Post on 13-Apr-2018
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DISEÑO DE ZAPA
es: PD = 180 tn y PL = 130 tn . El peso especifico del suelo es 1800esta sometido a la accion de una sorecarga de %00 #g/m". El concr
D$)*+ ,E-E$LE+:
SECCION DE COLUMNA t1 = 0.45 mts. 0.45
t2 = 0.45 mts. 0.45
CARGA MUERTA: PD = 180.00 Tn. 180.00CARGA VIVA: PL = 130.00 Tn. 130.00
CAPACIDAD PORTANTE DEL SUELO: t = 1.00 !"#$m2. 10.00
PRO%UNDIDAD DE DESPLANTE: D& = 1.00 mts. 1.00
PESO ESPECI%ICO DEL TERRENO: 't = 1.80 Tn#m3. 1.80
RESISTENCIA DEL CONCRETO DE LA (APATA: &)$ = 210.00 !"#$m2. 210.00
SO*RECARGA DEL PISO: s#$ = 500.00 !"#m2. 0.50
RESISTENCIA DEL ACERO: %+ = 4200.00 !"#$m2. 4200.00
RECU*RIMIENTO R = ,.50 $mt 0.0,5
DIAMETRO DE LAS VARILLAS DE RE%UER(O: - = 2.54 $m. 2.54
PISO DE CONCRETO /=10 /= 10 $m. 0.10
$L)$ $ -EL DE P+* )E2-$D* / & = 1.10 mts.
E+E4* -E)* DEL )EE-* 5 6n 5:n = 7."8 Tn#m2
$E$ DE L$ 4$P$)$ 5 $(ap 5: A = '".%8 m2 S) T) = .530 .530 m2
P$$ 2PL L91 = L9"
T = .52 mts. Ut67 T = .%%0 mt
S = .52 mts. Ut67 S = .%%0 mt
+$ + ; ) .%%0 ; .%%0
L1 = L2 = 3.0%03.050
E$*- -E)$ DEL )EE-* 5 <nu 5: Donde:
Pu = '73 Tn Pu = C7" U6tm
$( = '".0 m"
n9 = 11 0" Tn#m2
transmite
AzS
Az=T
q
PAzap
−=
=
8n9P9
A012=
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D2E-+*-$2E-)* DE L$ $L)$ 5 > 5 DE L$ 4$P$)$ P* P-4*-$2E-)*:*-D*- DE D+E?*:
c = u/@ = APuB<u.m.nC/@. A C
TAM*IEN: - = 0.8%c = 1.0AfFcC;o;d .A C
I = II%7mn; 9n <$9$n ;< s<"9n; G7;
= 533.242148> = 244.4
$ = ?4,0.,,
Entn$<s ; = 0.737 mt
/ = 1.2 > = 0.000 $m
d = 0.7' m
E$*- DE *)$-)E:
L = 3.0%0 mts.
V;9 = 1. Tn.
Vn = 1.' Tn.
V$ = 371.0' Tn @ Vn *-*2E
+E-)D* L*-,)D-$L:
D+E?* P* LEG*-:
M9 = 33%.88 Tn?m
; = 73.7 $m2.
%)$= "10.00 !"#$m2
%+ = '"00.00 !"#$m2
> = %%.00 $m
)E$-D*:@d = $)* DE ED*- DE D+E?* ,$L $ 0.H -; = 0.0 As9m<n; = 14.,5 $m
As = 133.8 $m2 = 4.80 $m
As = 124.54 $m2 = 4.4,4 $m As = 124.24 $m2 = 4.43
As = 124.24 $m2
sar $s = 1"'."' cm" a = '.'3
E$*- DE $E* 2-2*:
cm usar
VnVc
bdcf’0.53=Vc
(WnuxB)(!=Vdu
2
tT!
≥
−=
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Asmn = Bt<m.>.;
$smin = 8. cm". I 1"'."' $m2. *K J
$s = 1"'."' cm".
$LL* DE $LL$+:
$@ = $E$ DE L$ $LL$ $ +$ E- cm". 5.1 A- = $m2.
n = As#A- = 24.3 VARILLAS
usar n = $LL$+
7 = RECU*RIMIENTO EN mts. USUALMENTE 0.0,5
- = DIAMETRO DE LA VARILLA USADA EN mts. - =
+eparacion = A + B"r B @9 C / An B 1C
S<7$n = 2,.00 $m
Us7 S<7$n = 28 $m
+$: "' $LL$+ 0 "8 cm
+E-)D* )$-+E+$L:
As6 = 124.24 $m2
$st = 1"'."' $m2
A- = $m2. 5.1
n = As#A- = 24.3 VARILLAS
usar n = $LL$+
r = E2E-)* E- mts. +$L2E-)E 0.07%@9 = D$2E)* DE L$ $LL$ +$D$ E- mts. - =
S<7$n = S ?27 ? - # n ? 1
S<7$n = 2,.00 mts.
