Losa Alivianada Bidireccional

7/28/2019 Losa Alivianada Bidireccional

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1.1 .- Tableros entre columnas y vigas

Tableros S L

N m m

1 5.80 6.20 0.94

2 5.80 6.50 0.89

3 5.80 6.50 0.89

4 6.20 6.20 1.00

5 6.20 6.50 0.95

6 5.60 6.20 0.90

7 5.60 6.50 0.86

8 5.60 6.50 0.86

m >= 0,5 Losas armadas en dos direccionesm


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2.- Mayorizacin de cargas

qm= 604 Kg/cm2

qv= 500 Kg/cm2

qm= PPL

qu= 1,4D + 1,7L

qu= 1,4*(0,604)+1,7(0,5)

qu= 1.70 Ton/m


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Tablero Apoyo o Coef. qu Mu

N S L m=s/L caso Tramo Momentos (Ton/m) (ton)

A 0.0268 1.528A-B 0.0406 2.315

B 0.0538 3.068

B 0.0410 2.672

B-C 0.0310 2.020

C 0.0410 2.672

C 0.0570 3.030

C-D 0.0430 2.286

D 0.0280 1.489

A 0.0210 1.369A-B 0.0310 2.020

B 0.0410 2.672

C 0.0445 2.900

C-D 0.0335 2.183

D 0.0225 1.466

A 0.0280 1.489

A-B 0.0430 2.286

B 0.0570 3.030

B 0.0508 2.701

B-C 0.0380 2.020

C 0.0508 2.701

C 0.0598 3.179

C-D 0.0450 2.392

D 0.0296 1.574

1 0.0250 1.426

1;2 0.0370 2.110

2 0.0490 2.794

2 0.0410 2.6722;3 0.0310 2.020

3 0.0410 2.672

3 0.0490 2.605

3;4 0.0370 1.967

4 0.0250 1.329

1 0.0210 1.369

1;2 0.0310 2.020

DETERMINACION DE MOMENTOS Y CORTES

Faja VI

4 6.20 6.20 1.00 II 1.70

6.20 6.20 1.00 II

Faja V

1 5.80 6.20 0.94 III

1.702

3 5.60 6.20 0.90 III

1.705 5.60 6.50 0.86 II

8 5.60 6.50 0.86 III

Faja IV

3 5.60 6.20

Faja II

2 6.20 6.20 1.00 II 1.70

Faja III

7 6.20 6.50 0.95 II 1.70

0.90 III

4 6.20 6.20 1.00 II

6 5.60 6.20 0.90 III

6.20 0.94 III

1.70

Dimensiones Identificacin

Faja I

1 5.80


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2 0.0410 2.672

3 0.0410 2.672

3;4 0.0310 2.020

4 0.0210 1.369

1 0.0250 1.3291;2 0.0370 1.967

2 0.0490 2.605

2 0.0410 2.180

2;3 0.0310 1.648

3 0.0410 2.180

3 0.0490 2.605

3;4 0.0370 1.967

4 0.0250 1.329

Mu= coef*qu*s^2

Vs= qu*s/3

VL= qu*s/3*((3-m^2/2)

