Diseño Viga Riostra Proyecto Final

2014

Cimentaciones en Roca Caliza en la Ciudad de Santo Domingo

DISEÑO DE VIGA RIOSTRA CAPAZ DE RESISTIR UN ASENTAMIENTO ASENTAMIENTO DIFERENCIAL IGUAL A 2.5CM(ASENTAMIENT 2.5CM(ASENTAMIENTO O PERM PERMIS ISIB IBLE LE SEGÚ SEGÚN N R-024 -024), ), LA MI MISM SMA A CUMPL UMPLIIRA CON LOS LOS ARTICULOS !0,!,!4,!! CORRESPONDIENTE AL CAPITULO V" DEL R-0. VIGAS (P23-A7),(P24-O7) : DATOS#$ b(cm)

h(cm)

I(cm4)

f’c(kg/cm2

Ec(kg/cm2)

L(cm)

fy(kg/cm2)

∆(cm)

4!0

4,200

2.5

)

Ec =15,100 √

3

bh I = 12

%0

%0

$,0&0,000.0 0

2&0

252,%!$.

P L 3 EI ∆ 3 ( 252,671.33∗1,080,000.00 ) si,∆ max= =2.5 cm ∴ P = 3 = =19,712.76 kg 3 3 EI L 470 3

M = PL=19,712.76 ( 470 ) =9,264,996.64 kg.cm

Di!"# % &'!i*+

'*❶ C+ /131 ' M6

0.719−

M d 0.53 ( b ) ( d

2

) ( f c ) '

=¿ 0.848 −

9,264,996.64

√

0.719−

w =0.848 −√ ¿

'

( )

f c 280 ρ= w =0.2977 =0.019849 f y 4200

78.1/

9,264,996.64 0.53 ( 60 ) ( 50

2

) ( 280 )

=0.2977

2014 ρb= 0.72

( ) f 'c fy

Cimentaciones en Roca Caliza en la Ciudad de Santo Domingo

(

0.003

0.003 +

)

= 0.72

fy 6

2.1 ¿ 10

( ) 280 4200

(

0.003 4200 0.003 + 6 2.1 ¿ 10

)

=0.0288

ρmax =0.75 ρb= 0.75 ( 0.0288 )=0.0216 ρ < ρmax

D39 " :38 1* 3/'" /+.

P* ❷ D39 " :38 1* 3/'" /+. 3 3 2 ' ' ' ' A s = ρ∗b∗ d =0.01984∗60∗50=59.55 cm → 10 ∅ 1 [ ¿ 8 ]+ 3 ∅ 3 / 4 [ ¿ 6 ]

%%ci.%. % !*i* y % c#m0!i* c#m0!i* (h!1!# %0c'# %0c'# 374 .!' -533)+6

T3;  1* 3'+*# As superir =59.22 cm → ! 1= 0.9 ( f y ) ( Assuperir ) =0.9 ( 4200 ) ( 59.22 )=223,851.60 kg 2

As i"ferir =1.424 cm →! 2=0.9 ( f y y ) ( As i"ferir ) =0.9 ( 4200 ) ( 1.424 ) =5,382.72 kg 2

R313  " 1*/'3;, ∅60.%5 #

[

]

# c =∅ 0.85 ( f ' c ) ( b∗h ) =0.65 [ 0.85 ( 280 ) ( 60∗60 ) ] =556,920.00 kg

Fuerza axial que deberá resistir la viga: Pur =0.25 ( A a )( P u ) donde: Pu = Carga vertical factorizada del elemento más cargado de los dos interconectados [g!" #a = #celeraci$n s%smica &orizontal del terreno 'fracci$n de g("

Com)arando ma*or carga factorizada de los elementos interconectados+ tenemos: ,- '.on( 4 9 0< 0 

556"27 26"53"58 8"5;

P/01 23'.on( 22"28 ;"23 -3"8-6">>

Para$ Para $ 7 :

1 ¿ 1.4 ( % )=1.4 ( 115.26 )=161.36 !" 2 ¿ 1.2 ( % )+ 1.6 ( L )=1.2 (115.26 )+1.6 ( 25.07 )=178.42 !"

3 ¿ 1.2 ( %)+ f 1 ( L)= 1.2 ( 115.26 )+ 1 ( 25.07 )=163.38 !"

4 ¿ Es&a es igua a a 3 ¿ 5 ¿ 1.2 ( %)+ 0.7 ( Ex )+ 0.3 ( Ey )+ L =1.2 ( 115.26 )+ 0.7 ( 14.19 )+0.3 (9.13 )+ 25.07 =174.1 !"

6 ¿ 0.9 ( % )=0.9 ( 115.26 )=103.73 !" 7 ¿ 0.9 ( % )+ 0.7 ( Ex )+ 0.3 ( Ey )=0.9 ( 115.26)+ 0.7 (14.19 )+ 0.3 ( 9.13 )=114.38 !"

P O! " /<* 1*/=313; 1*'*  " 2) 6$!&.424 T* Para pier 24 : 1 ¿ 1.4 ( % )=1.4 ( 22.29 )= 31.206 !" 2 ¿ 1.2 ( % )+ 1.6 ( L )=1.2 (22.29 )+ 1.6 (3.24 )=31.93 !"

3 ¿ 1.2 ( %)+ f 1 ( L)= 1.2 ( 22.29 )+( 1 ( 3.24 ))=29.988 !" 4 ¿ Es&a es igua a a 3 ¿

5 ¿ 1.2 ( %)+ 0.7 ( Ey )+ 0.3 ( Ex )+ L =1.2 ( 22.29 )+ 0.7 ( 75.88 )+ 0.3 ( 74.97 )+ 3.24 =105.6 !" 6 ¿ 0.9 ( % )=0.9 ( 22.29 )=20.06 !"

7 ¿ 0.9 ( % )+ 0.7 ( Ey )+ 0.3 ( Ex )=0.9 ( 22.29 )+ 0.7 (75.88 )+ 0.3 ( 74.97 )= 95.668 !"

P '3 24 " /<* 1*/=313; 1*'*  " 5) 6$05.5>5 T* 178.424 !" > 105.595 !" ∴ Pu=178.42 !"

