Moment Area: IKE A Å 112. Skips t 10 kips VC 200 ft kips * 10 ft Find Of using moment Area method 30et 12. Skips *

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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Moment Area: Find theta B using moment area method

(constant EI)

### Moment Area Method for Beam Analysis

**Objective:** Find \(\theta_B\) using the Moment Area Method.

#### Diagram Explanation:

- The diagram represents a beam supported at two ends: point A with a fixed support and point B with a roller support.

- **Loads and Reactions:**
  - A downward point load of 10 kips is applied at a point between supports.
  - A moment of \(200 \, \text{ft} \cdot \text{kips}\) is applied counterclockwise at the same location as the point load.
  - Reaction forces are indicated as \(12.5 \, \text{kips}\) at support A and \(2.5 \, \text{kips}\) at support B.

- **Dimensions:**
  - The span of the beam is \(40 \, \text{ft}\).
  - The segment between support A and the load application is \(10 \, \text{ft}\).
  - The segment between the load application and support B is \(30 \, \text{ft}\).

#### Analysis:

To find \(\theta_B\), the Moment Area Method involves calculating the areas under the bending moment diagram and applying the fundamental theorems of flexure. The methods for finding these areas and solving for \(\theta_B\) consist of mathematical and graphical approaches to understand the flexural behavior of the beam under given loads.
Transcribed Image Text:### Moment Area Method for Beam Analysis **Objective:** Find \(\theta_B\) using the Moment Area Method. #### Diagram Explanation: - The diagram represents a beam supported at two ends: point A with a fixed support and point B with a roller support. - **Loads and Reactions:** - A downward point load of 10 kips is applied at a point between supports. - A moment of \(200 \, \text{ft} \cdot \text{kips}\) is applied counterclockwise at the same location as the point load. - Reaction forces are indicated as \(12.5 \, \text{kips}\) at support A and \(2.5 \, \text{kips}\) at support B. - **Dimensions:** - The span of the beam is \(40 \, \text{ft}\). - The segment between support A and the load application is \(10 \, \text{ft}\). - The segment between the load application and support B is \(30 \, \text{ft}\). #### Analysis: To find \(\theta_B\), the Moment Area Method involves calculating the areas under the bending moment diagram and applying the fundamental theorems of flexure. The methods for finding these areas and solving for \(\theta_B\) consist of mathematical and graphical approaches to understand the flexural behavior of the beam under given loads.
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