Falla Compresion
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Transcript of Falla Compresion
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
UNSCH HUANCA RAY
≔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
UNSCH HUANCA RAY
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
UNSCH HUANCA RAY
≔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
UNSCH HUANCA RAY
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
UNSCH HUANCA RAY
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
UNSCH HUANCA RAY
UNSCH HUANCA RAY