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A 30 kN/m 2.4 m C 50 kN 1.2 m D 1.2 m B Q4. Determine the deflection and slope at point C by using singularity function method.

A 30 kN/m 2.4 m C 50 kN 1.2 m D 1.2 m B Q4. Determine the deflection and slope at point C by using singularity function method.

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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### Structural Analysis Problem: Beam Deflection and Slope Calculation **Question:** Determine the deflection and slope at point \( C \) by using the singularity function method. **Diagram Explanation:** - **A Simply Supported Beam:** The diagram features a simply supported beam \( AB \), which is acted upon by two different loads. - **Support Conditions:** - **Point \( A \):** This end of the beam is supported by a pin support. - **Point \( B \):** This end of the beam is supported by a roller support. - **Loading Conditions:** - There is a uniformly distributed load of \( 30 \, \text{kN/m} \) acting over the length \( AC \) (2.4 m from \( A \)). - Additionally, there is a concentrated load of \( 50 \, \text{kN} \) acting at point \( D \), which is 1.2 meters from \( B \). - **Dimensions:** - From \( A \) to \( C \): \( 2.4 \, \text{m} \) - From \( C \) to \( D \): \( 1.2 \, \text{m} \) - From \( D \) to \( B \): \( 1.2 \, \text{m} \) **Objective:** - Determine the deflection (vertical displacement) and slope (angular displacement) at point \( C \). **Methods:** - Use the singularity function method for calculating the deflection and slope at the specified point on the beam.
Transcribed Image Text:### Structural Analysis Problem: Beam Deflection and Slope Calculation **Question:** Determine the deflection and slope at point \( C \) by using the singularity function method. **Diagram Explanation:** - **A Simply Supported Beam:** The diagram features a simply supported beam \( AB \), which is acted upon by two different loads. - **Support Conditions:** - **Point \( A \):** This end of the beam is supported by a pin support. - **Point \( B \):** This end of the beam is supported by a roller support. - **Loading Conditions:** - There is a uniformly distributed load of \( 30 \, \text{kN/m} \) acting over the length \( AC \) (2.4 m from \( A \)). - Additionally, there is a concentrated load of \( 50 \, \text{kN} \) acting at point \( D \), which is 1.2 meters from \( B \). - **Dimensions:** - From \( A \) to \( C \): \( 2.4 \, \text{m} \) - From \( C \) to \( D \): \( 1.2 \, \text{m} \) - From \( D \) to \( B \): \( 1.2 \, \text{m} \) **Objective:** - Determine the deflection (vertical displacement) and slope (angular displacement) at point \( C \). **Methods:** - Use the singularity function method for calculating the deflection and slope at the specified point on the beam.
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