ESTRUCTURACION Y PREDIMENCIONAMIENT0.docx

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ANALISIS ESTRUCTURAL IESTRUCTURACION Y PREDIMENSIONAMIENTO Y METRADO DE

CARGAS

1.- ESTRUCTURACION:

1.1.- Elección de ejes:

De acuerdo al plano de arquiecura se colocara los ejes

principales ! secundarios de acuerdo a las disancias arquiecónicas.

Se esco"ieron los ejes principales ! secundarios# o$ando las

disancias de las luces $as lar"as para ejes principales.



ANALISIS ESTRUCTURAL I

2.- PRE DIMENSIONAMIENTO:

2.1.- Pre dimensionamiento de losa aligerada:

Lu% $&s lar"a ' ($

Alura:h=

L

18h=

L

25

h= 4

18h=

4

25

h=0.22h=0.16

)alor pro$edio por proceso consruci*o h=0.17

2.2.- Pre dimensionamiento de igas

a+ )i"as que soporan losas ar$adas en una sola dirección:Lu% $&s lar"a ' ,.,




hv= L

9hv=

L

12

hv=0.59 mhv=0.45 m

)alor pro$edio por proceso consruci*ohv=0.50m

ara la /ase de )i"a principal lo 0ace$os con la si"uiene or$ula:

At ❑=m+n

2

Ree$pla%ando en la or$ula:

At ❑=4+4

2=4 m

La /ase de la *i"a principal ser&:

bv= At

20=

4

20=0.20 m

Considera$os co$o *alor $2ni$o:

bv=0.25 m

Di$ensiones de la *i"a principal




/+ )i"as secundarias:

Lu% $as lar"a ' ($

hv= L

14

hv= 4

14=0.29 m

hv=0.30m

La /ase de la *i"a secundaria

bvs=0.30

2=0.15 m

ero considera$os por ra%ones consruci*as:

bvs=0.25 m

Di$ensiones de la *i"a secundaria:



ANALISIS ESTRUCTURAL I2.!.- Pre dimensionamiento de "ol#mnas:

De acuerdo a e3peri$enos japoneses se o/u*o la si"uiene

or$ula para calcular las di$ensiones de una colu$na.

bd= P

n∗f ' c

$iso % ! 2 1Peso de&osa 45, 45, 45, 45, 11(6Peso deCol#mna (6 76 76 76 446Peso deiga 166 166 166 166 (66

Peso deM#ro 146 1,6 1,6 1,6 ,86Peso dea"a'ados 166 166 166 166 (66so're"arga 1,6 466 466 466 8,6

total (56

De acuerdo al ipo de colu$na:




a+ Colu$na inerior C 9 1:

• Calcula$os el &rea ri/uaria# o$a$os el eje 9

At =

4.00+4.002

∗5.35+5.00

2

At =20.7 m2

• Calcula$os el ;

PG=total∗ At

PG=3480∗20.7=72036 Kg

P=1.1∗ PG

P=79239.6 Kg

De acuerdo a la ór$ula:

bd= P

n∗f ' c




bd= 79239.6

0.30∗210

bd=1257.77

Enonces o$a$os ' ( ).!)m * d ( ).%)m

/+ Colu$na e3erior C 9 4

• Calcula$os el &rea ri/uaria# o$a$os el eje 9 ,

At =

4.00

2∗5.35+5.00

2

At =10.35 m2

• Calcula$os el ;

PG=total∗ At

PG=3480∗10.35=36018 Kg

P=1.25∗ PG

P=45022.5 Kg

De acuerdo a la or$ula:

bd= P

n∗f ' c




bd= 45022.5

0.25∗210

bd=857.57

Enonces o$a$os ' ( ).!)m * d ( ).!)m

c+ Colu$na e3erior C 9

• Calcula$os el &rea ri/uaria# o$a$os el eje A 9 (

At =

4.00+4.00

2∗5.35

2

At =10.7 m2

• Calcula$os el ;

PG=total∗ At

PG=3480∗10.7=37236 Kg

P=1.25∗ PG

P=46545 Kg


bd= P

n∗f ' c

bd= 46545

0.25∗210



ANALISIS ESTRUCTURAL Ibd=886.57

Enonces o$a$os ' ( ).!)m * d ( ).!)m

d+ Colu$na e3erior ipo C 9 (

• Calcula$os el &rea ri/uaria# o$a$os el eje A 9 ,

At =

4.00

2∗5.35

2

At =5.35 m2

• Calcula$os el ;

PG=total∗ At

PG=3480∗5.35=18618 Kg

P=1.50∗ PG

P=27927 Kg


bd= P

n∗f ' c

bd= 46545

0.20∗210

bd=664.93




Enonces o$a$os ' ( ).2+m * d ( ).2+m

!.- METRADO DE CAR,AS:

Resumen de dimensiones de Columna:

' "m d "mC - 1 !) %)C - 2 !) !)C - ! !) !)C - % 2+ 2+

!.1 Peso de la losa aligerada:

• eso losa ali"erada 1er piso ! a%oea

area total=356.42 m2

area vigas principales=5∗(0.25∗20.75)

area vigas principales=−25.94 m2

area vigas secundarias=5∗(0.25∗16.30)



ANALISIS ESTRUCTURAL Iarea vigas secundarias=−20.38 m

2

area escaleras=2.65∗4.03

areaescaleras=−10.68m2

area vacia=3.70∗9.80

areavigas secundarias=−36.26m2

Area Neta=263.16 m2

Peso losaaligerada1 er nivel y azotea=380 Kg

m2∗263.16 m

2=100000.8 Kg❑

!.2 Peso losa aligerada 2do * !er ni/el:

area total=339.545 m2

area vigas principales=5∗(0.25∗20.75)

area vigas principales=−25.94 m2

area vigas secundarias=5∗(0.25∗16.30)

area vigas secundarias=−20.38 m

2

area escaleras=2.65∗4.03

areaescaleras=−10.68m2

area vacia=3.70∗9.80

areavigas secundarias=−36.26m2




Area Neta=246.285 m2

Peso losaaligerada2 do y 3 er nivel=380 Kg

m2∗246.285 m

2=93588.3 Kg❑

!.! Peso de /igas:

pesovigas principales=5∗( 0.25∗0.50∗20.75 )∗2400=31125 Kg

pesovigas secundarias=5∗(0.25∗0.30∗16.30)∗2400=14670 Kg

pesovigas paratodonivel=45795 Kg

!.% Peso de "ol#mnas:

peso2 do−4 ¿ piso columas=( 9 (0.30∗0.40 )2.6+12 (0.30∗0.30 ) 2.6+4 (0.25∗0.25 )2.6 )∗2400

peso2 do−4 ¿ piso columas=13353.6 Kg

peso1 er piso columas=(9∗(0.30∗0.40 ) 4.6+12∗(0.30∗0.30 ) 4.6+4∗(0.25∗0.25 ) 4.6)∗2400

peso1 er piso columas=26606.4 Kg

pesoazotea columas=(14 (0.25∗0.25 ) 0.8+4∗(0.25∗0.25 )∗2 )∗2400=2880 Kg

pesoasignado a nivel de la azotea=13353.6

2+2880=9556.8 Kg

pesoasignado 2do y 3 er nivel=¿13353.6 Kg

pesoasignadoa1ernivel=13353.6

2+

26606.4

2=19980.00 Kg



ANALISIS ESTRUCTURAL I!.+ $eso es"aleras:

