As we know that masonry structure cannot resist tension, hence all the lateral force should be resisted by its weight component only. In this article we will derive expression for width/height ratio for a simple rectangular masonry structure.

Let,

γ=density of water

S_{m}=specific gravity of masonry material

S_{L}=specific gravity of material giving lateral force (e.g. water, soil etc)

h=height of the structure

x=width of the structure

W=weight of structure=h*x*s* γ

μ= coefficient of friction

Case1: For overturning

Moment dut to lateral force=moment due to weight of the material

½* γ*s_{L}*h^{2}*h/3 =W*x/2

Or, ½* γ*h^{2}*h/3*s_{L} = γ *s_{m}*h*x*x/2

Or, (x/h)^{2}=(s_{L}/(3*s_{m}))

Or, x/h=sqrt(s_{L}/s_{m}/3)

*For water s _{L}=1;for stone masonry s_{m}=22/9.81=2.14*

*Therefore, x/h=0.394≈0.4*

Case2: For Sliding

Horizontal force=friction factor*weight of the structure

½* γ*s_{L}*h^{2}= μ (γ*s_{m}*h*x)

Or, x/h=s_{L}/(2*s_{m}* μ)

*For water and stone masonry and using μ=0.65*

*x/h=0.359≈0.4*

Thus from above derivation we see that the minimum base width/height ratio of the rectangular block to resist the lateral (triangular here) force with safety factor 1 is 0.4.

With safety factor of 1.5 the minimum width/height ratio becomes 1.5*0.4=0.6.