Us7 S<7$n = 28 mts.
+$: "' $LL$+ "8 cm
L*-,)D DE DE+$*LL* DEL EE4*
Longitud disponile para cada arraL; = "7.%0 $m
Para arras en )raccion :A> = 5 1 $m2
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%$ = 210.00 "#$m2
%+ = 4200.00 "#$m2
;> = 2.548 $m
L;1 = 88. $m
L;2 = 1.00 $mL;3 = 30.00 $m
Ld = 88.87 $m
sar Ld = ,0.50 cm I L;s = 2,.500 $m conforme
T7ns&<7<n$ ;< &9<7 <n 6 nt<7&s< ;< $69mn + $m<nt$n
a.B )ransferencia al $plastamiento sore la columnaP9 = 4,3 Tn
Pn = 7"7. Tn >
esistencia al $plastamiento de la columna Pn
Pn> = 31.'"% Tn
Pn M Pn> conforme
.B esistencia al $plastamiento en el concreto de la imentacion
Pn = ,2,.
= .55 mt
A2 = 42.025 mt
A1 = 0.2025 mt
A2#A1F05 = 14.5 9s7 2.00
A = 0.405
Pn> = ,22.25 Tn
Pn M Pn> conforme
DoNells entre columna y cimentacion
s Pn M Pn> usar $smin = 10.13 $m2
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A AISLADA
g/m3 y su carga de traa!o es ".8#g/cm". $demasto de la columna es de f&c = '"0#g/cm". Para la (apata emplear fc = "10 #g/cm" y
mts.
mts.
Tn.Tn.
tn#m2.
mts.
Tn#m3.
!"#$m2.
tn#m2.
!"#$m2.
mts.
$m.
mts.
D
& /
&
S
T
t 2
t 1
2
)t2-t1(
2
)t2-t1(
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$s mOn = 0.0018 d
;#2
;#2
m = tH;
n
=
> H ;
t
>
T
Sd)-
M9=n9 3 *CL
2
As=M9
-%+;?1
2
1 As.%+
0.85&)$>
2
)
=
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$s M $s mOn *K JJ
Q
$Q
n B1
R arilla A n C = $s
Espaciam = B "r.e B @
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@ 0.8% f Fc $s1$ colum = t
Pu I A @ 0.8% f Fc $1C$Q
$s mOn = 0.00% $1
$Q$s col. M $s mOn *K JJ
R arilla = $s1
CONDICION:Pn > Pnb
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fy='"00 #g/cm".
*
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P"n 13 ;< 33
D+E * DE 4$P$)$ *2-$D$
La columna 1 es de '0;'0 cmS y la columna " es de %0;%0 cm. $mas estan refor(adas con
suelo es "100 #g/m3S su carga de traa!o es ".0 #g/cm" y esta sometido a la accion de una sEl concreto de la columna es de fc='"0 #g/cm". Emplear fc="10 #g/cm" y fy='"00 #g/cm".
*L: +E*- E. PD PLC1 40 40 - 3#4J 20 12 PL1
C2 50 50 - 3#4J 38 18
> t A$<7 tn tn S/C = 500 !"#
4.70 m 1.40
D& = 1.0 m *tros olumna 4apata2100 !"#m3 S#C = 500 !"#mK & ) $ = 420 !"#$mK & ) $ = 210 !"#$mK
= 2.00 !"#$m2 ;<<?<<= 4.5 m & + = 4200 !"#$mK
1.B D2E-+*-$2E-)* DE L$ 4$P$)$ A $( = +) C
Øb ( 3/4" ) = 1.1 cm
7& )$ 0.08 x Øb x fy / f ´c = 44 cm
.004*øb*fy = 32 cm OK !!
