Summary of the data:

P = 170 kN
E = 200 GPa
The column is free at one end and fixed at the other; L_e = 2L = 2(0.55) = 1.10 m
Use the allowable-stress method
Determine the largest allowable e_x , given that e_y is a) zero b) 8 mm

A = (50 mm)(75 mm) = 3750 mm²

The slenderness ratio is L_e/r_min = (1.10 m)/(14.43 x 10^-3 m) = 76.2. This is less than C_C, so I use equations 10.44 and 10.45 on page 639:

Next, I compute the allowable stress:

Finally, I use the allowable-stress criterion:

a) Substituting e_y = 0 into the above equation, I get e_x = 11.76 mm.

b) Repeating this for e_y = 8 mm, I get e_x = 6.43 mm.