The permanent action $($G$)($including self$-$weight$)$ applied to a beam is $15$kN$/$m and the imposed load $($Q$)$ is $12$kN$/$m$.$ The loads to use for a strength limit state analysis, and to calculate the short term deflection of a beam in an office respectively are: $($a$)$ None of the other answers is correct$\{$b$)$ w$*=36\mathrm{.}9$ kN$/$m; Ws $=23\mathrm{.}4$ kN$/$m $($c$)$ w$*=36$ kN$/$m; Ws $=19\mathrm{.}8$ kN$/$m$($d$)$ w$*=36$ kN$/$m; Ws $=19\mathrm{.}8$ kN$/$m$($e$)$ w$*=36$ kN$/$m; Ws $=23.\mathrm{.}4$ kN$/$m

a$)$ Calculate from first principles $($ERSB$)$ the value of the design pure axial compression

capacity $o($in kN $).$

b$)$ Calculate the depth of the plastic centroid, dpc $,$ from the indicated compression face and

explain the significance of this point in terms of the behaviour of the column $($ie if a load is

applied at this point, what is the effect on the column$).$

c$)$ Show that the design bending capacity under pure moment, $$ Muo, is $1345$ kNm using

the ERSB. To do this you will need to calculate the effective depth, d $,$ and the neutral axis

depth parameter, ku $,$ to check ductility. Hint: assume that $A{s}_1$ is in compression and $A{s}_2$

and $A{s}_3$ are in tension.

d$)$ Calculate from first principles $($ERSB$)$ the design capacities at the 'balanced' condition, $$ Mub

and $$ Nub.

e$)$ Approximating this column's design interaction diagram as a straight line between pure

compression $$ Nuo and the 'balanced' condition $b$ and $b,$ and another straight line

between pure moment $$ Muo and the 'balanced' condition, is this proposed column cross$-$

section adequate to carry the design actions $N^{**}$ and $M^{**}?$ Verify this by plotting these

various values on the following page.