PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls

7/23/2019 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 definitivo , de&" -!"## m

Predimensionamiento de la 'iga en 'oladi/o en el de $"##m"

Luz libre del portico principal L 0"1# m

#"*# 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



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



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$


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


T #"!! m

"$$ 5 >

FALLA DUCTIL

C = 0

si ).m(le lase))ion

si ).m(le lase))ion



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


!#"## )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$



+ !"## 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


!#"## )m !!"## )m

2$50.00 cm2


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$


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 """


si ).m(le lase))ion

si ).m(le lase))ion



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



/ 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



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



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





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




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 .



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



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



!!"## )m



gan



RETO

cas d

una



Ln

B

Coondi)io

J /

Condi)io

b J /

bKd J

L












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


%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











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





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 definitivo % de&" #"!# m



Predimensionamiento de la 'iga en 'oladi/o en el de $"##m"Luz libre del portico principal L 0"1# m

#"*# 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


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





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$



+ !"## 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$


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



,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$



+ !"## 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$


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$


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



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 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


,*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



URALES P0 P$

"## Tn 0$"## Tn

!"## m

>"## m C=$

#"*# m$"## m 0"*# m

$"## m

-#"## m

#"!# m

-#"## m

-#"## m

#"*# m

ARIATEGUI



-#"## 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


T #"!! m

"$$ 5 >$"## m 0"*# m

FALLA DUCTIL$"## m

Falla &ragil (or a(lastamiento de,ido a )argas a9ialese9e)i'as



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


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



!#"## )m#"## )m



L(;

= $.5

= #.5= !.5

rio

te por vigas

rio



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



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



!#"## )m

!!"## )m

T

%n % de e6ea e6e

L



!#"## )m !#"## )m!!"## )m !!"## )m


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



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 .




P P1 P

0#"## Tn 0#"## Tn "## Tn

C=$

$"!# m

0"1# m $"## m $"!# m

!"*# m $"!# m

B



P P1 P

0#"## Tn 0#"## Tn "## Tn

C=$

$"!# m

0"1# m $"## m $"!# m

!"*# m $"!# m



B



!#"## )m*!"## )m















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











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











"## 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#

$"## m >"1# m !"*# m

datos

Carga m.erta $"# tn@m

Carga 'i'a 0"# tn@m

F3) $0# g@)m$

F38 >$## g@)m$



0#"## Tn "## Tn

$"!# m

$"## m $"!# m

$"!# m



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



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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. 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


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



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#



N-L(EO N-L(EO

0.011#1 0.0122!

HVALUE HVALUE

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

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


"""""" """"""

"!.$$ 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




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


-s J 2!.4# cm2


As """"""

A3s "0.$# cm2

P N-L(EO

P3 "0.0004

As0

M.0 M.0

M.=M.0

As0 A3s



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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. 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


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



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

""""" """""


31.22 cm2 32.2# cm2

2.31 cm2 4.50 cm2

0.01$5 0.01##

0.0013 0.002



0.012 0.012

0.011#1 0.0122!

SI FLUQE SI FLUQE

LEMENTE REFORADAS



#$ )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


"""""" """"""

"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




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#


-s J 11.02 cm2


As """"""

A3s "15.!# cm2

P N-L(EO

P3 "0.00#5

As0

M.0 M.0

M.=M.0

As0 A3s



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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 0.11

M 1 J 0.11$

M 2 J 1.5$#

P J 0.005#



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



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


11.$! cm2 12.3 cm2


"""""" """"""

"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

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 0.13

0.132 0.144

1.53 1.551

0.00 0.00$2

SIMPLEM" REFORADA SIMPLEM" REFORADA11.$! cm2 12.3 cm2


"""""" """"""

"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




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


-s J 2$.2# cm2


As """"""

A3s "2.35 cm2

P N-L(EO

P3 "0.0012

As0

M.0 M.0

M.=M.0

As0 A3s



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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. 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$



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



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#


""""" """""


2!.5 cm2 30.54 cm2

0.4 cm2 2.$5 cm2

0.01 0.01$#

0.0004 0.001

M.0



0.012 0.012

0.011#1 0.0122!

