183. A solid rectangular beam of uniform depth fixed at one end and loaded at the other, should he on plan in the shape of a triangle, as Fig. 48.

Fig. 48.

Fig. 49.

184. If the beam he loaded uniformly it will still he triangular on plan, hut the sides of the triangle instead of being straight lines will be parabolas whose common vertex is at A (Fig. 49).

185. When the breadth is constant and the top is horizontal, the depth should increase from the point of application of the weight towards the support in the form of a parabolic curve, whose vertex is at A and axis horizontal (Fig. 50).

Fig. 50.

Fig. 51.

With a uniform load, when the breadth is constant the elevation of the beam will be triangular.

186. In a solid round beam fixed at one end and loaded at the other, the form required for uniform strength is that generated by the revolution of a cubic parabola round a horizontal axis (Fig. 51).