The bar OABC has multiple bends in different direction has a force F₁ = {-100.} N applied at point B, anc force ₂ ={-100 + 300 · 3 + 100 · } N applied a F2 i C. Using the listed parameters, find the equivalent force moment applied at O as Cartesian vectors. X Z CC 30 BY NO SA 2021 Cathy Zupke Al দ ----2-- parameter value BI units F₁ -3 C y F2

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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**Analysis of Forces and Moments on a Bent Bar:**

The bar \( OABC \) has multiple bends in different directions. It has a force \( \vec{F_1} = \{-100 \cdot \hat{k}\} \) N applied at point \( B \), and a force \( \vec{F_2} = \{-100 \cdot \hat{i} + 300 \cdot \hat{j} + 100 \cdot \hat{k}\} \) N applied at point \( C \). Using the listed parameters, find the equivalent force and moment applied at \( O \) as Cartesian vectors.

### Diagram Explanation:

- **Diagram Description:** 
  - A three-dimensional diagram depicts a bent bar \( OABC \) with three segments.
  - The z-axis is vertical, the x-axis is horizontal towards the right, and the y-axis is towards the back.
  - Point \( O \) is on the x-axis. From \( O \), the bar goes vertically up \( L_1 \) to point \( A \), horizontally along the y-axis \( L_2 \) to point \( B \), and then diagonally in the yz-plane \( L_3 \) to point \( C \).

- **Forces:**
  - \( \vec{F_1} \) is a vertical downward force at point \( B \).
  - \( \vec{F_2} \) is a force acting at point \( C \) with components in all three directions.

### Parameters Table:

| Parameter | Value | Units |
|-----------|-------|-------|
| \( L_1 \) | 0.5   | m     |
| \( L_2 \) | 1     | m     |
| \( L_3 \) | 1     | m     |

**NOTE:** Use \( i, j, k \) for \( \hat{i}, \hat{j}, \hat{k} \).

#### Calculations to be Performed:

- **Resultant Force at Point \( A \):**
  \( \text{The resultant force at point } A = \{\} \) N

- **Resultant Couple Moment About Point \( A \):**
  \( \text{The resultant couple moment about point } A = \{\} \) N·m
Transcribed Image Text:**Analysis of Forces and Moments on a Bent Bar:** The bar \( OABC \) has multiple bends in different directions. It has a force \( \vec{F_1} = \{-100 \cdot \hat{k}\} \) N applied at point \( B \), and a force \( \vec{F_2} = \{-100 \cdot \hat{i} + 300 \cdot \hat{j} + 100 \cdot \hat{k}\} \) N applied at point \( C \). Using the listed parameters, find the equivalent force and moment applied at \( O \) as Cartesian vectors. ### Diagram Explanation: - **Diagram Description:** - A three-dimensional diagram depicts a bent bar \( OABC \) with three segments. - The z-axis is vertical, the x-axis is horizontal towards the right, and the y-axis is towards the back. - Point \( O \) is on the x-axis. From \( O \), the bar goes vertically up \( L_1 \) to point \( A \), horizontally along the y-axis \( L_2 \) to point \( B \), and then diagonally in the yz-plane \( L_3 \) to point \( C \). - **Forces:** - \( \vec{F_1} \) is a vertical downward force at point \( B \). - \( \vec{F_2} \) is a force acting at point \( C \) with components in all three directions. ### Parameters Table: | Parameter | Value | Units | |-----------|-------|-------| | \( L_1 \) | 0.5 | m | | \( L_2 \) | 1 | m | | \( L_3 \) | 1 | m | **NOTE:** Use \( i, j, k \) for \( \hat{i}, \hat{j}, \hat{k} \). #### Calculations to be Performed: - **Resultant Force at Point \( A \):** \( \text{The resultant force at point } A = \{\} \) N - **Resultant Couple Moment About Point \( A \):** \( \text{The resultant couple moment about point } A = \{\} \) N·m
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