abacos biaxial
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DIAGRAMAS DE FLEXION BIAXIALA. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 . . . . . . . . . . . . . . . . Columnas con 8 barras fy = 420 MPa (1 - 16) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa = 0.8 f'c = 40 MPa = 0.8 f'c = 45 MPa = 0.8 f'c = 50 MPa = 0.8 f'c = 55 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa f'c = 40 MPa f'c = 45 MPa f'c = 50 MPa f'c = 55 MPa = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9
B. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
. . . . . . . . . . . . . . . .
Columnas con Armadura Perimetral fy = 420 MPa (17 - 32) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa = 0.8 f'c = 40 MPa = 0.8 f'c = 45 MPa = 0.8 f'c = 50 MPa = 0.8 f'c = 55 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa f'c = 40 MPa f'c = 45 MPa f'c = 50 MPa f'c = 55 MPa = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9 = 0.9
C. 33 34 35 36 37 38 39 40
. . . . . . . .
Columnas con 8 barras fy = 280 MPa (33 - 40) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa = 0.9 = 0.9 = 0.9 = 0.9
D. 41 42 43 44 45 46 47 48
. . . . . . . .
Columnas con Armadura Perimetral fy = 280 MPa (41 - 48) = 0.8 f'c = 20 MPa = 0.8 f'c = 25 MPa = 0.8 f'c = 30 MPa = 0.8 f'c = 35 MPa f'c = 20 MPa f'c = 25 MPa f'c = 30 MPa f'c = 35 MPa = 0.9 = 0.9 = 0.9 = 0.9
1.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 20 MPa fy = 420 MPa = 0.8
Mhb b
g = 1% 2 4 6 8 10 y 10
y 10 8 6 4 4 2 x 2
10
8
6
4
2
x
= 21.0
= 0.0g = 8%
8 6
= 19.0g = 8%
g = 8% 6%
= 2.0
5% 4%
1%
g = 8% 1% 1%
4 4 2 x 2
2% 1%
g = 8%
g = 8%
4 6 8 10 y
= 16.0g = 8% g = 8%
= 6.0
4 6 8
= 13.0 10 8 6 4 2 x 2
= 9.0
10 6 8 10 y
4
2.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 25 MPa fy = 420 MPa = 0.8
Mhb b
g = 1% 2 4 6 8 10 y 10
y 10 8 6 4 4 2 x 2 4 6 8 10 y
10
8
6
4
2
x
= 23.0
= 0.0g = 8%
8 6
= 20.0g = 8%
g = 8%
= 2.56% g = 8%
4 4 2 x 2
5%
1%
1%
3%
1%
1% 1% g = 8%
g = 8%
= 16.5g = 8% g = 8%
4 = 7.2 6 8
= 13.0 10 8 6 4 2 x 2
= 10.0
10 6 8 10 y
4
3.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 30 MPa fy = 420 MPa = 0.8
Mhb b
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 3.0 6 4 4 2 x 2g = 8%
y 10 8 6 4 4 2 x 2
10
8
6
4
2
x
= 25.5g = 8%
g = 8%
= 21.0g = 8% 4% 3%
6%
g = 8%
1% 1% 1% 1% 1%
g = 8%
4 6 8 10 y
= 18.0g = 8% g = 8%
4 = 7.5 6 8
= 15.0 10 8 6 4 2 x 2
= 12.0
10 6 8 10 y
4
4.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 35 MPa fy = 420 MPa = 0.8
Mhb b
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 3.5 6 4 4 2 x 2g = 8%
