concreto armado 2 diseÑo de columna inter. y exter.docx
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
UNIVERSIDAD NACIONAL DE SAN ANTONIO ABAD DEL CUSCO
FACULTAD DE INGENIERIA CIVIL
LINEA DE ESTRUCTURAS
CONCRETO ARMADO II
EMA:
ANALISIS Y DISEO DE COLUMNAS
- DOCENTE:Ing. FRANCISCO SERRANO FLORES
- ESTUDIANTES:
1. VILLCAS HURTADO, FILIO DAMIAN - 110581
2. VILLALOBOS GOMEZ,
- FECHA DE ENTREGA:301215
- SEMESTRE:2015-II
1
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
INDICE:
1.- ESBELTEZ ENCOLUMNAS pag: 3
ESBELTEZ DE LA COLUMNA INTERIOR SENTIDOX.pag: 5
ESBELTEZ DE LA COLUMNA EXTERIOR SENTIDO X.pag: 9
ESBELTEZ DE LA COLUMNA INTERIOR SENTIDO Y.pag: 13
ESBELTEZ DE LA COLUMNA EXTERIOR SENTIDO Y.pag: 1
!.- DISE"O DE COLUMNAS #OR BRESLER Y $ACOBSEN
DISE"O DE COLUMNA EXTERIOR.pag: !1
DISE"O DE COLUMNA INTERIOR.pag: !%
3.- DISE"O DE COLUMNAS #OR EL METODO DECONTORNO DE CAR&A
DISE"O COLUMNA EXTERIOR ..pag: !
DISE"O DE COLUMNA INTERIOR.pag: !'
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
1.- ESBEL EZ EN COLUMNAS
VISTA EN PLANTA Y ELEVACION
VISTA EN ELEVACION Y-Y
3
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
SECCION DE LAS COLUMNAS, ELEVACION.
!
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
ESBEL EZ DE LA COLUMNA
IN ERIOR SEN IDO X
DATOS
".#. C$%#&n' (n)*+($+ 3.0 )n ".#.C$%#&n' $+/*101.20 )n
".#. C$%#&n' *#(n'3.10 )n M'2.00 Tn-& M'3.!0 Tn-& M'12.0 Tn-& M'11.20 Tn-&
CALCULO DE 1, 2 4
1=0 2=Kcol umna
Kpiso
K Columna:
5
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
K1=
40(253 )12
300=173.61
K2=
40(253)12
240=217.01
Kcol=173.61+217.01=390.62 &3
K Piso:
Kpiso=It
L
It=Io+A d2
()g*+a A Y, AY,1 50 5 3250! 650 25 18650 1!00 22000
Yc=22000
1400=15.71cm
()g*+a I/ A 0 0! A0!
1 5!1.
6
50 10.61 11!.60
6!555
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
! 5250 650 7.27 8.30 !625 1.
613728
0
It=61666.67+139280=200946.67 cm4
Eje B:
2= 390.62
200946.67
425
=0.83
Eje C Y D:
2= 390.62
( 200946.67425
2)=0.41
Eje E:
2= 390.62
200946.67
425+200946.67
476
=0.4 4
Eje G:
2= 390.62
200946.67
476
=0.93
CALCLULO DE 4
'.- S(n (&$4
E9* B 1=0 , 2=0.83 0.2
E9* C 1=0 , 2=0.41 0.5!
E9* D 1=0 , 2=0.41 0.5!
E9* E 1=0 , 2=0.44 0.52
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
E9* G 1=0 , 2=0.93 0.3
.- C$n (&$4
E9* B 1=0 , 2=0.83 1.!!
E9* C 1=0 , 2=0.41 1.08
E9* D 1=0 , 2=0.41 1.08
E9* E 1=0 , 2=0.44 1.35
E9* G 1=0 , 2=0.93 1.55
VERIFICO SI HA: CHE;UEO "OR ESBELTEZ
'.- S(n (&$4
Kln
r 34 12
M1b
M2b
r=0.30 t=0.30(25)=7.5(RADIO DEGIRO ).
0.633007.5
34122.00
3.40
25.20
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
's= 1.00
1(u(c
(u=36.60 (6 )+101.20 (10 )+63.10 (4 )=1484.00)n .
