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UNIVERSIDAD DE GUANAJUATO
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
UNIVERSIDAD DE GUANAJUATO
RESISTENCIA DE MATERIALES III
ANTONIO EMMANUEL REGALADO GONZALEZ
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
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
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
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