EJEMPLO DE APLICACIÓN COLUMNAS: COLUMNAS: 0.6m x 0.6m f’c= 210 kg/cm2 fy= 4200 kg/cm2 ENSAYOS ENSAYOS DE D E SUELO: SUE LO: σ SUELO =0.9 kg / c m
2
K= 2400 T/m !"#" $% m$&#"'( '$ c"#g") )$ c(*)+'$#" ,* -$)( '$ 1 T*/m 2 -(# c"'" *+$% m$&#"'( "-#(x+m"'(. 6 NIVELES 5 NIVELES
3
6 3
3 6 3
3 6 3
6,5
6,5
6,5
PLATEA
PLANTA
ELEVACIÓN
!ESO EN COLUMNAS: #$" &#+,&"#+": 20.1 3 . 3
1
4
4
1
2
3
3
2
2
3
3
2
1
4
4
1
6
6
3 . 3
3.55
6 .5
6 .5
C(%,m*") &+-(: 1. . . x .3 .33 3 x 1 T*/m T*/m2 x 3 *+$%$) = 3 T*
3.55
6 . 8 1
2. . 4. 3. 6.
6.0 x .33 x 1 T*/m2 x 3 *+$%$) = 105 T* 6.0 x 6.30 x 1 T*/m2 x 6 *+$%$) = 24 T* . x 6.30 x 1 T*/m2 x 6 *+$%$) = 12 T* . x .33 x 1 T*/m2 x 6 *+$%$) = 51 T* 6.0 x .33 x 1 T*/m2 x 6 *+$%$) =12 T*
59 T
129
129
107
234
234 128
107
234
234 128
59
129
129
ES!ESO7 DE LA !LATEA: Ef$c&( -(# c(#&$ -(# !,*8(*"m+$*&( 9)=24 T* 9c=0.3 √ f ’ c ( ' 9c= f,$#8" c(#&"*&$ -$#m+)+%$ -(# !,*8(*"m+$*&( (= !$#m$&#( (= 4' ;240 cm
9,=9c
71
2400 kg=0.3 √ 210 ( 4 d + 240) ' = 6 cm E)-$)(#: &= ' ; #$c,#+m+$*&( ;
diámetrovarilla 2
&= 6 ; 5.3 cm ; 2.3/2 = 51. &= 53 cm $)-$)(# '$ %" -%"&$" <7ANAS DE C>MENTAC>?N @
D>7ECC>?N 3 , 3
FRANJA 1
6
FRANJA 2 x
6
FRANJA 3 FRANJA 4
3 , 3
20,1
@
D>7ECC>?N Y 5
6
7
8
Y 6 , 8 1
3,55
λ =
√
k s b
4
k s=
4 E c I
1 12
<#"*":
&
3
b t
A
B
6,5
6,5
3,55
7$m-%"8"*'( B $* A: λ =
√ 4
2
( b + 1) k s= k (2 b)
3 k s
2
3
Ec t
Ec= 2.15 x 106 T/m2 &= 0.53 m k=2400 T*/m 2
(b +1 ) ( 2b)
b
λ ( m
−1
Ks
2
D+#$cc+* D+#$cc+* Y D>7ECC>?N : D>7ECC>?N Y:
6 . 6.3 .33
0.4 0.42 0. 0.41
16 100 52 4
0.225 0.24 0.226 0.2
)
17
λ
5.51 5.2 5.54 5.3
>= 6.3 m < 5.2 y 5.51 >= 6.0 m < 5.3 y 5.54
E* "m() c")() '$ c,m-%$ ,$: I
<
1.75
λ
S$ -,$'$ ,&+%+8"# $% mF&('( #g+'( c(*$*c+(*"%. CLCULO DE LAS !7ES>ONES DE CONTACTO Y
6
59 T
129
129
107
234
234 128
107
234
234 128
59
129
129
71
6
6
71 X
6,5
CENT7O DE 7>G>DEH: D$ %" Ig,#" "*&$#+(#
6,5
6,5
FRANJA S 2Y 1Y4 6Y5 3Y
P(Tn) 12 12 24 24 12 12 24 24 51 51 12 12 3 3 105 105
X(m) 6.3 6.3 6.3 6.3 1 1 1 1 1.3 1.3 1.3 1.3
∑!=212
Px .3 .3 1321 1321 1655 1655 042 042 14.3 14 246 246
∑!x=211.0
XC.R. = 21918/2182 = 1.! P(Tn) 12 x 2 3 51 24 x 2 105 12 24 x 2 105 12 2 x 12 3 51
∑!=212
"(m) 1 1 1 12 12 12 6 6 6
P# 4644 1062 125 3616 124 136 20 642 56
∑!x=16.0