8 5.60 6.50 0.86 III

5.60 6.50 0.86 II

Faja VIII

6 5.60 6.20 0.90 III

1.707

Faja VII

5 6.20 6.50 0.95 II 1.70


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Vs VL 1 0.0490

0.94 0.0538

0.9 0.0570

nota: Borde continuo porque tiene tablero arriba y abajo

1 0.0210

0.95 0.0225

0.9 0.0240

0.9 0.0280

0.86 0.0296

0.8 0.0320

3.504 3.504

3.504 3.504

3.482 3.278

3.1653.456

3.456 3.165

3.572 3.165

3.572 3.165

3.504 3.504

3.662 3.504

Interpolacin

3.482

3.504

3.456

3.278

3.504

3.165

Corte


6/17

3.1653.572

3.572 3.165

3.456 3.165

3.662 3.504


7/17

CALCULO DEL ACERO DE REFUERZO

fc= 210 Kg/cm2

fy= 3500 Kg/cm2

d(asumido)= 17.30 cm

Ru= 57.370 Kg/cm2

Apoyo o

Tramo

A 1.528 30 0.06482 0.09907 0.10566

A-B 2.315 110 0.01768 0.04093 0.04197

B 3.068 30 0.06482 0.19889 0.23014

B-C 2.020 110 0.01768 0.03571 0.03650

C 3.030 30 0.06482 0.19644 0.22678C-D 2.286 110 0.01768 0.04041 0.04143

D 1.489 30 0.06482 0.09649 0.10272

A 1.369 30 0.06482 0.08871 0.09391

A-B 2.020 110 0.01768 0.03571 0.03650

B 2.672 30 0.06482 0.17320 0.19582

C 2.900 30 0.06482 0.18798 0.21534

C-D 2.183 110 0.01768 0.03859 0.03952

D 1.466 30 0.06482 0.09505 0.10107

A 1.489 30 0.06482 0.09649 0.10272

A-B 2.286 110 0.01768 0.04041 0.04143

B 3.030 30 0.06482 0.19644 0.22678

B-C 2.020 110 0.01768 0.03572 0.03650

C 3.179 30 0.06482 0.20608 0.24010

C-D 2.392 110 0.01768 0.04229 0.04341

D 1.574 30 0.06482 0.10201 0.10902

1 1.426 30 0.06482 0.09242 0.09810

1;2 2.110 110 0.01768 0.03730 0.03816

2 2.794 30 0.06482 0.18114 0.20624

2;3 2.020 110 0.01768 0.03571 0.036503 2.672 30 0.06482 0.17320 0.19582

3;4 1.967 110 0.01768 0.03478 0.03552

4 1.329 30 0.06482 0.08616 0.09105

1 1.369 30 0.06482 0.08871 0.09391

1;2 2.020 110 0.01768 0.03571 0.03650

2 2.672 30 0.06482 0.17320 0.19582

Faja

Faja

Faja

Faja

Diseo ductil

k

Faja

Faja

Mu b k w


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3 2.672 30 0.06482 0.17320 0.19582

3;4 2.020 110 0.01768 0.03571 0.03650

4 1.369 30 0.06482 0.08871 0.09391

1 1.329 30 0.06482 0.08616 0.09105

1;2 1.967 110 0.01768 0.03478 0.03552

2 2.605 30 0.06482 0.16887 0.190212;3 1.648 110 0.01768 0.02914 0.02966

3 2.605 30 0.06482 0.16887 0.19021

3;4 1.967 110 0.01768 0.03478 0.03552

4 1.329 30 0.06482 0.08616 0.09105

Faja

Faja


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As/m As/n varillas varillas As/N varillas

3.290 1.645 114 @ 10cm 1.097

4.792 2.396 212 @ 10cm 1.597

7.166 3.583 214 @ 10cm 2.389

4.168 2.084 212 @ 10cm 1.389

7.062 3.531 214 @ 10cm 2.3544.730 2.365 212 @ 10cm 1.577

3.199 1.599 114 @ 10cm 1.066

2.924 1.462 114 @ 10cm 0.975

4.168 2.084 212 @ 10cm 1.389

6.098 3.049 214 @ 10cm 2.033

6.706 3.353 214 @ 10cm 2.235

4.512 2.256 212 @ 10cm 1.504

3.147 1.574 114 @ 10cm 1.049

3.199 1.599 114 @ 10cm 1.066

4.730 2.365 212 @ 10cm 1.577

7.062 3.531 214 @ 10cm 2.354

4.168 2.084 212 @ 10cm 1.389

7.477 3.738 214 @ 10cm 2.492

4.956 2.478 212 @ 10cm 1.652

3.395 1.697 114 @ 10cm 1.132

3.055 1.527 114 @ 10cm 1.018

4.357 2.179 114 @ 10cm 1.452

6.422 3.211 214 @ 10cm 2.141

4.168 2.084 114 @ 10cm 1.3896.098 3.049 214 @ 10cm 2.033

4.056 2.028 212 @ 10cm 1.352

2.835 1.418 212 @ 10cm 0.945

2.924 1.462 114 @ 10cm 0.975

4.168 2.084 114 @ 10cm 1.389

6.098 3.049 212 @ 10cm 2.033

112 @ 10cm

V

VI

212 @ 10cm

212 @ 10cm

212 @ 10cm

212 @ 10cm

IV

214 @ 10cm

214 @ 10cm

214 @ 10cm

I

II

III

Faja central Franja Lateral

214 @ 10cm

214 @ 10cm

212 @ 10cm

212 @ 10cm


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6.098 3.049 214 @ 10cm 2.033

