The main objectives of this individual project are: 1) to further enhance the understanding of the numerical time integration method – Newmark’s algorithm by numerically investigating its accuracy and stability, and by implementing it using a computer programming language (e.g. MatLab, C, C++, or Python); 2) to generate the earthquake response spectra from a particular earthquake; and 3) to undertake an earthquake analysis of a simple frame structure.
One particular time stepping scheme (1/2γ=and a value of β of your choice) of the Newmark method is required to use and a proper programming language is employed to perform the simulations/computations concerned. The project consists of the following three parts:
Question 1: Accuracy and stability analysis of Newmark’s method
Question 2: Response spectra of SDOF systems under a ground motion
Question 3: Earthquake analysis of a simple frame structure
Use the response spectra obtained in Part 2 to compute the peak displacements and shear forces at the three floors for the following two cases:
- Only use a linearly increasing mode;
- Use a linearly increasing mode together with a second Ritz vector increasing quadratically with height, and adopt the SRSS modal combination to find the peak displacements and shear forces at the three floors.