A gravity dam built of concrete has dimensions as shown in the adjoining sketch.

Question

A gravity dam built of concrete has dimensions as shown in the adjoining sketch. It is filled with water to a depth of 18 m. To prevent cracking of the concrete or separation from the bedrock, the resultant force on the structure must pass through the middle third of the base so as to maintain compressive stress everywhere in the concrete and bedrock. By taking moments about the toe of the dam (Point O), determine the point (horizontal distance from Point O) through which the resultant force passes through the base and hence whether the dam is safe or not.

Explanation / Answer

Resultant force passing through base taking moment at point O = Pressure x Area.

Pressure = w x h.

w = Weight density of water = 1000 kg/m^3.

h = Height of water = 18m

Pressure = 1000 x 18 = 18000 Kg/m^2

Area = Depth of water x widht of dam = 18 x 5(since middle third of base = 15/3 = 5m) = 90 m^2

Resultant force passing through base taking moment at point O = Pressure x Area = 18000 x 90 = 1620000 Kg

TO CHECK DAM IS SAFE OR NOT:

Maxiumu resultant force acting on Dam = 18000 x 18 x 15 = 4860000 kg.

Since Resultant force at point O at 3rd middle base is lesser than maximum resultant force acting on Dam, the DAM is safe.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.