Diseo de viga 1DISEO DE VIGAS SIMPLEMENTE REFORZADAS
1)Caractersticas de la vigab =Ancho de viga25.00cmh =Altura de
viga50.00cmr =Recubrimiento4.00
Reque: Recubrimientos: NTP. E060 Concreto Armado, Capitulo7 (tem
7.7)cmf'c =Compresin del concreto210.0
Windows User: f'c=175 Kg/cm2f'c=210 Kg/cm2f'c=245 Kg/cm2f'c=280
Kg/cm2f'c=315 Kg/cm2f'c=350 Kg/cm2f'c=420 Kg/cm2Kg/cm50.00 cm1fy
=Resistencia de fluencia del acero4200.0
Windows User: fy = 4200 Kg/cm2. Existe un acero con mayor esfuerzo
a a fluencia poco comercial por su poca ductilidad, es el fy=5100
Kg/cm2.Kg/cm2b =Factor de Whitney0.853 =Factor de reduccin0.904b
=Dimetro de acero long. asumido1/25s =Dimetro del estribo3/86d =h -
r - s - b/2 (Peralte efect.)44.41
Windows User: Distancia del centroide del refuerzo en traccin a la
fibra en compresin ms alejada.cm25.00 cm3)rea de acero mnimoCant.As
(cm)Verif.=2.68 cm min =0.002431/23.80 cmOk!As min =3.70 cm0.00
cm=3.70 cmTotal3.80 cm
4)rea de acero mximaCant.As (cm)Verif.33/48.55 cmOk!As max
=17.70 cm25/83.96 cmTotal12.51 cm
5)Momentos de diseo
Tramos:6 (Ton-m)12.50013.40016.40012.30012.50013.60012.100
(Ton-m)10.21010.8109.40012.30010.2909.800
6)Clculo de Acero (As)
As (cm)8.1508.80311.0678.0068.1508.9507.863
As (cm)6.5346.9515.9788.0066.5896.252
As min =3.70 cm3 1/2+ 0 0As max =17.70 cm3 3/4+ 2 5/8
ACERO POSITIVOTramoM (Ton-m)a (cm)As+(cm) calculado As+ (cm)
diseoDistribucinOk!As principalAs bastn (cm)As+(cm) colocadoCant.As
Cant.1-210.2106.156.5346.53435/80.59611/27.205Ok
2-310.8106.546.9516.95135/81.01311/27.205Ok
3-49.4005.635.9785.97835/80.04011/27.205Ok
4-512.3007.538.0068.00635/82.06821/28.472Ok
5-610.2906.206.5896.58935/80.65211/27.205Ok
6-79.8005.886.2526.25235/80.31411/27.205OkOk
ACERO NEGATIVOApoyoM (Ton-m)a (cm)As-(cm) calculado As-(cm)
diseoDistribucinOk!As principalAs bastn (cm)As-(cm) colocadoCant.As
Cant.112.5007.678.1508.15035/82.21221/28.472Ok
213.4008.298.8038.80335/82.86525/89.897Ok
316.40010.4211.06711.06735/85.12923/411.638Ok
412.3007.538.0068.00635/82.06821/28.472Ok
512.5007.678.1508.15035/82.21221/28.472Ok
613.6008.428.9508.95035/83.01225/89.897OkOk712.1007.407.8637.86335/81.92521/28.472OkOk
7)Distribucin de Acero (As principal y As bastn)7.1 As principal
3 5/83 5/83 5/83 5/83 5/83 5/83 5/80 00 00 00 00 00 00 0
35/835/83 5/835/835/835/800000 0000000
7.2 As bastn 2 1/22 5/82 3/42 1/22 1/22 5/82 1/20 00 00 00 00 00
00 0
11/211/21 1/221/211/211/200000 0000000
8)Verificacin del cumplimiento de la norma E-060
Disposicin de la Norma E-060 - Refuerzo Longitudinal (Para
condiciones sismo-resistentes)
OkOkOkOkOkOk
OkOkOkOkOkOk
As-(cm)8.47 /39.90 /311.64 /38.47 /38.47 /39.90 /38.47 /3
As+(cm)5.945.945.945.945.945.945.94Falta AsOkOkOkOkOkOkOk
Los momentos que se presentan a continuacin son extraidos del
diagrama de momentos (ENVOL) del software Etabs V.9.0.2, los mismos
que son tomados a cara del apoyo. Deben tener refuerzo continuo, a
todo lo largo de la viga, constituido por 2 barras como mnimo,
tanto en la cara superior como en la inferior, con un rea de acero
no menor a 1/4 de la mxima requerida en los nudos, ni menor del rea
mnima exigida por flexin. La resistencia a momento positivo en la
cara del nudo (extremo inferior del tramo) no ser menor que 1/3 de
la resistencia a momento negativo en la misma cara del nudo
(extremo superior). La cuanta del refuerzo en traccin 0.025.
