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Abacos para mampostería confinada. Teoría de Resistencia Última.
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ESCUELA POLITCNICA NACIONAL FACULTAD DE INGENIERA CIVIL Y AMBIENTAL
MAESTRA EN ESTRUCTURAS
BACOS PARA MAMPOSTERA CONFINADA TEORA DE LTIMA RESISTENCIA
SISTEMAS ESTRUCTURALES ALTERNATIVOS
Jos Manuel Vargas Nieto Ingeniero Civil
10 de Julio de 2015
DESCRIPCIN DE LA TAREA
Trabajo No. 3 bacos realizados a partir de la teora de resistencia ltima para mampostera confinada.
1
MAMPOSTERA CONFINADA
1 Teora de ltima Resistencia
1.1 Modelo de Mampostera Confinada
Compresin = 0.852
Tensin
= Carga Axial
= Momento
= (
2
2) + (
2 ) ; = 0.85
1.2 Condicin Balanceada
=
; = 0.003; =
=
+ = 0.6
=0.852
+
1.3 Lmites
Carga ltima = 0.85
= ; = [1 (
40 )
3
]
Si la seccin tiene Pn > 0, sta se encuentra en compresin. = 0.60 Si la seccin tiene 0.1 Pnmax Pn > 0, entonces:
= 0.60 + 0.25 (0.1
0.1 )
Si la seccin tiene Pn 0, sta se encuentra en tensin. = 0.85 Momento ltimo
=
Mampostera Confinada. Teora de ltima Resistencia Ing. Jos Manuel Vargas
2
2 Clculo Tipo para bacos de Interaccin P-M
2.1.1 Propiedades de los Materiales
f'm = 25 kgf/cm2 Resistencia de la mampostera
fy = 4,200 kgf/cm2 Resistencia a la fluencia del acero
2.1.2 Abaco de Interaccin P-M
b = 15 cm Ancho del panel H = 270 cm Altura del panel
L = 240 cm Longitud del panel He = 0.9089 Factor de esbeltez
L/6 = 40 cm cb = 138 cm Condicin balanceada
d' = 10 cm Distancia al eje del refuerzo # var = 4 Nmero de varillas
d = 230 cm Longitud efectiva = 8 mm Dimetro de varillas
min = 0.00035 Cuanta min. de refuerzo c/extremo As total = 2.0106 cm2 rea total de acero
max = 0.00350 Cuanta mx. de refuerzo c/extremo = 0.00058 Cuanta de acero
Total /4 varillas c/varilla Ts = 8,445 tonf Fuerza de tensin
Asmin = 1.21 0.30 cm2 0.62 cm Pnmax = 69,529 tonf Carga mxima
Asmax = 12.08 3.02 cm2 1.96 cm 0.1 Pn = 6,953 tonf
k = c/d c a C Pn Mn Pu Mu
cm cm kgf tonf tonf-m tonf tonf-m
0.05 11.5 9.8 3,116 -5.3 12.88 0.85 -4.12 10.94
0.10 23.0 19.6 6,232 -2.2 16.16 0.85 -1.71 13.73
0.15 34.5 29.3 9,347 0.9 19.14 0.82 0.67 15.64
0.20 46.0 39.1 12,463 4.0 21.81 0.71 2.58 15.39
0.25 57.5 48.9 15,579 7.1 24.18 0.60 3.89 14.51
0.30 69.0 58.7 18,695 10.3 26.24 0.60 5.59 15.74
0.35 80.5 68.4 21,810 13.4 28.00 0.60 7.29 16.80
0.40 92.0 78.2 24,926 16.5 29.45 0.60 8.99 17.67
0.45 103.5 88.0 28,042 19.6 30.60 0.60 10.69 18.36
0.50 115.0 97.8 31,158 22.7 31.45 0.60 12.39 18.87
0.55 126.5 107.5 34,274 25.8 31.99 0.60 14.09 19.19
0.60 138.0 117.3 37,389 28.9 32.23 0.60 15.78 19.34
0.65 149.5 127.1 40,505 32.1 32.16 0.60 17.48 19.30
0.70 161.0 136.9 43,621 35.2 31.79 0.60 19.18 19.07
0.75 172.5 146.6 46,737 38.3 31.11 0.60 20.88 18.67
0.80 184.0 156.4 49,853 41.4 30.13 0.60 22.58 18.08
0.85 195.5 166.2 52,968 44.5 28.84 0.60 24.28 17.30
0.90 207.0 176.0 56,084 47.6 27.25 0.60 25.98 16.35
0.95 218.5 185.7 59,200 50.8 25.35 0.60 27.68 15.21
1.00 230.0 195.5 62,316 53.9 23.15 0.60 29.38 13.89
1.05 241.5 205.3 65,431 57.0 20.65 0.60 31.08 12.39
1.10 253.0 215.1 68,547 60.1 17.84 0.60 32.78 10.70
1.15 264.5 224.8 71,663 63.2 14.73 0.60 34.47 8.84
1.20 276.0 234.6 74,779 66.3 11.31 0.60 36.17 6.78
1.25 287.5 244.4 77,895 69.4 7.59 0.60 37.87 4.55
1.30 299.0 254.2 81,010 72.6 3.56 0.60 39.57 2.13
1.35 310.5 263.9 84,126 75.7 -0.77 0.60 41.27 -0.46
