SYSTEM $1$:

The plan and the side$-$views of a two$-$story building are as given Figures a and $b.$

A side beam system $(ABC)$ of this building will be designed.

The loadings transmitted from the slabs of the building to the beam system ABC are calculated as seen in Figure c$.$

STEP $1$:

Select the proper system for the design of the beam system ABC. The alternatives for this system are as given in Figure d$.$ Explain the reason for your selection.

$($HINT FOR STEP$1$: Calculate the degree of indeterminacy for each system.

State whether the systems are stable or unstable.

Then, explain the reason for the selection that you made in STEP$1).$

STEP$2$:

Apply all loadings given in Figure $c$ on the proper beam system that you selected in STEP$1.$ Then,

a$)$ Calculate the support reactions

b$)$ Calculate the shear force $($V$)$ and the bending $($M$)$ moment functions for each loading regions.

c$)$ Draw the shear force $($V$)$ and the bending $($M$)$ moment diagrams for each loading regions.

IMPORTANT NOTE:

DRAW ALL FREE BODY DIAGRAMS and SHOW ALL THE EQULIBRIUM EQUATIONS, which are NECESSARY FOR YOUR CALCULATIONS.

a $)$ The plan$-$view of the bul$$ding

b$)$ The side$-$view of the building

d$)$ Alternative beam systems for the design of the beam ABC