Built-up Sal column, 50x250 planks, 925 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 $S = 3.50$ m, axial load $N = 925$ 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):

The question gives $E = 12700$ N/mm², $f_{cp} = 10.6$ N/mm² (the Table 1 value for Sal, Grade I, inside), $U = 0.6$ and $q = 1$; these are used.

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 $d_1 = 500$ mm, inside side $d_2 = 500 - 2\times50 = 400$ mm.

$$A = d_1^2 - d_2^2 = 500^2 - 400^2 = 90,000\ \text{mm}^2$$ $$\begin{aligned} \frac{S}{\sqrt{d_1^2 + d_2^2}} &= \frac{3500}{\sqrt{500^2 + 400^2}} = \frac{3500}{640.3} = 5.47 \\ K_9 &= \frac{\pi}{2}\sqrt{\frac{UE}{5qf_{cp}}} = \frac{\pi}{2}\sqrt{\frac{0.6\times12700}{5\times1.0\times10.60}} = 18.83 \end{aligned}$$

The ratio 5.47 is less than 8, so it is a short column (cl. 7.6.2.1): $f_c = q f_{cp} = 1.0\times10.60 = 10.60$ N/mm².

Check

$$P = f_cA = 10.60\times90,000/10^3 = 954\ \text{kN} > N = 925\ \text{kN}$$

Safe.

Arrangement of planks (250 mm × 50 mm planks)

   +------------------------------+
   |  plank 50 mm thick           |
   |   +----------------------+   |
   |   |        hollow        |   |   outside 500 x 500 mm
   |   |      400 x 400       |   |
   |   +----------------------+   |
   +------------------------------+

Each 500 mm face is made of two 250 mm planks placed side by side; each 400 mm face is made of one 250 mm and one 150 mm plank (a plank ripped to width), so all planks are 50 mm thick. They 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 500 mm × 500 mm formed with 50 mm thick Sal planks (inside 400 mm). Capacity 954 kN $>$ 925 kN.