dise+æo de vigas

8/18/2019 DISE+æO DE VIGAS

1/44

DISEÑO DE VIGAS PRINCIPALES (DAMERO 2)

TRAMO 5-6

b = 35 cm

h = 55 cm

f'c = 250

9247.85 km-m fy = 4200

MU= 92.48 km-cm rec = 4 cm

Estimando d!-6 (As "n #na $i%a)

d= 49 cm

Ca%%o d" %a ant'a

w= 0.85 - 0.7225 -1.7*MU

w = 0.85 -Ø f'c b d2

w = 0.0005

w= Pfy

0.0005 = P250

P = 0.0084f'c 4200

As=P*b*d As = 14.41 cm2

CANTA MNIMA * M+,IMA

0.7 = 0.7250

f'c

4200

0.75 = 0.75 0.85 !f'c

*"000

fy "000 # fy

Acero mínimo y máximo

Asm$%=Pm$%*b*d Asm$% = 4.459 cm2 &$ cm()e ) f)) dc+$

Asm,=Pm,*b*d Asm$% = 32.585 cm2 cm()e f)) dc+$)

cosideramos el As mín = 4.459 cm2

+"a d" a&"os+

km/cm2

km/cm2

Pm$% = Pm$%

Pm, = Pb


2/44

1 5.07

r$))s= As=

4.459 3/4 2.85

As e)e$d 1.98 5/8 1.98

1/2 1.29

r$))s= 2.3 3/8 0.71

&e c)cr% 3 Ø 1/2 $me+r de cers

0 Diam"to(&mV"i$i&ando "% $i"o 1 2.54

3/4 1.91

e= 2* 4 # 0.95 * 2 # 3 * 1.29 # 2 * 1.98 5/8 1.59

1/2 1.27

e= 17.73 3/8 0.95

V"i$i&ando "% 1"a%t" "$"&ti/o

d= h - rec - Ø es+r$b. - Ø/2

d= 49.4

a%%ando "% mom"nto "sist"nt"

6M%=6*b*d2*w*f'c*1-0.59*w 0.9 35 2440.3" 0.0084 250 1 - 0.

6M%=6*A&*fy*d*1-0.59*fy/fc*As/b*d 6M% = 811353."58

6M% > M


TRAMO 6-3

b = 35 cm

h = 55 cm

f'c = 250

1108".14 km-m fy = 4200

MU= 110.8" km-cm rec = 4 cm


km/cm2

km/cm2


3/44

Ca%%o d" %a ant'a

w= 0.85 - 0.7225 -1.7*MU

w = 0.85 -Ø f'c b d2

w = 0.0005

w= Pfy

0.0005 = P250

P = 0.0084f'c 4200

As=P*b*d As = 14.41 cm2


0.7 = 0.7250

f'c4200

0.75 = 0.75 0.85 !f'c

*"000

fy "000 # fy





+"a d" a&"os

N.m"o d" /ai%%as 0 +"a (&m2)1 5.07

r$))s= As=

4.459 3/4 2.85

As e)e$d 1.98 5/8 1.98

1/2 1.29

r$))s= 2.3 3/8 0.71



3/4 1.91

e= 2* 4 # 0.95 * 2 # 3 * 1.29 # 2 * 1.98 5/8 1.59

1/2 1.27

e= 17.73 3/8 0.95


d= h - rec - Ø es+r$b. - Ø/2

Pm$% = Pm$%

Pm, = Pb


4/44

d= 49.4


6M%=6*b*d2*w*f'c*1-0.59*w 0.9 35 2440.3" 0.0084 250 1 - 0.

6M%=6*A&*fy*d*1-0.59*fy/fc*As/b*d 6M% = 811353."58

6M% > M


TRAMO 3-4

b = 35 cm

h = 55 cm

f'c = 250

3241."5 km-m fy = 4200



3d= 49 cm

Ca%%o d" %a ant'a

w= 0.85 - 0.7225 -1.7*MU

w = 0.85 -Ø f'c b d2

w = 0.0005

w= Pfy

0.0005 = P250

P = 0.0084f'c 4200

km/cm2

km/cm2


5/44

As=P*b*d As = 14.41 cm2


0.7 = 0.7250

f'c

4200

0.75 = 0.75 0.85 !f'c

*"000

fy "000 # fy





+"a d" a&"os

N.m"o d" /ai%%as 0 +"a (&m2)1 5.07

r$))s= As=

4.459 3/4 2.85

As e)e$d 1.98 5/8 1.98

1/2 1.29

r$))s= 2.3 3/8 0.71



3/4 1.91

e= 2* 4 # 0.95 * 2 # 3 * 1.29 # 2 * 1.98 5/8 1.59

1/2 1.27

e= 17.73 3/8 0.95


d= h - rec - Ø es+r$b. - Ø/2

d= 49.4


6M%=6*b*d2*w*f'c*1-0.59*w 0.9 35 2440.3" 0.0084 250 1 - 0.

