集中力下的剪力与弯矩图
几何画板及绘图内容加载中,请稍等……
①本范例演示了在集中力作用下梁的剪力与弯矩图绘制;②涉及的核心数学概念包括积分、三角函数和微积分;③作图要点提炼了使用GeoGebra命令/对象:Point, Vector, If, Sort, Max, Min, member, Segment, Textfield, Polygon;④适合高中及以上学生或工程技术人员学习结构力学和工程应用。
GeoGebra 命令及参数
Point(xAxis) → BPoint(xAxis) → EPoint(xAxis) → DPoint(xAxis) → CPoint(xAxis) → AVector(A, E) → r_EVector(A, D) → r_DVector(A, B) → r_BVector(A, C) → r_CIf(x(D) < x(E), D, E) → startIf(start ≟ D, E, D) → endSort(Unique[x({A, B, C, D, E})]) → pointsPoint(x = ((-AxisStepX[])) / 4) → VMax(x({A, C, B, D, E})) → rightMin(x({A, C, B, D, E})) → leftmember((Min[x({A, C, E, D, B})], 0), (Max[x({A, C, E, D, B})], 0), (0.2 * AxisStepY[])) → beam, beam1, beam2, beam3, beam4Segment((x(A), v'(x(A))), (x(A), v'(x(A) + 0.001))) → v_ASegment((x(B), v'(x(B))), (x(B), v'(x(B) + 0.001))) → v_BPoint(x = ((-AxisStepX[])) / 4) → MSegment((x(C), v'(x(C))), (x(C), v'(x(C) + 0.001))) → v_CSegment(V', (x(V'), v'(right))) → v_rMax(Join[{{0}, y(Sequence[Max[m, points(k), points(k + 1)], k, 1, Length[points] - 1])}]) → M_{max}Min(Join[{{0}, y(Sequence[Min[v, points(k), points(k + 1)], k, 1, Length[points] - 1])}]) → V_{min}Textfield(Scale_V) → InputBox1Textfield(Scale_M) → InputBox2Polygon((right, y(Corner[2])), (right, y(Corner[3])), Corner[3], Corner[2]) → mask, mask_l, mask_t, mask_r, mask_bSegment((0, y(V)), (right, y(V))) → VaxisSegment((0, y(M)), (right, y(M))) → MaxisMax(Join[{{0}, y(Sequence[Max[v, points(k), points(k + 1)], k, 1, Length[points] - 1])}]) → V_{max}Min(Join[{{0}, y(Sequence[Min[m, points(k), points(k + 1)], k, 1, Length[points] - 1])}]) → M_{min}Segment((x(D), v'(x(D))), (x(D), v'(x(D) + 0.001))) → v_DSegment((x(E), v'(x(E))), (x(E), v'(x(E) + 0.001))) → v_EIf(F_C > 0, Vector[C + (1.2 * j), C], Vector[C, C + (1.2 * j)]) → p_CIf(F_E > 0, Vector[E + (1.2 * j), E], Vector[E, E + (1.2 * j)]) → p_EIf(F_D > 0, Vector[D + (1.2 * j), D], Vector[D, D + (1.2 * j)]) → p_DVector(A - j, A) → aVector(B - j, B) → b
AI 绘图提示语参考
画一个梁结构在集中力作用下的剪力图和弯矩图,包含横轴上的五个关键点,向量表示各点间的关系,并标出剪力和弯矩的最大最小值。先画出梁和关键点,再根据力的方向绘制剪力图和弯矩图,最后标注数值和单位。
以上提示语为根据原始绘图命令整理而来,仅供参考。