# Rayleigh Ritz method

__Rayleigh Ritz method applied to Beams__

U__#1) Find the deflection at the centre using Rayleigh Ritz method for the simply supported beam subjected to Concentrated load at the centre__

Solution:

Take y = .

According to Rayleigh Ritz method = U – W and where π = Potential energy U = Strain energy and W is the external work done.

where y_{c} is the deflection at the centre.

--------(1.a)

We Know that when ** m** is not equal to

**.**

*n*
when **m** = **n** Hence equation 1.a becomes,

--------------(1b)

From 1 b eqn,

There fore ------------(1c)

To find out y_{c} substitute x = l/2. in above equation (1.c)

Hence we have which is the deflection at the centre.