Warehouse exterior wall, wind 860 N/m2, fixed base

Data and assumptions

• Exterior wall of a single-storey warehouse, 3.5 m high, fixed at base (continuous with the foundation) and tied with a metal anchor at roof level: a propped cantilever. $P=25$ kN/m (axial); wind 860 N/m$^2$.
• Fixed at the base and laterally supported (not rotationally restrained) at the top: $h_{ef}=0.85H$ (Table 4 Sl. 2). Maximum moment is at the fixed base, $M=wH^2/8$ (hogging); sagging moment $9wH^2/128$ is smaller.
• 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=860 N/m2
  ------+-----------   load P=25 kN/m
        |   |
        | wall, H=3.5 m
        |   |  M = wH^2/8 at the fixed base
  ======+===========   foundation (fixed)

Step 1: Wind moment

$$\begin{aligned} w &= 0.860\ \text{kN/m (per m of wall)}\\ M &= 0.860\times3.5^2/8 = 1.317\ \text{kNm/m} \end{aligned}$$

Step 2: Trial thickness 230 mm, load and slenderness

$$\begin{aligned} \text{Self weight of wall} &= 0.230\times3.50\times19 = 15.30\ \text{kN/m}\\ N\ (\text{at base}) &= 40.30\ \text{kN/m}\\ h_{ef} &= 0.85\times3.5=2.975\ \text{m} \\ SR &= \frac{2.975}{0.230} = 12.93\ (<27) \end{aligned}$$

Step 3: Stresses at the base section

$$\begin{aligned} \sigma_a &= \frac{N}{A}=\frac{40.30\times10^3}{230\times10^3} = 0.1752\ \text{N/mm}^2\\ \sigma_b &= \frac{6M}{t^2} = \frac{6\times1.317\times10^6}{1000\times230^2} = 0.1494\ \text{N/mm}^2\\ \sigma_{max} &= \sigma_a+\sigma_b = 0.3246,\qquad \sigma_{min} = \sigma_a-\sigma_b = 0.0258\ \text{N/mm}^2 \end{aligned}$$

$\sigma_{min}>0$: the whole section is in compression, no tension (the resultant eccentricity $e=M/N=0.0327$ m, $e/t=0.142<1/6$).

Step 4: Required basic compressive stress

Resultant eccentricity ratio $e/t = M/(Nt) = 0.142$. From Table 9: $k_s=0.753$ ($SR=12.93$). $k_a=1$, $k_p=1$. Since $1/24<e/t\le1/6$, a 25 percent increase is allowed (cl. 5.4.1.4 a).

$$f_b \ge \frac{\sigma_a}{k_sk_ak_p\times1.25} = \frac{0.1752}{0.753\times1.25} = 0.186\ \text{N/mm}^2$$

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

Answer: 230 mm thick wall; bricks not less than 3.5 N/mm$^2$ with cement mortar M1 (1:5) or richer (practically 5 N/mm$^2$ bricks, 1:5 mortar). Base section: $\sigma_{max}=0.325$, $\sigma_{min}=0.026$ N/mm$^2$ (all compression). Anchor the roof to the wall and tie the wall to the footing with dowels to ensure fixity.