2.14 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 36 kN. TWATER LBVEL We 36 kN F- 20 KN A 3m. 3 m.
2.14 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 36 kN. TWATER LBVEL We 36 kN F- 20 KN A 3m. 3 m.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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 36 kN.
Transcribed Image Text:### Problem 2.14: Resultant Moment in a Dam Structure
**Problem Statement:**
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 36 kN.
**Provided Data and Diagram Explanation:**
- The diagram depicts a triangular dam structure with specific dimensions and forces applied.
- The water level is indicated by a horizontal dashed line, and it exerts a horizontal water pressure force (Fw) of 20 kN on the dam.
- The height at the top of the dam from the base (toe) is 1 meter.
- The height at the bottom of the dam from the toe is 3 meters.
- The water pressure force, Fw = 20 kN, acts at a distance of 1 meter from the base.
- The self-weight of the dam, W = 36 kN, acts vertically downwards from the center of the dam.
The following distances and forces are represented:
- The base width of the dam (horizontal distance at the bottom) is 3 meters.
- Point A is the toe of the dam, located at the bottom-left corner of the structure.
- The moment arm distances are affected by the dimensions and force points.
#### Objective:
To calculate the resultant moment at point A (the toe of the dam), considering the given forces and dimensions.
**Procedure:**
1. **Calculate the Moment due to Water Pressure (Fw):**
The horizontal force due to water pressure, Fw = 20 kN, acts at a height of 1 meter above the base.
- Distance of Fw from point A = 1 meter
- Moment due to Fw about point A = Fw * distance = 20 kN * 3 m = 60 kN·m
2. **Calculate the Moment due to the Weight of the Dam (W):**
The weight of the dam, W = 36 kN, acts vertically downward from the center of the dam. The center of the dam's weight is located at half of its base, 1.5 meters from A.
- Moment arm (distance from A to the center of weight) = 1.5 m
- Moment due to W about point A = W * 1.5 m =
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