PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls
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FACULTAD DE INGENIERIASESCUELA PROFESIONAL DE INGENIERÍA CIVIL
PREDIMENSIONAMIENTO DE ELMENTOS ESTRUCTURALES
Predimensionamiento de la losa aligerada
Luz libre del portico L !"## m#"$# m
Espesor de losa % #"$# m
Espesor de losa def. % de&" #"$# m !"## m
Predimensionamiento de la 'iga (rin)i(al
#"*# m
Luz libre del portico principal L !"*# m
Luz libre del portico segundario + !"## m
Peralte de viga % 0.51 m
Peralte de viga definitivo % de&" #"*# m
Base de la viga , 0.25 m
Base de la viga definitivo , de&" -!"## m -!
Predimensionamiento de la 'iga seg.ndaria
Luz libre del portico principal L !"## m
#
Luz libre del portico segundario + *"## m Peralte de viga % 0.45 m
Peralte de viga definitivo % de&" #"!# m
Base de la viga , 0.30 m
Base de la viga definitivo , de&" -!"## m
Predimensionamiento de la 'iga en 'oladi/o en el de $"##m"
Luz libre del portico principal L 0"1# m
#"*# m
Luz libre del portico segundario + !"## m
Peralte de viga % 0.4 m
Peralte de viga definitivo % de&" #"*# m
Base de la viga , 0.25 m
Base de la viga definitivo , de&" -!"## m -!"## m
Predimensionamiento de la 'iga en 'oladi/o en el de $"!#m"
Luz libre del portico principal L $"-# m
#"*# m
Luz libre del portico segundario + *"## m
Peralte de viga % 0.5! m
Peralte de viga definitivo % de&" #"*# m
Base de la viga , 0.30 m
Base de la viga definitivo , de&" -!"## m -!
Por lo ta
n
UNIVERSIDAD :OSE CARLOS MARIATEGUI
PARA LOSA ALIGERADA <Seg.n R"N"E" en la norma E = #*# Art" 0#">"0"0?
PARA LAS VIGAS <Seg.n R"N"E" en la norma E = #*# Art" 0#">"0"- 8 el ingeniero Antonio +lan)o +las)o re)omiendan.sar (eraltes?
PARA COLUMNAS <Seg.n el ingeniero antonio ,lan)o ,las)o re)omienda <A)Pser'i)io@#">!4F3)? 8<A)Pser'i)io@#"-!4F3)? esto en el )aso de tener (la)as o m.ros )ortantes
PARA COLUMNAS Pero el ICG lo determina )on <,TP@nF3)? 8 n estara en &.n)ion de ;.e ti(o de )ol.mna sea ti(o0#"- ti(o $8-#"$! 8 ti(o >#"$
h ≥ L/25
h ≥ L/16 ; L/10 a L/12 ; b=B/20
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F
se re)omineda .sar2%n
5 > T
C = $
datos P# #"## Tn Carga m.erta $"# tn@m P0 "## Tn Carga 'i'a 0"# tn@m P$ 0$"## Tn
F3) $0# g@)m$ ( #"*1 tn@m$
F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"*# m Ti(o de Col2 2
+ !"## m n 0.25
""" 0.25 """
At 2#.00 m2 . 0"*> Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 32$$.14 cm2 Pg 13$.40 %n
, d 5$.25 cm P 1$2.050 %n
""" 1$2.05 """
se))ion de )ol.mna de&"!#"## )m #"## )m
3500.00 cm2
Par este )aso tenos .n %n >"## m
T #"# m
!"0>- 5 >
FALLA DUCTIL
C = 0
datos P!@$ >"!# Tn
Carga m.erta $"# tn@m P> "## Tn
Carga 'i'a 0"# tn@m P- 0$"## Tn
F3) $0# g@)m$ ( #"1 tn@m$
F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"$# m Ti(o de Col2 1
+ !"## m n 0.30
""" """ 0.30
At 2.00 m2 . 0"> Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 243.14 cm2 Pg 151.3#0 %n
, d 51.41 cm P 1.51# %n
""" """ 1.52
se))ion de )ol.mna de&"
!#"## )m !!"## )m
2$50.00 cm2
Par este )aso tenos .n %n >"## m
T #"!! m
"$$ 5 >
FALLA DUCTIL
C = 0
si ).m(le lase))ion
si ).m(le lase))ion
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At 2#.00 m2 . 0"1# Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 23#.!5 cm2 Pg 151.140 %n
, d 51.3$ cm P 1.254 %n
""" """ 1.25
se))ion de )ol.mna de&"
!#"## )m !!"## )m
2$50.00 cm2
Par este )aso tenos .n %n 0"!# m T #"!! m
$"$- 5 >
FALLA FRAGIL
C = 0
datos P!@$ >"!# Tn
Carga m.erta $"# tn@m P* "## Tn
Carga 'i'a 0"# tn@m P 0#"## Tn F3) $0# g@)m$ ( #"1> tn@m$
F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"*# m Ti(o de Col2 1
+ !"## m n 0.30
""" """ 0.30
At 2#.00 m2 . 0"1# Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 23#.!5 cm2 Pg 151.140 %n
, d 51.3$ cm P 1.254 %n
""" """ 1.25
se))ion de )ol.mna de&"
!#"## )m !!"## )m
2$50.00 cm2
Par este )aso tenos .n %n >"## m
T #"!! m
"$$ 5 >
FALLA DUCTIL
C = $
datos P# #"## Tn
Carga m.erta $"# tn@m P1 0#"## Tn
Carga 'i'a 0"# tn@m P "## Tn
F3) $0# g@)m$ ( #"*> tn@m$
F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"-# m Ti(o de Col2 2
+ !"## m n 0.25""" 0.25 """
At 2.50 m2 . 0"*# Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 3031.43 cm2 Pg 12$.320 %n
, d 55.0 cm P 15!.150 %n
""" 15!.15 """
se))ion de )ol.mna de&"
si ).m(le lase))ion
si ).m(le lase))ion
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PREDIMENSIONAMIENTO DE LOSAS
ALIGERADOS
E& '(&)*+& ,E L-. L()E.
Para losas .nidire))ionales
LU <m? % <)m? / $.00 otro
/ $.00 otro / 20.00
/ $.00 / 25.00 otro
/ $.00 / 30.00 / 25.00
,imensionamiento valido para aligerados armados en una direccion
con sobrecargas maimas de 300 " 350 gm2
El dimensionamineto tambien se ace teniendo en cuenta la fleca maima
defleion seg6n la norma E"00
Para losas ,idire))ionales
LU <m? % <)m? / $.00 / 25.00 / 25.00
/ $.00 otro / 30.00
Los aligerados armados en 2 direcciones se usan gralment cuando se tienen
pa7os mas o menos cuadrados 8 luces ma8ores a los m
Para luces ma8ores no es usual considerar ninguno de estos aligerados pues
no resultan livianos ni economicos en comparacion con las losas nervadas
LOSAS NERVADAS
suponiendo una distancia de e9es entre viguetas de $0cm se considera el sgte
dimensionamiento para viguetas en una direccion
PE:-L%E L(;
bl d 10<15 / 5 00 5
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/ 2.00 / 20.00
/ 2.00 / 25.00
Las losas pueden estar soportadas perimetral e interiormente por vigas
monol>ticas de ma8or peralte? por vigas de otros materiales independientes
o integradas a la losa@ o soportadas por muros de concreto ? muros de
mamposter>a o muros de otro material. ,ise7o de losas macizastml
PREDIMENSIONAMIENTO DE VIGAS
,*AE&*+&E ((-LE ,E L- *C-
L(; ,*AE&*+&Ecomentario
/ .00 otro
/ .00 25D0 30D0 40D0
/ .00 25D$0 30D$0 40D$0 40D$0
/ .00 30D$5 40D$5 30D#0 40D#0
/ .00 30D#5 30D!0 40D#5 40D!0
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P0 P$ P- P>
"## Tn 0$"## Tn 0$"## Tn "## Tn
Carg V"
Carga M"
>"## m C=$ C=0
$"## m 0"*# m 0"*# m 0"*# m 0"># m 0"># m
$"## m >"1# m !"*
-!"## m
L
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P0 P$ P- P> P
"## Tn 0$"## Tn 0$"## Tn "## Tn "
Carga 'i'a
Carg m.erta
>"## m C=$ C=0
$"## m 0"*# m 0"*# m 0"*# m 0"># m 0"># m
$"## m >"1# m !"*# m
T
,
T
sismo
%n % de e6ea e6e
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PREDIMENSIONAMIENTO DE COLUMNAS
0J CASOPara edificios tengan muros de corte en las dos direcciones? tal la rigidez la
8 la resitencia van a estar principalmente controladas por los muros? las column
se pueden dimensionar suponiendo un area igual aF
P servicio / 50.00REA DE COLUMN /
fGc / 210.00
$J CASOPara el mismo tipo de edificio ? el dimensionamiento d las columnas con menos
carga aial caso de eteriores o esuineras? se ara un area igual aF
P servicio / 50.00REA DE COLUMN /
fGc / 210.00
-J CASO
Para edificios aporticados integramente se recomienda no eeder de 3 o 4 pis
las columnas deberan dimensionarse mediante alguna estimacion del momento d
del mH de sismo? se pueden reuerir columnas con areas entre 1000 8 2000 cm
vigas conluces ma8ores a $m
Para este tipo de edificios se dispondran columnas de 3535? 4040? 2550? 3
o circulares de 40 o 50 cm de diametro. Estas altenativas se escogeran seg6n
cuadradas o rectangulares de los pa7os Blanco Blasco )ap3Pg4
AREAcolumna= P( servicio)0.45 f ' c
AREAcolumna= P( servicio)0.35 f ' c
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PREDIMENSIONAMIENTO DE PLACAS O
Las placas pueden acerse minimo de 10 cm de espesor
Pero gnralmente se consideran de 15cm de espesor en casos de edificios
%ambien de 20? 25? 30 cm conforme aunmentemos el nH de pisos.
En el Peru se an pro8ectado una serie de edificaciones de asta 20 piso
espesor de 25 cm las cuales tb tenian longitudes apreciables@ i eistier
direccion probalemente se necesitaran espesores ma8ores como 40? 50 o
Para realizar la evaluacion final se debera acer un analisis sismico .
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P*
"## Tn
P P1 P
0#"## Tn 0#"## Tn "## Tn
C=0
C=0 C=$
$"!# m
0"># m 0"1# m 0"1# m $"## m $"!# m
!"*# m $"!# m
B
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P*
"## Tn
P P1 P
0#"## Tn 0#"## Tn "## Tn
C=0
C=0 C=$
$"!# m
0"># m 0"1# m 0"1# m $"## m $"!# m
!"*# m $"!# m
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!!"## )m
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gan
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RETO
cas d
una
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Ln
B
Coondi)io
J /
Condi)io
b J /
bKd J
L
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PREDIMENSIONAMIENTO DE VIGAS
J 54.55 cm
J 0.00 cm
)ondicion
b J 2$.50 cm b J 1#.00 cm
b J 30.00 cm b J 30.00 cm
PREDIMENSIONAMIENTO DE COLUMNAS
%ipo de columna / 1.00
n J / 0.45
/ 0.45
"""
P servicio 25000. g fGc J 210. gcm2
b K d J 24.55 cm2
b J d J 1.2$ cm
b J 20.00 cm
0.30 b 0.5
B
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FACULTAD DE INGENIERIASESCUELA PROFESIONAL DE INGENIERÍA CIVIL
PREDIMENSIONAMIENTO DE ELMENTOS ESTRUC
Predimensionamiento de la losa aligerada
Luz libre del portico L !"## m#"$# m
Espesor de losa % #"$# m
Espesor de losa def. % de&" #"$# m
Predimensionamiento de la 'iga (rin)i(al
Luz libre del portico principal L !"*# m
Luz libre del portico segundario + !"## m
Peralte de viga % 0.51 m
Peralte de viga definitivo % de&" #"*# m
Base de la viga , 0.25 m
Base de la viga definitivo , de&" -#"## m
Predimensionamiento de la 'iga seg.ndaria
Luz libre del portico principal L !"## m
Luz libre del portico segundario + *"## m
Peralte de viga % 0.45 m
Peralte de viga definitivo % de&" #"!# m
Base de la viga , 0.30 m
Base de la viga definitivo , de&" -#"## m
Predimensionamiento de la 'iga en 'oladi/o en el de $"##m"Luz libre del portico principal L 0"1# m
#"*# m
Luz libre del portico segundario + !"## m
Peralte de viga % 0.4 m
Peralte de viga definitivo % de&" #"*# m
Base de la viga , 0.25 m
Base de la viga definitivo , de&" -#"## m
Predimensionamiento de la 'iga en 'oladi/o en el de $"!#m"
Luz libre del portico principal L $"-# m
Luz libre del portico segundario + *"## m Peralte de viga % 0.5! m
Peralte de viga definitivo % de&" #"*# m
UNIVERSIDAD :OSE CARLOS
PARA LOSA ALIGERADA <Seg.n R"N"E" en la norma E = #*# Art" 0#">"0"0?
PARA LAS VIGAS <Seg.n R"N"E" en la norma E = #*# Art" 0#">"0"- 8 el ingeniero Antonio +lan)o +las)ore)omiendan .sar (eraltes?
h ≥ L/25
h ≥ L/16 ; L/10 a L/12 ; b=B/20
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Base de la viga , 0.30 m
Base de la viga definitivo , de&" -#"## m
F.er/a )ortante
De&i)ien)ia de an)la6e del a)ero en las 'igas
De&i)ien)ia en los em(almes del a)ero en las )ol.mnas
Por a(lastamiento
Seg.n ensa8os e9(erimentales en :a(on se o,t.'o ;.e 2
se re)omineda .sar2%n
5 > T
C = $
datos P# #"## Tn
Carga m.erta $"# tn@m P0 "## Tn
Carga 'i'a 0"# tn@m P$ 0$"## Tn
F3) $0# g@)m$ ( #"*1 tn@m$ F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"*# m Ti(o de Col2 2
+ !"## m n 0.25
""" 0.25 """
At 2#.00 m2 . 0"*> Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 32$$.14 cm2 Pg 13$.40 %n se))ion de )ol
, d 5$.25 cm P 1$2.050 %n !#"## )m
""" 1$2.05 """ 3500.00
C = 0
datos P!@$ >"!# Tn
Carga m.erta $"# tn@m P> "## Tn
Carga 'i'a 0"# tn@m P- 0$"## Tn
F3) $0# g@)m$ ( #"1 tn@m$
F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"$# m Ti(o de Col2 1
+ !"## m n 0.30
""" """ 0.30 At 2.00 m2 . 0"> Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
PARA COLUMNAS <Seg.n el ingeniero antonio ,lan)o ,las)o re)omienda <A)Pser'i)io@#">!4F3)? 8<A)Pser'i)io@#"-!4F3)? esto en el )aso de tener (la)as o m.ros )ortantes
PARA COLUMNAS Pero el ICG lo determina )on <,TP@nF3)? 8 n estara en &.n)ion de ;.e ti(o de )ol.mna sea ti(o0#"- ti(o $8-#"$! 8 ti(o >#"$
Seg.n la dis).sion de alg.nos res.ltados de in'estiga)iones en :a(on de,ido al sismo de TOBACI 0*1 donde)ola(saron m.)%as )ol.mnas (or2
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,d 243.14 cm2 Pg 151.3#0 %n se))ion de )ol
, d 51.41 cm P 1.51# %n !#"## )m
""" """ 1.52 2$50.00
C = 0
datos P!@$ >"!# Tn
Carga m.erta $"# tn@m P* "## Tn Carga 'i'a 0"# tn@m P# 0#"## Tn
F3) $0# g@)m$ ( #"1> tn@m$
F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"*# m Ti(o de Col2 1
+ !"## m n 0.30
""" """ 0.30
At 2#.00 m2 . 0"1# Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 23#.!5 cm2 Pg 151.140 %n se))ion de )ol
, d 51.3$ cm P 1.254 %n !#"## )m""" """ 1.25 2$50.00
C = 0
datos P!@$ >"!# Tn
Carga m.erta $"# tn@m P* "## Tn
Carga 'i'a 0"# tn@m P 0#"## Tn
F3) $0# g@)m$ ( #"1> tn@m$
F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"*# m Ti(o de Col2 1 + !"## m n 0.30
""" """ 0.30
At 2#.00 m2 . 0"1# Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 23#.!5 cm2 Pg 151.140 %n se))ion de )ol
, d 51.3$ cm P 1.254 %n !#"## )m
""" """ 1.25 2$50.00
C = $
datos P# #"## Tn
Carga m.erta $"# tn@m P1 0#"## Tn Carga 'i'a 0"# tn@m P "## Tn
F3) $0# g@)m$ ( #"*> tn@m$
F38 >$## g@)m$ d #"* tn@m$
Predimensionamiento de )ol.mnas
L !"-# m Ti(o de Col2 2
+ !"## m n 0.25
""" 0.25 """
At 2.50 m2 . 0"*# Tn@m$
&3) $0# g@)m$ H de Pisos 3.0
,d 3031.43 cm2 Pg 12$.320 %n se))ion de )ol
, d 55.0 cm P 15!.150 %n !#"## )m
""" 15!.15 """ 3250.00
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PREDIMENSIONAMIENTO DE LOSAS
ALIGERADOS
E& '(&)*+& ,E L-. L()E.
Para losas .nidire))ionales
LU <m? % <)m? / $.00 otro
/ $.00 otro / 20.00
/ $.00 / 25.00 otro
/ $.00 / 30.00 / 25.00
,imensionamiento valido para aligerados armados en una direccion
con sobrecargas maimas de 300 " 350 gm2
El dimensionamineto tambien se ace teniendo en cuenta la fleca maima
defleion seg6n la norma E"00
Para losas ,idire))ionales
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LU <m? % <)m? / $.00 / 25.00 / 25.00
/ $.00 otro / 30.00
Los aligerados armados en 2 direcciones se usan gralment cuando se tienen
pa7os mas o menos cuadrados 8 luces ma8ores a los m
Para luces ma8ores no es usual considerar ninguno de estos aligerados puesno resultan livianos ni economicos en comparacion con las losas nervadas
LOSAS NERVADAS
suponiendo una distancia de e9es entre viguetas de $0cm se considera el sgte
dimensionamiento para viguetas en una direccion
PE:-L%E
-nco variable de 10<15cm / 35.00
-nco variable de 10<15cm / 40.00-nco variable de 10<15cm / 50.00
LOSAS MACIAS
% L.)es <m?coment
/ 2.00 12 o 13
/ 2.00 / 15.00
/ 2.00 / 20.00
/ 2.00 / 25.00
Las losas pueden estar soportadas perimetral e interiorme
monol>ticas de ma8or peralte? por vigas de otros materiales independientes
o integradas a la losa@ o soportadas por muros de concreto ? muros de
mamposter>a o muros de otro material. ,ise7o de losas macizastml
PREDIMENSIONAMIENTO DE VIGAS
,*AE&*+&E ((-LE ,E L- *C-
L(; ,*AE&*+&E coment / .00 otro
/ .00 25D0 30D0 40D0
/ .00 25D$0 30D$0 40D$0 40D$0
/ .00 30D$5 40D$5 30D#0 40D#0
/ .00 30D#5 30D!0 40D#5 40D!0
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URALES P0 P$
"## Tn 0$"## Tn
!"## m
>"## m C=$
#"*# m$"## m 0"*# m
$"## m
-#"## m
#"!# m
-#"## m
-#"## m
#"*# m
ARIATEGUI
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-#"## m
Por lo tanto si2
n P
F3) 4 , 4 T
n 50-
n 70
- Falla d.)til
P0 P$
Par este )aso tenos .n %n >"## m "## Tn 0$"## Tn
T #"# m
!"0>- 5 >
FALLA DUCTIL
mna de&"
#"## )m
si ).m(le la se))ion
>"## m C=$
cm2
Par este )aso tenos .n %n >"## m
T #"!! m
"$$ 5 >$"## m 0"*# m
FALLA DUCTIL$"## m
Falla &ragil (or a(lastamiento de,ido a )argas a9ialese9e)i'as
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mna de&"
!!"## )m
si ).m(le la se))ioncm2
Par este )aso tenos .n %n 0"!# m
T #"!! m
$"$- 5 >
FALLA FRAGIL
mna de&"
!!"## )m si ).m(le la se))ioncm2
Par este )aso tenos .n %n >"## m
T #"!! m
"$$ 5 >
FALLA DUCTIL
mna de&"
!!"## )m si ).m(le la se))ioncm2
Par este )aso tenos .n %n $"!# m
T #"*! m
-"1>*$ 5 >
FALLA FRAGIL
mna de&"
*!"## )m
si ).m(le la se))ioncm2
,
T
sismo
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!#"## )m#"## )m
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L(;
= $.5
= #.5= !.5
rio
te por vigas
rio
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P- P> P! P*
0$"## Tn "## Tn "## Tn "## Tn
C=0
Carg V" 0"# tn@m
Carga M" $"# tn@m
C=0 C=0
0"*# m 0"*# m 0"># m 0"># m 0"># m 0"># m 0"1# m
>"1# m !"*# m
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P- P> P! P*
0$"## Tn "## Tn "## Tn "## Tn
C=0
Carga 'i'a 0"# tn@m
Carg m.erta $"# tn@m
C=0 C=0
0"*# m 0"*# m 0"># m 0"># m 0"># m 0"># m 0"1# m
>"1# m !"*# m
L
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!#"## )m
!!"## )m
T
%n % de e6ea e6e
L
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!#"## )m !#"## )m!!"## )m !!"## )m
PREDIMENSIONAMIENTO DE COLUMNAS
0J CASOPara edificios tengan muros de corte en las dos direcciones? tal la rigidez lateral
8 la resitencia van a estar principalmente controladas por los muros? las columnas
se pueden dimensionar suponiendo un area igual aF
P servicio / 50.00EA DE COLUM / 0.53
fGc / 210.00
$J CASOPara el mismo tipo de edificio ? el dimensionamiento d las columnas con menos
AREAcolumna= P( servicio )0.45 f ' c
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carga aial caso de eteriores o esuineras? se ara un area igual aF
P servicio / 50.00 EA DE COLUM / 0.#fGc / 210.00
-J CASO
Para edificios aporticados integramente se recomienda no eeder de 3 o 4 pisos
las columnas deberan dimensionarse mediante alguna estimacion del momento de sismo
del mH de sismo? se pueden reuerir columnas con areas entre 1000 8 2000 cm2? salvo tengan
vigas conluces ma8ores a $m
Para este tipo de edificios se dispondran columnas de 3535? 4040? 2550? 300? 3040 3050?
o circulares de 40 o 50 cm de diametro. Estas altenativas se escogeran seg6n las dimensionescuadradas o rectangulares de los pa7os Blanco Blasco )ap3Pg41"42
>J CASOPara edificios con luces ma8ores a $ u # m debe tenerse especial cuidado con las columnas
eteriores pudiendo dimensionarse el peralte de la columna en un $0 u #0I del peralte de la
viga principal
PREDIMENSIONAMIENTO DE PLACAS O MUROS DE CONCRETO
Las placas pueden acerse minimo de 10 cm de espesor
Pero gnralmente se consideran de 15cm de espesor en casos de edificios de pocos pisos.
%ambien de 20? 25? 30 cm conforme aunmentemos el nH de pisos.
En el Peru se an pro8ectado una serie de edificaciones de asta 20 pisos considerando placas d
espesor de 25 cm las cuales tb tenian longitudes apreciables@ i eistieran pocas placas en una
direccion probalemente se necesitaran espesores ma8ores como 40? 50 o 0 cm
Para realizar la evaluacion final se debera acer un analisis sismico .
AREAcolumna= P( servicio)0.35 f ' c
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P P1 P
0#"## Tn 0#"## Tn "## Tn
C=$
$"!# m
0"1# m $"## m $"!# m
!"*# m $"!# m
B
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P P1 P
0#"## Tn 0#"## Tn "## Tn
C=$
$"!# m
0"1# m $"## m $"!# m
!"*# m $"!# m
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B
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!#"## )m*!"## )m
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PREDIMENSIONAMIENTO D
Ln .00 m
B 5.50 m
Coondi)ion
JLn J 54.55 cm
/ 11.00 J 0.00 cm
Condi)ion
b JB b J 2$.50 cm
/ 20.00 b J 30.00 cm
PREDIMENSIONAMIENTO DE
%ipo de columna
n J
P servicio
fGc J
bKd JP b K d J
nKfGc b J d J
b J
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E VIGAS
)ondicion
b J 1#.00 cm
b J 30.00 cm
OLUMNAS
/ 1.00
/ 0.45
/ 0.45
"""
25000. g
210. gcm2
24.55 cm2
1.2$ cm
20.00 cm
0.30 b 0.5
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"## Tn 0$"## Tn 0$"## Tn "## Tn "## Tn "## Tn
>"## m
$"## m 0"*# m 0"*# m 0"*# m 0"># m 0"># m 0"># m 0"># m 0"1#
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datos
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F38 >$## g@)m$
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0#"## Tn "## Tn
$"!# m
$"## m $"!# m
$"!# m
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 354000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.012
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "1401042.01 g.cm
A3s M. A3s "$.5 cm2
4F384<d=d3?
