3 m wall under wind: free top, fixed bottom

Data and assumptions

• Wall 3.0 m high, free at the top and fixed at the base: a cantilever (free-standing) wall. Uniform wind pressure taken as stated, 12 N/m$^2$ (0.012 kN/m$^2$) [reading: given value is very small, so stability is easily satisfied; if the wind pressure is larger, repeat with the same steps].
• Design by IS 1905:1987 cl. 5.5.2.1 and Table 11, Table 4 Sl. 4. Per metre run; masonry 19 kN/m$^3$; trial thickness 230 mm.

        ^ free top
        |<-- w = 12 N/m2
        |  wall H = 3.0 m
        |  M = wH^2/2 at base
  ======+======  fixed base

Step 1: Slenderness (cl. 4.3, Table 4 Sl. 4)

For a free top and a fixed base $h_{ef}=1.5H=4.5$ m, so $SR = 4.5/0.23 = 19.6<27$ (cement mortar), but the slenderness check alone would give $t\ge4.5/27=0.167$ m.

Step 2: Bending and stresses

$$\begin{aligned} M &= \frac{wH^2}{2} = \frac{0.012\times3^2}{2} = 0.054\ \text{kNm/m}\\ \text{Self weight} &= 0.23\times3\times19 = 13.11\ \text{kN/m}\\ \sigma_a &= \frac{13.11\times10^3}{230\times10^3} = 0.0570\ \text{N/mm}^2\\ \sigma_b &= \frac{6M}{t^2} = \frac{6\times0.054\times10^6}{1000\times230^2} = 0.0061\ \text{N/mm}^2\\ \sigma_{max} &= 0.0631,\ \ \sigma_{min} = 0.0509\ \text{N/mm}^2 \end{aligned}$$

No tension at the base ($\sigma_{min}>0$), and the compressive stress is far below the allowable value for the lowest brick grade.

Step 3: Stability (cl. 4.2.2.4 a)

Free-standing wall: stability moment must be at least 1.5 times the overturning moment:

$$M_{stab}=W\frac{t}{2} = 13.11\times0.115 = 1.51\ \text{kNm/m}\ \gg\ 1.5\times0.054 = 0.081\ \text{kNm/m}$$

Step 4: Table 11 check

IS 1905 Table 11 allows a free-standing wall without calculation (seismic zones I and II, mortar not leaner than M1) when $H/t \le 10$ for pressures up to 285 N/m$^2$: $t\ge3.0/10=0.30$ m. Our wall satisfies stress and stability by calculation; if the simplified table is preferred, adopt 345 mm (one and a half brick).

Answer: the wall is safe with 230 mm thickness by calculation ($\sigma_{max}=0.063$ N/mm$^2$, stability factor 28); bricks of at least 3.5 N/mm$^2$ in cement mortar M1 (1:5), practical 5 N/mm$^2$. If the wall is built without calculation use $t=345$ mm (Table 11, $H/t\le10$). Provide a damp-proof course and a coping to protect the top.