University of California, Los Angeles
Department of Civil & Env. Engineering
CEEC137/C239: Elementary Structural Dynamics
Instructor: Mahdi Ebrahimian – Fall 2018
Homework 9 (Bonus)
(Due: Monday, Dec 10, 11:59PM)
Submissions Instructions. This is a bonus assignment. To earn full credit, please note the
following:
1. Please submit all your files at CCLE by the submission deadline note above. Late submissions
will not be accepted, regardless of the cause.
2. Submitted Matlab codes should run by themselves. Any run time error—or missing script or
function that prevents the codes from executing properly—will automatically disqualify the
submission. To avoid problems, please include all necessary Matlab Files under a single folder.
This folder should be labelled ”YourlastnameYourfirstname-Bonus”, should be
compressed/zipped, and uploaded as a single file to CCLE.
3. The Matlab codes should be accompanied by a PDF report file that explains the solution and
presents the results in a neat and concise manner. The report is worth half of the points for any
of the problems below. The report should be labelled ”YourlastnameYourfirstname-Bonus.pdf”
4. Given the requirements above, please note that you will be allowed to submit only two files: (i)
your pdf report, and (ii) your zipped folder containing your Matlab files.
5. You are not allowed to work with teams. You are welcome to ask questions to each other and
exchange ideas. However, copying codes, code segments, or reports will disqualify the
submission, and may also result in further penalties.
Problem.[3 points] Consider the five-story building shown below. All the floors have the same
height. The structure has a Rayleigh damping with the viscous damping ratios corresponding to
the first and third natural frequency given as ξ = 5%.
1. Determine the natural frequencies, natural periods, and mode shapes of the building. Mode
shapes should be normalized with respect to the mass matrix. Plot the mode shapes.
2. Determine the effective modal mass and height for each mode.
3. Determine the modal damping ratios and damping matrix c of the building.
4. Using modal analysis approach, determine the following response quantities versus time due to
the ground motion induced by the 1989 Loma Prieta Earthquake 1 . Please use the Newmark’s
time-stepping method with γ = 0.5 and β = 0.25 to obtain the response at each mode.
R(t) = [utop (t), ∆4 (t), Vb (t), Mb (t)]
5. Repeat part 4 by using Duhamel integration approach.
1
The data file for this earthquake is given in LomaPriate.mat.
(1)
6. Plot computed response quantities versus time. A total of 4 plots should be presented. In each
plot please present (i) response quantity obtained from modal analysis considering all 5 modes,
(ii) response quantity from modal analysis considering only the first mode, and (iii) response
quantity obtained from Duhamel integration approach. For each response quantity, please
comment on the accuracy of the methods used.
Note: You may use the ShearBuildingInputTemplate.m and ShearBuilding2BMod.m
as a starting point for your numerical calculations (you may also develop your own scripts).
These Matlab files are available at the CCLE.