CACULO DE "C
(c=( *2 )EI
(Kln )2
Ec=15000+ c=15000210=217370.65-
cm
EI=
EcI-2.5
1+d
I-=40252
12=52083.33 c m4
d=5.40
29.02=0.19
EI=
217370.6552083.332.5
1+0.19=3.8109
E9*
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
1
=
40(253 )12
300 =173.61
K2=
40(253)12
240=217.01
Kcol=173.61+217.01=390.62 &3
#)6/:
Kpiso=It
L
It=Io+A d2
()g*+a A Y, AY,
1 50 5 3250
! 650 25 18650
1!00 22000
Yc=22000
1400=15.71 cm
()g*+a I/ A 0 0! A0!
1 5!1.6 50 10.61 11!.60 6!555! 5250 650 7.27 8.30 !625 1.
6137280
It=61666.67+139280=200946.67cm4
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
E9*
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
E9* D 1=0 , 2=0.41 1.08
E9* E 1=0 , 2=0.44 1.35
E9* G
1=0 , 2=0.93
1.55
VERIFICO SI HA: CHE;UEO "OR ESBELTEZ
'.- S(n (&$4
Kln
r 34 12
M1b
M2b
r=0.30 t=0.30(25)=7.5(RADIO DEGIRO ).
0.633007.5
34120.68
1.11
25.20
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
(c=( *2 )EI
(Kln )2
Ec=15000+ c=15000210=217370.65-
cm
EI=
EcI-2.5
1+d
I-=40252
12=52083.33 c m4
d=1.79
18.59
=0.096
EI=
217370.6552083.332.5
1+0.096=4.1109
E9*
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
(c=(4 ) 216.83+ (8 ) 385.47+(4 )246.70+ (4 )187.14=5686.44)n
's= 1.00
1(u
(c
= 1.00
1 1484.00
0.705686.44
=1.594
MOMENTOS FINALES
M12 .7' T4-.M!2 1.11 T4-.M162 1.!81.59%2 17.!59T4-.M!627.781.59%2 1.5!T4-.
ESBEL EZ DE LA COLUMNA IN ERIOR SEN IDO Y
DATOS
o ".#. C$%#&n' (n)*+($+ 3.0)no ".#.C$%#&n' $+/*101.20)no ".#. C$%#&n' *#(n'3.10)no M'2.00 Tn-&o M'3.!0 Tn-&o M'12.0 Tn-&o M'11.20 Tn-&
CALCULO DE 1, 2 4
1=0
2=Kcol umna Kpiso
K Columnas:
15
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
K1=
25(403)12
300=444.4
K2=
25(403)12
240=555.6
Kcol=444.4+555.6=1000 &3
K Piso:
Kpiso=It
L It=Io+A d2
()g*+a A Y, AY,
1 50 5 3250
! 650 25 18650 1!00 22000
Yc=22000
1400=15.71cm
()g*+a I/ A 0 0! A0!
1 5!1.6 50 10.61 11!.60 6!555
! 5250 650 7.27 8.30 !625
1
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
1.6 137280
It=61666.67+139280=200946.67 cm4
E9*
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
Kln
r 34 12
M1b
M2b
r=0.30 t=0.30(25)=7.5(RADIO DEGIRO ).
0.613007.5
34 122.00
3.40
24.4
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
d=5.40
29.02=0.19
EI=
217370.65133333.332.5
1+0.19=9.7109
E9*
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
DATOS
o ".#.C$%.(n)*+($ 3.0)no ".#.C$%.*#(n'3.10)no ".#.C$%.$+/*101.20)no M'0.8 Tn-&o M'1.11 Tn-&o M'10.20 Tn-&o M'.0 Tn-&
CALCULO DE 1, 2 4
1=0
2=KcolKpiso
C/;:
20
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
K1=
25(403 )12
300=444.4
K2=25(40
3
)12
240=555.6
Kcol=444.4+555.6=1000 &3
#)6/:
Kpiso=It
L
It=Io+A d2
()g*+a A Y, AY,
1 50 5 3250
! 650 25 18650
1!00 22000
Yc=22000
1400
=15.71 cm
()g*+a I/ A 0 0! A0!