Escaleras pri$er ni*el:

peso peldaños 1 er piso=10∗( 0.30∗0.18

2 )∗1.25∗2400=810 Kg

peso peldaños 1 er piso=9∗( 0.30∗0.18

2 )∗1.25∗2400=729 Kg

pesogarganta 1 er piso+ triangulito=2 (3.10∗0.10∗1.25 )∗2400+(0.40∗0.67

2)∗1.25∗2400=226

pesodescanso primer piso=0.14∗1.2∗2.65∗2400=1068.48 Kg

pesototal escaleras 1er piso=4860.48 Kg

Escaleras ipicas:

peso peldañostipicos=15∗

(0.30∗0.18

2

)∗1.25∗2400=1215 Kg



ANALISIS ESTRUCTURAL I pesogargantas=( (0.16∗2.77 )∗1.25+ (0.16∗2.45 )∗1.25)∗2400=2505.60 Kg

pesodescanso=1.52∗0.20∗2.65∗2400=1933.44 Kg

pesototal escaleras t ipicas=5654.04 Kg

pesoatribuido ala azotea=5654.04

2=2827.02 Kg

pesoatribuido al2do y 3 er nivel=5654.04=5654.04 Kg

pesoatribuido al 1 er nivel=

5654.04

2 +

4860.48

2 =5257.42 Kg

!.0 Peso de m#ros:

longitud de muros por ejes=¿

Ni/el aotea

eje 1=19.35 m

eje2=1m

eje3=0.00m

eje4=10.00m

eje 5=19.35 m

eje A=2∗4.1+8.18=16.38m

ejeB=7.80 m(h=2.00 m)

eje =3.70m

eje !=14.80 m



ANALISIS ESTRUCTURAL Itotal(h=0.80)=84.58 m

total (h=2.00 )=7.80m

pesodemuros azotea (h=0.80 )=19284.24 Kg

pesomuro cajon escalera(h=2.00)=4446 Kg

pesototal azotea=23730.24 Kg

• %to $iso:

eje1=19.35∗2.30∗500=22252.5 Kg

eje 2=(9.95∗2.30−2.1∗0.90 )∗500=10497.5 Kg

eje3=( 9.95∗2.30−3∗2.1∗0.90 )∗500=8607.5 Kg

eje 4=(16.15∗2.30−3∗2.1∗0.90−4.70∗1.1−4.6∗1.1 )∗500=11025 Kg

eje 5=19.35∗2.30∗500=22252.5 Kg

eje A=( 4.2∗2.6 )∗500=5460 Kg

ejeB=(7.4∗2.5)∗500=9250 Kg

eje =(14.78∗2.5−2.47∗0.25−1.8∗2.1 )∗500=16276.25 Kg

eje != (4∗3.7∗2.5)∗500=18500 Kg

!ntre A y B= (7.4∗2.6−2.1∗0.90 )∗285=4944.75 Kg

!ntreB y =(7.4∗2.6)∗285=5483.4 Kg

Peso totalmuros 4¿ piso=134,549.40 Kg

• 2do * !er $iso:



ANALISIS ESTRUCTURAL Ieje1=19.35∗2.30∗500=22252.5 Kg

eje 2=(16.15∗2.30−2.1∗0.90 )∗500=17627.5 Kg

eje3=(11.65∗2.30−3∗2.1∗0.90 )∗500=10562.5 Kg

eje 4=(16.15∗2.30−3∗2.1∗0.90−4.70∗1.1−2.47∗0.25 )∗500=14234.25 Kg

eje 5=19.35∗2.30∗500=22252.5 Kg

eje A=( 4.2∗2.6 )∗500=5460 Kg

ejeB=(11.10∗2.5 )∗500=13875 Kg

eje =(3.7∗2.3−2.47∗.025)∗500=3946.25 Kg

eje "=(11.10∗2.3−3∗2.1∗0.9)∗500=9930 Kg

eje != (4∗3.7∗2.5)∗500=18500 Kg

!ntre3 y 4=(4.7∗2.6)∗285=3482.70 Kg

!ntre A y B= (7.4∗2.6−2.1∗0.90 )∗285=4944.75 Kg

!ntreB y =(3.7∗2.6)∗285=2741.7 Kg

!ntre y "=(8.10∗2.6−2.1∗0.90−2.45∗0.50 )∗285=5114.325 Kg

#olado=(13.68∗0.80 )∗285=3119.040 Kg

Peso totalmuros3 er piso=154923.975 Kg

Pesototalmuros 2do piso=158043.015 Kg

1er $iso:



ANALISIS ESTRUCTURAL Ieje 1=19.35∗3.20∗500=30960 Kg

eje 2=( 4.6∗3.2−2.1∗0.90 )∗500=6415 Kg

eje3=(18.55∗3.20 )∗500=29680 Kg

eje4=( 4.6∗3.20−2.1∗0.90−2.47∗1.55 )∗500=4500.75 Kg

eje 5=19.35∗3.20∗500=30960 Kg

eje A=(2∗3.75∗3.4−2∗1.55∗2.05 )∗500=9572.5 Kg

ejeB=(3.7∗3.4)∗500=6290 Kg

eje =(2.25∗3.4−2.1∗0.9−1.35∗1.55)∗500=1833.75 Kg

eje "=(10.07∗3.4 )∗500=17119 Kg

eje != (4∗3.7∗2.5)∗500=18500 Kg

!ntre1 y 2=( 4.13∗3.6 )∗285=7705.26 Kg

!ntre4 y 5= (5.00∗3.6+3.38∗3.6 )∗285=8597.88 Kg

!ntreA y B= (4.10∗3.6)∗285=4237.38 Kg

Peso totalmuros1er piso=176301.52 Kg

Peso atribuido azotea=(23730.4)+(134,549.40

2 )=91005.10 Kg

Peso atribuido3 er nivel=134,549.40

2+

154923.975

2=144736.688 Kg

Peso atribuido2 donivel=154923.975

2+

158043.015

2=86983.495 Kg

Peso atribuido1 er nivel=158043.015

2 +176301.52

2 =167172.268 Kg




!. Peso de $#ertas:

Puertas4¿ piso=9∗(0.90∗2.10∗0.04 )∗700=476.28 $g

(1.80∗2.10∗0.04 )∗700=105.84 Kg

total puertas4¿ piso=582.12 Kg

Puertas3 er y 2 do piso=12∗(0.90∗2.10∗0.04 )∗700=635.04 $g

total puertas 3 er y 2 do piso=635.04 Kg

Puertas1 er piso=5∗(0.90∗2.10∗0.04 )∗700=264.60 $g

3 (0.70∗2.10∗0.04 )∗700=123.48 Kg

total puertas1er piso=388.08 Kg

Peso atribuido azotea=291.06 Kg

Pesoatribuido3ernivel=(582.12

2+ 635.04

2 )=608.58 Kg

Peso atribuido2do nivel=635.04=635.04 Kg


2+

388.08

2=511.56 Kg

!.3 Peso entanas:

ventanas azotea=1.2∗11.77∗50=706.20 $g ventanas 4 ¿ piso

sentido principal= (9.30∗2.30∗50)=1069.5 Kg

sentido secundario=(2.47∗0.25∗50 )+(11.2∗2.60 )∗50=1486.875 Kg

total peso ventanas4¿ piso=2556.375 Kg



ANALISIS ESTRUCTURAL Iventanas 3 er y 2do piso=¿

sentido principal= (4.70∗2.30∗50 )+ (2.47∗0.25∗50 )=571.375$G

sentido secundario=(2.75∗0.25∗50 )=30.875 Kg

%nteriores=2.45∗1.2∗50=147.00 Kg

total peso ventanas3 er y 2 do piso=749.25 Kg

ventanas 1er piso=¿

sentido principal= (2.57∗1.55∗50)=199.175 Kg

sentido secundario=(2.75∗0.25∗50 )=30.875 Kg

%nteriores=2.45∗1.2∗50=147.00 Kg total peso ventanas1er :=377.05 Kg

Pesoatribuidoazotea=706.20+2556.375

2=1984.388 Kg

Pesoatribuido3ernivel=(2556.375

2+ 749.25

2 )=1652.813 Kg

Pesoatribuido2donivel=(749.25 )=749.25 Kg


2+

377.05

2=563.15 Kg



ANALISIS ESTRUCTURAL IRESUMEN

DESCRIPCION aotea ! 2 1&osa 4 $isoterminado

1))))).3

5!+33.!

5!+33.!

1))))).3

+/igas %+5+ %+5+ %+5+ %+5+

"ol#mnas 5++0.31!!+0.

!1!!+0.

! 1553)

es"aleras232.)

2+0+%.)

%+0+%.)

%+2+.%

2

m#ros51))+.

11%%!0

.0333053!.

%5+1012

.203

$#ertas 251.)0 0)3.+3 0!+.)% +11.+0

/entanas153%.!

3310+2.3

1! %5.2+ +0!.1+

total "argas2+1%0)

.103!)+!51

.212%001

.%2+!!523)

.153

!.5 So're"argas:

Nivel azotea:

area totalnivel azotea=346.52 m2 area muro eje 1=19.05∗0.2=−3.81

areamuro2=1∗0.15=−0.15 area muro eje4=10.3∗0.15=−1.545

area muro eje5=19.05∗0.2=−3.81 area muro eje A=15.43∗0.15=−2.31

area muro eje !=4∗3.7∗0.15=−2.22

areacolumnas=11∗0.3∗0.3+4∗0.25∗0.25+3∗0.3∗0.4=−1.6

area vacia=3.95∗9.8=−38.71

areaazotea=292.365 m2 &B(!A(GA A)*!A=0.25∗292.365∗150

&B(!A(GA A)*!A=10963.69 Kg

Nivel 3ro:

area total3 er nivel=339.545 m2 area muroseje1=19.05∗0.2=−3.81

areamuroseje2=9.05∗0.15=−1.358 area muroseje 3=7∗0.15=−1.05



ANALISIS ESTRUCTURAL Iareamuroseje4=4.45∗0.15=−0.67 area muros eje 5=19.05∗0.2=−3.81

areamuroseje A=15.6∗0.15=−2.34

areamurosentre eje A y B=7.46∗0.15=−1.10

area muros eje B=7.4∗0.15=−1.11

areamurosentre eje B y =3.95∗0.15=−2.96

area muroseje =12.09∗0.15=−1.81 area muroseje !=4∗3.7∗0.2=−2.96

ar eavacia=3.95∗9.8=−38.71

areacolumnas=12∗0.3∗0.4+12∗0.3∗0.3+4∗0.25∗0.25=−2.97

area 3 er nivel=274.887 m2

&B(!A(AGA 3 er N%#!L=0.25∗284.887∗250

&B(!A(GA 3 er N%#!L=17180.44 Kg

Nivel 2do y 1ro:

area total2 donivel=339.545 m2

area total1 er nivel=356.42m2

area muros eje 1=19.05∗0.2=−3.81 area muroseje 2=13.5∗0.15=−2.03

area muros eje 3=8.35∗0.15=−1.25 area muroseje3−4=4.8∗0.15=−0.72

areamuroseje4=13.6∗0.15=−2.04 area muros eje 5=19.5∗0.2=−3.81

areamuroseje A=15.6∗0.15=−2.34 area muroseje A−B=7.36∗0.15=−1.10

area muros eje B=3∗3.7∗0.15=−1.67 area muros eje B− =4.1∗0.15=−0.62

areamuroseje =4.1∗0.15=−0.62 area muroseje − "=7.2∗0.15=−1.08

areamuroseje"=8.4∗0.15=−1.26 area muroseje !=4∗3.7∗0.2=−2.96

area vacia=3.95∗9.8=−38.71

areacolumnas=12∗0.4∗0.3+12∗0.3∗0.3+4∗0.25∗0.25=−2.97

area muros volado=13.34∗0.15=−1.99




area 2do nivel=272.555 m2 &B(!A(GA 2do N%#!L=0.25∗272.555∗250

&B(!A(GA 2 do N%#!L=17034.69 Kg

area 1er nivel=287.744 m2 &B(!A(GA 1 er N%#!L=0.25∗287.744∗250

&B(!A(GA 1er N%#!L=17984.00 Kg

RESUMEN 6INA&

aotea ! 2 1Cargas degra/edad

2+1%0).103

!)+!51.21

2%001.%2+

!!523).153

so're"argas1)50!.0

5113).%

%1)!%.0

5 153%

total202%2!.

3+3!22+2.

10120!50.

11+!+20%.

153

ANA&ISIS DE CAR,A SISMICA

aotea ! 2 1Cargas degra/edad

2+1%0).103

!)+!51.21

2%001.%2+

!!523).153

so're"argas

1)50!.05

113).%%

1)!%.05 153%

total202%2!

.3+3!22+2

.10120!50

.11+!+20%

.153

<( < <4 <1

SUMA474(4.

5,544,84.

171478=7.

11,,847(.

1=5

oal14676,7

.

>uer%a corane en la /ase? se calcula con la siguiente expresion

# =)+&

( ∗ P



ANALISIS ESTRUCTURAL ICalcula$os los coe@cienes deacuerdo al Re"la$eno Nacional De

Edi@caciones.

7oni8"a"ion 6a"tor 7:

Deacuerdo a nuesro re"la$eno cada %ona del pais iene un factor Z

deacuerdo a su u/icación se"n la a/la si"uiene:

ara uno Bona 4 ? 7().!

6a"tor de #so e im$ortan"ia U:

El coe@ciene de uso e i$porancia U+# es de@nida de acuerdo a la

si"uiene a/la.




ara una $unicipalidad Edi@cacion i$porane

U'1.

6a"tor de S#elo S:El >acor de suelo es de@nida deacuerdo a la si"uiene a/la.



