3. Calculate the distribution factors based on the stiffness
coefficient of the member.
Distribution factor can be defined as the ratio of
stiffness coefficient of a member to the sum of the stiffness
coefficient of all the members meeting at that joint. If BA, BC and
BD are connected at joint B, then the Distribution factor (D) can be
easily calculated as follows;
D_{BA}
= k_{BA} /(k_{BA}
+ k_{BC} + k_{BD}
)
D_{BC}
= k_{BC} /(k_{BA}
+ k_{BC} + k_{BD}
) D_{BD}
= k_{BD} /(k_{BA}
+ k_{BC} + k_{BD}
) Distribution factor for a
pinned support or roller at the end of beam is taken as 1 whereas for a fixed
support at the end of beam the distribution factor is taken as zero.
4. Balance all the joints by applying the balancing moments in the
proportions of distribution factors.
5. Carry over half of the balancing moments to the opposite ends
of the span. If the opposite end is pinned there should be no carry
over moment to that end (as in the case of pinned support at the
ends of the beam).
6. Continue these cycles of balancing and carryover till the
joints reach equilibrium state when the unbalanced moment is
negligible (based on desired accuracy).
7. Take the sum of all the moments (fixed end moment, balancing
moment, carryover moment) at each end.
Problem 81,
Problem 82 solved by moment distribution
You can also use our
Moment Distribution Calculator
for solving Continuous beams
Use our
Fixed Beam
Calculator to
determine fixedend moments for different loading cases.
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