ANÁLISIS Y DISEÑO EN CONCRETO CONCRETO ARMADO DE COLUMNAS DATOS GEOMÉTRICOS: b h d' d
= = = =
PROPIEDADES GEOMÉTRICAS 0.250 m 0.600 m 0.060 m 0.540 m
f'c = f'y =
0.210 T/cm2 4.200 T/cm2
SECCIÓN DE PERALTE MAYOR f'c f'y Ec Es Ø
= = = = =
0.210 T/cm2 4.200 T/cm2 217.371 T/cm2 2000.000 T/cm2 0.700 (Colm!" Es#$%b"d"&
Centroide de la Sei!n c = c =
As1 = As2 = As3 = As4 = As5 = As# =
3.960 cm2 3.960 cm2 3.960 cm2 9.900 cm2 9.900 cm2 31.680 cm2
De"or#aione$ Unitaria$ 0.125 m 0.362 m
c = y =
d1 = d2 = d3 = d4 = d5 =
0.060 m 0.170 m 0.280 m 0.410 m 0.540 m
A$ M%ni#o & M'(i#o
0.003 0.002
Asm)!. = Asm. = Aso#. =
15.000 cm2 90.000 cm2 30.000 cm2
*+,*+,-
P)nto de la ar*a #'(i#a a o#+re$i!n A = o = Ø o = 0.80o =
2375.000 cm2 551.339 T!. 385.937 T!. 441.071 T T! !.
P) , -./-(01(Po2 ,
3-/.45- Tn Tn.
P)nto de "i$)rai!n ini+iente c = 0.003 y = 0.002 = 0.000 d= 0.540 m c = cd/(c ( y& & = Es = 2000.000 T/ T/cm2 d1 = 0.06000 m d2 = 0.17000 m d3 = 0.28000 m d4 = 0.41000 m d5 = 0.54000 m "$$" As1 As2 As3 As4
fs1 (T/cm2& 4.20000 4.11111 2.88889 1.44444
0.540 m s1 s2 s3 s4 s5
s1 (T!& 16.63200 16.28000 11.44000 14.30000
= = = = =
0.00267 0.00206 0.00144 0.00072 0.00000 d% (m& 0.060 0.170 0.280 0.410
fs1 fs2 fs3 fs4 fs5
= = = = =
4.20000 T/cm2 4.11111 T/cm2 2.88889 T/cm2 1.44444 T/cm2 0.00000 T/cm2
c (m&
o (m&
0.540
0.362
$" $"o o (o (od d%& 0.302 0.192 0.082 0.048
s1 s2 s3 s4 s5 !% (Tm (Tm&& 5.018 3.121 0.935 0.691
= = = = =
16.63200 T! 16.28000 T! 11.44000 T! 14.30000 T! 0.00000 T! Cc = 0.85 0.85 fc" fc" b
! (Tm (Tm&&
Ø ! (Tm&
204.829
36.840
25.788
As5
0.00000
Cc =
204.829 T!.
Pn , 1 Pn ,
673.8/9 Tn. 9/8.834 Tn.
0.00000 58.65200
0.540
Mn , 1Mn ,
0.178
0.000 9.764
37./8- T# 65.4// T#
P)nto de ;, -.5c = 0.003 y = 0.002 = 0.500 d= 0.540 m c = cd/(c ( y& & = Es = 2000.000 T/cm2 d1 = 0.06000 m d2 = 0.17000 m d3 = 0.28000 m d4 = 0.41000 m d5 = 0.54000 m
"$$" As1 As2 As3 As4 As5
fs1 (T/cm2& 4.20000 3.45000 1.80000 0.15000 2.10000
Cc =
151.725 T!.
Pn , 1 Pn ,
977./46 Tn. 997./9- Tn.
