The equivalent forces due to water pressure and the self-weight of the dam 
are shown. Determine the resultant moment at the toe of the dam (point A). Is 
the dam able to resist the applied water pressure? The weight of the dam is 
36kN.

To determine the resultant moment at the toe of the dam (point A) due to the water pressure and the self-weight of the dam, we'll break the process down step by step:

### Given Data:
- **Weight of the dam (W)** = 36 kN
- **Water pressure distribution:** This force is usually triangular, with the pressure increasing linearly with depth.
  
We will assume a triangular pressure distribution on the dam due to the water.

Let’s proceed with these steps:

### 1. **Water Pressure Force Calculation (Fw):**
The total force due to water pressure is determined by the area under the triangular pressure distribution curve. For a dam, the pressure at the top is 0 and at the bottom of the dam, it's \( \rho g h \), where:
- \( \rho \) is the density of water (assumed to be 1000 kg/m³)
- \( g \) is the acceleration due to gravity (9.81 m/s²)
- \( h \) is the height of water acting on the dam.

The total force \( F_w \) is given by:
\[
F_w = \frac{1}{2} \cdot \rho g h \cdot h = \frac{1}{2} \cdot \rho g h^2
\]

### 2. **Location of Water Force:**
The equivalent force due to water pressure acts at one-third the height of the water from the base of the dam (h/3).

### 3. **Moment Due to Water Pressure (Mw):**
The moment at point A due to water pressure is the product of the force \( F_w \) and the distance from point A (which is h/3):
\[
M_w = F_w \cdot \frac{h}{3}
\]

### 4. **Moment Due to the Self-Weight of the Dam (Md):**
The weight of the dam acts through its center of gravity. Assuming the dam is a uniform rectangular block, its weight acts at the midpoint of its base. The moment arm from point A to the center of gravity is half the base width of the dam (b/2). Thus, the moment due to the dam's weight is:
\[
M_d = W \cdot \frac{b}{2}
\]
where \( b \) is the base width of the dam.

### 5. **Resultant Moment at Point A:**
The resultant moment at point A is the sum of the moment due to water pressure and the moment due to the self-weight of the dam. Assuming counterclockwise moments are positive, we calculate:
\[
M_{resultant} = M_w - M_d
\]

### **Determine Stability:**
For the dam to resist the applied water pressure, the resultant moment at point A must not cause overturning. This depends on whether the dam's weight provides enough stabilizing moment to counteract the overturning moment from the water pressure.

If the resultant moment \( M_{resultant} \) is positive or small, the dam can resist the applied pressure. If the moment is large and negative, it suggests potential instability.

---

To fully determine this, we need the height and base width of the dam (h and b). If you provide these values, I can calculate the exact resultant moment and check whether the dam can resist the applied water pressure.

Do you have the height and base width of the dam, or would you like to provide them?

### Further Questions:
1. What is the height of the dam (h)?
2. What is the base width of the dam (b)?
3. What is the depth of the water acting on the dam?
4. Are there any additional forces acting on the dam, like uplift pressure?
5. What material is the dam made of (to check for any buoyancy effects)?

### Tip:
Always verify the water depth and ensure it's included in the calculation of both force and moment due to water pressure.

The equivalent forces due to water pressure and the self-weight of the dam are shown. Determine the resultant moment at the toe of the dam (point A). Is the dam able to resist the applied water pressure? The weight of the dam is 36kN.

Learn how to calculate the resultant moment at the toe of a dam due to water pressure and the dam's self-weight. The solution involves hydrostatic pressure formulas and the principle of moments, with an example featuring a 36kN dam. Suitable for advanced high school and college-level students.

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