Dynamic Analysis of Euler Bernoulli Beams — Lesson 2

This lesson covers the dynamic analysis of Euler Bernoulli beams subjected to moving loads and support excitation. It explains the concept of force vibration, the importance of dynamic response in practical design, and the use of mode superposition method for analysis. The lesson also discusses the impact of moving load speed on the impact factor, which is crucial in bridge design. It further elaborates on the calculation of mid-span deflection, bending moment, and shear force. The lesson concludes with the analysis of a beam subjected to support excitation, a scenario common in earthquake response studies.

Video Highlights

01:53 - Magnification of static response due to dynamic effect of the load.
03:45 - Concept of generalized force and its calculation using the properties of the direct Delta function.
07:40 - Decoupled equation of motion and the calculation of the constants of integration using initial conditions.
10:49 - Impact of the speed of the moving load on the dynamic response of the beam.
46:37 - Concept of impact factor and its calculation for deflection, bending moment, and shear force.

Key Takeaways

- The dynamic response of a beam subjected to moving load is crucial in practical design and research.
- The mode superposition method is an effective technique for analyzing systems subjected to moving loads.
- The speed of the moving load significantly impacts the impact factor, which is a multiplier used to magnify static live load stresses in bridge design.
- The calculation of mid-span deflection, bending moment, and shear force is essential in dynamic analysis.
- The analysis of a beam subjected to support excitation is vital in studying earthquake responses.