Step 2: Stiffness Coefficients
k_{AB}
= 4EI/L = 4EI/5 =0.8EI
k_{BA}
= 3EI/L = 3EI/5 =0.6EI
k_{BC}
= 4EI/L = 4EI/4 = EI
k_{CB}
= 4EI/L = 4EI/4 = EI
k_{CD}
= 4EI/L = 4EI/4 = EI
k_{DC}
= 4EI/L = 4EI/4 = EI
Step 3: Distribution factors
D_{AB}
= 1
D_{BA}
= 0.6EI/(0.6EI+EI) = 0.375
D_{BC}
= EI/(0.6EI+EI) = 0.625
D_{CB}
= EI/(EI+EI) =0.5
D_{CD}
= EI/(EI+EI) = 0.5
D_{DC}
= 0
Calculation for moment distribution is
shown in a systematic way in a tabular form.
Each joint is balanced by distributing the unbalanced moment into
the connected members in proportion of distribution factors.
These calculation steps for balancing of joints are shown with grey
colour. The carry-over moments (half of the balancing moment at near
end) are applied on the far end, e.g. carry-over half of the
balancing moment from BC to CB. Resultant bending moment diagram
in figure 8-1(b) is plotted by superposing the span moment diagram
and support moment diagram.
Note: Please use
bending moment calculator
to get the values of span moments |