0.400 m s1 s2 s3 s4 s5
= = = = =
s1 (T!& 16.63200 13.66200 7.12800 1.48500 20.79000
0.00255 0.00173 0.00090 0.00007 0.00105
d% (m& 0.060 0.170 0.280 0.410 0.540
Mn , 1Mn ,
fs1 fs2 fs3 fs4 fs5
= = = = =
4.20000 T/cm2 3.45000 T/cm2 1.80000 T/cm2 0.15000 T/cm2 2.10000 T/cm2
c (m&
o (m&
0.400
0.362
$"o (od%& 0.302 0.192 0.082 0.048 0.178
s1 s2 s3 s4 s5
= = = = =
!% (Tm& 5.018 2.619 0.582 0.072 3.707 11.998
16.63200 T! 13.66200 T! 7.12800 T! 1.48500 T! 20.79000 T! 15.147 T! Cc = 0.85fc"b
! (Tm&
151.725
41.082
89.-/6 T# 6/.454 T#
P)nto de
0.318 m s1 s2 s3 s4
= = = =
0.00243 0.00139 0.00036 0.00087
fs1 fs2 fs3 fs4
= = = =
4.20000 T/cm2 2.78889 T/cm2 0.71111 T/cm2 1.74444 T/cm2
s1 s2 s3 s4
= = = =
16.63200 T! 11.04400 T! 2.81600 T! 17.27000 T!
( ( ( (
C& C& C& T&
Ø ! (Tm&
28.757
d5 =
"$$" As1 As2 As3 As4 As5
0.54000 m
s5 =
fs1 (T/cm2& 4.20000 2.78889 0.71111 1.74444 4.20000
s1 (T!& 16.63200 11.04400 2.81600 17.27000 41.58000 89.34200 >o#"? <% los sf$os @fs%@ so! !"#%os so B%$ Cc = 120.488 T!.
Pn , 1 Pn ,
>6.93- Tn. 78.8>9 Tn.
0.00210
d% (m& 0.060 0.170 0.280 0.410 0.540
fs5 =
4.20000 T/cm2
:A;+< (m& o ( "/2& $"o (m& 0.302 0.192 0.227 0.082 0.048 0.178
o (m&
0.362
s5 =
!% (Tm& 5.018 2.117 0.230 0.834 7.414 15.613
41.58000 T! ( T & 28.358 T!
Cc = 0.85fc"b
! (Tm&
Ø ! (Tm&
120.488
42.927
30.049
dc%$ B l"s b"$$"s s#"$! s#"s " T$"cc%!.
Mn , 1Mn ,
86.>64 T# 3-.-8> T#
P)nto de Ca#?io de 1 c = 0.003 y = 0.002 = 3.000 d= 0.540 m c = cd/(c ( y& & = Es = 2000.000 T/cm2 d1 = 0.06000 m d2 = 0.17000 m d3 = 0.28000 m d4 = 0.41000 m d5 = 0.54000 m
"$$" As1 As2 As3 As4 As5
s1 s2 s3 s4 s5
= = = = =
s1 (T!& 15.57599 0.57198 14.43198 41.58000 41.58000 81.44401 >o#"? <% los sf$os @fs%@ so! !"#%os so B%$ Cc = 66.074 T!.
Pn , 1 Pn ,
fs1 (T/cm2& 3.93333 0.14444 3.64444 4.20000 4.20000
0.174 m
95.34- Tn. 9-.45> Tn.
0.00197 0.00007 0.00182 0.00406 0.00630
d% (m& 0.060 0.170 0.280 0.410 0.540
fs1 fs2 fs3 fs4 fs5
o (m&
0.362
= = = = =
3.93333 T/cm2 0.14444 T/cm2 3.64444 T/cm2 8.12222 T/cm2 12.60000 T/cm2 :A;+< (m& c ( "/2& $"o (m& 0.302 0.192 0.100 0.082 0.048 0.178
dc%$ B l"s b"$$"s s#"$! s#"s " T$"cc%!.
Mn , 1Mn ,
66.-6> T# 95.86- T#
fs1 fs2 fs3 fs4 fs5
!% (Tm& 4.699 0.110 1.179 2.009 7.414 15.411
= = = = =
3.93333 T/cm2 0.14444 T/cm2 3.64444 T/cm2 4.20000 T/cm2 4.20000 T/cm2
Cc = 0.85fc"b
! (Tm&
Ø ! (Tm&
66.074
22.029
15.420
P)nto de Ca#?io de 1 , -.>c = 0.003 y = 0.002 = 4.660 d= 0.540 m c = cd/(c ( y& & = Es = 2000.000 T/cm2 d1 = 0.06000 m d2 = 0.17000 m d3 = 0.28000 m d4 = 0.41000 m d5 = 0.54000 m
"$$" As1 As2 As3 As4 As5
0.127 m s1 s2 s3 s4 s5
= = = = =
fs1 (T/cm2& 3.15867 2.05044 4.20000 4.20000 4.20000
s1 (T!& 12.50833 8.11974 16.63200 41.58000 41.58000 95.40341 >o#"? <% los sf$os @fs%@ so! !"#%os so B%$ Cc = 48.059 T!.
