CÁLCULO PARA EL DISEÑO DE ZAPATA AISLADA Diseño de una zapata centrica en el ee D!D" # ee $!$% Columna
σ T s/c f'c fy hf PD PL
Datos 40x40
cm
20 0.2 210 4200 1.65 49.6 10.24
tn/m2 tn/m2 kg/cm2 kg/cm2 m tn tn
NPT=0.15
NFZ=1.50
D!"ccon longtu$nal %D 0.062 tn&m %L 0.00 tn&m %) &4.9*6 tn&m P)y 20.594 tn
(sx (sy
D!"ccon t!ans+"!sal %D 0.119 tn&m %L 0.04 tn&m %) &2.19 tn&m P)x &1.516 tn
t
,
s L
1. -)- N-T D-L )-L
_( )= _( )−/ − ℎ _( ) ᵟ_( )
3N
=
16.5
tn/m2
_( _( )= 〖 1.3 〗 _( )−/ − ℎ _( ) ᵟ_( )
3N)
=
22.5
tn/m2
s t
0.4 0.4
2. D%-N)N(%-NT -N PL(NT(&C(() D- )-C 2
1
L+2 = L+1
Lv2
= √(_ ) (−!)/"
Lv1
(: = P/σN
B 4
3
#= √(_ ) − (−!)/"
P=PD;PL
L
P= ( = L= ,=
59.74 .6 1.90 1.90
tn m2 m m
L ,
2.1 -C(CN D- -)- -N -L )-L (8 C(() D- (-D(D , L ( PD;L %L %T
1.90 1.90 .61 59.74 0.0* 0.16
m m m2 tn tn&m tn&m
σ N
16.50
tn/m2
_($ )= %/ &
('_)/(# " ) &
('_)/( #" )
σ 1 σ 2 σ 3 σ 4
16.**
tn/m2
-C(
16.66
tn/m2
-C(
16.49
tn/m2
16.7
tn/m2
Incre&entando AZ
1.90 1.90
m m
$+$!,= _,- − _
%=
0.02
AZ =
3.67
m2
= √(_ ) (−!)/" L L
_
#= √(_ ) − (−!)/" B B
1.916 2.00
1.916 2.00
'allando nue(os ) n con las nue(as di&eniones σ 1 σ 2 σ 3 σ 4
15.1
tn/m2
15.0
tn/m2
14.79
tn/m2
14.*9
tn/m2
,8 C(() D- (-D(D ; ))% LNTD(N(L <( , L ( PD;L;0.7)y %L %T
2.00 2.00 4.00 *6.2 &.92 0.16
m m m2 tn tn&m tn&m
σ NS
22.50
tn/m2
_($ )= %/ &
%=%_ %_.0%_ _ =_ _.0_ _ =_ _
('_)/(# " ) &
('_)/( #" )
σ 1 σ 2 σ 3 σ 4
16.26
tn/m2
22.1
tn/m2
16.02
tn/m2
21.90
tn/m2
C8 C(() D- (-D(D ; ))% LNTD(NL (NT<( , L ( PD;L&0.7) %L %T
2.00 2.00 4.00 4.6 4.05 0.16
m m m2 tn tn&m tn&m
σ NS
22.50
tn/m2
_($ )= %/ &
%=%_ %_−.0%_ _ =_ _−.0_ _ =_ _
('_)/(# " ) &
('_)/( #" )
σ 1 σ 2 σ 3 σ 4
1.99
tn/m2
*.9
tn/m2
1.*6
tn/m2
*.69
tn/m2
D8 C(() D- (-D(D ; ))% T(N)-)(L <( , L ( PD;L;0.7)x %L %T
2.00 2.00 4.00 57.6 0.0* &1.*0
m m m2 tn tn&m tn&m
σ NS
22.50
tn/m2
_($ )= %/ &
%=%_ %_.0%_ _ =_ _ 〖 〗 _ =_ _ .0_
('_)/(# " ) &
('_)/( #" )
σ 1 σ 2 σ 3
1.4
tn/m2
1.4
tn/m2
15.97
tn/m2
σ 4
15.77
