General Expression of Elastic Curve for Beam-Column — Lesson 5

This lesson covers the derivation of the equation of the elastic curve and the load displacement curve when a beam is subjected to axial load along with transverse load at the center. It explains the general expression of the elastic curve when the transverse load is applied at any place of the beam. The lesson further extends this concept to find the critical load for a continuous beam when it is subjected to both transverse and axial load. It provides a detailed procedure to analyze a simple supported one span beam column. The lesson concludes with the calculation of the maximum bending moment.

Video Highlights

00:39 - Explanation of the general expression of the elastic curve when the transverse load is at any place of the beam.
05:15 - Explanation of the equation of the elastic curve for the left and right part of the load.
12:45 - Explanation of how to find the constants A, B, C, and D.
25:23 - Explanation of the final equation of the elastic curve.
28:15 - Explanation of how to find the slope at the center and at the end of the beam.

Key Takeaways

- The equation of the elastic curve and the load displacement curve can be derived when a beam is subjected to both axial and transverse loads.
- The general expression of the elastic curve can be written when the transverse load is applied at any point along the beam.
- The critical load for a continuous beam subjected to both transverse and axial loads can be found using the derived equations.
- Constants in the equation can be found using boundary conditions.
- The slope at the center and the maximum bending moment can be calculated using the derived equations.