losas aligeradas

DISEÑO DE LOSA ALIGERADA POR FLEXION CONCRETO ARMADO I

=

=

=

=

=

=

1 2

* =

* = = hf

*

= = c = =

c = < a =

*

0.52 cm 5 cm

Para M12+ = 1380 Kg.m

Cuantias maximas y minimas:

TRAMO 1 - 2

Determinacion del acero

a

0.85

⟹

0.52 cm

EJE NEUTRO SE UBICA EN EL ALA DE LA SECCION POR CONSIGUIENTE SE DISEÑA COMO SECCION RECTANGULAR

DE ANCHO b = 100cm

4200 Kg/cm²

β 0.85

Diam. As

5 cm

Determinacion del valor de "a" con las siguientes formulas,y comparar con el valor asumido

3.23 m

M12+ = 1380 Kg.m

Verificacion de la posicion del eje neutro para el máximo Momento positivo

Para M12+ = 1380 Kg.m

d 21.87 cm

Asumir que: a

VI. DISEÑO DE LOSA ALIGERADA

ALIGERADO TIPO A:

A- NIVELES 1ER, 2DO, 3ERO Y 4TO:

M1- = 470 Kg.m M2- = 470 Kg.m

25 cm Ø 0.9

DATOS GENERALES A TOMAR PARA EL CALCULO:

Seccion de viga en "T", asumida para el diseño: Valores asumidos para el Diseño:

100 cm f'c 210 Kg/cm²

Para el diseño de losas aligeradas se asume la equivalencia de que en 1 metro hay 2.5 viguetas, esto para

diseñar para un ancho b=1 m

25 cm

5 cm fy

1.27 cm (Ø 1/2'')

recubr. 2.50 cm

0.90 * fy * (d - a/2) 0.85 * f'c * b

As 1.89 cm² >>> a 0.44 cm

As =Mu

; a

>>>

=As * fy

1


f'c =

fy

= =

= >>> =

= =

Asmax vigu. = 3Ø 1/2'' =

Asmin vigu. = 1Ø 3/8'' =

Consideramos a = d , y teniendo en cuenta las sgtes formulas, iteramos, para

determinar el area de acero.

"a" incial: a = d , a =

= a =

= a =

= a =

= =

= + =

3 3

* = = 4 3

=

=

= >>> =

= =


= a =

= a =

= a =

= =

+ =

3 3

As./2.5 viguetas 0.230 cm²

se coloca el acero minimo:


M2(-)M1(-)

As/1mtr 0.576 cm²

Para

3/8" 0.71 cm²

25.00 cm

ρmin 0.00241523 >>> Asmin 5.28 cm²

3/8"1 Ø 0 Ø

0.71

As 1.685 >>>

0.71

Se desarrollo el calculo asumiendo que 1 m de losa aligerada equivale a 2.5 viguetas, por tanto el acero

calculado es para 1metro, debemos determinarlo por vigueta:

ρmax 0.01625625 Asmax 35.54 cm²

As/1mtr 1.685 cm²

0.397

0.71

As./2.5 viguetas 0.674 cm² 1 Ø 3/8"

470 Kg.m

d 21.87 cm

b

3/8"0 Ø 0.71 cm² OK

As 1.686 >>> 0.397

=As * fy

0.90 * fy * (d - a/2) 0.85 * f'c * b

10 % >>> 2.187

As =Mu

a

As 1.758 >>> 0.414

ρmax

ρmin

0.01625625

0.00241523 >>>

Asmax

Asmin

8.89 cm²

1.32 cm²

3.55 cm²

0.53 cm²

3.87 cm²

0.71 cm²

10 %

ρb6300

ρmax

ρb

0.75 * ρb ρmin 0.7 *

= 0.85 * β * *(6300 + fy)

0.021675

OK

0.71

1.29

As 0.576 >>> 0.542

As 0.576 >>> 0.542

2.187

As 0.599 >>> 0.563

10 % >>>

𝑓′𝑐

𝑓𝑦

2


1 2

*

=

=


= a =

= a =

= a =

= =

se coloca el acero minimo: + =

3 3

* = 4 3

=

=


= a =

= a =

= a =

= =

se coloca el acero minimo: 1Ø 3/8'' = OK

3 3

1 2

M1- = 233 Kg.m M2- = 233 Kg.m

2.35 m

M12+ = 731 Kg.m

b 100.00 cm


1.159 >>> 0.273

Determinacion del acero de refuerzo

Para

10 % >>> 2.187

ALIGERADO TIPO B:

