Safe load, 225x225 select Sal column, 3 m

Approach. Safe axial load of a solid column, IS 883:1994 cl. 7.6.1: $P = f_c\times A$, where $f_c$ depends on the slenderness $S/d$.

Data and permissible stresses

Section 225 × 225 mm, unsupported length $S = 3000$ mm (pin ends), Select grade Sal.

Species: Sal (Shorea robusta), Group A. Location: inside. Grade: Select grade (Grade I values multiplied by 1.16, IS 883:1994 cl. 6.3).

Permissible stresses (IS 883:1994 Table 1, inside location):

Location not stated: inside.

Slenderness

$$\begin{aligned} S/d &= \frac{3000}{225} = 13.33 \\ K_8 &= 0.584\sqrt{\frac{E}{f_{cp}}} = 0.584\sqrt{\frac{12670}{12.30}} = 18.75 \end{aligned}$$

$11 < S/d = 13.33 < K_8 = 18.75$, so it is an intermediate column.

$$f_c = f_{cp}\left[1 - \frac{1}{3}\left(\frac{S/d}{K_8}\right)^4\right] = 12.30\left[1 - \frac{1}{3}\left(\frac{13.33}{18.75}\right)^4\right] = 11.25\ \text{N/mm}^2$$

Safe load

$$P = f_cA = 11.25\times50,625/10^3 = 569\ \text{kN}$$

Answer: the safe axial load is about 569 kN (permissible stress $f_c = 11.25$ N/mm²; $S/d = 13.3 < 50$).