i want the method to calculate deflection of beam without using moment of inertial?

Answer 1

I would like to see it too, since I am not aware of any method for calculating beam deflections that do not use the moment of inertia of the beam.
The only (3) methods that I am aware of are:

Double Integration method
Method of Singularity Functions
Elastic Energy Methods

All of them require using the moment of inertia.

Answer 2

Moment of Inertia is fundemental to calculating beam deflection... Of course, if you are always using beams of the same shape (i.e. rectangular), you can rewrite the equations in terms of height and width.. Same goes for any predefined shape. Engineering texts often will have common cases compiled in an annex, or I have found many beam calculators on the net.

Of course if you don't want to have to think at all.. there is always finite element method, where you model the structure and let the computer figure it out.

Answer 3

Even in FEA, the "I " of the beam is input as a variable into beam elements.

Answer 4

Use the radius of gyration