Trabajo escolar. Memoria de cálculo para vigas de amarre de azotea.
UNIVERSIDAD AUTONOMA DE NUEVO LEONFACULTAD DE ARQUITECTURAING.
DAVID RAMIREZTEMA: CALCULO DE LOSA DE AZOTEA
CALCULO DE LOSA DE AZOTEA
CALCULO DEL PESO PROPIO DE LA LOSA:C.V.= 100 Kg. / m2Peso propio
Impermeabilizante: 15 Kg. / m2Peso propio Empastado: 100 Kg. /
m2Peso propio Relleno Pluvial: 90 Kg. / m2Peso propio Losa Solida
de Concreto: 168 Kg. / m2Peso propio Lmina Galvanizada: 6.73 Kg. /
m2Peso propio Vigas Joist: 7.91 Kg. / m2Peso propio Ductos A/C: 40
Kg. / m2Peso propio Plafn Cielo: C.M. = 445.4 Kg / M2 = 445 Kg. /
Ml
7.76 Kg. / m2Ws = CM + CV = 445 + 100 = 545 Kg / m2
Peso propio Elemento Secundario: 10.00 Kg. / m2VIGAS DE AMARRE
DE AZOTEA
VIGA VA-1EVALUACION DE LA CARGA LTIMA DE DISEO:Carga Muerta:Ws
Va-2 = (545)(.60) + 30 Kg / Ml + (12.5)(18)(1.80) = 762 Kg / m2Ws
Va-2 = 762 Kg / ml
Reacciones = Wl / 2 = 762(5.5) / 2 = 2096Momento Mayor = Wl^2 /8
= 762 (5.5)^2 / 8 = 2881Modulo Secc. Sxx = MMax (100) / Fb = 2881
(100) / 1520 = 190 cms2
Propone Perfil IPR 8 x 5 1/4 Seccin: 206 mm x 133 mmPeso: 29.8
Kg. / Mlrea: 37.93 cms2Sx: 279 cms3Ix: 2880 cms4Rx: 8.71 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (762) (5.5)^4 / 384
(2,100,000) (2880)Amax. = 1.50 < Perm. = 550/360 = 1.52 cms.
Revisin por Corte:Fv= Vmax./ rea = 2096 / 37.93 = 55.25 < Fv=
1050 Kg/cm2
VIGA VA-2EVALUACION DE LA CARGA LTIMA DE DISEO:Carga Muerta:Ws
Va-3 = (545)(.60) + 30 Kg / Ml + (12.5)(18)(1.80) = 762 Kg / m2Ws
Va-3 = 762 Kg / ml
Reacciones = Wl / 2 = 762(3.8) / 2 = 1448Momento Mayor = Wl^2 /8
= 762 (3.8)^2 / 8 = 1448Modulo Secc. Sxx = MMax (100) / Fb = 1448
(100) / 1520 = 95 cms2
Propone Perfil IPR 8 x 4 Seccin: 201 mm x 100 mmPeso: 14.9 Kg. /
Mlrea: 19.03 cms2Sx: 127 cms3Ix: 1282 cms4Rx: 8.20 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (762) (3.8)^4 / 384
(2,100,000) (1282)Amax. = .77 < Perm. = 380/360 = 1.05 cms.