Pur =0.25 ( 0.3 ) ( 178,424 )=13,381.80 kg

! 1 =223,851.60 kg > Pur=13,381.80 kg ∴ El acero resiste la fuerza axial $(

! 2 =5,382.72kg < Pur=13,381.80 kg ∴ El acero no resiste la fuerza axial .

D3'* +:*   1* ' ?+ T 2  1'@  33 " +@ 3" (P + ). 3 ' ' 3 ∅1 / 2 [ ¿ 4 ]

As i"ferir ¿ 3.81 cm → ! 2= 0.9 ( f y ) ( Asi"ferir )= 0.9 ( 4200 ) ( 3.81 ) =14,401.80 kg 2

! 2 =14,401.80 kg > Pur =13,381.80 kg ∴ El acero resiste la fuerza axial . $(

C?+*  1+ ' " 1* 3'+*.

ρ=

As superir + Asi"ferir b∗d

=

59.22 +3.81 =0.02101 < ρ max= 0.0216 ∴ $( . 60∗50

Di!"# #0%*!+

D*.$ &E8A O9A9E

;O;E9O DE DISE
)d =19,712.76 kg

M d= 9,264,996.64 kg

A9IA ρ=

63.03 =0.02101 60∗50

P* A) 1"1+"* " +@* 1* " 39*. * d =

)d ∅bd

=

19,712.76 kg = 8.76 2 0.75 ( 60 ) 50 cm

P* B) 1"1+"*  +@* ?+ = 33 " 1*1*. * cr =0.5 √ f ' c + 175

ρ∗) d∗d M d

=0.5 √ 280 + 175

( 0.02101 )∗19,712.76∗50 9,264,996.64

= 8.77

kg 2 cm

C?+*. *cr max= 0.93 √ 210 =13.476

kg cm

2

* cr +*cr max ie"-

P* C) :331 3 " :38 ?+3 3=*. * d =8.76

kg 2

cm

< * cr =8.77

kg cm

2

∴

E" 1*1* 3 " +@* 1*.

P* ) 1?+*  " */ (V $,$1)#

+

{

d

2 60 cm max =34.20

 dis =25 cm

E3=* H&  251/

VIGAS (D=-D7),(L=-L7) : DATOS#2 b(cm)

h(cm)

I(cm4)

f’c(kg/cm2)

50

50

L(cm)

fy(kg/cm2)

∆(cm)

!50

4,200

2.5

Ec =15,100 √

3

I =

Ec(kg/cm2)

bh

12

520,&.

2$0

2$&,&$>.!>

3 EI ∆ 3 ( 218,819.79∗520,833.33 ) P L si,∆ max= =2.5 cm ∴ P = 3 = =2,026.11 kg 3 3 EI 750 L 3

M = PL=2,026.11 ( 750 )=1,519,581.87 kg.cm

D39*  F"3;. '*❶ C+ /131 ' M6$,5$>,5&$.&! 78.1/ 0.719−

M d 0.53 ( b ) ( d

2

) ( f c ) '

√ =

=¿ 0.848 −

0.719−

1,519,581.87 0.53 ( 50 ) ( 40

2

) ( 210 )

=0.07502

w 0.848 −√ ¿

( )

'

f c 210 ρ= w =0.07502 = 0.005375 f y 4200

ρb= 0.72

( ) f 'c fy

(

0.003

0.003 +

0.0216 ρmax =0.75 ρb= 0.75 ¿

)

= 0.72

fy 6

2.1 ¿ 10

( ) 210

4200

(

0.003

0.003 +

4200 2.1 ¿ 10

6

)

=0.0216

)60.0$%2

ρ < ρmax D39 " :38 1* 3/'" /+.

P* ❷ D39 " :38 1* 3/'" /+.

4 2 '' A s = ρ∗b∗ d =0.005375∗50∗40=10.75 cm → 4 ∅3 / 4 [ ¿ 6 ]

C'13  3; <  1*/'3; (C?+* 1+"* !4 " R-0).2

T3;  1* 3'+*# As superir =11.4 cm → ! 1=0.9 ( f y ) ( Assuperir ) =0.9 ( 4200 ) ( 11.4 )= 43,092.00kg 2

As i"ferir ¿ 1.42 cm → ! 2= 0.9 ( f y ) ( Asi"ferir )=0.9 ( 4200 ) ( 1.42 ) =5,382.72kg 2

R313  " 1*/'3;, ∅60.%5 #

[

]

# c =∅ 0.85 ( f ' c ) ( b∗h ) =0.65 [ 0.85 ( 210 ) ( 50∗50 ) ] =290,062.50 kg


Com)arando ma*or carga factorizada de los elementos interconectados+ tenemos: 4 9 0< 0 

98 '.on( ;3"75 8"37 2"2 5"6

9-'.on( 5>"5> 2>";> -8"56 5"26

Para L 9 : 1 ¿ 1.4 ( % )=1.4 ( 34.61 )= 48.454 !"

2 ¿ 1.2 ( % ) + 1.6 ( L )=1.2 ( 34.61 )+ 1.6 ( 9.46 )=56.67 !" 3 ¿ 1.2 ( % ) + f 1 ( L )=1.2 ( 34.61 ) + 1 ( 9.46 )=50.99 !" 4 ¿ Es&a es igua a a 3 ¿

5 ¿ 1.2 ( % ) + 0.7 ( Ex )+ 0.3 ( Ey ) + L= 1.2 ( 34.61 ) + 0.7 ( 2.02 ) + 0.3 ( 1.50 ) + 9.46 =52.85!" 6 ¿ 0.9 ( % )=0.9 ( 34.61 )=31.15 !" 7 ¿ 0.9 ( % )+ 0.7 ( Ex )+ 0.3 ( Ey )=0.9 ( 34.61)+ 0.7 (2.02)+ 0.3 (1.50 )=33.01 !"

P L> " /<* 1*/=313; 1*'*  " 2) 65%.%%& T* Para L 7 : 1 ¿ 1.4 ( % ) =1.4 (108.18 )=151.45 !"

