A rigid dam is composed of material of SG = 5 . The dam height is 20 m . What is the minimum thickness b of the dam necessary to prevent it from tipping about the point O when the water reaches the top of the dam considering unit width? Assume that the maximum hydrostatic pressure acts over the bottom of the dam.

b = 5.164 m is the minimum thickness of the dam

Explanation:

Given

SG = 5

h = 20 m

b = ?

w = 1 m

γw = 9800 N/m³

We  can get the forces as follows

Fp =  γw*(h/2)*(h*w)

⇒ Fp = (9800 N/m³)*(20 m/2)*(20 m*1 m) = 1.96*10⁶N

W = (SG*γw)*(h*b*w)

⇒  W = (5*9800 N/m³)*(20 m*b*1 m) = (9.8*10⁵N/m)*b

Then, we apply

∑M₀ = 0  (counterclockwise)

- Fp*(h/3) + W*(b/2) = 0

⇒   - 1.96*10⁶N*(20 m/3) + (9.8*10⁵N/m)*b*(b/2) = 0

- 13.066*10⁶N-m + (4.9*10⁵N/m)*b² = 0

⇒  b = 5.164 m is the minimum thickness of the dam

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