Diseño de Escaleras IE PARACHIQUE 2014 Ok
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![Page 1: Diseño de Escaleras IE PARACHIQUE 2014 Ok](https://reader033.fdocumento.com/reader033/viewer/2022052401/563db810550346aa9a903852/html5/thumbnails/1.jpg)
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
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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
![Page 3: Diseño de Escaleras IE PARACHIQUE 2014 Ok](https://reader033.fdocumento.com/reader033/viewer/2022052401/563db810550346aa9a903852/html5/thumbnails/3.jpg)
Momento (-) 1.6531 tn-m 1.6531
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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
![Page 5: Diseño de Escaleras IE PARACHIQUE 2014 Ok](https://reader033.fdocumento.com/reader033/viewer/2022052401/563db810550346aa9a903852/html5/thumbnails/5.jpg)
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
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Ld=x+d= 0.92865
CHEQUEO POR CORTE
Vc=0.53x√f'cxdxb
Vc= 16303.4401 tn okey
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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=
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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
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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
![Page 10: Diseño de Escaleras IE PARACHIQUE 2014 Ok](https://reader033.fdocumento.com/reader033/viewer/2022052401/563db810550346aa9a903852/html5/thumbnails/10.jpg)
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
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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
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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
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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
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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
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0.0024
0.0212
0.0159
r min=
r balanc.=
r max=
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una sola capa
0.0024
0.0212
0.0159
r min=
r balanc.=
r max=
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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=
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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
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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
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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
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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
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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