tomando t = 67 cm 1/4 3 Ks λ = E x T^3 λ =

0.00260

1,75 / λ

=

672.38

>

OK!

METODO RIGIDO

5 CALCULO DEL FACTOR DE MODIFICACION DE CARGA "F" PARA CADA FRANJA FRANJA 1 A B C D E F E F H G G H I J K L A B J I G E B C J K C D F H K L

q 1.16 1.164898121 1.158561083 1.154688449 1.153396613 1.139783717 1.153396613 1.139783717 1.112407678 1.126020574 1.126020574 1.112407678 1.108682416 1.105279192 1.098942155 1.09506952 1.16 1.164898121 1.105279192 1.108682416 1.126020574 1.153396613 1.164898121 1.158561083 1.105279192 1.098942155 1.158561083 1.154688449 1.139783717 1.112407678 1.098942155 1.09506952

q prom 1.155

b 245

L 1160.00

P P1 P2 P3

ΣP 375500

CP 351906.95

F 1

1.133

450

1160.00

P4 P5 P6

492000

541687.46

1.10 1.22

1.108

285

1160.00

P7 P8 P9

419000

392608.36

1.00

1.136

290

980.00

P1 P4 P7

375500

349229.52

1.00

1.132

540

980.00

P2 P5 P8

492000

545506.07

1.11 1.22

1.127

330

980.00

P3 P6 P9

419000

391667.25

1.00

Página 4

6.-

DISEÑO DE LA LOSA FRANJA 1 Calculo de la cargas actuantes LADO IZQ A E q1

q 1.160 1.153 283.391 282.000

q=w=

LADO DERE D F

q 1.155 1.140

b 245

q2

281.073

P 1 2 3

P (Kg) 105500 135000 135000

k/cm2

105500

135000

135000

W= 282.000 20

540

540

60 69700

52420

5640

-65300

-82580

-99860

-17624485.82

X1 Max= X2 Max=

-24213830

374.11 478.72

56400

507600 12752400

Verificación del corte por flexión b= 245 d= 57 t= 67

Vmax= L=

Vu= Vc=

ØVc=

78146.00 107257.20 91168.62

Ok

99860 20

Refuerzo Superior Mu= 24213829.79 Kg-cm AS=

Por tanteo

As = As min=

Ing.db

Mu 0.9 Fy (d-a/2)

a´ 5.00 11.29 11.979 12.060 125.68 29.55 1

a= As 117.537 124.733 125.578 125.678 cm2 cm2 plg

a 11.288 11.979 12.060 12.070

As Fy 0.85 Fć b

f 1.00 1.0 1.0

p*f 105500 135000 135000

Página 5

Nº varillas 25

Espaciamiento 9 cm

Refuerzo Inferiorr Mu= 12752400

u s a r

Kg-cm

Mu 0.9 Fy (d-a/2)

AS=

Por tanteo

Ing.db

62.47 29.55

As Fy 0.85 Fć b

a=

a´ 5.00 5.94 6.00 6.00

As = As min=

26 Ø 1" @ 9cm

As 61.902 62.443 62.473 62.475

a 5.94 6.00 6.00 6.00

cm2 cm2

Nº varillas 22

3/4 plg Espaciamiento 11 cm

u s a r

23 Ø 3/4" @ 10 cm

FRANJA 2 LADO IZQ E G q1

q 1.153 1.126 512.869 510.000

q=w=

LADO DERE F H

q 1.140 1.112

q2

506.743

b 450

P 4 5 6

P (Kg) 135000 208000 149000

k/cm2 162000

249600

178800

W= 510.000 20

540

540

60 149400

123600

10200

-29400 -126000 -151800

X1 Max= X2 Max=

317.65 350.59 -22489411.76

102000

-20614588

918000 7512000

f 1.10

p*f 148500 228800 163900

Página 6

Verificación del corte por flexión b= 450 d= 57 t= 67 151800 Vmax= 20 L=

Vu= Vc=

ØVc=

112530 197003.02 167452.57

Ok


Por tanteo

Usar As = As min=

Ing.db Nº varillas 22

u s a r

Mu 0.9 Fy (d-a/2)

a´ 5.00 5.71 5.745 5.747 109.92 54.27 1

Por tanteo

As = As min=


u s a r

As 109.167 109.880 109.918 109.920

As Fy 0.85 Fć b

a 5.71 5.75 5.747 5.747

cm2 cm2 plg

Espaciamiento 21 cm

23 Ø 1" @ 20 cm.

Refuerzo Inferiorr Mu= 7512000 AS=

a=

Kg-cm

Mu 0.9 Fy (d-a/2)

a=

a´ 5.00 1.91 1.85 1.85 54.27 54.27 3/4

As 36.464 35.458 35.441 35.441

As Fy 0.85 Fć b

a 1.91 1.85 1.85 1.85

cm2 cm2 plg

Espaciamiento 24 cm

18 Ø 3/4" @ 25 cm.

FRANJA 3 LADO IZQ G I q1 q=w=

q 1.126 1.109 318.445 317.000

LADO DERE H L

q 1.112 1.095

q2

314.566

k/cm2

b 285

P 4 5 6

P (Kg) 135000 208000 149000

f 1.00 1.00 1.00

p*f 135000 208000 149000

Página 7

135000

208000

149000

W= 317.000 20

540

540

60 5700

42520

X1 Max= X2 Max=

425.8675079 470.0315457 6340

-143300 -165480 -128660

-26046056.78

-26077350

63400

570600 23194400


Vu= Vc=

ØVc=

104251.00 124768.58 106053.29

Ok


Por tanteo

Usar As = As min=


u s a r

Mu 0.9 Fy (d-a/2)

a´ 5.00 10.45 11.001 11.06 134.03 34.37 1

As 126.583 133.246 133.958 134.034

As Fy 0.85 Fć b

a 10.45 11.00 11.059 11.07

cm2 cm2 plg

Espaciamiento 11 cm

26 Ø 1" @ 11

Refuerzo Inferiorr Mu= 23194400 =

a=

Mu

Kg-cm =

As Fy

Página 8

0.85 Fć b

0.9 Fy (d-a/2)

Por tanteo

a´ 5.00 9.30 9.68 9.71 9.72

Usar As = As min=


u s a r

117.68 34.37 1

As 112.589 117.207 117.636 117.676 117.679

a 9.30 9.68 9.71 9.72 9.72

cm2 cm2 plg

Espaciamiento 12 cm

23 Ø 1" @ 12 cm.

