Page 170 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.153

due to end moments M 1 and M 2 are in opposite directions, then M 1 /M 2 is negative;
otherwise M 1 /M 2 is positive.
(2) For beam-columns subjected to transverse loads between supports, if the ends are
restrained against rotation, C m 0.85; if the ends are unrestrained against rota-
tion, C m 1.0.

Two equations are given for B 2 in the AISC LRFD Specification:

1
B 1 ______________ (H1-5)

HL
oh
1 – P u
or
1
B 2 (H1-6)
P u
1 –
P e
where P u required axial strength of all columns in a story (i.e., the total factored
gravity load above that level), kips
ch translational deflection of the story under consideration, in.
H sum of all horizontal forces producing oh , kips
L story height, in.
P e summation of P e for all columns in a story.
Values of P e are obtained from Eq. [8.1], considering the actual K and l of each column in
its plane of bending. Equation (H1-5) is generally the more convenient of the two formu-
las for evaluating B 2 . The quantity oh /L is the story drift index. Often, especially for tall
buildings, the maximum drift index is a design criterion. Using it in Eq. (H1-5) facilitates
the determination of B 2 .
For columns with biaxial bending in frames unbraced in both directions, two values of
B 1 (B 1x and B 1y ) are needed for each column and two values of B 2 for each story, one for
each major direction. Once the appropriate B 1 and B 2 have been evaluated, Eq. (H1-2) can
be used to determine M ux and M uy for the applicable interaction formula.

Preliminary Design
The selection of a trial W shape for beam-column design can be facilitated by means of an
approximate interaction equation given in the AISC LRFD Manual. Bending moments
are convened to equivalent axial loads as follows.
P u,eff P u + M ux m + M uy mU [8.2]

where P u,eff is the effective axial load to be checked against the Column Load Table in
Part 2 of the AISC LRFD Manual; P u , M ux , and M uy are as defined in interaction formulas
(H1-1a) and (H1-1b) (P u , kips; M ux , M uy , kip-ft); and m and U are factors adapted from
the AISC LRFD Manual.
Once a satisfactory trial section has been selected (i.e., P u,eff the tabulated c P n ), it
should be verified with formula (H1-1a) or (H1-1b).
For a braced frame, K 1.0 for design; K x L x K y L y 1.0 15 ft. Select a trial W14
shape using Eq. [8.2].
P u,eff P u + M ux m + M uy mU