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Steel Designers' Manual - 6th Edition (2003)
some BMs change their signs as the frames change their proportions. This will be
appreciated by examining the charts.
For simple frames, i.e. for single-storey frames, the formulae for reactions immediately
follow the formulae for BMs for each load.
Considering the simple frames only, the type of formula depends on the degree
of indeterminacy and the shape of the frame.Auxiliary coefficients X are introduced
whenever the direct expressions become complicated or for other reasons of
expediency.
No hard and fast rules can be laid down for the notation and it must be noted
that each set of symbols and constants applies only to the particular frame under
consideration, although, of course, an attempt has been made to produce similarity
in the types of symbols.
11.1.3 Sign conventions
All computations must be carried out algebraically, hence every quantity must
be given its correct sign. The results will then be automatically correct in sign and
magnitude.
The direction of the load or applied moment shown in the left-hand diagram for
each load condition is considered to be positive. If the direction of the load or
moment is reversed, the signs of all the results obtained from the formulae as printed
must be reversed.
For simple frames, the moments causing tension on the inside faces of the frame
are considered to be positive. Upward vertical reactions and inward horizontal reactions
are also positive.
For multi-storey or multi-bay frames the same general rules apply to moments
and vertical reactions.
11.1.4 Checking calculations for indeterminate frames
Formulae for rigid frames 345
Calculations for indeterminate frames may be checked by using some other method
of analysis, but it is also possible to check any frame or portion of a frame, such as
that above the line AB in Fig. 11.2, by ensuring that the following rules are obeyed:
(1) the three fundamental statical equations, i.e. SH = 0, SV = 0 and SM = 0, have
been satisfied, and, in addition, either that
(2) the sum of the areas of the M/EI diagram above any line, such as AB, is zero if
A and B are fully fixed; or
(3) the sum of the moments, with respect to the base AB, of the areas of the M/EI
diagram above the line AB is zero if A and B are partially restrained (as shown
in Fig. 11.2) or are hinged.