Explanation: The design compressive strength of member is given by Pd = Aefcd, where Ae is effective sectional area, fcd is design compressive stress.

Explanation: The design compressive stress, fcd of column is given by fcd = [fy / γm0] / [φ + (φ2-λ2)0.5], where fy is yield stress of material, φ is dependent on imperfection factor, λ is non dimensional effective slenderness ratio.

Explanation: The value of imperfection factor, α for buckling class a is 0.21. The imperfection factor considers all the relevant defects in real structure when considering buckling, geometric imperfections, eccentricity of applied loads and residual stresses.

Explanation: For buckling class c, the value of imperfection factor is 0.49. The imperfection factor takes into account all the relevant defects in real structure when considering buckling, geometric imperfections, eccentricity of applied loads and residual stresses.

Explanation: The value of φ in the equation of design compressive strength is given by φ = 0.5[1+α(λ-0.2)+λ2], where α is imperfection factor(depends on buckling class) and λ is non-dimensional effective slenderness ratio.

Explanation: Euler buckling stress fcc is given by fcc = (π2E)/(KL/r)2, where E is modulus of elasticity of material and KL/r is effective slenderness ratio i.e. ratio of effective length, KL to appropriate radius of gyration, r.

Explanation: The value of non dimensional slenderness ratio λ in the equation of design compressive strength is given by λ = √(fy /fcc) , where fy is yield stress of material and fcc = (π2E)/(KL/r)2, where E is modulus of elasticity of material and KL/r is effective slenderness ratio i.e. ratio of effective length.

Explanation: The design compressive strength in terms of stress reduction factor is given by fcd = Xfy / γm0 , where X = stress reduction factor for different buckling class, slenderness ratio and yield stress = 1/ [φ + (φ2-λ2)0.5], fy is yield stress of material and γm0 is partial safety factor for material strength.

Explanation: The value of design compressive strength is given by fcd = [fy / γm0] / [φ + (φ2-λ2)0.5] ≤ fy / γm0 i.e. fcd should be less than or equal to fy / γm0.

Pd = Ae fcd = 7846 x 47.85 = 375.43 kN.