As Total As """"""
Total A3s "$.5 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.1!M 1 J 0.21$
M 2 J 1.4$#
P J 0.010!
ceueo de P J SIMPLEM" REFORADA
-s J 20.53 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "$.5 cm2
P N-L(EO
P3 "0.0040
As0
M.0 M.0
M.=M.0
As0 A3s
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
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0.!0
'iga, 35. cm
% 0. cm
r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 2#11000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.012
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "2244042.01 g.cm
A3s M. A3s "12.12 cm2
4F384<d=d3?
As Total As """"""
Total A3s "12.12 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.15
M 1 J 0.11
M 2 J 1.534
P J 0.00#1
ceueo de P J SIMPLEM" REFORADA -s J 15.22 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "12.12 cm2
P N-L(EO
P3 "0.004
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
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LEMENTE REFORADAS
#$ )a(as #- )a(as
354000. g.cm 354000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.012 0.012
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"#54!$2.5 g.cm "50#21.!5 g.cm
"4.!2 cm2 "3.0 cm2
"""""" """"""
"4.!2 cm2 "3.0 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.21 0.230.24! 0.2$5
1.44 1.420
0.0124 0.013$
SIMPLEM" REFORADA SIMPLEM" REFORADA
22.22 cm2 23.54 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"4.!2 cm2 "3.0 cm2
N-L(EO N-L(EO
"0.002# "0.001#
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N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
LEMENTE REFORADAS
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#$ )a(as #- )a(as
2#11000. g.cm 2#11000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.012 0.012
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"1!$!$2.5 g.cm "135121.!5 g.cm
"!.$$ cm2 "#.12 cm2
"""""" """"""
"!.$$ cm2 "#.12 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.1 0.1#
0.1#3 0.201
1.512 1.4!4
0.00!2 0.0100
SIMPLEM" REFORADA SIMPLEM" REFORADA1.35 cm2 1$.22 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"!.$$ cm2 "#.12 cm2
N-L(EO N-L(EO
"0.0055 "0.004$
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 4!10000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.012
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "145042.01 g.cm
A3s M. A3s "0.$# cm2
4F384<d=d3?
As Total As """"""
Total A3s "0.$# cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.25M 1 J 0.312
M 2 J 1.3#3
P J 0.015
ceueo de P J SIMPLEM" REFORADA
-s J 2!.4# cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "0.$# cm2
P N-L(EO
P3 "0.0004
As0
M.0 M.0
M.=M.0
As0 A3s
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
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0.!0
'iga, 35. cm
% 0. cm
r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 3#$000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.012
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "13#042.01 g.cm
A3s M. A3s "$.3! cm2
4F384<d=d3?
As Total As """"""
Total A3s "$.3! cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.1!
M 1 J 0.220
M 2 J 1.4$5
P J 0.0110
ceueo de P J SIMPLEM" REFORADA -s J 20.$5 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "$.3! cm2
P N-L(EO
P3 "0.003!
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
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LEMENTE REFORADAS
#$ )a(as #- )a(as
4!10000. g.cm 4!10000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.012 0.012
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
40102$.35 g.cm $4$$3#.05 g.cm
2.31 cm2 4.50 cm2
31.22 cm2 32.2# cm2
2.31 cm2 4.50 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.2! 0.310.33 0.40$
1.332 1.2##
0.01#2 0.0203
DO+"REFORADA DO+"REFORADA
""""" """""
ION DO+LEMENTE REFORADA
31.22 cm2 32.2# cm2
2.31 cm2 4.50 cm2
0.01$5 0.01##
0.0013 0.002
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0.012 0.012
0.011#1 0.0122!
SI FLUQE SI FLUQE
LEMENTE REFORADAS
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#$ )a(as #- )a(as
3#$000. g.cm 3#$000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.012 0.012
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"#21!$2.5 g.cm "4$521.!5 g.cm
"4.$3 cm2 "2.# cm2
"""""" """"""
"4.$3 cm2 "2.# cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.21 0.23
0.252 0.2$#
1.443 1.41$
0.012 0.013!
SIMPLEM" REFORADA SIMPLEM" REFORADA22.4 cm2 23.#1 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"4.$3 cm2 "2.# cm2
N-L(EO N-L(EO
"0.002 "0.001$
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 20!5000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "2!0042.01 g.cm
A3s M. A3s "15.!# cm2
4F384<d=d3?
As Total As """"""
Total A3s "15.!# cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.11M 1 J 0.11$
M 2 J 1.5$#
P J 0.005#
ceueo de P J SIMPLEM" REFORADA
-s J 11.02 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "15.!# cm2
P N-L(EO
P3 "0.00#5
As0
M.0 M.0
M.=M.0
As0 A3s
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
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0.!0
'iga, 35. cm
% 0. cm
r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 20!5000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "2!0042.01 g.cm
A3s M. A3s "15.!# cm2
4F384<d=d3?
As Total As """"""
Total A3s "15.!# cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.11
M 1 J 0.11$
M 2 J 1.5$#
P J 0.005#
ceueo de P J SIMPLEM" REFORADA -s J 11.02 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "15.!# cm2
P N-L(EO
P3 "0.00#5
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
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LEMENTE REFORADAS
#$ )a(as #- )a(as
20!5000. g.cm 20!5000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"2413!$2.5 g.cm "20$21.!5 g.cm
"13.## cm2 "12.43 cm2
"""""" """"""
"13.## cm2 "12.43 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.12 0.130.132 0.144
1.53 1.551
0.00 0.00$2
SIMPLEM" REFORADA SIMPLEM" REFORADA
11.$! cm2 12.3 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"13.## cm2 "12.43 cm2
N-L(EO N-L(EO
"0.00$# "0.00$2
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N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
LEMENTE REFORADAS
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#$ )a(as #- )a(as
20!5000. g.cm 20!5000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"2413!$2.5 g.cm "20$21.!5 g.cm
"13.## cm2 "12.43 cm2
"""""" """"""
"13.## cm2 "12.43 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.12 0.13
0.132 0.144
1.53 1.551
0.00 0.00$2
SIMPLEM" REFORADA SIMPLEM" REFORADA11.$! cm2 12.3 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"13.## cm2 "12.43 cm2
N-L(EO N-L(EO
"0.00$# "0.00$2
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 420000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "435042.01 g.cm
A3s M. A3s "2.35 cm2
4F384<d=d3?
As Total As """"""
Total A3s "2.35 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.24M 1 J 0.2#!
M 2 J 1.40
P J 0.0144
ceueo de P J SIMPLEM" REFORADA
-s J 2$.2# cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "2.35 cm2
P N-L(EO
P3 "0.0012
As0
M.0 M.0
M.=M.0
As0 A3s
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
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0.!0
'iga, 35. cm
% 0. cm
r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 30000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "144!042.01 g.cm
A3s M. A3s "$.#2 cm2
4F384<d=d3?
As Total As """"""
Total A3s "$.#2 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.1!
M 1 J 0.214
M 2 J 1.4#1
P J 0.010$
ceueo de P J SIMPLEM" REFORADA -s J 20.22 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "$.#2 cm2
P N-L(EO
P3 "0.0041
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
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LEMENTE REFORADAS
#$ )a(as #- )a(as
420000. g.cm 420000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53 B.
2#.!2 cm2 2$.$# cm2 As
450#!$2.5 g.cm 41221.!5 g.cm
11102$.35 g.cm 45$$3#.05 g.cm Mr
0.4 cm2 2.$5 cm2 A3s
2!.5 cm2 30.54 cm2 As
0.4 cm2 2.$5 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.2$ 0.2!0.335 0.3$3
1.30 1.322
0.01$ 0.01#
DO+"REFORADA DO+"REFORADA
""""" """""
ION DO+LEMENTE REFORADA
2!.5 cm2 30.54 cm2
0.4 cm2 2.$5 cm2
0.01 0.01$#
0.0004 0.001
M.0
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0.012 0.012
0.011#1 0.0122!
SI FLUQE SI FLUQE
LEMENTE REFORADAS
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#$ )a(as #- )a(as
30000. g.cm 30000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53 B.
2#.!2 cm2 2$.$# cm2 As
450#!$2.5 g.cm 41221.!5 g.cm
"!02!$2.5 g.cm "5521.!5 g.cm Mr
"5.1! cm2 "3.34 cm2 A3s
"""""" """""" As "5.1! cm2 "3.34 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.21 0.23
0.245 0.2$0
1.450 1.425
0.0122 0.0135
SIMPLEM" REFORADA SIMPLEM" REFORADA21.#$ cm2 23.1 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"5.1! cm2 "3.34 cm2
N-L(EO N-L(EO
"0.002! "0.0020
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
M.0
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 5125000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
M. B. 4!.53
,4d$
P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr !!5$.!! g.cm
M. A3s 0.3# cm2
4F384<d=d3?
Total As 31.00 cm2
Total A3s 0.3# cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.2$M 1 J 0.330
M 2 J 1.35
P J 0.015
ceueo de P J DO+"REFORADA
-s J """""
ANALISIS O VERIFICACION DE UNA SECC
As 31.00 cm2
A3s 0.3# cm2
P 0.014
P3 0.0002
As0
M.0
M.=M.0
As0 A3s
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P = P3 0.012
VERF" 0.01115
SI FLUQE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
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0.!0
'iga, 35. cm
% 0. cm
r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 4000000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
M. B. 4!.53
,4d$
P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr "1055042.01 g.cm
M. A3s "5.$0 cm2
4F384<d=d3?
Total As """"""
Total A3s "5.$0 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.21
M 1 J 0.242
M 2 J 1.453
P J 0.0121
ceueo de P J SIMPLEM" REFORADA -s J 22.# cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "5.$0 cm2
P N-L(EO
P3 "0.0030
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0
M.=M.0
As0 A3s
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LEMENTE REFORADAS
#$ )a(as #- )a(as
5125000. g.cm 5125000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
102$.35 g.cm !2$3#.05 g.cm
3.54 cm2 5.$! cm2
32.4 cm2 33.5$ cm2
3.54 cm2 5.$! cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.30 0.320.3# 0.434
1.30! 1.21
0.01!3 0.021$
DO+"REFORADA DO+"REFORADA
""""" """""
ION DO+LEMENTE REFORADA
32.4 cm2 33.5$ cm2
3.54 cm2 5.$! cm2
0.01#2 0.01!
0.0020 0.0034
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0.012 0.012
0.011#1 0.0122!
SI FLUQE SI FLUQE
LEMENTE REFORADAS
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#$ )a(as #- )a(as
4000000. g.cm 4000000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"50#!$2.5 g.cm "1221.!5 g.cm
"2.!3 cm2 "0.!# cm2
"""""" """"""
"2.!3 cm2 "0.!# cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.23 0.25
0.2$# 0.30#
1.41$ 1.3#$
0.013! 0.0154
SIMPLEM" REFORADA SIMPLEM" REFORADA24.#2 cm2 2.3! cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"2.!3 cm2 "0.!# cm2
N-L(EO N-L(EO
"0.001 "0.000
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 3051000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "2004042.01 g.cm
A3s M. A3s "10.#2 cm2
4F384<d=d3?
As Total As """"""
Total A3s "10.#2 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.1M 1 J 0.1$$
M 2 J 1.51#
P J 0.00##
ceueo de P J SIMPLEM" REFORADA
-s J 1.! cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "10.#2 cm2
P N-L(EO
P3 "0.005$
As0
M.0 M.0
M.=M.0
As0 A3s
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
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0.!0
'iga, 35. cm
% 0. cm
r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 3051000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "2004042.01 g.cm
A3s M. A3s "10.#2 cm2
4F384<d=d3?
As Total As """"""
Total A3s "10.#2 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.1
M 1 J 0.1$$
M 2 J 1.51#
P J 0.00##
ceueo de P J SIMPLEM" REFORADA -s J 1.! cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "10.#2 cm2
P N-L(EO
P3 "0.005$
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
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LEMENTE REFORADAS
#$ )a(as #- )a(as
3051000. g.cm 3051000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"145$!$2.5 g.cm "111121.!5 g.cm
"#.3# cm2 ".# cm2
"""""" """"""
"#.3# cm2 ".# cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.1# 0.1!0.201 0.221
1.4!4 1.4$4
0.0101 0.0110
SIMPLEM" REFORADA SIMPLEM" REFORADA
1$.! cm2 1#.!4 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"#.3# cm2 ".# cm2
N-L(EO N-L(EO
"0.004$ "0.003!
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N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
LEMENTE REFORADAS
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#$ )a(as #- )a(as
3051000. g.cm 3051000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"145$!$2.5 g.cm "111121.!5 g.cm
"#.3# cm2 ".# cm2
"""""" """"""
"#.3# cm2 ".# cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.1# 0.1!
0.201 0.221
1.4!4 1.4$4
0.0101 0.0110
SIMPLEM" REFORADA SIMPLEM" REFORADA1$.! cm2 1#.!4 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"#.3# cm2 ".# cm2
N-L(EO N-L(EO
"0.004$ "0.003!
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 4253000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "#02042.01 g.cm
A3s M. A3s "4.33 cm2
4F384<d=d3?
As Total As """"""
Total A3s "4.33 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.22M 1 J 0.21
M 2 J 1.434
P J 0.0130
ceueo de P J SIMPLEM" REFORADA
-s J 24.2 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "4.33 cm2
P N-L(EO
P3 "0.0023
As0
M.0 M.0
M.=M.0
As0 A3s
![Page 100: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/100.jpg)
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
![Page 101: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/101.jpg)
7/23/2019 PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls
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0.!0
'iga, 35. cm
% 0. cm
r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 32$!000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "1$$042.01 g.cm
A3s M. A3s "!.5! cm2
4F384<d=d3?
As Total As """"""
Total A3s "!.5! cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.1$
M 1 J 0.1!2
M 2 J 1.503
P J 0.00!
ceueo de P J SIMPLEM" REFORADA -s J 1#.11 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "!.5! cm2
P N-L(EO
P3 "0.0051
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
![Page 102: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/102.jpg)
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LEMENTE REFORADAS
#$ )a(as #- )a(as
4253000. g.cm 4253000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"255!$2.5 g.cm !0$3#.05 g.cm
"1.4$ cm2 0.55 cm2
"""""" 2#.33 cm2
"1.4$ cm2 0.55 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.25 0.2$0.300 0.333
1.3!4 1.32
0.0150 0.01$
SIMPLEM" REFORADA DO+"REFORADA
2.#1 cm2 """""
ION DO+LEMENTE REFORADA
"""""" 2#.33 cm2
"1.4$ cm2 0.55 cm2
N-L(EO 0.015
"0.000# 0.0003
![Page 103: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/103.jpg)
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N-L(EO 0.012
0.011#1 0.0122!
HVALUE SI FLUQE
LEMENTE REFORADAS
![Page 104: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/104.jpg)
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#$ )a(as #- )a(as
32$!000. g.cm 32$!000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"122!!$2.5 g.cm "##321.!5 g.cm
"$.0$ cm2 "5.31 cm2
"""""" """"""
"$.0$ cm2 "5.31 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.1! 0.21
0.21! 0.241
1.4$ 1.454
0.010! 0.0120
SIMPLEM" REFORADA SIMPLEM" REFORADA1!.53 cm2 20.3 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"$.0$ cm2 "5.31 cm2
N-L(EO N-L(EO
"0.0040 "0.0031
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
![Page 105: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/105.jpg)
7/23/2019 PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 44$!000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "5$042.01 g.cm
A3s M. A3s "3.11 cm2
4F384<d=d3?
As Total As """"""
Total A3s "3.11 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.23M 1 J 0.2$#
M 2 J 1.41$
P J 0.013!
ceueo de P J SIMPLEM" REFORADA
-s J 2.24 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "3.11 cm2
P N-L(EO
P3 "0.001
As0
M.0 M.0
M.=M.0
As0 A3s
![Page 106: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/106.jpg)
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
![Page 107: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/107.jpg)
7/23/2019 PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls
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0.!0
'iga, 35. cm
% 0. cm
r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 35#1000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "14$4042.01 g.cm
A3s M. A3s "$.! cm2
4F384<d=d3?
As Total As """"""
Total A3s "$.! cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.1!
M 1 J 0.212
M 2 J 1.4#3
P J 0.010
ceueo de P J SIMPLEM" REFORADA -s J 20.05 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "$.! cm2
P N-L(EO
P3 "0.0042
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
![Page 108: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/108.jpg)
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LEMENTE REFORADAS
#$ )a(as #- )a(as
44$!000. g.cm 44$!000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"2!!$2.5 g.cm 31$3#.05 g.cm
"0.1$ cm2 1.!0 cm2
"""""" 2!.! cm2
"0.1$ cm2 1.!0 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.2 0.2#0.321 0.35$
1.3$4 1.33#
0.011 0.01$!
SIMPLEM" REFORADA DO+"REFORADA
2#.$ cm2 """""
ION DO+LEMENTE REFORADA
"""""" 2!.! cm2
"0.1$ cm2 1.!0 cm2
N-L(EO 0.01$3
"0.0001 0.0011
![Page 109: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/109.jpg)
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N-L(EO 0.012
0.011#1 0.0122!
HVALUE SI FLUQE
LEMENTE REFORADAS
![Page 110: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/110.jpg)
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#$ )a(as #- )a(as
35#1000. g.cm 35#1000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"!2$!$2.5 g.cm "5#121.!5 g.cm
"5.34 cm2 "3.4! cm2
"""""" """"""
"5.34 cm2 "3.4! cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.21 0.23
0.243 0.2#
1.452 1.42$
0.0121 0.0134
SIMPLEM" REFORADA SIMPLEM" REFORADA21.# cm2 22.! cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"5.34 cm2 "3.4! cm2
N-L(EO N-L(EO
"0.0030 "0.0020
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
![Page 111: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/111.jpg)
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 23#1000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "2$4042.01 g.cm
A3s M. A3s "14.44 cm2
4F384<d=d3?
As Total As """"""
Total A3s "14.44 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.12M 1 J 0.134
M 2 J 1.51
P J 0.00$
ceueo de P J SIMPLEM" REFORADA
-s J 12.$ cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "14.44 cm2
P N-L(EO
P3 "0.00$
As0
M.0 M.0
M.=M.0
As0 A3s
![Page 112: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/112.jpg)
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
![Page 113: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/113.jpg)
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0.!0
'iga, 35. cm
% 0. cm
r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 23#1000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "2$4042.01 g.cm
A3s M. A3s "14.44 cm2
4F384<d=d3?
As Total As """"""
Total A3s "14.44 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.12
M 1 J 0.134
M 2 J 1.51
P J 0.00$
ceueo de P J SIMPLEM" REFORADA -s J 12.$ cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "14.44 cm2
P N-L(EO
P3 "0.00$
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
![Page 114: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/114.jpg)
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LEMENTE REFORADAS
#$ )a(as #- )a(as
23#1000. g.cm 23#1000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"212$!$2.5 g.cm "1$#121.!5 g.cm
"12.24 cm2 "10.$1 cm2
"""""" """"""
"12.24 cm2 "10.$1 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.14 0.150.152 0.1
1.543 1.52!
0.00$ 0.00#3
SIMPLEM" REFORADA SIMPLEM" REFORADA
13.5$ cm2 14.25 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"12.24 cm2 "10.$1 cm2
N-L(EO N-L(EO
"0.00! "0.002
![Page 115: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/115.jpg)
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N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
LEMENTE REFORADAS
![Page 116: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/116.jpg)
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#$ )a(as #- )a(as
23#1000. g.cm 23#1000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"212$!$2.5 g.cm "1$#121.!5 g.cm
"12.24 cm2 "10.$1 cm2
"""""" """"""
"12.24 cm2 "10.$1 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.14 0.15
0.152 0.1
1.543 1.52!
0.00$ 0.00#3
SIMPLEM" REFORADA SIMPLEM" REFORADA13.5$ cm2 14.25 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"12.24 cm2 "10.$1 cm2
N-L(EO N-L(EO
"0.00! "0.002
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
![Page 117: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/117.jpg)
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 551!000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr 43!5$.!! g.cm
A3s M. A3s 2.50 cm2
4F384<d=d3?
As Total As 33.12 cm2
Total A3s 2.50 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.2!M 1 J 0.35
M 2 J 1.330
P J 0.01#2
ceueo de P J DO+"REFORADA
-s J """""
ANALISIS O VERIFICACION DE UNA SECC
As 33.12 cm2
A3s 2.50 cm2
P 0.01$5
P3 0.0013
As0
M.0 M.0
M.=M.0
As0 A3s
![Page 118: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/118.jpg)
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P = P3 0.012
VERF" 0.01115
SI FLUQE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
![Page 119: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/119.jpg)
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0.!0
'iga, 35. cm
% 0. cm
r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 432!000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr Mr "$2042.01 g.cm
A3s M. A3s "3.!2 cm2
4F384<d=d3?
As Total As """"""
Total A3s "3.!2 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.22
M 1 J 0.2
M 2 J 1.42!
P J 0.0133
ceueo de P J SIMPLEM" REFORADA -s J 25.1 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "3.!2 cm2
P N-L(EO
P3 "0.0021
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0 M.0
M.=M.0
As0 A3s
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LEMENTE REFORADAS
#$ )a(as #- )a(as
551!000. g.cm 551!000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53 B.
2#.!2 cm2 2$.$# cm2 As
450#!$2.5 g.cm 41221.!5 g.cm
101002$.35 g.cm 135$3#.05 g.cm Mr
5.#1 cm2 #.1 cm2 A3s
34.$3 cm2 35.!4 cm2 As
5.#1 cm2 #.1 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.32 0.350.430 0.4##
1.25 1.20$
0.0215 0.0244
DO+"REFORADA DO+"REFORADA
""""" """""
ION DO+LEMENTE REFORADA
34.$3 cm2 35.!4 cm2
5.#1 cm2 #.1 cm2
0.01!5 0.0210
0.0033 0.004#
M.0
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0.012 0.012
0.011#1 0.0122!
SI FLUQE SI FLUQE
LEMENTE REFORADAS
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#$ )a(as #- )a(as
432!000. g.cm 432!000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53 B.
2#.!2 cm2 2$.$# cm2 As
450#!$2.5 g.cm 41221.!5 g.cm
"1$!!$2.5 g.cm 1$3#.05 g.cm Mr
"1.04 cm2 1.00 cm2 A3s
"""""" 2#.$! cm2 As "1.04 cm2 1.00 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.25 0.2$
0.30$ 0.341
1.3## 1.354
0.0154 0.01$1
SIMPLEM" REFORADA DO+"REFORADA2$.43 cm2 """""
ION DO+LEMENTE REFORADA
"""""" 2#.$! cm2
"1.04 cm2 1.00 cm2
N-L(EO 0.01#
"0.000 0.000
N-L(EO 0.012
0.011#1 0.0122!
HVALUE SI FLUQE
M.0
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 35. cm
% 0. cm r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 5053000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
M. B. 4!.53
,4d$
P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr "2042.01 g.cm
M. A3s "0.01 cm2
4F384<d=d3?
Total As """"""
Total A3s "0.01 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.2M 1 J 0.324
M 2 J 1.3$1
P J 0.012
ceueo de P J SIMPLEM" REFORADA
-s J 30.0 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "0.01 cm2
P N-L(EO
P3 0.0000
As0
M.0
M.=M.0
As0 A3s
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P = P3 N-L(EO
VERF" 0.01115
HVALUE
DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
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0.!0
'iga, 35. cm
% 0. cm
r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm #- )a(as 4!. cm
DATOS #0 )a(a
M. 4144000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
M. B. 4!.53
,4d$
P4,4d 30.2 cm2
B.4,4d$ 5055042.01 g.cm
Mr "!11042.01 g.cm
M. A3s "4.!2 cm2
4F384<d=d3?
Total As """"""
Total A3s "4.!2 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.21
M 1 J 0.252
M 2 J 1.442
P J 0.012
ceueo de P J SIMPLEM" REFORADA -s J 23.#5 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "4.!2 cm2
P N-L(EO
P3 "0.002
P = P3 N-L(EO
VERF" 0.01115
HVALUE
As0
M.0
M.=M.0
As0 A3s
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LEMENTE REFORADAS
#$ )a(as #- )a(as
5053000. g.cm 5053000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
54402$.35 g.cm #!0$3#.05 g.cm
3.13 cm2 5.3 cm2
32.05 cm2 33.14 cm2
3.13 cm2 5.3 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.2! 0.320.3$# 0.424
1.31$ 1.2$0
0.01#! 0.0212
DO+"REFORADA DO+"REFORADA
""""" """""
ION DO+LEMENTE REFORADA
32.05 cm2 33.14 cm2
3.13 cm2 5.3 cm2
0.01#0 0.01!3
0.001# 0.0031
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0.012 0.012
0.011#1 0.0122!