NIVELES 1ER, 2DO, 3ERO Y 4TO:

M12+ = 952 Kg.m

As/1mtr 1.159 cm²

As

A-5TO NIVEL :

M1- = 324 Kg.m

Para M1- = 324 Kg.m

M2- = 324 Kg.m

3.23 m

M12+ = 952 Kg.m

TRAMO 1 - 2

1.29 0.71

3/8"

As 1.159 >>> 0.273

As

OK1 Ø 3/8" 0 Ø

0.71

0.158 cm²

0.396 >>> 0.372

>>>

As 0.396 >>> 0.372

0.71 cm²

b 25.00 cm

10 % 2.187

As

1.212 >>> 0.285

d 21.87 cm

d 21.87 cm

0.71 cm²

0.71

M2(-)

As/1mtr 0.396 cm²

0.71 0.71

As./2.5 viguetas

As 0.413 >>> 0.389

3


*

=

=


= a =

= a =

= a =

= =


* = 4 3

=

=


= a =

= a =

= a =

= =


1 2

1 3

NIVEL 5TO:

M1- = 161 Kg.m M2- = 161 Kg.m

2.35 m

M12+ = 504 Kg.m

se coloca el acero mínimo

tanto para los momentos

negativos y momentos

positivos.

0.888 >>> 0.209

As 0.888 >>> 0.209

25.00 cm

10 % >>> 2.187

As 0.297 >>> 0.280

21.87 cm

b 100.00 cm

10 % >>> 2.187

d 21.87 cm

b

0.888 cm² As./2.5 viguetas 0.355 cm²

0.284 >>> 0.267

0.71 cm²

Para M1- = 233 Kg.m M2(-)

Para M12+ =

As 0.931 >>> 0.219

d

731 Kg.m

As

As 0.284 >>> 0.267

As

As/1mtr 0.284 cm² As./2.5 viguetas 0.114 cm²

0.71 cm²

0.711.29

As/1mtr

2.25 m

M3- = 268 Kg.m

M23+ = 487 Kg.m

2

ALIGERADO TIPO C:

C - NIVELES 1ER, 2DO, 3ERO Y 4TO:

M1- = 386 Kg.m M2- = 720 Kg.m

2.70 m

M12+ = 701 Kg.m

4


*

=

=


= a =

= a =

= a =

= =


*

=

=


= a =

= a =

= a =

= =


* 4 3

=

=


= a =

= a =

= a =

= =


* 4 3

=

=

Para M12+ =

>>>

b 100.00 cm

701 Kg.m

d 21.87 cm


0.71 cm²

As 0.620 >>>

0.71 cm²

2.187

As 0.591 >>> 0.139

As 0.472 0.444

Para M1- = 386 Kg.m 1.29 0.71

d 21.87 cm

b 25.00 cm

10 % >>> 2.187

As 0.491 >>> 0.462

As 0.472 >>> 0.444

Para M2- = 720 Kg.m 1.29 0.71


0.71 cm²

>>>

>>> 0.210

Para M23+ = 487 Kg.m

d 21.87 cm

b 100.00 cm

10 % >>>


0.146

As 0.591 >>> 0.139

d 21.87 cm

b 25.00 cm

10 %

As 0.893

>>> 0.201

As 0.853 >>> 0.201

As 0.853

2.187

5



= a =

= a =

= a =

= =


*


1 3

=

1 2

*

=

=


= a =

= a =

= a =

= =

se coloca : 1Ø 1/2'' = OK

ALIGERADO TIPO E:

NIVELES 1ER, 2DO, 3ERO Y 4TO:

M1- = 667 Kg.m M2- = 667 Kg.m

3.80 m

M12+ = 1910 Kg.m

Para M12+ = 1910 Kg.m

d 21.87 cm

10 % >>>

As 2.433 >>>

b 100.00 cm

As 2.341 >>> 0.551

0.936 cm²

As 2.342 >>> 0.551

As/1mtr 2.341 cm² As./2.5 viguetas

1.29 cm²

ALIGERADO TIPO D: ALIGERADO TIPO B:

2.187

0.572

0.71 cm²

>>>

10 % >>> 2.187

M3- = 268 Kg.m

As 0.917 >>> 0.864

As 0.889 >>> 0.837

As 0.889 0.836

M12+ = 484 Kg.m M23+ = 336 Kg.m

As/1mtr 0.889 cm² As.0.71/2.5 viguetas

C - NIVELES 5TO:

M1- = 266 Kg.m M2- = 497 Kg.m M3- =

Para

0.355 cm²

0.71 cm²

185 Kg.m

2

2.70 m 2.25 m

6


* = 4 3

=

=


= a =

= a =

= a =

= =


1 2

*

=

=


= a =

= a =

= a =

= =


* = 4 3

=

=


= a =

= a =

= a =As 0.563 >>> 0.530

10 % >>> 2.187

As 0.586 >>> 0.551

As 0.564 >>> 0.531

Para M1- = 460 Kg.m M2(-) 1.29 0.71

d 21.87 cm

b 25.00 cm

As 1.608 >>> 0.378


0.71 cm²

2.187

As 1.678 >>> 0.395

As 1.609 >>> 0.379

Para M12+ = 1318 Kg.m

d 21.87 cm

b 100.00 cm

10 % >>>

0.71 cm²

NIVEL 5TO:

M1- = 460 Kg.m M2- = 460 Kg.m

3.80 m

M12+ = 1318 Kg.m

0.329 cm²

As 0.822 >>> 0.774

10 % >>> 2.187

As 0.849 >>> 0.799

0.71

d 21.87 cm

M1- = 667 Kg.m M2(-) 1.29

b 25.00 cm

Para

As 0.821 >>> 0.773

As/1mtr 0.821 cm² As./2.5 viguetas

7


= =


1 2 3

=

* = = hf

*

= = c = =

c = < a =

*

=

=


= a =

= a =

= a =

= =

entonces se coloca: 2Ø 1/2'' + 1Ø 3/8'' = OK

* 4 3

=

=


= a =

= a =

= a =


0.71 cm²

0.652 >>> 0.614

As 0.652 >>> 0.613

1.29 0.71

d 21.87 cm

b 25.00 cm

10 % >>> 2.187

6210 Kg.m d 21.87 cm

entonces se diseña como una viga reforzada de ancho 1.0 m

As 8.48 cm² >>> a 2.00 cm >>> a 2.35 cm

0.85

Asumir que: a 5 cm


As =Mu

; a =As * fy

0.90 * fy * (d - a/2)

As 7.909 >>> 1.861

As 7.848 >>> 1.846

Para M12+ = 6210 Kg.m

d 21.87 cm

b 100.00 cm

10 % >>>

As 7.845 >>> 1.846


3.29 cm²

Para M1- = 531 Kg.m

As 0.676 >>> 0.637

As

0.80 m4.55 m

6210 Kg.mM12+ =

ALIGERADO TIPO F:

M1- = 531 Kg.m M2- =

F - NIVELES 1ER, 2DO, 3ERO Y 4TO:

930 Kg.m

0.85 * f'c * b

2.187

⟹ 2.35 cm 5 cm

M12+ =

8


= =


* 4 3

=

=


= a =

= a =

= a =

= =


1 2 3

*

=

=


= a =

= a =

= a =

= =

entonces se coloca: 1Ø 5/8'' + 2Ø 3/8'' = OK

* 4 3

=

=

"a" incial: a = d , a =10 % >>> 2.187

3.29 cm²

Para M1- = 675 Kg.m 1.29 0.71

d 21.87 cm

b 25.00 cm

As 7.374 >>> 1.735

As 7.370 >>> 1.734

As/1mtr 7.370 cm² As.=/2.5 viguetas 2.948 cm²

b 100.00 cm

10 % >>> 2.187

As 7.451 >>> 1.753

Para M12+ = 5850 Kg.m

d 21.87 cm

ALIGERADO TIPO F:E - NIVEL 5TO:

As 1.154

4.55 m

>>> 1.086


0.71 cm²

10 % >>> 2.187

As 1.184 >>> 1.115

As 1.155 >>> 1.087

0.71 cm²

Para M2- = 930 Kg.m 1.29 0.71

d 21.87 cm

b 25.00 cm


0.80 m

5850 Kg.mM12+ =

M1- = 675 Kg.m M2- = 830 Kg.m

9


= a =

= a =

= a =

= =


* 4 3

=

=


= a =

= a =

= a =

= =


As 0.860 >>> 0.809

As 0.832 >>> 0.783

0.71 cm²

10 % >>> 2.187

As 1.057 >>> 0.995

As 1.028 >>> 0.967

As 1.027 >>> 0.967


1.29 0.71

d 21.87 cm

b 25.00 cm

As 0.831 >>> 0.783


0.71 cm²

Para M2- = 830 Kg.m

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