Brick and mortar for wall with timber flooring

Data and assumptions

• Wall 230 mm thick, local bricks (assumed $230\times110\times55$ mm, $k_p=1$), $e/t=1/12$, load 135 kN/m at the top. Wall 4 m long, clear height 3 m.
• The RCC slab at the bottom gives lateral and rotational restraint; the timber floor at the top is assumed to be adequately anchored but not spanning onto the wall (lateral restraint only). Hence Table 4 Sl. 2 applies: $h_{ef}=0.85H$.
• Design code: IS 1905:1987; NBC 109 follows the same method.
• Brick masonry 19 kN/m$^3$ (IS 875 Part 1).

Step 1: Effective height, length and slenderness ratio (IS 1905 cl. 4.3, 4.4, 4.6)

Height of the wall $H = 3.00$ m (clear height, as no slab thickness is given). Effective height $h_{ef} = 0.85 H = 0.85\times3.00 = 2.550$ m. Effective length (wall supported by a cross wall at each end, Table 5 Sl. 3) $L_{ef} = 1.0L = 4.00$ m. The lesser value governs:

$$SR = \frac{h_{ef}}{t} = \frac{2.550}{0.230} = 11.09\ (<27,\ \text{Table 7, cement mortar})$$

Step 2: Design load per metre run at the base

$$\begin{aligned} \text{Self weight} &= t\,H_c\,\gamma = 0.230\times3.00\times19 = 13.11\ \text{kN/m}\\ P &= 135.00 + 13.11 = 148.11\ \text{kN/m} \end{aligned}$$

Stress on the wall:

$$\sigma = \frac{P}{A} = \frac{148.11\times10^3}{230\times10^3\ \text{mm}^2/\text{m}} = 0.644\ \text{N/mm}^2$$

Step 3: Reduction factors

• Stress reduction factor $k_s$ (Table 9, $SR=11.09$, $e/t=0.083$, by linear interpolation) $= 0.837$
• Area reduction factor $k_a$ (cl. 5.4.1.2): the area per metre, 0.23 m$^2$, is not less than 0.2 m$^2$, so $k_a = 1.0$
• Shape factor $k_p = 1.0$ (brick height/width $\le 0.75$, Table 10)
• Since $e/t > 1/24$, a 25 percent increase in permissible stress is allowed (cl. 5.4.1.4 a), factor 1.25

Step 4: Required basic compressive stress

$$\sigma \le f_b\,k_s\,k_a\,k_p\times1.25 \Rightarrow f_b \ge \frac{0.644}{0.837\times1.0\times1.0\times1.25} = 0.615\ \text{N/mm}^2$$

(Without the 25 percent increase the requirement would be $f_b \ge 0.769$ N/mm$^2$.)

Step 5: Strength of brick and grade of mortar (IS 1905 Table 8)

Smallest standard unit strength giving $f_b \ge 0.615$ N/mm$^2$:

Answer: use bricks of crushing strength not less than 10 N/mm$^2$ with mortar M2 (cement:sand 1:6) ($f_b = 0.81$ N/mm$^2$ $\ge$ 0.615). The other combinations in the table are also acceptable; a stronger mortar allows a weaker brick (e.g. 7.5 N/mm$^2$ bricks with M1 mortar).