ANALISIS ESTRUCTURAL IEl acor de suelo lo eli"ire$os co$o el $as criico suelo Fe3i/le o

con esraos de "ran espesor+:

S'1.(

6a"tor de am$li8"a"ion sismi"a C:

Se usa la si"uiene e3presion:

=2.5∗(* p* )1.25

,-0.25

De acuerdo a la a/la anerior ene$os:

* p=0.9

Galla$os el periodo unda$enal T con la si"uiene e3presion:

* = . n

*

To$a$os:

* =35

01 .8

04 4.5

0 4.5

0( 4.5

9n 12.1

Enonces ree$pla$os:

* = . n

* =

12.1

35* =0.346

Ree$pla%ando los daos:

=2.5∗( 0.9

0.346 )1.25

=8.258/2.5 ma0=2.5

6a"tor de red#""ion sismi"a R:

Se o$ara de acuerdo a la si"uiene a/la:




Co$o nuesra edi@cacion *a ser consruida en Concreo Ar$ado ! con

poricos o$a$os co$o R:

(=8

Ree$pla%a$os en la or$ula de >uer%a corane en la ase:

# =

)+&

( ∗ P # =

(0.3) (0.346 ) (2.5 ) (1.4 )8 ∗1206056.33 # =54760.033

DISTRIUCION DE 6UER7AS SISMICAS

1i= Pi.i∗#

∑ Pi.i

NIE& P 9 Pi9i 6i

%474(4.5

,5 14.118,45.

75

,(876.6

133+.5)+!

!44,84.1

71 =.4====41.

113!!.1

3+5

2478=7.1

1, 7.,181(78(.

8,1)152.5

20

1 ,847(.1=5 .8 141588., 3+.5052+



ANALISIS ESTRUCTURAL ISu$a

=411564.67

+%0).)!!

DETERMINACION DE RI,IDECES RE&ATIAS ;

1 En el sentido Prin"i$al

Prin"i$ales:

6.4,

G 6.,6

Se"#ndarias:

6.4,

G 6.62 Col#mnas

DC1 ).% ).!

C2 ).! ).!

C3 ).! ).!

C4 ).2+ ).2+

&n1 &n1 &n1 &n1

.8 4.5 4.5 4.5

N1 N2 N! N%

;C1 (4.( ,81.( ,81.( ,81.(

;C2 154.( 4(1.68 4(1.68 4(1.68

;C! 154.( 4(1.68 4(1.68 4(1.68

;C% 58.=5 117.47 117.47 117.47

Rigide"es $or$lanta C1 C2 C! C% SUMA

P1 P&ANTA )1 = 7 7 ( 6433.00

P2 P&ANTA )2 = 7 7 ( 8500.74

P! P&ANTA )! = 7 7 ( 8500.74

P% P&ANTA )% = 7 7 ( 8500.74




DISTRIUCION DE 6UER7AS POR PORTICO

PP ;<E=E

N1 6i6i<E>e;g

1 84.4,

85,8.=8

55.(7

41774.1

7 466.,

1774.1

7 466.,

(1774.1

7 466.,

, 84.4, 55.(7

SUHA 6433.00 7857.97

N2 6i6i<E>e;g

1 =,,.8

161=4.=8

11(,.=5

441=7.(

47.78

41=7.(

47.78

(41=7.(

47.78

, =,,.8 11(,.=5SUHA 8500.74 10192.97

N! 6i6i<E>e;g

1 =,,.8

185.1=

,,(.,

441=7.(

148=.=

5

41=7.(

148=.=

5

(41=7.(

148=.=

5

, =,,.8 ,,(.,

SUHA68(.,

4 49307.01

N% 6i6i<E>e;g

1 =,,.8 1558,.=1

,578.78

4 41=7.( 1(5(.=6




41=7.(

1(5(.=

6

(41=7.(

1(5(.=

6

, =,,.8 ,578.78

SUHA68(.,

4 52190.03

ANALISIS DE LSA DEL EJE SECUNDARI:

a+ Car"as Hueras

P=280∗1=280 Kg

m

/+ Aca/ados:

PP* =100∗1=100

$g

m

c+ eso de $uros:

m 1=285∗2.6=741 $g

m m2=285∗2.6=741

Kg

m m3=285∗2∗0.24=136.8 Kg

m4=285∗2∗0.23=131.1 Kg

d+ Car"as *i*as:

&

ficina

=500∗1=500$g

m

&

&&..

=300∗1=300$g

m

&

corredores

=400∗1=400$g

m




Area de losa o$ada enre los ejes ! C del ercer ni*el.

An?lisis de &osa

PRIMER CASO

• Calculo de K :

% =4

L=4

$ = %

L=

4

4=1m

3

• Calculo de $o$enos de e$pora$ieno:

2 AB= 2 AB 1 + !K (4 3 i+23 j)



ANALISIS ESTRUCTURAL I 2 BA= 2 BA

1 + !K (23i+43 j)

T rao A!:

2 AB

1 =− 2 BA

1 =4 L

2

12=

1621∗42

12=2161.333 $g∗m

2 AB 1 =2161.333 $g∗m

2 BA 1 =−2161.333 $g∗m

T rao !C:

2 B 1 =− 2 B

1 =4 L

2

12=

880∗42

12=1173.333$g∗m

2 B 1 =1173.333 $g∗m

2 B 1 =−1173.333 $g∗m

T rao CD:

2 "

1 =− 2 "

1 =4 L

2

12=

780∗42

12=1040.00 $g∗m

2 " 1 =1040.00 $g∗m

2 " 1 =−1040.00 $g∗m

T rao DE:

2 "!

1 ' =4 L

2

12=

1421∗42

12=1894.667 $g∗m

2 "! 1 ' =1894.667 $g∗m




⇒ 2 "!

1 ' ' = P1 a b

2

L2 =

136.8∗1.07∗2.932

42

=78.539 $g∗m

⇒ 2 "!

1 ' ' = P2 a b2

L2 =136.8∗2.07∗1.932

42

=65.925 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

131.1∗2.67∗1.332

42

=38.699 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗3.06∗0.942

42

=93.118$g∗m $g∗m

Sumamos:

2 "! 1 = 2 "!

1' + 2 "! 1 ''

2 "! 1 =1894.667+78.539+65.925+38.699+93.118

2 "! 1 =2160.948 $g∗m

T rao ED:

2 !"

1 ' =4 L

2

12=

1421∗42

12=−1894.667 $g∗m

2 !" 1 ' =−1894.667 $g∗m

⇒ 2 !"

1 ' ' = P1 a b

2

L2 =

136.8∗2.93∗1.072

42

=−28.681 $g∗m

⇒ 2 !" 1 '' =

P2ab2

L2 =

136.8∗1.93∗2.072

42

=−70.707 $g∗m$g∗m




⇒ 2 !"

1 ' ' = P3 a b

2

L2 =

131.1∗1.33∗2.672

42

=−77.689 $g∗m $g∗m

⇒ 2 !"

1 ' ' = P4 a b2

L2 =136.8∗0.94∗3.062

42

=−75.255 $g∗m$g∗m

Sumamos:

2 !" 1 = 2 !"

1 ' + 2 !" 1 ' '

2 !" 1

=−1894.667−28.681−70.707−77.689−75.255

2 !" 1 =−2147.000 $g∗m

Ree"lazao# e$:

T rao A!:

2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 AB=2161.333+1∗1(43 A+23B)

2 AB=2161.333+4 3 A+2 3B

2 BA=−2161.333+23 A+43B

T rao !C:

2 B = 2 AB 1 + !K (4 3i+23 j)

2 B =1173.333+1∗1(4 3B+23 )

2 B =1173.333+4 3 B+2 3



ANALISIS ESTRUCTURAL I 2 B=−1173.333+23 B+4 3

T rao CD:

2 "= 2 " 1 + !K (43i+23 j)

2 "=1040+1∗1(4 3 +2 3 ")

2 "=1040+43 +23 "

2 " =−1040+2 3 +4 3 "

T rao DE:

2 "!= 2 "! 1 + !K (43i+23 j)

2 "!=2160.948+1∗1(4 3 "+2 3 !)