SI FLUQE SI FLUQE

LEMENTE REFORADAS



#$ )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


"""""" """"""

"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




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 """""


As 31.00 cm2

A3s 0.3# cm2

P 0.014

P3 0.0002

As0

M.0

M.=M.0

As0 A3s



P = P3 0.012

VERF" 0.01115

SI FLUQE


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. 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


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



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$


""""" """""


32.4 cm2 33.5$ cm2

3.54 cm2 5.$! cm2

0.01#2 0.01!

0.0020 0.0034



0.012 0.012

0.011#1 0.0122!

SI FLUQE SI FLUQE

LEMENTE REFORADAS



#$ )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


"""""" """"""

"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




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##


-s J 1.! cm2


As """"""

A3s "10.#2 cm2

P N-L(EO

P3 "0.005$

As0

M.0 M.0

M.=M.0

As0 A3s



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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 0.1

M 1 J 0.1$$

M 2 J 1.51#

P J 0.00##

ceueo de P J SIMPLEM" REFORADA -s J 1.! cm2


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



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


1$.! cm2 1#.!4 cm2


"""""" """"""

"#.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

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" REFORADA1$.! cm2 1#.!4 cm2


"""""" """"""

"#.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




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


-s J 24.2 cm2


As """"""

A3s "4.33 cm2

P N-L(EO

P3 "0.0023

As0

M.0 M.0

M.=M.0

As0 A3s



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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. 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


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



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 """""


"""""" 2#.33 cm2

"1.4$ cm2 0.55 cm2

N-L(EO 0.015

"0.000# 0.0003



N-L(EO 0.012

0.011#1 0.0122!

HVALUE SI FLUQE

LEMENTE REFORADAS



#$ )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


"""""" """"""

"$.0$ 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




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!


-s J 2.24 cm2


As """"""

A3s "3.11 cm2

P N-L(EO

P3 "0.001

As0

M.0 M.0

M.=M.0

As0 A3s



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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. 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



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



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$!


2#.$ cm2 """""


"""""" 2!.! cm2

"0.1$ cm2 1.!0 cm2

N-L(EO 0.01$3

"0.0001 0.0011



N-L(EO 0.012

0.011#1 0.0122!

HVALUE SI FLUQE

LEMENTE REFORADAS



#$ )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


"""""" """"""

"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




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 """"""


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$


-s J 12.$ cm2


As """"""

A3s "14.44 cm2

P N-L(EO

P3 "0.00$

As0

M.0 M.0

M.=M.0

As0 A3s



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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 """"""


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


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



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


13.5$ cm2 14.25 cm2


"""""" """"""

"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

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 0.15

0.152 0.1

1.543 1.52!

0.00$ 0.00#3

SIMPLEM" REFORADA SIMPLEM" REFORADA13.5$ cm2 14.25 cm2


"""""" """"""

"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




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 """""


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



P = P3 0.012

VERF" 0.01115

SI FLUQE


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. 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



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



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


""""" """""


34.$3 cm2 35.!4 cm2

5.#1 cm2 #.1 cm2

0.01!5 0.0210

0.0033 0.004#

M.0



0.012 0.012

0.011#1 0.0122!

SI FLUQE SI FLUQE

LEMENTE REFORADAS



#$ )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 """""


"""""" 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




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


-s J 30.0 cm2


As """"""

A3s "0.01 cm2

P N-L(EO

P3 0.0000

As0

M.0

M.=M.0

As0 A3s



P = P3 N-L(EO

VERF" 0.01115

HVALUE


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. 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


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



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


""""" """""


32.05 cm2 33.14 cm2

3.13 cm2 5.3 cm2

0.01#0 0.01!3

0.001# 0.0031



0.012 0.012

0.011#1 0.0122!

SI FLUQE SI FLUQE

LEMENTE REFORADAS



#$ )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


"""""" """"""

"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



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( *& =





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( *; =





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





DISE O POR CORTANTE

F'c = 210. kg/cm2

F'y = 4200. kg/cm2


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


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( *. =





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( *. =





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


64. cm 61. cm 59. cm19661.90 kg 18740.25 kg 18125.81 kg



Si C*4%5( Si C*4%5( Si C*4%5(


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

;/&#3 4 &/9# 4 ;/<.# 4





DISE O POR CORTANTE

F'c = 210. kg/cm2

F'y = 4200. kg/cm2


Av = 0.71 cm2

β = 0.85

Ø = 0.85

distancia = ;/&#3 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( *. =





;/<.# 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

./3.# 4






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


-s J 21.1 cm2


As """"""

A3s "3.$ cm2

As0

M.0 M.0

M.=M.0

As0 A3s



P N-L(EO

P3 "0.0023

P = P3 N-L(EO

VERF" 0.01115

HVALUE




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!


