The symmetric concrete “gravity” dam is held in place by its own weight. If the density of concrete is ρc and water has a density ρw, determine the smallest distance d at its base that will prevent the dam from overturning about its end A. The dam has a width w.

Units Used:

Mg = 10³ kg    MN = 10⁶ N

Given:

a = 1.5 m         ρc = 2.5Mg/m³

b = 9 m

                        ρw = 1.0Mg/m³

w = 8 m

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b