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Steel Designers' Manual - 6th Edition (2003)
312 Introduction to manual and computer analysis
CA I
MFAB
Fig. 9.23 Slope–deflection method
Fig. 9.24 Moment-distribution method
I
M
A3M 0
(a) (b) (c)
where MFAB, MFBA are the fixed end moments at A and B due to loading and
settlement of supports (counter clockwise positive); qA and qB are end rotations;
and D is the downward settlement of support B relative to support A.
9.5.5 The moment-distribution method
The moment-distribution method can be employed to analyse continuous beams or
rigid frames. Essentially it consists of solving the simultaneous equations in the slope
–deflection method by successive approximations. Since the solution is by successive
iteration, it is not even necessary to determine the degree of redundancy.
Two facets of the method must be appreciated (see Fig. 9.24):
• When a stiff joint in a structural system absorbs an applied moment with
rotational movement only (i.e. no translation), Fig. 9.24(a), the moment resisted
by the various members meeting at the joint is in proportion to their respective
stiffnesses (Fig. 9.24(b)).
• When a member is fixed at one end and a moment, M, is applied at the other
freely supported end, the moment induced at the fixed end is half the applied