6M%=6*A&*fy*d*1-0.59*fy/fc*As/b*d 6M% = 811353."58

Pm$% = Pm$%

Pm, = Pb


6/44

6M% > M


TRAMO -7

b = 35 cm

h = 55 cm

f'c = 2509099.9" km-m fy = 4200



d= 49 cm

Ca%%o d" %a ant'a

w= 0.85 - 0.7225 -1.7*MU

w = 0.85 -

Ø f'c b d2

w = 0.0005

w= Pfy

0.0005 = P250

P = 0.0084f'c 4200

As=P*b*d As = 14.41 cm2


0.7 = 0.7250

f'c

4200

0.75 = 0.75 0.85 !f'c

*"000

fy "000 # fy



Asm,=Pm,*b*d Asm$% = 32 585 cm2 cm()e f)) dc+$)

km/cm2km/cm2

Pm$% = Pm$%

Pm, = Pb


7/44


+"a d" a&"os

N.m"o d" /ai%%as 0 +"a (&m2)1 5.07

r$))s= As

=

4.459 3/4 2.85

As e)e$d 1.98 5/8 1.981/2 1.29

r$))s= 2.3 3/8 0.71



3/4 1.91

e= 2* 4 # 0.95 * 2 # 3 * 1.29 # 2 * 1.98 5/8 1.59

1/2 1.27

e= 17.73 3/8 0.95


d= h - rec - Ø es+r$b. - Ø/2

d= 49.4


6M%=6*b*d2*w*f'c*1-0.59*w 0.9 35 2440.3" 0.0084 250 1 - 0.

6M%=6*A&*fy*d*1-0.59*fy/fc*As/b*d 6M% = 811353."58

6M% > M


TRAMO 7-

b = 35 cm

h = 55 cm

f'c = 250 km/cm2


8/44

55

35

0.7225 -1.7 *

0.9 250

= 0.002"

= 0.019

)


9/44

9 0.0084 = 1

55

35


10/44

0.7225 -1.7 *

0.9 250

= 0.002"

= 0.019

)


11/44

9 0.0084 = 1

55 cm

cm

0.7225 -1.7 *

0.9 250


12/44

= 0.002"

= 0.019

)

9 0.0084 = 1


13/44

55

35

0.7225 -1.7 *

0.9 250

= 0.002"

= 0.019

)


14/44

9 0.0084 = 1


15/44

DISEÑO DE VIGAS DE PORTICO SECNDARIO

$ser ) $ de ) f$r f'c= 210 :/cm2 f'y = 4200 :/cm2.

0.2

0.25

3.80 M 25

DISEÑO POR 8LE,ION

MU= 3.04 MU= 3.37

MU= 1.71

+"a d" a&"os

M# (tn9&m)0 +"a (&m2)1 5.07

3.044 25 19.91 4.53 4.2" 3/4 2.851.7115 25 19.91 2.41 2.27 5/8 1.98

3.37 25 19.91 5.09 4.79 1/2 1.27

3/8 0.71

3 6 5/8 3 6 5/8 3 6 5/8

26 1/2 26 1/2 46 1/2

16 5/8

As = 2.54 cm2 As = 2.54 cm2 As = 5.08 cm2

1.98

4.52

0.7 = 0.7210

= 0.0024f'c

4200

f'c "000

:(&m;)

d(&m;)

As(&m2)

a(&m)

Pm$% = Pm$%


16/44

. . .fy "000 # fy

.

0.85 !f'c "000

= 0.85 0.85210 "000

= 0.02125fy "000 # fy 4200 "000 # 4200

As =

4.53 = 0.007

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

As =

2.41 = 0.004

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

As =

5.09 = 0.008

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

(r ) secc$% med$ se d$se c% ) c%+$ m$%$m

MU= 3.78 MU= 4.30

MU= 2.10

+"a d" a&"os

M# (tn9&m)0 +"a (&m2)1 5.07

3.783 25 19.91 5.83 5.49 3/4 2.85

2.095 25 19.91 3.00 2.82 5/8 1.98

4.30 25 19.91 ".81 ".41 1/2 1.27

3/8 0.71

3 6 5/8 3 6 5/8 3 6 5/8

26 1/2 16 1/2

36 5/8 26 3/4

As = 5.94 cm2 As = 2.54 cm2 As = 5.70 cm2

1.27

".97

0.7 = 0.7210

= 0.0024f'c

4200

0.75 = 0.75 0.85 !f'c "000

= 0.0159fy "000 # fy

f'c "000 =

210 "000 =

Pb =

P1 =

P2 =

P3 =

:(&m;)

d(&m;)

As(&m2)

a(&m)

Pm$% = Pm$%

Pm, = Pb

=


17/44

.fy "000 # fy

. .4200 "000 # 4200

.

