Rayleigh Ritz method

17/12/2011 13:37

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 yc 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 yc substitute x = l/2. in above equation (1.c)

 

 

Hence we have  which is the deflection at the centre.