6; @= 0.004 > &+
Toma ! = 44 cm Ln"t9; ;< ;<s77
/$ = 6; H 7.< H -> .# = ,.50 cm
/m = D& ? /$ $ c = 54.00 cm
$ % = 10.00 cm
Toma $% = 10.00 cm
&m = 1.0 '/cm
Tlculo del Trea de la (apata A $( C
Ps1 = P1D H P1L P1 = 3+ T, P
Ps2 = P2D H P2L
Prolema 3C DiseUar la (apata cominada Vue soportara las columnas mostradas en la figura. Las cargas Vue p
γ m
γ m =
Tlculo del peralte de la (apata A>c )
6; = 0.08 -> %+
Tlculo de la presiWn neta del suelo ( qm )
m = ? γ m/m ?'$/$ ? s#$
1 2
t1 t2
> 1
> 2
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P"n 14 ;< 33
Rs = P1s t1#2 H P2s 455
470.00
- = 88 T,
P1 = 32 T,
L # 2 P+ = 5 T,
< = L # 2 ? - = 88 T,
L # o = 30.3 cm
< L#
L = 40.00 cm
L L L / + = 320.00 cm
# = 13.4 cm
L / = 10, cm
ε M = 0
12 = Rs 1 <
0
o
H
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P"n 15 ;< 33
L = 13 $m
* = 0 $m
* =P1s HP2s tmms * = 85 $m
n L
omo +/ = %00 #g/cmXS erificamos las presiones del suelo B $D*-$L A V 1S" CPs1 = P1D H 50P1L
Ps2 = P2D H P2L P1 = + T, P
R1s = P1s H P2s
+0 +0 30 3
R1s = P1s t1#2 H P2s 455
470.00
< = 1 ? P1 = 2 T, -1 = 8+ T,
P+ = 5 T,
= Ps H M$ = Ps H Ps < -1 = 82 T,
o1 = 32,.32 cm < = 20. $m
= 43.18 !"#$m2
V I Vm cumple 5 *K 5V M Vm no cumple 5$2E-)$2*+ EL $
A9m<ntms <6 An$/ /$ = 150 $m
Un n9< $6$96
Ps = 82000 !" & = 1.13 OK !!< = 20. $m
* = 25 $m
,4531250
Ps1 = P1D H P1L
Ps2 = P2D H 50P2L P1 = 3+ T, P
R2s = P1s H P2s
+0 +0 30 3
R2s = P1s t1#2 H P2s 455
470.00
L # 2
<2 = L # 2 ? P1 = 32 T, -+ = 7 T,
L # P+ = 4, T,
<2 L# -+ = , T,
o = 28,.,2 cm
* < = 18.4 $m
@ m n $9m6< JAUMENTAMOS EL ANCO *J = 1., !"#$m2
m $9m6< J O J
L = 2
ε M = 0
A I A I
I =
ε M = 0
12 = R2s 1 <2
H
0
o
H
0
o
!"#$m2
$m4
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P"n 1 ;< 33
".B D+E?* E- +E-)D* L*-,)D-$L P1 = 3+ T,
n = P1s H P2s 0.+ m 4.50 m
A&, = 541,.2181 '/m N m6&$;
P7 9n;; ;< Ln"t9;
m = m1* Po 2,a # L6T2 &m = 541,.22 '/m
Tlculo de la presiWn neta por unidad de longitud m
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P"n 1, ;< 33
V 484
1083.44
H 1.7537 m
?
?,5
?301.5
' 9 m
?2,000.
M
?
H
108.34 ' 9 m
530
En$nt7ms <6 ;"7m ;< &9<7s $7tnt<s <7&$ms <6 $7t< 7 %6<n:
; = ?7<< H /$ 1.50 V9 = 58,28., !" + 9< : % =
; = 141.00 $m
V9 = Vm ? n >2#2 H ; = 3152.44 !" % =
A7t< ;<6 Cn$7<t : V$ = 0.53 & ) $ > ; = 28,.25 !" u I 0 ; c umple JJ
0.85 V$ = 24332.3 !" OK !!
A9m<ntms <6 P<76t< / = 150 $m. ; = /? 7<<
; = 141 $m
V9 = Vm ? n >2#2 H ; = 3152.44 !"
A7t< ;<6 Cn$7<t : V$ = 0.53 & ) $ > ; = 28,.25 !" u I 0 ; c umple JJ
0.85 V$ = 24332.3 !" Vu < O x Vc CUMPLE !!
VERIFICACION POR CORTE ( Ø = 0.85 )
*L2-$ EG)E* : *L2-$ -)E* :V9 = 1.50 P9 ? n9 m n = 31,4,.3 ' V9 = 1.50 P9 ? n9 m n
V9 = 31,4,.33 !" V9 = 528 !"
