Safe load on a brick masonry column

Slenderness (column)

Slenderness is based on the least lateral dimension:

$$H_{eff} = 3500\ \text{mm}, \qquad SR = \frac{3500}{340} = 10.29$$ $$k_s = 0.89 - \frac{0.29}{2}\times 0.05 = 0.883$$

Area factor

$A = 0.34 \times 0.46 = 0.1564$ m² $< 0.2$ m²

$$k_a = 0.7 + 1.5\times0.1564 = 0.935$$

$k_p = 1.0$ for brick.

Permissible stress and safe load

$$\begin{aligned} f_c &= f_b\,k_s\,k_a\,k_p = 1.1 \times 0.883 \times 0.935 \times 1.0 = 0.907\ \text{N/mm}^2 \\ P &= f_c A = 0.907 \times 340 \times 460 = 141\,900\ \text{N} \approx 142\ \text{kN} \end{aligned}$$

Comparison with 460 × 460 mm column

For $SR < 10$ the full IS 1905 table is needed (SR 6 → 1.00, SR 8 → 0.95). $SR = 3500/460 = 7.61$, so $k_s = 0.95 + (8 - 7.61)/2 \times 0.05 = 0.96$; $A = 0.2116$ m² $> 0.2$, so $k_a = 1.0$.

$$f_c = 1.1 \times 0.96 \times 1.0 = 1.056\ \text{N/mm}^2, \qquad P = 1.056 \times 460 \times 460 = 223\,400\ \text{N} = 223\ \text{kN}$$

The larger column carries 57 percent more load because of its larger area and lower slenderness. The self-weight of the column ($19 \times 0.1564 \times 3.5 = 10.4$ kN) should be deducted from the safe load to get the superimposed load, about 131 kN for the 340 × 460 column.

Answer: Safe axial load ≈ 142 kN for 340 × 460 mm (about 131 kN superimposed after self-weight) and ≈ 223 kN for 460 × 460 mm.