1 5!1.6 50 10.61 11!.60 6!555! 5250 650 7.27 8.30 !625 1.6 137280
It=61666.67+139280=200946.67 cm4
E9*
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
CALCLULO DE 4
'.- S(n (&$4
E9* 1 1=0 , 2=1.57 0.1
E9* 2 1=0 , 2=0.78 0.52
E9* 3 1=0 , 2=0.78 0.52
E9* ! 1=0 , 2=1.57 0.1
.- C$n (&$4
E9* 1 1=0 , 2=1.57 1.10
E9* 2 1=0 , 2=0.78 1.05
E9* 3 1=0 , 2=0.78 1.05
E9* ! 1=0 , 2=1.57 1.10
VERIFICO SI HA: CHE;UEO "OR ESBELTEZ'.- S(n (&$4
Kln
r 34 12
M1b
M2b
r=0.30 t=0.30(25)=7.5(RADIO DEGIRO ).
0.613007.5 34 12
0.68
1.11
24.4
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
1.103007.5
>22
44.00>22 &i!a"c!#$u#o%
'b=1.00
's= 1.00
1(u(c
1.1.3.CACULO DE "C
(c= ( *2 )EI
(Kln )2
Ec=15000+ c=15000210=217370.65-
cm
EI=
EcI-2.5
1+d
I-=25402
12=133333.33 c m4
d=1.79
18.59=0.096
EI=
217370.65133333.332.5
1+0.096=10.6109
E9*
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
(c=(10 )960.678+(10)1054.349=20150.27 )n
's= 1.00
1(u
(c
= 1.00
1 1447.08
0.720150.27
=1.11
MOMENTOS FINALES
M12.7' T4-.M!21.11 T4-.M1621.!81.112 11.3! T4-.M!627.781.112 .33 T4-.
2.- DISEO DE COLUMNAS POR BRESLER Y JACOBSEN
DISEO DE COLUMNA EX ERIOR
D')$4
"# 5.80 Tn
M#> 8.20 Tn-&
M#? !.30 Tn-&
@ 210 g&2 @? !200 g&2
+ 5&
C'%#%$ /* *
#/=Mu"
(u=
4.30
56.80=7.57 cm
#"=Mu/(u = 8.20
56.80=14.44cm
#0=#/
2+#"2( t/t")2
=7.572+14.442=16.30 cm
C'%#%$ /* %' C#'n)'
1=t2 r
t=
401040
=0.75
2!
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
A'$ *) "#Ag !L-3 0.65 0.!1 5.8 1.!)> "#>Ag!L-3 0. 1.20 0.3 85
(u/
A-=85
-
cm2( u/=852540=85)n
SENTIDO Y
A'$ *?)? "#?Ag!L-3 0.65 1.20 0.!1 5
(u"
A-=65
-
cm2( u"=652540=65)n
C'%#%$ /* "$
(o=0.80[0.85+0c(A-As )+As+" ]A-=2540=1000 cm2
As=0.0121000=12.00 cm 2
(o=0.700.80[0.85210(100012.00)+12.004200 ]
(o=138.244)n
C'%#%$ /* "#
1
(u=
1
(u/+
1
(u"
1
(o
1
(u=
1
85+ 1
65
1
138.24
(u=51.23)n>50.)nO2%
V*+('(n
25
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
(u
(no 0.1
51.23
138.24
=0.37 0.1OK 2%
C'%#%$ /*% J+*' /* '*+$
3 &=(0.012)(25 )(40)
65/8 )3 &=12cm 24
C'%#%$ /* E)+($ DUAL 2
Lo
(Mayo
r
Ln300
50 cm OK!!
25 &!0& !0 &
So
(Mnor
K/K0.7
5.! &
'3 !03 13.3!
10& 1 , OK!!
