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UNIVERSIDAD DE GUANAJUATO
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
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UNIVERSIDAD DE GUANAJUATO
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
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UNIVERSIDAD DE GUANAJUATO
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
D.C.L. (1)
+ x - 7.0 x -1 - 7.0 x -3
x + x2 - 3.5 x -1 - 3.5 x -3 + C1
x2 + x3 - x -1 -
1.167 x -3 + C1x + C2
Si x = 0 : 0 , C2 = 0
Si x = 0 : 0 , C1 = 0
Si x = 4 : (dy/dx)B= qB= 1/2EI
D.C.L. (2)
+ x - x2
x + x2 - x3 + C3
x2
+ x3
- x4
+ C3 x + C4
Si x = 0 : 0 , C4 = 0
Si x = 5 : 0 , C3 =
Si x = 0 : (dy/dx)B= qB= EI
FACULTAD DE INGENIERIA CIVIL
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
EI
-0.4598
-3.0834 1.2601 0.125
y =
y =
-0.4598
qB=-0.45975
-6.1669 7.5605 1.5
-6.1669 3.7802 0.5
dy/dx =
-0.9206
-0.4603
EIqB=
-4.7934 6.6566
-2.3967 1.1094 1.1667
y =
-4.7934 3.3283
DIAGRAMAS DE LA ELASTICA (DOBLE INTEGRACIÓN)
2 2
3
3
=2
2
2dx
ydEI
=dx
dyEI2
=EIy2
=2
2
dx
ydEI
=dx
dyEI
=EIy
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UNIVERSIDAD DE GUANAJUATO
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
D.C.L. (3)
+ x - x -2
x + x2 - 5 x -2 + C5
x2 + x3 - x -2 + C5 x + C6
Si x = 0 : 0 , C6 = 0
Si x = 0 : 0 , C5 = 0
Si x = 3 : (dy/dx)B= qB= 1/2EI
FACULTAD DE INGENIERIA CIVIL
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
-2.9323 0.8814 1.6667
y =
dy/dx =
qB=0.60157
EI
1.2031
10.0-5.8646
-5.8646 2.6441
5.2882
2-
3
=2
2
2dx
ydEI
=dx
dyEI2
=EIy2
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UNIVERSIDAD DE GUANAJUATO
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
TRAMO AB TRAMO BC TRAMO CD
x x x
0.1 0.1 0.1
0.2 0.2 0.2
0.3 0.3 0.3
0.4 0.4 0.4
0.5 0.5 0.5
0.6 0.6 0.6
0.7 0.7 0.7
0.8 0.8 0.8
0.9 0.9 0.9
1.0 1.0 1.0
1.1 1.1 1.1
1.2 1.2 1.2
1.3 1.3 1.3
1.4 1.4 1.4
1.5 1.5 1.5
1.6 1.6 1.6
1.7 1.7 1.7
1.8 1.8 1.8
1.9 1.9 1.9
2.0 2.0 2.0
2.1 2.1 2.1
2.2 2.2 2.2
2.3 2.3 2.3
2.4 2.4 2.4
2.5 2.5 2.5
2.6 2.6 2.6
2.7 2.7 2.7
2.8 2.8 2.8
2.9 2.9 2.93.0 3.0 3.0
3.1 3.1
3.2 3.2
3.3 3.3
3.4 3.4
3.5 3.5
3.6 3.6
3.7 3.7
3.8 3.8
3.9 3.94.0 4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.95
FACULTAD DE INGENIERIA CIVIL
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
-2.3457 0.8262
-2.3001 0.9911
-2.2474 1.1089
-1.6475
-2.3391 -1.1528
-2.3854 -0.7051
-2.4104 -0.3046
-4.8280
-1.8115 -4.0976
-1.9483 -3.4144
-2.0721 -2.7783
-0.7127 -10.1994
-0.8663 -9.1864
-1.0255 -8.2205
-0.1201 -15.9714
-0.2064 -14.7228
-0.3115 -13.5213
y/EI q/EI
-0.0142 -18.6100
-0.0551 -17.2672
-2.1302 1.2031-2.1900 1.1796
-2.4063 0.3550
-2.3819 0.6142
-2.4166 0.0488
-2.1802 -2.1894
-2.2701
-1.5096 -5.6054
-1.6644
-1.1875 -7.3017
-1.3497
-0.4326 -12.3669
-0.5673 -11.2596
0.7117
2.9993
2.7765
2.4943
2.1498
1.7398
1.2614
3.2567
3.32733.3565
3.3413
3.2787
3.1657
2.1318
2.3878
2.6204
2.8265
3.0033
3.1477
-0.0630
0.2728
0.6061
0.9340
1.25361.5617
-1.9597
-1.6726
-1.3699
-1.0545
-0.7296
-0.3981
-1.9831
-2.3537
-2.6606
-2.9070
-3.0957
-3.2299
0.6224
0.4793
0.2995
0.0829
-0.1703-0.4603
0.72760.7873
0.8277
0.8315
0.7985
0.7288
0.3334
0.4034
0.4717
0.5382
0.6031
0.6662
-0.1225
-0.0422
0.0363
0.1132
0.1883
0.2617
-0.6403
-0.5497
-0.4608
-0.3737
-0.2882
-0.2045
-0.4128
-0.5692
-0.6924
-0.7823
-0.8389
-0.8623
-0.8523
-0.8091
-0.7326
-2.6261
-2.2723
-1.9058
-1.8479
-1.8028
-1.7433
-1.6696
-1.5820
-1.4810
-4.3136
-4.0966
-3.8511
-3.5790
-3.2824
-2.9638
1.8555
-4.9253
-4.8688
-4.7789
-4.6559
-4.5004-1.1005-0.9489
-0.7868
-0.6203
-0.0100
-1.8760
-1.8925
-1.8930
-1.8780
-0.4567
-0.3033
-0.1676
-0.0568
0.0217
-1.5435
-1.6445
-1.7279
-1.7941
-1.8433
0.0524
0.0606
-1.3668
-1.2399
-0.0870
-0.1858
-0.3125
-0.4605
-0.7939
-0.9659
-1.1326
-1.2873
-1.4245
-4.0113
-4.2241
-4.4135
-2.6973
-2.4751
-2.2282
-3.2594
-3.5258
-3.7775
-3.1866
-3.0561
-2.8920
-2.4081
-2.6966
-2.9817
-3.3464
-3.3347
-3.2805 -6.4300
-1.5684
-1.8392
-2.1207 -3.3124
-0.6232
-1.5459
TABULACIÓN DE LA ELASTICA Y LAS PENDIENTES.
y/EI q/EI
-0.0229 -0.2230
-1.3138
-4.9378
-4.9482
y/EI q/EI
-0.4893 -1.0391
-0.5732
-0.7043
-0.8757
-1.0809
1.2561
1.4972
1.69381.8390
-1.5303-1.1498
-0.7685
-0.3911
-0.0225
0.3322
0.6674
0.9774
-4.5771
-4.7129
-4.8191
-4.8945