Deflections Determined by Three-Moment Equation

Summary of key points

  1. The three-moment equation can be applied at any three points in any beam. It will determine the relation among the moments at these points.
  2. The terms $6A\bar{a}/L$ and $6A\bar{b}/L$ refer to the moment diagram by parts resulting from the simply supported loads between any two adjacent points described in (1).
  3. The heights h1 and h3 from the equation
     

    $M_1L_1 + 2M_2(L_1 + L_2) + M_3L_2 + \dfrac{6A_1\bar{a}_1}{L_1} + \dfrac{6A_2\bar{b}_2}{L_2} = 6EI \left( \dfrac{h_1}{L_1} + \dfrac{h_3}{L_2} \right)$
     

    refer to the respective vertical distance of points 1 and 3 from point 2. The height h is positive if above point 2 and negative if below it.

Problem 859
Determine the value of EIδ under P in Fig. P-859. What is the result if P is replaced by a clockwise couple M?
 

859-overhang-with-concentrated-load.gif

 

Solution 859

 

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