Response History Analysis — Lesson 1

This lesson covers the concept of response due to support motion in a multi-degree of freedom (MDOF) system. It delves into the process of determining the response of an MDOF system when the support motion of the system is given. The lesson uses a three-story structure as an example, with each level defined by masses M1, M2, and M3, and lateral stiffness K1, K2, and K3. The lesson also explains how to derive the equation of motion in absolute and relative terms. It further discusses two methods to solve the problem: modal decomposition and numerical integration. The lesson concludes with a practical application of these concepts using a coding example.

Video Highlights

Explanation of the problem of finding out the response of an MDOF system when the support motion of the system is given - 1:10
Description of the three-story system with masses at each level defined as M1, M2, M3, and the collective lateral stiffness and damping for each story - 1:45
Explanation of the equation of motion in absolute and relative terms - 2:55
Discussion on how to derive the equation of motion - 4:49
Explanation of two options to solve the problem: model decomposition and numerical integration - 5:45
Demonstration of how to solve the problem using model decomposition - 6:22
Introduction to an example problem of a three-story system - 8:37
Explanation of how to develop the code for the MD system - 11:58
Demonstration of how to run the code and compare the results obtained from model superposition and Wilson Theta - 15:07
Explanation of how to calculate the sheer force acting at each floor and the bending moment at the base - 21:56
Discussion on how to calculate the level of comfort for the occupants at different floor levels - 22:59

Key Takeaways:

- The response of an MDOF system can be determined when the support motion of the system is given.
- The equation of motion can be derived in absolute and relative terms.
- Modal decomposition and numerical integration are two methods to solve the problem.
- The response of a structure can be calculated at each floor level, which is essential for design purposes.
- The acceleration at each floor level can be calculated, which defines the level of comfort for the occupants.