1. Resistência dos Materiais, 5ª ed.
13 – Flambagem de
Colunas
R.C. Hibbeler
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2. ©2004 by Pearson Education FG13_00CO.TIF Notes:
The columns for this building are used to support the floor loading. Engineers design
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3. FG13_01a.TIF
Notes:
critical load
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4. FG13_01b.TIF
Notes:
critical load
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5. FG13_02a.TIF
Notes:
critical load
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6. FG13_02b.TIF
Notes:
critical load
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7. FG13_02c.TIF
Notes:
critical load
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8. FG13_03.TIF
Notes:
stages of equlibrium
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9. ©2004 by Pearson Education FG13_03-01UN.TIF Notes:
Some pin-connected members used in moving machinery
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10. FG13_04a.TIF
Notes:
ideal column
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11. ©2004 by Pearson Education FG13_04b.TIF Notes:
column with small lateral force, F
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12. FG13_04c.TIF
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column with F removed
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13. FG13_05a.TIF
Notes:
n=1
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14. FG13_05a_repeat.TIF
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n=1
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15. ©2004 by Pearson Education FG13_05b.TIF Notes:
ideal column with pin supports
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16. FG13_05c.TIF
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curvy column, n = 2
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17. ©2004 by Pearson Education FG13_06.TIF Notes:
column with bifurcation point
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18. FG13_07.TIF
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meter stick
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19. ©2004 by Pearson Education FG13_07-01UN.TIF Notes:
typical interior steel pipe columns used to support the roof of a single story bldg
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20. ©2004 by Pearson Education FG13_08.TIF Notes:
structural steel, aluminum alloy graph curves
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21. FG13_09.TIF
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Example 13-1
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22. FG13_10.TIF
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Example 13-2
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23. FG13_11a.TIF
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buckling of columns
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24. FG13_11b.TIF
Notes:
buckling of columns
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25. ©2004 by Pearson Education FG13_11-01UN.TIF Notes:
tubular columns used to support this water tank have been braced at 3 locations
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26. FG13_12a.TIF
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pinned ends
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27. FG13_12b.TIF
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fixed and free ends
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28. FG13_12c.TIF
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fixed ends
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29. FG13_12d.TIF
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pinned and fixed ends
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30. FG13_13a.TIF
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Example 13-3
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31. ©2004 by Pearson Education FG13_13b.TIF Notes:
Example 13-3 (x-x axis buckling)
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32. ©2004 by Pearson Education FG13_13c.TIF Notes:
Example 13-3 (y-y axis buckling)
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33. FG13_14a.TIF
Notes:
Example 13-4
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34. ©2004 by Pearson Education FG13_14b.TIF Notes:
Example 13-4 (x-x axis buckling)
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35. ©2004 by Pearson Education FG13_14c.TIF Notes:
Example 13-4 (y-y axis buckling)
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36. FG13_14-01UNP01.TIF
Notes:
Problem 13-1
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37. ©2004 by Pearson Education FG13_14-02UNP02_03.TIF Notes:
Problem 13-2/13-3
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38. FG13_14-03UNP04.TIF
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Problem 13-4
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39. FG13_ UNP05.TIF
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Problem 13-5
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40. ©2004 by Pearson Education FG13_14-04UNP06_07.TIF Notes:
Problem 13-6/7
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41. ©2004 by Pearson Education FG13_14-05UNP08_09.TIF Notes:
Problem 13-8/9
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42. ©2004 by Pearson Education FG13_14-06UNP10_11.TIF Notes:
Problem 13-10/11
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43. ©2004 by Pearson Education FG13_14-07UNP12_13.TIF Notes:
Problem 13-12/13-13
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44. ©2004 by Pearson Education FG13_14-08UNP14_15.TIF Notes:
Problem 13-14/13-15
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45. FG13_14-09UNP16.TIF
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Problem 13-16
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46. ©2004 by Pearson Education FG13_14-10UNP17_18.TIF Notes:
Problem 13-16/17
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47. ©2004 by Pearson Education FG13_14-11UNP19_20.TIF Notes:
Problem 13-19/13-20
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48. ©2004 by Pearson Education FG13_14-12UNP21_22.TIF Notes:
Problem 13-21/22
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49. ©2004 by Pearson Education FG13_14-13UNP23_24.TIF Notes:
Problem 13-23/24
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50. ©2004 by Pearson Education FG13_14-14UNP25_26.TIF Notes:
Problem 13-25/26
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51. FG13_14-15UNP27.TIF
Notes:
Problem 13-27
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52. ©2004 by Pearson Education FG13_14-16UNP28.TIF Notes:
Problem (repeat of Problem 13-27)
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53. FG13_14-17UNP29.TIF
Notes:
Problem 13-29
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54. FG13_14-18UNP30.TIF
Notes:
Problem 13-30
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55. FG13_14-19UNP31.TIF
Notes:
Problem 13-31
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56. FG13_14-20UNP32.TIF
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Problem 13-32
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57. FG13_14-21UNP33.TIF
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Problem 13-33
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58. ©2004 by Pearson Education FG13_14-22UNP34_35.TIF Notes:
Problem 13-34/35
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59. ©2004 by Pearson Education FG13_14-23UNP36_37.TIF Notes:
Problem 13-36/13-37
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60. FG13_14-24UNP38.TIF
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Problem 13-38
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61. FG13_14-25UNP39.TIF
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Problem 13-39
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62. FG13_14-26UNP40.TIF
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Problem 13-40
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63. FG13_14-27UNP41.TIF
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Problem 13-41
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Problem 13-44
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65. FG13_14-29UNP45.TIF
Notes:
Problem 13-45