" C.R. = 19$%8/2182 = 9. m
CENTRO DE RI&IDE'
CENTRO DE &RAEDAD
EXCENTRICIDAD
10.04
.53
x= 0.246556315
.00
y= 0
Y
CENTR !E "RAVE!A! 8 1
ex
X
CENTR !E RI"I!E#
20,1
J= 212 T* A= 20.10 x 1.60 m = 5.6 m 2 My= Jx $x = 212 x 0.2 = 62.5 T*@m Mx= Jx $y = 212 x 0 = 0
I# = 18.$ x 2.1% /12 = 128$.9% m! Ix= 2.1 x 18.$%/12 = 1**8.%8 m! Q ! " # $ q = ± ± A I! I# q=
2182 373.86
±0±
632.78 $ 12586.93
q =5.83 ± 0.0502 $
ESF+ER'OS SO,RE EL S+ELO -mx=.8% .2(1.) = $.%% Tn/m2 P0 3435 60 7 370 !$)(/#$" 20.1 ! 18.6 ! 0.75 ! 2.4 %& / m
3
20.1 ! 18.6
!#+m$# -+)( S/C c"#g" +" !#+m$# -+)( &"+,$#":
= 1. T*/m2 230 kg/m2= 0.23 T*/m 2 130 kg/m2=0.13 T*/m2 T(&"% =.3 T*/ m2
σ SUELO =0.9
kg cm
2
<¿ 9
%& m
2
>¿ 8.% Tn/m2 CONFORME
A
$
C
E
F
"
I
J
&
L
%
N
P
!
'
L() -,*&() ,$ $)&F* " %" '$#$c" '$% $$ Y &$*'#* "%(#$) -()+&+() -"#" :
P+NTO
-/A
X
A E > M B < N
3. 3. 3. 3. 3. 3. 3. 3.
@.53 @.53 @.53 @.53 @.23 @.23 @.23 @.23
P+NTO
-/A
X
C G K O D L !
3. 3. 3. 3. 3. 3. 3. 3.
.23 .23 .23 .23 .53 .53 .53 .53
PRESIÓN PROMEDIO POR FRANJA
.2 X @0.4 @0.4 @0.4 @0.4 @0.4 @0.4 @0.4 @0.4
:( Tn/m2 3.3 3.3 3.3 3.3 3.65 3.65 3.65 3.65
.2 X 0.16 0.16 0.16 0.16 0.4 0.4 0.4 0.4
:( Tn/m2 3. 3. 3. 3. 6.1 6.1 6.1 6.1
5.35
5.67
5.99
5.35
5.35
5.67
5.99
6.31
5.35
5.67
5.99
6.31
5.35
5.67
5.99
6.31
FRANJA 1 2 % ! $ * 8
:(n/m2) 3.3;6.1/2 = 3. 3. 3. 3. 3.3;3.3/2=3.3 3.65 3. 6.1
P+NTOS A;D/2 E;/2 >;L/2 M;!/2 A;M/2 B;N/2 C;O/2 D;!/2
Mm0n(T;m/m 60 n<) FRANJAS :>(T/m) I(m) 1/9 :?I 3. 6.30 25.6 1 2 3. 6.30 25.6 3. 6.30 25.6 % 3. 6.30 25.6 ! 3.3 6.00 21.4 3.65 6.00 22.6 $ 3. 6.00 2.6 * 6.1 6.00 23.4 8 @<#"*") 1 "% :
1/1 :?@2 24.6 24.6 24.6 24.6 1.26 20.41 21.36 22.51
1*9 + , -
2
1*9 + , 1*10 +- ,
)
(
1*10 +- ,
2
DISEO POR FLEXIÓN 9$#+Ic"c+* '$ %" "%&,#" '$ %" -%"&$": f s =0.4 f # =0.4 ( 4200 )=1680
kg cm
2
f s=0.45 f ' c =0.45 ( 210 )= 94.5 E s (d)lo de elasticidad delacero &= = E c (d)lo de elasticidad del co&creto 7
&=
2.17 * 10 1
k = 1
+
f s
6
=9
1
= 1
& f c
+
=0.336
1680
(
9 94.5
)
k + = 1− =0.888 3
1
1
2
2
k = f c k+=
( 94.5 ) ( 0.336 ) ( 0.888 ) =14.10
b =100 cm 5 ma!= 27.4 * 10 d mi&imo= =44 cm Kb
√
)
) (
2.1 * 10
2
1*10 + - ,
2
2
E304 mBn5m & = 'm*+m( ; #$c,#+m+$*&( ; '+"m. D$ "#+%%" P & = 44; 5.3 ; 2.3/2 &= 3 cm Q & = 53 cm A<04 60 4004 > = 0.
