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桁架结构 - 创摩纳图解法

桁架结构 - 创摩纳图解法
几何画板及绘图内容加载中，请稍等……
2014-05-09 02:00
向量解析几何几何作图
本范例演示了如何使用创摩纳图解法分析桁架结构。核心数学概念包括向量和几何。通过使用GeoGebra命令如Segment, Vector, Line, Intersect等，可以直观地展示力的平衡和结构稳定性。适合高中及以上学生学习结构力学和几何作图。

GeoGebra 命令及参数

  1. Segment(Z1, Z5) → a
  2. Segment(Z1, Z7) → b
  3. Segment(Z7, Z5) → c
  4. Segment(Z2, Z8) → d
  5. Segment(Z8, Z3) → e
  6. Segment(Z3, Z7) → f
  7. Segment(Z4, Z6) → g
  8. Segment(Z6, Z3) → h
  9. Segment(Z1, Z14) → i
  10. Segment(Z14, Z10) → j
  11. Segment(Z10, Z1) → k
  12. Segment(Z12, Z13) → l
  13. Segment(Z11, Z9) → m
  14. Segment(Z9, Z5) → nn
  15. Segment(Z5, Z11) → p
  16. Vector(Z15, Z8) → vecF1
  17. Vector(Z16, Z7) → vecF2
  18. Vector(Z17, Z6) → vecF3
  19. Segment(Z18, Z20) → q
  20. Segment(Z21, Z23) → r
  21. Vector(Z19, Z22) → u
  22. Vector(Z22, Z19) → v
  23. Segment(Z29, Z27) → s
  24. Segment(Z26, Z24) → t
  25. Vector(Z28, Z25) → w
  26. Vector(Z25, Z28) → z
  27. Vector(Z30, Z31) → u_1
  28. Vector(Z31, Z32) → v_1
  29. Vector(Z32, Z33) → w_1
  30. Segment(Z30, Z34) → a_1
  31. Segment(Z31, Z34) → b_1
  32. Segment(Z32, Z34) → c_1
  33. Segment(Z33, Z34) → d_1
  34. Line(Z15, Z8) → e_1
  35. Line(Z16, Z7) → f_1
  36. Line(Z6, Z17) → g_1
  37. Line(Z1, a_1) → h_1
  38. Intersect(e_1, h_1) → A
  39. Line(A, b_1) → i_1
  40. Intersect(i_1, f_1) → B
  41. Line(B, c_1) → j_1
  42. Intersect(g_1, j_1) → C
  43. Line(C, d_1) → k_1
  44. Intersect(k_1, l_1) → D
  45. Segment(A, B) → n_1
  46. Segment(B, C) → p_1
  47. Segment(C, D) → q_1
  48. Segment(D, Z30) → r_1
  49. Line(Z34, r_1) → s_1
  50. Line(Z33, Z33 + (0, 1)) → t_1
  51. Intersect(s_1, t_1) → E
  52. Vector(Z33, E) → z_1
  53. Vector(E, Z30) → u_2
  54. Segment(E, Z34) → a_2
  55. Segment(Z1, A) → m_1
  56. Point(Z5, Vector[(0.1 * (-z_1))]) → F
  57. Vector(F, Z5) → v_2
  58. Distance(Z33, E) → velB
  59. Distance(E, Z30) → velA
  60. Point(Z1, Vector[(0.1 * (-u_2))]) → G
  61. Vector(G, Z30) → w_2
  62. Line(E, a) → b_2
  63. Line(Z30, b) → c_2
  64. Intersect(c_2, b_2) → I
  65. Segment(Z30, I) → d_2
  66. Segment(I, E) → e_2
  67. Segment(I, E) → f_2
  68. Line(Z31, b) → g_2
  69. Line(I, e) → h_2
  70. Intersect(h_2, g_2) → J
  71. Segment(I, J) → i_2
  72. Segment(J, Z31) → j_2
  73. Line(Z32, c) → k_2
  74. Line(J, f) → l_2
  75. Intersect(k_2, l_2) → K
  76. Segment(J, K) → m_2
  77. Segment(K, Z32) → n_2
  78. Line(K, h) → p_2
  79. Line(E, a) → q_2
  80. Intersect(p_2, q_2) → M
  81. Segment(K, M) → r_2
  82. Segment(M, E) → s_2
  83. Segment(M, E) → t_2
  84. Segment(M, Z33) → a_3
  85. If(UnitVector[Vector[I, E]] ≟ UnitVector[Vector[Z1, Z2]], Distance[I, E], (-Distance[I, E])) → velN1
  86. If(UnitVector[Vector[Z30, I]] ≟ UnitVector[Vector[Z1, Z8]], Distance[Z30, I], (-Distance[I, Z30])) → velN5
  87. Vector(Z30, I) → z_2
  88. Vector(I, E) → u_3
  89. Vector(E, Z30) → v_3
  90. Vector(E, I) → b_3
  91. Vector(I, E) → c_3
  92. Vector(Z30, Z31) → e_3
  93. Vector(Z31, J) → f_3
  94. Vector(J, I) → h_3
  95. If(UnitVector[Vector[Z31, J]] ≟ UnitVector[Vector[Z8, Z7]], Distance[J, Z31], (-Distance[J, Z31])) → velN6
  96. If(UnitVector[Vector[J, I]] ≟ UnitVector[Vector[Z8, Z3]], Distance[J, I], (-Distance[J, I])) → velN10
  97. Vector(Z31, Z32) → m_3
  98. Vector(Z32, K) → n_3
  99. Vector(K, J) → p_3
  100. Vector(J, Z31) → q_3
  101. Vector(I, Z30) → w_3
  102. Vector(E, I) → z_3
  103. Vector(I, J) → d_3
  104. Vector(J, K) → g_3
  105. Vector(K, M) → i_3
  106. Vector(M, E) → j_3
  107. If(UnitVector[Vector[K, M]] ≟ UnitVector[Vector[Z3, Z6]], Distance[K, M], (-Distance[K, M])) → velN12
  108. If(UnitVector[Vector[M, E]] ≟ UnitVector[Vector[Z3, Z4]], Distance[M, E], (-Distance[M, E])) → velN3
  109. Vector(E, M) → k_3
  110. Vector(M, E) → l_3
  111. Vector(Z32, Z33) → r_3
  112. Vector(Z33, M) → s_3
  113. Vector(M, K) → t_3
  114. Vector(K, Z32) → u_4
  115. If(UnitVector[Vector[K, J]] ≟ UnitVector[Vector[Z7, Z3]], Distance[K, J], (-Distance[K, J])) → velN11
  116. If(UnitVector[Vector[Z32, K]] ≟ UnitVector[Vector[Z7, Z6]], Distance[Z32, K], (-Distance[Z32, K])) → velN7
  117. If(UnitVector[Vector[Z33, M]] ≟ UnitVector[Vector[Z6, Z5]], Distance[Z33, M], (-Distance[Z33, M])) → velN8
  118. Vector(Z33, E) → v_4
  119. Vector(E, M) → w_4
  120. Vector(M, Z33) → z_4