**Problem 12-35: Beam Analysis****Objective:**Determine the equations of the slope and elastic curve of the beam. Assume \( EI \) (flexural rigidity) is constant.**Diagram Explanation:**The diagram shows a simply supported beam with length 8 meters. The beam is supported at two points: a pinned support at point A and a roller support at point B.- **Loads:** - A uniformly distributed load of 2 kN/m is applied over a span of 5 meters from point A. - A concentrated moment of 8 kN·m is applied at the right end of the beam.- **Supports:** - \( A \): Pinned support, generates reactions in vertical and horizontal directions. - \( B \): Roller support, allows horizontal movement and generates a vertical reaction.- **Measurements:** - The distance from point A to point B is 5 meters. - The distance from point B to the end of the beam is 3 meters. - The variable \( x \) represents a position on the beam measured from point A.**Analysis Requirement:**- Use the given loads and moments to derive the equations for the slope and the deflection (elastic curve) of the beam as functions of \( x \).These calculations are fundamental in structural engineering to understand how beams respond to various loads and ensure structural integrity and safety.

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Answered: 12-35. Determine the equations of the…

Engineering

Mechanical Engineering

12-35. Determine the equations of the slope and elasti curve. El is constant. 2 kN/m 5 m B -3m- 8 kN-m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Question

**Problem 12-35: Beam Analysis**

**Objective:**
Determine the equations of the slope and elastic curve of the beam. Assume \( EI \) (flexural rigidity) is constant.

**Diagram Explanation:**
The diagram shows a simply supported beam with length 8 meters. The beam is supported at two points: a pinned support at point A and a roller support at point B.

- **Loads:**
- A uniformly distributed load of 2 kN/m is applied over a span of 5 meters from point A.
- A concentrated moment of 8 kN·m is applied at the right end of the beam.

- **Supports:**
- \( A \): Pinned support, generates reactions in vertical and horizontal directions.
- \( B \): Roller support, allows horizontal movement and generates a vertical reaction.

- **Measurements:**
- The distance from point A to point B is 5 meters.
- The distance from point B to the end of the beam is 3 meters.
- The variable \( x \) represents a position on the beam measured from point A.

**Analysis Requirement:**
- Use the given loads and moments to derive the equations for the slope and the deflection (elastic curve) of the beam as functions of \( x \).

These calculations are fundamental in structural engineering to understand how beams respond to various loads and ensure structural integrity and safety.

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