Problem: A proposal is made for a braced rectangular reinforced concrete $(RC)$ column, as

depicted in the sketch below, along with its cross$-$section and reinforcement details. The

concrete's characteristic strength is specified as $f_c=32$MPa. The column is considered braced

with an unsupported length of $L_u=8\mathrm{.}0m.$ The idealized end restraint conditions are shown in

the figure. The nominal axial compression loads, including self$-$weight, that the column is

expected to carry are as follows: Dead load $($G$),N_G=2000kN$ and Live load $($Q$),N_Q=1000$

$kN.$ The line of action of the applied axial loads is at an eccentricity of $e=100mm,$ oriented

such that the induced moment causes tension at the face with $4N32$ reinforcement. The

eccentricity for the column is also illustrated $($representing a single curvature along the

column's length$).$

a$)$ Calculate the depth to the plastic centroid from the compression face, $d_{pc},$ and the design

capacity in pure compression, $N_{uo}.$

b$)$ Compute the design capacities at balanced failure, $N_{ub}$ and $M_{ub}.$

c$)$ Determine whether this column is classified as short or slender.

FULL WORKING OUT FOR ALL WITH SOLUTIONS