DISEÑO DE ESCALERA 1° tramo

DATOS

P:paso

CP:contra paso

t:espesor del cuello

B:Ancho de la ecalera

L: Lon. de esc.

ρ 2400 kg/cm²

P = 0.28 m

CP = 0.1652 m

t = 0.175 m

B= 1.65 m

COS(α)= 0.861

L= 2.52 M

1.9 M

S/C= 400 kg/m²

S/C=acab. 100 kg/m²

recub.= 4

F'c= 210 kg/m²

fy=. 4200 kg/m²

1)METRADO DE CARGAS

a). Descanso

carga muerta

peso propio= CpxBxρ= 654.192

Acabados= BxS/Cacab=. 165

WD = 819.192 Kg/m

Sobrecarga S/CxB=

WL= 660 Kg/m

CARGA ULTIMA Wu=1.5xWd+1.8xWL

Wu= 2268.9 Kg/m

L1: Lon. de esc. Descanso

L1=

cm²

Cp=0.18m

P=0.28m

t=L/20 Ó L/25

b). Tramo inclinado

peso propio=2.4 b (Cp/2+ t/cosα)

peso propio= 1131.72 Kg/m² 1131.72 Kg/m

Acabados= Bx S/C acab=. 165 Kg/m

WD = 1296.72 Kg/m

Sobrecarga S/C=BX400

WL= 660 Kg/m

CARGA ULTIMA Wu=1.5xWd+1.8xWL

Wu= 2937.4 Kg/m

2)ESQUEMA ESTRUCTURAL

Estado de cargas

1,165.86 positivo

1,865.37 negativo

1,653.10 negativo

819.06 negativo

682.55 positivo

como es hiperestático cálculamos los momentos

Momento (+) 1.1659 tn-m 1.1659

Momento (-) 1.8654 tn-m 1.8654

M1=1/16 a 1/12 WL2 M1=

M2=1/10 WL2 M2=

M3=1/9 W((L1+L2)/2)2 M3=

M4=1/10 WL22 M4=

M5=1/16 a 1/12 WL22 M5=

L=2.52m L2=1.90m

WL

Wddes

L=2.52m L2=1.90m

M1

M2

M4

M3 M5

Momento (-) 1.6531 tn-m 1.6531

Cálculo del peralte

d=t-(recub--Ø/2)

considerando Ø 1/2= 1.27 cm

d= 12.865 cm

CALCULO DEL AREA DE ACERO (-)

Mu=Kuxbxd²

Ku= 6.8308

En la tabla Ku vs ρ para f'c=175kg/cm

f'c = 210 Kg/cm²

fy = 4200 Kg/cm² = 0.0018

Ku = 6.8308

0.0018

As = rBd/100

As = 3.820905 cm²

Verificación de acero minimo

Asmin = 2.3157 cm²

As dis = 3.820905 cm²

Refuerzo Longitudinal

ø3/8"= 0.71 cm2

Smax<=45cm ó 3t ø1/2"= 1.29 cm2

ø5/8"= 2 cm2

ø3/4"= 2.84 cm2

Alternativa 1 USAR Ø 3/8" @ 19 cm n de varillas 5

Alternativa 2 USAR Ø 1/2" @ 34 cm n de varillas 4

USAR USAR Ø 1/2" @ 30cm 4.00varillas

Astemp. =0.0018xbxt

Astemp. = 2.3157

Alternativa 1 USAR Ø 3/8" @ 30 cm n de varillas 4

Alternativa 2 USAR Ø 1/2" @ 44 cm n de varillas 3

USAR USAR Ø 3/8" @ 30cm 4.00varillas una sola capa

rdiseño

ρ diseño =

Asmin = 0.0018 Bd

Ø3/8 =0.71 cm²

CALCULO DEL AREA DE ACERO (+)

