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Steel Designers' Manual - 6th Edition (2003)
A
negative moment positive moment
(counter clockwise) (clockwise)
convention: clockwise moments are positive
convention: downward settlement of B with
respect to A is positive
Fig. 9.25 Sign conventions used in moment-distribution method
Analysis of skeletal structures 313
moment and acts in the same direction as M. (This is frequently referred to as
the carry over.) (Fig. 9.24(c).)
Figure 9.25 shows the sign conventions employed in the moment-distribution
method and Fig. 9.26 illustrates the moment-distribution procedure.
The moment-distribution method consists of locking all joints first and then
releasing them one at a time. To begin with, all joints are locked, which implies that
the fixed end moments due to applied loading will be applied at each joint. By
releasing one joint at a time, the unbalanced moment at each joint is distributed to
the various members meeting at the joint. Half of these applied moments are then
carried over to the other end of each member. This creates a further imbalance at
each joint and the unbalanced moments are once again distributed to all members
meeting at each joint in proportion to their respective stiffnesses.
This procedure is repeated until the totals of all moments at each joint are sufficiently
close to zero. At this stage the moment-distribution process is stopped and
the final moments are obtained by summing up all the numbers in the respective
columns.
9.5.6 Unit load method
Energy methods provide powerful tools for the analysis of structures. The unit load
method can be directly derived from the complementary energy theorem, which