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 27.5
g = 8%
g = 8%
= 23.5
g = 8%
6%
g = 8%
4%
1% 1%
2%
1% 1%
2 4 6
1% g = 8%
= 19.5g = 8% g = 8%
4 = 8.8 6 8 10
8 10 y 10 8 6 = 15.5 4 2 x
= 12.5
2
4
6
8
10
y
5.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 40 MPa fy = 420 MPa = 0.8
Mhb b
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 4.0 6 4 4 2 xg = 8%
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 29.5g = 8% g = 8%
= 25.0g = 8% 4%
6%
g = 8%
1% 1% 2%
1% 1%
2g = 8%
2 4
1%
4 6
= 21.0g = 8%
= 9.6g = 8%
6 8 10
8 10 y 10 8 6 = 17.0 4 2 x 2
= 13.5
4
6
8
10
y
6.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 45 MPa fy = 420 MPa = 0.8
Mhb b
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 4.5 6 4 4 2 x 21% g = 8%
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 31.5g = 8%
g = 8%
= 27.0g = 8% 4%
6% g = 8%
1% 1%
2%
1% 1%
2g = 8%
4 6 8 10 y
= 23.0
4 = 10.0g = 8% g = 8%
6 8 10
= 18.0 10 8 6 4 2 x 2
= 14.0
4
6
8
10
y
7.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 50 MPa fy = 420 MPa = 0.8
Mhb b
g = 1% 2 4 6 = 0.0g = 8%
y 10 8
10
8
6
4 = 33.0
2
x
8
10
y 10 8
g = 8%
66%
= 5.0g = 8%
6 4 4 2 x 2
4 4 2 x 2 4 6 8 10 y
= 29.0g = 8% 4% 1% 1%
2% 1% g = 8%
1%
1%
g = 8%
4 = 9.0g = 8% g = 8%
= 24.5
6 8
= 20.0 10 8 6 4 2 x 2
= 15.5 4 6 8 10
10 y
8.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 55 MPa fy = 420 MPa = 0.8
Mhb b
g = 1% 4 6 8 10 12 y 12 10g = 8%
y 12 10 8 6 4 4 2 x
12 10
8
6
4
2
x 2
= 35.8
= 0.0
g = 8% 6%
8 = 5.5g = 8%
6 4 4 2 x
= 30.0g = 8% 3%
1% 1%
1%
2 4 6 8 10 12 y 12 10 8 = 20.0 6 4 2 x 21% 1%
1% g = 8%
2 4
= 25.0
g = 8%
= 11.0g = 8% g = 8%
6 8 10 12
= 15.0
4
6
8
10 12
y
9.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 20 MPa fy = 420 MPa = 0.9
Mhb b
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 2.0 6 4 4 2 x 2g = 8%
y 10 8 6
10
8
6
4
2
x
= 21.0
g = 8%
g = 8%
4 4 2 x
= 19.0
g = 8%
6%
g = 8%
5%
1% 1% 1% 2% 1%
4%
2 4 6 8 10 y 10 8 6 = 13.0 4 2 = 16.0g = 8%
4 = 6.0g = 8% g = 8%
6 8 10
= 9.0
x
2
4
6
8
10
y
10.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 25 MPa fy = 420 MPa = 0.9
Mhb b
g = 1% 4 6 8 10 12 y 12 10g = 8%
y 12 10 8 6 4 4 2 x
12 10
8
6
4
2
x 2
= 0.0 = 23.0
8 = 2.5 = 20.0g = 8% g = 8% g = 8% 6%
6 4 4 2 x 2
5%
1% 1% 3% 1% 1% 1%
2 4 6 8 10 12 y 12 10 = 16.5
g = 8%
g = 8%
4 = 7.2g = 8% g = 8%
6 8 10 12
= 13.0 8 6 4 2 x 2
= 10.0
4
6
8
10 12
y
11.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 30 MPa fy = 420 MPa = 0.9
Mhb b
g = 1% 4 6 8 10 12 y 12 10g = 8%
y 12 10 8 6 4 4 2 x 2 4 6 8 10 12 y
12 10
8
6
4
2
x 2
= 0.0 = 25.5
= 3.0 = 21.0g = 8% 1% 4% 3% 1% 1% 1% 1% g = 8% g = 8% 6%