2 ¿ 1.2 ( % )+ 1.6 ( L )=1.2 (108.18 )+ 1.6 ( 28.38 )=175.225 !" 3 ¿ 1.2 ( %)+ f 1 ( L)= 1.2 ( 108.18)+( 1 ( 28.38 ))=158.196 !" 4 ¿ Es&a es igua a a 3 ¿ 5 ¿ 1.2 ( %)+ 0.7 ( Ey )+ 0.3 ( Ex )+ L =1.2 ( 108.18 )+ 0.7 (79.15 )+ 0.3 (10.25 )+ 28.4 =216.7 !"

6 ¿ 0.9 ( % )=0.9 ( 108.18)= 97.36 !" 7 ¿ 0.9 ( % )+ 0.7 ( Ey )+ 0.3 ( Ex )=0.9 (108.18)+ 0.7 (79.15 )+ 0.3 ( 10.25 )=155.84 !"

P '3 L! " /<* 1*/=313; 1*'*  " 5) 62$%.!T* 216.7 !" > 56.67 !" ∴ Pu=216.7 !"

Pur =0.25 ( 0.3 ) ( 216.7 ) =16,250.70 kg

! 1 =43,092 kg > Pur =16,250.70 kg ∴ El acero resiste la fuerza axial $(


D3'* +:*   1* ' ?+ T 2  1'@  33 " +@ 3" (P + ). 4 ' ' 4 ∅1 / 2 [ ¿ 4 ] As i"ferir ¿ 5.08 cm → ! 2 =0.9 ( f y ) ( Asi"ferir )= 0.9 ( 4200 ) ( 5.08 )=19,202.40 kg 2

! 2 =19,202.40> Pur=16,250.70 kg ∴ El acero resiste la fuerza axial .$(

C?+*  1+ ' " 1* 3'+*. ρ=


=

11.4 + 5.08 = 0.00824 < ρmax =0.0162 ∴ $( . 50∗40

# c =435,093.75 > Pur ∴ El concreto resiste la fuerza axial $( .

Di!"# #0%*!+2

D*. &E8A O9A9E

;O;E9O DE DISE
) d =2,026.11 kg

M d=1,519,581.87 kg

A9IA ρ=

16.48 =0.00824 50∗40

P* A) 1"1+"* " +@* 1* " 39*.

* d =

)d ∅bd

=

2,026.11 kg =1.3507 2 0.75 (50 ) 40 cm

P* B) 1"1+"*  +@* ?+ = 33 " 1*1*. * cr =0.5 √ f ' c + 175

ρ∗) d∗d M d

=0.5 √ 210 + 175

( 0.00824 )∗2,026.11∗40 1,59,581.87

=7.32

kg 2 cm

C?+*. *cr max= 0.93 √ 210 =13.476

kg cm

2


P* C) :331 3 " :38 ?+3 3=*. * d =1.35

kg cm

< * cr =7.32 2

kg cm

2

∴

E" 1*1* 3 " +@* 1*.

P* C) 1?+*  " */ (V $,$1)#

.+

{

d

2 60 cm .max =34.20

 dis =20 cm

E3=* H&  201/

VIGAS :

(&=-P65),(>=-P66)

DATOS# b(cm)

h(cm)

I(cm4)

f’c(kg/cm2

Ec(kg/cm2)

L(cm)

fy(kg/cm2)

∆(cm)

!%0

4,200

2.5

)

Ec =15,100 √

3

I =

50

50

bh

12

520,&.

2$0

2$&,&$>.!>

P L 3 EI ∆ 3 ( 218,819.79∗520,833.33 ) =2.5 cm ∴ P = 3 = =1,947.18 kg 3 3 EI L 760 3

si,∆ max=

M = PL=1,947.18 ( 760 )=1,479,855.96 kg.cm

Di!"# % &'!i*+ '*❶ C+ /131 ' M6 0.719−

M d 0.53 ( b ) ( d

2

) ( f c ) '

1,479,855.96

√ =

=¿ 0.848 −

0.719−

78.1/

1,479,855.96 0.53 ( 50 ) ( 40

2

) ( 210 )

=0.104495

w 0.848 −√ ¿

( )

'

f c 210 ρ= w =0.104495 = 0.005224782 f y 4200

ρb= 0.72

( ) f 'c fy

(

0.003

0.003 +

0.0216 ρmax =0.75 ρb= 0.75 ¿

)

= 0.72

fy 6

2.1 ¿ 10

( ) 210 4200

(

0.003 4200 0.003 + 6 2.1 ¿ 10

)

=0.0216

)60.0$%2

ρ < ρmax D39 " :38 1* 3/'" /+.

P* ❷ D39 " :38 1* 3/'" /+. A s = ρ∗b∗ d =0.005224782∗50∗40 =10.43 cm

2

4 ' ' 4 ∅3 / 4 [ ¿ 6 ]

C'13  3; <  1*/'3; (C?+* 1+"* !4 " R-0).

T3;  1* 3'+*# As superir =11.4 cm → ! 1=0.9 ( f y ) ( Assuperir ) =0.9 ( 4200 ) ( 11.4 )= 43,092.00kg 2


R313  " 1*/'3;, ∅60.%5 #

[

]

# c =∅ 0.85 ( f ' c ) ( b∗h ) =0.65 [ 0.85 ( 210 ) ( 50∗50 ) ] =290,062.50 kg


Com)arando ma*or carga factorizada de los elementos interconectados+ tenemos: F8 '.on( 4 9 0< 0 

;8"-> 5">7 ">2"85

P/01 5'.on( ;62";; >5"-5 ;;"65 66">;

Para / 9: 1 ¿ 1.4 ( % )=1.4 ( 39.78 )=55.69 !"

2 ¿ 1.2 ( % ) + 1.6 ( L )=1.2 ( 39.78 )+ 1.6 (10.86 )=65.112 !" 3 ¿ 1.2 ( % ) + f 1 ( L )=1.2 ( 39.78 ) + 1 ( 10.86 )=58.596 !" 4 ¿ Es&a es igua a a 3 ¿

5 ¿ 1.2 ( % ) + 0.7 ( Ex )+ 0.3 ( Ey ) + L= 1.2 ( 39.78 ) + 0.7 ( 2.91 ) + 0.3 ( 0.87 ) + 10.86 =60.894 !" 6 ¿ 0.9 ( % )=0.9 ( 39.78 )=35.802 !" 7 ¿ 0.9 ( % )+ 0.7 ( Ey )+ 0.3 ( Ex )=0.9 ( 39.78 )+ 0.7 (2.91 )+ 0.3 (0.87 )=38.1 !"