-s J 15.53 cm2


As0

M.0 M.0

M.=M.0

As0 A3s



As """"""

A3s "#.22 cm2

P N-L(EO

P3 "0.0051

P = P3 N-L(EO

VERF" 0.01115

HVALUE



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$


23.05 cm2 """""


"""""" 24.33 cm2

"1.21 cm2 0.52 cm2

M.0



N-L(EO 0.01

"0.000# 0.0004

N-L(EO 0.012

0.011#1 0.0122!

HVALUE SI FLUQE



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


1.$4 cm2 1$.! cm2


M.0



"""""" """"""

".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



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



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




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



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



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

""""" -s J

A

31.4# cm2 As

$. cm2 A3s

As0

M.0 M.0

M.=M.0

As0 A3s



0.0214 P

0.0052 P3

0.012 P = P3

0.0122!VERF"

SI FLUQE



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


""""" -s J

A

As0

M.0 M.0

M.=M.0

As0 A3s



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 -@>




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$$


10.!5 cm2 11.$3 cm2

ALISIS O VERIFICACION DE UNA SECCION DO+LEMENTE REFORADA

"""""" """"""

"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




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$$


10.!5 cm2 11.$3 cm2




"""""" """"""

"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



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.

,4d$

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?

"""""" As Total As

"!.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

M.=M.0

As0 A3s



N-L(EO P

"0.002 P3

N-L(EO P = P3

0.0122!VERF"

HVALUE



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.

,4d$

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?

"""""" As Total As

"!.0# cm2 Total A3s

03 capas DATOS

0.5! a J

"1.00 b J

0.15 c J

0.1# M 1 J

1.52$ M 2 J

0.00#4 P J


12.33 cm2 -s J

A

As0

M.0 M.0

M.=M.0

As0 A3s



"""""" As

"!.0# cm2 A3s

N-L(EO P

"0.002 P3

N-L(EO P = P3

0.0122!VERF"

HVALUE

$ Ø 0

0 Ø -@>




TOS

0.#5

0.!0

30. cm

0. cm5. cm

5. cm

54. cm

51. cm

4!. cm

#0 )a(a #$ )a(as

45!1000. g.cm 45!1000. 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

25#10.#5 g.cm $21.30 g.cm

1.3! cm2 4.1# cm2

2$.4 cm2 2#.! cm2

1.3! cm2 4.1# cm2

01 capa 02 capas

0.5! 0.5!

"1.00 "1.00

0.2# 0.31

0.350 0.411

1.345 1.2#4

0.01$5 0.0205


""""" """""


2$.4 cm2 2#.! cm2

1.3! cm2 4.1# cm2



0.01$1 0.01#!

0.000! 0.002$

0.012 0.012

0.01115 0.011#1

SI FLUQE SI FLUQE




TOS

0.#5

0.!030. cm

0. cm

5. cm

5. cm

54. cm

51. cm

4!. cm

#0 )a(a #$ )a(as

35#3000. g.cm 35#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

"$4!#!3.15 g.cm "2#1#33.$0 g.cm

"4.05 cm2 "1.2 cm2

"""""" """"""

"4.05 cm2 "1.2 cm2

01 capa 02 capas

0.5! 0.5!

"1.00 "1.00

0.22 0.24

0.255 0.2!4

1.440 1.401

0.012# 0.014$


20. cm2 22.4! cm2




"""""" """"""

"4.05 cm2 "1.2 cm2

N-L(EO N-L(EO

"0.0025 "0.0011

N-L(EO N-L(EO

0.01115 0.011#1

HVALUE HVALUE



DA

'iga,

% r

d3

d

#0 )a(a

#$ )a(as

#- )a(as

#- )a(as DATOS

45!1000. 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$53.10 g.cm B.4,4d$

102334.!0 g.cm Mr Mr

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0.34 c J0.45 M 1 J

1.230 M 2 J

0.0232 P J


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35$53.10 g.cm B.4,4d$

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0.0! cm2 Total A3s

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0.32 M 1 J

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210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

0.02 0.02

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4332#!3.15 g.cm 3#4#33.$0 g.cm

$$110.#5 g.cm 123!1.30 g.cm

4.1 cm2 $.13 cm2

30.41 cm2 31.!1 cm2

4.1 cm2 $.13 cm2

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0.40 0.4#5

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54. cm

51. cm

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3!!0000. g.cm 3!!0000. g.cm

210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

0.02 0.02

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4332#!3.15 g.cm 3#4#33.$0 g.cm

"342#!3.15 g.cm 1251.30 g.cm

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M. B.