As =

5.83 = 0.009

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

As =

3.00 = 0.005

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

As =

".81 = 0.011

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

MU= 4.87 MU= 4.33

MU= 2.5"

+"a d" a&"os

M# (tn9&m)0 +"a (&m2)1 5.07

4.8"9 25 19.91 7.97 7.50 3/4 2.85

2.5"3 25 19.91 3.74 3.52 5/8 1.98

4.33 25 19.91 ".8" ".4" 1/2 1.27

3/8 0.71

3 6 5/8 3 6 5/8 3 6 5/8

26 5/8

46 5/8 26 1/2 26 5/8

As = 7.92 cm2 As = 3.81 cm2 As = 3.9" cm2

2.54

".50

0.7 = 0.7210

= 0.0024f'c

4200

0.75 = 0.75 0.85 !f'c "000

= 0.0159fy "000 # fy

0.85 !f'c "000

= 0.85 0.85210 "000

= 0.02125fy "000 # fy 4200 "000 # 4200

As =

7.97 = 0.013

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

P1 =

P2 =

P3 =

:(&m;)

d(&m;)

As(&m2)

a(&m)

Pm$% = Pm$%

Pm, = Pb

Pb =

P1 =


18/44

As =

3.74 = 0.00"

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

As =

".8" = 0.011

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

DISEÑO DE VIGAS DE LA A


19/44

+$)$?ms ) c%+$ m$%$m 2.7cm2

MU= 2.01 MU= 1.9"

MU= 1.24

+"a d" a&"os

M# (tn9&m)0 +"a (&m2)1 5.07

2.008 25 19.91 2.8" 2."9 3/4 2.85

1.23" 25 19.91 1.71 1."1 5/8 1.98

1.9" 25 19.91 2.78 2."2 1/2 1.27

3/8 0.71

3 6 5/8 3 6 5/8 3 6 5/8

26 1/2

36 1/2 26 1/2

As = 3.81 cm2 As = 3.81 cm2 As = 3.81 cm2

0.7 = 0.7210

= 0.0024f'c

4200

0.75 = 0.75 0.85 !f'c "000

= 0.0159fy "000 # fy

0.85 !f'c "000

= 0.85 0.85210 "000

= 0.02125fy "000 # fy 4200 "000 # 4200

As =

2.8" = 0.005

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

As =

1.71 = 0.003

< cm()e c% ) c%+$ m;%$m

bd "25

As =

2.78 = 0.004

&$ cm()e c% ) c%+$ m;%$m y m,$m

bd "25

+$)$?ms ) c%+$ m$%$m 2.7cm2

:(&m;)

d(&m;)

As(&m2)

a(&m)

Pm$% = Pm$%

Pm, = Pb

Pb =

P1 =

P2 =

P3 =


20/44

D"t"mina&i=n d"% >"a d" a&"o

As=M

Ø fy d- /2

= d/5

0.85 !f'c

fy



d= 49

Ca%%o d" %a ant'a

w= 0.85 -

w= Pfy

f'c

Pb =


21/44

As=P*b*d


0.7

0.75


Asm$%=Pm$%*b*d

Asm,=Pm,*b*d

cosideramos el As mín

N.m"o d" /ai%%as

r$))s = A

As e)e$d

r$))s = 3.

&e c)cr%

V"i$i&ando "% $i"o

e= 2* 4 # 0.95 *

e= 17."4


d= h - rec - Ø

d= 49.4


6M%=6*b*d2*w*f'c*1-0.59*

* * * *

Pm$% =

Pm, =


22/44

-


23/44


24/44


25/44


26/44

As = 2449020 cm2

= 0.7f'c

42

= 0.75

Asm$% =

Asm$% =

= 4.459 cm2

s=

4.459

1.29

.5

3.5 Ø 1/2

2 # 3.5 * 1.29 # 2.5

es+r$b. - Ø/2

0.9 35

* * *

Pb


27/44

.


28/44


29/44


30/44

0.85250

"000

4200 "000 #

b = 35 cm

h = 55 cm

f'c = 250

fy = 4200

rec = 4 cm

w = 0.

w =

P = 1428

km/cm2

km/cm2


31/44

250

00

0.85 !f'c

*"000

fy "000

4.459 cm2 &$ cm()e ) f)) dc+$)

32.585 cm2 cm()e f)) dc+$)

+"a d" a&"os

01

3/4

5/8

1/2

3/8

$me+r

01

3/4

* 1.29 5/8

1/2

3/8

2440.3" 1428 250 1


32/44

.

6M% > M


33/44


34/44


35/44

= 0.02534200

55

35

5 - 0.7225 -1.

0.

85


36/44

= 0.002"

= 0.019 # fy

+"a (&m2)5.07

2.85

1.98

1.29

0.71

de cers

iam"to(&m)2.54

1.91

1.59

1.27

0.95

- 0.59 1428

Pm$%


37/44


38/44


39/44


40/44

.7 * 92.48

.9 250 35 2401


41/44

= -23093890903137."0


42/44


43/44


44/44

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