2 "!=2160.948+4 3 "+23 !

2 !"=−2147.00+23 "+4 3 !

Por "ondi"iones de Contin#idad

2 BA+ 2 B =0

−2161.333+4 3B+23 A+1173.333+4 3 B+2 3 =0

−988+8 3B+23 A+23 =0

23 A+8 3B+23 =988

2 B+ 2 "=0



ANALISIS ESTRUCTURAL I−1173.333+23B+43 +1040+43 +23 "=0

23 B+8 3 +2 3 "=133.333

2 " + 2 "!=0

−1040+23 +4 3 "+2160.948+4 3 "+23 !=0

−1040+23 +4 3 "+2160.948+4 3 "+23 !=0

23 +8 3 "+23 !=−1120.948

2 AB=2161.333+4 3 A+2 3B=0

2 !"=−2147.00+23 "+43 !=0

Armando las e"#a"iones:

23 A+8 3B+23 =988

23 B+4 3 +2 3 "=133.333

23 +8 3 "+23 !=−1120.948

4 3 A+2 3B=−2161.333

23 "+4 3 !=2147.00

Ensam'lando las e"#a"iones:




[

2 8 2 0 0

0 2 8 2 0

0 0 2 8 2

0 0 0 2 44 2 0 0 0

]∗

[

3 A3B3

3 "3 !

]=

[

988

133.333

−1120.948

2147.000−2161.333

]Resol/iendo:

3 A=−684.569

3B=288.471

3 =24.685

3 "=−320.546

3 !=697.023

Reem$laando: 2 AB=0

2 BA=−2376.587

2 B =2376.587

2 B=−497.648

2 "=497.650

2 " =−2272.814

2 "!=272.814




SE,UNDO CASO

• Calculo de K :

% =4

L=4

$ = %

L=

4

4=1m

3


2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 BA= 2 BA 1 + !K (23i+43 j)

T rao A!:




2 AB

1 =− 2 BA

1 =4 L

2

12=

1621∗42

12=2161.333 $g∗m

2 AB

1

=2161.333 $g∗m

2 BA 1 =−2161.333 $g∗m

T rao !C:

2 B

1 =− 2 B

1 =4 L

2

12=

380∗42

12=506.667 $g∗m

2 B 1 =506.667 $g∗m

2 B 1 =−506.667 $g∗m

T rao CD:

2 "

1 =− 2 "

1 =4 L

2

12=

780∗42

12=1040.00 $g∗m

2 B 1 =1040.00 $g∗m

2 " 1 =−1040.00 $g∗m

T rao DE:

2 "!

1 '

=4 L

2

12 =1121∗4

2

12 =1494.667 $g∗m

2 "! 1 ' =1494.667 $g∗m

⇒ 2 "!

1 ' ' = P1 a b

2

L2 =

136.8∗1.07∗2.932

42

=78.539 $g∗m




⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗2.07∗1.932

42

=65.925 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b2

L2 =131.1∗2.67∗1.332

42

=38.699 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗3.06∗0.942

42

=93.118 $g∗m $g∗m

Sumamos:

2 "! 1 = 2 "!

1' + 2 "! 1 ''

2 "! 1 =1494.667+78.539+65.925+38.699+93.118

2 "! 1 =1760.948 $g∗m

T rao ED:

2 !"

1 ' =4 L

2

12=

1121∗42

12=−1494.667 $g∗m

2 !" 1 ' =−1494.667 $g∗m

⇒

2 !"

1 ' '

=

P1 a b2

L2 =

136.8∗2.93∗1.072

42 =−28.681 $g∗m

⇒ 2 !"

1 ' ' = P2 a b

2

L2 =

136.8∗1.93∗2.072

42

=−70.707 $g∗m $g∗m

⇒ 2 !"

1 ' ' = P3 a b

2

L2 =

131.1∗1.33∗2.672

42

=−77.689 $g∗m $g∗m




⇒ 2 !"

1 ' ' = P4 a b

2

L2 =

136.8∗0.94∗3.062

42

=−75.255 $g∗m$g∗m

Sumamos:

2 !" 1 = 2 !"

1 ' + 2 !" 1 ' '

2 !" 1 =−1494.667−28.681−70.707−77.689−75.255

2 !" 1 =−1747.000 $g∗m

Ree"lazao# e$:

T rao A!:

2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 AB=2161.333+1∗1(43 A+23B)

2 AB=2161.333+4 3 A+2 3B

2 BA=−2161.333+23 A+43B

T rao !C:

2 B = 2 B

1

+ !K (4 3i+2 3 j)

2 B =506.667+1∗1(4 3B+23 )

2 B =506.667+4 3B+23

2 B=−506.667+23B+43

T rao CD:



ANALISIS ESTRUCTURAL I 2 "= 2 "

1 + !K (43i+23 j)

2 "=1040+1∗1(43 +23 ")

2 "=1040+43 +23 "

2 " =−1040+2 3 +4 3 "

T rao DE:

2 "!= 2 "! 1 + !K (43i+23 j)

2 "!=1760.948+1∗1(43 "+23 !)

2 "!=1760.948+4 3 "+2 3 !

2 !"=−1747.00+2 3 "+4 3 !


2 BA+ 2 B =0

−2161.333+4 3B+23 A+506.667+4 3B+23 =0

−1654.666+83B+2 3 A+23 =0

23 A+83B+23 =1654.666

2 B+ 2 "=0

−506.667+23B+4 3 +1040+4 3 +23 "=0



ANALISIS ESTRUCTURAL I23 B+8 3 +2 3 "=−533.333

2 " + 2 "!=0

−1040+23 +4 3 "+1760.948+4 3 "+23 !=0

23 +8 3 "+23 !=−720.948

2 AB=2161.333+4 3 A+2 3B=0

2 !"=−1747.00+2 3 "+4 3 !=0


23 A+83B+23 =1654.666

23 B+8 3 +2 3 "=−533.333

23 +8 3 "+23 !=−720.948

4 3 A+2 3B=−2161.333

23 "+43 !=1747.00





[

2 8 2 0 0

0 2 8 2 0

0 0 2 8 2

0 0 0 2 44 2 0 0 0

]∗

[

3 A3B3

3 "3 !

]=

[

1654.666

−533.333

−720.948

1747.000−2161.333

]Resol/iendo:

3 A=−753.616

3B=426.566

3 =−125.315

3 "=−191.974

3 !=532.737

Reem$laando:

2 AB=0

2 BA=−1962.301

2 B =+1962.301

2 B=−154.793

2 "=154.793

2 " =−2058.526

2 "!=2058.526

2 !"=0




TERCER CASO

• Calculo de K :

% =4

L=4

$ = % L=4

4 =1m3


2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 BA= 2 BA 1 + !K (23i+43 j)

T rao A!:




2 AB

1 =− 2 BA

1 =4 L

2

12=

1121∗42

12=1494.667 $g∗m

2 AB 1

=1494.667 $g∗m

2 BA 1 =−1494.667 $g∗m

T rao !C:

2 B 1 =− 2 B

1 =4 L

2

12=

880∗42

12=1173.333$g∗m

2 B 1 =1173.333 $g∗m

2 B 1 =−1173.333 $g∗m

T rao CD:

2 "

1 =− 2 "

1 =4 L

2

12=

380∗42

12=506.667 $g∗m

2 " 1 =506.667 $g∗m

2 " 1 =−506.667 $g∗m

T rao DE:

2 "!