P F> " /<* 1*/=313; 1*'*  " 2) 6%5.$$2 T* Para PIE0 10 : 1 ¿ 1.4 ( % ) =1.4 (352.33 )=493.27 !"

2 ¿ 1.2 ( % )+ 1.6 ( L )=1.2 ( 352.33 )+ 1.6 ( 81.71)=553.53 !"

3 ¿ 1.2 ( %)+ f 1 ( L)= 1.2 ( 352.33)+( 1 ( 81.71 ))=504.50!" 4 ¿ Es&a es igua a a 3 ¿ 5 ¿ 1.2 ( %)+ 0.7 ( Ey )+ 0.3 ( Ex )+ L =1.2 ( 352.33 )+ 0.7 (55.83 )+ 0.3 (33.5 )+ 81.7 =553.64 !"

6 ¿ 0.9 ( % )=0.9 ( 352.3)= 317.09 !" 7 ¿ 0.9 ( % )+ 0.7 ( Ey )+ 0.3 ( Ex )=0.9 ( 352.33)+ 0.7 (55.83 )+ 0.3 ( 33.51 )=366.23 !"

P '3 $0 " /<* 1*/=313; 1*'*  " 5) 655.%T* 553.64 > 65.112 !" ∴ Pu=553.64 !"

Pur =0.25 ( 0.3 ) ( 553.64 ) =41,522.68 kg


! 2 =5,382.72 kg < Pur= 41,522.68 kg ∴ El acero no resiste la fuerza axial.

D3'* +:*   1* ' ?+ T 2  1'@  33 " +@ 3" (P + ). 4 ' ' 4 ∅3 / 4 [ ¿ 6 ] As i"ferir ¿ 11.4 cm →! 2= 0.9 ( f y ) ( Asi"ferir )=0.9 ( 4200 ) ( 11.4 )= 43,092.00 kg 2

! 2 =43,092.00 > Pur =41,522.68 kg ∴ El acero resiste la fuerza axial .$(

C?+*  1+ ' " 1* 3'+*. ρ=

Assuperir + Asi"ferir b∗d

=

11.4 + 11.4 =0.0114 < ρ max=0.0162 ∴ $( . 50∗40


Di!"# #0%*!+

D*. &E8A O9A9E

;O;E9O DE DISE
)d =1,947.18

M d=1,479,855.96 kg.cm

A9IA ρ=

22.8 =0.0114 50∗40

P* A) 1"1+"* " +@* 1* " 39*. * d =

)d ∅bd

=

1,947.18 kg =1.298 2 0.75 (50 ) 40 cm

P* B) 1"1+"*  +@* ?+ = 33 " 1*1*. * cr =0.5 √ f ' c + 175

ρ∗) d∗d M d

=0.5 √ 210 + 175

( 0.0114 )∗1,947.18∗40 1,479,855.96

=7.35

kg 2 cm

C?+*. *cr max= 0.93 √ 210 =13.476

kg cm

2


P* C) :331 3 " :38 ?+3 3=*. * d =1.298

kg cm

2

< * cr =7.35

kg cm

2

∴

E" 1*1* 3 " +@* 1*.

P* C) 1?+*  " */ (V $,$1)#

+

{

d

2 60 cm max =34.20

 dis =20 cm

E3=* H&  201/

VIGAS :

(A7-57),(L7-D7),(A?-D?),(L?-O?)

DATOS#4 b(cm)

h(cm)

I(cm4)

f’c(kg/cm2

Ec(kg/cm2)

L(cm)

fy(kg/cm2)

∆(cm)

!00

4,200

2.5

)

Ec 15,100 =√

3

I =

%0

%0

bh

12

$,0&0,000.0 0

2$0

2$&,&$>.!>

P L 3 EI ∆ 3 ( 218,819.79∗1,080,00.00 ) si,∆ max= =2.5 cm ∴ P = 3 = =5,167.46 kg 3 3 EI L 700 3

M = PL=5,167.46 ( 700 )=3,617,225.08 kg.cm

Di!"# % &'!i*+

'*❶ C+ /131 ' M6 0.719−

M d 0.53 ( b ) ( d

2

) ( f c ) '

3,617,225.08

√ =

=¿ 0.848 − 0.719−

78.1/

3,617,225.08 0.53 ( 60 ) ( 50

2

) ( 210 )

=0.13924

w 0.848 −√ ¿

( )

'

f c 210 ρ= w =0.13924 =0.00696 f y 4200

ρb= 0.72

( ) f 'c fy

(

0.003

0.003 +

0.0216 ρmax =0.75 ρb= 0.75 ¿

)

= 0.72

fy 6

2.1 ¿ 10

( ) 210 4200

(

0.003 4200 0.003 + 6 2.1 ¿ 10

)

=0.0216

)60.0$%2

ρ < ρmax D39 " :38 1* 3/'" /+.

P* ❷ D39 " :38 1* 3/'" /+. A s = ρ∗b∗ d =0.00696∗60∗ 50=20.89 cm

2

4 ' ' 4 ∅1 [ ¿ 8 ]

C'13  3; <  1*/'3; (C?+* 1+"* !4 " R-0).4

T3;  1* 3'+*# As superir =20.27 cm →! 1=0.9 ( f y ) ( Assuperir ) =0.9 ( 4200 ) ( 20.27 )=76,613.040 kg 2


R313  " 1*/'3;, ∅60.%5 #

[

]

# c =∅ 0.85 ( f ' c ) ( b∗h ) =0.65 [ 0.85 ( 210 ) ( 50∗50 ) ] =290,062.50 kg



,7 '.on( >6">7 5-"8; 52"3 55"36

97'.on( 582">; 6"; ;6"8 >";6

Para$ 6 : 1 ¿ 1.4 ( % )=1.4 ( 85.86 ) =120.204 !"