Revisin por Corte:Fv= Vmax./ rea = 1448 / 19.03 = 76 < Fv=
1050 Kg/cm2
VIGA VA-3EVALUACION DE LA CARGA LTIMA DE DISEO:Carga Muerta:Ws
Va-5 = (545)(.60) + 30 Kg / Ml + (12.5)(18)(1.80) = 762 Kg / m2Ws
Va-5 = 762 Kg / ml
Reacciones = Wl / 2 = 762(4.5) / 2 = 1715Momento Mayor = Wl^2 /8
= 762 (4.5)^2 / 8 = 1929Modulo Secc. Sxx = MMax (100) / Fb = 1929
(100) / 1520 = 127 cms2
Propone Perfil IPR 8x 4 Seccin: 206 mm x 102 mmPeso: 22.4 Kg. /
Mlrea: 28.58 cms2Sx: 193 cms3Ix: 1998 cms4Rx: 8.35 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (762) (4.5)^4 / 384
(2,100,000) (1998)Amax. = .97 < Perm. = 450/360 =1.25
cms.Revisin por Corte:Fv= Vmax./ rea = 1715 / 28.58 = 60 < Fv=
1050 Kg/cm2
VIGA VA-4EVALUACION DE LA CARGA LTIMA DE DISEO:Carga Muerta:Ws
Va-1 = (545)(1.35) + 60 Kg / Ml = 796 Kg / m2Ws Va-1 = 796 Kg /
ml
Reacciones = Wl / 2 = 796(5.50) / 2 = 2189Momento Mayor = Wl^2
/8 = 796 (5.50)^2 / 8 = 3010Modulo Secc. Sxx = MMax (100) / Fb =
3010 (100) / 1520 = 198 cms2
Propone Perfil IPR 10 x 4 Seccin: 260 mm x 102 mmPeso: 28.3 Kg.
/ Mlrea: 36.19 cms2 Sx: 308 cms3 Ix: 4004 cms4Rx: 10.52 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (796) (5.5)^4 / 384
(2,100,00) (4004)Amax. = 1.13 < Perm. = 550/360 = 1.53 cms.
Revisin por Corte:Fv= Vmax./ rea = 2189 / 36.19 = 61 < Fv=
1050 Kg/cm2
VIGA VA-5EVALUACION DE LA CARGA LTIMA DE DISEO:Carga Muerta:Ws
Va-5 = (545)(1.35) + 60 Kg / Ml = 796 Kg / m2Ws Va-5 = 796 Kg /
ml3.8
Reacciones = Wl / 2 = 796 (3.8) / 2 = 1512Momento Mayor = Wl^2
/8 = 796 (3.8)^2 / 8 = 1437Modulo Secc. Sxx = MMax (100) / Fb =
1437 (100) / 1520 = 95 cms2
Propone Perfil IPR 6 x 4 Seccin: 159 mm x 102 mmPeso: 23.8 Kg. /
Mlrea: 30.45 cms2Sx: 165 cms3Ix: 1319 cms4Rx: 6.58 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (796) (3.8)^4 / 384
(2,100,000) (1319)Amax. = .78 < Perm. = 380/360 =
1.06cms.Revisin por Corte:Fv= Vmax./ rea = 1512/ 30.45 = 50 <
Fv= 1050 Kg/cm2
VIGA VA-6EVALUACION DE LA CARGA LTIMA DE DISEO:Carga Muerta:Ws
Va-6 = (545)(.60) + 50 Kg / Ml + (12.5 x 18 x 1.8) = 782 Kg / m2Ws
Va-6 = 782 Kg / ml 2.35
Reacciones = Wl / 2 = 782(2.35) / 2 = 919Momento Mayor = Wl^2 /8
= 782 (2.35)^2 / 8 = 540Modulo Secc. Sxx = MMax (100) / Fb = 540
(100) / 1520 = 36 cms2
Propone Perfil IPR 6 x 4 Seccin: 152 mm x 102 mmPeso: 17.9 Kg. /
Mlrea: 22.77 cms2Sx: 119 cms3Ix: 903 cms4Rx: 6.58 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (782) (2.35)^4 / 384
(2,100,000) (903)Amax. = .16 < Perm. = 235/360 =.65 cms.Revisin
por Corte:Fv= Vmax./ rea = 919 / 22.77 = 40 < Fv= 1050
Kg/cm2
VIGA VA-7EVALUACION DE LA CARGA LTIMA DE DISEO:Carga Muerta:Ws