SI FLUQE SI FLUQE
LEMENTE REFORADAS
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#$ )a(as #- )a(as
4144000. g.cm 4144000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2#.!2 cm2 2$.$# cm2
450#!$2.5 g.cm 41221.!5 g.cm
"34!$2.5 g.cm "1#21.!5 g.cm
"2.10 cm2 "0.11 cm2
"""""" """"""
"2.10 cm2 "0.11 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.24 0.2
0.2!1 0.322
1.404 1.3$3
0.0145 0.011
SIMPLEM" REFORADA SIMPLEM" REFORADA25.!5 cm2 2$.2 cm2
ION DO+LEMENTE REFORADA
"""""" """"""
"2.10 cm2 "0.11 cm2
N-L(EO N-L(EO
"0.0012 "0.0001
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
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DISE O POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 70 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = 89 cm 86 cm
19513.20 kg = 35. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%as
d = 54. cm 51. cm
c =14516.01 kg 13709.57 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 8440.69 kg 9247.14 kg
S = 38.16 cm 32.89 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(
S 4a6 = 27.00 cm 25.50 cm &da C,nd/ =
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 54. cm 51. cm0.49 m 0.46 m
2.80 Und 6.13 Und
Est"i,s 8 =1 0.05 1 0.054 0.18 7 0.08
Avanc( 8 = #/93 4 #/3: 4
$/3. 4 $/;. 4
*$ =
C,"tant( *& =
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F'c =
F'y =
COLUMNA=
Av =
β =
Ø =
84 cm distancia =
=
! =
" =
#; ca%as
49. cm d =
13171.94 kg c =
N(c(sita R()*("+,9784.77 kg s =
29.87 cm S =
24.50 cm d-& =
60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/3
24.50 cm S 4a6 =N, C*4%5(&da C,nd/ =
s=7$/$11d1F'c2#/3
0.00 cm S 4a6 =
49. cm d =
0.44 m1.76 Und
1 0.05Est"i,s 8 =
06 0.25 2
$/33 4 Avanc( 8 =
&/&< 4
*& =
C,"tant( *; =
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DISE O POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 70 cm (h)
0.71 cm2
0.85
0.85
$/3. 4 $/;. 4 &/&< 420000.00 kg
40. cm70. cm5. cm
#$ ca%a #& ca%as #; ca%as
64. cm 61. cm 59. cm19661.90 kg 18740.25 kg 18125.81 kg
N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,3867.51 kg 4789.16 kg 5403.60 kg
98.69 cm 75.96 cm 65.12 cm32.00 cm 30.50 cm 29.50 cm60.00 cm 60.00 cm 60.00 cm16.00 cm 15.25 cm 14.75 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(
32.00 cm 30.50 cm 29.50 cm N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm64. cm 61. cm 59. cm0.59 m 0.61 m 0.59 m
1.84 Und 8.13 Und 7.87 Und0.05 1 0.00 1 0.000.32 7 0.08 6 0.08
#/.# 4 #/3; 4 #/.3 4
&/$:# 4 $/:# 4 &/9.# 4
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DISE O POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 70 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = &/$:# 4 $/:# 435380.00 kg
= 40. cm ! = 70. cm " = 4. cm
#$ ca%a #& ca%as
d = 64. cm 61. cm
c =19661.90 kg 18740.25 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 21961.63 kg 22883.28 kg
S = 17.38 cm 15.90 cm d-& = 32.00 cm 30.50 cm , = 60.00 cm 60.00 cm
d-. = 16.00 cm 15.25 cm , = 30.00 cm 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(
S 4a6 = 17.38 cm 15.90 cm &da C,nd/ =
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 64. cm 61. cm0.64 m 0.61 m
3.66 Und 4.07 Und
Est"i,s 8 =1 0.00 1 0.003 0.18 4 0.15
Avanc( 8 = #/3; 4 #/# 4
&/9#3 4 &/.# 4
*; =
C,"tant( *. =
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F'c =
F'y =
COLUMNA=
Av =
β =
Ø =
&/9.# 4 distancia =
=
! =
" =
#; ca%as
59. cm d =
18125.81 kg c =
N(c(sita R()*("+,23497.72 kg s =
14.97 cm S =
29.50 cm d-& =
60.00 cm , =
14.75 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/3
14.97 cm S 4a6 =N, C*4%5(&da C,nd/ =
s=7$/$11d1F'c2#/3
0.00 cm S 4a6 =
59. cm d =
0.59 m3.93 Und
1 0.00Est"i,s 8 =
14 0.15 2
#/# 4 Avanc( 8 =
;/;.# 4
*; =
C,"tant( *. =
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DISE O POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 70 cm (h)
0.71 cm2
0.85
0.85
&/9#3 4 &/.# 4 ;/;.# 430420.00 kg
40. cm70. cm4. cm
#$ ca%a #& ca%as #; ca%as
64. cm 61. cm 59. cm19661.90 kg 18740.25 kg 18125.81 kg
N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,16126.34 kg 17047.99 kg 17662.42 kg
23.67 cm 21.34 cm 19.92 cm32.00 cm 30.50 cm 29.50 cm60.00 cm 60.00 cm 60.00 cm16.00 cm 15.25 cm 14.75 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(
23.67 cm 21.34 cm 19.92 cm N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm64. cm 61. cm 59. cm0.64 m 0.61 m 0.59 m
2.56 Und 4.07 Und 3.93 Und0.00 1 0.00 1 0.000.25 2 0.15 4 0.15
#/3# 4 #/;# 4 #/# 4
;/ 4 &/9# 4 ;/<.# 4
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DISE O POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 70 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = ;/ 4 &/9# 411090.00 kg
= 40. cm ! = 70. cm " = 4. cm
#$ ca%a #& ca%as
d = 64. cm 61. cm
c =19661.90 kg 18740.25 kg
R()*("+, Mini4, R()*("+, Mini4,s = -6614.84 kg -5693.19 kg
S = -57.70 cm -63.90 cm d-& = 32.00 cm 30.50 cm , = 60.00 cm 60.00 cm
d-. = 16.00 cm 15.25 cm , = 30.00 cm 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(
S 4a6 = -57.70 cm -63.90 cm &da C,nd/ =
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 64. cm 61. cm0.64 m 0.61 m
2.56 Und 4.07 Und
Est"i,s 8 =1 0.00 1 0.001 0.25 1 0.15
Avanc( 8 = #/&3 4 #/$3 4
;/.33 4 &/<$# 4
*; =
C,"tant( *. =
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;/<.# 4
#; ca%as
59. cm18125.81 kg
R()*("+, Mini4,-5078.76 kg
-69.28 cm29.50 cm60.00 cm14.75 cm30.00 cm
Si C*4%5(
-69.28 cm N, C*4%5(0.00 cm59. cm0.59 m
3.93 Und1 0.004 0.15
#/# 4
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 30. cm
% 0. cm r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 354000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.02
B. M. B. 4!.53
,4d$
As P4,4d 2.24 cm2
B.4,4d$ 4332#!3.15 g.cm
Mr Mr "$##!3.15 g.cm
A3s M. A3s "3.$ cm2
4F384<d=d3?
As Total As """"""
Total A3s "3.$ cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.22M 1 J 0.21
M 2 J 1.434
P J 0.0131
ceueo de P J SIMPLEM" REFORADA
-s J 21.1 cm2
ANALISIS O VERIFICACION DE UNA SECC
As """"""
A3s "3.$ cm2
As0
M.0 M.0
M.=M.0
As0 A3s
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P N-L(EO
P3 "0.0023
P = P3 N-L(EO
VERF" 0.01115
HVALUE
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DISEKO DE ACERO PARA VIGAS DO
DATOS
0.#5
0.!0
'iga, 30. cm
% 0. cm
r 5. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a
M. 2#11000. g.cm
&3) 210. gcm2
&38 4200. gcm2
Pma9 0.012
B. M. B. 4!.53
,4d$
As P4,4d 2.24 cm2
B.4,4d$ 4332#!3.15 g.cm
Mr Mr "1521#!3.15 g.cm
A3s M. A3s "#.22 cm2
4F384<d=d3?
As Total As """"""
Total A3s "#.22 cm2
DATOS 01 capa
a J 0.5!
b J "1.00
c J 0.1$
M 1 J 0.1!2
M 2 J 1.503
P J 0.00!
ceueo de P J SIMPLEM" REFORADA
-s J 15.53 cm2
ANALISIS O VERIFICACION DE UNA SECC
As0
M.0 M.0
M.=M.0
As0 A3s
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As """"""
A3s "#.22 cm2
P N-L(EO
P3 "0.0051
P = P3 N-L(EO
VERF" 0.01115
HVALUE
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LEMENTE REFORADAS
#$ )a(as #- )a(as
354000. g.cm 354000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53 B.
24.$! cm2 23.#1 cm2 As
3#4#33.$0 g.cm 35$53.10 g.cm
"210#33.$0 g.cm #34.!0 g.cm Mr
"1.21 cm2 0.52 cm2 A3s
"""""" 24.33 cm2 As
"1.21 cm2 0.52 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.25 0.2$
0.301 0.334
1.3!4 1.31
0.0151 0.01$
SIMPLEM" REFORADA DO+"REFORADA
23.05 cm2 """""
ION DO+LEMENTE REFORADA
"""""" 24.33 cm2
"1.21 cm2 0.52 cm2
M.0
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N-L(EO 0.01
"0.000# 0.0004
N-L(EO 0.012
0.011#1 0.0122!
HVALUE SI FLUQE
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LEMENTE REFORADAS
#$ )a(as #- )a(as
2#11000. g.cm 2#11000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.012 0.012
4!.53 4!.53 B.
24.$! cm2 23.#1 cm2 As
3#4#33.$0 g.cm 35$53.10 g.cm
"1053#33.$0 g.cm "$553.10 g.cm Mr
".0 cm2 "4.55 cm2 A3s
"""""" """""" As
".0 cm2 "4.55 cm2
02 capas 03 capas
0.5! 0.5!
"1.00 "1.00
0.1! 0.21
0.21! 0.241
1.4$ 1.454
0.010! 0.0120
SIMPLEM" REFORADA SIMPLEM" REFORADA
1.$4 cm2 1$.! cm2
ION DO+LEMENTE REFORADA
M.0
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"""""" """"""
".0 cm2 "4.55 cm2
N-L(EO N-L(EO
"0.0040 "0.0031
N-L(EO N-L(EO
0.011#1 0.0122!
HVALUE HVALUE
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
DATOS
0.#5
0.!0
'iga, 30. cm
% 0. cm r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a #$ )a(as
M. 4#42000. g.cm 4#42000. g.cm
&3) 210. gcm2 210. gcm2
&38 4200. gcm2 4200. gcm2
Pma9 0.02 0.02
M. B. 4!.53 4!.53
,4d$
P4,4d 2.24 cm2 24.$! cm2
B.4,4d$ 4332#!3.15 g.cm 3#4#33.$0 g.cm
Mr 50!10.#5 g.cm !$$1.30 g.cm
M. A3s 2.$5 cm2 5.2 cm2
4F384<d=d3?
Total As 2#.!! cm2 30.41 cm2
Total A3s 2.$5 cm2 5.2 cm2
DATOS 01 capa 02 capas
a J 0.5! 0.5!
b J "1.00 "1.00
c J 0.2! 0.33
M 1 J 0.3$ 0.445
M 2 J 1.31# 1.250
P J 0.01## 0.0223
ceueo de P J DO+"REFORADA DO+"REFORADA
-s J """"" """""
ANALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
As 2#.!! cm2 30.41 cm2
A3s 2.$5 cm2 5.2 cm2
As0
M.0
M.=M.0
As0 A3s
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P 0.01$! 0.01!!
P3 0.001$ 0.003$
P = P3 0.012 0.012
VERF" 0.01115 0.011#1
SI FLUQE SI FLUQE
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
DATOS
0.#5
0.!0
'iga, 30. cm
% 0. cm
r 4. cm
d3 5. cm
d
#0 )a(a 54. cm
#$ )a(as 51. cm
#- )a(as 4!. cm
DATOS #0 )a(a #$ )a(as
M. 31!000. g.cm 31!000. g.cm
&3) 210. gcm2 210. gcm2
&38 4200. gcm2 4200. gcm2
Pma9 0.012 0.012
M. B. 4!.53 4!.53
,4d$
P4,4d 2.24 cm2 24.$! cm2
B.4,4d$ 4332#!3.15 g.cm 3#4#33.$0 g.cm
Mr "$13#!3.15 g.cm "245#33.$0 g.cm
M. A3s "3.#5 cm2 "1.41 cm2
4F384<d=d3?
Total As """""" """"""
Total A3s "3.#5 cm2 "1.41 cm2
DATOS 01 capa 02 capas
a J 0.5! 0.5!
b J "1.00 "1.00
c J 0.22 0.25
M 1 J 0.25# 0.2!#
M 2 J 1.43$ 1.3!$
P J 0.012! 0.014!
ceueo de P J SIMPLEM" REFORADA SIMPLEM" REFORADA
-s J 20.!2 cm2 22.$$ cm2
ANALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
As0
M.0
M.=M.0
As0 A3s
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As """""" """"""
A3s "3.#5 cm2 "1.41 cm2
P N-L(EO N-L(EO
P3 "0.0024 "0.000!
P = P3 N-L(EO N-L(EO
VERF" 0.01115 0.011#1
HVALUE HVALUE
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DA
'iga,
% r
d3
d
#0 )a(a
#$ )a(as
#- )a(as
#- )a(as DATOS
4#42000. g.cm M.
210. gcm2 &3)
4200. gcm2 &38
0.02 Pma9
4!.53 B.
M. B.
,4d$
23.#1 cm2 As P4,4d
35$53.10 g.cm B.4,4d$
12$434.!0 g.cm Mr Mr
$. cm2 A3s
M. A3s
4F384<d=d3?
31.4# cm2 As Total As
$. cm2 Total A3s
03 capas DATOS
0.5! a J
"1.00 b J
0.3 c J0.50# M 1 J
1.1#$ M 2 J
0.0254 P J
DO+"REFORADA ceueo de P J
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A
31.4# cm2 As
$. cm2 A3s
As0
M.0 M.0
M.=M.0
As0 A3s
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0.0214 P
0.0052 P3
0.012 P = P3
0.0122!VERF"
SI FLUQE
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DA
'iga,
%
r
d3
d
#0 )a(a
#$ )a(as
#- )a(as
#- )a(as DATOS
31!000. g.cm M.
210. gcm2 &3)
4200. gcm2 &38
0.012 Pma9
4!.53 B.
M. B.
,4d$
23.#1 cm2 As P4,4d
35$53.10 g.cm B.4,4d$
5134.!0 g.cm Mr Mr
0.31 cm2 A3s
M. A3s
4F384<d=d3?
24.12 cm2 As Total As
0.31 cm2 Total A3s
03 capas DATOS
0.5! a J
"1.00 b J
0.2$ c J
0.330 M 1 J
1.35 M 2 J
0.015 P J
DO+"REFORADA ceueo de P J
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A
As0
M.0 M.0
M.=M.0
As0 A3s
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24.12 cm2 As
0.31 cm2 A3s
0.014 P
0.0002 P3
0.012 P = P3
0.0122!VERF"
SI FLUQE
> Ø 0
$ Ø -@>
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
TOS
0.#5
0.!0
30. cm
0. cm4. cm
5. cm
54. cm
51. cm
4!. cm
#0 )a(a #$ )a(as
205$000. g.cm 205$000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2.24 cm2 24.$! cm2
4332#!3.15 g.cm 3#4#33.$0 g.cm
"22$5#!3.15 g.cm "1#0$#33.$0 g.cm
"12.2! cm2 "10.40 cm2
"""""" """"""
"12.2! cm2 "10.40 cm2
01 capa 02 capas
0.5! 0.5!
"1.00 "1.00
0.12 0.14
0.135 0.153
1.50 1.542
0.00# 0.00$$
SIMPLEM" REFORADA SIMPLEM" REFORADA
10.!5 cm2 11.$3 cm2
ALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
"""""" """"""
"12.2! cm2 "10.40 cm2
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N-L(EO N-L(EO
"0.00$ "0.00#
N-L(EO N-L(EO
0.01115 0.011#1
HVALUE HVALUE
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
TOS
0.#5
0.!030. cm
0. cm
4. cm
5. cm
54. cm
51. cm
4!. cm
#0 )a(a #$ )a(as
205$000. g.cm 205$000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2.24 cm2 24.$! cm2
4332#!3.15 g.cm 3#4#33.$0 g.cm
"22$5#!3.15 g.cm "1#0$#33.$0 g.cm
"12.2! cm2 "10.40 cm2
"""""" """"""
"12.2! cm2 "10.40 cm2
01 capa 02 capas
0.5! 0.5!
"1.00 "1.00
0.12 0.14
0.135 0.153
1.50 1.542
0.00# 0.00$$
SIMPLEM" REFORADA SIMPLEM" REFORADA
10.!5 cm2 11.$3 cm2
ALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
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"""""" """"""
"12.2! cm2 "10.40 cm2
N-L(EO N-L(EO
"0.00$ "0.00#
N-L(EO N-L(EO
0.01115 0.011#1
HVALUE HVALUE
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DA
'iga,
% r
d3
d
#0 )a(a
#$ )a(as
#- )a(as
#- )a(as DATOS
205$000. g.cm M.
210. gcm2 &3)
4200. gcm2 &38
0.02 Pma9
4!.53 B.
M. B.
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23.#1 cm2 As P4,4d
35$53.10 g.cm B.4,4d$
"151053.10 g.cm Mr Mr
"!.0# cm2 A3s
M. A3s
4F384<d=d3?
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"!.0# cm2 Total A3s
03 capas DATOS
0.5! a J
"1.00 b J
0.15 c J0.1# M 1 J
1.52$ M 2 J
0.00#4 P J
SIMPLEM" REFORADA ceueo de P J
12.33 cm2 -s J
A
"""""" As
"!.0# cm2 A3s
As0
M.0 M.0
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
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N-L(EO P
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0.0122!VERF"
HVALUE
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1.43 M 2 J
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
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210. gcm2 210. gcm2
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0.02 0.02
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ALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
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N-L(EO N-L(EO
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TOS
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440#000. g.cm 440#000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
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$510.#5 g.cm 5431.30 g.cm
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0.0003 0.0020
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SI FLUQE SI FLUQE
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
TOS
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210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
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2.24 cm2 24.$! cm2
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0.01! P
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TOS
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210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
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2.24 cm2 24.$! cm2
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TOS
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0.00!4 P J
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13.#$ cm2 -s J
A
"""""" As
"$.$2 cm2 A3s
As0
M.0 M.0
M.=M.0
As0 A3s
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N-L(EO P
"0.0053 P3
N-L(EO P = P3
0.0122!VERF"
HVALUE
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DA
'iga,
%
r
d3
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#0 )a(a
#$ )a(as
#- )a(as
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210. gcm2 &3)
4200. gcm2 &38
0.02 Pma9
4!.53 B.
M. B.
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23.#1 cm2 As P4,4d
35$53.10 g.cm B.4,4d$
"12#453.10 g.cm Mr Mr
"$.$2 cm2 A3s
M. A3s
4F384<d=d3?
"""""" As Total As
"$.$2 cm2 Total A3s
03 capas DATOS
0.5! a J
"1.00 b J
0.1$ c J
0.1#! M 1 J
1.50 M 2 J
0.00!4 P J
SIMPLEM" REFORADA ceueo de P J
13.#$ cm2 -s J
A
As0
M.0 M.0
M.=M.0
As0 A3s
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"""""" As
"$.$2 cm2 A3s
N-L(EO P
"0.0053 P3
N-L(EO P = P3
0.0122!VERF"
HVALUE
- Ø 0
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
TOS
0.#5
0.!0
30. cm
0. cm5. cm
5. cm
54. cm
51. cm
4!. cm
#0 )a(a #$ )a(as
533!000. g.cm 533!000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2.24 cm2 24.$! cm2
4332#!3.15 g.cm 3#4#33.$0 g.cm
10010.#5 g.cm 14$41.30 g.cm
5.43 cm2 #.4# cm2
31.# cm2 33.2 cm2
5.43 cm2 #.4# cm2
01 capa 02 capas
0.5! 0.5!
"1.00 "1.00
0.32 0.3
0.434 0.524
1.21 1.1$1
0.021$ 0.022
DO+"REFORADA DO+"REFORADA
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ALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
31.# cm2 33.2 cm2
5.43 cm2 #.4# cm2
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0.01! 0.021$
0.0034 0.0055
0.012 0.012
0.01115 0.011#1
SI FLUQE SI FLUQE
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
TOS
0.#5
0.!030. cm
0. cm
5. cm
5. cm
54. cm
51. cm
4!. cm
#0 )a(a #$ )a(as
41$3000. g.cm 41$3000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2.24 cm2 24.$! cm2
4332#!3.15 g.cm 3#4#33.$0 g.cm
"15!#!3.15 g.cm 30#1.30 g.cm
"0.# cm2 1.$$ cm2
"""""" 2.5 cm2
"0.# cm2 1.$$ cm2
01 capa 02 capas
0.5! 0.5!
"1.00 "1.00
0.25 0.2#
0.30! 0.35!
1.3# 1.33
0.0154 0.01$!
SIMPLEM" REFORADA DO+"REFORADA
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ALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
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"""""" 2.5 cm2
"0.# cm2 1.$$ cm2
N-L(EO 0.01$4
"0.0005 0.0012
N-L(EO 0.012
0.01115 0.011#1
HVALUE SI FLUQE
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DA
'iga,
% r
d3
d
#0 )a(a
#$ )a(as
#- )a(as
#- )a(as DATOS
533!000. g.cm M.
210. gcm2 &3)
4200. gcm2 &38
0.02 Pma9
4!.53 B.
M. B.
,4d$
23.#1 cm2 As P4,4d
35$53.10 g.cm B.4,4d$
1$$134.!0 g.cm Mr Mr
10.5 cm2 A3s
M. A3s
4F384<d=d3?
34.4 cm2 As Total As
10.5 cm2 Total A3s
03 capas DATOS
0.5! a J
"1.00 b J
0.3! c J0.1 M 1 J
1.0$! M 2 J
0.030# P J
DO+"REFORADA ceueo de P J
""""" -s J
A
34.4 cm2 As
10.5 cm2 A3s
As0
M.0 M.0
M.=M.0
As0 A3s
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0.0234 P
0.00$2 P3
0.012 P = P3
0.0122!VERF"
SI FLUQE
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'iga,
%
r
d3
d
#0 )a(a
#$ )a(as
#- )a(as
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41$3000. g.cm M.
210. gcm2 &3)
4200. gcm2 &38
0.02 Pma9
4!.53 B.
M. B.
,4d$
23.#1 cm2 As P4,4d
35$53.10 g.cm B.4,4d$
0534.!0 g.cm Mr Mr
3.4 cm2 A3s
M. A3s
4F384<d=d3?
2$.45 cm2 As Total As
3.4 cm2 Total A3s
03 capas DATOS
0.5! a J
"1.00 b J
0.31 c J
0.402 M 1 J
1.2!3 M 2 J
0.0201 P J
DO+"REFORADA ceueo de P J
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A
As0
M.0 M.0
M.=M.0
As0 A3s
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2$.45 cm2 As
3.4 cm2 A3s
0.01#$ P
0.0025 P3
0.012 P = P3
0.0122!VERF"
SI FLUQE
> Ø 0
$ Ø -@>
$ Ø -@>
$ Ø 0
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
TOS
0.#5
0.!0
30. cm
0. cm5. cm
5. cm
54. cm
51. cm
4!. cm
#0 )a(a #$ )a(as
5053000. g.cm 5053000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2.24 cm2 24.$! cm2
4332#!3.15 g.cm 3#4#33.$0 g.cm
$2010.#5 g.cm 11##1.30 g.cm
3.#! cm2 .#3 cm2
30.13 cm2 31.2 cm2
3.#! cm2 .#3 cm2
01 capa 02 capas
0.5! 0.5!
