Stiffness-Factor Modifications

 

Three cases where moment-distribution process can be simplified

 

1. Member Pin (or Roller) Supported at Far End

carry-over factor = 0

if the far end was fixed supported, the stiffness factor K = 4EI/L would have to be modified by 3/4 to model the case of having the far end pin supported

 

2. Symmetric Beam and Loading

for center span:

the center span's stiffness factor will be one half that usually determined using K = 4EI/L

 

3. Symmetric Beam and Antisymmetric Loading

for center span:

the stiffness factor is one and a half times as large as that determined using K = 4EI/L

 

Procedure for Analysis

  1. draw FBDs of spans and joints
     
  2. determine distribution factors and fixed-end moments  (click)
     
    1. identify joints (free ends are not joints)
    2. determine stiffness factor K for each span  (click)
      • K = 4EI/L for far-end fixed
      • K = 3EI/L for far-end pinned or roller supported
      • K = 2EI/L for symmetric span and loading
      • K = 6EI/L for antisymmetric loading
      • K = ∞ for ground
      • K = 0 for air
    3. determine distribution factor DF=K/ΣK for each span  (click)
      • DF = 0 for fixed end
      • DF = 1 for an end pin or roller supported
      • DF = 0 for overhung (free) side of joint; DF = 1 for other side
      • ΣDF = 1 at each joint
    4. determine FEMs from inside back cover (positive = clockwise)
       
  3. perform moment distribution process  (click)
     
    1. lock all joints
    2. determine moment needed for joint equilibrium (switch sign)
    3. unlock pin and roller joints (fixed joints stay locked) and distribute the counterbalancing moments into the connecting span at each joint
    4. use +1/2 carry-over factor to carry half of these moments to span's other end  (click)
      • don't carry from fixed joints
      • don't carry to end pin or roller joints
      • don't carry to free ends
    5. repeat until desired degree of accuracy is reached (don't carry-over final distribution)
    6. sum columns of FEMs, distributed moments, and carry-over moments
       
  4. place summed moments on FBDs
     
  5. use equilibrium to determine shear forces and ground forces
     
  6. draw V&M diagrams