Va-7 = (545)(.60) + 40 Kg / Ml + (12.5)(18)(1.80) = 772 Kg / m2Ws
Va-7 = 772 Kg / ml3.5
Reacciones = Wl / 2 = 772(3.5) / 2 = 1351Momento Mayor = Wl^2 /8
= 772 (3.5)^2 / 8 = 1182Modulo Secc. Sxx = MMax (100) / Fb = 1182
(100) / 1520 = 78 cms2
Propone Perfil IPR 6 x 4 Seccin: 152 mm x 102 mmPeso: 17.9 Kg. /
Mlrea: 22.77 cms2Sx: 119 cms3Ix: 903 cms4Rx: 6.58 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (772) (3.5)^4 / 384
(2,100,000) (903)Amax. = .79 < Perm. = 350/360 = .97 cms.Revisin
por Corte:Fv= Vmax./ rea = 1351 / 22.77 = 59 < Fv= 1050
Kg/cm2
EVALUACION DE LA CARGA LTIMA DE DISEO:VA-8 ENTREPISOWs VA-8 =
(Ws Azotea) (At) + (P.P. VA-8) + (12.5)(18)(1.80) = Ws VA-8 = (545)
(.725) + (50) + (12.5)(18)(1.80) = 850Ws VA-8 = 850 Kg / ml3.50
Reacciones = Wl / 2 = 850 (3.5) / 2 = 1488 KgMomento Mayor =
Wl^2 /8 = 850 (3.5)^2 / 8 = 1302 Kg/MModulo Secc. Sxx = MMax (100)
/ Fb = 1302(100) / 1520 = 86 cms2
Propone Perfil IPR 6 x 4 Seccin: 152 mm x 102 mmPeso: 17.9 Kg. /
Ml rea: 22.77 cms2Sx: 119 > 86 cms3Ix: 903 cms4Rx: 6.30 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (850) (3.5)^4 / 384
(2,100,000) (903)Amax. = .88 cm < Perm. = 350/360 = .97 cms.
Revisin por Corte:Fv= Vmax./ rea = 1488 / 22.77 = 65 < Fv=
1050 Kg/cm2
EVALUACION DE LA CARGA LTIMA DE DISEO:VA-9 ENTREPISOWs VA-9 =
(Ws Azotea) (At) + (P.P. VA-9) + (P.P. Muro perimetral)Ws VA-9 =
(545) (.60) + (25) + (12.5 x 18 x 1.8 )Ws VA-9 = 757 Kg / ml
2.00
Reacciones = Wl / 2 = 757 (2) / 2 = 757 KgMomento Mayor = Wl^2
/8 = 757 (2)^2 / 8 = 379 Kg/MModulo Secc. Sxx = MMax (100) / Fb =
379 (100) / 1520 = 25 cms2
Propone Perfil IPR 6 x 4 Seccin: 148 mm x 100 mmPeso: 12.7 Kg. /
Ml rea: 16.13 cms2Sx: 83 > 25 cms3Ix: 616 cms4Rx: 6.17 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (757) (2)^4 / 384
(2,100,000) (616)Amax. = .12 cm < Perm. = 200/360 = .55 cms.
Revisin por Corte:Fv= Vmax./ rea = 757 / 16.13 = 47 < Fv=
1050 Kg/cm2
EVALUACION DE LA CARGA LTIMA DE DISEO:VA-10 ENTREPISOWs VA-10 =
(Ws Entrepiso) (At) + (P.P. VA-10) + (P.P. Muro Perimetral)Ws VA-10
= (545) (.75) + (25) + (12.5 x 18 x 1.8 )Ws VA-10 = 839 Kg /
ml2.00
Reacciones = Wl / 2 =839 (4.5) / 2 = 1888 KgMomento Mayor = Wl^2
/8 = 839 (4.5)^2 / 8 = 2124 Kg/MModulo Secc. Sxx = MMax (100) / Fb
= 2124 (100) / 1520 = 140 cms2
Propone Perfil IPR 8 x 4 Seccin: 203 mm x 102 mmPeso: 19.4 Kg. /
Ml rea: 24.71 cms2Sx: 162 > 140 cms3Ix: 1644 cms4Rx: 8.15 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,100 Kg./cm3Amax. = 5 (839) (2)^4 / 384
(2,100,000) (1644)Amax. = .05 cm < Perm. = 200/360 = .55
cms.