"1.00 "1.00
0.31 0.34
0.400 0.4$$
1.2!5 1.21#
0.0200 0.023#
DO+"REFORADA DO+"REFORADA
""""" """""
ALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
30.13 cm2 31.2 cm2
3.#! cm2 .#3 cm2
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0.01# 0.020$
0.0024 0.0045
0.012 0.012
0.01115 0.011#1
SI FLUQE SI FLUQE
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DISEKO DE ACERO PARA VIGAS DO+LEMENTE REFORADAS
TOS
0.#5
0.!030. cm
0. cm
5. cm
5. cm
54. cm
51. cm
4!. cm
#0 )a(a #$ )a(as
4144000. g.cm 4144000. g.cm
210. gcm2 210. gcm2
4200. gcm2 4200. gcm2
0.02 0.02
4!.53 4!.53
2.24 cm2 24.$! cm2
4332#!3.15 g.cm 3#4#33.$0 g.cm
"1###!3.15 g.cm 2$!1.30 g.cm
"1.02 cm2 1.1 cm2
"""""" 2.3! cm2
"1.02 cm2 1.1 cm2
01 capa 02 capas
0.5! 0.5!
"1.00 "1.00
0.25 0.2#
0.30 0.35
1.3#! 1.33!
0.0153 0.01$#
SIMPLEM" REFORADA DO+"REFORADA
24.$$ cm2 """""
ALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA
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"""""" 2.3! cm2
"1.02 cm2 1.1 cm2
N-L(EO 0.01$2
"0.000 0.0010
N-L(EO 0.012
0.01115 0.011#1
HVALUE SI FLUQE
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#- )a(as
5053000. g.cm
210. gcm2
4200. gcm2
0.02
4!.53
23.#1 cm2
35$53.10 g.cm
14#534.!0 g.cm
#.!3 cm2
32.$4 cm2
#.!3 cm2
03 capas
0.5!
"1.00
0.3$
0.54!
1.14
0.02$4
DO+"REFORADA
"""""
32.$4 cm2
#.!3 cm2
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0.0223
0.001
0.012
0.0122!
SI FLUQE
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#- )a(as
4144000. g.cm
210. gcm2
4200. gcm2
0.02
4!.53
23.#1 cm2
35$53.10 g.cm
5$34.!0 g.cm
3.4$ cm2
2$.2# cm2
3.4$ cm2
03 capas
0.5!
"1.00
0.30
0.3!#
1.2!$
0.01!!
DO+"REFORADA
"""""
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2$.2# cm2
3.4$ cm2
0.01#
0.0024
0.012
0.0122!
SI FLUQE
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DISE O POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = 89 cm
19513.2 = 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 10514.41 kg
S = 30.63 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 27.00 cm &da C,nd/ =
s=7$/$11d1F'c2#/3 N, C*4%5(S 4a6 = 0.00 cm
d = 54. cm0.49 m
2.80 Und
Est"i,s 8 =1 0.05 14 0.18 2
Avanc( 8 = #/93 4
$/. 4
*$ =
C,"tant( *& =
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DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85 Ø = 0.85
distancia = 89 cm
30972.8 = 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c = 12442.30 kg N(c(sita R()*("+,
s = 23996.29 kg
S = 13.42 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 13.42 cm
&da C,nd/ = s=7$/$11d1F'c2#/3 N, C*4%5(S 4a6 = 0.00 cm
d = 54. cm0.49 m
2.80 Und
Est"i,s 8 =1 0.05 14 0.18 5
Avanc( 8 = #/93 4
$/. 4
*$ =
C,"tant( *& =
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DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b) Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = 82 cm
33134.4 = 30. c ! = 60. c " = 5. c
#$ ca%ad = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 26539.35 kg
S = 12.14 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ = s=0&/$11d1F'c2#/3 Si C*4%5(S 4a6 = 12.14 cm
s=7$/$11d1F'c2#/3 Si C*4%5(
*$ =
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/S 4a6 = 12.14 cm
d = 54. cm0.49 m
2.80 Und
Est"i,s 8 =1 0.05 14 0.18 5
Avanc( 8 = #/93 4$/39 4
DISE O POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = 82 cm
38973.0 = 30. c
! = 60. c " = 5. c
C,"tant( *& =
*$ =
![Page 237: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/237.jpg)
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#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 33408.29 kg
S = 9.64 cm
d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 9.64 cm
&da C,nd/ =s=7$/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 9.64 cm d = 54. cm
0.49 m
2.80 Und
Est"i,s 8 =1 0.05 14 0.18 7
Avanc( 8 = #/93 4
$/39 4C,"tant( *& =
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DISE O POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = 82 cm
32762.4 = 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 26101.70 kg
S = 12.34 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 12.34 cm &da C,nd/ =
s=7$/$11d1F'c2#/3 Si C*4%5(S 4a6 = 12.34 cm
d = 54. cm0.49 m
2.80 Und
Est"i,s 8 =1 0.05 14 0.18 5
Avanc( 8 = #/93 4
$/39 4
*$ =
C,"tant( *& =
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DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = 82 cm
29021.4 = 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 21700.53 kg
S = 14.84 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 14.84 cm
&da C,nd/ =s=7$/$11d1F'c2#/3 N, C*4%5(
S 4a6 = 0.00 cm d = 54. cm
0.49 m2.80 Und
Est"i,s 8 =1 0.05 1
4 0.18 4 Avanc( 8 = #/93 4
$/39 4
*$ =
C,"tant( *& =
![Page 240: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/240.jpg)
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DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = 87 cm
32736.3 = 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 26071.00 kg
S = 12.35 cm d-& = 27.00 cm , = 60.00 cm
*$ =
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d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 12.35 cm
&da C,nd/ =s=7$/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 12.35 cm
d = 54. cm0.49 m
2.80 Und
Est"i,s 8 =1 0.05 14 0.18 4
Avanc( 8 = #/93 4
$/& 4
DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85 Ø = 0.85
distancia = 87 cm
C,"tant( *& =
![Page 242: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/242.jpg)
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23553.6 = 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 15267.82 kg
S = 21.09 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =
s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 21.09 cm
&da C,nd/ =s=7$/$11d1F'c2#/3 N, C*4%5(
S 4a6 = 0.00 cm d = 54. cm
0.49 m2.80 Und
Est"i,s 8 =1 0.05 14 0.18 4
Avanc( 8 = #/93 4
$/& 4
*$ =
C,"tant( *& =
![Page 243: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/243.jpg)
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ORTANTE
m2
cm2
70 cm (h)
2
86 cm 84 cm
kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,11205.65 kg 11666.47 kg
27.14 cm 25.05 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5($"a C,nd/ =
25.50 cm 24.50 cm N, C*4%5( N, C*4%5(&da C,nd/ =
0.00 cm 0.00 cm51. cm 49. cm0.46 m 0.44 m
1.84 Und 1.76 Und0.05 1 0.05
Est"i,s 8 =0.25 6 0.25
#/33 4 $/33 4
$/.$ 4 &/;< 4
![Page 244: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/244.jpg)
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ORTANTE
m2
cm2
70 cm (h)
2
86 cm 84 cm
kg
#& ca%as #; ca%as
51. cm 49. cm
11751.06 kg 11290.23 kg N(c(sita R()*("+, N(c(sita R()*("+,
24687.53 kg 25148.36 kg
12.32 cm 11.62 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5($"a C,nd/ =
12.32 cm 11.62 cm
Si C*4%5( Si C*4%5( &da C,nd/ =12.32 cm 11.62 cm51. cm 49. cm0.46 m 0.44 m
4.60 Und 1.76 Und0.05 1 0.05
Est"i,s 8 =0.10 6 0.25
#/33 4 $/33 4
$/.$ 4 &/;< 4
![Page 245: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/245.jpg)
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ORTANTE
m2
cm2
55 cm (h) 2
79 cm 77 cm
kg
#& ca%as #; ca%as51. cm 49. cm
11751.06 kg 11290.23 kg N(c(sita R()*("+, N(c(sita R()*("+,
27230.59 kg 27691.42 kg
11.17 cm 10.55 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( $"a C,nd/ =11.17 cm 10.55 cm
Si C*4%5( Si C*4%5(
![Page 246: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/246.jpg)
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11.17 cm 10.55 cm /
51. cm 49. cm0.46 m 0.44 m
4.60 Und 1.76 Und0.05 1 0.05
Est"i,s 8 =0.10 6 0.25
#/33 4 $/33 4$/;. 4 &/;& 4
ORTANTE
m2
cm2
55 cm (h)
2
79 cm 77 cm
kg
![Page 247: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/247.jpg)
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#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,34099.53 kg 34560.36 kg
8.92 cm 8.46 cm
25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5($"a C,nd/ =
8.92 cm 8.46 cm Si C*4%5( Si C*4%5(
&da C,nd/ =8.92 cm 8.46 cm51. cm 49. cm0.46 m 0.44 m
6.13 Und 1.76 Und0.05 1 0.05
Est"i,s 8 =0.075 6 0.25
#/3: 4 $/33 4
$/; 4 &/;& 4
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ORTANTE
m2
cm2
55 cm (h)
2
79 cm 77 cm
kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,26792.94 kg 27253.77 kg
11.35 cm 10.72 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5($"a C,nd/ =
11.35 cm 10.72 cm Si C*4%5( Si C*4%5(&da C,nd/ =
11.35 cm 10.72 cm51. cm 49. cm0.46 m 0.44 m
4.60 Und 1.76 Und0.05 1 0.05
Est"i,s 8 =0.100 6 0.25
#/33 4 $/33 4
$/;. 4 &/;& 4
![Page 249: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/249.jpg)
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ORTANTE
m2
cm2
55 cm (h)
2
79 cm 77 cm
kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,22391.77 kg 22852.59 kg
13.58 cm 12.79 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5($"a C,nd/ =
13.58 cm 12.79 cm N, C*4%5( N, C*4%5(
&da C,nd/ =0.00 cm 0.00 cm51. cm 49. cm0.46 m 0.44 m
3.68 Und 1.76 Und0.05 1 0.05
Est"i,s 8 =
0.125 6 0.25#/33 4 $/33 4
$/;. 4 &/;& 4
![Page 250: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/250.jpg)
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ORTANTE
m2
cm2
65 cm (h)
2
84 cm 82 cm
kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,26762.24 kg 27223.06 kg
11.37 cm 10.73 cm25.50 cm 24.50 cm60.00 cm 60.00 cm
![Page 251: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/251.jpg)
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12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5($"a C,nd/ =
11.37 cm 10.73 cm Si C*4%5( Si C*4%5(
&da C,nd/ =11.37 cm 10.73 cm
51. cm 49. cm0.46 m 0.44 m
3.68 Und 4.40 Und0.05 1 0.05
Est"i,s 8 =0.125 5 0.10
#/33 4 #/33 4
$/;< 4 $/;9 4
ORTANTE
m2
cm2
65 cm (h)
2
84 cm 82 cm
![Page 252: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/252.jpg)
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kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,15959.06 kg 16419.89 kg
19.06 cm 17.80 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5(
$"a C,nd/ =19.06 cm 17.80 cm N, C*4%5( N, C*4%5(
&da C,nd/ =0.00 cm 0.00 cm51. cm 49. cm0.46 m 0.44 m
3.68 Und 2.93 Und0.05 1 0.05
Est"i,s 8 =0.125 3 0.15
#/33 4 #/3# 4
$/;< 4 $/;& 4
![Page 253: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/253.jpg)
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DISE O POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 70 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = $/. 4 $/.$ 415084.30 kg
= 30. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%as
d = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 5303.94 kg 5995.18 kg
S = 60.72 cm 50.73 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(
S 4a6 = 27.00 cm 25.50 cm s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 54. cm 51. cm0.54 m 0.51 m
1.69 Und 2.04 Und0 0.00 0 0.00 02 0.32 2 0.25 6
Avanc( 8 = #/.# 4 #/3# 4
&/&: 4 $/<$ 4
*& =
C,"tant( *; =
![Page 254: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/254.jpg)
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DISEÑO POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 70 cm (h)
Av = 0.71 cm2
β = 0.85Ø = 0.85
distancia = $/. 4 $/.$ 427672.80 kg
= 30. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%as
d = 54. cm 51. cm
c = 12442.30 kg 11751.06 kg N(c(sita R()*("+, N(c(sita R()*("+,
s = 20113.94 kg 20805.18 kg
S = 16.01 cm 14.62 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(S 4a6 = 16.01 cm 14.62 cm
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 54. cm 51. cm0.54 m 0.51 m
1.69 Und 4.08 Und0 0.00 0 0.00 02 0.320 4 0.125 6
Avanc( 8 = #/.# 4 #/3# 4
&/&: 4 $/<$ 4
*& =
C,"tant( *; =
![Page 255: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/255.jpg)
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DISEÑO POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 55 cm (h) Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = $/39 4 $/;. 429834.40 kg
= 30. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%asd = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 22657.00 kg 23348.24 kg
S = 14.21 cm 13.03 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(S 4a6 = 14.21 cm 13.03 cm
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(
*& =
![Page 256: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/256.jpg)
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S 4a6 = 0.00 cm 0.00 cm d = 54. cm 51. cm
0.54 m 0.51 m1.69 Und 4.08 Und
0 0.00 0 0.00 02 0.320 4 0.125 6
Avanc( 8 = #/.# 4 #/3# 4&/&$ 4 $/:. 4
DISE O POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 55 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = $/39 4 $/; 434544.10 kg
= 30. cm
! = 60. cm " = 5. cm
C,"tant( *; =
*& =
![Page 257: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/257.jpg)
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#$ ca%a #& ca%as
d = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 28197.82 kg 28889.06 kg
S = 11.42 cm 10.53 cm
d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(S 4a6 = 11.42 cm 10.53 cm
s=7$/$11d1F'c2#/3 Si C*4%5( Si C*4%5(S 4a6 = 11.42 cm 10.53 cm
d = 54. cm 51. cm0.54 m 0.51 m
1.69 Und 5.10 Und0 0.00 0 0.00 02 0.320 5 0.100 6
Avanc( 8 = #/.# 4 #/3# 4
&/&$ 4 $/: 4C,"tant( *; =
![Page 258: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/258.jpg)
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DISE O POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 55 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = $/39 4 $/;. 428904.30 kg
= 30. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%as
d = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 21562.76 kg 22254.00 kg
S = 14.94 cm 13.67 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(
S 4a6 = 14.94 cm 13.67 cm s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 54. cm 51. cm0.54 m 0.51 m
1.69 Und 4.08 Und0 0.00 0 0.00 02 0.320 4 0.125 6
Avanc( 8 = #/.# 4 #/3# 4
&/&$ 4 $/:. 4
*& =
C,"tant( *; =
![Page 259: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/259.jpg)
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DISEÑO POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 55 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = $/39 4 $/;. 425721.40 kg
= 30. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%as
d = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 17818.17 kg 18509.41 kg
S = 18.07 cm 16.43 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(S 4a6 = 18.07 cm 16.43 cm
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 54. cm 51. cm0.54 m 0.51 m
1.69 Und 3.40 Und0 0.00 0 0.00 0
2 0.320 4 0.150 6 Avanc( 8 = #/.# 4 #/# 4
&/&$ 4 $/<. 4
*& =
C,"tant( *; =
![Page 260: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/260.jpg)
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DISEÑO POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 65 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = $/& 4 $/;< 429160.90 kg
= 30. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%as
d = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 21864.65 kg 22555.88 kg
S = 14.73 cm 13.48 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
*& =
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d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(S 4a6 = 14.73 cm 13.48 cm
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 54. cm 51. cm0.54 m 0.51 m
1.69 Und 3.40 Und0 0.00 0 0.00 02 0.320 4 0.150 4
Avanc( 8 = #/.# 4 #/# 4
&/& 4 $/<< 4
DISEÑO POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 65 cm (h)
Av = 0.71 cm2
β = 0.85Ø = 0.85
distancia = $/& 4 $/;< 4
C,"tant( *; =
![Page 262: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/262.jpg)
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19668.60 kg = 30. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%as
d = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 10697.23 kg 11388.47 kg
S = 30.11 cm 26.71 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(
S 4a6 = 27.00 cm 25.50 cm s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(
S 4a6 = 0.00 cm 0.00 cm d = 54. cm 51. cm
0.54 m 0.51 m1.69 Und 3.40 Und
0 0.00 0 0.00 02 0.320 4 0.150 2
Avanc( 8 = #/.# 4 #/# 4
&/& 4 $/<< 4
*& =
C,"tant( *; =
![Page 263: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/263.jpg)
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F'c =
F'y =
COLUMNA=
Av =
β =
Ø =
&/;< 4 distancia =
=
! =
" =
#; ca%as
49. cm d =
11290.23 kg c =
N(c(sita R()*("+,6456.00 kg s =
45.27 cm S =
24.50 cm d-& =
60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/3
24.50 cm S 4a6 =N, C*4%5(&da C,nd/ =
s=7$/$11d1F'c2#/3
0.00 cm S 4a6 =
49. cm d =
0.49 m6.53 Und
0.00Est"i,s 8 =
10.08 3
#/.3 4 Avanc( 8 =
&/:. 4
*; =
C,"tant( *. =
![Page 264: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/264.jpg)
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F'c =
F'y =
COLUMNA=
Av =
β =Ø =
&/;< 4 distancia =
=
! =
" =
#; ca%as
49. cm d =
11290.23 kg c =N(c(sita R()*("+,
21266.00 kg s =
13.74 cm S =
24.50 cm d-& =
60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/313.74 cm S 4a6 =
N, C*4%5( &da C,nd/ = s=7$/$11d1F'c2#/30.00 cm S 4a6 =
49. cm d =
0.49 m6.53 Und
0.00Est"i,s 8 =
10.075 3
#/.3 4 Avanc( 8 =
&/:. 4
*; =
C,"tant( *. =
![Page 265: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/265.jpg)
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F'c =
F'y =
COLUMNA=Av =
β =
Ø =
&/;& 4 distancia =
=
! =
" =
#; ca%as49. cm d =
11290.23 kg c =
N(c(sita R()*("+,23809.06 kg s =
12.27 cm S =
24.50 cm d-& =
60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5( $"a C,nd/ = s=0&/$11d1F'c2#/312.27 cm S 4a6 =
Si C*4%5( s=7$/$11d1F'c2#/3
*; =
![Page 266: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/266.jpg)
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12.27 cm /
S 4a6 =
49. cm d =
0.49 m6.53 Und
0.00Est"i,s 8 =
10.075 3
#/.3 4 Avanc( 8 =&/99 4
F'c =
F'y =
COLUMNA=
Av =
β =
Ø =
&/;& 4 distancia =
=
! =" =
C,"tant( *. =
*; =
![Page 267: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/267.jpg)
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#; ca%as
49. cm d =
11290.23 kg c =
N(c(sita R()*("+,29349.89 kg s =
9.96 cm S =
24.50 cm d-& =60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/39.96 cm S 4a6 =
Si C*4%5(&da C,nd/ =
s=7$/$11d1F'c2#/3
9.96 cm S 4a6 =
49. cm d =
0.49 m
6.53 Und0.00
Est"i,s 8 =1
0.075 3#/.3 4 Avanc( 8 =
&/99 4 C,"tant( *. =
![Page 268: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/268.jpg)
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F'c =
F'y =
COLUMNA=
Av =
β =
Ø =
&/;& 4 distancia =
=
! =
" =
#; ca%as
49. cm d =
11290.23 kg c =
N(c(sita R()*("+,22714.83 kg s =
12.87 cm S =
24.50 cm d-& =
60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/3
12.87 cm S 4a6 =N, C*4%5(&da C,nd/ =
s=7$/$11d1F'c2#/3
0.00 cm S 4a6 =
49. cm d =
0.49 m6.53 Und
0.00Est"i,s 8 =
10.075 3
#/.3 4 Avanc( 8 =
&/99 4
*; =
C,"tant( *. =
![Page 269: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/269.jpg)
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F'c =
F'y =
COLUMNA=
Av =
β =
Ø =
&/;& 4 distancia =
=
! =
" =
#; ca%as
49. cm d =
11290.23 kg c =
N(c(sita R()*("+,18970.24 kg s =
15.40 cm S =
24.50 cm d-& =
60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/315.40 cm S 4a6 =
N, C*4%5(&da C,nd/ =
s=7$/$11d1F'c2#/3
0.00 cm S 4a6 =
49. cm d =
0.49 m6.53 Und
0.00Est"i,s 8 =
1
0.075 3#/.3 4 Avanc( 8 =
&/99 4
*; =
C,"tant( *. =
![Page 270: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/270.jpg)
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F'c =
F'y =
COLUMNA=
Av =
β =
Ø =
$/;9 4 distancia =
=
! =
" =
#; ca%as
49. cm d =
11290.23 kg c =
N(c(sita R()*("+,23016.71 kg s =
12.70 cm S =24.50 cm d-& =
60.00 cm , =
*; =
![Page 271: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/271.jpg)
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12.25 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/312.70 cm S 4a6 =
N, C*4%5(&da C,nd/ =
s=7$/$11d1F'c2#/3
0.00 cm S 4a6 =
49. cm d =0.49 m
3.92 Und0.00
Est"i,s 8 =1
0.125 3#/3# 4 Avanc( 8 =
$/:9 4
F'c =
F'y =
COLUMNA=
Av =
β =Ø =
$/;& 4 distancia =
C,"tant( *. =
![Page 272: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/272.jpg)
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=
! =
" =
#; ca%as
49. cm d =11290.23 kg
c =N(c(sita R()*("+,
11849.30 kg s =
24.66 cm S =
24.50 cm d-& =
60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5(
$"a C,nd/ =
s=0&/$11d1F'c2#/3
24.50 cm S 4a6 =N, C*4%5(
&da C,nd/ =s=7$/$11d1F'c2#/3
0.00 cm S 4a6 =
49. cm d =
0.49 m2.18 Und
0.00Est"i,s 8 =
10.225 3
#/.3 4 Avanc( 8 =
$/99 4
*; =
C,"tant( *. =
![Page 273: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/273.jpg)
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DISE O POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 70 cm (h)
0.71 cm2
0.85
0.85
&/&: 4 $/<$ 4 &/:. 411200.00 kg
30. cm60. cm5. cm
#$ ca%a #& ca%as #; ca%as
54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg
R()*("+, Mini4, R()*("+, Mini4, R()*("+, Mini4,734.17 kg 1425.41 kg 1886.24 kg
438.66 cm 213.39 cm 154.93 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(
27.00 cm 25.50 cm 24.50 cm N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
3.09 Und 2.04 Und 3.27 Und0.00 1 0.00 1 0.000.18 r 0.25 4 0.15
#/3; 4 >ALUE? #/# 4
&/:#3 4 >ALUE? ;/..# 4
![Page 274: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/274.jpg)
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DISEÑO POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 70 cm (h)
0.71 cm2
0.850.85
&/&: 4 $/# 4 &/:. 426532.80 kg
30. cm60. cm5. cm
#$ ca%a #& ca%as #; ca%as
54. cm 51. cm 49. cm
12442.30 kg 11751.06 kg 11290.23 kg N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,
18772.76 kg 19464.00 kg 19924.83 kg
17.16 cm 15.63 cm 14.67 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(17.16 cm 15.63 cm 14.67 cm
N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
3.09 Und 3.40 Und 3.27 Und0.00 1 0.00 1 0.000.18 4 0.15 4 0.15