2 ¿ 1.2 ( % ) + 1.6 ( L )=1.2 ( 85.86 ) + 1.6 ( 17.93 )=131.72 !" 3 ¿ 1.2 ( % ) + f 1 ( L )=1.2 ( 85.86 ) + 1 ( 17.93 )=120.96 !" 4 ¿ Es&a es igua a a 3 ¿

5 ¿ 1.2 ( % ) + 0.7 ( Ex )+ 0.3 ( Ey ) + L= 1.2 ( 85.86 ) + 0.7 ( 12.04 )+ 0.3 ( 11.4 )+ 17.93 =132.83 !" 6 ¿ 0.9 ( % )=0.9 ( 85.56 ) =77.27!" 7 ¿ 0.9 ( % )+ 0.7 ( Ey )+ 0.3 ( Ex )=0.9 ( 85.56 )+ 0.7 (12.04 )+ 0.3 ( 11.4 )= 89.139 !"

P O% " /<* 1*/=313; 1*'*  " 5) 6$2.&2! T* Para L 6 : 1 ¿ 1.4 ( % ) =1.4 (192.83 )=269.962 !"

2 ¿ 1.2 ( % )+ 1.6 ( L )=1.2 ( 192.83 )+ 1.6 ( 50.03 )=311.44 !"

3 ¿ 1.2 ( %)+ f 1 ( L)= 1.2 ( 192.83)+( 1 ( 50.03 ))=281.43!" 4 ¿ Es&a es igua a a 3 ¿ 5 ¿ 1.2 ( %)+ 0.7 ( Ex )+ 0.3 ( Ey )+ L =1.2 ( 192.83 )+ 0.7 (35.9 )+ 0.3 (8.35 )+ 50.03 =311.44 !"

6 ¿ 0.9 ( % )=0.9 ( 192.83)= 173.55 !" 7 ¿ 0.9 ( % )+ 0.7 ( Ex )+ 0.3 ( Ey )=0.9 ( 192.83)+ 0.7 (35.9 )+ 0.3 (8.35 )=190.16 !"

P L% " /<* 1*/=313; 1*'*  " 2) 6$$.44T* 311.44 > 132.83 !" ∴ Pu=311.44 !"

Pur =0.25 ( 0.3 ) ( 311.44 )=23,358.30 kg


! 2 =5,382.72 kg < Pur=23,358 kg ∴ El acero no resiste la fuerza axial .

D3'* +:*   1* ' ?+ T 2  1'@  33 " +@ 3" (P + ). 5 ' ' 5 ∅1 / 2 [ ¿ 4 ] As i"ferir ¿ 7.774 cm →! 2=0.9 ( f y )( As i"ferir ) =0.9 ( 4200 ) ( 7.774 ) =29,385.72kg 2

! 2 =29,385.72> P ur=23,358.00 kg ∴ El acero resiste la fuerza axial .$(

C?+*  1+ ' " 1* 3'+*. ρ=


=

20.568+ 7.774 =0.00934733 < ρ max=0.0162 ∴ $( . 60∗50


Di!"# #0%*!+

D*.4 &E8A O9A9E

;O;E9O DE DISE
)d =5,167.46 kg

M d= 3,617,225.08 kg .cm

A9IA ρ=

28.04 =0.0714285 60∗50

P* A) 1"1+"* " +@* 1* " 39*. * d =

)d ∅bd

=

5,167.46 kg =2.296 2 0.75 ( 60 ) 50 cm

P* B) 1"1+"*  +@* ?+ = 33 " 1*1*. * cr =0.5 √ f ' c + 175

ρ∗) d∗d M d

=0.5 √ 210 + 175

( 0.0714285 )∗5,167.46∗50 3,617,225.08

=7.36

kg 2 cm

C?+*. *cr max= 0.93 √ 210 =13.476

kg cm

2


P* C) :331 3 " :38 ?+3 3=*. kg

* d =2.296

2

cm

< * cr =7.36

kg 2

cm

∴

E" 1*1* 3 " +@* 1*.

P* C) 1?+*  " */ (V $,$1)#

+

{

d

2 60 cm max =34.20

 dis =25 cm

E3=* H&  251/

VIGAS :

(@-PIE64),(;@-PIE25)

DATOS#% b(cm)

h(cm)

I(cm4)

f’c(kg/cm2

Ec(kg/cm2)

L(cm)

fy(kg/cm2)

∆(cm)

!45

4,200

2.5

)

Ec =15,100 √

3

I =

50

50

bh

12

520,&.

2$0

2$&,&$>.!>

P L 3 EI ∆ 3 ( 218,819.79∗520,833.33 ) si,∆ max= =2.5 cm ∴ P = 3 = =2,067.18 kg 3 3 EI L 745 3

M = PL=2,067.18 ( 745 )=1,540,047.39 kg.cm

Di!"# % &'!i* .

'*❶ C+ /131 ' M6 0.719−

M d 0.53 ( b ) ( d

2

) ( f c ) '

1,540,047.39

√ =

=¿ 0.848 −

0.719−

78.1/

1,540,047.39 0.53 ( 50 ) ( 40

2

) ( 210 )

=0.109055

w 0.848 −√ ¿

( )

'

f c 210 ρ= w =0.109055 = 0.005452784 f y 4200

ρb= 0.72

( ) f 'c fy

(

0.003

0.003 +

0.0216 ρmax =0.75 ρb= 0.75 ¿

)

= 0.72

fy 6

2.1 ¿ 10

( ) 210 4200

(

0.003 4200 0.003 + 6 2.1 ¿ 10

)

=0.0216

)60.0$%2

ρ < ρmax D39 " :38 1* 3/'" /+.