1 '

=4 L

2

12 =1421∗4

2

12 =1894.667 $g∗m

2 "! 1 ' =1894.667 $g∗m

⇒ 2 "!

1 ' ' = P1 a b

2

L2 =

136.8∗1.07∗2.932

42

=78.539 $g∗m




⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗2.07∗1.932

42

=65.925 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b2

L2 =131.1∗2.67∗1.332

42

=38.699 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗3.06∗0.942

42

=93.118 $g∗m $g∗m

Sumamos:

2 "! 1 = 2 "!

1' + 2 "! 1 ''

2 "! 1 =1894.667+78.539+65.925+38.699+93.118

2 "! 1 =2160.948 $g∗m

T rao ED:

2 !"

1 ' =4 L

2

12=

1421∗42

12=−1894.667 $g∗m

2 !" 1 ' =−1894.667 $g∗m

⇒

2 !"

1 ' '

=

P1 a b2

L2 =

136.8∗2.93∗1.072

42 =−28.681 $g∗m

⇒ 2 !"

1 ' ' = P2 a b

2

L2 =

136.8∗1.93∗2.072

42

=−70.707 $g∗m $g∗m

⇒ 2 !"

1 ' ' = P3 a b

2

L2 =

131.1∗1.33∗2.672

42

=−77.689 $g∗m $g∗m




⇒ 2 !"

1 ' ' = P4 a b

2

L2 =

136.8∗0.94∗3.062

42

=−75.255 $g∗m$g∗m

Sumamos:

2 !" 1 = 2 !"

1 ' + 2 !" 1 ' '

2 !" 1 =−1894.667−28.681−70.707−77.689−75.255

2 !" 1 =−2147.000 $g∗m

Ree"lazao# e$:

T rao A!:

2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 AB=1494.667+1∗1(43 A+23B)

2 AB=1494.667+4 3 A+2 3B

2 BA=−1494.667+23 A+4 3 B

T rao !C:

2 B = 2 AB

1

+ !K (4 3i+23 j)

2 B =1173.333+1∗1(43B+23 )

2 B =1173.333+4 3 B+2 3

2 B=−1173.333+23 B+4 3

T rao CD:




1 + !K (43i+23 j)

2 "=506.667+1∗1(43 +23 ")

2 "=506.667+43 +23 "

2 " =−506.667+2 3 +4 3 "

T rao DE:

2 "!= 2 "! 1 + !K (43i+23 j)

2 "!=2160.948+1∗1(43 "+23 !)

2 "!=2160.948+4 3 "+23 !

2 !"=−2147.00+23 "+4 3 !


2 BA+ 2 B =0

−1494.667+43B+23 A+1173.333+43B+23 =0

−321.334+83B+23 A+23 =0

23 A+8 3B+23 =321.334

2 B+ 2 "=0

−1173.333+23B+43 +506.667+43 +23 "=0



ANALISIS ESTRUCTURAL I23 B+8 3 +2 3 "=666.666

2 " + 2 "!=0

−506.667+23 +4 3 "+2160.948+4 3 "+2 3 !=0

23 +8 3 "+23 !=−1654.281

2 AB=1494.667

+43 A+

23B=

0

2 !"=−2147.00+23 "+43 !=0


23 A+8 3B+23 =321.334

23 B+8 3 +2 3 "=666.666

23 +8 3 "+23 !=−1654.281

4 3 A+2 3B=−1494.667

23 "+4 3 !=2147.00


[2 8 2 0 0

0 2 8 2 0

0 0 2 8 2

0 0 0 2 4

4 2 0 0 0]∗

3 A

3B

3

3 "

3 !

=[ 321.334

666.666

−1654.281

2147.000

−1494.667]



ANALISIS ESTRUCTURAL IResol/iendo:

3 A=−426.236

3B=105.138

3 =166.352

3 "=−437.212

3 !=755.356

Reem$laando:

2 AB=0

2 BA=−1926.588

2 B =1926.588

2 B=−297.650

2 "=297.650

2 " =−1922.811

2 "!=1922.811

2 !"=0




CUARTO CASO

• Calculo de K :

% =4

L=4

$ = % L= 4

4=1m

3


2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 BA= 2 BA 1 + !K (23i+43 j)

T rao A!:




2 AB

1 =− 2 BA

1 =4 L

2

12=

1621∗42

12=2161.333 $g∗m

2 AB

1

=2161.333 $g∗m

2 BA 1 =−2161.333 $g∗m

T rao !C:

2 B 1 =− 2 B

1 =4 L

2

12=

880∗42

12=1173.333$g∗m

2 B 1 =1173.333 $g∗m

2 B 1 =−1173.333 $g∗m

T rao CD:

2 "

1 =− 2 "

1 =4 L

2

12=

380∗42

12=506.667 $g∗m

2 " 1 =506.667 $g∗m

2 " 1 =−506.667 $g∗m

T rao DE:

2 "!

1 '

=4 L

2

12 =1421∗4

2

12 =1894.667 $g∗m

2 "! 1 ' =1894.667 $g∗m

⇒ 2 "!

1 ' ' = P1 a b

2

L2 =

136.8∗1.07∗2.932

42

=78.539 $g∗m




⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗2.07∗1.932

42

=65.925 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b2

L2 =131.1∗2.67∗1.332

42

=38.699 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗3.06∗0.942

42

=93.118 $g∗m $g∗m

Sumamos:

2 "! 1 = 2 "!

1' + 2 "! 1 ''

2 "! 1 =1894.667+78.539+65.925+38.699+93.118

2 "! 1 =2160.948 $g∗m

T rao ED:

2 !"

1 ' =4 L

2

12=

1421∗42

12=−1894.667 $g∗m

2 !" 1 ' =−1894.667 $g∗m

⇒

2 !"

1 ' '

=

P1 a b2

L2 =

136.8∗2.93∗1.072

42 =−28.681 $g∗m

⇒ 2 !"

1 ' ' = P2 a b

2

L2 =

136.8∗1.93∗2.072

42

=−70.707 $g∗m $g∗m

⇒ 2 !"

1 ' ' = P3 a b

2

L2 =

131.1∗1.33∗2.672

42

=−77.689 $g∗m $g∗m




⇒ 2 !"

1 ' ' = P4 a b

2

L2 =

136.8∗0.94∗3.062

42

=−75.255 $g∗m$g∗m

Sumamos:

2 !" 1 = 2 !"

1 ' + 2 !" 1 ' '

2 !" 1 =−1894.667−28.681−70.707−77.689−75.255

2 !" 1 =−2147.000 $g∗m

Ree"lazao# e$:

T rao A!:

2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 AB=2161.333+1∗1(43 A+23B)

2 AB=2161.333+4 3 A+2 3B

2 BA=−2161.333+23 A+43B

T rao !C:

2 B = 2 AB

1

+ !K (4 3i+23 j)

2 B =1173.333+1∗1(43B+23 )

2 B =1173.333+4 3 B+2 3

2 B=−1173.333+23 B+4 3

T rao CD:




1 + !K (43i+23 j)

2 "=506.667+1∗1(43 +23 ")

2 "=506.667+43 +23 "

2 " =−506.667+2 3 +4 3 "

T rao DE:

2 "!= 2 "! 1 + !K (43i+23 j)

2 "!=2160.948+1∗1(43 "+23 !)