#/3; 4 #/# 4 #/# 4
&/:$ 4 &/&# 4 ;/.. 4
![Page 275: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/275.jpg)
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DISEÑO POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 55 cm (h)0.71 cm2
0.85
0.85
&/&$ 4 $/# 4 &/99 428275.00 kg
30. cm60. cm5. cm
#$ ca%a #& ca%as #; ca%as54. cm 51. cm 49. cm
12442.30 kg 11751.06 kg 11290.23 kg N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,
20822.41 kg 21513.65 kg 21974.47 kg
15.47 cm 14.14 cm 13.30 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(15.47 cm 14.14 cm 13.30 cm
N, C*4%5( N, C*4%5( N, C*4%5(
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0.00 cm 0.00 cm 0.00 cm54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
3.09 Und 4.08 Und 3.27 Und0.00 1 0.00 1 0.000.18 4 0.125 4 0.15
#/3; 4 #/3# 4 #/# 4&/9; 4 &/$# 4 ;/;9 4
DISE O POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 55 cm (h)
0.71 cm2
0.85
0.85
&/&$ 4 $/: 4 &/99 419503.50 kg
30. cm
60. cm5. cm
![Page 277: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/277.jpg)
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#$ ca%a #& ca%as #; ca%as
54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,10503.00 kg 11194.24 kg 11655.06 kg
30.66 cm 27.17 cm 25.07 cm
27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(27.00 cm 25.50 cm 24.50 cm
N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
3.09 Und 2.04 Und 3.27 Und0.00 1 0.00 1 0.000.18 2 0.250 4 0.15
#/3; 4 #/3# 4 #/# 4
&/9; 4 &/; 4 ;/;9 4
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DISE O POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 55 cm (h)
0.71 cm2
0.85
0.85
&/&$ 4 $/:. 4 &/99 414609.40 kg
30. cm60. cm5. cm
#$ ca%a #& ca%as #; ca%as
54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,4745.23 kg 5436.47 kg 5897.30 kg
67.87 cm 55.95 cm 49.55 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(
27.00 cm 25.50 cm 24.50 cm N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
3.09 Und 2.04 Und 3.27 Und0.00 1 0.00 1 0.000.18 2 0.250 4 0.15
#/3; 4 #/3# 4 #/# 4
&/9; 4 &/;. 4 ;/;9 4
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DISEÑO POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 55 cm (h)
0.71 cm2
0.85
0.85
&/&$ 4 $/:# 4 &/99 422961.40 kg
30. cm60. cm5. cm
#$ ca%a #& ca%as #; ca%as
54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,14571.12 kg 15262.35 kg 15723.18 kg
22.10 cm 19.93 cm 18.59 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(22.10 cm 19.93 cm 18.59 cm
N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
3.09 Und 2.91 Und 3.27 Und0.00 1 0.00 1 0.00
0.18 3 0.175 4 0.15#/3; 4 #/3; 4 #/# 4
&/9; 4 &/;; 4 ;/;9 4
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DISEÑO POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 65 cm (h)
0.71 cm2
0.85
0.85
&/& 4 $/<< 4 $/:9 426160.90 kg
30. cm60. cm5. cm
#$ ca%a #& ca%as #; ca%as
54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,18335.23 kg 19026.47 kg 19487.30 kg
17.56 cm 15.99 cm 15.00 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm
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13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(17.56 cm 15.99 cm 15.00 cm
N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm
54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
3.09 Und 2.91 Und 3.27 Und0.00 1 0.00 1 0.000.18 3 0.175 4 0.15
#/3; 4 #/3; 4 #/# 4
&/9: 4 &/3$ 4 &/.9 4
DISEÑO POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 65 cm (h)
0.71 cm2
0.850.85
&/& 4 $/<< 4 $/99 4
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16172.10 kg30. cm60. cm5. cm
#$ ca%a #& ca%as #; ca%as
54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+, N(c(sita R()*("+,6583.70 kg 7274.94 kg 7735.77 kg
48.92 cm 41.81 cm 37.78 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(
27.00 cm 25.50 cm 24.50 cm N, C*4%5( N, C*4%5( N, C*4%5(
0.00 cm 0.00 cm 0.00 cm54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
3.09 Und 2.91 Und 2.18 Und0.00 1 0.00 1 0.000.18 3 0.175 2 0.225
#/3; 4 #/3; 4 #/.3 4
&/9: 4 &/3$ 4 &/&& 4
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Est"i,s 8 = $ 8 #/#3@ & 8 #/&3@ & 8
Est"i,s 8 = $ 8 #/#3@ & 8 #/#93@ ; 8 #/$#@ ;
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DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85Ø = 0.85
distancia = &/:$ 48128.4
= 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c = 12442.30 kg R()*("+, Mini4,
s = -2879.47 kg
S = -111.85 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = -111.85 cm
&da C,nd/ = s=7$/$11d1F'c2#/3 N, C*4%5(S 4a6 = 0.00 cm
d = 54. cm0.54 m
2.16 Und
Est"i,s 8 =1 0.00 12 0.25 r
Avanc( 8 = #/3# 4
;/;$ 4
*; =
C,"tant( *. =
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DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b) Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = &/9; 410274.4
= 30. c ! = 60. c " = 5. c
#$ ca%ad = 54. cm
c =12442.30 kg
R()*("+, Mini4,s = -354.77 kg
S = -907.80 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ = s=0&/$11d1F'c2#/3 Si C*4%5(S 4a6 = -907.80 cm
s=7$/$11d1F'c2#/3 N, C*4%5(
*; =
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/S 4a6 = 0.00 cm
d = 54. cm0.54 m
2.16 Und
Est"i,s 8 =1 0.00 12 0.25 r
Avanc( 8 = #/3# 4;/&; 4
DISE O POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = &/9; 416503.5
= 30. c
! = 60. c " = 5. c
C,"tant( *. =
*; =
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#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 6973.59 kg
S = 46.18 cm
d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 27.00 cm
&da C,nd/ =s=7$/$11d1F'c2#/3 N, C*4%5(
S 4a6 = 0.00 cm d = 54. cm
0.54 m
2.16 Und
Est"i,s 8 =1 0.00 12 0.25 2
Avanc( 8 = #/3# 4
;/&; 4C,"tant( *. =
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DISE O POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = &/9; 411609.4
= 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
R()*("+, Mini4,s = 1215.82 kg
S = 264.89 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 27.00 cm &da C,nd/ =
s=7$/$11d1F'c2#/3 N, C*4%5(S 4a6 = 0.00 cm
d = 54. cm0.54 m
2.16 Und
Est"i,s 8 =1 0.00 12 0.25 r
Avanc( 8 = #/3# 4
;/&; 4
*; =
C,"tant( *. =
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DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = &/9; 47366.2
= 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
R()*("+, Mini4,s = -3776.18 kg
S = -85.29 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = -85.29 cm
&da C,nd/ =s=7$/$11d1F'c2#/3 N, C*4%5(
S 4a6 = 0.00 cm d = 54. cm
0.54 m2.16 Und
Est"i,s 8 =1 0.00 1
2 0.25 r Avanc( 8 = #/3# 4
;/&; 4
*; =
C,"tant( *. =
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DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85
Ø = 0.85
distancia = &/9: 425381.5
= 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 17418.29 kg
S = 18.49 cm d-& = 27.00 cm , = 60.00 cm
*; =
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d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 18.49 cm
&da C,nd/ =s=7$/$11d1F'c2#/3 N, C*4%5(
S 4a6 = 0.00 cm
d = 54. cm0.54 m
2.16 Und
Est"i,s 8 =1 0.00 12 0.25 1
Avanc( 8 = #/3# 4
;/&: 4
DISEÑO POR
F'c = 210. kg/
F'y = 4200. kg/
COLUMNA= 50 cm (b)
Av = 0.71 c
β = 0.85Ø = 0.85
distancia = &/9: 4
C,"tant( *. =
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12675.6 = 30. c ! = 60. c " = 5. c
#$ ca%a
d = 54. cm
c =12442.30 kg
N(c(sita R()*("+,s = 2470.17 kg
S = 130.38 cm d-& = 27.00 cm , = 60.00 cm
d-. = 13.50 cm , = 30.00 cm
$"a C,nd/ =
s=0&/$11d1F'c2#/3 Si C*4%5(
S 4a6 = 27.00 cm
&da C,nd/ =s=7$/$11d1F'c2#/3 N, C*4%5(
S 4a6 = 0.00 cm d = 54. cm
0.54 m2.16 Und
Est"i,s 8 =1 0.00 12 0.25 1
Avanc( 8 = #/3# 4
;/&: 4
*; =
C,"tant( *. =
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#/&3@ Rst,/ 8 #/&3
#/$3@ & 8 #/&#@ Rst,/ 8 #/&3
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ORTANTE
m2
cm2
70 cm (h)
2
&/&# 4 ;/.. 4 kg
#& ca%as #; ca%as
51. cm 49. cm
11751.06 kg 11290.23 kg R()*("+, Mini4, R()*("+, Mini4,
-2188.23 kg -1727.41 kg
-139.00 cm -169.18 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5(-139.00 cm -169.18 cm
N, C*4%5( N, C*4%5(0.00 cm 0.00 cm51. cm 49. cm0.51 m 0.49 m
2.04 Und 3.27 Und0.00 1 0.00
Est"i,s 8 =0.25 4 0.15
>ALUE? #/# 4Est"i,s 8 =
>ALUE? ./#. 4
![Page 295: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/295.jpg)
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ORTANTE
m2
cm2
55 cm (h) 2
&/$# 4 ;/;9 4 kg
#& ca%as #; ca%as51. cm 49. cm
11751.06 kg 11290.23 kg R()*("+, Mini4, R()*("+, Mini4,
336.47 kg 797.30 kg
903.98 cm 366.53 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5(25.50 cm 24.50 cm
N, C*4%5( N, C*4%5(
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0.00 cm 0.00 cm51. cm 49. cm0.51 m 0.49 m
2.04 Und 3.27 Und0.00 1 0.00
Est"i,s 8 =0.25 4 0.15
>ALUE? #/# 4 Est"i,s 8 =>ALUE? ;/<9 4
ORTANTE
m2
cm2
55 cm (h)
2
&/; 4 ;/;9 4 kg
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#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,7664.82 kg 8125.65 kg
39.68 cm 35.96 cm
25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5($"a C,nd/ =
25.50 cm 24.50 cm N, C*4%5( N, C*4%5(
&da C,nd/ =0.00 cm 0.00 cm51. cm 49. cm0.51 m 0.49 m
2.04 Und 3.27 Und0.00 1 0.00
Est"i,s 8 =0.25 4 0.15
#/3# 4 #/# 4
&/: 4 ;/<9 4
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ORTANTE
m2
cm2
55 cm (h)
2
&/;. 4 ;/;9 4 kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
R()*("+, Mini4, N(c(sita R()*("+,1907.06 kg 2367.89 kg
159.49 cm 123.42 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5(
25.50 cm 24.50 cm N, C*4%5( N, C*4%5(0.00 cm 0.00 cm51. cm 49. cm0.51 m 0.49 m
2.04 Und 3.27 Und0.00 1 0.000.25 4 0.15
>ALUE? #/# 4
>ALUE? ;/<9 4Est"i,s 8 =
Est"i,s 8 =
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ORTANTE
m2
cm2
55 cm (h)
2
&/;; 4 ;/;9 4 kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
R()*("+, Mini4, R()*("+, Mini4,-3084.94 kg -2624.11 kg
-98.60 cm -111.37 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5(-98.60 cm -111.37 cm
N, C*4%5( N, C*4%5(0.00 cm 0.00 cm51. cm 49. cm0.51 m 0.49 m
2.04 Und 3.27 Und0.00 1 0.00
Est"i,s 8 =
0.25 4 0.15>ALUE? #/# 4Est"i,s 8 =
>ALUE? ;/<9 4
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ORTANTE
m2
cm2
65 cm (h)
2
&/3$ 4 &/## 4 kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,18109.53 kg 18570.36 kg
16.80 cm 15.74 cm25.50 cm 24.50 cm60.00 cm 60.00 cm
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12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5($"a C,nd/ =
16.80 cm 15.74 cm N, C*4%5( N, C*4%5(
&da C,nd/ =0.00 cm 0.00 cm
51. cm 49. cm0.51 m 0.49 m
2.04 Und 3.27 Und0.00 1 0.00
Est"i,s 8 =0.25 3 0.15
#/&3 4 #/.3 4
&/9 4 &/.3 4
ORTANTE
m2
cm2
65 cm (h)
2
&/3$ 4 &/&& 4
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kg
#& ca%as #; ca%as
51. cm 49. cm11751.06 kg 11290.23 kg
N(c(sita R()*("+, N(c(sita R()*("+,3161.41 kg 3622.24 kg
96.21 cm 80.68 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm
Si C*4%5( Si C*4%5(
25.50 cm 24.50 cm N, C*4%5( N, C*4%5(
0.00 cm 0.00 cm51. cm 49. cm0.51 m 0.49 m
2.04 Und 2.18 Und0.00 1 0.00
Est"i,s 8 =0.25 r 0.225
#/&3 4 >ALUE?Est"i,s 8 =
&/9 4 >ALUE?
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$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ . 8 #/$3@ Rst
$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ & 8 #/$3@ & 8 #/&#
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$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ . 8 #/$&3@ Rs
$ 8 #/#3@ 3 8 #/$#@ 8 #/$&3@ & 8 #/$3@ & 8 #/&#
DISE O POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 55 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = ;/&; 4 &/:# 413863.50 kg
= 30. cm
! = 60. cm " = 5. cm
*; =
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#$ ca%a #& ca%as
d = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
N(c(sita R()*("+, N(c(sita R()*("+,s = 3867.70 kg 4558.94 kg
S = 83.27 cm 66.72 cm
d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(S 4a6 = 27.00 cm 25.50 cm
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 54. cm 51. cm0.54 m 0.51 m
2.16 Und 2.04 Und1 0.00 1 0.00 11 0.25 1 0.25 4
Avanc( 8 = #/&3 4 #/&3 4
;/.: 4 ;/#3 4C,"tant( *. =
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$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ & 8 #/&3@ Rs
$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ & 8 #/$3@ & 8 #/&
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$ 8 #/#3@ . 8 #/$&3@ . 8 #/$3@ ; 8 #/$93@ Rs
$ 8 #/#3@ ; 8 #/#93@ . 8 #/$#@ . 8 #/$3@ ; 8 #/$
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DISEÑO POR CORTANTE
F'c = 210. kg/cm2
F'y = 4200. kg/cm2
COLUMNA= 50 cm (b) 65 cm (h)
Av = 0.71 cm2
β = 0.85
Ø = 0.85
distancia = ;/&: 4 &/:# 410180.90 kg
= 30. cm ! = 60. cm " = 5. cm
#$ ca%a #& ca%as
d = 54. cm 51. cm
c =12442.30 kg 11751.06 kg
R()*("+, Mini4, R()*("+, Mini4,s = -464.77 kg 226.47 kg
S = -692.94 cm 1343.05 cm d-& = 27.00 cm 25.50 cm , = 60.00 cm 60.00 cm
*; =
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d-. = 13.50 cm 12.75 cm , = 30.00 cm 30.00 cm
s=0&/$11d1F'c2#/3 Si C*4%5( Si C*4%5(S 4a6 = -692.94 cm 25.50 cm
s=7$/$11d1F'c2#/3 N, C*4%5( N, C*4%5(S 4a6 = 0.00 cm 0.00 cm
d = 54. cm 51. cm0.54 m 0.51 m
2.16 Und 2.04 Und1 0.00 1 0.00 11 0.25 1 0.25 r
Avanc( 8 = #/&3 4 #/&3 4
;/3; 4 ;/#3 4C,"tant( *. =
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$ 8 #/#3@ ; 8 #/$3@ & 8 #/&&3@ & 8 #/&&3@ Rs
$ 8 #/#3@ & 8 #/$#@ & 8 #/$3@ ; 8 #/$93 & 8 #/&#@
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,/ 8 #/&3
@ Rst,/ 8 #/&3
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,/ 8 #/&3
@ Rst,/ 8 #/&3
F'c =
F'y =
COLUMNA=
Av =
β =
Ø =
;/<9 4 distancia =
=
! =" =
*; =
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#; ca%as
49. cm d =
11290.23 kg c =
N(c(sita R()*("+,5019.77 kg s =
58.22 cm S =
24.50 cm d-& =60.00 cm , =
12.25 cm d-. =
30.00 cm , =
Si C*4%5($"a C,nd/ =
s=0&/$11d1F'c2#/324.50 cm S 4a6 =
N, C*4%5(&da C,nd/ =
s=7$/$11d1F'c2#/3
0.00 cm S 4a6 =
49. cm d =
0.49 m
3.27 Und0.00
Est"i,s 8 =1
0.15 1#/# 4 Avanc( 8 =
./39 4 C,"tant( *. =
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,/ 8 #/&3
@ Rst,/ 8 #/&3
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t,/ 8 #/&3
3@ & 8 #/&#@ Rst,/ 8 #/&3
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&/.3 4
#; ca%as
49. cm11290.23 kg
R()*("+, Mini4,687.30 kg
425.20 cm24.50 cm60.00 cm
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12.25 cm30.00 cm
Si C*4%5(24.50 cm
N, C*4%5(0.00 cm
49. cm0.49 m
3.27 Und0.00
Est"i,s 8 = $ 8 #/#3@ 3 80.15>ALUE?
Est"i,s 8 = $ 8 #/#3@ & 8 #>ALUE?
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, 8 #/&&3/
Rst,/ 8 #/&&3
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DISE O POR CORTANTE
210. kg/cm2
4200. kg/cm2
50 cm (b) 55 cm (h)
0.71 cm2
0.85
0.85
;/.: 4 ;/#3 4 ./39 42543.60 kg
30. cm
60. cm5. cm
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#$ ca%a #& ca%as #; ca%as
54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg
R()*("+, Mini4, R()*("+, Mini4, R()*("+, Mini4,-9449.83 kg -8758.59 kg -8297.76 kg
-34.08 cm -34.73 cm -35.22 cm
27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm
Si C*4%5( Si C*4%5( Si C*4%5(-34.08 cm -34.73 cm -35.22 cm
N, C*4%5( N, C*4%5( N, C*4%5(0.00 cm 0.00 cm 0.00 cm54. cm 51. cm 49. cm0.54 m 0.51 m 0.49 m
2.16 Und 2.04 Und 3.27 Und0.00 1 0.00 1 0.000.25 r 0.25 4 0.15
#/&3 4 >ALUE? #/# 4
;/9; 4 >ALUE? 3/$9 4
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/$#@ . 8 #/$&3@ . 8 #/$3@ ; 8 #/$3@ Rst,/ 8 #/&3
/#93@ . 8 #/$#@ . 8 #/$&3@ 9 8 #/$3@ & 8 #/&#@ R
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Est"i,s 8 = $ 8 #/#3@ 9 8 #/#93@ 3 8 #/$#@
Est"i,s 8 = $ 8 #/#3@ 9 8 #/#93@ 3 8 #/$#@ .
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t,/ 8 #/&3
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8 #/&3@ & 8 #/&3@ Rst,/ 8 #/&3
8 #/$3@ & 8 #/&#@ Rst,/ 8 #/&3
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VERIFI!I"# $E U#! VI%! $"&'EE#E REF"R*!$!
F'c = 210 kg/cm2
Fy = 4200 kg/cm2
F's = +β = , 0.85 = , 0.90
As = 20.40 cm2 As = 5.18 cm2 b c
" d' = 6.00 cm 2
Es = 2000000.00 cm , 5.18 , -116760.00
= 30.00 cm
! = 55.00 cm 3562.51
)s = 3562.51 kg/cm2 18978.03 #" F'UE c
C 14.77 cm d1 49.00 a 12.55 d2 46.00
d3 44.00
T,4and, 4,4(nt,s (n (5 %*nt, d(5 a"(a (n t"acci,n t(n(4,s#$ ca%a #& ca%as #; ca%as
M* 31.158 kg-cm 28.973 kg-cm 27.516 kg-cm
C = , 0.25 , 0.25CM = , 1.00 , 1.00M* = 1.8V1.5 1.8V1.5 1.8V1.5CM = 15.98 n 14.86 n 14.11 n C = 3.99 n 3.71 n 3.53 n
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VERIFI!I"# $E U#! VI%! $"&'EE#E REF"R*!$!
F'c = 210 kg/cm2
Fy = 4200 kg/cm2
F's = +β = , 0.85 = , 0.90
As = 20.40 cm2 As = 5.18 cm2 b c
" d' = 6.00 cm 2
Es = 2000000.00 cm , 5.18 , -116760.00
= 30.00 cm
! = 55.00 cm 3562.51
)s = 3562.51 kg/cm2 18978.03 #" F'UE c
C 14.77 cm d1 49.00 a 12.55 d2 46.00
d3 44.00
T,4and, 4,4(nt,s (n (5 %*nt, d(5 a"(a (n t"acci,n t(n(4,s#$ ca%a #& ca%as #; ca%as
M* 31.158 kg-cm 28.973 kg-cm 27.516 kg-cm
C = , 0.25 , 0.25CM = , 1.00 , 1.00M* = 1.8V1.5 1.8V1.5 1.8V1.5CM = 15.98 n 14.86 n 14.11 n C = 3.99 n 3.71 n 3.53 n
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VERIFI!I"# $E U#! VI%! $"&'EE#E REF"R*!$!
F'c = 210 kg/cm2
Fy = 4200 kg/cm2
F's = +β = , 0.85 = , 0.90
As = 20.40 cm2 As = 5.18 cm2 b c
" d' = 6.00 cm 2
Es = 2000000.00 cm , 5.18 , -116760.00
= 30.00 cm
! = 55.00 cm 3562.51
)s = 3562.51 kg/cm2 18978.03 #" F'UE c
C 14.77 cm d1 49.00 a 12.55 d2 46.00
d3 44.00
T,4and, 4,4(nt,s (n (5 %*nt, d(5 a"(a (n t"acci,n t(n(4,s#$ ca%a #& ca%as #; ca%as
M* 31.158 kg-cm 28.973 kg-cm 27.516 kg-cm
C = , 0.25 , 0.25CM = , 1.00 , 1.00M* = 1.8V1.5 1.8V1.5 1.8V1.5CM = 15.98 n 14.86 n 14.11 n C = 3.99 n 3.71 n 3.53 n
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VERIFI!I"# $E U#! VI%! $"&'EE#E REF"R*!$!
F'c = 210 kg/cm2
Fy = 4200 kg/cm2
F's = +β = , 0.85 = , 0.90
As = 20.40 cm2 As = 5.18 cm2 b c
" d' = 6.00 cm 2
Es = 2000000.00 cm , 5.18 , -116760.00
= 30.00 cm
! = 55.00 cm 3562.51
)s = 3562.51 kg/cm2 18978.03 #" F'UE c
C 14.77 cm d1 49.00 a 12.55 d2 46.00
d3 44.00
T,4and, 4,4(nt,s (n (5 %*nt, d(5 a"(a (n t"acci,n t(n(4,s#$ ca%a #& ca%as #; ca%as
M* 31.158 kg-cm 28.973 kg-cm 27.516 kg-cm
C = , 0.25 , 0.25CM = , 1.00 , 1.00M* = 1.8V1.5 1.8V1.5 1.8V1.5CM = 15.98 n 14.86 n 14.11 n C = 3.99 n 3.71 n 3.53 n
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PREDIMENSIONAMIENTO
IA L LOSA G IA PERIMETRAL IA T
$"a C,ndici :m;< $"a C,ndiciHn :m;< $"a C,ndiciHn
&da C,ndici :m;< &da C,ndiciHn :m;< &da C,ndiciHn
;"a C,ndici :m;< ;"a C,ndiciHn :m;<
DISEÑO DE ACERO PARA IAS DOBLEMENTE REFOR
DATOS
β = , 0.85
Ø = , 0.90
viJa = 40. cm
! = 70. cm " = 4. cm
d' = 5. cm
d =#$ ca%a #& ca%as
64. cm 61. cm
M* = 5365000. kg.cm 5365000. kg.cm
)'c = 210. kg/cm2 210. kg/cm2
)'y = 4200. kg/cm2 4200. kg/cm2
P4a6 = , 0.02 , 0.02
DATOS #$ ca%a #& ca%as
= , 0.59 , 0.59
b = , -1.00 , -1.00
c = 0.17 0.19
> 1 = 0.196 0.219
> 2 = 1.499 1.476
? = 0.0098 0.0110
ch<@:<A d< ? = SIMP/ REFORADA SIMP/ REFORADA
! = 25.07 cm2 26.72 cm2
K* = , 49.53 , 49.53
41.47 cm2 39.53 cm2
8115011.58 kg.cm 7372060.08 kg.cm
M" = -2750011.58 kg.cm -2007060.08 kg.cm
A's = -12.33 cm2 -9.48 cm2
T,ta5 As = 29.14 cm2 30.05 cm2
T,ta5 A's = -12.33 cm2 -9.48 cm2
IA T LOSA G IAINTERIOR
As$ =M*$ =
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ISLADA
#A :m;<
:m;<
DAS DISEÑO DE IA T G L
β = , 0.85
Ø = 0.90 Ln =
viJa
= 80. cm " =
40. cm d' =
! = 70. cm F'c =
!) = 10. cm F'y =120. cm F's =
120. cm M* =
#; ca%asd =
#$ ca%a #& ca%as
59. cm 64. cm 61. cm
5365000. kg.cm K* = 16.06 17.67
210. kg/cm2 P = 0.00442 0.00552
4200. kg/cm2 As = 22.63 cm2 26.94 cm2
, 0.02 a = 4.99 cm 5.94 cm IA RECT/ IA RECT/
#; ca%as
, 0.59
, -1.00
0.20
0.237
1.458 22.67 cm2 22.67 cm2
0.0119 5055120. kg.cm 4798080. kg.cm
SIMP/ REFORADA 205880. kg.cm 462920. kg.cm
28.91 cm2 K* = 1.26 3.11
, 49.53 P = , 0.00 , 0.01
38.23 cm2 0.84 cm2 26.84 cm2
6896571.12 kg.cm As t,ta5 = 23.51 cm2 49.51 cm2
-1531571.12 kg.cm
-7.50 cm2
30.73 cm2
-7.50 cm2
=
s =
s $ =
As$ =M*$ =
M*& =
As& =
!!1
b
b>
h
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DISEÑO DE ACERO PARA IAS DOB
6.60 m DATOS
4. cm β = , 0.85
5. cm Ø = , 0.90
280. kg/cm2 viJa
= 40. cm
4200. kg/cm2 ! = 70. cm4200. kg/cm2 " = 5. cm
5261000. kg.cm d' = 5. cm
#; ca%asd =
#$ ca%a
59. cm 64. cm
18.89 M* = 9076000. kg.cm
0.00508 )'c = 210. kg/cm2
23.98 cm2 )'y = 4200. kg/cm2
5.29 cm P4a6 = , 0.02IA RECT/
DATOS #$ ca%a
= , 0.59
b = , -1.00
c = 0.29
> 1 = 0.377
22.67 cm2 > 2 = 1.318
4626720. kg.cm ? = 0.0188
634280. kg.cm ch<@:<A d< ? = DOB/REFORADA
! = 48.25 cm24.56
, 0.00 K* = , 49.53
0.87 cm2 41.47 cm2
23.54 cm2 8115011.58 kg.cm
M" = 960988.42 kg.cm
A's = 4.31 cm2
T,ta5 As = 45.78 cm2
T,ta5 A's = 4.31 cm2
As$ =M*$ =
2
h
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EMENTE REFORADASβ =
Ø =
viJa
=
! =
!) =
#& ca%as #; ca%asd =
61. cm 59. cm
9076000. kg.cm 9076000. kg.cm K* =
210. kg/cm2 210. kg/cm2 P =
4200. kg/cm2 4200. kg/cm2 As =
, 0.02 , 0.02 a =
#& ca%as #; ca%as
, 0.59 , 0.59
, -1.00 , -1.00
0.32 0.34
0.434 0.482
1.261 1.213
0.0217 0.0241
DOB/REFORADA DOB/REFORADA
52.89 cm2 58.79 cm2 K* =
, 49.53 , 49.53 P =
39.53 cm2 38.23 cm2
7372060.08 kg.cm 6896571.12 kg.cm As t,ta5 =
1703939.92 kg.cm 2179428.88 kg.cm
8.05 cm2 10.68 cm2
47.58 cm2 48.91 cm2
8.05 cm2 10.68 cm2
=
s =
s $ =
As$ =M*$ =
M*& =
As& =
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DISEÑO DE IA T G L DISEÑO, 0.85
0.90 Ln = 5.60 m
80. cm " = 5. cm β
40. cm d' = 5. cm Ø
70. cm F'c = 210. kg/cm2 viJa
10. cm F'y = 4200. kg/cm2120. cm F's = 4200. kg/cm2 "
120. cm M* = 2492000. kg.cm d'
#$ ca%a #& ca%as #; ca%asd
64. cm 61. cm 59. cm
7.60 8.37 8.95 M*
0.00205 0.00552 0.00233 )'c
10.50 cm2 26.94 cm2 11.00 cm2 )'y
3.09 cm 7.92 cm 3.23 cm P4aIA RECT/ IA RECT/ IA RECT/
DA
b
c
> 1
17.00 cm2 17.00 cm2 17.00 cm2 > 2
3791340. kg.cm 3598560. kg.cm 3470040. kg.cm ?