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66. ©2004 by Pearson Education FG13_14-30UN.TIF Notes:
these timber columns can be considered pinned at their bottom
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67. FG13_15a.TIF
Notes:
the secant formula
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68. FG13_15b.TIF
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the secant formula
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69. FG13_15c.TIF
Notes:
the secant formula
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70. ©2004 by Pearson Education FG13_16.TIF Notes:
ideal column (small deflections), inelastic behavior
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71. FG13_17a.TIF
Notes:
column diagrams
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72. FG13_17b.TIF
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varoius types of stress
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73. ©2004 by Pearson Education FG13_18.TIF Notes:
Euler's formula, A-36 structural steel
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74. FG13_19.TIF
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Example 13-5
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75. FG13_20a.TIF
Notes:
Example 13-6
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76. ©2004 by Pearson Education FG13_20b.TIF Notes:
Example 13-6 (y-y axis buckling)
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77. ©2004 by Pearson Education FG13_20c.TIF Notes:
Example 13-6 (x-x axis buckling)
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78. ©2004 by Pearson Education FG13_20-01UN.TIF Notes:
crane boom failed by buckling caused by an overload
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79. ©2004 by Pearson Education FG13_20-02UN.TIF Notes:
crane boom failure; localized collapse
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80. FG13_21a.TIF
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slope at point D
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81. ©2004 by Pearson Education FG13_21b.TIF Notes:
inelastic and elastic columns
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82. FG13_22.TIF
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Example 13-7
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83. ©2004 by Pearson Education FG13_22-01UNP46_47.TIF Notes:
Problem 13-46/47
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Problem 13-48/49
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Problem 13-50/51/52
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Problem 13-53/54
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Problem 13-55/56
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Problem 13-57/58
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Problem 13-59/60
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Problem 13-61/62
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91. FG13_22-09UNP63.TIF
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Problem 13-63
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92. ©2004 by Pearson Education FG13_22-10UNP64_65.TIF Notes:
Problem 13-64/65
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93. ©2004 by Pearson Education FG13_22-11UNP67_69.TIF Notes:
Problem 13-67/68/69
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94. FG13_22-12UNP70.TIF
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Problem 13-70
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95. ©2004 by Pearson Education FG13_22-13UN.TIF Notes:
these long unbraced timber columns are used to support the roof of this building
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96. ©2004 by Pearson Education FG13_23.TIF Notes:
Euler formula for short, intermediate and long columns
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97. FG13_24.TIF
Notes:
Eq and Eq 13-21
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98. ©2004 by Pearson Education FG13_25.TIF Notes:
Eq 13-24, and 13-26
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99. ©2004 by Pearson Education FG13_26.TIF Notes:
Eq 13-27, and 13-29
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100. FG13_27.TIF
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Example 13-8
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101. FG13_28.TIF
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Example 13-9
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102. FG13_29.TIF
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Example 13-10
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Example 13-11
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104. FG13_30-01UNP79.TIF
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Problem 13-79
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105. FG13_30-02UNP84.TIF
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Problem 13-84
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Problem 13-85/86
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Problem 13-87/88
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Problem 13-91/92/93
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Problem 13-95/96
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Problem 13-97/98
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111. FG13_30-08UNP99.TIF
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Problem 99
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112. FG13_30-09UNP100.TIF
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Problem 100
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113. ©2004 by Pearson Education FG13_31a.TIF Notes:
design of columns for eccentric loading
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114. ©2004 by Pearson Education FG13_31b.TIF Notes:
ideal column with pin supports
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115. ©2004 by Pearson Education FG13_31-01UN.TIF Notes:
typical example of a column used to support an eccentric roof loading
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116. FG13_32.TIF
Notes:
Example 13-12
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117. FG13_33.TIF
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Example 13-13
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118. FG13_34.TIF
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Example 13-14
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119. FG13_34-01UNP101.TIF
Notes:
Problem
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120. ©2004 by Pearson Education FG13_34-02UNP102.TIF Notes:
Problem (repeat of Problem )
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121. ©2004 by Pearson Education FG13_34-03UNP103_106.TIF Notes:
Problem /104/ 105/106
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Problem /108/109
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Problem
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Problem
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Problem /113
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126. FG13_34-08UNP114.TIF
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Problem
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127. ©2004 by Pearson Education FG13_34-09UNP115.TIF Notes:
Problem (repeat of Problem )
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128. FG13_34-10UNP116.TIF
Notes:
Problem
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129. ©2004 by Pearson Education FG13_34-11UNP117.TIF Notes:
Problem (repeat of Problem )
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Problem /120
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131. FG13_34-14UNP121.TIF
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Problem
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132. ©2004 by Pearson Education FG13_34-15UNP122.TIF Notes:
Problem (repeat of Problem )
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133. ©2004 by Pearson Education FG13_34-16UNP123_124.TIF Notes:
Problem /124
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134. ©2004 by Pearson Education FG13_34-17UNP125_126.TIF Notes:
Problem /126
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135. FG13_34-19UNP128.TIF
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Problem 128
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