**Problem 6: Determining Slope and Displacement Using the Moment Area Method****Objective:**To determine the slope and displacement at point C using the moment area method for a beam.**Diagram Overview:**The provided diagram illustrates a horizontal beam fixed at point A and subjected to a vertical load \( P \) at point C. - **Beam Configuration:** - The beam is fixed at the left end (point A). - The force \( P \) is applied vertically downward at the right end (point C). - A moment \( M_0 = Pa \) is applied at point B, in the counter-clockwise direction.- **Beam Length:** - The total length of the beam is \( 2a \). - The beam is divided into two segments, each with a length of \( a \).**Goal:**Apply the moment area method to calculate:1. Slope at point C.2. Displacement at point C. **Analytical Approach:**- Use the principles of the moment area method, which involves evaluating the areas under the moment diagram and using these areas to compute slope and displacement.- Recognize that the moment area method calculates the rotation (slope) and deflection (vertical displacement) based on the areas of the bending moment diagram.

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Answered: 6. Use the moment area method to…

Engineering

Civil Engineering

6. Use the moment area method to determine the slope and displacement at C Mo = Pa B

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

**Problem 6: Determining Slope and Displacement Using the Moment Area Method**

**Objective:**
To determine the slope and displacement at point C using the moment area method for a beam.

**Diagram Overview:**
The provided diagram illustrates a horizontal beam fixed at point A and subjected to a vertical load \( P \) at point C.

- **Beam Configuration:**
- The beam is fixed at the left end (point A).
- The force \( P \) is applied vertically downward at the right end (point C).
- A moment \( M_0 = Pa \) is applied at point B, in the counter-clockwise direction.

- **Beam Length:**
- The total length of the beam is \( 2a \).
- The beam is divided into two segments, each with a length of \( a \).

**Goal:**
Apply the moment area method to calculate:
1. Slope at point C.
2. Displacement at point C.

**Analytical Approach:**
- Use the principles of the moment area method, which involves evaluating the areas under the moment diagram and using these areas to compute slope and displacement.
- Recognize that the moment area method calculates the rotation (slope) and deflection (vertical displacement) based on the areas of the bending moment diagram.

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