Beam Deflection (Statically Indeterminate)  -  Method of Superposition

 

Example:  (continued)

                              

                        

 

For compatibility the end of the beam deflects the same for the beam and for the rod.      

 

                                               ∆beam  =  ∆rod                     where

 

                        ∆beam  =  qL4/8EI   –  TL3/3EI     and    ∆rod  =  TH/AE

 

 

Solve for T.                   T  =  3 q L / [ 8(1 + 3(I H / AL3 ) ]

               

 

So the axial stress in the rod is   σ  =   3 q L / [ 8(1 + 3(I H / AL3 )A ]

 

 

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