tn/m2
-8 C(() D- (-D(D ; ))% T(N)-)(L (NT<( , L ( PD;L&0.7)x %L %T
2.00 2.00 4.00 61.05 0.0* 2.01
m m m2 tn tn&m tn&m
σ NS
22.50
tn/m2
_($ )= %/ &
%=%_ %_−.0%_ _ =_ _ 〖 〗 _ =_ _ −.0_
('_)/(# " ) &
('_)/( #" )
σ 1 σ 2 σ 3 σ 4
16.72
tn/m2
16.*
tn/m2
1.70
tn/m2
1.*0
tn/m2
. -)-) LT%) -N -L )-L&C(() (%PLC(D() (8 C(() D- (-D(D , L ( PD;L %L %T
2.00 2.00 4.00 76.75 0.09 0.2
m m m2 tn tn&m tn&m
σ N
16.50
tn/m2
_($ )= %/ & ('_)/( #" )
('_)/(# " ) &
σ 1 σ 2 σ 3 σ 4
21.96
tn/m2
21.72
tn/m2
21.60
tn/m2
21.4*
tn/m2
,8 C(() D- (-D(D ; ))% LNTD(N(L <( , L ( PD;L;)y %L %T
2.00 2.00 4.00 95.9 &4.79 0.20
m m m2 tn tn&m tn&m
σ NS
22.50
tn/m2
_($ )= %/ &
%= 〖 1."2% 〗 _ 1."2%_%_ _ = 〖 1."2 〗 _ 〖 1."2 〗 __ _ =1."2_ 〖 1."2 〗 _
('_)/(# " ) &
('_)/( #" )
σ 1 σ 2 σ 3 σ 4
20.
tn/m2
2*.6*
tn/m2
20.0
tn/m2
2*.*
tn/m2
C8 C(() D- (-D(D ; ))% LNTD(NL (NT<( , L ( PD;L;)y %L %T
2.00 2.00 4.00 54.21 5.06 0.20
m m m2 tn tn&m tn&m
σ NS
22.50
tn/m2
_($ )= %/ & ('_)/( #" )
%= 〖 1."2% 〗 _ 〖 1."2% 〗 _−%_ _ = 〖 1."2 〗 _ 〖 1."2 〗 _−_ _ =1."2_ 1."2 _
('_)/(# " ) &
σ 1 σ 2 σ 3 σ 4
1*.49
tn/m2
9.91
tn/m2
1*.20
tn/m2
9.61
tn/m2
D8 C(() D- (-D(D ; ))% T(N)-)(L <( , L ( PD;L;)y %L %T
2.00 2.00 4.00 *.27 0.07 &2.12
m m m2 tn tn&m tn&m
σ NS
22.50
tn/m2
_($ )= %/ &
%= 〖 1."2% 〗 _ 〖 1."2% 〗 _%_ _ = 〖 1."2 〗 _ 1."2_ 〖 〗 _ = 〖 1."2 〗 _ 〖 1."2 〗 _ _ ('_)/(# " ) &
('_)/( #" )
σ 1 σ 2 σ 3 σ 4
16.*9
tn/m2
16.6*
tn/m2
19.9*
tn/m2
19.75
tn/m2
-8 C(() D- (-D(D ; ))% T(N)-)(L (NT<( , L ( PD;L;)y %L %T
2.00 2.00 4.00 *6.2 0.07 2.52
m m m2 tn tn&m tn&m
σ NS
22.50
tn/m2
_($ )= %/ & ('_)/( #" )
%= 〖 1."2% 〗 _ 〖 1."2% 〗 _−%_ _ = 〖 1."2 〗 _ 〖 1."2 〗 _ 〖 〗 _ = 〖 1."2 〗 _ 〖 1."2 〗 _ −_ ('_)/(# " ) &
σ 1 σ 2
21.0
tn/m2
20.91
tn/m2
σ 3 σ 4
1*.25
tn/m2
1*.1
tn/m2
σu$
27.67
t!"m2
4. (LT( D- C%-NT(CN
ℎ_ 4_5/" _6= ( −)/"
Lv=0.#m
$=0.50
σ /=27.7
L ? L ?
Po! !g$": 0.70 0.40 0.70 0.40
m m m m
Po! longtu$ $" $"sa!!ollo $"la columna@ la altu!a $" la :aAata s"!a 0.50
?
