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Simply Supported Beam Reactions to Oblique Force

Simply Supported Beam Reactions to Oblique Force
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2019-06-26 00:41
VectorCoordinate GeometryGeometric Construction
This example demonstrates the calculation and graphical representation of reactions in a simply supported beam under an oblique force. Key math concepts include force decomposition, vector operations, and geometric constructions. Construction highlights involve using GeoGebra commands such as Line, Point, OrthogonalLine, Intersect, Polygon, Rotate, Circle, Segment, Ray, Midpoint, Mirror, Vector, and Translate for force analysis and graphical construction. Suitable for high school students and engineering professionals studying mechanics and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → f
  2. Line(B, f) → g
  3. Point(f) → C
  4. OrthogonalLine(C, f) → h
  5. Point(g) → D
  6. OrthogonalLine(D, f) → i
  7. Intersect(f, i) → E
  8. Intersect(g, h) → F_1
  9. Polygon(C, E, D, F_1) → c1, c, e, d, f_1
  10. Line(G, g) → j
  11. Rotate(g, -60°, F_1) → g'
  12. Intersect(j, g') → H
  13. Polygon(H, F_1, 3) → polígono1, k, l, m, I
  14. Intersect(h, j) → J
  15. Circle(J, F_1) → p
  16. Intersect(p, j, 1) → K
  17. Intersect(p, j, 2) → L
  18. Segment(K, L) → n
  19. Intersect(i, j) → M
  20. Ray(D, M) → q
  21. Rotate(D, 30°, D) → D'
  22. Rotate(M, 30°, D) → M'
  23. Ray(D', M') → q'
  24. Line(N, j) → r
  25. Intersect(i, r) → O
  26. Midpoint(O, M) → P
  27. Line(P, j) → s
  28. Intersect(s, q') → R
  29. Midpoint(P, R) → S
  30. Circle(S, Distance[O, P]) → t
  31. Intersect(r, q') → T
  32. Polygon(T, D, 3) → polígono2, a, b, g_1, U
  33. Mirror(t, q) → t'
  34. Point(d) → V
  35. Vector(W, V) → F
  36. Line(V, W) → h_1
  37. Intersect(i, h_1) → Z
  38. Line(F_1, Z) → i_1
  39. Vector(F_1, D') → v
  40. Translate(K, v) → K'
  41. Translate(L, v) → L'
  42. Segment(K', L') → n'
  43. Translate(Z, F) → Z'
  44. Line(Z', i) → j_1
  45. Line(Z', i_1) → k_1
  46. Intersect(i_1, j_1) → A_1
  47. Segment(A_1, Z') → l_1
  48. Intersect(i, k_1) → B_1
  49. Segment(Z', B_1) → m_1
  50. Vector(A_1, Z) → w
  51. Vector(B_1, Z) → u_1
  52. Vector(Z, D') → v_1
  53. Vector(Z, F_1) → w_1
  54. Vector(Z, A_1) → a_1
  55. Vector(Z, B_1) → b_1
  56. Translate(F_1, a_1) → Q
  57. Vector(F_1, Q) → c_1
  58. Translate(D, b_1) → D'_1
  59. Vector(D, D'_1) → d_1
  60. Vector(Q, F_1) → R_1
  61. Vector(D'_1, D) → R_2
  62. Vector(Z', Z) → u