P* ❷ D39 " :38 1* 3/'" /+. A s = ρ∗b∗ d =0.00545∗50∗ 40=10.905 cm

2

2 1 ' ' ' ' 2 ∅1 [ ¿ 8 ] + 1 ∅1 / 2 [ ¿ 4 ]

C'13  3; <  1*/'3; (C?+* 1+"* !4 " R-0).%

T3;  1* 3'+*# As superir =11.4 cm →! 1=0.9 ( f y )( As superir )= 0.9 ( 4200 ) (11.4 ) =43,107.12 kg 2


R313  " 1*/'3;, ∅60.%5 #

[

]

# c =∅ 0.85 ( f ' c ) ( b∗h ) =0.65 [ 0.85 ( 210 ) ( 50∗50 ) ] =290,062.50 kg


Com)arando ma*or carga factorizada de los elementos interconectados+ tenemos: C6 '.on( 4 9 0< 0 

--"35 56"87 32"-8 -";3

P/0153'.o n( 2-8";5 76">; ;"7; 5-"72

Para# 5 : 1 ¿ 1.4 ( % )=1.4 ( 77.41 )=108.37 !" 2 ¿ 1.2 ( % ) + 1.6 ( L )=1.2 ( 77.41 )+ 1.6 ( 15.96 )=118.85 !" 3 ¿ 1.2 ( % ) + f 1 ( L )=1.2 ( 77.41 ) + 1 ( 15.96 )=108.85 !" 4 ¿ Es&a es igua a a 3 ¿

5 ¿ 1.2 ( % ) + 0.7 ( Ex )+ 0.3 ( Ey ) + L= 1.2 ( 77.41 )+ 0.7 ( 42.79 ) + 0.3 ( 7.34 )+ 15.96=126.82 !" 6 ¿ 0.9 ( % )=0.9 ( 77.41 )=87.64 !" 7 ¿ 0.9 ( % )+ 0.7 ( Ey )+ 0.3 ( Ex )=0.9 ( 77.41)+ 0.7 (42.79 )+ 0.3 ( 7.34 )= 87.64 !"

P C5 " /<* 1*/=313; 1*'*  " 5) 6$2%.&2 T* Para PIE0 14 : 1 ¿ 1.4 ( % )=1.4 ( 279.31 )=391.03 !" 2 ¿ 1.2 ( % )+ 1.6 ( L )=1.2 (279.31 )+ 1.6 (65.83 )=440.50 !"

3 ¿ 1.2 ( %)+ f 1 ( L)= 1.2 ( 279.31)+( 1 ( 65.83 ))= 401.01!" 4 ¿ Es&a es igua a a 3 ¿

5 ¿ 1.2 ( %)+ 0.7 ( Ex )+ 0.3 ( Ey )+ L =1.2 ( 279.31)+ 0.7 ( 30.6 )+ 0.3 ( 17.6 )+ 65.8 =427.73 !" 6 ¿ 0.9 ( % )=0.9 ( 279.31)=251.37 !"

7 ¿ 0.9 ( % )+ 0.7 ( Ex )+ 0.3 ( Ey )=0.9 ( 279.31)+ 0.7 ( 30.63 )+ 0.3 ( 17.62)= 278.11 !"

P PIER$4 " /<* 1*/=313; 1*'*  " 2) 6440.50 T* 440.50 !" > 126.827 !" ∴ Pu= 440.50 !"

Pur =0.25 ( 0.3 ) ( 440.5 )=33,037.78 kg

! 1 =43,107.12 kg > Pur =33,037.78 kg ∴ El acero resiste la fuerza axial $(

! 2 =5,382.72 kg < Pur=33,037.78 kg ∴ El acero no resiste la fuerza axial .

D3'* +:*   1* ' ?+ T 2  1'@  33 " +@ 3" (P + ). 2 ' ' 2 ∅1 [ ¿ 8 ] As i"ferir ¿ 10.134 m → ! 2=0.9 ( f y )( Asi"ferir ) =0.9 ( 4200 ) ( 10.134 )=38,306.52 kg 2

! 2 =38,306.52kg > Pur =33,037.78 kg ∴ El acero resiste la fuerza axial . $(

C?+*  1+ ' " 1* 3'+*. ρ=


=

11.4 . +10.13 =0.010769 < ρ max= 0.0162 ∴ $( . 50∗40


Di!"# #0%*!+?

D*. &E8A O9A9E

;O;E9O DE DISE
)d =2,067.18 kg

M d=1,540,047.39 kg.cm

A9IA ρ=

21.54 =0.010769 50∗40

P* A) 1"1+"* " +@* 1* " 39*. * d =

)d ∅bd

=

2,067.18 kg =1.378 2 0.75 (50 ) 40 cm

P* B) 1"1+"*  +@* ?+ = 33 " 1*1*. * cr =0.5 √ f ' c + 175

ρ∗) d∗d M d

=0.5 √ 210 + 175

( 0.010769 )∗2,067.18∗40 1,540,047.39

=7.3468

kg 2 cm

C?+*. *cr max= 0.93 √ 210 =13.476

kg cm

2


P* C) :331 3 " :38 ?+3 3=*. * d =1.378

kg

kg

cm

cm

< * cr =7.346 2

2

∴

E" 1*1* 3 " +@* 1*.

P* C) 1?+*  " */ (V $,$1)#

+

{

d

2 60 cm max =34.20

 dis =20 cm

E3=* H&  201/

VIGAS :

(E@-PIE),(B@-PIE=)

DATOS#! b(cm)

h(cm)

I(cm4)

f’c(kg/cm2)

50

55

L(cm)

fy(kg/cm2)

∆(cm)

!5

4,200

2.5

Ec =15,100 √

3

I =

Ec(kg/cm2)

bh

12

%>,22>.$!

2&0

252,%!$.


M = PL=3,308.51 (735 )=2,431,752.52 kg.cm

Di!"# % &'!i*+

'*❶ C+ /131 ' M6 0.719−

M d 0.53 ( b ) ( d

2

) ( f c ) '

1,540,047.39

√ =

=¿ 0.848 −

0.719−

78.1/

2,431,752.52 0.53 ( 50 ) ( 45

2

) ( 280 )

=0.1015696

w 0.848 −√ ¿

( )

'

f c 280 ρ= w =0.1015696 =0.006771309 f y 4200

ρb= 0.72

( ) f 'c fy

(

0.003

0.003 +

)

= 0.72

fy 6

2.1 ¿ 10

( ) 280 4200

(

0.003 4200 0.003 + 6 2.1 ¿ 10

)

=0.0288

ρmax =0.75 ρb= 0.75 ( 0.0288 )=0.0216

ρ < ρmax D39 " :38 1* 3/'" /+.