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35$53.10 g.cm B.4,4d$

15334.!0 g.cm Mr Mr

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M. A3s

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0.3$ c J0.50 M 1 J

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35$53.10 g.cm B.4,4d$

42234.!0 g.cm Mr Mr

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51. cm

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2!!1000. g.cm 2!!1000. g.cm

210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

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54. cm

51. cm

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2!!1000. g.cm 2!!1000. g.cm

210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

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"1341#!3.15 g.cm "#$3#33.$0 g.cm

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01 capa 02 capas

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"3.4$ cm2 Total A3s

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0.22 c J0.25! M 1 J

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M. B.

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35$53.10 g.cm B.4,4d$

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"3.4$ cm2 A3s

M. A3s

4F384<d=d3?

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"3.4$ cm2 Total A3s

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0.22 c J

0.25! M 1 J

1.43 M 2 J

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0. cm4. cm

5. cm

54. cm

51. cm

4!. cm

#0 )a(a #$ )a(as

42#0000. g.cm 42#0000. g.cm

210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

0.02 0.02

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2.24 cm2 24.$! cm2

4332#!3.15 g.cm 3#4#33.$0 g.cm

"52#!3.15 g.cm 4151.30 g.cm

"0.2! cm2 2.3! cm2

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"0.2! cm2 2.3! cm2

01 capa 02 capas

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0.!030. cm

0. cm

4. cm

5. cm

54. cm

51. cm

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3304000. g.cm 3304000. g.cm

210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

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4332#!3.15 g.cm 3#4#33.$0 g.cm

"102##!3.15 g.cm "50#33.$0 g.cm

"5.55 cm2 "3.23 cm2

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01 capa 02 capas

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1#.$5 cm2 20.32 cm2




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HVALUE HVALUE



DA

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42#0000. g.cm M.

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4200. gcm2 &38

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4!.53 B.

M. B.

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23.#1 cm2 As P4,4d

35$53.10 g.cm B.4,4d$

$1234.!0 g.cm Mr Mr

4.2# cm2 A3s

M. A3s

4F384<d=d3?

2#.10 cm2 As Total As

4.2# cm2 Total A3s

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0.31 c J0.41$ M 1 J

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35$53.10 g.cm B.4,4d$

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4F384<d=d3?

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"1.5! cm2 Total A3s

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0.5! a J

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0.24 c J

0.2!4 M 1 J

1.401 M 2 J

0.014$ P J


21.5$ cm2 -s J

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0.#5

0.!0

30. cm

0. cm5. cm

5. cm

54. cm

51. cm

4!. cm

#0 )a(a #$ )a(as

440#000. g.cm 440#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

$510.#5 g.cm 5431.30 g.cm

0.41 cm2 3.12 cm2

2.5 cm2 2$.!1 cm2

0.41 cm2 3.12 cm2

01 capa 02 capas

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0.331 0.3#$

1.34 1.30$

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SI FLUQE SI FLUQE




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0.#5

0.!030. cm

0. cm

5. cm

5. cm

54. cm

51. cm

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351000. g.cm 351000. g.cm

210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

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"4.41 cm2 "2.01 cm2

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01 capa 02 capas

0.5! 0.5!

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20.20 cm2 21.! cm2




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HVALUE HVALUE



DA

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440#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$53.10 g.cm B.4,4d$

#4034.!0 g.cm Mr Mr

5.05 cm2 A3s

M. A3s

4F384<d=d3?

2#.#$ cm2 As Total As

5.05 cm2 Total A3s

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0.5! a J

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0.32 c J0.43 M 1 J

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351000. g.cm M.

