Abstract
STABILITY OF A POINT Recall from elementary statics or physics that a point in 3D space has three degrees of freedom, it can only translate in the X, Y, Z directions (or any other mutually orthogonal set of axes). This is visualized by imagining a ball flying through the air, the ball is free to travel in any direction, it is unstable. The point is infinitely small, all loads hit it directly at its centroid. This explains why there is no rotational degrees of freedom for a point in space, thus the ball does not spin. Loads have no eccentricity to the point’s centroid. Since the point is free to translate in three directions, the point requires three supports to stabilize it. Of course the supports must be able to carry tension or compression. Traditionally, a pinned support (boundary condition) is assumed to carry three mutually perpendicular (orthogonal) forces as reactions. In this first example it is noted that each strut is pinned-pinned without any transverse loads, thus the net reaction must align with the axis of each supporting strut as shown in Fig. 7.1.
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