Box column of teak planks, 400 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; 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 $S = 4.50$ m, axial load $N = 400$ kN, plank thickness $t = 50$ mm. Pin ends, effective length $= S$.

Species: Teak (Tectona grandis), Group B. Location: inside. Grade: Grade I (standard) (Table 1 values are for Grade I).

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

Location is not stated, so inside and Grade I are assumed.

For plank thickness 50 mm (cl. 7.6.2.5): $U = 0.6$, $q = 1.0$ (values given for 25 mm and 50 mm planks).

Trial section

Square box, overall side $d_1 = 300$ mm, inside side $d_2 = 300 - 2\times50 = 200$ mm.

$$A = d_1^2 - d_2^2 = 300^2 - 200^2 = 50,000\ \text{mm}^2$$ $$\begin{aligned} \frac{S}{\sqrt{d_1^2 + d_2^2}} &= \frac{4500}{\sqrt{300^2 + 200^2}} = \frac{4500}{360.6} = 12.48 \\ K_9 &= \frac{\pi}{2}\sqrt{\frac{UE}{5qf_{cp}}} = \frac{\pi}{2}\sqrt{\frac{0.6\times9970}{5\times1.0\times9.40}} = 17.72 \end{aligned}$$

$8 < 12.48 < K_9 = 17.72$, so it is an intermediate column:

$$f_c = q f_{cp}\left[1 - \frac{1}{3}\left(\frac{S}{K_9\sqrt{d_1^2 + d_2^2}}\right)^4\right] = 1.0\times9.40\left[1 - \frac{1}{3}\left(\frac{12.48}{17.72}\right)^4\right] = 8.63\ \text{N/mm}^2$$

Check

$$P = f_cA = 8.63\times50,000/10^3 = 431\ \text{kN} > N = 400\ \text{kN}$$

Safe.

Arrangement

   +------------------------------+
   |  plank 50 mm thick           |
   |   +----------------------+   |
   |   |        hollow        |   |   outside 300 x 300 mm
   |   |      200 x 200       |   |
   |   +----------------------+   |
   +------------------------------+

The 50 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 50 mm thick Teak planks (inside 200 mm). Capacity 431 kN $>$ 400 kN.