8 6 4 4 2 x 2
g = 8%
= 18.0g = 8% g = 8%
g = 8%
4 6 8 10 12
= 7.5
= 15.0 12 10 8 6 4 2 x 2
= 12.0
4
6
8
10 12
y
12.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 35 MPa fy = 420 MPa = 0.9
Mhb b
g = 1% 4 6 8 10 12 y 12 10g = 8%
y 12 10 8 6 4 4 2 x
12 10
8
6
4
2
x 2
= 0.0 = 27.5g = 8%
8 = 3.5g = 8%
6 4 4 2 x 2
= 23.56% g = 8% 4% 1% 1% 3% 1% 1% 1%
2 4 6 8 10 12 y 12 10 8 = 15.5 6 4 2 = 19.5g = 8%
g = 8%
4 = 8.8 6 8 10 12
g = 8%
g = 8%
= 12.5
x 2
4
6
8
10 12
y
13.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 40 MPa fy = 420 MPa = 0.9
Mhb b
g = 1% 4 6 8 10 12 y 12 10g = 8%
y 12 10 8 6 4 4 2 x 2 4 6 8 10 12 y
12 10
8
6
4
2
x 2
= 0.0 = 29.5g = 8%
8 = 25.0g = 8% 4% 1% 1%
= 4.06% g = 8%
6 4 4 2 x 2
2% 1%
1% 1%
= 21.0
g = 8%
g = 8%
4 = 9.6 6 8 10 12
g = 8%
g = 8%
= 17.0 12 10 8 6 4 2 x 2
= 13.5
4
6
8
10 12
y
14.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 45 MPa fy = 420 MPa = 0.9
Mhb b
g = 1% 4 6 8 10 12 y 12 10 = 4.5 8 6
y 12 10 8 6 4 4 2 x 2 4 6 8 10 12 y
12 10
8
6
4
2
x 2
= 0.0 = 31.5g = 8% g = 8%
= 27.0g = 8%
6%
g = 8%
4%
1%
4 4 2 x 2
1%
2%
1% 1% 1% g = 8%
= 23.0
g = 8%
4 6 8
= 10.0g = 8% g = 8%
= 18.0 12 10 8 6 4 2 x 2
= 14.0
10 12 8 10 12 y
4
6
15.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 50 MPa fy = 420 MPa = 0.9
Mhb b
g = 1% 4 6 8 10 12 y 12 10 8 = 5.0
y 12 10 8 6 4 4 2 x 2 4 6 8 10 12 y
12 10
8
6
4
2
x 2
= 0.0 = 33.0 = 29.0g = 8% 4% 1% 1% g = 8% 6% g = 8% g = 8%
6 4 4 2 x 2
2% 1% g = 8%
1%
1%
g = 8%
4 6 8
= 24.5g = 8% g = 8%
= 9.0
= 20.0 12 10 8 6 4 2 x 2
= 15.5
10 12 8 10 12 y
4
6
16.- FLEXION BIAXIAL EN COLUMNAS ARMADAS CON 8 BARRASAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 55 MPa fy = 420 MPa = 0.9
Mhb b
g = 1% 4 6 8 10 12 y 12 10 8 = 5.5
y 12 10 8 6 4 4 2 x 2 4 6 8 10 12 y
12 10
8
6
4
2
x 2
= 35.8
= 0.0g = 8%
g = 8%
= 30.0
6 4 4 2 x
6% g = 8%
g = 8%
3%
1%
1%
1%
1%
2g = 8%
1%
1%
4 6 8 10 12
g = 8%
= 25.0g = 8% g = 8%
= 11.0
= 20.0 12 10 8 6 4 2 x 2
= 15.0
4
6
8
10 12
y
17.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 20 MPa fy = 420 MPa Mhb b
= 0.8
g = 1% 2 4 6 8 10 y 10 8 = 2.0g = 8%
y 10 8 6 4 4 2 x 2 4 6 8 10 y
10
8
6
4
2
x
= 21.0
= 0.0g = 8%
6 4 4 2 x
= 19.0g = 8%
g = 8%
6%
5%
1% 1% 1% 2% 1% g = 8%
4%
g = 8%
2 4 6 8 10
= 16.0g = 8% g = 8%
= 6.0
= 13.0
= 9.0
10
8
6
4
2
x
2
4
6
8
10
y
18.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 25 MPa fy = 420 MPa Mhb b
= 0.8
g = 1% 2 4 6 8 10 y 10 8 = 2.5 6 4 4 2 xg = 8%
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 23.0
= 0.0g = 8%
= 20.0g = 8%
g = 8% 6% 1% 1% 3% 1% 1%
g = 8%
5%