& 0 525cm
" # $%&' 5cm) # $%&' *0cm" # $%&' *5cmr # $%&' "0cm
F(n'%&*n)* *% '+&'/$ *+4
2
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
DISEO DE COLUMNA IN ERIOR
DATOS
"# 35.!8 )n
M#> 12.5 )n-&
M#? 0.3 )n-&
@ 210 g&2
@? !200 g&2 + 5 &
CALCULOS
#0=#/2+#"2(
t/
t")
2
#/=Mu"
(u =
0.63
35.48=1.8cm
26
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
#"=Mu/
(u=
12.65
35.48=35.7 cm
#0=
1.82+35.72(
25
40
)2
=29.80 cm
1=4010
40=0.75
#
t=
29.80
40=0.745
(u
A-=
35.48103
2540=35.48 -/cm 2
C$&'+'n/$ $n '$1=0.75=0.012
C$&+$'n/$ $+ BRESLER
SENTIDO X
1=0.60
#/t/=1.8
25=0.072=0.012
(u/
A-=150(u/=1502540=150tn
SENTIDO Y
1=0.75
#"
t"=
35.7
40=0.89=0.012
(u"
A-=36(u"=362540=36 tn
CALCULO DE "$
(o=0.70.8 (0.85210(254012.00 )+12.004200)
28
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
(o=138.244 tn
R**&%''n/$ '%$+*
1
(u=
1
150+
1
36
1
138.244
(u=36.75>35.48 OK %
V*+('n/$
(u
(o>0.1
36.75
138.244>0.1
0.26>0.1OK %
CALCULO DE ACERO
3 &=0.0122540=12 cm2
665 /8 0 0
C'%#%$ /* E)+($ DUAL 2
Lo
(Mayo
r
Ln300
50 cm OK!!
25 &
!0& !0 &
So
(Mno
r
K/ K0.7 5.! &
'3 !03 13.3
!
10& 1 , OK!!
& 0 525 cm
" # $%&' 5cm) # $%&' *0cm" # $%&' *5cmr # $%&' "0cm
27
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
2.- DISEO DE COLUMNAS POR EL ME ODO DE CON ORNO
DE CARGA
DISEO COLUMNA EX ERIOR
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
DATOS4
"# 5.80 Tn
M#> 8.20 Tn-&
M#? !.30 Tn-&
@ 210 g&2
@? !200 g&2
+ 5&
DETERMINAR LA RESISTENCIA NOMINAL RE;UERIDA4
"n"# 5.800.5 86.38
Mn> M#> 8.200.5 12.2
Mn? M#? !.300.5 .2
ASUMINOS4 0.5
DETERMINACIN DE VALOR A 1.5
Mn"
Mn/=
6.62
12.62=0.52 E &*n$+ #*
25
40=0.63
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
S* )(*n* #n' $%#&n' +*)'ng#%'+ /* 25>!0 * /*)*+&(n' %''+&'/#+' '+' #n' '+g' '>('% "n 86.38 )n ? #n' +*()*n(' '%&$&*n)$ #n('>('% *#('%*n)* Mn$>10.86 )nK&
ABACO4
Mn$? 20.5 )nK&
S* *+(@('4 '+' P 1
Mn/
Mno/+
Mn"
Mno"=
10.87
12.92+
6.62
20.65=0.950
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
DISEO DE COLUMNA IN ERIOR
DATOS
"# 35.!8 )n
M#> 12.5 )n-&
M#? 0.3 )n-&
@ 210 g&2
@? !200 g&2
+ 5 &
DETERMINAR LA RESISTENCIA NOMINAL RE;UERIDA4
"n"# 35.!80.5 55!.58
Mn> M#> 12. 50.5 17.!
Mn? M#? 0.30.5 0.76
ASUMINOS4 0.5
DETERMINACIN DE VALOR A 1.5
Mn"
Mn/=
0.97
19.46=0.05 * &*n$+ #*
25
40=0.63
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
Mno/=19.46+0.97
40
25(10.65 )
0.65=20.30 )nK&
S* )(*n* #n' $%#&n' +*)'ng#%'+ /* 25>!0 * /*)*+&(n' %''+&'/#+' '+' #n' '+g' '>('% "n 35.!8 )n ? #n' +*()*n(' '%&$&*n)$ #n('>('% *#('%*n)* Mn$>20.30 )n &
ABACO4
Mn$? !0.53 )nK&
S* *+(@('4 '+' P 1
Mn/
Mno/+
Mn"
Mno"=
19.46
20.30+
0.97
40.53=0.983
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CONCRETO ARMADO IIINGENIERIA CIVIL-UNSAAC
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