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. Identify the properties of the steel: For a UC 89 steel, the yield strength (py) is typically 275 N/mm^2.

2. Calculate the cross-sectional area (A): For a 254 x 254 section, A = 254 x 254 = 64516 mm^2.

3. Calculate the slenderness ratio (λ): This is the effective length (Le) divided by the radius of gyration (r). For a 254 x 254 section, r is typically around 102.5 mm. So for an effective length of 12 m (or 12000 mm), λ = Le / r = 12000 / 102.5 = 117.07.

4. Determine the reduction factor (χ): This can be found using the formula χ = 1 / [0.5 + 0.5 * (λ / λp)^2], where λp is the limiting slenderness for the steel. For a UC 89 steel, λp is typically around 76. So χ = 1 / [0.5 + 0.5 * (117.07 / 76)^2] = 0.67.

5. Finally, calculate the compression resistance (Ncr): This is given by the formula Ncr = χ * A * py = 0.67 * 64516 * 275 = 11868035 N, or 11.87 MN.

Please note that these calculations are based on typical values for a UC 89 steel and a 254 x 254 section. The actual values may vary depending on the specific properties of the steel and the section.