Diseo de viga 2DISEO DE VIGAS SIMPLEMENTE REFORZADAS
1)Caractersticas de la vigab =Ancho de viga25.00cmh =Altura de
viga50.00cmr =Recubrimiento4.00
Reque: Recubrimientos: NTP. E060 Concreto Armado, Capitulo7 (tem
7.7)cmf'c =Compresin del concreto210.0
Windows User: f'c=175 Kg/cm2f'c=210 Kg/cm2f'c=245 Kg/cm2f'c=280
Kg/cm2f'c=315 Kg/cm2f'c=350 Kg/cm2f'c=420 Kg/cm2Kg/cm50.00 cm1fy
=Resistencia de fluencia del acero4200.0
Windows User: fy = 4200 Kg/cm2. Existe un acero con mayor esfuerzo
a a fluencia poco comercial por su poca ductilidad, es el fy=5100
Kg/cm2.Kg/cm2b =Factor de Whitney0.853 =Factor de reduccin0.904b
=Dimetro de acero long. asumido1/25s =Dimetro del estribo3/86d =h -
r - s - b/2 (Peralte efect.)44.41
Windows User: Distancia del centroide del refuerzo en traccin a la
fibra en compresin ms alejada.cm25.00 cm3)rea de acero mnimoCant.As
(cm)Verif.=2.68 cm min =0.002431/23.80 cmOk!As min =3.70 cm0.00
cm=3.70 cmTotal3.80 cm
4)rea de acero mximaCant.As (cm)Verif.63/417.10 cmOk!As max
=17.70 cm0.00 cmTotal17.10 cm
5)Momentos de diseo
Tramos:6 (Ton-m)6.9907.6107.7907.4707.6906.6006.530
(Ton-m)4.5606.3506.2906.6606.4606.5706.180
6)Clculo de Acero (As)
As (cm)4.3664.7754.8944.6824.8284.1104.065
As (cm)3.7013.9483.9094.1504.0194.0913.837
As min =3.70 cm3 1/2+ 0 0As max =17.70 cm6 3/4+ 0 0
ACERO POSITIVOApoyoM (Ton-m)a (cm)As+(cm) calculado As+ (cm)
diseoDistribucinOk!As principalAs bastn (cm)As+(cm) colocadoCant.As
Cant.14.5602.632.7993.70125/8No
va31/23.959Ok31/226.3503.723.9483.94825/8No
va35/83.959Ok31/236.2903.683.9093.90925/8No
va33/43.959Ok31/246.6603.914.1504.15025/80.19111/25.225Ok
56.4603.784.0194.01925/80.06111/25.225Ok
66.5703.854.0914.09125/80.13211/25.225OkOk76.1803.613.8373.83725/8No
va31/23.959Ok3Ok
ACERO NEGATIVOApoyoM (Ton-m)a (cm)As-(cm) calculado As-(cm)
diseoDistribucinOk!As principalAs bastn (cm)As-(cm) colocadoCant.As
Cant.16.9904.114.3664.36625/80.40711/25.225Ok
27.6104.494.7754.77525/80.81611/25.225Ok
37.7904.614.8944.89425/80.93511/25.225Ok
47.4704.414.6824.68225/80.72311/25.225Ok
57.6904.544.8284.82825/80.86911/25.225Ok
66.6003.874.1104.11025/80.15211/25.225OkOk76.5303.834.0654.06525/80.10611/25.225OkOk
7)Distribucin de Acero (As principal y As bastn)7.1 As principal
2 5/82 5/82 5/82 5/82 5/82 5/82 5/80 00 00 00 00 00 00 0
2 5/82 5/82 5/82 5/82 5/82 5/82 5/80 00 00 00 00 00 00 0
7.2 As bastn 1 1/21 1/21 1/21 1/21 1/21 1/21 1/20 00 00 00 00 00
00 0
3 1/23 5/83 3/41 1/21 1/21 1/23 1/23 1/23 1/23 1/20 00 00 03
0
8)Verificacin del cumplimiento de la norma E-060
Disposicin de la Norma E-060 - Refuerzo Longitudinal (Para
condiciones sismo-resistentes)
OkOkOkOkOkOk
OkOkOkOkOkOk
As-(cm)5.23 /35.23 /35.23 /35.23 /35.23 /35.23 /35.23 /3
As+(cm)3.963.963.963.963.963.963.96Falta AsOkOkOkOkOkOkOk
Los momentos que se presentan a continuacin son extraidos del
diagrama de momentos (ENVOL) del software Etabs V.9.0.2, los mismos
que son tomados a cara del apoyo. Deben tener refuerzo continuo, a
todo lo largo de la viga, constituido por 2 barras como mnimo,
tanto en la cara superior como en la inferior, con un rea de acero
no menor a 1/4 de la mxima requerida en los nudos, ni menor del rea
mnima exigida por flexin. La resistencia a momento positivo en la
cara del nudo (extremo inferior del tramo) no ser menor que 1/3 de
la resistencia a momento negativo en la misma cara del nudo
(extremo superior). La cuanta del refuerzo en traccin 0.025.
