To find out the EI(rigidity) of a beam by using an overhanging beam

AIM: To find out the rigidity(EI) of a beam by using an overhanging beam apparatus.

Overhanging beam apparatus

APPARATUS:  One can use a overhanging beam apparatus along with the other weights which are used to be hanged and the dial gauge to note down the deflection.
Theory:

We know that if we apply a load equal to W at the two far ends of the overhangs of length 'a' each of an overhanging beam with the central span equal to 'L' then the amount of central deflection is 

given  by   y = W.a.L^2/ 8.E.I  

Now to find out EI, you have to use the following formula

EI= W.a.L^2/ 8.y

W, L and a are known from the above apparatus dimensions and the loads which are to be used are also known to you, and you have to note down the central up-rise(deflection) i.e. y with the help of the dial gauge and then put the values in the above formula.

So you get the value of the rigidity of the given overhanging beam.

Compare the values obtained for different loads and for different deflections and use the average.

Thank you!