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4200. gcm2 &38

0.02 Pma9

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35$53.10 g.cm B.4,4d$

"5153.10 g.cm Mr Mr

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"0.31 cm2 Total A3s

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0.5! a J

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0.2 c J

0.31# M 1 J

1.3$$ M 2 J

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0.#5

0.!0

30. cm

0. cm5. cm

5. cm

54. cm

51. cm

4!. cm

#0 )a(a #$ )a(as

22#3000. g.cm 22#3000. g.cm

210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

0.02 0.02

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2.24 cm2 24.$! cm2

4332#!3.15 g.cm 3#4#33.$0 g.cm

"204!#!3.15 g.cm "15#1#33.$0 g.cm

"11.0$ cm2 "!.10 cm2

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01 capa 02 capas

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0.14 0.15

0.152 0.1$2

1.543 1.523

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12.2# cm2 13.1# cm2


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0.#5

0.!030. cm

0. cm

5. cm

5. cm

54. cm

51. cm

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22#3000. g.cm 22#3000. g.cm

210. gcm2 210. gcm2

4200. gcm2 4200. gcm2

0.02 0.02

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4332#!3.15 g.cm 3#4#33.$0 g.cm

"204!#!3.15 g.cm "15#1#33.$0 g.cm

"11.0$ cm2 "!.10 cm2

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01 capa 02 capas

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0.14 0.15

0.152 0.1$2

1.543 1.523

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12.2# cm2 13.1# cm2




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HVALUE HVALUE



DA

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#0 )a(a

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22#3000. g.cm M.

210. gcm2 &3)

4200. gcm2 &38

0.02 Pma9

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M. B.

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35$53.10 g.cm B.4,4d$

"12#453.10 g.cm Mr Mr

"$.$2 cm2 A3s

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"$.$2 cm2 Total A3s

03 capas DATOS

0.5! a J

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0.1$ c J0.1#! M 1 J

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22#3000. g.cm M.

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4200. gcm2 &38

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M. B.

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35$53.10 g.cm B.4,4d$

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0.5! a J

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0.1#! M 1 J

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HVALUE

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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

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31.# cm2 33.2 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




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$!


24.!! cm2 """""




"""""" 2.5 cm2

"0.# cm2 1.$$ cm2

N-L(EO 0.01$4

"0.0005 0.0012

N-L(EO 0.012

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HVALUE SI FLUQE



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?


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


""""" -s J

A

34.4 cm2 As

10.5 cm2 A3s

As0

M.0 M.0

M.=M.0

As0 A3s



0.0234 P

0.00$2 P3

0.012 P = P3

0.0122!VERF"

SI FLUQE



DA

'iga,

%

r

d3

d

#0 )a(a

#$ )a(as

#- )a(as

#- )a(as DATOS

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


""""" -s J

A

As0

M.0 M.0

M.=M.0

As0 A3s



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




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#


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30.13 cm2 31.2 cm2

3.#! cm2 .#3 cm2



0.01# 0.020$

0.0024 0.0045

0.012 0.012

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SI FLUQE SI FLUQE




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$#


24.$$ cm2 """""




"""""" 2.3! cm2

"1.02 cm2 1.1 cm2

N-L(EO 0.01$2

"0.000 0.0010

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HVALUE SI FLUQE



#- )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

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32.$4 cm2

#.!3 cm2



0.0223

0.001

0.012

0.0122!

SI FLUQE



#- )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



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( *& =



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( *& =



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(

*$ =



/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( *& =

*$ =



#$ 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( *& =



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( *& =



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( *& =



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

*$ =



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( *& =



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( *& =



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



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


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



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


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(



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



#& ca%as #; ca%as

51. cm 49. cm11751.06 kg 11290.23 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



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



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



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



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(


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



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


11.37 cm 10.73 cm25.50 cm 24.50 cm60.00 cm 60.00 cm



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



kg

#& ca%as #; ca%as

51. cm 49. cm11751.06 kg 11290.23 kg



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(


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



DISE O POR CORTANTE

F'c = 210. kg/cm2

F'y = 4200. kg/cm2


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


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( *; =



DISEÑO POR CORTANTE

F'c = 210. kg/cm2

F'y = 4200. kg/cm2


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( *; =




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


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=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 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


Av = 0.71 cm2

β = 0.85

Ø = 0.85

distancia = $/39 4 $/; 434544.10 kg

= 30. cm

! = 60. cm " = 5. cm

C,"tant( *; =

*& =



#$ ca%a #& ca%as

d = 54. cm 51. cm

c =12442.30 kg 11751.06 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=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( *; =