P* ❷ D39 " :38 1* 3/'" /+. A s = ρ∗b∗ d =0.00671309∗ 50∗45=15.23 cm

2

3 ' ' 3 ∅1 [ ¿ 8 ]

C'13  3; <  1*/'3; (C?+* 1+"* !4 " R-0).! T3;  1* 3'+*#

As superir =15.201cm →! 1=0.9 ( f y )( As superir )= 0.9 ( 4200 ) (15.459.78) = 57,459.78 kg 2

As i"ferir ¿ 1.42 cm → ! 2= 0.9 ( f y ) ( Asi"ferir )=0.9 ( 4200 ) ( 1.42 ) =5,382.72 kg 2

R313  " 1*/'3;, ∅60.%5 #

[

]

# c =∅ 0.85 ( f ' c ) ( b∗h ) =0.65 [ 0.85 ( 280 ) ( 50∗55 ) ] = 425,425.00 kg



?3 '.on( 2;7"6-2"-"7 57">;

P/018'.on( 732"55 575"85 72"5-7"7-

Para( 4 :

1 ¿ 1.4 ( % )=1.4 ( 236.57 )= 331.198!" 2 ¿ 1.2 ( % ) + 1.6 ( L )=1.2 ( 236.57 ) + 1.6 ( 72.07 )=399.196 !"

3 ¿ 1.2 ( % ) + f 1 ( L )=1.2 ( 236.57 ) + 1 ( 72.07 )=355.954 !" 4 ¿ Es&a es igua a a 3 ¿ 5 ¿ 1.2 ( % ) + 0.7 ( Ex )+ 0.3 ( Ey ) + L=1.2 ( 236.6 ) + 0.7 ( 16.8 ) + 0.3 ( 7.6 )+ 72.07 =370.01 !"

6 ¿ 0.9 ( % )=0.9 ( 236.57 )= 212.91!" 7 ¿ 0.9 ( % )+ 0.7 ( Ey )+ 0.3 ( Ex )=0.9 ( 236.57 )+ 0.7 (16.83 )+ 0.3 ( 7.6 )=226.97 !"

P J5 " /<* 1*/=313; 1*'*  " 2) 6>>.$>% T* Para PIE0 9 : 1 ¿ 1.4 ( % ) =1.4 ( 642.11)=898.95 !"

2 ¿ 1.2 ( % )+ 1.6 ( L )=1.2 ( 642.11 )+ 1.6 ( 161.91)=1,029.59 !" 3 ¿ 1.2 ( %)+ f 1 ( L)= 1.2 ( 642.11 )+( 1 ( 161.91 ))=932.44 !" 4 ¿ Es&a es igua a a 3 ¿ 5 ¿ 1.2 ( %)+ 0.7 ( Ex )+ 0.3 ( Ey )+ L =1.2 ( 642.1 )+ 0.7 ( 76.67 )+ 0.3 (62.2 )+ 161.9 =1004.8 !"

6 ¿ 0.9 ( % )=0.9 ( 642.11 )=577.89 !" 7 ¿ 0.9 ( % )+ 0.7 ( Ex )+ 0.3 ( Ey )=0.9 (642.1)+ 0.7 (76.67 )+ 0.3 (62.2 )=650.219 !"

P PIER> " /<* 1*/=313; 1*'*  " 2) 6$,02>.5> T* 1,029.59 !" > 399.196 !" ∴ Pu =1,029.59 !"

Pur =0.25 ( 0.3 ) ( 1,029.59 )=77,219.28 kg

! 1 =57,459.78 kg < Pur =77,219.28 kg ∴ El acero no resiste la fuerza axial.


D3'* +:*   1* ' ?+ T $ K T2  1'@  33 " +@ 3" (P + ).

5 ' ' 5 ∅3 / 4 [ ¿ 6 ] 

5 ' ' 5 ∅1 / 2 [ ¿ 4 ]

As superir =20.6 cm →! 1=0.9 ( f y ) ( Assuperir ) =0.9 ( 4200 ) ( 20.6 )=77,868.00 kg 2

As i"ferir ¿ 20.6 cm → ! 2=0.9 ( f y )( Asi"ferir ) =0.9 ( 4200 ) ( 20.6 )=77,868.00 kg 2

! 1 =! 2=77,868.00 kg > Pur =77,219.28 kg ∴ El acero resiste la fuerza axial . $(

C?+*  1+ ' " 1* 3'+*. ρ=


=

20.6 + 20.6 =0.018311< ρmax =0.0216 ∴ $( . 50∗45


Di!"# #0%*!+7

D*. &E8A O9A9E

;O;E9O DE DISE
)d =3,308.51 kg

M d= 2,431,752.52 kg.cm

A9IA ρ=

41.2 =0.018311 50∗45

P* A) 1"1+"* " +@* 1* " 39*. * d =

)d ∅bd

=

3,308.51 kg =1.96 2 0.75 (50 ) 45 cm

P* B) 1"1+"*  +@* ?+ = 33 " 1*1*. * cr =0.5 √ f ' c + 175

C?+*.

ρ∗) d∗d M d

=0.5 √ 280 + 175

( 0.018311 )∗2,067.18∗40 2,431,752.52

=8.56

kg 2 cm

kg

*cr max= 0.93 √ 280 =15.56

2

cm


P* C) :331 3 " :38 ?+3 3=*. * d =1.96

kg

kg

cm

cm

< * cr =8.56 2

2

∴

E" 1*1* 3 " +@* 1*.

P* C) 1?+*  " */ (V $,$1)#

+

{

d

2 60 cm max =34.20

 dis =22 cm

E3=* H&  22 1/

VIGAS :

(PIE-PIE6@),(PIE=-PIE6=)

DATOS#& b(cm)

h(cm)

I(cm4)

f’c(kg/cm2

Ec(kg/cm2)

L(cm)

fy(kg/cm2)

∆(cm)

!%0

4,200

2.5

)

Ec =15,100 √

3

I =

50

%0

bh

12

>00,000.00

2&0

252,%!$.


M = PL=3,885.25 ( 760 )=2,952,789.93 kg.cm

D39*  F"3;. '*❶ C+ /131 ' M6 2,952,789.93 78.1/ 0.719−

M d 0.53 ( b ) ( d

2

) ( f c ) '

√ =

=¿ 0.848 −

0.719−

2,952,789.93 0.53 ( 50 ) ( 50

2

) (280 )

= 0.099788

w 0.848 −√ ¿

( )

'

280 f c ρ= w =0.099788 = 0.006652589 4200 f y

ρb= 0.72

( ) f 'c fy

(

0.003

0.003 +

)

= 0.72

fy 6

2.1 ¿ 10

( ) 280

4200

ρmax =0.75 ρb= 0.75 ( 0.0288 )=0.0216 ρ < ρmax D39 " :38 1* 3/'" /+.

