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Reactions of Three-Supported Beam to Oblique Force

Reactions of Three-Supported Beam to Oblique Force
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2019-06-28 22:48
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the reactions of a three-supported beam under an oblique force. Key mathematical concepts include trigonometry and coordinate geometry. Using GeoGebra commands such as Line, Point, OrthogonalLine, and Intersect, the force analysis model of the beam is constructed. Suitable for high school physics and mathematics education to help students understand the decomposition and synthesis of forces.

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. Rotate(D, 30°, D) → D'
  11. Point(d) → V
  12. Vector(W, V) → F
  13. Line(V, W) → h_1
  14. Line(G, xAxis) → j
  15. Point(d) → H
  16. Point(j) → I
  17. Segment(H, I) → k
  18. Point(d) → J
  19. Point(j) → K
  20. Segment(J, K) → l
  21. Point(d) → L
  22. Point(j) → M
  23. Segment(L, M) → m
  24. Line(I, H) → n
  25. Line(K, J) → a
  26. Line(M, L) → b
  27. Intersect(n, a) → N
  28. Intersect(h_1, b) → O
  29. Line(N, O) → g_1
  30. Translate(O, F) → O'
  31. Line(O', g_1) → i_1
  32. Line(O', b) → j_1
  33. Intersect(j_1, g_1) → P
  34. Segment(O', P) → k_1
  35. Intersect(b, i_1) → Q
  36. Segment(O', Q) → l_1
  37. Vector(P, O) → v
  38. Vector(Q, O) → w
  39. Translate(N, v) → N'
  40. Vector(N, N') → a_1
  41. Line(N', a) → m_1
  42. Line(N', n) → n_1
  43. Intersect(n, m_1) → R
  44. Vector(N, R) → b_1
  45. Intersect(a, n_1) → S
  46. Vector(N, S) → d_1
  47. Segment(R, N') → p_1
  48. Segment(N', S) → q_1
  49. Translate(M, w) → M'
  50. Vector(M, M') → R_3
  51. Translate(I, b_1) → I'
  52. Vector(I, I') → R_1
  53. Translate(K, d_1) → K'
  54. Vector(K, K') → R_2
  55. Circle(M, 0.15) → c_1
  56. Circle(H, 0.15) → p
  57. Circle(I, 0.15) → q
  58. Circle(J, 0.15) → r
  59. Circle(K, 0.15) → s
  60. Circle(L, 0.15) → t
  61. Vector(O', O) → u

AI Drawing Prompt Reference

Draw a three-supported beam subjected to an oblique force. Start by drawing the x-axis, then take points A and B on it. Draw a perpendicular line f through A and a perpendicular line g through B. On f, take point C and on g, take point D. Draw perpendicular lines h and i through C and D, respectively, with their intersections at E and F_1. Construct quadrilateral CEDF_1. Rotate point D by 30 degrees to get D', and construct vector VD. Draw line h_1 through D and D'. Construct a perpendicular line j through the x-axis, and take points H and I on it. Draw line segment HI, then take points J and K on j, draw line segment JK, and take points L and M on j, draw line segment LM. Draw lines n through H and I, a through J and K, and b through M and L, with their intersections at N and O. Draw line NO to get g_1. Translate point O to get O', and draw lines i_1 through O' to g_1, and j_1 through O' to b, with their intersection at P. Draw line segment OP, and construct vectors v and w from O to P. Draw line segments p_1 from N to N' and q_1 from N' to S.
The prompt above was compiled from the original drawing commands and is for reference only.