Pn , 1 Pn ,
84.388 Tn. 86.79- Tn.
0.00158 0.00103 0.00363 0.00671 0.00979
d% (m& 0.060 0.170 0.280 0.410 0.540
fs1 fs2 fs3 fs4 fs5
= = = = =
3.15867 T/cm2 2.05044 T/cm2 7.25956 T/cm2 13.41578 T/cm2 19.57200 T/cm2 :A;+< (m& o ( "/2& $"o (m& 0.302 0.192 0.308 0.082 0.048 0.178
o (m&
0.362
fs1 fs2 fs3 fs4 fs5
= = = = =
!% (Tm& 3.774 1.556 1.359 2.009 7.414 16.112
3.15867 T/cm2 2.05044 T/cm2 4.20000 T/cm2 4.20000 T/cm2 4.20000 T/cm2
Cc = 0.85fc"b
! (Tm&
Ø ! (Tm&
48.059
30.906
27.816
dc%$ B l"s b"$$"s s#"$! s#"s " T$"cc%!.
Mn , 1Mn ,
3-.>-7 T# 64./97 T#
P)nto
= = = = = = = =
0.540 m 0.197 m 2000.000 T/cm2 0.06000 m 0.17000 m 0.28000 m 0.41000 m 0.54000 m
s1 s2 s3 s4 s5
= = = = =
0.00209 0.00041 0.00127 0.00325 0.00523
fs1 fs2 fs3 fs4 fs5
= = = = =
4.17073 T/cm2 0.81707 T/cm2 2.53659 T/cm2 6.50000 T/cm2 10.46341 T/cm2 :A;+< (m&
fs1 fs2 fs3 fs4 fs5
= = = = =
4.17703 T/cm2 0.81707 T/cm2 2.53649 T/cm2 4.20000 T/cm2 4.20000 T/cm2
"$$" As1 As2 As3 As4 As5
fs1 (T/cm2& 4.17703 0.81707 2.53649 4.20000 4.20000
s1 (T!& 16.54104 3.23560 10.04450 41.58000 41.58000 73.42786 >o#"? <% los sf$os @fs%@ so! !"#%os so B%$ Cc =
74.649 T!.
Pn , 1 Pn ,
9.669 Tn. 9.->> Tn.
d% (m& 0.060 0.170 0.280 0.410 0.540
o (m&
o ( "/2&
0.362
0.113
$"o (m& 0.302 0.192 0.082 0.048 0.178
!% (Tm& 4.990 0.620 0.821 2.009 7.414 15.854
Cc = 0.85fc"b
! (Tm&
Ø ! (Tm&
74.649
24.301
21.871
dc%$ B l"s b"$$"s s#"$! s#"s " T$"cc%!.
Mn , 1Mn ,
68.3-9 T# 69./49 T#
As1 As2 As3 As4 As5
3.96000 cm2 3.96000 cm2 3.96000 cm2 9.90000 cm2 9.90000 cm2
P)nto: Trai!n P)ra f'y d1 d2 d3 d4 d5
= = = = = =
Pn , 1 Pn ,
4.200 T/cm2 0.06000 m 0.17000 m 0.28000 m 0.41000 m 0.54000 m
= = = = =
s1 s2 s3 s4 s5
= = = = =
16.632 T! 16.632 T! 16.632 T! 41.58 T! 41.58 T! 133.056 T!
933.-57 Tn. 99>.45- Tn. TA=LA RESUMEN
Pn
1 Pn
Mn
!#o d c"$" m%m" " com$s%! !#o d %s$"c%! D!c%%!# !#o d =0.50 !#o d "ll" "l"!c"d" !#o d c"mb%o d Ø !#o d l%! $" !#o d T$"cc%! $"
441.071 263.481 166.872 92.130 47.344 0 133.056
308.750 184.437 116.810 64.491 42.610 0 119.750
0 36.840 41.082 42.927 30.906 24.301 0.000
1Mn 0 25.788 28.757 30.049 27.816 21.871 0.000
CARGAS ACTUANTES = =
126.00 T!. 15.80 Tm
@Nota: <% l"s c"$"s "c#"!#s s !c!#$"! d!#$o dl d%"$"m" d %!#$"cc%! B%$ dc%$ B l"s colm!" soo$#"$ s%! $oblm" l"s c"$"s B ! ll" "c#"$!.
Diagrama de Interacción Principal 500.000 400.000 300.000 200.000 100.000 0.000 0
5
10
15
20
25
30
35
40
-100.000 -200.000 Col umn F
126.00
Col umn G
45
50
Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Load (ton) Moment (ton-m) -114.62 0.66 -74.14 13.88 -57.04 19.35 -39.63 24.18 -20.54 28.93 13.13 33.6 42.76 32.6 69.19 31.6 106.58 31.09 157.14 28.09 206.15 23.56 252.1 17.47 283.72 11.91 283.72 1.67 283.72 0