0.50
m
4.18 -C(CN D- -( CT(NT- P L->N A& '*++,N --
6_78 96_+ 6_78:#_7 :=5− B
_=ℎ_ −+7;−9_;<
L
〖96〗 _=9.23√(> +)#
'AT,S B L AZ ?
2.00 2.00 4 0.50
m m m2 m
σ /
27.67 0.#0 1.27
t!"m2 m m
Lv
d* + X= Vu=
0.42 0.38 20.83
m m tn
ØVc =
55.31
tn
CORRECTO
B& '*++,N --
6_78 96_+ 6_78:?_7 :=5−
L B
_-=ℎ_
−+7;−9;−9_;<
〖96〗 _=9.23√(> +) 'AT,S B L AZ ?
2.00 2.00 4.00 0.50
m m m2 m
σ /
27.67 0.#0 1.27
t!"m2 m m
Lv
d# + X= Vu=
0.41 0.39 21.53
m m tn
ØVc =
53.66
tn
CORRECTO
4.28 -C(CN D- -( CT(NT- P PNN(%-NT
6_78 96_+
/" 2 /" 2 !
t /" 2 /"
S
6_78%_7−_7_
m
=A_
〖96〗 _=9(.231.1/@)√(> +);_
$=!_;_="($)
〖96〗 _=91.1√(> +);_
_=$
'AT,S B L AZ s
2.00 2.00 4 0.40
m m m2 m
t
0.40 0.42 0.41
m m m
0.41
m
27.67 73.2#
t!"m2 t!
/ / /
σ / 8
1
m= n= b0 =
0.82 0.81 3.27
m m m
A0 = Vup = ØVcp = ØVcp =
0.67 54.80 263.39 182.03
m2 tn tn tn
ØVcp =
182.03
tn
CORRECTO
4.8 -C(CN D- -( CT(NT- P (PL()T(%-NT
'AT,S B L AZ s
2.00 2.00 4 0.40
m m m2 m
t σ /
0.40
m
27.67
t!"m2
73.2#
t!
_,4,A!,$!=%7/(A!) +$!,+!/B,,!, 8 1/3 f9:; =0.7
f aAlas. = f aAlas. =
457.0 45.70
(con./(:aA.
0.04
tn/m2 kg/cm2 B1/ Ao! lo tanto f u@aA =
f u@aA =
149.1
0.*10 f'c
kg/cm2
f u@aA f aAlastam"nto
5. -- P L->N A& '*++,N --
_A=_7/(9-(−,/")) ,=(_A-)/(.02> +;)
_7=(C_7_5")/" C_78 _7# 〖 D 〗 _;,,A=_A$/_;, 'AT,S
a=
7.4*
m
B L AZ /
2.00 2.00 4
m m m2
(s =
1.0091*0*7
m2
a=
1.504906*99
m
(s =
11.926205
m2
0.42
m
a=
1.402*702415
m
σ /
27.67
t!"m2
(s =
11.9055*45
m2
? Lv A::
0.50 0.#0
m m m2
a=
1.4006027**
m
(s =
11.90505027
m2
a=
1.4005941505
m
(s =
11.90504512
m2
1.27
,u Mu A!m"n A!
55.34 17.71 18.00 18.00
#$b%&&%! #$b%&&%! '
14.17 15.00 0.14
tn/m tnm cm2 cm2
Usar - ./01 2 3%.4& m
B& '*++,N --
_A=_7/(9-(−,/")) ,=(_A-)/(.02> +;)
_7=(C_7_5")/" C_78 _7 〖 D 〗 _;,,A=_A$/_;,
'AT,S
a=
7.219
m
B L AZ /
2.00 2.00 4
m m m2
(s =
12.9659714
m2
a=
1.525409*71
m
(s =
11.9229094
m2
0.41
m
a=
1.4026945706
m
σ /
27.67
t!"m2
(s =
11.9054521
m2
? Lv A::
0.50 0.#0
m m m2
a=
1.40062774*7
m
(s =
11.9050500*
m2
a=
1.400594126
m
(s =
11.90504511
m2
1.27
,u Mu A!m"n A!
55.34 17.71 18.00 18.00
#$b%&&%! #$b%&&%! '
14.17 15.00 0.14
tn/m tnm cm2 cm2
Usar - ./01 2 3%.4& m
0 f<