4.168 2.084 114 @ 10cm 1.389

2.924 1.462 212 @ 10cm 0.975

2.835 1.418 114 @ 10cm 0.945

4.056 2.028 212 @ 10cm 1.352

5.923 2.962 214 @ 10cm 1.9743.386 1.693 114 @ 10cm 1.129

5.923 2.962 214 @ 10cm 1.974

4.056 2.028 114 @ 10cm 1.352

2.835 1.418 212 @ 10cm 0.945

112 @ 10cm

112 @ 10cm

II

III

214 @ 10cm

214 @ 10cm


11/17

CHEQUEO A LA FLEXION Y CORTE

FLEXIN

Momento Crtico Mu = 3.179Ton/m

Corte Crtico Vu = 3.66Ton

hmin= 25 cm

fc= 210 Kg/cm2fy= 3500 Kg/cm2

Ru= 57.370 Kg/cm2

dn= 17.55 cm

dex= 22.30 cm

dex >> dn

22.3 cm ok 17.55 cm

Mn= 20*22,30 2*57,370

Mn= 603451.47 Kg-cm

Mn= 5.71 Ton-m

Mn= 0,9*6,03

Mn= 5.14 Ton-m

Mu vs Mn

3.179Ton-m


12/17

CHEQUEO DE DEFLEXIONES (Tramo corto)

Momento Crtico Mu(+)= 2.392Ton-m

qm= 604 Kg/cm2

qv= 500 Kg/cm2

ppl= 0.60 Ton/m2 520833.333

L= 6.50 m 213333.333

bw= 20.00 m 2500

b= 100 cm 1600

hmin= 25 cm 287.11

hf= 5 cm

fc= 210 Kg/cm2

fy= 3500 Kg/cm2

Y= 16.94 cm

Ig= 49097 cm4

c= 0.021

L= 5.60m

Mv= 0.329Ton-m

Mm= 0.398Ton-m

Ec= 218820 Kg/cm2

Ie= 44188 cm4

(v)= 0.135 cm

(m)= 0.109 cm

(s)= 0.176 cm

(LP)= 0.528cm

T= 0.663 cm

adm= 1.354cm

adm VS T

1.354cm >> 0.663 cm

ok

= ^2

=0,5*0,021*5,60^2

= ^2

=0,60*0,021*5,60^2

= 15100

= 15100 240

= 0,9

= 0,9 66667

()=3

32

()=3 (0,792 10) 4 3 0

32 218820 72542

()=1

16

()=

1 1,123 100000 430

16 218820 72542

= +%

= 0,137+(0,50)*(0,145)

=

= 3 0,123

=

= 0,094 0,368

=

480

=430

480

=

()

()

=

()

()

Ig=(

()

)-((b*h)-(b-bw)*(h-hf))

Ig=(

()

)-((110*30)-(110-30)*(30-5)) 18,85


13/17

CHEQUEO DE DEFLEXIONES (Tramo Largo)

Momento Crtico Mu(+)= 2.392Ton-m

qm= 604 Kg/cm2

qv= 500 Kg/cm2

ppl= 0.60 Ton/m2 520833.333L= 6.50 m 213333.333

bw= 20.00 m 2500

b= 100 cm 1600

hmin= 25 cm 287.11

hf= 5 cm

fc= 210 Kg/cm2

fy= 3500 Kg/cm2

Y= 16.94 cm

Ig= 49097 cm4

c= 0.031

L= 5.60m

Mv= 0.486Ton-m

= ^2

=0,5*0,021*5,60^2

=

()

()

=

()

()

Ig=(

()

)-((b*h)-(b-bw)*(h-hf))

Ig=(

()

