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

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
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**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.
Transcribed Image Text:**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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