Matlab Coding

Prof. Emel Seyhan CE447 – Intro to Geotechnical Earthquake Engineering

CSULB - FALL 2020

HOMEWORK #2

Official due: Oct, 1st, 2020, 11.59PM Penalty due: Up to Oct 6th, 2020, 11.59PM

1. (5 pts) a) Draw the free body diagrams and show all the acting forces on both systems. b) Derive the equation of motion of both systems. Show each step of your calculations.

Hint: Use substituion of damping ratio,  and natural frequency, .

Fig 1. Damped single degree-of-freedom

system

Fig 2. Forced vibration of amped single degree-of-freedom system by ground excitation

2. (8 pts) Using PEER strong ground motion database link,

https://ngawest2.berkeley.edu/spectras/329198/searches/new, find and download the acceleration time series (.at2 files) for below input values. Get familiar with PEER and what it does. Do not print the m files, submit your codes electronically in addition to any figures you include here. Comment code lines using % to explain what you did. ZIP all your files and submit with name “Lastname_Firstname_HW#2”.

Earthquake name: M6.69 Northridge Station details:

VS30 (m/s) = 740.05 and 277.98, firm rock and stiff soil, respectively a) Using MATLAB and lecture notes, plot the acceleration time series for three components (H1, H2

and V) in one figure with two columns using same vertical axis scale (Hint: Use column and subplot command. Expecting six panels). Pay attention to the units, use g-unit. Include axis labels, title, legend and other required details on the figure.

b) Find the absolute values of PGA and mark them on the figure.

3. (5 pts) Using MATLAB and lecture notes, convert the time series per station into response spectra. (Hint: Use piecewise linear interpolation as a separate function and call that in your main code). Bonus points if you code the piecewise function.

Prof. Emel Seyhan CE447 – Intro to Geotechnical Earthquake Engineering

4. (6 pts) a) Compare your response spectra PSA vs T to mean PEER spectra using below input values. Use

0.01 binning from 0.01 to 0.1, 0.1 binning from 0.1 to 1 and 1 binning from 1 to 10sec. Plot in log-log scale.

b) Extract PSA at T = 0.01, 0.5, 1 and 3sec. Comment on significant findings comparing the recordings from these two stations (Hint: Examing the station locations relative to the earthquake and site conditions). Also, link your answer to building response assumed as SDOF systems.

Spectral ordinate: GeoMean Damping ratio: 5% Suite average: Arithmetic c) If your spectra matches the one from PEER, why is that? (Hint: The advantages/disadvantages of

the method you used).

5. (4 pts) Using the same recordings from #1, plot GeoMean of acceleration, velocity and displacement time series in one figure with two columns. Find the absolute value of PGA, PGV and PGD, mark them on the figure. Be consistent with the units (g-unit, cm/s, cm).

6. (2 pts) Comment on your findings comparing the recordings from these two stations (Hint: Examine the station locations relative to the earthquake epicenter location with given site conditions as VS30, e.g. do you expect to see higher or lower amplification for softer station? etc).