(Solved): A pin-jointed frame \( A B C D \), made of steel tube with outer diameter of \( 50 \mathrm{~mm} \) ...

A pin-jointed frame \( A B C D \), made of steel tube with outer diameter of \( 50 \mathrm{~mm} \) and a wall thickness of \( 5 \mathrm{~mm} \), is subjected to a uniformly distributed load of \( w \mathrm{~N} / \mathrm{m} \) acting on CD as shown in Figure 2. Its tensile yield strength is \( 520 \mathrm{MPa} \) and modulus of elasticity is 220 GPa. Assuming that buckling occurs only in the plane of the structure, determine the: (a) formula which is applicable in determine the critical load of AC, (5 marks) (b) allowable load of \( \mathrm{AC} \) with safety factor of \( 1.8 \), and (2 marks) [48.56 kN] (c) the allowable uniformly distributed load, \( w \) in unit \( \mathrm{N} / \mathrm{m} \), which the frame can carry without exceeding the allowable load in AC. \( [25.75 \mathrm{kN} / \mathrm{m}] \) (3 marks)