$4.$ Exercise on Limit State Design $-$ Serviceability Limit State

A reinforced concrete beam forms part of a building used as an office area. The beam is designed to carry $2($two$)$ permanent loads equal to $\backslash (5\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )$ and $\backslash (10\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ),$ a leading variable load equal to $\backslash (5\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )$ and $2($two$)$ accompanying variable loads equal to $\backslash (14\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )$ and $\backslash (18\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ).$

Calculate the serviceability limit sate design values, namely:

a$)$ Combination design value.

b$)$ Frequent design value.

c$)$ Quasi$-$permanent design value.