Allowable load on 30 x 60 cm column

Data and assumptions

• Column 300 mm $\times$ 600 mm, height 3.2 m, supporting an RCC beam and slab roof, so it is laterally supported in both directions and $h_{ef}=H=3.2$ m (IS 1905 cl. 4.3.2, Note 2).
• Brick $200\times100\times100$ mm, so height/width $=1.0$ and $k_p$ comes from Table 10. The brick strength and mortar are not given, so 7.5 N/mm$^2$ brick with cement mortar 1:5 (M1) is assumed as the basic case; other grades are tabulated below.

Step 1: Factors

$$\begin{aligned} SR &= \frac{h_{ef}}{t} = \frac{3.2}{0.30} = 10.67\ (<12)\\ A &= 0.30\times0.60 = 0.18\ \text{m}^2\ (<0.2)\ \Rightarrow\ k_a=0.7+1.5\times0.18 = 0.970\\ k_s &= 0.873\ \text{(Table 9, } e=0)\\ k_p &= 1.10\ \text{(7.5 N/mm}^2\text{, } h/w=1.0) \end{aligned}$$

Step 2: Allowable load

$$\begin{aligned} f_c &= f_b k_s k_a k_p = 0.74\times0.873\times0.970\times1.10 = 0.690\ \text{N/mm}^2\\ P &= f_c A = 0.690\times0.18\times10^3 = 124.1\ \text{kN} \end{aligned}$$

Self weight $=0.18\times3.2\times19 = 10.9$ kN, so the load that can be applied from the roof is $124.1 - 10.9 = 113.2$ kN.

Step 3: Allowable total load for other grades (kN)

Answer: allowable axial load = 124.1 kN at the base (about 113.2 kN of roof load after deducting self weight), for 7.5 N/mm$^2$ brick in 1:5 cement mortar. With 5 N/mm$^2$ brick and 1:6 mortar the capacity is only 80.5 kN.