Box deodar column, 60 mm planks, 350 kN

Approach. Box (built-up) column designed to IS 883:1994 cl. 7.6.2: the planks are nailed or bolted to form a hollow square section (a square is a special case of the rectangular box); the strength depends on $S/\sqrt{d_1^2 + d_2^2}$, where $d_1$ is the overall side and $d_2$ the inside side of the box.

Data and permissible stresses

Length $S = 5.00$ m, axial load $N = 350$ kN, plank thickness $t = 60$ mm. Pin ends, effective length $= S$.

Species: Deodar (Cedrus deodara), Group C. Location: inside. Grade: Grade I (standard) (Table 1 values are for Grade I).

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

Location and grade are not stated, so inside and Grade I (standard) are assumed.

For plank thickness 60 mm (cl. 7.6.2.5): $U = 0.6$, $q = 1.0$ (the code gives values for 25 mm and 50 mm planks; the 50 mm values are used).

Trial section

Square box, overall side $d_1 = 300$ mm, inside side $d_2 = 300 - 2\times60 = 180$ mm.

$$A = d_1^2 - d_2^2 = 300^2 - 180^2 = 57,600\ \text{mm}^2$$ $$\begin{aligned} \frac{S}{\sqrt{d_1^2 + d_2^2}} &= \frac{5000}{\sqrt{300^2 + 180^2}} = \frac{5000}{349.9} = 14.29 \\ K_9 &= \frac{\pi}{2}\sqrt{\frac{UE}{5qf_{cp}}} = \frac{\pi}{2}\sqrt{\frac{0.6\times9480}{5\times1.0\times7.80}} = 18.97 \end{aligned}$$

$8 < 14.29 < K_9 = 18.97$, so it is an intermediate column:

$$f_c = q f_{cp}\left[1 - \frac{1}{3}\left(\frac{S}{K_9\sqrt{d_1^2 + d_2^2}}\right)^4\right] = 1.0\times7.80\left[1 - \frac{1}{3}\left(\frac{14.29}{18.97}\right)^4\right] = 6.96\ \text{N/mm}^2$$

Check

$$P = f_cA = 6.96\times57,600/10^3 = 401\ \text{kN} > N = 350\ \text{kN}$$

Safe.

Arrangement

   +------------------------------+
   |  plank 60 mm thick           |
   |   +----------------------+   |
   |   |        hollow        |   |   outside 300 x 300 mm
   |   |      180 x 180       |   |
   |   +----------------------+   |
   +------------------------------+

The 60 mm thick planks are fixed with staggered nails or bolts at a pitch not exceeding about 150 mm to 200 mm so that they act as one unit; the ends are fitted with solid end blocks.

Answer

Provide a box column of overall size 300 mm × 300 mm formed with 60 mm thick Deodar planks (inside 180 mm). Capacity 401 kN $>$ 350 kN.