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.

SYSTEM $2$:

Assume that the loadings and the support conditions for the same ABC beam system in the same frame system $($given in SYSTEM $1)$ are as given in Figure a and b$,$ below, STEP $1$:

Calculate the degree of indeterminacy of the system.

State whether the system stable or unstable. Explain the reason for your determination. STEP$2$:

Apply all loadings given in Figure a on the beam system given in Figure b$.$

Then,

d$)$ Calculate the support reactions

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

f$)$ Draw the shear force $($V$)$ and the bending $($M$)$ moment functions for each loading IMPORTANT NOTE:

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