FALLA POR TENSION:

≔b 30≔h 38 ≔β 0.85≔d 32≔d' 6 ≔e 30≔As 19.239≔As' 19.239≔F'c 280≔Fy 4200≔Es ⋅2.039 10

6

UNSCH HUANCA RAY

≔cb =⋅d ――――0.003

+0.003 ――Fy

Es

18.973 ≔ab =⋅β cb 16.127 ≔F's =⋅⋅Es 0.003 ――−cb d'

cb⋅4.183 10

3

acero en la zona de compresion fluye por lo tanto se tiene:

≔y =―h

219

≔Pnb =−+⋅⋅⋅0.85 F'c b ab ⋅As' F's ⋅As Fy ⋅1.148 105

≔Mnb =++⋅⋅⋅⋅0.85 F'c b ab⎛⎜⎝

−y ―ab

2

⎞⎟⎠

⋅⋅As' F's (( −y d')) ⋅⋅As Fy (( −d y)) ⋅3.356 106

≔eb =――Mnb

Pnb29.229

FALLA POR TENSION:

≔a →⋅0.85 c ⋅0.85 c

≔F's →⋅⋅Es 0.003 ――−c d'

c―――――

⋅6117.0 (( −c 6))

c

≔Pn →−+⋅⋅⋅0.85 F'c b a ⋅As' F's ⋅As Fy −+⋅6069.0 c ―――――――――⋅19.239 (( −⋅6117.0 c 36702.0))

c80803.8

≔Mn ―――→++⋅⋅⋅⋅0.85 F'c b a⎛⎜⎝

−y ―a

2

⎞⎟⎠

⋅⋅As' F's (( −y d')) ⋅⋅As Fy (( −d y))simplify

+−−⋅115311.0 c ――――――⋅9.179427114 10

6

c⋅2579.325 c

2⋅2.580353919 10

6

UNSCH HUANCA RAY

GRAFICA DE LA FUNCION PARA IDENTIFICAR LAS RAICES

≔f ―――――→−――Mn

Pn30

,substitute ＝c x――――――――――――――――――――――

+−−⋅⋅4.91306343 108x ⋅⋅2.2253 10

7x

2⋅859775.0 x

3⋅4.001288742 10

9

−+⋅⋅2.023 106x

2⋅⋅1.2293721 10

7x ⋅2.35369926 10

8

≔x , ‥0 0.1 40

-1.3⋅10³

-650

0

650

1.3⋅10³

1.95⋅10³

2.6⋅10³

3.25⋅10³

3.9⋅10³

-2.6⋅10³

-1.95⋅10³

4.55⋅10³

8 12 16 20 24 28 32 360 4 40

x

――――――――――――――――――――――+−−⋅⋅4.91306343 10

8x ⋅⋅2.2253 10

7x

2⋅859775.0 x

3⋅4.001288742 10

9

−+⋅⋅2.023 106x

2⋅⋅1.2293721 10

7x ⋅2.35369926 10

8

UNSCH HUANCA RAY

≔f ―――――→−――Mn

Pn30

,substitute ＝c t――――――――――――――――――――――

+−−⋅⋅4.91306343 108t ⋅⋅2.2253 10

7t2

⋅859775.0 t3

⋅4.001288742 109

−+⋅⋅2.023 106t2

⋅⋅1.2293721 107t ⋅2.35369926 10

8

≔t ‥15 22

-3

-1.5

0

1.5

3

4.5

6

7.5

-6

-4.5

9

16.4 17.1 17.8 18.5 19.2 19.9 20.6 21.315 15.7 22

t

――――――――――――――――――――――+−−⋅⋅4.91306343 10

8t ⋅⋅2.2253 10

7t2

⋅859775.0 t3

⋅4.001288742 109

−+⋅⋅2.023 106t2

⋅⋅1.2293721 107t ⋅2.35369926 10

8

UNSCH HUANCA RAY

≔c →rootrootrootroot

⎛⎜⎜⎜⎜⎝

,,,−―――――――――――――――――――――

+−−⋅115311.0 c ――――――⋅9.179427114 10

6

c⋅2579.325 c

2⋅2.580353919 10

6

−+⋅6069.0 c ―――――――――⋅19.239 (( −⋅6117.0 c 36702.0))

c80803.8

30 c 10 40

⎞⎟⎟⎟⎟⎠

18.525147325293386787

≔a →⋅0.85 c 15.746375226499378769

≔F's →⋅⋅Es 0.003 ――−c d'

c4135.8011811442507681 solo necesitara una aproximacion (<4200)

≔Pn →−+⋅⋅⋅0.85 F'c b a ⋅As' F's ⋅As Fy 111193.99804123980494

≔Mn →++⋅⋅⋅⋅0.85 F'c b a⎛⎜⎝

−y ―a

2

⎞⎟⎠

⋅⋅As' F's (( −y d')) ⋅⋅As Fy (( −d y)) ⋅3.3358199412371941482 106

≔e =――Mn

Pn30

UNSCH HUANCA RAY