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Forces Acting on Dams To design a dam, various forces must be considered to insure the safety of the dam. The most important forces are: Weight of dam Water Pressure Uplift Wave pressure Earthquake forces

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Weight of Dam The weight of the dam is calculated as follows: Where γm is the specific weight of the dam’s material.

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**Where γw is the specific weight of water and h is the height of water.**

Water Pressure Water pressure acts perpendicular to the surface of the dam and is calculated per unit width as follows: Where γw is the specific weight of water and h is the height of water. Pw h/3 h

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**Dams are subjected to uplift force under its base. Uplift acts upward.**

Where B is the width of the base of the dam. h U B B/3

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**Where hw is the wave height.**

Wave Pressure The upper part of the dam (above the water level) is subjected to the impact of waves. The maximum wave pressure per unit width is: Where hw is the wave height. Pw 0.375 hw hw

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Earthquake Forces Dams are subjected to vibration during earthquakes. Vibration affects both the body of the dam and the water in the reservoir behind the dam. Vibration forces are function of both the intensity (Rechter Scale) and its duration. The most danger effect occurs when the vibration is perpendicular to the face of the dam.

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Body Forces: Body force acts horizontally at the center of gravity and is calculated as: Where α is the earthquake coefficient and W is the weight of the dam Is taken 0.2 for practical reasons. W1 0.1 W1 W2 0.1 W2

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**Water vibration produces a force on the dam acting horizontally;**

Water Force: Water vibration produces a force on the dam acting horizontally; Where Ce is another coefficient (0.82) and h is the height of the water 2/5 h h Pew

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**Calculate the forces on given dam if; **

Example: Calculate the forces on given dam if; γm = 2.5 t/m3, γw =1 t/m3, hw = 1.5 m 6 m 10 m 33 m 30 m 24 m

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**1. Weight of water W1=2.5 * 6 * 40 = 600 t W2=2.5 *0.5*18*30 = 675 t**

2. Water Pressure P = 0.5 * 1.0 * (33)2 = t w1 w2 P

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**3. Uplift U = 0.5 * 1.0 * 33 * 24 = 396 t 4. Wave Pressure**

Pw = 2.4 * 1.0 * 1.5 = 3.6 t U Pw

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**5. Earthquake Forces a. Body Forces Pem1= 0.1 * 600 = 60 t**

b. water Force Pew=(2/3)*0.82*0.1*(33)2 = t Pem1 Pew Pem2

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Chapter 12: Forces and Fluids

Chapter 12: Forces and Fluids

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