Step 2: Stiffness Coefficients
k_{AB}
= 4EI/L = 4EI/5 =0.8EI
k_{BA}
= 4EI/L = 4EI/5 =0.8EI
k_{BC}
= 4EI/L = 4EI/4 = EI
k_{C}_{B}
= 4EI/L = 4EI/4 = EI
k_{CD}
= 4EI/L = 4EI/4 = EI
k_{DC}
= 4EI/L = 4EI/4 = EI
k_{CE}
= 4EI/L = 4EI/4 = EI
k_{EC}
= 4EI/L = 4EI/4 = EI
Step 3: Distribution factors
D_{AB}
= 0
D_{BA}
= 0.8EI/(0.8EI+EI) = 0.44
D_{BC}
= EI/(0.8EI+EI) = 0.56
D_{CB}
= EI/(EI+EI+EI) =0.33
D_{CD}
= EI/(EI+EI+EI) = 0.33
D_{CE}
= EI/(EI+EI+EI) = 0.33
D_{DC}
= 0
D_{EC}
= 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 carryover moments (half of the balancing moment at near
end) are applied on the far end, e.g. carryover half of the
balancing moment from BC to CB. Resultant bending moment diagram in
figure 82(b) is plotted by superposing the span moment diagram and
support moment diagram.
Note: Please use our
bending moment calculator
to get the values of span moments

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