2 "!=2160.948+4 3 "+23 !

2 !"=−2147.00+23 "+4 3 !


2 BA+ 2 B =0

−2161.333+4 3B+23 A+1173.333+4 3 B+2 3 =0

−988+8 3B+23 A+23 =0

23 A+8 3B+23 =988

2 B+ 2 "=0

−1173.333+23B+43 +506.667+43 +23 "=0




2 " + 2 "!=0

−506.667+23 +4 3 "+2160.948+4 3 "+2 3 !=0

−506.667+23 +4 3 "+2160.948+4 3 "+2 3 !=0

23 +8 3 "+23 !=−1654.281

2 AB=2161.333+4 3 A+2 3B=0

2 !"=−2147.00+23 "+43 !=0


23 A+8 3B+23 =988

23 B+4 3 +2 3 "=666.666

23 +8 3 "+23 !=−1654.281

4 3 A+2 3B=−2161.333

23 "+4 3 !=2147.00





[

2 8 2 0 0

0 2 8 2 0

0 0 2 8 2

0 0 0 2 44 2 0 0 0

]∗

[

3 A3B3

3 "3 !

]=

[

988

666.666

−1654.281

2147.000−2161.333

]Resol/iendo:

3 A=−670.283

3B=259.899

3 =124.685

3 "=−425.307

3 !=749.404

Reem$laando: 2 AB=0

2 BA=−2462.301

2 B =2462.301

2 B=−154.794

2 "=154.794

2 " =−1958.525

2 "!=1958.525

2 !"=0




@UINTO CASO

• Calculo de K :

% =4

L=4

$ = %

L=

4

4=1m

3




ANALISIS ESTRUCTURAL I 2 AB= 2 AB

1 + !K (4 3 i+23 j)

2 BA= 2 BA 1 + !K (23i+43 j)

T rao A!:

2 AB

1 =− 2 BA

1 =4 L

2

12=

1121∗42

12=1494.667 $g∗m

2 AB 1 =1494.667 $g∗m

2 BA 1

=−1494.667 $g∗m

T rao !C:

2 B 1 =− 2 B

1 =4 L

2

12=

880∗42

12=1173.333$g∗m

2 B 1 =1173.333 $g∗m

2 B 1 =−1173.333 $g∗m

T rao CD:

2 "

1 =− 2 "

1 =4 L

2

12=

780∗42

12=1040.00 $g∗m

2 " 1 =1040.00 $g∗m

2 " 1 =−1040.00 $g∗m

T rao DE:

2 "!

1 ' =4 L

2

12=

1121∗42

12=1494.667 $g∗m

2 "! 1 ' =1494.667 $g∗m




⇒ 2 "!

1 ' ' = P1 a b

2

L2 =

136.8∗1.07∗2.932

42

=78.539 $g∗m

⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗2.07∗1.932

42

=65.925 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

131.1∗2.67∗1.332

42

=38.699 $g∗m $g∗m

⇒ 2 "!

1 ' '

= P2 a b

2

L2 =

136.8∗3.06∗0.942

42 =93.118$g∗m $g∗m

Sumamos:

2 "! 1 = 2 "!

1' + 2 "! 1 ''

2 "! 1 =1494.667+78.539+65.925+38.699+93.118

2 "! 1 =1770.948 $g∗m

T rao ED:

2 !"

1 ' =4 L

2

12=

1121∗42

12=−1494.667 $g∗m

2 !" 1 ' =−1494.667 $g∗m

⇒ 2 !"

1 ' ' = P1 a b

2

L2 =

136.8∗2.93∗1.072

42

=−28.681 $g∗m

⇒ 2 !" 1 '' =

P2ab2

L2 =

136.8∗1.93∗2.072

42

=−70.707 $g∗m$g∗m




⇒ 2 !"

1 ' ' = P3 a b

2

L2 =

131.1∗1.33∗2.672

42

=−77.689 $g∗m $g∗m

⇒ 2 !"

1 ' ' = P4 a b2

L2 =136.8∗0.94∗3.062

42

=−75.255 $g∗m$g∗m

Sumamos:

2 !" 1 = 2 !"

1 ' + 2 !" 1 ' '

2 !" 1

=−1494.667−28.681−70.707−77.689−75.255

2 !" 1 =−1747.000 $g∗m

Ree"lazao# e$:

T rao A!:

2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 AB=1494.667+1∗1(4 3 A+2 3B)

2 AB=1494.667+4 3 A+2 3B

2 BA=−1494.667+23 A+4 3 B

T rao !C:

2 B = 2 AB 1 + !K (4 3i+23 j)

2 B =1173.333+1∗1(4 3B+23 )

2 B =1173.333+4 3 B+2 3



ANALISIS ESTRUCTURAL I 2 B=−1173.333+23 B+4 3

T rao CD:

2 "= 2 " 1 + !K (43i+23 j)

2 "=1040+1∗1(4 3 +2 3 ")

2 "=1040+43 +23 "

2 " =−1040+2 3 +4 3 "

T rao DE:

2 "!= 2 "! 1 + !K (43i+23 j)

2 "!=1770.948+1∗1(43 "+23 !)

2 "!=1770.948+4 3 "+2 3 !

2 !"=−1747.00+2 3 "+4 3 !


2 BA+ 2 B =0

−1494.667+43B+23 A+1173.333+43B+23 =0

−321.334+83B+23 A+23 =0

23 A+8 3B+23 =321.334

2 B+ 2 "=0



ANALISIS ESTRUCTURAL I−1173.333+23B+43 +1040+43 +23 "=0

23 B+8 3 +2 3 "=133.333

2 " + 2 "!=0

−1040+23 +4 3 "+1760.948+4 3 "+23 !=0

23 +8 3 "+23 !=−730.948

2 AB=1494.667+43 A+23B=0

2 !"=−1747.00+2 3 "+4 3 !=0


23 A+8 3B+23 =321.334

23 B+4 3 +2 3 "=133.333

23 +8 3 "+23 !=−730.948

4 3 A+2 3B=−1494.667

23 "+43 !=1747.00





[

2 8 2 0 0

0 2 8 2 0

0 0 2 8 2

0 0 0 2 44 2 0 0 0

]∗

[

3 A

3B

3

3 "

3 !

]=

[

321.334

133.333

−720.948

1747.000−1494.667

]Resol/iendo:

3 A=−444.033

3B=140.733

3 =41.769

3 "=−241.141

3 !=557.320

Reem$laando: 2 AB=0

2 BA=−1819.802

2 B =1819.802

2 B=−724.792

2 "=724.792

2 " =−1921.025

2 "!=1921.025

2 !"=0




SETO CASO

• Calculo de K :

% =4

L=4

$ = %

L=

4

4=1m

3


2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 BA= 2 BA 1 + !K (23i+43 j)

T rao A!:




2 AB

1 =− 2 BA

1 =4 L

2

12=

1621∗42

12=2161.333 $g∗m

2 AB

1

=2161.333 $g∗m

2 BA 1 =−2161.333 $g∗m

T rao !C:

2 B

1 =− 2 B

1 =4 L

2

12=

380∗42

12=506.667 $g∗m

2 B 1 =506.667 $g∗m

2 B 1 =−506.667 $g∗m

T rao CD:

2 "

1 =− 2 "

1 =4 L

2

12=

780∗42

12=1040.00 $g∗m

2 " 1 =1040.00 $g∗m

2 " 1 =−1040.00 $g∗m

T rao DE:

2 "!