-1299340. kg.cm -1106560. kg.cm -978040. kg.cm ch<@:<A
!---- ---- ----
, 0.01 , 0.01 , 0.01
28.16 cm2 26.84 cm2 25.96 cm2
45.16 cm2 43.84 cm2 42.96 cm2
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DE ACERO PARA IAS DOBLEMENTE REFORADAS
DATOS
= , 0.85
= , 0.90
= 40. cm
! = 70. cm 5. cm
= 5. cm
=#$ ca%a #& ca%as #; ca%as
64. cm 61. cm 59. cm
= 6049000. kg.cm 6049000. kg.cm 6049000. kg.cm
= 210. kg/cm2 210. kg/cm2 210. kg/cm2
= 4200. kg/cm2 4200. kg/cm2 4200. kg/cm2
6 = , 0.02 , 0.02 , 0.02
OS #$ ca%a #& ca%as #; ca%as
= , 0.59 , 0.59 , 0.59
= , -1.00 , -1.00 , -1.00
0.20 0.22 0.23
= 0.225 0.253 0.274
= 1.470 1.442 1.421
= 0.0113 0.0126 0.0137
d< ? = IMPLEM/ REFORAD IMPLEM/ REFORAD IMPLEM/ REFORADA
= 28.84 cm2 30.83 cm2 33.46 cm2
K* = , 49.53 , 49.53 , 49.53
41.47 cm2 39.53 cm2 38.23 cm2
8115011.58 kg.cm 7372060.08 kg.cm 6896571.12 kg.cm
M" = -2066011.58 kg.cm -1323060.08 kg.cm -847571.12 kg.cm
A's = -9.26 cm2 -6.25 cm2 -4.15 cm2
T,ta5 As = 32.21 cm2 33.28 cm2 34.08 cm2
T,ta5 A's = -9.26 cm2 -6.25 cm2 -4.15 cm2
As$ =M*$ =
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DISEÑO DE IA T G L
β = , 0.85
Ø = 0.90 Ln = 6.00 m
viJa
= 80. cm " = 5. cm
40. cm d' = 5. cm
! = 70. cm F'c = 210. kg/cm2
!) = 10. cm F'y = 4200. kg/cm2120. cm F's = 4200. kg/cm2
120. cm M* = 5069000. kg.cm
d =#$ ca%a #& ca%as #; ca%as
64. cm 61. cm 59. cm
K* = 15.47 17.03 18.20
P = 0.00488 0.00552 0.01524
As = 24.99 cm2 26.94 cm2 71.93 cm2
a = 7.35 cm 7.92 cm 21.16 cm IA RECT/ IA RECT/ a 7 !) == IA T
17.00 cm2 17.00 cm2 17.00 cm2
3791340. kg.cm 3598560. kg.cm 3470040. kg.cm
1277660. kg.cm 1470440. kg.cm 1598960. kg.cm
K* = 7.80 9.88 11.48
P = , 0.01 , 0.01 , 0.01
28.16 cm2 26.84 cm2 25.96 cm2
As t,ta5 = 45.16 cm2 43.84 cm2 42.96 cm2
=
s =
s $ =
As$ =M*$ =
M*& =
As& =
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DISEÑO DE ACERO PARA IAS DOBLEMENTE REFOR
DATOS
β = , 0.85
Ø = , 0.90
viJa = 40. cm
! = 70. cm " = 5. cm
d' = 5. cm
d =#$ ca%a #& ca%as
64. cm 61. cm
M* = 9076000. kg.cm 9076000. kg.cm
)'c = 210. kg/cm2 210. kg/cm2
)'y = 4200. kg/cm2 4200. kg/cm2
P4a6 = , 0.02 , 0.02
DATOS #$ ca%a #& ca%as
= , 0.59 , 0.59
b = , -1.00 , -1.00
c = 0.29 0.32
> 1 = 0.377 0.434
> 2 = 1.318 1.261
? = 0.0188 0.0217
ch<@:<A d< ? = DOB/REFORADA DOB/REFORADA
! = 48.25 cm2 52.89 cm2
K* = , 49.53 , 49.53
41.47 cm2 39.53 cm2
8115011.58 kg.cm 7372060.08 kg.cm
M" = 960988.42 kg.cm 1703939.92 kg.cm
A's = 4.31 cm2 8.05 cm2
T,ta5 As = 45.78 cm2 47.58 cm2
T,ta5 A's = 4.31 cm2 8.05 cm2
As$ =M*$ =
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ADAS DISEÑO DE IA T G L
β = , 0.85
Ø = 0.90 Ln =
viJa
= 80. cm " =
40. cm d' =
! = 70. cm F'c =
!) = 10. cm F'y =120. cm F's =
120. cm M* =
#; ca%asd =
#$ ca%a #& ca%as
59. cm 64. cm 61. cm
9076000. kg.cm K* = 15.47 17.03
210. kg/cm2 P = 0.00488 0.00552
4200. kg/cm2 As = 24.99 cm2 26.94 cm2
, 0.02 a = 7.35 cm 7.92 cm IA RECT/ IA RECT/
#; ca%as
, 0.59
, -1.00
0.34
0.482
1.213 17.00 cm2 17.00 cm2
0.0241 3791340. kg.cm 3598560. kg.cm
DOB/REFORADA 1277660. kg.cm 1470440. kg.cm
58.79 cm2 K* = 7.80 9.88
, 49.53 P = , 0.01 , 0.01
38.23 cm2 28.16 cm2 26.84 cm2
6896571.12 kg.cm As t,ta5 = 45.16 cm2 43.84 cm2
2179428.88 kg.cm
10.68 cm2
48.91 cm2
10.68 cm2
=
s =
s $ =
As$ =M*$ =
M*& =
As& =
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6.00 m
5. cm
5. cm
210. kg/cm2
4200. kg/cm24200. kg/cm2
5069000. kg.cm
#; ca%as
59. cm
18.20
0.01524
71.93 cm2
21.16 cm a 7 !) == IA T
17.00 cm2
3470040. kg.cm
1598960. kg.cm
11.48
, 0.01
25.96 cm2
42.96 cm2
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DISEÑO DE IA POR TORSION
$!" 45 cm F'c = 210. kg/cm2 F'y = 4200. kg/cm2 Ø = , 0.85
r< B 3/8C = 0.71 cm2 60 cm 45 cm
d 1 72 cm M* = 1132000 kg-cm * = 4845.01 kg 4845.01 kg 35 cm T* = 300830 kg-cm 300830 kg-cm
C,5*4na = 35 cm 30 cm iJa = 60 cm 35 cm
d = 54 cm
T = 15 cm COND/ 0 G D = =
E;. 01 = 35 cm 60 cm E;. 02 = 15 cm 45 cm
, 83625.00
T* = 133908 kg-cm
Ct = 0.02260 Tc = 233084.29 kg-cm c = 3979.17 kg
t = , 1.30 = 1.50
Ts = 120833.36s = 1720.84$ , 27.00 G$ , 52.00
$ 1 G$ , 1404.00
Av-S = 0.0076At-S = 0.0158 S = 36.21. cm
#A :m;<19.75
C*4%5(19.75
Est"i,s 82.48
, 1.00 , 0.05, 6.00 , 0.08
AANCE 8 0.50 m
T*& y *& 8 $/#. 4 #/3# 4
ACERO LONITUDINAL TRAMO I$
Q & 1 G =
Dis(, %," t,"si,n t"ansv("sa5 y5,nJit*dina5
$"a c,ndici,nS0=$G$-.&da c,ndici,nS0=;#c4/
1
2
TS= At ∗αt ∗ X 1∗Y 1∗fy / S
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01 CAPA 02 CAPAS
2.50
S46 20 cm
As
$RA CONDICINA5=&1At16$y$-s
AtAt0=&1Av
&da CONDICINs0=$y$-3
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DISE O DE IA POR TORSION
$!"15 cm F'c = 210. kg/cm2
F'y = 4200. kg/cm2 Ø = , 0.85
r< B 3/8C = 0.71 cm2
d 1 89 cm M* = 1263000 kg-cm * = 8018.35 kg 8018.35 kg T* = 665385 kg-cm 665385 kg-cm
C,5*4na = 35 cm 40 cm iJa = 60 cm 35 cm
d = 54 cm
T = 15 cm COND/ 0 G D = =
E;. 01 = 35 cm 60 cm E;. 02 = 15 cm 45 cm
, 83625.00
T* = 133908 kg-cm
Ct = 0.02260 Tc = 237037.11 kg-cm c = 3027.85 kg
t = , 1.16 = 1.50
Ts = 545768.77s = 6405.50$ , 30.00 G$ , 45.00
$ 1 G$ , 1350.00
Av-S = 0.0282At-S = 0.0833 S = 7.29. cm
:m;<
7.29
C*4%5(7.29
Est"i,s 86.73
, 1.00 , 0.05, 9.00 , 0.05
AANCE 8 0.50 m
T*& y *& 8 $/#. 4 #/3# 4
ACERO LONITUDINAL TRAMO I$
Q & 1 G =
Dis(, %," t,"si,n t"ansv("sa5 y5,nJit*dina5
$"a c,ndici,nS0=$G$-.&da c,ndici,nS0=;#c4/
TS= At ∗αt ∗ X 1∗Y 1∗fy / S
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01 CAPA 02 CAPAS
12.50$RA CONDICIN
A5=&1At16$y$-s
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45 cm15 cm
60 cm 45 cm
35 cm
1
2
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$IE" $E UR"
DATOSF'c = 210. kg/cm2 ALT/ MURO = 300.00 cm
F'y = 4200. kg/cm2 ESPESOR = 12.00 cm Ø = , 0.70
K = , 0.80K = 1.0 K = 2.0 ESPESOR = 25.00 cm Lc = 300.00 cm SOLO UNA CAPA = 100.00 cm
P* = 78.00. n
TANTEANDO PARA UN ESPESOR DE MUROT = 14.00 cm
AJ = 1400.00 cm2
ØPn = 80705.63 kg
ØPn = 80.71 n PU 0 ØPn SI PASA
LUEO DISEÑAMOS LOS ACEROSACERO ERTICAL DISTRIBUCION DEL ACERO
N DE FILAS = S =0.71 cm2 2.37 42.26 cm1.29 cm2 1.30 76.79 cm
P = , 0.00 Ø ;-:V 8 = 40.00 cm As = 1.68 cm2 Ø $-&V 8 = 75.00 cm
LUEO DISEÑAMOS LOS ACEROSACERO WORIONTAL DISTRIBUCION DEL ACERON DE FILAS = S =
0.71 cm2 3.94 25.36 cm1.29 cm2 2.17 46.07 cm
P = , 0.00 Ø ;-:V 8 = 25.00 cm As = 2.80 cm2 Ø $-&V 8 = 45.00 cm
:ndA <; <<Ar < mGAr 25
cm d<b<r An<r< r<:<rHA <n ;dA cr
a"(a Ø ;-:V =a"(a Ø $-&V =
a"(a Ø ;-:V =a"(a Ø $-&V =
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$IE" $E UR"
DATOSF'c = 210. kg/cm2 ALT/ MURO = 300.00 cm
F'y = 4200. kg/cm2 ESPESOR = 12.00 cm Ø = , 0.70
K = , 0.80K = 1.0 K = 2.0 ESPESOR = 25.00 cm Lc = 300.00 cm ACERO A DOS CAPAS = 100.00 cm
P* = 200.00. n
TANTEANDO PARA UN ESPESOR DE MUROT = 27.00 cm
AJ = 2700.00 cm2
ØPn = 201451.25 kg
ØPn = 201.45 n PU 0 ØPn SI PASA
LUEO DISEÑAMOS LOS ACEROSACERO ERTICAL DISTRIBUCION DEL ACERO
N DE FILAS = S =0.71 cm2 2.28 43.83 cm1.29 cm2 1.26 79.63 cm
P = , 0.00 Ø ;-:V 8 = 40.00 cm As = 1.62 cm2 Ø $-&V 8 = 75.00 cm
LUEO DISEÑAMOS LOS ACEROSACERO WORIONTAL DISTRIBUCION DEL ACERON DE FILAS = S =
0.71 cm2 3.80 26.30 cm1.29 cm2 2.09 47.78 cm
P = , 0.00 Ø ;-:V 8 = 25.00 cm As = 2.70 cm2 Ø $-&V 8 = 45.00 cm
:ndA <; <<Ar < mGAr 25
cm d<b<r An<r< r<:<rHA <n ;dA cr
a"(a Ø ;-:V =a"(a Ø $-&V =
a"(a Ø ;-:V =a"(a Ø $-&V =
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$IE" $E UR"
DATOSF'c = 210. kg/cm2 ALT/ MURO = 300.00 cm
F'y = 4200. kg/cm2 ESPESOR = 12.00 cm Ø = , 0.70
K = , 0.80K = 1.0 K = 2.0 ESPESOR = 25.00 cm Lc = 300.00 cm SOLO UNA CAPA = 100.00 cm
P* = 78.00. n
TANTEANDO PARA UN ESPESOR DE MUROT = 14.00 cm
AJ = 1400.00 cm2
ØPn = 80705.63 kg
ØPn = 80.71 n PU 0 ØPn SI PASA
LUEO DISEÑAMOS LOS ACEROSACERO ERTICAL DISTRIBUCION DEL ACERO
N DE FILAS = S =0.71 cm2 2.37 42.26 cm1.29 cm2 1.30 76.79 cm
P = , 0.00 Ø ;-:V 8 = 40.00 cm As = 1.68 cm2 Ø $-&V 8 = 75.00 cm
LUEO DISEÑAMOS LOS ACEROSACERO WORIONTAL DISTRIBUCION DEL ACERON DE FILAS = S =
0.71 cm2 3.94 25.36 cm1.29 cm2 2.17 46.07 cm
P = , 0.00 Ø ;-:V 8 = 25.00 cm As = 2.80 cm2 Ø $-&V 8 = 45.00 cm
:ndA <; <<Ar < mGAr 25
cm d<b<r An<r< r<:<rHA <n ;dA cr
a"(a Ø ;-:V =a"(a Ø $-&V =
a"(a Ø ;-:V =a"(a Ø $-&V =
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FISURACIONES POR FLEION
DATOS
ETERIOR = 26000.00
INTERIOR = 31000.00
Cas, = &/##
C,ndici,n = INTERIOR)'y = 4200.00
! = 50.00
= 30.00
" = 4.00
Ø = 1.59
Ø d( ;-:V 0.95
N d( a""as 2.00
PARA UNA CAPA
dc = 5.75
&dc = 11.49
A = 172.35
Fs = 2520.00
= 25116.99
NO PASA
&3$$/<<
SI PASA
CALCULO DE ANCWE DE RIETA
ETERIORX4a6 = #/;$
#/&.
SI PASA
INTERIORX4a6 = #/;9
#/&.
SI PASA
CONDICIONETERIOR
CONDICIONINTERIOR
X4a6 $"ac,ndici,n =
X4a6 &dac,ndici,n =
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FISURACIONES POR FLEION
DATOS
ETERIOR = 26000.00
INTERIOR = 31000.00
Cas, = $/##
C,ndici,n = ETERIOR)'y = 4200.00
! = 50.00
= 30.00
" = 4.00
Ø $ Y5a = 2.54
Ø & Y5a = 1.59
Ø d( ;-:V 0.95
N d( a""as 4.00
$ = 4.57
PARA DOS CAPAS
dc = 6.22
&dc = 12.44
y=dc = 6.22
A = 127.54
Fs = 2520.00
= 23327.95
&;;&9/<3
SI PASA
NO PASA
CALCULO DE ANCWE DE RIETA
ETERIORX4a6 = #/;$
#/&&
SI PASA
INTERIORX4a6 = #/;9
#/&&
SI PASA
CONDICIONETERIOR
CONDICIONINTERIOR
X4a6 $"ac,ndici,n =
X4a6 &dac,ndici,n =
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FISURACIONES POR FLEION
DATOS
ETERIOR = 26000.00
INTERIOR = 31000.00
Cas, = $/##
C,ndici,n = ETERIOR)'y = 4200.00
! = 50.00
= 30.00
" = 4.00
Ø $ Y5a = 2.54
Ø & Y5a = 2.54
Ø ; Y5a = 2.54
Ø d( ;-:V 0.95
N d( a""as 6.00
$ = 5.04
& = 5.04
PARA TRES CAPAS
dc = 6.22
&dc = 12.44
y=dc = 6.22
A = 112.60
Fs = 2520.00
= 22379.14
&&;9</$.
SI PASA
NO PASA
CALCULO DE ANCWE DE RIETA
ETERIORX4a6 = #/;$
#/&$
SI PASA
INTERIORX4a6 = #/;9
#/&$
SI PASA
CONDICIONETERIOR
CONDICIONINTERIOR
X4a6 $"ac,ndici,n =
X4a6 &dac,ndici,n =
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DIARAMA DE INTERACCION
DATOS
F'c = 210.00 " = 4.00 5.10
F'y = 4200.00 Ø = 0.95 2.54
Ø = 0.85 d' = 6.22
As$ = 15.30 5.10
As& = 10.20 2.54
As; = 15.30
5.10
SECCION DE COLUMNA 2.54
30.00 40.00
CALCULO DE CENTROIDE PLASTICO
F*("+a ZJ 6 M,4(nt, ZJ4Cc/ = 214200.00 20.00 4284000.00
AsI = 61528.95 35.00 2153513.25
AsII = 41019.30 20.00 820386.00
AsIII = 61528.95 5.00 307644.75
378277.20 7565544.00
CP = 20.00
PUNTO N #$ d = 40.00Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias
2000000.000.00[$ = 0.00 F's$ = 4200.00 0.00
[& = 0.00 F's& = 4200.00 0.000.00
[; = 0.00 F's; = 4200.00
0.00Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP 0.00
Cc/ = 214200.00 0.00
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a ca"Ja a6ia5 n,
P$ = 64260.00 15.00P& = 42840.00 0.00
Pn$ = ;:3P; = 64260.00 -15.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 0.00
M$ = 963900.00Mn$ =
M& = 0.00
M; = -963900.00
PUNTO N #; d = ;#/##Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias a = &3/3#
2000000.00 0.00
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[$ = 0.00 F's$ = 4200.00 0.00
[& = 0.00 F's& = 2000.00 0.000.00
[; = 0.00 F's; = 1000.000.00
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP 0.00Cc/ = 136552.50 7.25
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a ca"Ja a6ia5 n,
P$ = 64260.00 15.00
P& = 20400.00 0.00Pn; = 
P; = -15300.00 -15.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 990005.63
M$ = 963900.00Mn; = &$:M& = 0.00
M; = 229500.00
PUNTO N #3 d = ;3/##Ca5c*5,s d( 5as d(),"4aci,n(s *nita"ias a = &</93
2000000.00 0.00[$ = 0.00 F's$ = 4200.00 0.00
[& = 0.00 F's& = 2571.43 0.000.00
[; = 0.00 F's; = 857.140.00
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP 0.00Cc/ = 159311.25 5.12
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a ca"Ja a6ia5 n,
P$ = 64260.00 15.00
P& = 26228.57 0.00Pn3 = &;
P; = -13114.29 -15.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/Mcc = 815673.60
M$ = 963900.00Mn3 = $<9
M& = 0.00
M; = 196714.29
CUADRO DE RESUMEN DISTANCIA
Pn$ = ;:33#/## Mn$ = #/## 40.00
Pn& = &::.#3/## Mn& = $;;9<:3/## 40.00
Pn; = <$&/3# Mn; = &$:;.#3/; 30.00Pn. = <$#;3/## Mn. = &<9.9#&/3# 20.00
Pn3 = &;:3/3. Mn3 = $<9&:9/:< 35.00
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Pn = :3$/&3 Mn = &:$$:&&/3; 15.00
0.00 385560.00
1337985.00 288405.00
1976287.89 236685.54
2183405.63 205912.502974702.50 91035.00
2811822.53 85616.25
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3 1 6.22
2 140.00
3 1
30.00
CP
[ F'c
1 0.00[$ P$40.00 40.00
2 0.00[& P&40.00 40.00
3 0.00[; P;40.00 40.00
ina5
3#/##
/##
[ F'c
1 0.00
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25.00 30.0025.50
2 0.00[& P&10.00 30.00
3 0.00[; P;5.00 30.00
ina5
<$&/3#
.#3/;
[ F'c
1 0.00[$ P$30.00 35.00
29.75
2 0.00[& P&15.00 35.00
3 0.00[; P;5.00 35.00
ina5
:3/3.