DISE O POR CORTANTE

F'c = 210. kg/cm2

F'y = 4200. kg/cm2


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


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( *; =




F'c = 210. kg/cm2

F'y = 4200. kg/cm2


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


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=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( *; =




F'c = 210. kg/cm2

F'y = 4200. kg/cm2


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


S = 14.73 cm 13.48 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=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


F'c = 210. kg/cm2

F'y = 4200. kg/cm2


Av = 0.71 cm2

β = 0.85Ø = 0.85

distancia = $/& 4 $/;< 4

C,"tant( *; =



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


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( *; =



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( *. =



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( *. =



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

*; =



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( *. =

*; =



#; 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( *. =



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( *. =



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( *. =



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 , =

*; =



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( *. =



=

! =

" =

#; 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( *. =



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


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


Si C*4%5( Si C*4%5( Si C*4%5(


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




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


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


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




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



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 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




54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 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



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



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


54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg



Si C*4%5( Si C*4%5( Si C*4%5(


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




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


54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg





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




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


54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 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



13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 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


210. kg/cm2

4200. kg/cm2

50 cm (b) 65 cm (h)

0.71 cm2

0.850.85

&/& 4 $/<< 4 $/99 4



16172.10 kg30. cm60. cm5. cm


54. cm 51. cm 49. cm12442.30 kg 11751.06 kg 11290.23 kg



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



Est"i,s 8 = $ 8 #/#3@ & 8 #/&3@ & 8

Est"i,s 8 = $ 8 #/#3@ & 8 #/#93@ ; 8 #/$#@ ;



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( *. =



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(

*; =



/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( *. =

*; =



#$ 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( *. =



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( *. =



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( *. =



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

*; =



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( *. =



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( *. =



#/&3@ Rst,/ 8 #/&3

#/$3@ & 8 #/&#@ Rst,/ 8 #/&3



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



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


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 0.00

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



#& ca%as #; ca%as

51. cm 49. cm11751.06 kg 11290.23 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(


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



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


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 =



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



ORTANTE

m2

cm2

65 cm (h)

2

&/3$ 4 &/## 4 kg

#& ca%as #; ca%as

51. cm 49. cm11751.06 kg 11290.23 kg


16.80 cm 15.74 cm25.50 cm 24.50 cm60.00 cm 60.00 cm



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



kg

#& ca%as #; ca%as

51. cm 49. cm11751.06 kg 11290.23 kg



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?





$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ . 8 #/$3@ Rst

$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ & 8 #/$3@ & 8 #/&#





$ 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


Av = 0.71 cm2

β = 0.85

Ø = 0.85

distancia = ;/&; 4 &/:# 413863.50 kg

= 30. cm

! = 60. cm " = 5. cm

*; =



#$ ca%a #& ca%as

d = 54. cm 51. cm

c =12442.30 kg 11751.06 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=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( *. =



$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ & 8 #/&3@ Rs

$ 8 #/#3@ 3 8 #/$#@ . 8 #/$&3@ & 8 #/$3@ & 8 #/&



$ 8 #/#3@ . 8 #/$&3@ . 8 #/$3@ ; 8 #/$93@ Rs

$ 8 #/#3@ ; 8 #/#93@ . 8 #/$#@ . 8 #/$3@ ; 8 #/$




F'c = 210. kg/cm2

F'y = 4200. kg/cm2


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

*; =



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( *. =



$ 8 #/#3@ ; 8 #/$3@ & 8 #/&&3@ & 8 #/&&3@ Rs

$ 8 #/#3@ & 8 #/$#@ & 8 #/$3@ ; 8 #/$93 & 8 #/&#@





,/ 8 #/&3

@ Rst,/ 8 #/&3





,/ 8 #/&3

@ Rst,/ 8 #/&3

F'c =

F'y =

COLUMNA=

Av =

β =

Ø =

;/<9 4 distancia =

=

! =" =

*; =



#; 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( *. =



,/ 8 #/&3

@ Rst,/ 8 #/&3



t,/ 8 #/&3

3@ & 8 #/&#@ Rst,/ 8 #/&3



&/.3 4

#; ca%as

49. cm11290.23 kg

R()*("+, Mini4,687.30 kg

425.20 cm24.50 cm60.00 cm



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?