)-((110*30)-(110-30)*(30-5)) 18,85


14/17

Mm= 0.587Ton-m

Ec= 218820 Kg/cm2

Ie= 44188 cm4

(v)= 0.199 cm

(m)= 0.160 cm

(s)= 0.260 cm

= ^2

=0,60*0,021*5,60^2

= 15100

= 15100 240

= 0,9

= 0,9 66667

()=3

32

()=3 (0,792 10) 4 3 0

32 218820 72542

()=1

16

()=1 1,123 100000 430

16 218820 72542

=

+%

= 0,137+(0,50)*(0,145)

=

=


15/17

(LP)= 0.780cm

T= 0.979 cm

adm= 1.354cm

adm VS T1.354cm >> 0.979 cm

ok

,

=

= 0,094 0,368

=

480

=430

480


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bw= 20cm

NEV= 2

fy= 3500 Kg/cm2

Y= 2.60 cm

AHT= 104 cm2

AEHT= 52.00 cm2 por cada varilla

fs= 2100 Kg/cm2

w= 0.129cm

wadm vs wcal

0.400 cm >> 0.129 cm

ok

CHEQUEO DE AGRIETAMIENTOS

= /2

= 2 0,6

AHT =2*bw*Y

AHT =2*30*2,6

=

=162

2

f = 0,6

f = 0,6 2800

=

= 1,2 1680 2,6 86,67

/100000


17/17

f'c= 210 Kg/cm2 L= 6.50 m

fy= 3500 Kg/cm2

qm= 604 Kg/cm2

qv= 500 Kg/cm2

qu= 1,4D + 1,7L

qu= 1,4*(0,2)+1,7(0,6)

qu= 1.70 Ton/m

B1= 0.85

qu*= 1.695 Ton/m

1.- MOMENTO ULTIMO

Mu= 8.95 Ton/m

2.- CUANTIA BALANCEADA

0.04335 0.63157895

b= 0.027378947

b= 2.74 %

3.- "PREDISEO"

Tablas: = 0.027379 "reeplazar los datos segn mi diseo en tablas"

w= 0.45646

Ru= 57.370 Kg/cm2 DISEO DUCTIL

b d h h b*h h/b

cm cm cm cm cm2

20 29.45 36.45 40.00 800 2.00 *

25 26.34 33.34 35.00 875 1.40

30 24.04 31.04 35.00 1050 1.17

35 22.26 29.26 35.00 1225 1.00

40 20.82 27.82 30.00 1200 0.75

(*nota)

escojo b= 0.20 m

h= 0.40 m

0.40

m

0.20

m

7.- PESO PROPIO DE LA VIGA (PPV)

PPV= 0.192 Ton/m

qPPV= 1,2*PPV

qPPV= 0.23 Ton/m

Mppv= 1.01 Ton/m

MT= 9.97 Ton/m

9.- dn (necesario)

* Momento mayor Mu= 9.97 Ton/m en mi caso es momento negativo

b= 0.20 m

dn= 31.07 cm

10.- PREDIMENSIONAMIENTO

r= 4 TN 1.27

As=*b*dn 5 22mm 19.01 cm2 = 1

As= 17.01 cm2 ns= 2

n= 3

"ver en tablas para el acero"

Er= 20 cm

Er=2r+2+ns+n

11.- d(existente)

d(exiatente)= h - y

d(existente)= 30.95cm

12.- As (negativo)

As(min)= 2.05 cm2

As(min)= 2.49 cm2 2 12mm 2.26 cm2

13.- COMPROBACION

Cc=Ts

0,85F`c*a*b=As*fs

a= 16.68

a= B1*C

C= 19.62

s= 0.00173cm/cm

y= 0.00167cm/cm

s vs y

0.00173cm/cm > 0.00167cm/cm

fs=fy

Cc= 0,85*f`c*a*b

Cc= 59543 kg

Ts= As*fy

Ts= 59543 kg

Mn= Ts*(dex-a/2)

Mn= 13.463Ton-m

Mu Vs Mn

9.97Ton/m < 12.117Ton-m

diseo ductil

1,5 < h/b < 2,0

PREDISEO DE LA VIGA

b=,

(

+)

=

=

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