Mu=Kuxbxd²

Ku= 4.2693

En la tabla Ku vs ρ para f'c=175kg/cm

f'c = 210 Kg/cm²

fy = 4200 Kg/cm² = 0.0011

Ku = 4.2693

0.0011

As = rBd/100

As diseño = 2.3349975 cm²

Verificación de acero minimo

Asmin = 2.3157 cm²

As dis = 2.3349975 cm²

refuerzo longitudinal

ø3/8"= 0.71 cm2

Smax<=45cm ó 3t ø1/2"= 1.29 cm2

ø5/8"= 2 cm2

ø3/4"= 2.84 cm2

Alternativa 1 USAR Ø 3/8" @ 30 cm n de varillas 3

Alternativa 2 USAR Ø 1/2" @ 45 cm n de varillas 3

USAR USAR Ø 3/8" @ 30 cm 3.00varillas

Astemp. =0.0018xbxt

Astemp. = 2.3157 cm2

Alternativa 1 USAR Ø 3/8" @ 31 cm n de varillas 4

Alternativa 2 USAR Ø 1/2" @ 45 cm n de varillas 3

USAR USAR Ø 3/8" @ 30cm 4.00varillas una sola capa

VERIFICACION POR CORTE (más crítico)

V =WuL/2-l(Ma+Mb)/L

V = 2.30490819 TN

M+WuxX²/2-V=0

X= 0.80000

rdiseño

ρ diseño =

Asmin = 0.0018 Bd

Ø3/8 =0.71 cm²

WuWBWA

x

Ld=x+d= 0.92865

CHEQUEO POR CORTE

Vc=0.53x√f'cxdxb

Vc= 16303.4401 tn okey

NominaciónArea Diámetrocm2 cm

Ø 1/4" 0.32 0.635Ø 3/8" 0.74 0.952Ø 1/2" 1.29 1.27

MOMENTO NEGATIVO Ø 5/8" 2 1.588Mu = 1.865 ton x m Ø 3/4" 2.84 1.805

b = 165.000 cm Ø 1" 5.1 2.54h = 17.500 cm Ø 1 1/4" 8.19 3.226d = 12.865 cm

f'c = 210.000 Kg/cm²Recubrim. = 3.000 cm 0.0024

Ku = Mu = = 6.83 As diseño = 5.095b.d².

Opcion 1 n de varillas Distribucion

D = 180.76 Ø 1/4" 16 @ 10 cm

0.0018 Ø 3/8" 7 @ 23 cm

0.0024 As min = 5.09 cm2 Ø 1/2" 4 @ 40 cm

0.0212 Ø 5/8" 3 @ 53 cm

0.0159 As max = 33.75 cm2 Ø 3/4" 2 @ 80 cm

Mrest = 13.334 Ø 1" 1 @ 159 cm

Ø 1 1/4" 1 @ 159 cm

MOMENTO POSITIVOMu = 1.166 ton x m

b = 165.000 cmh = 17.500 cmd = 12.865 cm

f'c = 210.000 Kg/cm²Recubrim. = 2.000 cm 0.0024

Ku = Mu = = 4.27 As = 5.095b.d².

