Download - Falla Tension
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