Check 25 cm x 25 cm Sal column, 200 kN + 20 kNm

Approach. Combined axial compression and bending, IS 883:1994 cl. 7.7.1: safe if $\dfrac{f_{ac}}{f_c} + \dfrac{f_{ab}}{f_b} \le 1$.

Data and permissible stresses

Section 250 × 250 mm, $S = 4000$ mm (pin ends), $N = 200$ kN, $M = 20$ kN·m.

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

Permissible axial stress

$$\begin{aligned} S/d &= 4000/250 = 16.0 \\ K_8 &= 0.584\sqrt{12670/10.6} = 20.19 \end{aligned}$$

$11 < S/d < K_8$: intermediate column.

$$f_c = 10.6\left[1 - \frac{1}{3}\left(\frac{16.0}{20.19}\right)^4\right] = 9.207\ \text{N/mm}^2$$

Actual stresses

$$\begin{aligned} f_{ac} &= \frac{200\times10^3}{250\times250} = 3.200\ \text{N/mm}^2 \\ f_{ab} &= \frac{6M}{bd^2} = \frac{6\times20\times10^6}{250^3} = 7.680\ \text{N/mm}^2 \end{aligned}$$

(The depth is 250 mm, which is less than 300 mm, so no form factor: $f_b = 16.9$ N/mm².)

Check

$$\frac{3.200}{9.207} + \frac{7.680}{16.9} = 0.348 + 0.454 = 0.802$$

Answer: the value is 0.80, which is less than 1: the column can carry the 200 kN load and 20 kN·m moment safely.