Hookes Law

Hooke’s Law-

       It states “when a material is loaded, within its elastic limit the stress is proportional to the strain.

Stress/Strain = E = Constant

                  

Modulus of Elasticity

Or

Yong modulus(E) –

      

A material is loaded within its elastic limit the stress is propotional to strain.

σαε=E×ε

                     

E=σ/ε

              

                                            Where  = stress 

                                                           = strain

                                                          E = constant

Deformation of a body due to force acting on it.

σ=P/A

Strain ε=σ/E=P/AE

δl=εl=σl/E=Pl/AE

Principal of Superposition-

       A body is subjected to a number of forces acting on its outer edges as well as at some other sections, along the length of the body. In such a case, the force are split up and their effects are considered on individual sections. The resulting deformation, of the body, is equal to the algebraic sum of deformations of the individual sections. Such a principle, of finding out of resultant deformation, is called the principal of superposition.

The relation for the resulting deformation may be modified as:

    

Types of Bars of Varying Sections-

1.      Bars of different section

2.      Bars of uniformly Sections

3.      Bars of composite sections