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Concentrated Forces: Shear and Bending Moment Diagrams

Concentrated Forces: Shear and Bending Moment Diagrams
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2019-06-12 03:31
VectorCalculusGeometric ConstructionGraphing
This example demonstrates the construction of Shear and Bending Moment diagrams under concentrated forces on a beam. Key math concepts include Integral Calculus, Sine functions, and Calculus. The construction utilizes GeoGebra commands like Point, Vector, If, Sort, Max, Min, member, Segment, Textfield, and Polygon. Suitable for high school students and engineering professionals studying structural mechanics and engineering applications.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Point(xAxis) → E
  3. Point(xAxis) → D
  4. Point(xAxis) → C
  5. Point(xAxis) → A
  6. Vector(A, E) → r_E
  7. Vector(A, D) → r_D
  8. Vector(A, B) → r_B
  9. Vector(A, C) → r_C
  10. If(x(D) < x(E), D, E) → start
  11. If(start ≟ D, E, D) → end
  12. Sort(Unique[x({A, B, C, D, E})]) → points
  13. Point(x = ((-AxisStepX[])) / 4) → V
  14. Max(x({A, C, B, D, E})) → right
  15. Min(x({A, C, B, D, E})) → left
  16. member((Min[x({A, C, E, D, B})], 0), (Max[x({A, C, E, D, B})], 0), (0.2 * AxisStepY[])) → beam, beam1, beam2, beam3, beam4
  17. Segment((x(A), v'(x(A))), (x(A), v'(x(A) + 0.001))) → v_A
  18. Segment((x(B), v'(x(B))), (x(B), v'(x(B) + 0.001))) → v_B
  19. Point(x = ((-AxisStepX[])) / 4) → M
  20. Segment((x(C), v'(x(C))), (x(C), v'(x(C) + 0.001))) → v_C
  21. Segment(V', (x(V'), v'(right))) → v_r
  22. Max(Join[{{0}, y(Sequence[Max[m, points(k), points(k + 1)], k, 1, Length[points] - 1])}]) → M_{max}
  23. Min(Join[{{0}, y(Sequence[Min[v, points(k), points(k + 1)], k, 1, Length[points] - 1])}]) → V_{min}
  24. Textfield(Scale_V) → InputBox1
  25. Textfield(Scale_M) → InputBox2
  26. Polygon((right, y(Corner[2])), (right, y(Corner[3])), Corner[3], Corner[2]) → mask, mask_l, mask_t, mask_r, mask_b
  27. Segment((0, y(V)), (right, y(V))) → Vaxis
  28. Segment((0, y(M)), (right, y(M))) → Maxis
  29. Max(Join[{{0}, y(Sequence[Max[v, points(k), points(k + 1)], k, 1, Length[points] - 1])}]) → V_{max}
  30. Min(Join[{{0}, y(Sequence[Min[m, points(k), points(k + 1)], k, 1, Length[points] - 1])}]) → M_{min}
  31. Segment((x(D), v'(x(D))), (x(D), v'(x(D) + 0.001))) → v_D
  32. Segment((x(E), v'(x(E))), (x(E), v'(x(E) + 0.001))) → v_E
  33. If(F_C > 0, Vector[C + (1.2 * j), C], Vector[C, C + (1.2 * j)]) → p_C
  34. If(F_E > 0, Vector[E + (1.2 * j), E], Vector[E, E + (1.2 * j)]) → p_E
  35. If(F_D > 0, Vector[D + (1.2 * j), D], Vector[D, D + (1.2 * j)]) → p_D
  36. Vector(A - j, A) → a
  37. Vector(B - j, B) → b

AI Drawing Prompt Reference

Draw shear and bending moment diagrams for a beam under concentrated forces, including five key points on the horizontal axis, vectors showing relationships between points, and marking maxima and minima of shear and moment. Start with the beam and key points, then draw the shear and moment diagrams based on force directions, and finally label values and units.
The prompt above was compiled from the original drawing commands and is for reference only.