4b) Calculate the compression resistance of a 254 x 254 UC 89 steel stanchion for thefollowing effective lengths:(i) 12 m, both ends fully restrained

To calculate the compression resistance of a 254 x 254 UC 89 steel stanchion, you need to follow these steps:

1. Determine the properties of the steel section: For a 254 x 254 UC 89, the properties are as follows: Area (A) = 11300 mm², Radius of gyration (r) = 132.6 mm, and Yield strength (Fy) = 275 N/mm².

2. Calculate the slenderness ratio (λ): The slenderness ratio is the effective length (Le) divided by the radius of gyration (r). For an effective length of 12 m (or 12000 mm), the slenderness ratio is 12000/132.6 = 90.5.

3. Determine the limiting slenderness (λp) for the steel section: For hot-rolled steel sections, the limiting slenderness is 76√(Fy/275). For Fy = 275 N/mm², λp = 76.

4. Check if the slenderness ratio is less than the limiting slenderness: If λ < λp, the section is short and the compression resistance (Pc) is given by Pc = A*Fy. If λ > λp, the section is slender and the compression resistance is reduced by the slenderness.

5. In this case, λ > λp, so the section is slender. The reduction factor (ψ) is given by ψ = 0.5[1 + α(λ/λp - 1) + (λ/λp)²], where α = 0.49. Substituting the values, ψ = 0.5[1 + 0.49(90.5/76 - 1) + (90.5/76)²] = 0.76.

6. The compression resistance is then given by Pc = ψAFy = 0.7611300275 = 2381700 N or 2381.7 kN.

So, the compression resistance of the 254 x 254 UC 89 steel stanchion for an effective length of 12 m, with both ends fully restrained, is 2381.7 kN.