University of Central Florida CES6220-19 – Wind and Earthquake Engineering Spring 2019 HOMEWORK #04 Due date: Monday, February 25, 2019, before the start of class at 4:30pm. Submission type: Either online at webcourses in form of single pdf file or hard copy, in person at classroom or during office hours, are acceptable. Homework dropped outside or under my office door will not be collected or graded. Homework Type: Individual assignment (no group or team work assignment) Reading Material: Minimum: Textbook Chapters 1-3 (Elnashai and Di Sarno, 2nd edition), Textbook Chapters 5-6 (Chopra, 5th edition), posted lecture notes, and class lecture notes. Requirements: 10% penalty may be applied if the requirements as detailed below are not followed: • • • • • All homework packages must include a coversheet which shows the student’s name, homework number and date. Alternatively, you can use the homework question page as the coversheet. No loose sheets. All pages should be tied together using a stapler or a clip. Any assumptions that are made must be clearly stated. References must be made for any values taken from tables and equations of the textbook. All calculations must be done neatly and legibly. Unreadable handwriting will not be deciphered. The calculations should be done in a logical and organized fashion. The final answers must be clearly shown and highlighted or underlined. Academic Integrity: Zero tolerance policy for cheating and plagiarism (see syllabus) Late submission: Homework must be turned in on the due date before the start of class. No late homework submission will be accepted or graded (includes both online or hard copy). Name: _______________________________ Date submitted: _______________________________ 1 University of Central Florida CES6220-19 – Wind and Earthquake Engineering Spring 2019 Problem 1 The SDOF system shown below, with properties 𝑇𝑛 = 1 𝑠𝑒𝑐 and 𝜁 = 0.02, is governed by the following differential equation: 𝑢̈ + 2𝜁𝜔𝑛 𝑢̇ + 𝜔𝑛2 𝑢 = −𝑢̈ 𝑔 (𝑡) where the dot denotes time derivative. Using EXCEL, find the response of the SDOF system above, when subjected under the provided El Centro 1940 (see attached file for North South Component, Peknold Version) ground motion for the following cases using: a) Central Difference Method b) Newmark’s Method (𝛽 = 1⁄4, 𝛾 = 1⁄2) Report your solution at equal time steps of 0.01 𝑠𝑒𝑐 for a duration of 30 𝑠𝑒𝑐. Plot the displacement, velocity, and acceleration response time-history and show the location and value of maximum responses. Compare the solutions obtained from a) and b). Deliverables are both a report (pdf) with results and plots and EXCEL files. (10 points total) 2 University of Central Florida CES6220-19 – Wind and Earthquake Engineering Spring 2019 Problem 2 Enrich the MATLAB ODE script provided to you, to be able to produce elastic response spectra (solve many SDOF systems for different periods). Using your enriched Elastic Spectra MATLAB script produce the deformation, pseudo-velocity, and pseudo-acceleration response spectra for the provided El Centro 1940 (see attached file for North South Component, Peknold Version) ground motion. Plot your three response spectra in linear scales (horizontal axis is period 𝑇𝑛 ), for periods between 0 ≤ 𝑇𝑛 ≤ 3 𝑠𝑒𝑐, and using period increment of 𝑑𝑇𝑛 = 0.01 𝑠𝑒𝑐. Report in tabular format the response spectra ordinates for periods 𝑇𝑛 = 0.5, 1.0, 1.5, 2.0 𝑠𝑒𝑐. If you don’t have access to MATLAB you may use EXCEL using the worksheets you developed in Problem 1. In that case you may use period increment of 𝑑𝑇𝑛 = 0.1 𝑠𝑒𝑐. Deliverables are both a report (pdf) with results and plots and MALTAB/EXCEL files. (10 points total) 3