A short column having the cross sectional properties shown in Figure $1$ is subjected to a mono$-$

tonically increasing axial load. Write a computer program that takes the material and geometric

properties of the column as input and produces the $N-M$ interaction diagram as output. The

following simple algorithm might be followed:

$($a$)$ Implement a routine that calculates the pure bending, axial tensile, axial compressive, and

balanced load capacities of the column and prints the output $(\{$:$M_o,N_t,N_o,N_b).$

$($b$)$ Implement a routine that computes a coordinate pair $(M,N)$ on the interaction diagram for

a given plastic neutral axis depth $c.$ Print the failure mode and the corresponding moment

and axial load capacities.

$($c$)$ For each plastic netural axis depth $c_i=c_{i-1}+c$ in the range cin$[0,)$ compute $(M_i,N_i)$

utilizing the routine developed in the previous step. You may take the maximum increment

as $c=0\mathrm{.}05h.$

$($d$)$ Plot the interaction diagram for these $N-M.$

Material grades are given as C$25$ and S$420.$ Use material factors $($i$.$e$.{}_{mc}=1\mathrm{.}5,{}_{ms}=1\mathrm{.}15).$

Note: Write the object and scope of the program. Clearly state the assumptions you make

on the constitutive modelling of the concrete and steel. Discuss briefly the limitations of the

program.

Figure $1$: Uross$-$section of the column. All dimensions are given in mm$.$