CON
E% '+)$( )$ " #$"%+8"'( -(# c"# ") '$ )$#+c+(
<)= 160 kg/cm2 A) = 160 kg/cm2 A)m+*= 0.01 ' = 0.1 ' 740 60 6G 7$c,#+m+$*&( ),-$#+(#: 3cm 7$c,#+m+$*&( +*f$#+(#: 5.3cm
R004 S30454 53 @ 3 @ 2.34/2 = 6.5 53 R 3 R 2.34 R 2.34/2 = 66.2cm R004 In0454 53 @ 5.3 @ 2.34/2 = 66.2 53 R 5.3 R 2.34 R 2.34/2 = 6.5cm
ALORES DE 6G LSA !E CI%ENTACIÓN 7 3 6 .
2 6 6 . 0
!IRECCIN X L() #$f,$#8() %(*g+&,'+*"%$) '$ %" Ig,#" $)&* $* %" -"#&$ $x&$#+(# y %() &#"*)$#)"%$) $* %" -"#&$ +*&$#+(# $% c(#&$ '$ %" Ig,#" )+$m-#$ )$ &(m" $* %" '+#$cc+* m) %"#g" $* *,$)&#( c")( $) %" '+#$cc+*
<7ANA 1
2
4
3
6
5
<7ANA 1
2 y 4
3
6
5
c($Ic+$*& $ 1/ @ 1/10@ 1/10; 1/ @ 1/10@ 1/10; 1/ @ 1/10@ 1/10; 1/ @ 1/10@ 1/10; 1/ @ 1/10@ 1/10; 1/ @ 1/10@ 1/10; 1/ @ 1/10@ 1/10; 1/ @ 1/10@ 1/10; A)cm2 26.5 24 24. 26.5 24 24. 21.5 1.3 20. 2 20.5 21.3 24. 21. 22.5 23.6
' cm 6.5 6.5 66.2 6.5 6.5 66.2 6.5 6.5 66.2 6.5 6.5 66.2 66.2 66.2 6.5 66.2 66.2 6.5 66.2 66.2 6.5 66.2 66.2 6.5 )cm φ 1 15.3 20 20 15.3 20 20 15.3 20 20 22.3 23 22.3 20 22.3 20 15.3
M A A T@m/m cm2 m+* 25.4 26.5 12.4 24.6 24 12.4 24.6 24. 11. 25.4 26.5 12.4 24.6 24 12.4 24.6 24. 11. 25.4 26.5 12.4 24.6 24 12.4 24.6 24. 11. 25.4 26.5 12.4 24.6 24 12.4 24.6 24. 11. 21.4 21.5 11. 1. 1.3 11. 1. 20. 11.3 22.5 2 11. 20.4 20.5 11. 20.4 21.3 11.3 24 24. 11. 21.6 21. 11. 21.6 22.5 11.3 23.2 23.6 11. 22.5 2 11. 22.5 2. 11.3
2 2.
20 20
L() $)-"c+"m+$*&() )$ "* &(m"'( $* mV%&+-%() '$ -,%g"'" c"'" 2.3 cm !(# $$m-%( -"#" %" f#"*" 1 A)=26.5 Y $% $)-"c+"m+$*&( $) : 3.05 x 100/26.5 =1. S$ ,&+%+8"# 15.3
ERIFICACIÓN DE LA F+ER'A CORTANTE '
, )=10
q l 2
= 100 cm '= 6.5 f’c= 210 kg/cm2 9c= 0.2 √ 210 ( 100 ) ( 63.7 )=26770 kg 9c=26.55 T* 9, mx = 1.4 T* Q 9c= 26.55 T* H CONFORME
