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Arbitrary Parabolic Loading: Shear and Bending Moment Diagram

Arbitrary Parabolic Loading: Shear and Bending Moment Diagram
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2019-06-21 05:41
FunctionCalculusIntegralGeometric ConstructionGraphing
This example demonstrates the calculation and visualization of shear and bending moment diagrams under arbitrary parabolic loading on a beam. Key math concepts include integral calculus, derivatives, function graphing, and vector operations. GeoGebra commands like Point, Polynomial, Integral, IntegralBetween, Segment, Textfield, Polygon, Length, Vector, Sequence, Max, Min are utilized to dynamically compute and display the load, shear force, and bending moment. Suitable for high school students and engineering professionals studying structural mechanics and engineering applications.

GeoGebra Commands & Parameters

  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}