How to Determine A Foundation Whether to be Designed as Flexible or Rigid Body?

In this post we will discuss about strip footing. These types of foundations are suitable where columns in one grid are too near to be founded by individual foundations beneath respective column or shear wall etc.

In case of site conditions or building geometries where transfer of lateral load to exterior columns is required, these foundations are used. It is the stiffness of the supporting structures which can restrict differential settlement of individual column.  But there the footings have to be designed as rigid body having linear soil pressure distribution. To predict approximate stiffness of the structure comparison between soil stiffness and followings are made :

Now we will go through right point: When a foundation can be
treated as flexible or rigid. In the above comparison a relative stiffness is determined  which is termed as K_r.

The K_r value indicates the rigidity or flexibility assumption to be
made for designing. Meyerhof in 1953 gave formula about relative stiffness. These is

Where E’IB=Summation of followings: 

• Flexural stiffness of foundation E’I_F
• Flexural stiffness of individual framed member E’I_b‘
• Flexural stiffness of all shear wall E’t_wh³_w/12
  t_{w=thickness of respective walls}
  h_{w=height of respective walls}
  

This is interesting to notice that when K_r value increases a rapid decrease in differential settlement is observed. We provide a table below about the relation between K_r and settlement values
below:

Footing size	Relative stiffness	(Differential settlement)/(Total settlement)
Long	Kr=0	0.5
Square	Kr=0	0.35
–	Kr=0.5	0.1

When a relative stiffness, derived from above equations or analysis, becomes o.5, the foundation are assumed rigid in design i.e. variation in soil pressure are derived by simple statics. But if relative stiffness is found less than 0.5 the foundation should be designed as flexible considering a approach of foundation modulus.