Warehouse exterior wall, wind 750 N/m2

Data and assumptions

• Exterior wall of a single-storey warehouse, height 3.5 m, tied by metal anchors at floor and roof levels, so it spans vertically as simply supported. Vertical roof load $P=30$ kN/m (assumed axial); wind pressure 750 N/m$^2$.
• Anchors give lateral restraint only (no rotational restraint), so the effective height is $h_{ef}=1.0H$ (IS 1905 Table 4 Sl. 3).
• Design by IS 1905:1987 cl. 5.4.1, 5.4.2, 5.5.2, 5.5.3 (NBC 109 follows the same method). Unit weight of masonry 19 kN/m$^3$. Per metre run of wall.

     roof anchor (support)
        |<-- wind w
  ------+-----------   load P (roof)
        |   |
        | wall, H=3.5 m
        |   |  M = wH^2/8 at mid-height
  ------+-----------
        floor anchor (support)

Step 1: Wind moment

$$\begin{aligned} w &= 0.750\ \text{kN/m (per m of wall)}\\ M &= 0.750\times3.5^2/8 = 1.148\ \text{kNm/m} \end{aligned}$$

Step 2: Trial thickness 230 mm, load and slenderness

$$\begin{aligned} \text{Self weight of wall} &= 0.230\times3.50\times19 = 15.30\ \text{kN/m}\\ N\ (\text{at mid-height}) &= 37.65\ \text{kN/m}\\ h_{ef} &= 1.0\times3.5=3.5\ \text{m} \\ SR &= \frac{3.500}{0.230} = 15.22\ (<27) \end{aligned}$$

Step 3: Stresses at the mid-height section

$$\begin{aligned} \sigma_a &= \frac{N}{A}=\frac{37.65\times10^3}{230\times10^3} = 0.1637\ \text{N/mm}^2\\ \sigma_b &= \frac{6M}{t^2} = \frac{6\times1.148\times10^6}{1000\times230^2} = 0.1303\ \text{N/mm}^2\\ \sigma_{max} &= \sigma_a+\sigma_b = 0.2939,\qquad \sigma_{min} = \sigma_a-\sigma_b = 0.0334\ \text{N/mm}^2 \end{aligned}$$

$\sigma_{min}>0$: the whole section is in compression, no tension (the resultant eccentricity $e=M/N=0.0305$ m, $e/t=0.133<1/6$).

Step 4: Required basic compressive stress

Resultant eccentricity ratio $e/t = M/(Nt) = 0.133$. From Table 9: $k_s=0.676$ ($SR=15.22$). $k_a=1$, $k_p=1$. Since $1/24<e/t\le1/6$, a 25 percent increase is allowed (cl. 5.4.1.4 a).

$$f_b \ge \frac{\sigma_a}{k_sk_ak_p\times1.25} = \frac{0.1637}{0.676\times1.25} = 0.194\ \text{N/mm}^2$$

Step 5: Brick and mortar (IS 1905 Table 8)

Answer: 230 mm thick wall (one brick). Bricks of at least 3.5 N/mm$^2$ crushing strength in cement mortar M1 (1:5) or richer; practically use 5 N/mm$^2$ bricks with 1:5 mortar. Maximum stress 0.294 N/mm$^2$ (compression) and minimum 0.033 N/mm$^2$; slenderness ratio 15.2 < 27. Provide metal anchors at roof and floor at close spacing to pass the wind load into the roof diaphragm and floor.