1 '

=4 L

2

12 =1421∗4

2

12 =1894.667 $g∗m

2 "! 1 ' =1894.667 $g∗m

⇒ 2 "!

1 ' ' = P1 a b

2

L2 =

136.8∗1.07∗2.932

42

=78.539 $g∗m




⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗2.07∗1.932

42

=65.925 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b2

L2 =131.1∗2.67∗1.332

42

=38.699 $g∗m $g∗m

⇒ 2 "!

1 ' ' = P2 a b

2

L2 =

136.8∗3.06∗0.942

42

=93.118 $g∗m $g∗m

Sumamos:

2 "! 1 = 2 "!

1' + 2 "! 1 ''

2 "! 1 =1894.667+78.539+65.925+38.699+93.118

2 "! 1 =2170.948 $g∗m

T rao ED:

2 !"

1 ' =4 L

2

12=

1421∗42

12=−1894.667 $g∗m

2 !" 1 ' =−1894.667 $g∗m

⇒

2 !"

1 ' '

=

P1 a b2

L2 =

136.8∗2.93∗1.072

42 =−28.681 $g∗m

⇒ 2 !"

1 ' ' = P2 a b

2

L2 =

136.8∗1.93∗2.072

42

=−70.707 $g∗m $g∗m

⇒ 2 !"

1 ' ' = P3 a b

2

L2 =

131.1∗1.33∗2.672

42

=−77.689 $g∗m $g∗m




⇒ 2 !"

1 ' ' = P4 a b

2

L2 =

136.8∗0.94∗3.062

42

=−75.255 $g∗m$g∗m

Sumamos:

2 !" 1 = 2 !"

1 ' + 2 !" 1 ' '

2 !" 1 =−1894.667−28.681−70.707−77.689−75.255

2 !" 1 =−2147.000 $g∗m

Ree"lazao# e$:

T rao A!:

2 AB= 2 AB 1 + !K (4 3 i+23 j)

2 AB=2161.333+1∗1(43 A+23B)

2 AB=2161.333+4 3 A+2 3B

2 BA=−2161.333+23 A+43B

T rao !C:

2 B = 2 AB

1

+ !K (4 3i+23 j)

2 B =506.667+1∗1(4 3B+23 )

2 B =506.667+4 3B+23

2 B=−506.667+23B+43

T rao CD:




1 + !K (43i+23 j)

2 "=1040+1∗1(43 +23 ")

2 "=1040+43 +23 "

2 " =−1040+23 +4 3 "

T rao DE:

2 "!= 2 "! 1 + !K (43i+23 j)

2 "!=2170.948+1∗1(43 "+23 !)

2 "!=2170.948+4 3 "+23 !

2 !"=−2147.00+23 "+4 3 !


2 BA+ 2 B =0

−2161.333+4 3B+23 A+506.667+4 3B+23 =0

−1654.666+83B+2 3 A+23 =0

23 A+83B+23 =1654.666

2 B+ 2 "=0

−506.667+23B+4 3 +1040+4 3 +23 "=0




2 " + 2 "!=0

−1040+23 +4 3 "+2170.948+4 3 "+23 !=0

23 +8 3 "+23 !=−1130.948

2 AB=2161.333+4 3 A+2 3B=0

2 !"=−2147.00+23 "+43 !=0


23 A+83B+23 =1654.666

23 B+8 3 +2 3 "=533.333

23 +8 3 "+23 !=−1130.948

4 3 A+2 3B=−2161.333

23 "+4 3 !=2147.00


[2 8 2 0 0

0 2 8 2 0

0 0 2 8 2

0 0 0 2 4

4 2 0 0 0]∗

3 A3B3 3 "3 !

=[ 1654.666

533.333

−1130.948

2147.000

−2161.333]



ANALISIS ESTRUCTURAL IResol/iendo:

3 A=−684.569

3B=288.471

3 =24.685

3 "=−320.546

3 !=697.023

Reem$laando:

2 AB=0

2 BA=−2376.587

2 B =2376.587

2 B=−497.648

2 "=497.650

2 " =−2272.8 14

2 "!=272.814




ANA&ISIS DE PORTICO:EN E& E=E PRINCIPA&:

Herado de car"as para porico principal:

Ni/el 1:

CAR,AS MUERTAS:

pesomurostipo soga=285 Kgm

2 ∗2.3m=741 Kgm

peso puntual demuro − "=285 Kg

m2∗3∗2.6=2223.00 Kg

peso puntual muro eje A−B=285 Kg

m2∗1.5∗2.6 m=1111.5 Kg




pesomuro carga puntual Avol1=285 Kg

m2∗2.6∗1.45=1055.6 Kg

pesomuro carga puntual Avol2=285

Kg

m2∗1.2∗2=684 Kg

pesode losa=280 Kg

m2∗4m=1120.00

Kg

m

Peso terminado=100 Kg

m2∗4 m=400.00

Kg

m

pesode viga=0.25∗0.5∗2400=300.00

Kg

m

CAR,AS IAS

&obrecarga oficina=500 Kg

m2∗4 m=2000.00

Kg

m

&obrecarga corredor=400 Kg

m2∗4 m=1600.00

Kg

m

&obrecarga balcon=200 Kg

m2∗4m=800.00

Kg

m

NI)EL 4:

CAR;AS HUERTAS:

pesomurostipo soga=285 Kg

m2∗2.3m=741

Kg

m

peso puntual demuro − "=285 Kg

m2∗3∗2.6=2223.00 Kg

peso puntual muro eje A−B=285 Kg

m2∗1.5∗2.6 m=1111.5 Kg





m2∗2.6∗1.45=1055.6 Kg

pesode losa=280

Kg

m2 ∗4m=1120.00

Kg

m


m2∗4 m=400.00

Kg

m

pesode viga=0.25∗0.5∗2400=300.00 Kg

m

CAR;AS )I)AS


m2∗4 m=2000.00

Kg

m

&obrecarga corredor=400 Kg

m2∗4 m=1600.00

Kg

m

NI)EL :

CAR;AS HUERTAS:

pesomurostipo soga=285 Kg

m2∗2.3m=741

Kg

m

peso puntual de muro B− =285 Kg

m2∗2∗2.6=1482.00 Kg

peso puntual muro eje A−B=285 Kgm

2∗1.5∗2.6 m=1111.5 Kg


m2∗2.6∗1.45=1055.6 Kg

pesode losa=280 Kg

m2∗4m=1120.00

Kg

m





m2∗4 m=400.00

Kg

m

pesode viga=0.25∗0.5∗2400=300.00 Kgm

CAR;AS )I)AS


m2∗4 m=2000.00

Kg

m

&obrecargateatro=750 Kg

m2∗4m=3000.00

Kg

m

NI)EL ABTEA:

CAR;AS HUERTAS:


m2∗2.6∗1.45=1055.6 Kg

pesode losa=280 Kg

m2∗4m=1120.00

Kg

m


m2∗4 m=400.00

Kg

m

pesode viga=0.25∗0.5∗2400=300.00 Kg

m

CAR;AS )I)AS

&obrecarga azotea=200 Kg

m2∗4 m=800.00

Kg

m

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