Opcion 1 n de varillas Distribucion

D = 183.89 Ø 1/4" 16 @ 10 cm

0.0011 Ø 3/8" 7 @ 23 cm

0.0024 As min = 5.09 cm2 Ø 1/2" 4 @ 40 cm

0.0212 Ø 5/8" 3 @ 54 cm

0.0159 As max = 33.75 cm2 Ø 3/4" 2 @ 81 cm

Mrest = 13.334 Ø 1" 1 @ 161 cm

Ø 1 1/4" 1 @ 161 cm

rdiseño =

r .b.d. =

r =

r min=

r balanc.=

r max=

rdiseño =

r .b.d. =

r =

r min=

r balanc.=

r max=

Peso linealKg/m

0.270.581.02

1.62.263.976.23

cm2

Opcion 2 n de varillas Distribucion

OK Ø 1/4" 16 @ 6 cm OK

OK Ø 3/8" 7 @ 15 cm OK

OK Ø 1/2" 4 @ 25 cm OK

OK Ø 5/8" 3 @ 39 cm OK

OK Ø 3/4" 2 @ 45 cm OK

OK Ø 1" 1 @ 45 cm OK

OK Ø 1 1/4" 1 @ 45 cm OK

cm2

Opcion 2 n de varillas Distribucion

OK Ø 1/4" 16 @ 6 cm OK

OK Ø 3/8" 7 @ 15 cm OK

OK Ø 1/2" 4 @ 25 cm OK

OK Ø 5/8" 3 @ 39 cm OK

OK Ø 3/4" 2 @ 45 cm OK

OK Ø 1" 1 @ 45 cm OK

OK Ø 1 1/4" 1 @ 45 cm OK

DISEÑO DE ESCALERA 2° tramo

DATOS

P:paso

CP:contra paso

t:espesor del cuello

B:Ancho de la ecalera

L: Lon. de esc.

ρ 2400 kg/cm²

P = 0.28 m

CP = 0.1652 m

t = 0.17 m

B= 1.65 m

COS(α)= 0.861

L= 2.52 M

1.9 M

S/C= 400 kg/m²

S/C=acab. 100 kg/m²

recub.= 4

F'c= 210 kg/m²

fy=. 4200 kg/m²

1)METRADO DE CARGAS

a). Descanso

carga muerta

peso propio CpxBxρ= 654.192

Acabados= BxS/Cacab=. 165

WD = 819.192 Kg/m

Sobrecarga S/CxB=

WL= 660 Kg/m

CARGA ULTIMA Wu=1.5xWd+1.8xWL

Wu= 2268.9 Kg/m

L1: Lon. de esc. Descanso

L1=

cm²

Cp=0.165m

P=0.30m

t=L/20 Ó L/25

Cp=0.1

P=0.

t=L/20 Ó L/25

b). Tramo inclinado

peso propio 2.4 b (Cp/2+ t/coseno α)

peso propio 1108.73 Kg/m² 1108.73 Kg/m

Acabados= Bx S/C acab=. 165 Kg/m

WD = 1273.73 Kg/m

Sobrecarga S/C=BX400

WL= 660 Kg/m

CARGA ULTIMA Wu=1.5xWd+1.8xWL

Wu= 2905.2 Kg/m

2)ESQUEMA ESTRUCTURAL

Estado de cargas

1153.0843

1844.9349 positivo

1642.8787 negativo

819.06164 negativo

682.55136 positivo

M1=1/16 a 1/12 WL2 M1=

M2=1/10 WL2 M2=

M3=1/9 W((L1+L2)/2)2 M3=

M4=1/10 WL22 M4=

M5=1/16 a 1/12 WL22 M5=

L=2.52m L2=1.90 m

WL

Wddes

L=2.70m L2=3.32m

M1

M2

M4

M3 M5M1

M2

M4

M5

como es hiperestático cálculamos los momentos

Momento (+ 0.6825 tn-m 0.6825514

Momento (- 0.8191 tn-m 0.8190616

Momento (- 1.6429 tn-m 1.6428787

Cálculo del peralte

d=t-(recub--Ø/2)

considerando Ø 1/2= 1.27 cm

d= 12.365 cm

CALCULO DEL AREA DE ACERO (-)

