For a 2-hinged arch, if one of the supports settles down vertically then the horizontal thrust

Concept:

Initially the horizontal thrust is towards right at A.

When support B sinks.

∑ M_B = 0

V_A × 1 – H_A × δ  = 0

So, H_A is acting towards left

So overall horizontal thrust will decrease.

Mistake Points When the support sinks/settles the horizontal thrust acts in the opposite direction, hence the horizontal thrust gets decreased. 

Alternate Method:

The equation for horizontal thrust in a 2-hinged parabolic arch is

Where A = Horizontal thrust

E = Modulus of elasticity of the arch material

I = moment of inertia of Arch cross-section

A = Area of cross-section of the arch

α = Coefficient of thermal expansion

t = Difference of temperature

l = length of arch, k = yielding of supports

Here there is no clear mention of temperature Change, (t = 0),

so the horizontal thrust will decrease as the support sinks, i.e k has some value.

And H inversely proportional to k