A $2-$story structure, which has $12mx8m$ dimensions in plan, will be constructed.

The typical plan view and the front view of this building is as given in Figures a and $b,$ respectively.

The building consists of frames and slabs as given in the same figures.

The lengths of each frame member and the dimensions of each slab is as given in the figures below.

As seen in Fig a$,$ each of the two floors has $7$ slabs and $1$ slab opening $($discontinuity in slab between the

points B$,$ C$,$ H$,$ and I$).$

All frame systems in the building consist of reinforced concrete beams and columns. The concrete class is

C$30.$

The dimensions of all columns are $50cm50cm$ while the dimensions of all beams are $30cm50cm.$

The magnitude of the loads on the slabs is calculated as $q=4k\frac{N}{m^2}.$

These loads on the slabs are transmitted to the floor beams on each sides of the slabs $($such as the

continuous beam ABCD in Fig b$.)$

STEP$-1$: Calculate the degree of static indeterminacy of the continuous beam system ABCD.

which is the side beam system in the second floor $($Fig b$).$

Calculate the degree of kinematic indeterminacy of the same continuous beam system

ABCD.

STEP$-2$: Calculate the loads transmitted from the related slabs to the continuous beam system

ABCD

NOTE: In addition to the slab loads. there is also a box with a weight of $W.$ which is

hanging on the span $BC$ of the beam system ABCD.

The weight of this box is equal to $10kN,$ and the location of this box is as given in Fig $b.$

STEP$-3$: Calculate the unknown displacements and the support reactions of the continuous

beam system ABCD USING THE STIFFNESS METHOD.

NOTE: Obtain and display all member stiffness matrices $(k).$ the structure stiffness matrix

$(K),$ as well as the structure matrix equation$).$

Assume that the beam and the column connection at point $A$ is designed as a fixed support

while the connections at points $B,C,$ and $D$ are designed as pin supports.

STEP$-4$: Calculate all member forces in the continuous beam system ABCD USING THE

STIFFNESS MIETHOD.

$($NOTE: Display all necessary sub$-$steps for the calculation of member forces.$)$

a$)$ Typical plan view of the building