Handbook of Civil Engineering Calculations

tions due to end moments M 1 and M 2 are in opposite directions, then M 1 IM 2 is

negative; otherwise M 1 IM 2 is positive.

(2) For beam-columns subjected to transverse loads between supports, if the ends are

restrained against rotation, Cm = 0.85; if the ends are unrestrained against rotation,

Cw=1.0.

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

B 1 = l- JT (Hl-5)

! 1 vp MfM

*

P

\S,HL)

or

«i-—b: <"">

'-XTT

where ^P 14 = required axial strength of all columns in a story (i.e., the total factored
gravity load above that level), kips
Xc/fc = translational deflection of the story under consideration, in
2/JT= sum of all horizontal forces producing A 0 ,,, kips
L = story height, in
SP]e = summation of Pe for all columns in a story.

Values of Pe are obtained from Eq. [8.1], considering the actual K and / of each column in
its plane of bending. Equation (H 1-5) is generally the more convenient of the two formu-
las for evaluating B 2. The quantity A 0 ,//, 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
BI (Bix and Bly) arc 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. (Hl-2) can
be used to determine M11x and Muy 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.

PUJB = Pu

+

M^m + MuymU [8.2]

where />„ eff is the effective axial load to be checked against the Column Load Table in
Part 2 of the AISC LRFD Manual, Pw M11x, and Muy are as defined in interaction formulas
(Hl-Id) and (Hl-Ib) (PU9 kips; M11x, Muy, 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 11 ^ the tabulated (^ 0 Pn), it
should be verified with formula (Hl-Id) or (Hl-Ib).
For a braced frame, K = 1.0 for design; KjLx = KyLy = 1.0 x 15 ft. Select a trial W14
shape using Eq. [8.2].

Pu^Pu + M^m+MuymU