For the $3-$storey building from $HW$#$3,$ and the $5\%$ damping displacement response spectrum from El

Centro, please answer the following questions:

If the natural periods and modes are as shown below, calculate:

a$)$ The maximum displacements

b$)$ Storey forces

c$)$ Base shear

d$)$ Overturning moments

Use Pseudo$-$Accelerations where appropriate

For the response spectrum with period spacing of $0\mathrm{.}1s,$ use linear interpolation to

determine spectral values

Use the SRSS method for modal combinations

If a modal test was performed and the natural periods of the building were found to be

$T_a=\left[\begin{array}{c}0\mathrm{.}315\\ 0\mathrm{.}198\\ 0\mathrm{.}135\end{array}\right]$

and assuming that the mode shapes are the same, how does that change the response

values computed in part $1)?$

If the building is damaged in an earthquake event, what do you expect to happen to the period

values? If the damage occurs early in a long duration event, what do you expect to happen to

the forces and overturning moments for the remainder of the shaking?

References:

Use El Centro RS$.$txt from FTP server. Spectral displacements $(cm)$ with period spacing $=0\mathrm{.}02s.$

For question #$1$ use:

$Tq1$ :$=([0\mathrm{.}395$

$0\mathrm{.}275$

$0\mathrm{.}116])$

$=([0\mathrm{.}329,-0\mathrm{.}736,-0\mathrm{.}588$

$0\mathrm{.}591,-0\mathrm{.}322,0\mathrm{.}737$

$0\mathrm{.}736,0\mathrm{.}595,-0\mathrm{.}334])$

Period $[$sec$]$ Damp.$=5\mathrm{.}0\%$

$0\mathrm{.}0000\mathrm{.}00000000$

$0\mathrm{.}0200\mathrm{.}00328385$

$0\mathrm{.}0400\mathrm{.}01896375$

$0\mathrm{.}0600\mathrm{.}06552011$

$0\mathrm{.}0800\mathrm{.}12373098$

$0\mathrm{.}1000\mathrm{.}20546455$

$0\mathrm{.}1200\mathrm{.}25342929$

$0\mathrm{.}1400\mathrm{.}39944061$

$0\mathrm{.}1600\mathrm{.}50597527$

$0\mathrm{.}1800\mathrm{.}58848107$

$0\mathrm{.}2000\mathrm{.}74214547$

$0\mathrm{.}2200\mathrm{.}96912832$

$0\mathrm{.}2401\mathrm{.}28037157$

$0\mathrm{.}2601\mathrm{.}55148098$

$0\mathrm{.}2801\mathrm{.}62276117$

$0\mathrm{.}3001\mathrm{.}68407418$

$0\mathrm{.}3201\mathrm{.}69585120$

$0\mathrm{.}3401\mathrm{.}63646389$

$0\mathrm{.}3601\mathrm{.}56778234$

$0\mathrm{.}3801\mathrm{.}57034924$

$0\mathrm{.}4002\mathrm{.}00318124$

$0\mathrm{.}4202\mathrm{.}55217304$

$0\mathrm{.}4402\mathrm{.}77768836$

$0\mathrm{.}4602\mathrm{.}66736611$

$0\mathrm{.}4802\mathrm{.}89784111$

$0\mathrm{.}5002\mathrm{.}88481229$

$0\mathrm{.}5202\mathrm{.}68185932$

$0\mathrm{.}5402\mathrm{.}53591565$

$0\mathrm{.}5602\mathrm{.}31549282$

$0\mathrm{.}5802\mathrm{.}23621864$

$0\mathrm{.}6002\mathrm{.}33241542$

$0\mathrm{.}6202\mathrm{.}38029186$

$0\mathrm{.}6402\mathrm{.}30366654$

$0\mathrm{.}6602\mathrm{.}20864495$

$0\mathrm{.}6802\mathrm{.}16900738$

$0\mathrm{.}7002\mathrm{.}23119428$

$0\mathrm{.}7202\mathrm{.}37854701$

$0\mathrm{.}7402\mathrm{.}56954067$

$0\mathrm{.}7602\mathrm{.}75069868$

$0\mathrm{.}7802\mathrm{.}88429378$

$0\mathrm{.}8002\mathrm{.}95553183$

$0\mathrm{.}8202\mathrm{.}96967652$

$0\mathrm{.}8402\mathrm{.}93598333$

$0\mathrm{.}8602\mathrm{.}88020253$

$0\mathrm{.}8802\mathrm{.}84554120$

$0\mathrm{.}9003\mathrm{.}14500657$

$0\mathrm{.}9203\mathrm{.}46256713$

$0\mathrm{.}9403\mathrm{.}65306167$

$0\mathrm{.}9603\mathrm{.}72624798$

$0\mathrm{.}9803\mathrm{.}68363790$

$1\mathrm{.}0003\mathrm{.}50526342$

$1\mathrm{.}0203\mathrm{.}71614317$

$1\mathrm{.}0404\mathrm{.}03908456$

$1\mathrm{.}0604\mathrm{.}37216511$

$1\mathrm{.}0804\mathrm{.}70401167$

$1\mathrm{.}1005\mathrm{.}01946095$

$1\mathrm{.}1205\mathrm{.}31833035$

$1\mathrm{.}1405\mathrm{.}59028486$

$1\mathrm{.}1605\mathrm{.}83444318$

$1\mathrm{.}1806\mathrm{.}05125057$

$1\mathrm{.}2006\mathrm{.}23341608$

$1\mathrm{.}2206\mathrm{.}37711068$

$1\mathrm{.}2406\mathrm{.}47869223$

$1\mathrm{.}2606\mathrm{.}70155755$

$1\mathrm{.}2806\mathrm{.}93613087$

$1\mathrm{.}3007\mathrm{.}13560530$

$1\mathrm{.}3207\mathrm{.}29660642$

$1\mathrm{.}3407\mathrm{.}41672605$

$1\mathrm{.}3607\mathrm{.}49494202$

$1\mathrm{.}3807\mathrm{.}53992066$

$1\mathrm{.}4007\mathrm{.}54661046$

$1\mathrm{.}4207\mathrm{.}51997224$

$1\mathrm{.}4407\mathrm{.}46696589$

$1\mathrm{.}4607\mathrm{.}39835401$

$1\mathrm{.}4807\mathrm{.}31202817$

$1\mathrm{.}5007\mathrm{.}20600048$

$1\mathrm{.}5207\mathrm{.}08307028$

$1\mathrm{.}5406\mathrm{.}94711176$

$1\mathrm{.}5606\mathrm{.}94535974$

$1\mathrm{.}5806\mathrm{.}96265754$

$1\mathrm{.}6006\mathrm{.}96917604$

$1\mathrm{.}6206\mathrm{.}96286433$

$1\mathrm{.}6406\mathrm{.}94036906$

$1\mathrm{.}6606\mathrm{.}91325201$

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