积极 AI Logo 积极 AI

任意抛物线载荷的剪力与弯矩图

任意抛物线载荷的剪力与弯矩图
几何画板及绘图内容加载中，请稍等……
2019-06-21 05:41
函数微积分积分几何作图函数图像
①本范例演示了在任意抛物线载荷作用下，梁的剪力与弯矩图的绘制与变化规律；②涉及的核心数学概念包括积分、导数、函数图像、向量运算等；③作图要点：使用了Point, Polynomial, Integral, IntegralBetween, Segment, Textfield, Polygon, Length, Vector, Sequence, Max, Min等GeoGebra命令与对象，实现了载荷、剪力、弯矩的动态计算与可视化；④适合高中及以上学生及工程技术人员学习结构力学与工程应用。

GeoGebra 命令及参数

  1. Point(Line[B, B + j]) → B'
  2. Point(Line[A, A + j]) → A'
  3. Polynomial(Stretch[{A', C', B'}, xAxis, Scale_w / AxisStepY[]]) → w
  4. Integral(w, 0, beamLen) → W
  5. IntegralBetween((w(x))^(2) / 2, 0, 0, beamLen) → Qx
  6. Integral((x * w(x)), 0, beamLen) → Qy
  7. Point(x = ((-AxisStepX[])) / 4) → V
  8. member(A, B, (0.2 * AxisStepY[])) → beam, beam_t, beam_b, beam_L, beam_r
  9. Point(x = ((-AxisStepX[])) / 4) → M
  10. Segment(V', (x(V'), v'(right))) → v_r
  11. Integral(v) → m
  12. Textfield(Scale_V) → InputBoxV
  13. Textfield(Scale_M) → InputBoxM
  14. Polygon((right, y(Corner[2])), (right, y(Corner[3])), Corner[3], Corner[2]) → mask, mask_l, mask_t, mask_r, mask_b
  15. Segment((0, y(V)), (right, y(V))) → Vaxis
  16. Segment((0, y(M)), (right, y(M))) → Maxis
  17. Length(userObjects) → c_1
  18. Length(userObjects) → c_1
  19. Length(userObjects) → c_1
  20. Length(userObjects) → c_1
  21. Length(userObjects) → c_1
  22. Length(userObjects) → c_1
  23. Length(userObjects) → c_1
  24. Length(userObjects) → c_1
  25. Length(userObjects) → c_1
  26. Length(userObjects) → c_1
  27. Length(userObjects) → c_1
  28. Length(userObjects) → c_1
  29. Length(userObjects) → c_1
  30. Length(userObjects) → c_1
  31. Length(userObjects) → c_1
  32. Length(userObjects) → c_1
  33. Length(userObjects) → c_1
  34. Length(userObjects) → c_1
  35. Length(userObjects) → c_1
  36. Length(userObjects) → c_1
  37. Length(userObjects) → c_1
  38. Length(userObjects) → c_1
  39. Length(userObjects) → c_1
  40. Length(userObjects) → c_1
  41. Length(userObjects) → c_1
  42. Length(userObjects) → c_1
  43. Length(userObjects) → c_1
  44. Length(userObjects) → c_1
  45. Length(userObjects) → c_1
  46. Length(userObjects) → c_1
  47. Length(userObjects) → c_1
  48. Length(userObjects) → c_1
  49. Length(userObjects) → c_1
  50. Length(userObjects) → c_1
  51. Length(userObjects) → c_1
  52. Length(userObjects) → c_1
  53. Length(userObjects) → c_1
  54. Integral(w', 0, beamLen) → W'
  55. Vector(A - (1.5 * j), A) → a
  56. Vector(B - (1.5 * j), B) → b
  57. Sequence(Vector[(k, w'(k)), (k, (0.4 * sgn(w'(k))))], k, 0, beamLen, 1) → distLoad
  58. Textfield(Scale_w) → InputBoxW
  59. Segment((0, y(V)), (0, v'(0.0001))) → v_A
  60. Max({y(Max[v, 0, beamLen]), F_A, (-F_B)}) → V_{max}
  61. Min({y(Min[v, 0, beamLen]), F_A, (-F_B)}) → V_{min}