2 4 6 8 10 y 10 8 6 = 13.0 = 16.5g = 8%
1%
2 4 6 8 10
= 7.2g = 8% g = 8%
= 10.0
4
2
x
2
4
6
8
10
y
19.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 30 MPa fy = 420 MPa Mhb b
= 0.8
g = 1% 2 4 6 8 10 y 10 8 = 3.0 6 4 4 2 x 2g = 8%
y 10 8 6 4 2 x 2
10
8
6
4
2
x
= 25.5
= 0.0g = 8%
= 21.0g = 8%
g = 8%
6% 1% 1% 1% 1%
g = 8%
4%
3% 1% g = 8%
4 6 8 10 y
= 18.0g = 8% g = 8%
= 7.5
4 6 8 10
= 15.0
= 12.0
10
8
6
4
2
x
2
4
6
8
10
y
20.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 35 MPa fy = 420 MPa Mhb b
= 0.8
g = 1% 2 4 6 8 10 y 10 8g = 8%
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 27.5
= 0.0
= 23.5g = 8%
g = 8% 6%
= 3.5g = 8% 1% 1% 2% 1% 1% 1%
6 4 4 2 x 2
4%
2 4 6 8 10 y 10 8 6 = 15.5 = 19.5g = 8%
g = 8%
= 8.8g = 8% g = 8%
4 6 8 10
= 12.5
4
2
x
2
4
6
8
10
y
21.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 40 MPa fy = 420 MPa Mhb b
= 0.8
g = 1% 2 4 6 8 10 y 10 8 = 4.0 6 4 4 2 x
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 29.5
= 0.0g = 8%
= 25.0g = 8%
g = 8%
6% g = 8% 4% 1%
1%
2%
1% 1% 1%
2 4 6 8 10 y 10 8 6 = 17.0 = 21.0g = 8%
2g = 8%
= 9.6g = 8% g = 8%
4 6
= 13.5
8 10
4
2
x
2
4
6
8
10
y
22.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 45 MPa fy = 420 MPa Mhb b
= 0.8
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 4.5 6 4 4 2 x
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 31.5g = 8% g = 8%
= 27.0
6% g = 8%
g = 8%
4%
1%
1%
2%
1% 1%
2g = 8%
21% g = 8%
4 6 8 10 y
= 23.0
= 10.0g = 8%
4 6
g = 8%
= 18.0
= 14.0
8 10
10
8
6
4
2
x
2
4
6
8
10
y
23.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 50 MPa fy = 420 MPa Mhb b
= 0.8
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 5.0 6 4 4 2 x
y 10 8 6 4 4 2 x 2 4 6 8 10 y
10
8
6
4
2
x
= 33.0g = 8% g = 8%
= 29.0g = 8% 4%
6% g = 8%
1%
1%
2%
1% g = 8% 1%
2 = 9.0 4 6
g = 8%
1%
= 24.5g = 8% g = 8%
8 10 6 8 10 y
= 20.0
= 15.5 x
10
8
6
4
2
2
4
24.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 55 MPa fy = 420 MPa Mhb b
= 0.8
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 5.5g = 8%
y 10 8 6 4 4 2 x 2 4 6 8 10 y
10
8
6
4
2
x
= 35.8g = 8% g = 8% 6%
6 4 4 2 x
= 30.0g = 8% 3%
1%
1%
1%
1% g = 8% 1% 1%
2 4 = 11.0 6 8 10 6 8 10 y
g = 8%
= 25.0g = 8% g = 8%
= 20.0
= 15.0 x
10
8
6
4
2
2
4
25.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 20 MPa fy = 420 MPa Mhb b
= 0.9
g = 1% 2 4 6 = 0.0 8 10 y 10 8 = 2.0 6 4 4 2 x 2g = 8%
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 21.0g = 8%
= 19.0g = 8%
g = 8% 6% g = 8%
5%
1%
1% 1%
4%
2 4 6 8 10 y 10 8 6 = 13.0g = 8%
2% 1%
= 16.0g = 8% g = 8%
4 = 6.0 6 8
= 9.0 x
10 6 8 10 y
4
2
2