E6 7t< ;<6 Cn$7<t : 1 E6 7t< ;<6 Cn$7<t :
412 $m
V$ = 1"2#$$1.3"" !" V$ = 2352311.5 !"
-V$ = 1332 18 !" -V$ = 144 8 !"
β $ = β $
> = > H 5; H 2 t H ; = > = > H 05; H 2 t H ;
V$ = 0.2, 2 H 4 & )$ > ; V$ = 0.2, 2 H 4 & β $ β $
?
H H
?
H
!"
!"
H
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P"n 18 ;< 33
V$ = 1.10 & )$ > ; = 130585 !" V$ = 1.10 & )$ >
V$ = 130584. !" V$ = 15,248. !"
-V$ = 111314,.1, !" -V$ = 135,1.3 !"
V9 -V$ CUMPLE !! V9 -V$ CUMPLE !!
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P"n 1 ;< 33
'.B $LL* DEL EE4* E- EL )$2* E-)$L
n ? P1 = 0
=P1
=5.1 M9 =n F2 P1
M9 = ?88113n 2
alculo de $s :M9 = 88113.42 !" ? m
As = M9 # - &+ ; ? #2 * = 25 .# .# = 8 ;> =1.1
= As &+ # 0.85 & )$ * ; = 141
= 2.,, V67 As9m;
As = 25.04 2.85
As mWn = 0.0018 * ; = 2.22 X V766 n =
As @ As mWn O YY 31
A> As = 25 - 3#4J Z 31
A> 2.85 V766 n = 24
n ?1 11
As mWn = ,.2 24 - 3#4J Z 11
As @ As mWn UMIR As mín !!
%.B $LL* DEL EE4* P* DE$Z* DE L$ *L2-$ -)E*
M9 = n L F2 M9 = 5308.8, !" ? m2
L = 1.1 m 1.4
C6$96 ;< As :M9 = 5308.8, !" ? m
As = M9 # - &+ ; ? #2 * = 25 .# .# = 8 ;> =1.1
= As &+ # 0.85 & )$ * ; = 141
= 0.18 V67 As9m;
As = 1.50 2.85
As mWn = 0.0018 * ; = 0.13 X V766 n = 1
As @ As mWn O YY XDIV#0Y
A> As = 1.4 1 - 3#4J Z XDIV#0Y
A> 2.85
V766 n = 25
n ?1 10
As mWn = ,1.55 25 - 3#4J Z 10
As @ $s mOn ASUMIR As mín !!
Ds<[7 <n s<nt; t7ns<7s6 $; $69mn 6< $77<sn;< 9n 7$n ;< (t
A> 3#4J =
Es$m
X V766 n = As
A> 3#4J =Es$m = * ? 27.< ? ->
Es$m
A> 3#4J =
Es$m
X V766 n = As
A> 3#4J =
Es$m = * ? 27.< ? ->
Es$m
$m
$m2
$m2
$m
$m2
$m
$m2
$m2$m2
mm
m
$m2
$m
$m
$m
$m
$m2
$m
$m2
$m2
$m
$m2
$m2
$m2
$m2$m2
$m2
$m
$m
$m
$m
$m2
14 - 5#8JZ 22
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P"n 20 ;< 33
1.205 1.1
4$P$)$ EG)E* 4$P$)$ -)E*
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P"n 21 ;< 33
n =P9
n = 1.52 !"#$m2 n =P9
n = 1. A A
M9 =n9 * LF2
M9 = 11505 M9 =n9 * LF2
M92 2
* = 120.5 .# .# = 8 ;> = 1.5 * = 11 .# .# = 8
; = 141 ; = 141
= 0.52 V67 As9m; = 0.4 V67 As9m
As = 2.18 As = 3.45
= 0.43 = 0.43
As = 2.18 2.85 As = 3.44
X V766 n = 11
10.00
As mWn = 32.54 11 - 3#4J Z 10 As mWn = 51.5,
6.- VERIFICACION DE LA CONEXIÓN ZAPATA - COLUMNA( Ø = 0.0 )
P7 6 s<$$n A $69mn = 5050 = 2500 $mK COLUMNA
- 0.85 & )$ As1 P9 = 48400
A $69m = > t A1 = 100
P9 - 0.85 & )$ A1 - 0.85 & )$ A1 = 3840 As mWn = 8.0
As mWn = 0.005 A1
P9 - 0.85 & )$ A1 CUMPLE !! As $6 @ As m
A>
As $6. @ As mWn O YY
P7 6 s<$$n * $69mn = 4050 = 2000 $mK COLUMNA
- 0.85 & )$ As1 P9 = 83800
A $69m = > t A1 = 2500
P9 - 0.85 & )$ A1 - 0.85 & )$ A1 = 24,50 As mWn = 12.
