Question

5) The beam structure supporting a uniformly distributed load (w) has its end A hinged & end B supported on a roller. Solve for the end rotations and support reactions using FE approach. Figure P4-14

Answer 1

Taking FINITE ELEMENT 'dx' at any section of beam at a distance 'x' from piont 'A'

taking section (dx finite element dx' SAL RARE Total Folce on beam وہ lwod nc . at Centre > WL of beam Reaction at A (RA) Lego RATRB = WL" Sumation of Faces • Taking moment about A in holizontal direction is z ero in equillibre WL x L - RBAL) = 0 -Um EFH=0 From eq IRA = WI

Reaction at A ={wL/2}

Reaction at B={wL/2}