Single-storey external wall: stress, brick, mortar

Data and assumptions

• Wall 230 mm thick, modular bricks ($k_p=1$); load at top 100 kN/m with eccentricity 12 mm, so $e/t=12/230=0.0522$ ($>1/24$).
• Plinth 1.5 m above top of footing, ceiling height 3.0 m, 12 cm RCC slab bearing on the wall. Walls longer than $h_{ef}$ (no cross walls given), so height governs.
• Brick masonry 19 kN/m$^3$. Design by IS 1905:1987; NBC 109 follows the same method. Critical section: base of wall at the top of the footing.

Step 1: Effective height and slenderness ratio

Height from top of footing to the centre of slab $H = 1.5+3.0+0.12/2 = 4.56$ m (IS 1905 Table 4 Note 1). The footing and the RCC slab give full restraint, so $h_{ef}=0.75H$:

$$\begin{aligned} h_{ef} &= 0.75\times4.56 = 3.420\ \text{m}\\ SR &= \frac{3.420}{0.23} = 14.87\ (<27) \end{aligned}$$

Step 2: Load and maximum stress at the base

$$\begin{aligned} \text{Self weight} &= 0.23\times4.5\times19 = 19.67\ \text{kN/m}\\ P &= 100+19.67 = 119.67\ \text{kN/m}\\ M &= 100\times0.012 = 1.20\ \text{kNm/m}\\ \sigma_{max} &= \frac{P}{A}+\frac{6M}{t^2} = \frac{119.67\times10^3}{230\times10^3}+\frac{6\times1.20\times10^6}{1000\times230^2} = 0.520+0.136 = 0.656\ \text{N/mm}^2 \end{aligned}$$

(At the top of the wall, under the load alone, $\sigma_{max}=\frac{100\times10^3}{230\times10^3}(1+\frac{6\times12}{230}) = 0.571$ N/mm$^2$.) The maximum stress in the wall is 0.656 N/mm$^2$ at the base (compression; no tension since $e<t/6$).

Step 3: Factors and required basic stress

• $k_s$ (Table 9, $SR=14.87$, $e/t=0.052$, interpolated) $= 0.732$
• $k_a=1.0$ (area 0.23 m$^2$/m), $k_p=1.0$
• $e/t>1/24$: 25 percent increase allowed (cl. 5.4.1.4 a)

$$f_b \ge \frac{\sigma}{k_sk_ak_p\times1.25} = \frac{0.520}{0.732\times1.25} = 0.569\ \text{N/mm}^2$$

Step 4: Brick and mortar (IS 1905 Table 8)

Answer: maximum stress = 0.656 N/mm$^2$. Required $f_b = 0.569$ N/mm$^2$, so use bricks of crushing strength not less than 7.5 N/mm$^2$ with M2 mortar (1:6, $f_b=0.59$ N/mm$^2$). A richer mortar (M1, H2, H1) also needs 7.5 N/mm$^2$ units, so there is no gain from a stronger mortar here.