, 8 #/&&3/

Rst,/ 8 #/&&3









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




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


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









/$#@ . 8 #/$&3@ . 8 #/$3@ ; 8 #/$3@ Rst,/ 8 #/&3

/#93@ . 8 #/$#@ . 8 #/$&3@ 9 8 #/$3@ & 8 #/&#@ R













Est"i,s 8 = $ 8 #/#3@ 9 8 #/#93@ 3 8 #/$#@

Est"i,s 8 = $ 8 #/#3@ 9 8 #/#93@ 3 8 #/$#@ .









t,/ 8 #/&3













8 #/&3@ & 8 #/&3@ Rst,/ 8 #/&3

8 #/$3@ & 8 #/&#@ Rst,/ 8 #/&3













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




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


M* 31.158 kg-cm 28.973 kg-cm 27.516 kg-cm





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


M* 31.158 kg-cm 28.973 kg-cm 27.516 kg-cm





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


M* 31.158 kg-cm 28.973 kg-cm 27.516 kg-cm




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*$ =





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





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





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& =





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





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*$ =





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& =





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*$ =





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& =





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





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



01 CAPA 02 CAPAS

2.50

S46 20 cm

As

$RA CONDICINA5=&1At16$y$-s

AtAt0=&1Av

&da CONDICINs0=$y$-3



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



01 CAPA 02 CAPAS

12.50$RA CONDICIN

A5=&1At16$y$-s



45 cm15 cm

60 cm 45 cm

35 cm

1

2





$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 =



$IE" $E UR"



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


AJ = 2700.00 cm2

ØPn = 201451.25 kg




P = , 0.00 Ø ;-:V 8 = 40.00 cm As = 1.62 cm2 Ø $-&V 8 = 75.00 cm


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



a"(a Ø ;-:V =a"(a Ø $-&V =

a"(a Ø ;-:V =a"(a Ø $-&V =



$IE" $E UR"



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


AJ = 1400.00 cm2

ØPn = 80705.63 kg




P = , 0.00 Ø ;-:V 8 = 40.00 cm As = 1.68 cm2 Ø $-&V 8 = 75.00 cm


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



a"(a Ø ;-:V =a"(a Ø $-&V =

a"(a Ø ;-:V =a"(a Ø $-&V =



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 =




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


ETERIORX4a6 = #/;$

#/&&

SI PASA

INTERIORX4a6 = #/;9

#/&&

SI PASA

CONDICIONETERIOR

CONDICIONINTERIOR

X4a6 $"ac,ndici,n =

X4a6 &dac,ndici,n =




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


ETERIORX4a6 = #/;$

#/&$

SI PASA

INTERIORX4a6 = #/;9

#/&$

SI PASA

CONDICIONETERIOR

CONDICIONINTERIOR

X4a6 $"ac,ndici,n =

X4a6 &dac,ndici,n =



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



[$ = 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


P$ = 64260.00 15.00

P& = 20400.00 0.00Pn; = &#3

P; = -15300.00 -15.00


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


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<$&/3# Mn; = &$:;.#3/; 30.00Pn. = <$#;3/## Mn. = &<9.9#&/3# 20.00

Pn3 = &;:3/3. Mn3 = $<9&:9/:< 35.00



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



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



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



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



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


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



$&/93[$ = 0.00 F's$ = 4200.00

[& = 0.00 F's& = 0.00

[; = 0.00 F's; = 4200.00


Cc/ = 91035.00 11.50


P$ = 64260.00 15.00

P& = 0.00 0.00Pn. =

P; = -64260.00 -15.00


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


Cc/ = 68276.25 13.62


P$ = 61200.00 15.00

P& = 20400.00 0.00Pn =

P; = -64260.00 -15.00


M$ = 918000.00Mn =

M& = 0.00

M; = 963900.00



00.00 2500000.00 3000000.00 3500000.00



[ 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



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;