Revisin por Corte:Fv= Vmax./ rea = 1888 / 24.71 = 76 < Fv=
1050 Kg/cm2
EVALUACION DE LA CARGA LTIMA DE DISEO:VA-11 ENTREPISOWs VA-11 =
(Ws Entrepiso) (At) + (P.P. VA-11) + (12.5 x 18 x 1.8 )Ws VA-11 =
(545) (.275) + (75) + (12.5 x 18 x 1.8 ) = 630Ws VA-11 = 630 Kg /
ml4.50
Reacciones = Wl / 2 = 630 (4.5) / 2 = 1418 KgMomento Mayor =
Wl^2 /8 = 630 (4.5)^2 / 8 = 1595 Kg/MModulo Secc. Sxx = MMax (100)
/ Fb = 1595 (100) / 1520 = 105 cms2
Propone Perfil IPR 8 x 4 Seccin: 203 mm x 102 mmPeso: 19.4 Kg. /
Ml rea: 24.71 cms2Sx: 162 > 105 cms3Ix: 1644 cms4Rx: 8.15 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (630) (4.5)^4 / 384
(2,100,000) (1644)Amax. = .97 cm < Perm. = 450/360 = 1.25
cms.
Revisin por Corte:Fv= Vmax./ rea = 1418 / 24.71 = 57 < Fv=
1050 Kg/cm2
EVALUACION DE LA CARGA LTIMA DE DISEO:VA-12 ENTREPISOWs VA-12 =
(Ws Entrepiso) (At) + (P.P. VA-12) + (12.5 x 18 x 1.8 )Ws VA-12 =
(545) (.275) + (45) + (12.5 x 18 x 1.8 ) = 600Ws VA-12 = 600 Kg /
ml5.50
Reacciones = Wl / 2 = 600 (5.5) / 2 = 1650 KgMomento Mayor =
Wl^2 /8 = 600 (5.5)^2 / 8 = 2269 Kg/MModulo Secc. Sxx = MMax (100)
/ Fb = 2269(100) / 1520 = 149 cms2
Propone Perfil IPR 8 x 4 Seccin: 206 mm x 102 mmPeso: 22.4 Kg. /
Ml rea: 28.58 cms2Sx: 193 > 149 cms3Ix: 1998 cms4Rx: 8.35 cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (600) (5.5)^4 / 384
(2,100,000) (1998)Amax. = 1.70 cm < Perm. = 615/360 = 1.71
cms.
Revisin por Corte:Fv= Vmax./ rea = 1650 / 28.58 = 58 < Fv=
1050 Kg/cm2
EVALUACION DE LA CARGA LTIMA DE DISEO:VA-13 ENTREPISOWs VA-13 =
(Ws Entrepiso) (At) + (P.P. VA-13) + (P.P. Muro Perimetral)Ws VA-13
= (545) (.275) + (35) + (12.5 x 18 x 1.8 )Ws VA-13 = 590 Kg /
ml
6.15
Reacciones = Wl / 2 = 590 (6.15) / 2 = 1814 KgMomento Mayor =
Wl^2 /8 = 590 (6.15)^2 / 8 = 2789 Kg/MModulo Secc. Sxx = MMax (100)
/ Fb = 2789 (100) / 1520 = 184 cms2
Propone Perfil IPR 10 x 4 Seccin: 260 mm x 102 mmPeso: 28.3 Kg.
/ Ml rea: 36.19 cms2Sx: 308 > 184 cms3Ix: 4004 cms4Rx: 10.52
cm
REVISIN POR DEFLEXION (Flecha Mx.):Mx. = 5WL^4 / 384EI = < AP
= L/360 = Perm.E= 2,100,000 Kg./cm3Amax. = 5 (590) (6.15)^4 / 384
(2,100,000) (4004)Amax. = 1.31 cm < Perm. = 615/360 = 1.71
cms.
Revisin por Corte:Fv= Vmax./ rea = 1814 / 36.19 = 50 < Fv=
1050 Kg/cm2
EQUIPO # 2 JUAN CARLOS LEURA ESPINOSAJESUS ARTEMIO CARRANZA
SILVAMIGUEL ALEJANDRO CARRANZA MENDOZALUIS ALAIN COBA REYES
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