12 A Cantilever Beam with Quarter-Ellipse Load Distribution

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xiii
4. About the Author xv
5. Part 1: List of Selected Integrals with their Step-By-Step Solutions
6. Integral 1 1
7. Integral 2 6
8. Integral 3 7
9. Integral 4 8
10. Integral 5 10
11. Integral 6 12
12. Integral 7 14
13. Integral 8 15
14. Integral 9 16
15. Integral 10 17
16. Integral 11 18
17. Integral 12 19
18. Integral 13 20
19. Integral 14 21
20. Integral 15 22
21. Integral 16 25
22. Integral 17 26
23. Integral 18 27
24. Integral 19 28
25. Integral 20 30
26. Integral 21 31
27. Integral 22 33
28. Integral 23 34
29. Integral 24 36
30. Integral 25 37
31. Integral 26 39
32. Integral 27 40
33. Integral 28 42
34. Integral 29 43
35. Integral 30 44
36. Integral 31 46
37. Integral 32 47
38. Integral 33 48
39. Integral 34 49
40. Integral 35 51
41. Integral 36 53
42. Integral 37 54
43. Integral 38 55
44. Integral 39 57
45. Integral 40 59
46. Integral 41 60
47. Integral 42 61
48. Integral 43 63
49. Integral 44 64
50. Integral 45 65
51. Integral 46 66
52. Integral 47 67
53. Integral 48 68
54. Integral 49 69
55. Integral 50 70
56. Integral 51 72
57. Integral 52 73
58. Integral 53 74
59. Integral 54 75
60. Integral 55 77
61. Integral 56 78
62. Integral 57 80
63. Integral 58 82
64. Integral 59 83
65. Integral 60 84
66. Integral 61 86
67. Integral 62 87
68. Integral 63 89
69. Integral 64 91
70. Integral 65 93
71. Integral 66 95
72. Integral 67 97
73. Integral 68 99
74. Integral 69 100
75. Integral 70 102
76. Integral 71 104
77. Integral 72 105
78. Integral 73 106
79. Integral 74 108
80. Integral 75 110
81. Integral 76 111
82. Integral 77 113
83. Integral 78 114
84. Integral 79 115
85. Integral 80 118
86. Integral 81 119
87. Integral 82 120
88. Integral 83 121
89. Integral 84 122
90. Integral 85 123
91. Integral 86 124
92. Integral 87 126
93. Integral 88 128
94. Integral 89 131
95. Integral 90 132
96. Integral 91 134
97. Integral 92 135
98. Integral 93 136
99. Integral 94 138
100. Integral 95 139
101. Integral 96 140
102. Integral 97 141
103. Integral 98 142
104. Integral 99 143
105. Integral 100 144
106. Part 2: Examples Applied in Engineering
107. 1 Semi-Circle Shapes 147
108. 2 Circular Segment Shapes 150
109. 3 Semi-Ellipse Shapes 156
110. 4 Two-Degree Polynomial Shape-Quadratic 159
111. 5 Three-Degree Polynomial Shape-Cubic 162
112. 6 n-Degree Polynomial Shape-Spandrel 165
113. 7 Sinusoidal Shapes 168
114. 8 Triangular Shapes 172
115. 9 Rectangular Shapes 174
116. 10 Complex Shapes 176
117. 11 A Cantilever Beam with Cubic Load Distribution 182
118. 12 A Cantilever Beam with Quarter-Ellipse Load Distribution 184
119. 13 A Cantilever Beam with Inverse Cosine Load Distribution 188
120. 14 A Cantilever Beam with Parabolic Load Distribution 191
121. 15 A Cantilever Beam with Circular Segment Cross-Section and Quarter-Ellipse Load Distribution 193
122. 16 Probability Density Functions-PDF 196
123. References 199