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


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#



[$ = 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


P$ = 32004.00 14.00

P& = 10668.00 0.00

P; = -6400.80 -14.00


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


P$ = 8764.04 15.00

P& = 21336.00 0.00

P; = -32004.00 -15.00


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 =



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



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



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


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


Pn3 = .&.&/3#

Mn3 = $;;../:&

DISTANCIA

#/## 40.00

$#933&;/.# 40.00

$:399./9# 30.00&&<$<:&/## 20.00

$;;../:& 7.34 450000.00



&&###$/9# 15.00

0.00 500000.00 100.00

50000.00

100000.00

150000.00

200000.00250000.00

300000.00

350000.00

400000.00



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



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


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


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



00000.00 1500000.00 2000000.00 2500000.00 3000000.00 3500000.00



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



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


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


15.00

0.00Pn = $#$9#;/##

-15.00

, a5 CP/

Mn = &&###$/9#





[ F'c

[$ P$ $9/##

34.00[& P&

[; P;

[ F'c

:/3#



17.00

[& P&

[; P;

[ F'c

[$ P$/;:

12.75

[& P&

[; P;





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&







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



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



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



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



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





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



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



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



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



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



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



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



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

0.01 49.00 0.00 17.38

0.01 49.00 0.01 49.00

0.01 49.00 0.01 49.00

0.01 49.00 0.00 15.11

0.01 49.00 0.01 49.00

0.01 49.00 0.01 49.00

0.01 49.00 0.01 49.000.01 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 49.00

0.01 49.00 0.01 49.00

0.01 49.00 0.01 49.00

0.01 49.00 0.00 8.55

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 49.00

0.01 49.00 0.01 49.000.01 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 49.00

0.01 49.00 0.00 1.41

0.01 49.00 0.01 49.00

0.01 49.00 #DIV/0! 49.00

0.01 49.00

0.01 49.00

0.01 49.00

0.00 16.06

0.01 49.000.01 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 49.00

0.01 49.00



0.01 49.00

0.00 7.60

0.01 49.00

0.01 49.00

0.01 49.00

0.01 49.00

0.01 49.00

0.01 49.000.01 49.00

0.01 49.00

0.00 1.26

0.01 49.00

0.00 49.00



Ku

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.000.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.000.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.00

0.02 49.000.02 49.00

0.02 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

x = ρ



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 49.000.01 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 49.00

0.01 49.00

0.01 49.00

0.01 49.00

0.01 49.000.01 49.00

0.01 49.00

0.01 49.00

0.01 49.00

#DIV/0! 49.00





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)


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



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


P$ = 64260.00 kg 15.00 cm

Pn& = &::.#3/## ZJP& = 30600.00 kg 0 cm

P; = 11475.00 kg -15.00 cm


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


P$ = 64260.00 kg 15.00 cm

Pn; = &#3<$&/3# ZJP& = 20400.00 kg 0 cm

P; = 15300.00 kg -15.00 cm


Mcc = 990005.63 kg-cm



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


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; = 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


P$ = 45900.00 kg 15.00 cm

Pn3 = <<<9/3# Z P& = 42840.00 kg 0 cm



P; = 64260.00 kg -15.00 cm


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







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)


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



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


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&


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




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


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&


Cc/ = 136552.50 kg 17.25 cm


P$ = 64260.00 kg 25.00 cm



P& = 17000.00 kg 8.33 cm Pn3 =

P; = 17000.00 kg -8.33 cm

P. = 64260.00 kg -25.00 cm


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 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&


Cc/ = 91035.00 kg 21.50 cm


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


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 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&



[; = , 0.00 F's; = .&##/ ZJ/c4&

[; = , 0.00 F's; = .&##/ ZJ/c4&


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





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. \ $/##



[ F'c

[$ P$& c4

3$/## c4[& P&

[; P; \ $/##

[3 P. \ $/##

[ F'c

[$ P$ &$/&3 c4

.&/3 c4 [& P&

[; P; \ $/##

[. P. \ $/##



[ F'c[$

P$$9/## c4

34 cm

[& P&

[; P; \ $/##

[. P. \ $/##

[ F'cP$

$&/93 c4 [$

&3/3# c4

[& P&

[; P; \ $/##

[. P. \ $/##



[ F'c

$9/## c4 P$

:/3# c4 [$

[& P& \ $/##

[; P; \ $/##

[. P. \ $/##

[ F'c

[$:/3# c4 P$ ./&3 c4

[& P& \ $/##

[; P; \ $/##



[. P. \ $/##

00





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













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













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













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


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













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













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













30.00 cm (hK)

50.00 cm (bK) >>>

30.00 cm (bKK) >>>

























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

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PREDIMENSIONAMIENTO CONCRETO ARMADO I 03_elmer.xls