$(30$ p$.)$ The $2-$story shear frame given in the figure has the following properties: $h=4m,m=45,000kg,I=30,000c{m}^4,E=200,000$MPa, and ${}_n=5\%.$ The first two natural frequencies and mode shapes are also given below.

a$)$ Determine the peak response values of displacement $D_n(t),$ and peak response values of spectral accelerations $A_n(t)$ from the design spectrum given for the first two modes of the structure,

b$)$ For each mode calculate the peak values of the following response quantities: $(1)$ the floor displacements $u,(2)$ the story shears $V,$ and $(3)$ the floor and base overturning moments $M.$

c$)$ Combine the peak modal responses using SRSS modal combination rule to obtain the peak value of the total response for each response quantity in part $($b$).$

beams

Natural frequencies

and modes:

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$([0\mathrm{.}1491])$

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