Beam Deflection by Double Integration   (continued)

 

For   0  ≤  x  ≤  L/2    Determine moment distribution in section 1 of beam.

                             

 

       ccw  ∑ M Q1  =  0     gives      M1  ˗  (3wL/8) x  +  wx (x/2)  =  0

 

So the moment distribution in section 1  is  M 1  =   3wLx/8  ˗  wx2/2

 

 

For   L/2  ≤  x  ≤  L   Determine moment distribution in section 2 of beam.

                     

 

           

      ccw  ∑ M Q2  =  0     gives      M2  ˗  (3wL/8) x  +  (wL//2)(x ˗ L/4)  =  0

 

So the moment distribution in section 1  is  M2  =   wL2/8 ˗  wLx/8 

 

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