P* ❷ D39 " :38 1* 3/'" /+. A s = ρ∗b∗ d =0.0066525∗50∗50 =16.63 cm

3 3 ' '

' '

4 ∅3 / 4 [ ¿ 6 ] + 4 ∅1 / 2 [ ¿ 4 ]

2

(

0.003

0.003 +

4200 2.1 ¿ 10

6

)

=0.0288

C'13  3; <  1*/'3; (C?+* 1+"* !4 " R-0).& T3;  1* 3'+*# As superir =16.48 cm →! 1=0.9 ( f y ) ( As superir ) = 0.9 ( 4200 ) ( 16.48 )=62,294.40 kg 2

As i"ferir ¿ 1.42 cm → ! 2= 0.9 ( f y ) ( Asi"ferir )=0.9 ( 4200 ) ( 1.42 ) =5,382.72 kg 2

R313  " 1*/'3;, ∅60.%5 #

[

]

# c =∅ 0.85 ( f ' c ) ( b∗h ) =0.65 [ 0.85 ( 280 ) ( 50∗50 ) ] = 464,100.00 kg


Com)arando la ma*or carga factorizada de los elementos interconectados+ tenemos:

4 9 0< 0  Para PIE0 19 :

P/0158 '.on( 7;-"-7 5;-"8> 5>";8 255"52

P/018'.on( 732"55 575"85 72"5-7"7-

1 ¿ 1.4 ( % )=1.4 ( 637.76 )= 892.85!" 2 ¿ 1.2 ( % ) + 1.6 ( L )=1.2 ( 637.76 ) + 1.6 ( 137.98 )=986.07 !" 3 ¿ 1.2 ( % ) + f 1 ( L )=1.2 ( 637.76 ) + 1 ( 137.98 )=903.28 !" 4 ¿ Es&a es igua a a 3 ¿

5)1.2 (  ) !0.7 ( Ex ) !0.3 ( E" ) !#=1.2 ( 637.8 ) !0.7 ( 211.1 ) !0.3 ( 180.4 ) !137.98=1,105.18$on 6 ¿ 0.9 ( % )=0.9 ( 637.36 )= 573.98!" 7 ¿ 0.9 ( % )+ 0.7 ( Ey )+ 0.3 ( Ex )=0.9 ( 637.36 )+ 0.7 ( 211.12)+ 0.3 ( 180.39 )=775.879 !"

P PIER $> " /<* 1*/=313; 1*'*  " 5) 6$,$05.$& T* Para PIE0 9 : 1 ¿ 1.4 ( % )=1.4 ( 642.11)= 898.95 !" 2 ¿ 1.2 ( % )+ 1.6 ( L )=1.2 (642.11 )+ 1.6 (161.91 )=1,029.59 !"

3 ¿ 1.2 ( %)+ f 1 ( L)= 1.2 ( 642.11 )+( 1 ( 161.91 ))= 932.44 !" 4 ¿ Es&a es igua a a 3 ¿

5 ¿ 1.2 ( %)+ 0.7 ( Ex )+ 0.3 ( Ey )+ L =1.2 ( 642.1)+ 0.7 ( 76.67 )+ 0.3 ( 62.2 )+ 161.9=1004.8 !" 6 ¿ 0.9 ( % )=0.9 ( 642.11 )=577.89 !"

7 ¿ 0.9 ( % )+ 0.7 ( Ex )+ 0.3 ( Ey )=0.9 ( 642.1)+ 0.7 ( 76.67 )+ 0.3 ( 62.2 )=650.219 !"

P PIER> " /<* 1*/=313; 1*'*  " 2) 6$,02>.5> T* 1,105.18 !" > 1,029.59 !" ∴ Pu =1,105.18 !"

Pur =0.25 ( 0.3 ) ( 1,105.18 )= 81,886.01 kg

! 1 =62,294.40 < Pur=81,886.01 kg ∴ El acero no resiste la fuerza axial.

! 2 =5,382.72 kg < Pur=81,886.018 kg ∴ El acero no resiste la fuerza axial .

D3'* +:*   1* ' ?+ T $ K T2  1'@  33 " +@ 3" (P + ). 1 ' ' 4 ∅1 [ ¿ 8 ] 

2 ' ' 2 ∅1 / 2 [ ¿ 4 ]

As superir =22.8 cm →! 1=0.9 ( f y ) ( As superir ) =0.9 ( 4200 ) ( 22.8 )=86,214.24 kg 2

As i"ferir ¿ 22.8 cm → ! 2 =0.9 ( f y ) ( Asi"ferir ) =0.9 ( 4200 ) ( 22.8 )=86,214.24 kg 2

! 1 =! 2= 86,214.24 kg > Pur =81,886.018 kg ∴ El acero resiste la fuerza axial .$(

C?+*  1+ ' " 1* 3'+*. ρ=

Assuperir + Asi"ferir b∗d

=

22.8+ 22.8 =0.01824 < ρmax =0.0216 ∴ $( . 50∗50


Di!"# #0%*!+

D*.& &E8A O9A9E )d =3,885.25 kg

;O;E9O DE DISE
A9IA ρ=

45.62 =0.0182464 50∗50

P* A) 1"1+"* " +@* 1* " 39*. * d =

)d ∅bd

=

3,885.25 0.75 (50 ) 50

=2.072

kg 2 cm

P* B) 1"1+"*  +@* ?+ = 33 " 1*1*. * cr =0.5 √ f ' c + 175

ρ∗) d∗d M d

=0.5 √ 280 + 175

( 0.0182464 )∗3,885.25∗50 2,952,789.93

=8.576

kg 2 cm

C?+*. *cr max= 0.93 √ 280 =15.56

kg 2

cm


P* C) :331 3 " :38 ?+3 3=*. * d =2.072

kg

kg

cm

cm

< * cr= 8.56 2

2

∴

E" 1*1* 3 " +@* 1*.

P* C) 1?+*  " */ (V $,$1)#

.+

{

d

2 60 cm .max =34.20

 dis =30 cm

E3=* H&  01/

Diseño Viga Riostra Proyecto Final

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