Mampostera Confinada. Teora de ltima Resistencia Ing. Jos Manuel Vargas
3
0.0
20.0
40.0
60.0
80.0
100.0
0.0 10.0 20.0 30.0 40.0 50.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
Abaco de Interaccin P-Mf'm = 25 kgf/cm2; L = 240 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
0.0
20.0
40.0
60.0
80.0
100.0
0.0 10.0 20.0 30.0 40.0 50.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
Abaco de Interaccin P-Mf'm = 25 kgf/cm2; L = 240 cm; H = 270 cm; b = 15 cm
Pn-Mn, 10
Pu-Mu, 10
0.0
20.0
40.0
60.0
80.0
100.0
0.0 10.0 20.0 30.0 40.0 50.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
Abaco de Interaccin P-Mf'm = 25 kgf/cm2; L = 240 cm; H =270 cm; b = 15 cm
Pn-Mn, 12
Pu-Mu, 12
Mampostera Confinada. Teora de ltima Resistencia Ing. Jos Manuel Vargas
4
3 bacos de Interaccin P-M
3.1 Mampostera Confinada fm = 25 kgf/cm2; L = 240 cm; H = 270 cm; b = 15 cm
3.2 Mampostera Confinada fm = 30 kgf/cm2; L = 240 cm; H = 270 cm; b = 15 cm
0.0
20.0
40.0
60.0
80.0
100.0
0.0 10.0 20.0 30.0 40.0 50.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
baco de Interaccin P-Mf'm = 25 kgf/cm2; L = 240 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
Pn-Mn, 10
Pu-Mu, 10
Pn-Mn, 12
Pu-Mu, 12
0.0
20.0
40.0
60.0
80.0
100.0
0.0 10.0 20.0 30.0 40.0 50.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
baco de Interaccin P-Mf'm = 30 kgf/cm2; L = 240 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
Pn-Mn, 10
Pu-Mu, 10
Pn-Mn, 12
Pu-Mu, 12
Mampostera Confinada. Teora de ltima Resistencia Ing. Jos Manuel Vargas
5
3.3 Mampostera Confinada fm = 25 kgf/cm2; L = 300 cm; H = 270 cm; b = 15 cm
3.4 Mampostera Confinada fm = 30 kgf/cm2; L = 300 cm; H = 270 cm; b = 15 cm
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
baco de Interaccin P-Mf'm = 25 kgf/cm2; L = 300 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
Pn-Mn, 10
Pu-Mu, 10
Pn-Mn, 12
Pu-Mu, 12
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
baco de Interaccin P-Mf'm = 30 kgf/cm2; L = 300 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
Pn-Mn, 10
Pu-Mu, 10
Pn-Mn, 12
Pu-Mu, 12
Mampostera Confinada. Teora de ltima Resistencia Ing. Jos Manuel Vargas
6
3.5 Mampostera Confinada fm = 25 kgf/cm2; L = 360 cm; H = 270 cm; b = 15 cm
3.6 Mampostera Confinada fm = 30 kgf/cm2; L = 360 cm; H = 270 cm; b = 15 cm
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
baco de Interaccin P-Mf'm = 25 kgf/cm2; L = 360 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
Pn-Mn, 10
Pu-Mu, 10
Pn-Mn, 12
Pu-Mu, 12
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
baco de Interaccin P-Mf'm = 30 kgf/cm2; L = 360 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
Pn-Mn, 10
Pu-Mu, 10
Pn-Mn, 12
Pu-Mu, 12
Mampostera Confinada. Teora de ltima Resistencia Ing. Jos Manuel Vargas
7
3.7 Mampostera Confinada fm = 25 kgf/cm2; L = 400 cm; H = 270 cm; b = 15 cm
3.8 Mampostera Confinada fm = 30 kgf/cm2; L = 400 cm; H = 270 cm; b = 15 cm
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
baco de Interaccin P-Mf'm = 25 kgf/cm2; L = 400 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
Pn-Mn, 10
Pu-Mu, 10
Pn-Mn, 12
Pu-Mu, 12
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0
Pu
/Pn
, to
nf
Mu/Mn, tonf-m
baco de Interaccin P-Mf'm = 30 kgf/cm2; L = 400 cm; H = 270 cm; b = 15 cm
Pn-Mn, 8
Pu-Mu, 8
Pn-Mn, 10
Pu-Mu, 10
Pn-Mn, 12
Pu-Mu, 12
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