Combinacin de AsCOMBINACIONES DE ACEROS COMERCIALES
ACEROS COMERCIALES1. Recomendaciones para la distribucin de
varillasBARRADIAMETRO PesoAreaNpulgcmKg/mcm2# 33/8"0.950.5590.71#
41/2"1.270.9931.29# 55/8"1.591.5521.98# 63/4"1.912.2352.85#
77/8"2.223.0423.88# 81"2.543.9735.1# 91 1/8"2.865.0286.45# 101
1/4"3.186.2078.19# 111 3/8"3.497.5119.58# 121 1/2"3.818.93811.4
2. Combinaciones
CombinacionesAs (cm2)Estribos (pulg)b min (cm)CombinacionesAs
(cm2)Estribos (pulg)b min (cm)23/81.4253/814.3521+
23/415.8353/826.423/811/2+ 13/81.9793/814.6721+
35/816.0723/829.911/233/82.1383/817.8433/4+
61/216.1513/843.5621/22.5343/814.9953/4+ 15/816.2303/833.7211/2+
23/82.6923/818.1643/4+ 41/216.4683/840.3943/82.8503/821.3433/4+
45/816.4683/837.2121/2+ 13/83.2463/818.4811+
43/416.4683/830.2315/8+ 11/23.2463/815.3053/4+
21/216.7853/837.2131/23.8003/818.8011+ 65/816.9433/837.2121/2+
23/83.9593/821.9763/417.1013/834.0425/83.9593/815.6231+
15/817.1813/826.7313/4+ 11/24.1173/815.6243/4+
35/817.3393/837.5331/2+ 13/84.5133/822.2943/4+
51/217.7353/844.2015/8+ 21/24.5133/819.1153/4+
31/218.0513/841.0213/4+ 15/84.8303/815.9421+
45/818.0513/834.0441/25.0673/822.6131+ 13/418.0513/827.0525/8+
11/25.2253/819.4353/4+ 25/818.2103/837.8531/2+
23/85.2253/825.7863/4+ 11/218.3683/837.8513/4+
21/25.3843/819.4333/4+ 55/818.4473/841.3423/45.7003/816.2621+
33/418.6853/830.8615/8+ 31/25.7803/822.9243/4+
61/219.0023/848.0135/85.9383/819.7531+
25/819.1603/830.8651/26.3343/826.4253/4+ 41/219.3183/844.8325/8+
21/26.4923/823.2443/4+ 45/819.3183/841.6613/4+ 31/26.6513/823.2411+
53/419.3183/834.6713/4+ 25/86.8093/820.0763/4+
21/219.6353/841.6623/4+ 11/26.9673/820.0721+
55/820.0313/838.1615/8+ 41/27.0463/826.7353/4+
35/820.1893/841.9711+ 15/87.0463/816.5753/4+
51/220.5853/848.6435/8+ 11/27.2053/823.5663/4+
31/220.9023/845.4761/27.6013/830.2331+ 23/420.9023/831.5023/4+
15/87.6803/820.3831+ 35/821.1393/834.9925/8+ 31/27.7593/827.0543/4+
55/821.2983/845.7845/87.9173/823.8821+ 43/421.5353/835.3113/4+
41/27.9173/827.0553/4+ 61/221.8523/852.4511+ 13/47.9173/816.8921+
65/822.0103/842.2923/4+ 21/28.2343/823.8863/4+
41/222.1683/849.2835/8+ 21/28.4723/827.3753/4+
45/822.1683/846.1033/48.5513/820.7011+ 63/422.1683/839.1213/4+
35/88.7883/824.1941+ 15/822.2483/831.8125/8+ 41/29.0263/830.8631+
45/823.1193/839.1211+ 25/89.0263/820.7041+ 13/423.1193/832.1345/8+
11/29.1843/827.6963/4+ 51/223.4353/853.0913/4+ 51/29.1843/830.8631+
33/423.7523/835.9423/4+ 31/29.5013/827.6953/4+
55/824.1483/850.2323/4+ 25/89.6593/824.5141+
25/824.2273/835.9435/8+ 31/29.7383/831.1821+
