Two architecturally identical looking building frames are being designed. All columns are made out of concrete. Columns have identical cross$-$sectional dimensions and height. The columns can be assumed axially incompressible. The floor slabs are rigid. Floor weights are shown on the sketches below. The weights of the columns are negligible compared to floor weights. The only difference between the two frames is that in one frame the ground story columns are pinned to the foundation while in the other one the ground story columns are attached to the foundation with fixed connections.

a$)$ Find the approximate fundamental modeshape for each frame using the displacements caused by mass$-$proportional loading. No need to iterate to improve your approximation.

b$)$ If the lateral stiffness of each column with both ends fixed is $1000ki\frac{p}{f}t$ and the weight of a bay$-$wide floor slab is $20$ kip $($i$.$e$.,W=20$ kip$),$ using your answers from above $($part a$),$ estimate the fundamental period of each frame using Ravieigh's quotient method.

c$)$ Considering the design spectrum shown belr w$,$ for each frame find the design base shear force due to fundamental mode response.

$[$pinned at foundation level$]$

$[$fixed at foundation level$]$

$[$design acceleration spectrum$]$