Multi-storey wall: stresses at each level

Step 1: Permissible stress

Each storey is fixed at both ends: $H_{eff} = 0.75 \times 3000 = 2250$ mm.

$$SR = \frac{2250}{230} = 9.78, \quad k_s = 0.89 + \frac{0.22}{2}\times 0.06 = 0.897$$

Area per metre $= 0.23$ m² $> 0.2$, so $k_a = 1.0$, $k_p = 1.0$:

$$f_c = 0.5 \times 0.897 = 0.448\ \text{N/mm}^2$$

Step 2: Self-weight per storey

$$W_{s} = 19 \times 0.23 \times 3.0 = 13.11\ \text{kN/m}$$

Step 3: Loads and stresses at each base level

Stress $= \text{load}/(230 \times 1000)$.

The ground storey stress exceeds the permissible value by about 1 percent, so it is not acceptable.

Step 4: Redesign of the ground storey with 345 mm wall

Self-weight of the 345 mm ground wall $= 19 \times 0.345 \times 3.0 = 19.67$ kN/m. Load at base:

$$P = 15 + 50 + 2 \times 13.11 + 19.67 = 110.89\ \text{kN/m}$$ $$\begin{aligned} SR &= \frac{2250}{345} = 6.52, \quad k_s \approx 0.99 \\ f_c &= 0.5 \times 0.99 = 0.49\ \text{N/mm}^2 \\ f &= \frac{110\,890}{345 \times 1000} = 0.321\ \text{N/mm}^2 < 0.49 \end{aligned}$$

A 345 mm wall at the ground storey is safe (stress ratio 0.65). The 230 mm upper wall should sit centrally on the 345 mm wall (57.5 mm projection on each side) so that the load stays concentric. If it were flush with one face, the eccentricity of 57.5 mm would add large bending stress and the check above would no longer hold.

Answer: Stresses at base: top 0.122, middle 0.288, ground 0.454 N/mm² (permissible 0.448). The ground storey needs a 345 mm wall (stress 0.321 N/mm² < 0.49).