53/424.3853/839.7533/4+ 11/29.8173/824.5163/4+
61/224.7023/856.9055/89.8973/828.0031+ 55/825.0983/843.2445/8+
21/210.4513/831.5041+ 23/425.9693/836.5813/4+ 61/210.4513/834.6741+
35/826.2063/840.0733/4+ 15/810.5303/824.8331+
43/426.6023/840.3923/4+ 41/210.7683/831.5031+
65/827.0773/847.3713/4+ 45/810.7683/828.3221+ 63/427.2363/844.2011+
23/410.7683/821.3451+ 15/827.3153/836.8935/8+ 41/211.0053/834.9941+
45/828.1863/844.2011+ 35/811.0053/824.8351+ 13/428.1863/837.2133/4+
21/211.0843/828.3241+ 33/428.8193/841.0243/411.4013/825.1551+
25/829.2943/841.0223/4+ 35/811.6383/828.6431+
53/429.4523/844.8345/8+ 31/211.7183/835.3141+
55/830.1653/848.3265/811.8763/832.1351+ 23/431.0363/841.6623/4+
51/212.0343/835.3151+ 35/831.2733/845.1521+ 15/812.1133/821.6541+
43/431.6693/845.4733/4+ 31/212.3513/832.1341+
65/832.1443/852.4533/4+ 25/812.5093/828.9631+
63/432.3033/849.2843/4+ 11/212.6683/828.9661+
15/832.3823/841.9713/4+ 55/812.7473/832.4551+
45/833.2533/849.2845/8+ 41/212.9843/839.1261+ 13/433.2533/842.2911+
45/812.9843/828.9651+ 33/433.8863/846.1021+ 13/412.9843/821.9761+
25/834.3613/846.1023/4+ 61/213.3013/839.1241+
53/434.5193/849.9143/4+ 15/813.3803/829.2751+
55/835.2323/853.4033/4+ 41/213.6183/835.9461+
23/436.1033/846.7423/4+ 45/813.6183/832.7761+ 35/836.3403/850.2311+
33/413.6183/825.7851+ 43/436.7363/850.5543/4+ 21/213.9343/832.7751+
65/837.2113/857.5321+ 25/814.0933/825.7841+
63/437.3703/854.3653/414.2513/829.5961+ 45/838.3203/854.3633/4+
35/814.4893/833.0861+ 33/438.9533/851.1833/4+ 51/214.8853/839.7551+
53/439.5873/854.9911+ 55/814.9643/833.0861+ 55/840.2993/858.4843/4+
31/215.2013/836.5861+ 43/441.8033/855.6343/4+ 25/815.3603/833.4061+
65/842.2783/862.6153/4+ 11/215.5183/833.4051+
63/442.4373/859.4423/4+ 55/815.5973/836.8961+ 53/444.6543/860.0761+
63/447.5043/864.52
&F
1) Considerar un nmero de varillas de refuerzo en relacin al
ancho de la viga. As para anchos menores o iguales a 30 cm.
considerar 2 barras y para anchos comprendidos entre 30 y 45 cm.
por lo menos 3.2) No usar simultneamente barras muy diferentes
dentro del diseo de un mismo elemento.3) Escoger dimetros de barras
de acuerdo a las caractersticas del elemento o de la estructura que
se proyecta. Esta recomendacin trata de evitar por ejemplo que se
coloque una barra de 3/4" en una vigueta de aligerado o que se
coloque una barra de 3/8 como bastn de una viga importante en
peralte y luz. Ser preferible acostumbrarse a armar las losas
macizas o aligeradas, considerando refuerzos de 3/8" y 1/2",
pudindose disponer de 5/8" en casos necesarios.