Mu=Kuxbxd²

Ku= 3.2467

En la tabla Ku vs ρ para f'c=175kg/cm

f'c = 210 Kg/cm²

fy = 4200 Kg/cm² = 0.0009

Ku = 3.2467

0.0009

As = rBd/100

As = 1.8362025 cm²

Verificación de acero minimo

Asmin = 2.2257 cm²

As dis = 2.2257 cm²

refuerzo longitudinal

ø3/8"= 0.71 cm2

Smax<=45cm ó 3t ø1/2"= 1.29 cm2

ø5/8"= 2 cm2

ø3/4"= 2.84 cm2

Alternativa 1 USAR Ø 3/8" @ 32 cm n de varillas 3

Alternativa 2 USAR Ø 1/2" @ 45 cm n de varillas 3

USAR USAR Ø 1/2" @ 30 cm 3.00varillas

Astemp. =0.0018xbxt

Astemp. = 2.2257 cm2

rdiseño

ρ diseño =

Asmin = 0.0018 Bd

Ø3/8 =0.71 cm²

Alternativa 1 USAR Ø 3/8" @ 32 cm n de varillas 4

USAR Ø 1/2" @ 45 cm n de varillas 3

USAR USAR Ø 3/8" @ 30cm 4.00varillas una sola capa

CALCULO DEL AREA DE ACERO (+)

Mu=Kuxbxd²

Ku= 2.7054

En la tabla Ku vs ρ para f'c=175kg/cm

f'c = 210 Kg/cm²

fy = 4200 Kg/cm² = 0.0007

Ku = 2.7054

0.0007

As = rBd/100

As diseño= 1.4281575 cm²

Verificación de acero minimo

Asmin = 2.2257 cm²

As dis = 2.2257 cm²

refuerzo longitudinal

ø3/8"= 0.71 cm2

Smax<=45cm ó 3t ø1/2"= 1.29 cm2

ø5/8"= 2 cm2

ø3/4"= 2.84 cm2

Alternativa 1 USAR Ø 3/8" @ 32 cm n de varillas 2

Alternativa 2 USAR Ø 1/2" @ 45 cm n de varillas 2

USAR USAR Ø 1/2" @ 30 cm 2.00varillas

Astemp. =0.0018xbxt

Astemp. = 2.2257 cm2

Alternativa 1 USAR Ø 3/8" @ 32 cm n de varillas 4

una sola capa USAR Ø 3/8" @30cm

VERIFICACION POR CORTE (más crítico)

rdiseño

ρ diseño =

Asmin = 0.0018 Bd

Ø3/8 =0.71 cm²

V =WuL/2-l(Ma+Mb)/L

V = 2.683624742 TN

M+WuxX²/2-V=0

X= 0.80000

Ld=x+d= 0.92365

CHEQUEO POR CORTE

Vc=0.53x√f'cxdxb

Vc= 15669.80463 tn okey

WuWBWA

xWuWBWA

x

CONTRA PASOS MINIMOS

Escaleras secundaria 18-20

Escaleras monumentales 13-15

Escaleras en edificios 15-17.5

Escalera en locales comerciales 18cm

B ANCHO MINIMOS

TIPO DE EDIF. B(m)

_Viviendas 1

_Auxiliares o de servicio 0.7

_Caracol 0.6

_Edif. De ofocinas 1.2

_locales comerciales 1.3

SOBRECARGAS RNC

TIPO DE EDIF. S/C (kg/m²)

_Viviendas y edif. Comerciales 200

_Viviendas y edif. residenciales 250-300

_Edif. Públicos 400

_Edif. De oficinas y tribunas 500

_Acabados 100

0.0024

0.0212

0.0159

r min=

r balanc.=

r max=

una sola capa

0.0024

0.0212

0.0159

r min=

r balanc.=

r max=

NominaciónArea Diámetrocm2 cm

Ø 1/4" 0.32 0.635Ø 3/8" 0.74 0.952Ø 1/2" 1.29 1.27

MOMENTO NEGATIVO Ø 5/8" 2 1.588Mu = 0.819 ton x m Ø 3/4" 2.84 1.805

b = 165.000 cm Ø 1" 5.1 2.54h = 17.000 cm Ø 1 1/4" 8.19 3.226d = 12.365 cm

f'c = 210.000 Kg/cm²Recubrim. = 4.000 cm 0.0024

Ku = Mu = = 3.25 As diseño = 4.897b.d².

