Consider the concrete dam shown in Figure 1 Consider the con

Consider the concrete dam shown in (Figure 1).

Consider the concrete dam shown in (Figure 1) Part A Determine the critical height h of the water level that causes the concrete gravity dam to be orn the verge of tipping over due to water pressure. The density of concrete is Pe 2.40 Mg/m3 Suppose that hd 48 m. Hint: Work the problem using a 1-m width of the dam. Express your answer to three significant figures and include the appropriate units h Value Units Figure 1of1 Submit Request Answer Provide Feedback Next > 6 m

Solution

The dam will try to tip over corner A.The critical height will be such that overturning moment at A due to water should be equal to moment due to self weight of dam at corner A

Let us consider unit length of dam

Area of cross section of dam=0.5*6*48=144 m²

Volume of dam = 144*1=144 m³

Density of concrete=2400 kg/m³=2400*9.8=23520 N/m³

Moment about A due to weight of dam = 23520*144*(2/3)*6=13547520 Nm

Let the critical height of water be h

Moment about A due to water of height h=0.5*h*(9.8*1000*h)*1*h/3=1633.33h³

1633.33h³ = 13547520

h=20.24m

Therefore, critical height =20.24m