As mWn = 0.005 A1
P9 - 0.85 & )$ A1 CUMPLE !! As $6 @ As m
A>
As $6. @ As mWn O YY D<t66< ;< 7<&9<7s <n 6 (t Cm>n; <7&$ms 7m<7 <6 <s
Es$m<nt ;<6 R<&9<7
45 $m450 OK !!
3 / = 450 $m
;#2 ;#2 ;#2
Longitud de desarrollo en Traccion ( Ld )
A> 3#4J =
Es$m =
X V766 = As1
X V766 = As1
$m2 $m2
$m
$m2
$m
$m2
$m2
$m2
$m2
$m
$m
$m
$m2
$m
$m
$m2
$m
$m2
$m
$m2
$m2!"
!"
$m2
$m2
!"
!"
$m2
11 - 3#4JZ 10$m 25 - 3#4JZ 10$m
24 -3#4JZ 11$m
18 - 3#4JZ 10$m
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P"n 22 ;< 33
-> L; = 5 L;1 = 42
L1 = L ? 7.<.<
L (t <s 7<$tn"967 s< ;<>< $m7t7 <6 R<&9<7 ;<$9;m<nt< ;< 6 s"9<nt< mn<7:
-> 3#4J = 1.1
1.00 -> 5#8J = 1.5 .50 2
0.80 7.<.< = ,.50 !t7 = 0
L; m<n7 (t 1.00 &+ = 4200
1.30 &)$ = 210 q >= 2.5 ,PONE
A> 1.00 q < 2.5 ,PON
Ln"t9; ;< ;<s7766 <n t7$$n
n ?1
L1 = 132.50 L; L1
C6$96 ;<6 7<&9<7 mnm : L; = 5.05
As mWn = ,1.55 efuer(o monta!e en forma de ,arrido
2.85 - 3#8J 7 7<&9<7 7n$6 - = 3#4J
X V766 n = 25 - 1#2J 7 7<&9<7 7n$6 - @ 3#4J
10.00 $n <s$m<nt mm ;< 45 $m.
25 - 3#4J Z 10
3.54 & )$F.5 C H 7
As$ = 2 Ast7 β H 1 β = C =
β = L; m+7 (t γ =
λ =
X V766 n = As α =
α1 =
Es$m = * ? 27.<.< ? ->
A> 3#4J =
Es$m =
$m
$m $m
$m2
$m
$m
$m2
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P"n 23 ;< 33
illas R. El peso especifico del
recarga de %00 #g/m".
PL+
$ % = 10.00
$c = 54.00
n $m7<sn
5 T,
ienen de las columnas son:
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P"n 24 ;< 33
0 cm
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P"n 25 ;< 33
5T,
0 cm
11153,0 $m4
AUMENTAMOS EL ANCHO B
* 5
47T,
m
,4531250 $m4
AUMENTAMOS EL ANCHO B
I = * LF3 #12
I =
I = * LF3 #12
I =
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P"n 2 ;< 33
P+ = 5 T,
&m
140.00 m
$m3
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P"n 2, ;< 33
.82 '
.108 '
' 9 m
.4 D H 1., L # D H L
1.5
528 !"
1
503 $m
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P"n 28 ;< 33
2EH00 !"
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P"n 2 ;< 33
!" ? m
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P"n 30 ;< 33
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P"n 31 ;< 33
!"#$m2
XXX
;> = 1.5
2.85
X V766 n = 18
10.00
18 - 3#4J Z 10
OK !!
OK !!
m<nt mm
A> 3#4J =
Es$m =
$m
$m2
$m
$m2
m2
m2
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P"n 32 ;< 33
& = ( C:'% )/ Øb
8.41
.5 !!
q !!
!
0.2
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1 0.32 1#4 J
2 0.71 3#8 J
3 1.27 1#2 J
4 1.98 5#8 J
5 2.853#4 J
6 5.1 1 J
1 0.32 1#4 J
2 0.71 3#8 J
3 1.27 1#2 J
4 1.98 5#8 J
5 2.85 3#4 J
6 5.1 1 J