Opcion 1 n de varillas Distribucion

D = 185.13 Ø 1/4" 16 @ 10 cm

0.0009 Ø 3/8" 7 @ 22 cm

0.0024 As min = 4.90 cm2 Ø 1/2" 4 @ 39 cm

0.0212 Ø 5/8" 3 @ 52 cm

0.0159 As max = 32.44 cm2 Ø 3/4" 2 @ 79 cm

Mrest = 12.317 Ø 1" 1 @ 157 cm

Ø 1 1/4" 1 @ 157 cm

MOMENTO POSITIVOMu = 0.683 ton x m

b = 165.000 cmh = 17.000 cmd = 12.365 cm

f'c = 210.000 Kg/cm²Recubrim. = 4.000 cm 0.0024

Ku = Mu = = 2.71 As diseño = 4.897b.d².

Opcion 1 n de varillas Distribucion

D = 185.78 Ø 1/4" 16 @ 10 cm

0.0007 Ø 3/8" 7 @ 22 cm

0.0024 As min = 4.90 cm2 Ø 1/2" 4 @ 39 cm

0.0212 Ø 5/8" 3 @ 52 cm

0.0159 As max = 32.44 cm2 Ø 3/4" 2 @ 79 cm

Mrest = 12.317 Ø 1" 1 @ 157 cm

Ø 1 1/4" 1 @ 157 cm

rdiseño =

r .b.d. =

r =

r min=

r balanc.=

r max=

rdiseño =

r .b.d. =

r =

r min=

r balanc.=

r max=

Peso linealKg/m

0.270.581.02

1.62.263.976.23

cm2

Opcion 2 n de varillas Distribucion

OK Ø 1/4" 15 @ 7 cm OK

OK Ø 3/8" 7 @ 15 cm OK

OK Ø 1/2" 4 @ 26 cm OK

OK Ø 5/8" 2 @ 41 cm OK

OK Ø 3/4" 2 @ 45 cm OK

OK Ø 1" 1 @ 45 cm OK

OK Ø 1 1/4" 1 @ 45 cm OK

cm2

Opcion 2 n de varillas Distribucion

OK Ø 1/4" 15 @ 7 cm OK

OK Ø 3/8" 7 @ 15 cm OK

OK Ø 1/2" 4 @ 26 cm OK

OK Ø 5/8" 2 @ 41 cm OK

OK Ø 3/4" 2 @ 45 cm OK

OK Ø 1" 1 @ 45 cm OK

OK Ø 1 1/4" 1 @ 45 cm OK

f'c = 280 Kg/cm² f'c = 210 Kg/cm² f'c = 175 Kg/cm²

fy = 4200 Kg/cm² fy = 4200 Kg/cm² fy = 4200 Kg/cm²

ρb = 0.0289 ρb = 0.0289 ρb = 0.0289

ρ Ku ρ Ku ρ Ku

0.0106 36.3093 0.0052 18.4500 0.0024 8.7637

0.0104 35.6938 0.0050 17.7847 0.0022 8.0570

0.0102 35.0756 0.0048 17.1164 0.0020 7.3457

0.0100 34.4548 0.0046 16.4442 0.0018 6.6306

0.0098 33.834 0.0044 15.7695 0.0016 5.9110

0.0096 33.2132 0.0042 15.0872 0.0014 5.1871

0.0094 32.5924 0.0040 14.4064 0.0012 4.4587

0.0092 31.9716 0.0038 13.7200 0.0010 3.7265

0.0090 31.3508 0.0036 13.0300 0.0008 2.9598

0.0088 30.73 0.0034 12.3364 0.0006 2.2497

0.0086 30.1092 0.0032 11.6393 0.0004 1.5350

0.0084 29.4884 0.0030 10.9386 0.0002 0.7539

0.0082 28.8676 0.0028 10.2343 0.0000 0.0000

0.0080 28.2468 0.0026 9.5265

0.0078 27.626 0.0024 8.8151

0.0076 26.7958 0.0022 8.1002

0.0074 26.14 0.0020 7.3816

