Box Sal column 5 m, 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 (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 $N = 400$ kN, plank thickness $t = 50$ mm. Pin ends, effective length $= S$.

Species: Sal (Shorea robusta), Group A. 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 $d_1 = 275$ mm, inside side $d_2 = 275 - 2\times50 = 175$ mm.

$$A = d_1^2 - d_2^2 = 275^2 - 175^2 = 45,000\ \text{mm}^2$$ $$\begin{aligned} \frac{S}{\sqrt{d_1^2 + d_2^2}} &= \frac{5000}{\sqrt{275^2 + 175^2}} = \frac{5000}{326.0} = 15.34 \\ K_9 &= \frac{\pi}{2}\sqrt{\frac{UE}{5qf_{cp}}} = \frac{\pi}{2}\sqrt{\frac{0.6\times12670}{5\times1.0\times10.60}} = 18.81 \end{aligned}$$

$8 < 15.34 < K_9 = 18.81$, so it is an intermediate column:

$$f_c = q f_{cp}\left[1 - \frac{1}{3}\left(\frac{S}{K_9\sqrt{d_1^2 + d_2^2}}\right)^4\right] = 1.0\times10.60\left[1 - \frac{1}{3}\left(\frac{15.34}{18.81}\right)^4\right] = 9.04\ \text{N/mm}^2$$

Check

$$P = f_cA = 9.04\times45,000/10^3 = 407\ \text{kN} > N = 400\ \text{kN}$$

Safe.

Arrangement

   +------------------------------+
   |  plank 50 mm thick           |
   |   +----------------------+   |
   |   |        hollow        |   |   outside 275 x 275 mm
   |   |      175 x 175       |   |
   |   +----------------------+   |
   +------------------------------+

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 275 mm × 275 mm formed with 50 mm thick Sal planks (inside 175 mm). Capacity 407 kN $>$ 400 kN.