FALLA POR COMPRESION:

≔b 30≔h 50 ≔β 0.85≔d 44≔d' 6 ≔e 25≔As 15.201≔As' 15.201≔F'c 210≔Fy 4200≔Es ⋅2.039 10

6

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≔cb =⋅d ――――0.003

+0.003 ――Fy

Es

26.088 ≔ab =⋅β cb 22.175 ≔F's =⋅⋅Es 0.003 ――−cb d'

cb⋅4.71 10

3

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

≔y =―h

225

≔Pnb =−+⋅⋅⋅0.85 F'c b ab ⋅As' F's ⋅As Fy ⋅1.265 105

≔Mnb =++⋅⋅⋅⋅0.85 F'c b ab⎛⎜⎝

−y ―ab

2

⎞⎟⎠

⋅⋅As' F's (( −y d')) ⋅⋅As Fy (( −d y)) ⋅4.225 106

≔eb =――Mnb

Pnb33.403

FALLA POR COMPRESION:

1ra aproximacion

≔a →⋅0.85 c ⋅0.85 c

≔F's →⋅⋅Es 0.003 ――−c d'

c―――――

⋅6117.0 (( −c 6))

c

≔Fs →⋅⋅Es 0.003 ――−d c

c−―――――

⋅6117.0 (( −c 44))

c

≔Pn →−+⋅⋅⋅0.85 F'c b a ⋅As' F's ⋅As Fs ++⋅4551.75 c ――――――――――⋅15.201 (( −⋅6117.0 c 269148.0))

c―――――――――

⋅15.201 (( −⋅6117.0 c 36702.0))

c

≔Mn ―――→++⋅⋅⋅⋅0.85 F'c b a⎛⎜⎝

−y ―a

2

⎞⎟⎠

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

―――――――――――――――――+−⋅113793.75 c

2⋅1934.49375 c

3⋅6.7134821274 10

7

c

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GRAFICA DE LA FUNCION PARA IDENTIFICAR LAS RAICES

≔f ―――――→−――Mn

Pn25

,substitute ＝c x−―――――――――――――――――――

⋅1.0 ⎛⎝ −+⋅859775.0 x3

⋅⋅2.0663226 109x ⋅8.1495763344 10

10⎞⎠

−+⋅⋅2.023 106x

2⋅⋅8.2652904 10

7x ⋅2.0663226 10

9

≔x , ‥0 0.1 40

-9⋅10⁴

-7.5⋅10⁴

-6⋅10⁴

-4.5⋅10⁴

-3⋅10⁴

-1.5⋅10⁴

0

-1.2⋅10⁵

-1.05⋅10⁵

1.5⋅10⁴

8 12 16 20 24 28 32 360 4 40

x

−―――――――――――――――――――⋅1.0 ⎛⎝ −+⋅859775.0 x

3⋅⋅2.0663226 10

9x ⋅8.1495763344 10

10⎞⎠

−+⋅⋅2.023 106x

2⋅⋅8.2652904 10

7x ⋅2.0663226 10

9

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≔f ―――――→−――Mn

Pn25

,substitute ＝c t−―――――――――――――――――――

⋅1.0 ⎛⎝ −+⋅859775.0 t3

⋅⋅2.0663226 109t ⋅8.1495763344 10

10⎞⎠

−+⋅⋅2.023 106t2

⋅⋅8.2652904 107t ⋅2.0663226 10

9

≔t ‥25 35

-6

-4

-2

0

2

4

6

8

10

12

-10

-8

14

27 28 29 30 31 32 33 3425 26 35

−―――――――――――――――――――⋅1.0 ⎛⎝ −+⋅859775.0 t

3⋅⋅2.0663226 10

9t ⋅8.1495763344 10

10⎞⎠

−+⋅⋅2.023 106t2

⋅⋅8.2652904 107t ⋅2.0663226 10

9

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t

≔c →rootrootrootroot

⎛⎜⎜⎜⎜⎝

,,,−―――――――――――――――――――――

−−+⋅113793.75 c ――――――⋅7.7735056212 10

7

c⋅1934.49375 c

2553666.023

++⋅4551.75 c ――――――――――⋅15.201 (( −⋅6117.0 c 269148.0))

c63844.2

25 c 10 40

⎞⎟⎟⎟⎟⎠

29.327352523460151059

≔a →⋅0.85 c 24.9282496449411284

≔F's →⋅⋅Es 0.003 ――−c d'

c4865.5402928668530094 MAYOR A 4200 (SEGUNDA APROXIMACION)

≔Fs →⋅⋅Es 0.003 ――−d c

c3060.3711856430779308

≔Pn →−+⋅⋅⋅0.85 F'c b a ⋅As' F's ⋅As Fs 160931.15244756834755

≔Mn →++⋅⋅⋅⋅0.85 F'c b a⎛⎜⎝

−y ―a

2

⎞⎟⎠

⋅⋅As' F's (( −y d')) ⋅⋅As Fs (( −d y)) ⋅3.9625775432379944932 106

≔e =――Mn

Pn24.623

2da aproximacion

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2da aproximacion

clearclearclearclear ((c))

≔a →⋅0.85 c ⋅0.85 c

≔F's 4200

≔Fs →⋅⋅Es 0.003 ――−d c

c−―――――

⋅6117.0 (( −c 44))

c

≔Pn →−+⋅⋅⋅0.85 F'c b a ⋅As' F's ⋅As Fs ++⋅4551.75 c ――――――――――⋅15.201 (( −⋅6117.0 c 269148.0))

c63844.2

≔Mn ―――→++⋅⋅⋅⋅0.85 F'c b a⎛⎜⎝

−y ―a

2

⎞⎟⎠

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

−−+⋅113793.75 c ――――――⋅7.7735056212 10

7

c⋅1934.49375 c

2553666.023

≔c →rootrootrootroot

⎛⎜⎜⎜⎜⎝

,,,−―――――――――――――――――――――

−−+⋅113793.75 c ――――――⋅7.7735056212 10

7

c⋅1934.49375 c

2553666.023

++⋅4551.75 c ――――――――――⋅15.201 (( −⋅6117.0 c 269148.0))

c63844.2

25 c 10 40

⎞⎟⎟⎟⎟⎠

29.327352523460151059

≔a →⋅0.85 c 24.9282496449411284

≔F's 4200

≔Fs →⋅⋅Es 0.003 ――−d c

c3060.3711856430779308

≔Pn →−+⋅⋅⋅0.85 F'c b a ⋅As' F's ⋅As Fs 150814.27445569931496

≔Mn →++⋅⋅⋅⋅0.85 F'c b a⎛⎜⎝

−y ―a

2

⎞⎟⎠

⋅⋅As' F's (( −y d')) ⋅⋅As Fs (( −d y)) ⋅3.7703568613924828739 106

≔e =――Mn

Pn25

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