0.0072 25.4819 0.0018 6.6575

0.0070 24.8209 0.0016 5.9339

0.0068 24.1572 0.0014 5.2016

0.0066 23.4909 0.0012 4.4718

0.0064 22.8218 0.0010 3.7354

0.0062 22.1501 0.0008 2.9855

0.0060 21.4758 0.0006 2.2520

0.0058 20.7987 0.0004 1.5047

0.0056 20.119 0.0002 0.7543

0.0054 19.4366 0.0000 0.0000

0.0052 18.7515

0.0050 18.0637

0.0048 17.3733

0.0046 16.6802

0.0044 15.9844

0.0042 15.4332

0.0040 14.7053

0.0038 13.9774

0.0036 13.2495

0.0034 12.5216

0.0032 11.7937

0.0030 11.0658

0.0028 10.3379

0.0026 9.61

0.0024 8.8821

0.0022 8.1542

0.0020 7.4263

0.0018 6.6957

0.0016 5.9624

0.0014 5.2265

0.0012 4.4879

0.0010 3.7166

0.0008 3.0027

TABLA Ku vs ρ

DIMENSIONES DEL ACERO PARA REFUERZO DEL CONCRETO

ACERO GRADO 60 fy = 4200 Kgs. / Cm2.

BARRA DIAMETRO AREA PERIMETRO PESO DE LA BARRA

N° Pulg. Cms. Cm2. Cm Kg/ml Kg

6 mm 0.60 0.28 1.88 0.22 1.98

2 1/4 0.64 0.32 2.00 0.25 2.25

8 mm 0.80 0.50 2.51 0.40 3.60

3 3/8 0.95 0.71 3.00 0.58 5.22

12 mm 1.20 1.13 3.77 0.89 8.01

4 1/2 1.27 1.27 4.00 1.02 9.185 5/8 1.59 1.98 5.00 1.60 14.406 3/4 1.91 2.85 6.00 2.26 20.348 1 2.54 5.07 8.00 4.04 36.36

10 1 1/4 3.18 7.92 0.00

DIMENSIONES DEL ACERO PARA REFUERZO DEL CONCRETO

ACERO GRADO 60 fy = 4200 Kgs. / Cm2. NORMA ASTM A - 615

NUMERO DE BARRAS CONOCIENDO EL AREA DEL ACERO EN ( Cm2. )

1 2 3 4 5 6 7 80.28 0.57 0.85 1.13 1.41 1.70 1.98 2.26

0.32 0.63 0.95 1.27 1.58 1.90 2.22 2.53

0.50 1.01 1.51 2.01 2.51 3.02 3.52 4.02

0.71 1.43 2.14 2.85 3.56 4.28 4.99 5.70

1.13 2.26 3.39 4.52 5.65 6.79 7.92 9.05

1.27 2.53 3.80 5.07 6.33 7.60 8.87 10.13

1.98 3.96 5.94 7.92 9.90 11.88 13.86 15.83

2.85 5.70 8.55 11.40 14.25 17.10 19.95 22.80

5.07 10.13 15.20 20.27 25.34 30.40 35.47 40.54

7.92 15.83 23.75 31.67 39.59 47.50 55.42 63.34

DIMENSIONES DEL ACERO PARA REFUERZO DEL CONCRETO

NORMA ASTM A - 615

NUMERO DE BARRAS CONOCIENDO EL AREA DEL ACERO EN ( Cm2. )

9 10 11 122.54 2.83 3.11 3.39

2.85 3.17 3.48 3.80

4.52 5.03 5.53 6.03

6.41 7.13 7.84 8.55

10.18 11.31 12.44 13.57

11.40 12.67 13.93 15.20

17.81 19.79 21.77 23.75

25.65 28.50 31.35 34.20

45.60 50.67 55.74 60.80

71.26 79.17 87.09 95.01