#Part–7/ #simply-support-beam-with -a-point-load at it's mid-point. ( Wi...

Q. A simply supported beam subjected to point load at the mid span.

 

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Beams freely supported at the teo ends.

  Shows a beam AB simply supported at the ends A and B. Let the span of the beam be l and the beam carry a concentrate load W at mid span.

   

     Since the load is symmetrically placed on the beam,

   Reaction at each support = W/2

        .: Va = Vb = W/2

For any section between A and D 

            S.F. = Sx = + W/2

 

For any section between C and D 

          S.F. = Sx = – W/2

At the section C the S.F. change from + W/ 2 to – W/2

At any section between A and C distance x from the end A, the bending moment is given by,

 Mx = +2\W × x (sagging moment)

At                      x = 0, Mx = 0

and at               x = l/2     Mx = Wl/4

Hence the B.M. increases uniformly from zero at A to Wl/4 at C.

Similarly the B.M. decreases uniformly from Wl/4 at C zero at B.

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