The solution of the consolidation equation is given by the series in the figure. By evaluation of the series, determine the average degree of consolidation Uavg to the nearest 0.001 for time factors 0.15, 0.6, 0.8 and infinity. Verify your computations by referring to the table provided for Uavg and T. Uavg(%) = 100 |1ΣΕΣn=0(2n + 1)2π2∙e(2n + 1)2π24T Uavg (%)01234567891011121314156788222222161718192021232425T00.000080.00030.000710.001260.001960.002830.003850.005020.006360.007850.00950.01130.01330.01540.01770.02010.02270.02540.02830.03140.03460.03800.04150.04520.0491Table 1: Degree of Drainage ValuesUavg (%)T260.0531270.0572280.061529303132333 लSSSS@ 47 48 499434353637383940414243454647484950510.06600.07070.07540.08030.08550.09070.09620.1020.1070.1130.1190.1260.1320.1380.1450.1520.1590.1660.1730.1810.1880.1970.204Uavg (%)5253545556575859606162636465666768697071727374757677T0.2120.2210.2300.2390.2480.2570.2670.2760.2860.2970.3070.3180.3290.3400.3520.3640.3770.3900.4030.4170.4310.4460.4610.4770.4930.511Uavg(%)78798081828384858687888990919293949596979899100T0.5290.5470.5670.5880.6100.6330.6580.6840.7120.7420.7740.8090.8480.8910.9380.9931.0551.1291.2191.3361.5001.781∞

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Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The solution of the consolidation equation is given by the series in the figure. By evaluation of the series, determine the average degree of consolidation U_avg to the nearest 0.001 for time factors 0.15, 0.6, 0.8 and infinity. Verify your computations by referring to the table provided for U_avg and T.

Uavg(%) = 100 |1
ΣΕ
Σ
n=0
(2n + 1)2π2
∙e
(2n + 1)2π2
4
T

Uavg (%)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
6788222222
16
17
18
19
20
21
23
24
25
T
0
0.00008
0.0003
0.00071
0.00126
0.00196
0.00283
0.00385
0.00502
0.00636
0.00785
0.0095
0.0113
0.0133
0.0154
0.0177
0.0201
0.0227
0.0254
0.0283
0.0314
0.0346
0.0380
0.0415
0.0452
0.0491
Table 1: Degree of Drainage Values
Uavg (%)
T
26
0.0531
27
0.0572
28
0.0615
29
30
31
32
33
3 लSSSS@ 47 48 4994
34
35
36
37
38
39
40
41
42
43
45
46
47
48
49
50
51
0.0660
0.0707
0.0754
0.0803
0.0855
0.0907
0.0962
0.102
0.107
0.113
0.119
0.126
0.132
0.138
0.145
0.152
0.159
0.166
0.173
0.181
0.188
0.197
0.204
Uavg (%)
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
T
0.212
0.221
0.230
0.239
0.248
0.257
0.267
0.276
0.286
0.297
0.307
0.318
0.329
0.340
0.352
0.364
0.377
0.390
0.403
0.417
0.431
0.446
0.461
0.477
0.493
0.511
Uavg
(%)
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
T
0.529
0.547
0.567
0.588
0.610
0.633
0.658
0.684
0.712
0.742
0.774
0.809
0.848
0.891
0.938
0.993
1.055
1.129
1.219
1.336
1.500
1.781
∞

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