Square deodar column 4 m, 350 kN, outside

Approach. Working stress design to IS 883:1994 (cl. 7.6 for columns, cl. 7.7 for combined axial compression and bending). Ends are taken as pin-ended, so the effective length equals the unsupported length $S$ (cl. 7.6.1.5).

Data and permissible stresses

Length $S = 4.00$ m = 4000 mm. Axial load $N = 350$ kN.

Species: Deodar (Cedrus deodara), Group C. Location: outside. Grade: Select grade (Grade I values multiplied by 1.16, IS 883:1994 cl. 6.3).

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

The question states outside location and Select grade.

Trial section

Try 250 mm × 250 mm (square). Area $A = 62,500$ mm²; least dimension $d = 250$ mm.

Slenderness and permissible axial stress (cl. 7.6.1)

$$\begin{aligned} S/d &= \frac{4000}{250} = 16.0 \\ K_8 &= 0.584\sqrt{\frac{E}{f_{cp}}} = 0.584\sqrt{\frac{9480}{8.00}} = 20.10 \end{aligned}$$

$11 < S/d = 16.0 < K_8 = 20.1$, so it is an intermediate column:

$$f_c = f_{cp}\left[1 - \frac{1}{3}\left(\frac{S/d}{K_8}\right)^4\right] = 8.00\left[1 - \frac{1}{3}\left(\frac{16.0}{20.1}\right)^4\right] = 6.93\ \text{N/mm}^2$$

$S/d = 16.0 < 50$ (cl. 7.6.1.4). OK.

Check

$$P = f_cA = 6.93\times62,500/10^3 = 433.3\ \text{kN} \ge N = 350\ \text{kN}$$

Safe.

Answer

Provide a solid Deodar column of 250 mm × 250 mm cross-section (Select grade, outside location). Capacity $433$ kN $> 350$ kN.