Assignment $1$

$($Due Friday, March $22$th$,2024)$

$1-$ Write down the formulations of piecewise linear exact method together with the formulations of recurrence

relations and coefficients $($hand written formulations on A$4$ size plain paper$)$

$2-$ Develop an Excel sheet to compute dynamic response of a linear elastic single degree of freedom $($SDOF$)$

system. Use piecewise linear exact method formulations presented in lecture notes. Time histories, that you

are asked to compute and plot, are listed below;

Displacement$-$time history,

Velocity$-$time history,

Acceleration$-$time history,

Pseudo Acceleration$-$time history,

Total Acceleration$-$time history.

$3-$ Compute dynamic responses of SDOF systems with natural vibration periods of $T_1,T_2$ and $T_3$ for $1940El$

Centro $($N$-$S$,$ sampling rate:$0\mathrm{.}02$ sec$,$ units:g$)$ earthquake ground motion record for damping ratio of ${}_1.$ For

the SDOF system, having natural vibration period of $T_{1}sec,$ repeat your analysis for different damping

ratios of ${}_2$ and ${}_3.$

$4-$ In each of your graphs, point out the peak response. Compare the differences in responses of SDOF

systems and comment on how peak responses are affected by damping ratio.

$5-$ Compute pseudo acceleration response spectrum and displacement response spectrum for $1940El$ Centro

$($N$-$S$)$ earthquake ground motion record with damping ratios of ${}_1,{}_2$ and ${}_3.$ There will be two graphs;

each of them shall include response spectrum values for three damping ratios. Compare your results and

comment on response spectrum characteristics.