Consider a large array of similar pillars on a regular grid that have a safety factor with respect to compressive failure of Fc. Suppose a single pillar fails and the load is then shared equally by the nearest neighboring pillars.

(a) Find the safety factor Fc needed to avoid failure of the nearest neighbor pillars and thus a domino effect and catastrophic collapse of the section.

(b) If the load is shared equally by all adjacent pillars, including the corner pillars, what is the safety factor necessary to avoid a cascade of failing pillars?