&:9/:<
450000.00
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0.00 500000.00 1000000.00 1500000.00 200000.00
50000.00
100000.00
150000.00
200000.00250000.00
300000.00
350000.00
400000.00
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PUNTO N #& d = .#/##Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias a = ;./##
2000000.00[$ = 0.00 F's$ = 4200.00
[& = 0.00 F's& = 3000.00
[; = 0.00 F's; = 750.00
a5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t Dist/ a5 CP
Cc/ = 182070.00 3.00
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a
P$ = 64260.00 15.00P& = 30600.00 0.00
Pn& =P; = 11475.00 -15.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 546210.00
M$ = 963900.00Mn& =
M& = 0.00
M; = -172125.00
PUNTO N #. d = &#/##Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias a = $9/##
2000000.00
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$&/93[$ = 0.00 F's$ = 4200.00
[& = 0.00 F's& = 0.00
[; = 0.00 F's; = 4200.00
a5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t Dist/ a5 CP
Cc/ = 91035.00 11.50
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a
P$ = 64260.00 15.00
P& = 0.00 0.00Pn. =
P; = -64260.00 -15.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 1046902.50
M$ = 963900.00Mn. =M& = 0.00
M; = 963900.00
PUNTO N # d = $3/##Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias a = $&/93
2000000.00
$./::[$ = 0.00 F's$ = 4000.00
[& = 0.00 F's& = 2000.00
[; = 0.00 F's; = 4200.00
a5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t Dist/ a5 CP
Cc/ = 68276.25 13.62
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a
P$ = 61200.00 15.00
P& = 20400.00 0.00Pn =
P; = -64260.00 -15.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/Mcc = 929922.53
M$ = 918000.00Mn =
M& = 0.00
M; = 963900.00
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00.00 2500000.00 3000000.00 3500000.00
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[ F'c
0.001 0.00
[$0.00 35.00 40.00
34.000.00 2 0.00[&
0.00 20.00 40.00
0.00 3 0.00[;
0.00 5.00 40.00
a"Ja a6ia5 n,4ina5
&::.#3/##
$;;9<:3/##
[ F'c
0.00 1 0.00
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0.00 15.00 20.00 17.00
0.00 2 0.00[&
0.00 0.00 20.00
0.00 3 0.00[;
0.00 15.00 20.00
a"Ja a6ia5 n,4ina5
<$#;3/##
&<9.9#&/3#
[ F'c
0.00 1 0.00[$
0.00 10.00 15.00 12.75
0.00 2 0.00[&
0.00 5.00 15.00
0.00 3 0.00[;
0.00 20.00 15.00
a"Ja a6ia5 n,4ina5
:3$/&3
&:$$:&&/3;
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DIARAMA
DATOS
F'c = 210.00
F'y = 4200.00
Ø = 0.85
As$ = 7.62 7.62
As& = 5.08 5.08
As; = 7.62 7.62
SECCION DE COLUMNA
40.00 40.00
CALCULO DE CENTROID
F*("+a ZJ 6Cc/ = 285600.00 20.00
AsI = 30643.83 35.00
AsII = 20429.22 20.00
AsIII = 30643.83 5.00
367316.88
CP = 20.00
PUNTO N #$ d =Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias
P$ $9/## [$ = 0.00 F's$ =
P&[& = 0.00 F's& =
[; = 0.00 F's; =
P; Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP
Cc/ = 285600.00 0.00
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(",
P$ = 32004.00 14.00P& = 21336.00 0.00
P; = 32004.00 -14.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 0.00
M$ = 448056.00
M& = 0.00
M; = -448056.00
PUNTO N #; d =Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias a =
:/3#
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[$ = 0.00 F's$ =
P&[& = 0.00 F's& =
[; = 0.00 F's; =
P; Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP
Cc/ = 182070.00 7.25
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(",
P$ = 32004.00 14.00
P& = 10668.00 0.00
P; = -6400.80 -14.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 1320007.50
M$ = 448056.00
M& = 0.00
M; = 89611.20
PUNTO N #3 d =Ca5c*5,s d( 5as d(),"4aci,n(s *nita"ias a =
P$/;:
[$ = 0.00 F's$ =
P&[& = 0.00 F's& =
[; = 0.00 F's; =P; Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP
Cc/ = 44546.46 16.88
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(",
P$ = 8764.04 15.00
P& = 21336.00 0.00
P; = -32004.00 -15.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/Mcc = 751944.24
M$ = 131460.57
M& = 0.00
M; = 480060.00
CUADRO DE RESUMEN
Pn$ = ;9#<../## Mn$ =
Pn& = &<9</<# Mn& =
Pn; = &$:;.$/&# Mn; =Pn. = $&$;:#/## Mn. =
Pn3 = .&.&/3# Mn3 =
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Pn = $#$9#;/## Mn =
0.00 370944.00
1075523.40 297966.90
1363464.82 42642.50
1857674.70 218341.202291982.00 121380.00
2200016.70 101703.00
![Page 404: PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls](https://reader031.fdocuments.in/reader031/viewer/2022020113/5695d1251a28ab9b029551b2/html5/thumbnails/404.jpg)
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E INTERACCION
2.54 3 1
2.54 2 140.00
2.54 3 1
40.00
PLASTICO
M,4(nt, ZJ45712000.00
1072534.05
408584.40
153219.15CP
7346337.60
40.00 [
2100000.000.00
1 0.00[$4200.00 0.00 40.00 40.00
4200.00 0.00 2 0.00[&
0.00 40.00 40.00
4200.00
0.00 3 0.00[;
0.00 40.00 40.00
Ca5c*5and, 5a ca"Ja a6ia5 n,4ina5
Pn$ = ;9#<../##
Mn$ = #/##
;#/## [&3/3#
2100000.00 0.00 1 0.00
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4200.00 0.00 24.00 30.00
2100.00 0.00 2 0.00[&
0.00 10.00 30.00
840.000.00 3 0.00
[;0.00 4.00 30.00
Ca5c*5and, 5a ca"Ja a6ia5 n,4ina5
Pn; = &$:;.$/&#
Mn; = $:399./9#
9/;. [/&.
2100000.00 0.00 1 0.00[$1150.14 0.00 1.34 7.34
4200.00 0.01 2 0.00[&
0.00 12.66 7.34
4200.000.01 3 0.00
[;0.00 26.66 7.34
Ca5c*5and, 5a ca"Ja a6ia5 n,4ina5
Pn3 = .&.&/3#
Mn3 = $;;../:&
DISTANCIA
#/## 40.00
$#933&;/.# 40.00
$:399./9# 30.00&&<$<:&/## 20.00
$;;../:& 7.34 450000.00
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&&###$/9# 15.00
0.00 500000.00 100.00
50000.00
100000.00
150000.00
200000.00250000.00
300000.00
350000.00
400000.00
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F'c PUNTO N #&Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias
P$ [$ = 0.00
P&[& = 0.00
[; = 0.00
P; a5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t
Cc/ = 242760.00
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 a
P$ = 32004.00P& = 16002.00
P; = 7200.90
Ca5c*5and, (5 4,4(nt, c,n "(s%(c
Mcc = 728280.00
M$ = 448056.00
M& = 0.00
M; = -100812.60
F'c PUNTO N #.Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias
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25.50 $&/93[$ = 0.00
P&[& = 0.00
[; = 0.00
P; a5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t
Cc/ = 121380.00
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 a
P$ = 32004.00
P& = 0.00
P; = -32004.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(c
Mcc = 1395870.00
M$ = 448056.00
M& = 0.00
M; = 448056.00
F'c PUNTO N #Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias
P$6.24 ;/$&
[$ = 0.00
P&[& = 0.00
[; = 0.00P; a5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t
Cc/ = 91035.00
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 a
P$ = 32004.00
P& = 10668.00
P; = -32004.00
Ca5c*5and, (5 4,4(nt, c,n "(s%(cMcc = 1239896.70
M$ = 480060.00
M& = 0.00
M; = 480060.00
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00000.00 1500000.00 2000000.00 2500000.00 3000000.00 3500000.00
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d = .#/##a = ;./##
2100000.000.00
1 0.00F's$ = 4200.00 0.00 34.00 40.00
F's& = 3150.00 0.00 2 0.00
0.00 20.00 40.00
F's; = 945.00
0.00 3 0.00Dist/ a5 CP 0.00 6.00 40.00
3.00
c(", a5c*5and, 5a ca"Ja a6ia5 n,4ina
14.000.00
Pn& = &<9</<#-14.00
, a5 CP/
Mn& = $#933&;/.#
d = &#/##a = $9/##
2100000.00 0.00 1 0.00
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F's$ = 4200.00 0.00 14.00 20.00
F's& = 0.00 0.00 2 0.000.00 0.00 20.00
F's; = 4200.000.00 3 0.00
Dist/ a5 CP 0.00 14.00 20.00
11.50
c(", a5c*5and, 5a ca"Ja a6ia5 n,4ina
14.00
0.00Pn. = $&$;:#/##
-14.00
, a5 CP/
Mn. = &&<$<:&/##
d = $3/##a = $&/93
2100000.00 0.00 1 0.00F's$ = 4200.00 0.00 10.00 15.00
F's& = 2100.00 0.00 2 0.000.00 5.00 15.00
F's; = 4200.000.00 3 0.00
Dist/ a5 CP 0.00 20.00 15.00
13.62
c(", a5c*5and, 5a ca"Ja a6ia5 n,4ina
15.00
0.00Pn = $#$9#;/##
-15.00
, a5 CP/
Mn = &&###$/9#
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[ F'c
[$ P$ $9/##
34.00[& P&
[; P;
[ F'c
:/3#
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17.00
[& P&
[; P;
[ F'c
[$ P$/;:
12.75
[& P&
[; P;
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ACEROSDIAMETRO DE BARRA SECCION PERIMETRO PESO F'c =
%*5Jadas c4/ c4 ZJ-4 F'y =
;-:V 0.95 0.71 2.99 0.56 % =
$-&V 1.27 1.29 3.99 0.99
3-:V 1.59 1.99 4.99 1.55
;-.V 1.91 2.84 5.98 2.24
$V 2.54 5.10 7.98 3.97
$ ;-:V 3.49 10.06 11.25 7.91
" = 4.00( = 2.50
c4&
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350.00 F'c = 280.00 F'c = 210.00
4200.00 F'y = 4200.00 F'y = 4200.000.03 % = 0.03 % = 0.03
P K* P K*0.02 66.04 0.02 49.530.02 65.37 0.02 49.060.02 65.10 0.02 48.590.02 64.63 0.02 48.110.02 64.15 0.02 47.630.02 63.67 0.02 47.150.02 63.19 0.02 46.660.02 62.71 0.01 46.170.02 62.22 0.01 45.680.02 61.73 0.01 45.18
0.02 61.24 0.01 44.680.02 60.74 0.01 44.180.02 60.24 0.01 43.670.02 59.74 0.01 43.160.02 59.24 0.01 42.640.02 58.73 0.01 42.120.02 58.23 0.01 41.600.02 57.72 0.01 41.080.02 57.20 0.01 40.550.02 56.68 0.01 40.010.02 56.17 0.01 39.480.02 55.64 0.01 38.94
0.02 55.12 0.01 38.390.02 54.59 0.01 37.850.02 54.06 0.01 37.290.02 53.53 0.01 36.240.02 52.99 0.01 36.180.02 52.46 0.01 35.620.02 51.92 0.01 35.060.02 51.37 0.01 34.490.02 50.83 0.01 33.920.02 50.28 0.01 33.340.02 49.73 0.01 32.760.02 49.17 0.01 32.18
0.01 48.62 0.01 31.390.01 48.06 0.01 31.000.01 47.50 0.01 30.410.01 46.93 0.01 29.810.01 46.36 0.01 29.210.01 45.79 0.01 28.600.01 45.22 0.01 28.000.01 44.65 0.01 27.390.01 44.07 0.01 26.770.01 43.49 0.01 26.15
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0.01 42.90 0.01 25.530.01 42.32 0.01 24.900.01 41.73 0.01 24.270.01 41.14 0.01 23.640.01 40.54 0.01 23.010.01 39.95 0.01 22.370.01 39.35 0.01 21.72
0.01 38.74 0.01 21.070.01 38.14 0.01 20.420.01 37.53 0.01 19.770.01 36.92 0.01 19.110.01 36.31 0.01 18.450.01 35.69 0.01 17.780.01 35.08 0.00 17.120.01 34.45 0.00 16.440.01 33.83 0.00 15.770.01 33.21 0.00 15.090.01 32.58 0.00 14.410.01 31.94 0.00 13.72
0.01 31.31 0.00 13.030.01 30.67 0.00 12.340.01 30.03 0.00 11.640.01 29.39 0.00 10.940.01 28.75 0.00 10.230.01 28.10 0.00 9.530.01 27.45 0.00 8.820.01 26.80 0.00 8.100.01 26.14 0.00 7.380.01 25.48 0.00 6.660.01 24.82 0.00 5.930.01 24.16 0.00 5.20
0.01 23.49 0.00 4.470.01 22.82 0.00 3.740.01 22.15 0.00 3.000.01 21.48 0.00 2.250.01 20.80 0.00 1.500.01 20.12 0.00 0.750.01 19.44 0.00 0.000.01 18.750.01 18.060.00 17.370.00 16.680.00 15.98
0.00 15.290.00 14.580.00 13.880.00 13.170.00 12.470.00 11.750.00 11.040.00 10.320.00 9.600.00 8.88
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0.00 8.150.00 7.430.00 6.700.00 5.960.00 5.230.00 4.490.00 3.75
0.00 3.000.00 2.260.00 1.510.00 0.750.00 0.00
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F'c = 175.00
F'y = 4200.00% = 0.03 INTERPOLANDO
P
P K* d = 0.02 =0.01 41.04 J = 0.02 b =0.01 40.57 < = 0.02 c =0.01 40.090.01 39.61 J = 0.020.01 39.130.01 38.640.01 38.150.01 37.640.01 37.150.01 36.65
0.01 36.140.01 35.620.01 35.100.01 34.580.01 34.050.01 33.520.01 32.990.01 32.450.01 31.900.01 31.360.01 30.800.01 30.25
0.01 29.680.01 29.120.01 28.550.01 27.980.01 27.400.01 26.810.01 26.230.01 25.640.01 25.040.01 24.440.01 23.840.01 23.23
0.01 22.620.01 22.000.01 21.380.01 20.750.01 20.120.01 19.490.01 18.850.01 18.210.01 17.560.00 16.91
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0.00 16.260.00 15.600.00 14.930.00 14.260.00 13.590.00 12.910.00 12.23
0.00 11.550.00 10.860.00 10.160.00 9.470.00 8.760.00 8.060.00 7.350.00 6.630.00 5.910.00 5.190.00 4.460.00 3.73
0.00 2.990.00 2.250.00 1.500.00 0.750.00 0.00
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f'c
fy
K* pb
47.63ρ
47.2847.15 0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.020.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.020.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.010.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
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0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.010.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.010.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.010.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.00
0.00
0.00
0.000.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
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0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.000.00
0.00
0.00
0.00
0.00
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TABLA Ku VS ρ
280.00 f'c 210.00 f'c 175.00
4200.00 fy 4200.00 fy 4200.00
0.03 pb 0.02 pb 0.02
Ku ρ Ku ρ Ku
66.04 0.02 49.53 0.01 41.04
65.57 0.02 49.06 0.01 40.57
65.10 0.02 48.59 0.01 40.09
64.63 0.02 48.11 0.01 39.61
64.15 0.02 47.63 0.01 39.13
63.67 0.02 47.15 0.01 38.64
63.19 0.02 46.66 0.01 38.15
62.71 0.01 46.17 0.01 37.65
62.22 0.01 45.68 0.01 37.15
61.73 0.01 45.18 0.01 36.6561.24 0.01 44.68 0.01 36.14
60.74 0.01 44.18 0.01 35.62
60.24 0.01 43.67 0.01 35.10
59.74 0.01 43.16 0.01 34.58
59.24 0.01 42.64 0.01 34.05
58.73 0.01 42.12 0.01 33.52
58.23 0.01 41.60 0.01 32.99
57.72 0.01 41.08 0.01 32.45
57.20 0.01 40.55 0.01 31.90
56.68 0.01 40.01 0.01 31.36
56.17 0.01 37.48 0.01 30.80
55.64 0.01 38.94 0.01 30.2455.12 0.01 38.39 0.01 29.68
54.59 0.01 37.85 0.01 29.12
54.06 0.01 37.29 0.01 28.55
53.33 0.01 36.74 0.01 27.98
52.98 0.01 36.18 0.01 27.40
52.46 0.01 35.62 0.01 26.81
51.92 0.01 35.06 0.01 26.23
51.37 0.01 34.49 0.01 25.64
50.83 0.01 33.92 0.01 25.04
50.28 0.01 33.34 0.01 24.44
49.73 0.01 32.76 0.01 23.84
49.17 0.01 32.18 0.01 23.2348.62 0.01 31.57 0.01 22.62
48.06 0.01 31.00 0.01 22.00
47.50 0.01 30.41 0.01 21.38
46.93 0.01 29.81 0.01 20.75
46.36 0.01 29.21 0.01 20.12
45.79 0.01 28.60 0.01 19.49
45.22 0.01 28.00 0.01 18.85
44.65 0.01 27.39 0.01 18.21
44.07 0.01 26.77 0.00 17.56
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43.49 0.01 26.15 0.00 16.91
42.90 0.01 25.53 0.00 16.26
42.32 0.01 24.80 0.00 15.60
41.73 0.01 24.27 0.00 14.93
41.14 0.01 23.64 0.00 14.26
40.54 0.01 23.01 0.00 13.59
37.92 0.01 22.37 0.00 12.91
38.35 0.01 21.72 0.00 12.2338.74 0.01 21.07 0.00 11.55
38.14 0.01 20.42 0.00 10.86
37.33 0.01 19.77 0.00 10.16
36.92 0.01 19.11 0.00 9.47
36.31 0.01 18.45 0.00 8.76
35.69 0.01 17.78 0.00 8.06
35.08 0.00 17.12 0.00 7.35
34.45 0.00 16.44 0.00 6.63
33.83 0.00 15.77 0.00 5.91
33.21 0.00 15.09 0.00 5.19
32.58 0.00 14.40 0.00 4.46
31.94 0.00 13.72 0.00 3.7331.31 0.00 13.03 0.00 2.99
30.67 0.00 12.34 0.00 2.25
30.03 0.00 11.64 0.00 1.50
29.39 0.00 10.94 0.00 0.75
28.75 0.00 10.23 0.00 0.00
28.10 0.00 9.53
27.45 0.00 8.82
26.80 0.00 8.10
26.14 0.00 7.38
25.48 0.00 6.66
24.82 0.00 5.93
24.16 0.00 5.2023.49 0.00 4.47
22.82 0.00 3.74
22.15 0.00 3.00
21.48 0.00 2.25
20.80 0.00 1.50
20.12 0.00 0.75
19.44 0.00 0.00
18.75
18.06
17.37
16.68
15.9815.29
14.58
13.88
13.17
12.47
11.75
11.04
10.32
9.60
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8.88
8.15
7.43
6.70
5.96
5.23
4.49
3.723.00
2.26
1.51
0.75
0.00
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Ku Ku
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 47.25
0.01 49.00 0.02 49.00
0.01 49.00 0.01 46.50
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.000.01 49.00 0.01 44.46
0.01 49.00 0.02 49.00
0.01 49.00 0.01 43.62
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.01 42.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.01 49.00
0.01 49.00 0.01 49.00
0.01 49.00 0.01 38.910.01 49.00 0.02 49.00
0.01 49.00 0.01 37.40
0.02 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.01 34.58
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.000.01 49.00 0.01 31.12
0.01 49.00 0.02 49.00
0.01 49.00 0.02 49.00
0.01 49.00 0.01 29.54
0.01 49.00 0.01 28.90
0.01 49.00 0.02 49.00
0.01 49.00 0.01 27.84
0.01 49.00 0.02 49.00
0.01 49.00 0.01 49.00
x = ρ x = ρ
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0.01 49.00 0.01 25.77
0.01 49.00 0.01 24.83
0.01 49.00 0.02 49.00
0.01 49.00 0.01 49.00
0.01 49.00 0.01 49.00
0.01 49.00 0.01 49.00
0.01 49.00 0.01 21.73
0.01 49.00 0.01 49.000.01 49.00 0.01 49.00
0.01 49.00 0.01 49.00
0.02 49.00 0.01 19.49
0.01 49.00 0.01 49.00
0.01 49.00 0.01 18.04
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DIARAMA DE INTERACCIONCALCULO DE CENTRO PLASTICO
DATOS
F'c = 210. kg/cm2 " = 3/## c4 5.10 cm2 ; Ø 1
F'y = 4200. kg/cm2 Ø = 0.95 cm 2.54 cm
Ø = , 0.85 d$' = ;3/## c4
As$ = 15.30 cm2 d&' = &#/## c4 5.10 cm2 & Ø 1
As& = 10.20 cm2 d;' = 3/## c4 2.54 cm
As; = 15.30 cm2
5.10 cm2 ; Ø 1
SECCION DE COLUMNA 2.54 cm30.00 cm (b) 40.00 cm (h)
CALCULO DE CENTROIDE PLASTICO
F*("+a ZJ 6 c4 M,4(nt, ZJ4
Cc/ = 214200.00 kg 20.00 cm 4284000.00 kg-cm
AsI = 61528.95 kg 35.00 cm 2153513.25 kg-cm
AsII = 41019.30 kg 20.00 cm 820386.00 kg-cm
AsIII = 61528.95 kg 5.00 cm 307644.75 kg-cm CP 20.00
378277.20 kg 7565544.00 kg-cm
CP = 20.00 cm
PUNTO N #$ d = 40.00 cm d$' = ;3/## c4
F'c = 210.00. kg/cm2 a = .#/## c4 d;' = &#/## c4
F'y = 4200.00. kg/cm2 CP = &#/## c4 d&' = 3/## c4
As$ = 15.30 cm2 SECCION DE COLUMNA
As& = 10.20 cm2 30.00 cm (b) 40.00 cm (h)
As; = 15.30 cm2
Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias , 2000000.00 , 0.00 1 ,
[$ = , 0.00 F's$ = .&##/ ZJ/c4& , 0.00 40.00 cm 40
[& = , 0.00 F's& = .&##/ ZJ/c4& , 0.00 2 ,
, 0.00 40.00 cm 40
[; = , 0.00 F's; = .&##/ ZJ/c4&
, 0.00 3 , Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP , 0.00 40.00 cm 40
Cc/ = 214200.00 kg 0.00 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a ca"Ja a6ia5 n,4ina5
P$ = 64260.00 kg 15.00 cm
Pn$ = ;:33#/## ZJP& = 42840.00 kg 0 cm
P; = 64260.00 kg -15.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 0.00 kg-cm
Mn$ = #/## ZJc4M$ = 963900.00 kg-cm
M& = 0.00 kg-cm M; = -963900.00 kg-cm
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PUNTO N #& d = .#/## c4 d$' = ;3/## c4 F'c = 210.00. kg/cm2 a = ;./## c4 d&' = &#/## c4 F'y = 4200.00. kg/cm2 CP = &#/## c4 d;' = 3/## c4 As$ = 15.30. kg/cm2 SECCION DE COLUMNA As& = 10.20. kg/cm2 30.00 cm (b) 40.00 cm (h)