4
26.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 25 MPa fy = 420 MPa Mhb b
= 0.9
g = 1% 2 4 6 8 10 y 10 8 = 2.5 6 4 4 2 x
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 0.0 = 23.0g = 8%
= 20.0g = 8%
g = 8% g = 8%
6%
5%
1%
1%
3%
2g = 8%
1%
1% 1% g = 8%
2 4 = 7.2
4 6 8 10 y
= 16.5g = 8% g = 8%
6 8 10
= 13.0
= 10.0 x
10
8
6
4
2
2
4
6
8
10
y
27.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 30 MPa fy = 420 MPa Mhb b
= 0.9
g = 1% 2 4 6 8 10 y 10 8 = 3.0 6 4 4 2 x 2g = 8%
y 10 8 6 4 4 2 x 2
10
8
6
4
2
x
= 0.0 = 25.5g = 8%
= 21.0g = 8%
g = 8% 6%
g = 8%
1% 4% 3% 1% g = 8% 1% 1% 1%
4 6
= 18.0g = 8% g = 8%
4 6 8 10
= 7.5
8 10 y 10 8 6 = 15.0
= 12.0 x
4
2
2
4
6
8
10
y
28.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 35 MPa fy = 420 MPa Mhb b
= 0.9
g = 1% 2 4 6 8 10 y 10 8 = 3.5 6 4 4 2 x 2g = 8%
y 10 8 6 4 4 2 x
10
8
6
4
2
x
= 0.0 = 27.5 = 23.5g = 8% g = 8%
g = 8% g = 8% 6%
4%
1% 1% 1% 1%
3%
2g = 8%
1%
4 6 8 10 y
= 19.5g = 8% g = 8%
4 6 8 10
= 8.8
= 15.5
= 12.5 x
10
8
6
4
2
2
4
6
8
10
y
29.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 40 MPa fy = 420 MPa Mhb b
= 0.9
g = 1% 4 6 10 12 y 12 10 = 4.0 8 6g = 8%
y 12 10 8 6 4 4 2 x
12 10
8
6
4
2
x 2
8
= 0.0 = 29.5g = 8%
= 25.0g = 8%
g = 8%
6%
4%
1% 1% 1% 1% 1% g = 8%
4 4 2 x 2 4 6 8 10 12 8 10 12 y
2%
2g = 8%
4 6 8 10 12 y 12 10 8 6 4 2 x 2 4 6 = 21.0g = 8% g = 8%
= 9.6
= 17.0
= 13.5
30.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 45 MPa fy = 420 MPa Mhb b
= 0.9
g = 1% 4 6 10 12 y 12 10 = 4.5 8 6
y 12 10 8 6 4 4 2 x
12 10
8
6
4
2
x 2
8
= 0.0 = 31.5g = 8%
= 27.0g = 8%
g = 8% 6% g = 8%
4%
1%
4 4 21% 1%
x 2
2%
2g = 8%
1%
4 6 8 10 12 y 12 10 8 6 4 2 = 23.0g = 8%
1% g = 8%
4 6 8 10 12
= 10.0g = 8%
= 18.0
= 14.0 x
2
4
6
8
10 12
y
31.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 50 MPa fy = 420 MPa Mhb b
= 0.9
g = 1% 4 6 10 12 y 12 10g = 8%
y 12 10 8 6 4 4 2 x 2 4 6 8 10 12 y
12 10
8
6
4
2
x 2
8 = 0.0
= 33.0 = 5.06% g = 8%
8 6 4 4 2 x
g = 8%
= 29.0g = 8% 4%
1%
1%
2% g = 8% 1%
1% g = 8% 1%
2 4
= 24.5g = 8% g = 8%
= 9.0
6 8 10 12
= 20.0
= 15.5 x
12 10
8
6
4
2
2
4
6
8
10 12
y
32.- FLEXION BIAXIAL EN COLUMNAS CON ARMADURA PERIMETRALAg = b h g = As / Ag h = Mh / (Agh) [Mpa] b = Mb / (Agb) [Mpa] = Pu / Ag [Mpa] x = Max {h, b} y = Min {h, b}h h
Mb f'c = 55 MPa fy = 420 MPa Mhb b
= 0.9
g = 1% 4 6 10 12 y 12 10 = 5.5 8 6 4 4 21%
y 12 10 8 6 4 4 2 x
12 10
8
6
4
2
x 2
8
= 0.0 = 35.8g = 8% g = 8%
= 30.0g = 8% 3%
6%
g = 8%
1%
x1% 1%
2 4 6 8 10 12 y 12 10 8 6 4 2 x 2 = 25.0g = 8% 1% 1%
2g = 8%
4 6 8 10 12
g = 8% g = 8%
= 11.0
= 20.0
= 15.0
4
6
8
10 12
y