FRANJA 4 LADO IZQ A I q1 q=w=

q 1.160 1.109 328.959 329.000

LADO DERE B J

q 1.165 1.105

b 290

q2

329.176

P 1 4 7

P (Kg) 105500 135000 135000

k/cm2

105500

135000

135000

W= 329.000 20

450

450

60 62180

49130

X1 Max= X2 Max=

320.668693 410.3343465 6580

-72820 -85870 -98920

-14805273.56

65800

592200 11136950

Verificación del corte por flexión

-19597568

f 1.00 1.00 1.00

p*f 105500 135000 135000

Página 9

b= d= t= Vmax= L=

290 57 67

Vu= Vc=

ØVc=

73587.00 126957.50 107913.88

Ok

98920 20


Por tanteo

As = As min=


u s a r

Mu 0.9 Fy (d-a/2)

a´ 5.00 7.72 7.916 7.93

Por tanteo

As 95.129 97.562 97.744 97.757

97.76 34.97

cm2 cm2

1

plg

Kg-cm

Mu 0.9 Fy (d-a/2)

a=

a´ 5.00 4.39 4.36 4.36 4.36

As 54.060 53.758 53.745 53.745 53.745

53.75 34.97

cm2 cm2

Ing.db

3/4

plg

u s a r

a 7.72 7.92 7.93 7.93

19 Ø 1" @ 16 cm.

Usar As = As min=

Nº varillas 19

As Fy 0.85 Fć b

Espaciamiento 16 cm


AS=

a=

As Fy 0.85 Fć b

a 4.39 4.36 4.36 4.36 4.36

Espaciamiento 16 cm

19 Ø 3/4" @ 16 cm.

FRANJA 5 LADO IZQ B C q1 q=w=

q 1.165 1.159 627.334 611.000

LADO DERE J K

q 1.105 1.099

q2

595.140

b 540

P 2 5 8

k/cm2

149850

230880

165390

P (Kg) 135000 208000 149000

f 1.11 1.11 1.11

p*f 149850 230880 165390

Página 10

W = 611 20

450

450

60 181390

X1 Max= X2 Max=

245.2536825 270.6873977

137320

12220

16000 -93560 -137630

-15378632.16

-12461094

122200

1099800 52450


Vu= Vc=

ØVc=

134343.00 236403.63 200943.08

Ok


Por tanteo

Usar As = As min=

Ing.d.b Nº varillas 26

u s a r

Mu 0.9 Fy (d-a/2)

a=

a´ 5.00 3.25 3.201 3.20 73.44 65.12

As 74.650 73.472 73.438 73.437 cm2 cm2

3/4 plg Espaciamiento 21 cm

26 Ø 3/4" @ 21


Kg-cm

a 3.25 3.20 3.20 3.20

As Fy 0.85 Fć b

Página 11

Mu 0.9 Fy (d-a/2)

AS=

Por tanteo

a´ 5.00 0.23 0.22 0.22

As 5.339 5.115 5.114 5.114

Usar As = As min=

65.12 65.12

cm2 cm2

Ing.db

3/4

plg

Nº varillas 23

u s a r

As Fy 0.85 Fć b

a= a 0.23 0.22 0.22 0.22

Espaciamiento 24 cm

23 Ø 3/4" @ 24 cm

FRANJA 6 LADO IZQ C D q1 q=w=

q 1.159 1.155 381.686 372.000

LADO DERE K L

q 1.099 1.095

b 330

q2

362.012

P 3 6 9

P (Kg) 135000 149000 135000

k/cm2 135000

149000

135000

W = 372 20

450

450

60 58240

X1 Max= X2 Max=

362.9032258 362.9032258

39840

7440

-76760 -109160 -127560

-21795967.74

74400

669600 19662600

Verificación del corte por flexión b= 330 d= 57

-16395968

Vu= Vc=

98916.00 144468.88

f 1.00 1.00 1.00

p*f 135000 149000 135000

Página 12

t= 67 127560 Vmax= 20 L= Refuerzo Superior Mu= 0 AS=

Por tanteo

As = As min=


u s a r

Por tanteo

Usar As = As min=


u s a r

a=

a´ 5.00 0.00 0.00 0.00 39.80 39.80

122798.55

Ok

Kg-cm

Mu 0.9 Fy (d-a/2)

As 0.000 0.000 0.000 0.000

As Fy 0.85 Fć b

a 0.00 0.00 0.00 0.00

cm2 cm2

1 plg Espaciamiento 46 cm

21 Ø 1" @ 16 cm.

Refuerzo Inferiorr Mu= 19662600 AS=

ØVc=

Kg-cm

Mu 0.9 Fy (d-a/2)

a=

a´ 5.00 6.81 6.92 6.93

As 95.445 97.052 97.156 97.163

97.16 39.80

cm2 cm2

1

plg

Espaciamiento 18 cm

19 Ø 1" @ 18 cm

a 6.81 6.92 6.93 6.93

As Fy 0.85 Fć b

Losa de Cimentacion

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