As; = 15.30. kg/cm2a5c*5, d( 5as d(),"4aci,n(s *nita"ia , 2000000.00 , 0.00 1 ,
[$ = , 0.00 F's$ = .&##/ ZJ/c4& , 0.00 35.00 40
[& = , 0.00 F's& = ;###/ ZJ/c4& , 0.00 2 , , 0.00 20.00 40
[; = , 0.00 F's; = 93#/ ZJ/c4&
, 0.00 3 , 5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"( Dist/ a5 CP , 0.00 5.00 40
Cc/ = 182070.00 kg 3.00 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a ca"Ja a6ia5 n,4ina5
P$ = 64260.00 kg 15.00 cm
Pn& = &::.#3/## ZJP& = 30600.00 kg 0 cm
P; = 11475.00 kg -15.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 546210.00 kg-cm Mn& = $;;9<:3/## ZJc4M$ = 963900.00 kg-cm
M& = 0.00 kg-cm
M; = -172125.00 kg-cm
PUNTO N #; d = $#/## c4 d$' = ;3/## c4 F'c = 210.00. kg/cm2 D = ;#/## c4 d&' = &#/## c4 F'y = 4200.00. kg/cm2 a = &3/3# c4 d;' = 3/## c4 35 As$ = 15.30. kg/cm2 CP = &#/## c4
As& = 10.20. kg/cm2 SECCION DE COLUMNA
As; = 15.30. kg/cm2 30.00 cm (b) 40.00 cm (h)
a5c*5, d( 5as d(),"4aci,n(s *nita"ia , 2000000.00 , 0.00 1 , [$ = , 0.00 F's$ = .&##/ ZJ/c4& , 0.00 25.00 30
[& = , 0.00 F's& = &###/ ZJ/c4& , 0.00 2 ,
, 0.00 10.00 30
[; = , 0.00 F's; = $###/ ZJ/c4&
, 0.00 3 ,
5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"( Dist/ a5 CP , 0.00 5.00 30
Cc/ = 136552.50 kg 7.25 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a ca"Ja a6ia5 n,4ina5
P$ = 64260.00 kg 15.00 cm
Pn; = <$&/3# ZJP& = 20400.00 kg 0 cm
P; = 15300.00 kg -15.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 990005.63 kg-cm
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M$ = 963900.00 kg-cm Mn; = &$:;.#3/; ZJc4 M& = 0.00 kg-cm
M; = 229500.00 kg-cm
PUNTO N #. d = &#/## c4 d$' = ;3/## c4
F'c = 210.00. kg/cm2 D = &#/## c4 d&' = &#/## c4
F'y = 4200.00. kg/cm2 a = $9/## c4 d;' = 3/## c4
As$ = 15.30. kg/cm2 CP = &#/## c4
As& = 10.20. kg/cm2 SECCION DE COLUMNA As; = 15.30. kg/cm2 30.00 cm (b) 40.00 cm (h)a5c*5, d( 5as d(),"4aci,n(s *nita"ia , 2000000.00 , 0.00 1 ,
[$ = , 0.00 F's$ = .&##/ ZJ/c4& , 0.00 15.00 20
[& = , - F's& = #/ ZJ/c4& , - 2 ,
, - 0.00 20 [; = , 0.00 F's; = .&##/ ZJ/c4&
, 0.00 3 , 5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"( Dist/ a5 CP , 0.00 15.00 20
Cc/ = 91035.00 kg 11.50 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a ca"Ja a6ia5 n,4ina5
P$ = 64260.00 g 15.00 cm Pn. = <$#;3/## ZJP& = 0.00 g 0 cm P; = 64260.00 kg -15.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/Mcc = 1046902.50 kg-cm
Mn. = &<9.9#&/3# ZJc4M$ = 963900.00 kg-cm M& = 0.00 kg-cm M; = 963900.00 kg-cm
PUNTO N #3 d = ;#/## c4 d$' = ;3/## c4 F'c = 210.00. kg/cm2 D = $#/## c4 d&' = &#/## c4 F'y = 4200.00. kg/cm2 a = :/3# c4 d;' = 3/## c4 ;3/ As$ = 15.30. kg/cm2 CP = &#/## c4
As& = 10.20. kg/cm2 SECCION DE COLUMNA
As; = 15.30. kg/cm2 30.00 cm (b) 40.00 cm (h)
a5c*5, d( 5as d(),"4aci,n(s *nita"ia , 2000000.00 , 0.00 1 , [$ = , 0.00 F's$ = ;###/ ZJ/c4& , 0.00 5.00 10
[& = , 0.00 F's& = .&##/ ZJ/c4& , 0.00 2 ,
, 0.00 10.00 10
[; = , 0.00 F's; = .&##/ ZJ/c4&
, 0.01 3 ,
5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"( Dist/ a5 CP , 0.00 25.00 10
Cc/ = 45517.50 kg 15.75 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5and, 5a ca"Ja a6ia5 n,4ina5
P$ = 45900.00 kg 15.00 cm
Pn3 = <<<9/3# Z P& = 42840.00 kg 0 cm
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P; = 64260.00 kg -15.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/
Mcc = 716900.63 kg-cm
Mn3 = &;<;##/; ZJc4M$ = 688500.00 kg-cm
M& = 0.00 kg-cm
M; = 963900.00 kg-cm
CUADRO DE RESUMEN DISTANCIA
Tn4 Tn c4
Mn$ = # ;: Pn$ = 40.00 cm
Mn& = $;;9<< &:: Pn& = 40.00 cm
Mn; = &$:;.$ &# Pn; = 10.00 cm
Mn. = &<9.9# <$ Pn. = 20.00 cm
Mn3 = &;<;# 9# Pn3 = 30.00 cm
0 50000 100000 150000 200000 250000 3000000
50
100
150
200
250
300
350
400
450 DIARAMA DE ITERACION
MOMENTOS Tn4
C A R A S
P U N T U A L E S
T n D
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DIARAMA DE INTERACALCULO DE CENTRO PLASTICO
DATOS
F'c = 210. kg/cm2 " = 3/## c4
F'y = 4200. kg/cm2 Ø = #/<3 c4
Ø = , 0.85 d$' = 33/## c4
As$ = 15.30 cm2 d&' = ;:/;; c4
As& = 10.20 cm2 d; = &$/9 c4
As; = 10.20 cm2 d.' = 3/## c4
As. = 15.30 cm2
SECCION DE COLUMNA30.00 cm (b) 60.00 cm (h)
CALCULO DE CENTROIDE PLASTICO
F*("+a ZJ 6 c4 M,4(nt, ZJ4
Cc/ = 321300.00 kg 30.00 cm 9639000.00 kg
AsI = 61528.95 kg 55.00 cm 3384092.25 kg
AsII = 41019.30 kg 38.33 cm 1572406.50 kg
AsIII = 41019.30 kg 21.67 cm 888751.50 kg
AsI = 61528.95 kg 5.00 cm 307644.75 kg
526396.50 kg 15791895.00 kg
CP = ;#/## c4
PUNTO N #$ d = 60.00 cm
F'c = 210.00. kg/cm2 a = #/## c4
F'y = 4200.00. kg/cm2 CP = ;#/## c4
As$ = 15.30 cm2 SECCION DE COLUMNA
As& = 10.20 cm2 30.00 cm (b) 60.00 cm (h)
F'c As; = 10.20 cm2
P$As. = 15.30 cm2
&# c4 Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias , 2000000
[$ = , 0.00 F's$ = .&##/ ZJ/c4&
P&[& = , 0.00 F's& = .&##/ ZJ/c4&
P; \ $/## [; = , 0.00 F's; = .&##/ ZJ/c4&
[. = , 0.00 F's. = .&##/ ZJ/c4&
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP
Cc/ = 321300.00 kg 0.00 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*
P$ = 64260.00 kg 25.00 cm
Pn$ =P& = 42840.00 kg 8.33 cm
P; = 42840.00 kg -8.33 cm
P. = 64260.00 kg -25.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and
Mcc = 0.00 kg-cm
Mn$ =M$ = 1606500.00 kg-cm M& = 357000.00 kg-cm
M; = -357000.00 kg-cm
M. = -1606500.00 kg-cm
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PUNTO N #& d = #/## c4 F'c = 210.00. kg/cm2 a = 3$/## c4 F'y = 4200.00. kg/cm2 CP = ;#/## c4 As$ = 15.30. kg/cm2 SECCION DE COLUMNA As& = 10.20. kg/cm2 30.00 cm (b) 60.00 cm (h)
F'c As; = 10.20. kg/cm2
P$As. = 15.30. kg/cm2
$9 c4 Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias , 2000000
[$ = 0.0021 F's$ = .&##/ ZJ/c4&
P&[& = 0.0019 F's& = ;:;;/ ZJ/c4&
P; \ $/##[; = 0.0011 F's; = &$9/ ZJ/c4&
[; = 0.0003 F's; = 3##/ ZJ/c4& Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CPCc/ = 273105.00 kg 4.50 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c
P$ = 64260.00 kg 25.00 cm
Pn& =P& = 39100.00 kg 8.33 cm P; = 22100.00 kg -8.33 cm P. = 7650.00 kg -25.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5andMcc = 1228972.50 kg-cm
Mn& =M$ = 1606500.00 kg-cm
M& = 325833.33 kg-cm
M; = -184166.67 kg-cm M. = 191250.00 kg-cm
PUNTO N #; d = $#/## c4 F'c = 210.00. kg/cm2 D = 3#/## c4 F'y = 4200.00. kg/cm2 a = .&/3# c4 As$ = 15.30. kg/cm2 CP = ;#/## c4
As& = 10.20. kg/cm2 SECCION DE COLUMNA
F'c As; = 10.20. kg/cm2 30.00 cm (b) 60.00 cm (h)
P$ As. = 15.30. kg/cm2$&/93 c4 Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias , 2000000
[$ = , 0.00 F's$ = .&##/ ZJ/c4&
P&[& = , 0.00 F's& = ;.##/ ZJ/c4&
P; \ $/##[; = , 0.00 F's; = $.##/ ZJ/c4&
[; = , 0.00 F's; = ##/ ZJ/c4&
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP
Cc/ = 227587.50 kg 8.75 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c
P$ = 64260.00 kg 25.00 cm
Pn; =P& = 34680.00 kg 8.33 cm
P; = 14280.00 kg -8.33 cm
P; = 9180.00 kg -25.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and
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Mcc = 1991390.63 kg-cm
Mn; =M$ = 1606500.00 kg-cm
M& = 289000.00 kg-cm
M; = -119000.00 kg-cm
M. = 229500.00 kg-cm
PUNTO N #. d = &#/## c4
F'c = 210.00. kg/cm2 D = .#/## c4
F'y = 4200.00. kg/cm2 a = ;./## c4
As$ = 15.30. kg/cm2 CP = ;#/## c4
As& = 10.20. kg/cm2 SECCION DE COLUMNA F'c As; = 10.20. kg/cm2 30.00 cm (b) 60.00 cm (h)
P$ :/3# c4 As. = 15.30. kg/cm2
Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias , 2000000.
[$ = , 0.00 F's$ = .&##/ ZJ/c4&
P& \ $/##[& = , 0.00 F's& = &93#/ ZJ/c4&
P; \ $/## [; = , 0.00 F's; = &3#/ ZJ/c4&
[; = , 0.00 F's; = &&3#/ ZJ/c4& Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CPCc/ = 182070.00 kg 13.00 cm
Ca c* a4,s a c,nt" *c ,n ( ac(", Ca c*P$ = 64260.00 g 25.00 cm
Pn. =P& = 28050.00 kg 8.33 cm P; = 2550.00 kg -8.33 cm P. = 34425.00 kg -25.00 cm Ca c* an , ( 4,4(nt, c,n "(s%(ct, a CP/ Ca c* anMcc = 2366910.00 kg-cm
Mn. =M$ = 1606500.00 kg-cm M& = 233750.00 kg-cm M; = 21250.00 kg-cm M. = 860625.00 kg-cm
PUNTO N #3 d = ;#/## c4 F'c = 210.00. kg/cm2 D = ;#/## c4 F'y = 4200.00. kg/cm2 a = &3/3# c4
As$ = 15.30. kg/cm2 CP = ;#/## c4
As& = 10.20. kg/cm2 SECCION DE COLUMNA
F'c As; = 10.20. kg/cm2 30.00 cm (b) 60.00 cm (h)
P$ ./&3 c4 As. = 15.30. kg/cm2
Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias , 2000000.
[$ = , 0.00 F's$ = .&##/ ZJ/c4&
P& \ $/##[& = , 0.00 F's& = $9/ ZJ/c4&
P; \ $/##[; = , 0.00 F's; = $9/ ZJ/c4&
[; = , 0.00 F's; = .&##/ ZJ/c4&
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP
Cc/ = 136552.50 kg 17.25 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*
P$ = 64260.00 kg 25.00 cm
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P& = 17000.00 kg 8.33 cm Pn3 =
P; = 17000.00 kg -8.33 cm
P. = 64260.00 kg -25.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and
Mcc = 2355530.63 kg-cm
Mn3 =M$ = 1606500.00 kg-cm
M& = 141666.67 kg-cm
M; = 141666.67 kg-cm
M. = 1606500.00 kg-cm
PUNTO N # d = .#/## c4 F'c = 210.00. kg/cm2 D = &#/## c4
F'y = 4200.00. kg/cm2 a = $9/## c4
As$ = 15.30. kg/cm2 CP = ;#/## c4
As& = 10.20. kg/cm2 SECCION DE COLUMNA
As; = 10.20. kg/cm2 30.00 cm (b) 60.00 cm (h)
As. = 15.30. kg/cm2
Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias , 2000000
[$ = , 0.00 F's$ = .&##/ ZJ/c4&
[& = , 0.00 F's& = 3##/ ZJ/c4&
[; = , 0.00 F's; = .&##/ ZJ/c4&
[; = , 0.00 F's; = .&##/ ZJ/c4&
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP
Cc/ = 91035.00 kg 21.50 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*
P$ = 64260.00 kg 25.00 cm
Pn3 =P& = 5100.00 kg 8.33 cm
P; = 42840.00 kg -8.33 cm
P. = 64260.00 kg -25.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and
Mcc = 1957252.50 kg-cm
Mn3 =M$ = 1606500.00 kg-cm
M& = -42500.00 kg-cm
M; = 357000.00 kg-cm
M. = 1606500.00 kg-cm
PUNTO N #9 d = 3#/## c4
F'c = 210.00. kg/cm2 D = $#/## c4
F'y = 4200.00. kg/cm2 a = :/3# c4
As$ = 15.30. kg/cm2 CP = ;#/## c4
As& = 10.20. kg/cm2 SECCION DE COLUMNA
As; = 10.20. kg/cm2 30.00 cm (b) 60.00 cm (b)
As. = 15.30. kg/cm2
Ca5c*5, d( 5as d(),"4aci,n(s *nita"ias , 2000000
[$ = , 0.00 F's$ = ;###/ ZJ/c4&
[& = , 0.00 F's& = .&##/ ZJ/c4&
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[; = , 0.00 F's; = .&##/ ZJ/c4&
[; = , 0.00 F's; = .&##/ ZJ/c4&
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 c,nc"(t, Dist/ a5 CP
Cc/ = 45517.50 kg 25.75 cm
Ca5c*5a4,s 5a c,nt"i*ci,n d(5 ac(", Ca5c*5a
P$ = 45900.00 kg 25.00 cm
Pn3 =P& = 42840.00 kg 8.33 cm
P; = 42840.00 kg -8.33 cm
P. = 64260.00 kg -25.00 cm
Ca5c*5and, (5 4,4(nt, c,n "(s%(ct, a5 CP/ Ca5c*5and,
Mcc = 1172075.63 kg-cm
Mn3 =M$ = 1147500.00 kg-cm
M& = -357000.00 kg-cm
M; = 357000.00 kg-cm
M. = 1606500.00 kg-cm
CUADRO DE RESUMEN
Tn4 Tn
Mn$ = # 3; Pn$ =
Mn& = &<99$. ;3. Pn& =
Mn; = ;99:< ;$& Pn; =
Mn. = .&&:.$ &9& Pn. = Mn3 = .&.3; &#$ Pn3 =
Mn = ;:9:&3 $$: Pn =
Mn9 = &;$<3: <$ Pn9 =
0 50000 100000 150000 200000 250
100
200
300
400
500
600 DIARAMA DE I
MOMENTOS Tn4
C A R A S
P U N T U A L E S
T n D
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CENTRO PLCALCULO DE CENTRO PLAST
DATOS
33/## c4 d$' = F'c = 210. kg/cm2
F'y = 4200. kg/cm2
Ø = , 0.85
60 cm (h)SECCION DE COLUMNA
40.00 cm (b) 70.00 cm (h)
>>>
N/ d( ca%as d( ac(", .$$
$$ Ca%as d' Ac(",
33/## c4 d.' = 19.17 11.508.21 5.75
(b) 0.00 0.00
0.00 0.00
0.00 0.00
0.00 5.75
3/93
[ F'c
[$ P$;# c4
[&60.00 cm
P&
[; P; \ $/##
[. P. \ $/##
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[ F'c
[$ P$& c4
3$/## c4[& P&
[; P; \ $/##
[3 P. \ $/##
[ F'c
[$ P$ &$/&3 c4
.&/3 c4 [& P&
[; P; \ $/##
[. P. \ $/##
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[ F'c[$
P$$9/## c4
34 cm
[& P&
[; P; \ $/##
[. P. \ $/##
[ F'cP$
$&/93 c4 [$
&3/3# c4
[& P&
[; P; \ $/##
[. P. \ $/##
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[ F'c
$9/## c4 P$
:/3# c4 [$
[& P& \ $/##
[; P; \ $/##
[. P. \ $/##
[ F'c
[$:/3# c4 P$ ./&3 c4
[& P& \ $/##
[; P; \ $/##
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[. P. \ $/##
00
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ULARV/&3 c4 a"(a Ø a"(a Ø
;/93 c4 5.10 cm2 . Ø 1 :;g. 5.10 cm2 # Ø 1 :;g.
70.0
3:/## c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1 :;g.
3&/&3 c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1 :;g.
./3# c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1 :;g.
.#/93 c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1 :;g.
;3/## c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1 :;g.
&</&3 c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1 :;g.
&;/3# c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1 :;g.
$9/93 c4 5.10 cm2 & Ø 2 :;g. 5.10 cm2 # Ø 1 :;g.$&/## c4 5.10 cm2 & Ø 3 :;g. 5.10 cm2 # Ø 1 :;g.
/&3 c4 5.10 cm2 . Ø 4 :;g. 5.10 cm2 # Ø 1 :;g.
OIDE PLASTICO
6 c4 M,4(nt, ZJ4
35.00 cm 17493000.00 kg-cm
63.75 cm 5229960.75 kg-cm
58.00 cm 2379119.40 kg-cm
CP ;3/#
52.25 cm 2143258.43 kg-cm
46.50 cm 1907397.45 kg-cm
40.75 cm 1671536.48 kg-cm
35.00 cm 1435675.50 kg-cm
29.25 cm 1199814.53 kg-cm
23.50 cm 963953.55 kg-cm
17.75 cm 728092.58 kg-cm
12.00 cm 492231.60 kg-cm
6.25 cm 512741.25 kg-cm
36156781.50 kg-cm
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CENTRO PLASTICO COLUMNA TIPO VELEVCALCULO DE CENTRO PLASTICO " = /&3 c4
DATOS As$ = 10.20 cm2 d$' = 9;/93 c4
F'c = 210. kg/cm2 As& = 10.20 cm2 d&' = 3/93 c4
F'y = 4200. kg/cm2 As; = 10.20 cm2 d; = 39/93 c4
Ø = , 0.85 As. = 10.20 cm2 d.' = .</93 c4
SECCION DE COLUMNA As3 = 10.20 cm2 d3' = .$/93 c4
40.00 cm (b) 80.00 cm (h) As = 20.40 cm2 d' = ;;/93 c4
40.00 cm (bK) 30.00 cm (hKK) As9 = 10.20 cm2 d9' = ;</;: c4
>>>
& , ; ca%as . , 3 ca%as As: = 10.20 cm2 d:' = &#/## c4
\ \ 3/## As< = 10.20 cm2 d<' = $;/$; c4&#/### \ :/## As$# = 20.40 cm2 d$#' = /&3 c4
:/###
>>>
& , ; ca%as . , 3 ca%as
\ \ 3/##
\ &9/3# /:93
/:93 CALCULO DE CENTROIDE PLA
F*("+a ZJ 6 c4
Cc$/ = 571200.00 kg 20.00 cm
Cc&/ = 214200.00 kg 60.00 cm
AsI = 41019.30 kg 73.75 cm
AsII = 41019.30 kg 65.75 cm
AsIII = 41019.30 kg 57.75 cm
AsI = 41019.30 kg 49.75 cm
As = 41019.30 kg 41.75 cm
AsI = 82038.60 kg 33.75 cm
AsII = 41019.30 kg 39.38 cm
AsIII = 41019.30 kg 20.00 cm
AsI = 41019.30 kg 13.13 cm
As = 82038.60 kg 6.25 cm
1277631.60 kg
CP = ;;/$9 c4
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a"(a Ø 50 cm (hK) 30.00 cm (hKK)
5.10 cm2 # Ø 1 :;g.
40.00 cm (bK)
80.00 cm (b
5.10 cm2 # Ø 1 :;g.
5.10 cm2 # Ø 1 :;g.
5.10 cm2 # Ø 1 :;g.
5.10 cm2 # Ø 1 :;g.
5.10 cm2 # Ø 1 :;g.
5.10 cm2 # Ø 1 :;g.
5.10 cm2 # Ø 1 :;g.
40.00 cm (bKK)5.10 cm2 # Ø 1 :;g.5.10 cm2 # Ø 1 :;g.
80.00 cm (h)
CP ;;/$9 c4
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TRO PLASTICO COLUMNA TIPO VTEEVASTICO " = /&3 c4 a"(a Ø
As$ = 10.20 cm2 d$' = 9;/93 c4 5.10 cm2 & Ø
As& = 10.20 cm2 d&' = 3/93 c4 5.10 cm2 & Ø
As; = 10.20 cm2 d; = 39/93 c4 5.10 cm2 & Ø
As. = 10.20 cm2 d.' = .</93 c4 5.10 cm2 & Ø
As3 = 10.20 cm2 d3' = .$/93 c4 5.10 cm2 & Ø
As = 20.40 cm2 d' = ;;/93 c4 5.10 cm2 . Ø
As9 = 10.20 cm2 d9' = ;</;: c4 5.10 cm2 & Ø
As: = 10.20 cm2 d:' = &#/## c4 5.10 cm2 & Ø
As< = 10.20 cm2 d<' = $;/$; c4 5.10 cm2 & Ø As$# = 20.40 cm2 d$#' = /&3 c4 5.10 cm2 . Ø
CALCULO DE CENTROIDE PLASTICO
F*("+a ZJ 6 c4 M,4(nt, ZJ4
Cc$/ = 571200.00 kg 20.00 cm 11424000.00 kg-cm
Cc&/ = 214200.00 kg 60.00 cm 12852000.00 kg-cm
AsI = 41019.30 kg 73.75 cm 3025173.38 kg-cm
AsII = 41019.30 kg 65.75 cm 2697018.98 kg-cm
AsIII = 41019.30 kg 57.75 cm 2368864.58 kg-cm
AsI = 41019.30 kg 49.75 cm 2040710.18 kg-cm
As = 41019.30 kg 41.75 cm 1712555.78 kg-cm
AsI = 82038.60 kg 33.75 cm 2768802.75 kg-cm
AsII = 41019.30 kg 39.38 cm 1615134.94 kg-cm
AsIII = 41019.30 kg 20.00 cm 820386.00 kg-cm
AsI = 41019.30 kg 13.13 cm 538378.31 kg-cm
As = 82038.60 kg 6.25 cm 512741.25 kg-cm
1277631.60 kg 42375766.13 kg-cm
CP = ;;/$9 c4
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25.00 cm (hK) 30.00 cm (hKK) 25.00 cm (hK) CALCULO DE
80.00 cm (b)
40.00 cm (bK) >>>
DATOS
F'c =
F'y = 4
Ø = ,
SECCION DE CO
30.00 cm (b) 120
50.00 cm (bK) 30.
40.00 cm (bKK) >>> >>>
& , ; ca%as .
\ \ &3/### \
80.00 cm (h)
>>>
& , ; ca%as .
\ \
\ $9/3#
;;/$9 c4
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A TIPO VUV" = /&3 c4 a"(a Ø a"(a Ø
d$' = 9;/93 c4 5.10 cm2 . Ø 1 :;g. 5.10 cm2 # Ø 1
d&' = ;/93 c4 5.10 cm2 . Ø 1 :;g. 5.10 cm2 # Ø 3/8
d; = 3;/93 c4 5.10 cm2 . Ø 1 :;g. 5.10 cm2 # Ø 1
d.' = .;/93 c4 5.10 cm2 . Ø 1 :;g. 5.10 cm2 # Ø 1
d3' = ;;/93 c4 5.10 cm2 . Ø 1 :;g. 5.10 cm2 # Ø 1
d' = &;/93 c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1
d9' = ;$/:: c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1
d:' = $3/## c4 5.10 cm2 & Ø 1 :;g. 5.10 cm2 # Ø 1
d<' = $#/; c4 5.10 cm2 . Ø 1 :;g. 5.10 cm2 # Ø 1 d$#' = /&3 c4 5.10 cm2 ; Ø 1 :;g. 5.10 cm2 # Ø 1
LCULO DE CENTROIDE PLASTICO
F*("+a ZJ 6 c4 M,4(nt, ZJ4
642600.00 kg 15.00 cm 9639000.00 kg-cm
267750.00 kg 55.00 cm 14726250.00 kg-cm
267750.00 kg 55.00 cm 14726250.00 kg-cm
82038.60 kg 73.75 cm 6050346.75 kg-cm
82038.60 kg 63.75 cm 4409574.75 kg-cm
82038.60 kg 53.75 cm 5229960.75 kg-cm
82038.60 kg 43.75 cm 3589188.75 kg-cm
82038.60 kg 33.75 cm 2768802.75 kg-cm
41019.30 kg 23.75 cm 974208.38 kg-cm
41019.30 kg 31.88 cm 1307490.19 kg-cm
41019.30 kg 15.00 cm 615289.50 kg-cm
82038.60 kg 10.63 cm 871660.13 kg-cm
61528.95 kg 6.25 cm 384555.94 kg-cm
1854918.45 kg 65292577.88 kg-cm
;3/&# c4
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30.00 cm (hK)
50.00 cm (bK) >>>
30.00 cm (bKK) >>>
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DISEÑO DE COLUMNAS $"a WIPOTESIS V$/31CM$/:1CV
DATOS SECCION DE COLUMNA F'c = &$#/ ZJ-c4& .#/## c4 .#/## c4 ! P* = &$/#3 Tn 5n = ;##/## c4
M* = #/9$ Tn4 "(c*"i4/ = ./## c4 M$ = #/;;3: Tn4 " = $&/##M& = #/<9< Tn4
Pa"a ()(ct,s 5,ca5(s s( %*(d(n d(s%"(cia" si Ln-" 0 ;.$&1M$-M&Ln-" ;.$&1M$-M&
&3/## ;</99
]5 = $/## Ca5c*5, d(5 Mc
Mc = #/9$ Tn4 J = #/:#
En (5 (( G d,nd( K = #/9:
En (5 (( ( = #/&9 c4d,nd( K1(-t = #/##3;
Pa"a (sta !i%,t(sis c,4, n, (sta a)(ctada %," 5a d( sis4, s,5,_*( da"a c,n 5a ),"4*5a Mc=]51M*v
Si c*4%5(` y ya n, (sn(c(sa"i, ca5c*5a" ]5 = $
Est, (s %a"a i" a5 c*ad", d( aac,s d( *ndiaJ"a4a d( it("aci,n d( c,5*4na