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                                                    CRITERIA FOR BUILDING DESIGN


                                                                               CRITERIA FOR BUILDING DESIGN  5.7

                                    Moments and forces may be obtained from a general second-order elastic analysis that considers
                                  both P–∆ and P–δ effects, where equilibrium is satisfied for the deformed geometry. Alternatively,
                                  moments and forces may be obtained by amplification of a traditional first-order elastic analysis,
                                  where equilibrium is satisfied for the original or undeformed structure. In low-rise moment frames,
                                  the amplification of axial forces is often negligible, but it becomes more significant in high-rise struc-
                                  tures. Amplified values of the required flexural strength and axial strength may be calculated from
                                  the following equations:
                                                                                                       (5.3)
                                                              M r = B 1 M nt + B 2 M lt
                                                                                                       (5.4)
                                                              P r = P nt + B 2 P lt
                                  where
                                                           B =    C m   ≥ 1                            (5.5)
                                                            1
                                                              ( 1− α PP /  e1 )
                                                                   r
                                                           B =      1     ≥ 1                          (5.6)
                                                              1−∑   P ∑ /  P e2
                                                            2
                                                                 α
                                                                    nt
                                                           α= 1.0 (LRFD) = 1.60 (ASD)
                                  The following definitions apply:
                                    M r = required second-order flexural strength, kip⋅in (N⋅mm)
                                    M nt = first-order moment, assuming no lateral translation of frame, kip⋅in (N⋅mm)
                                    M lt = first-order moment as a result of lateral translation of frame only, kip⋅in (N⋅mm)
                                    P r = required second-order axial strength, kips (N)
                                    P nt = first-order axial force, assuming no lateral translation of frame, kips (N)
                                    ∑P nt = total vertical load supported by a story, including gravity column loads, kips (N)
                                    P lt = first-order axial force, as a result of lateral translation of frame only, kips (N)
                                    C m = coefficient assuming no lateral translation of frame, the value of which is taken as follows:
                                    • For beam-columns not subject to transverse loading between supports in the plane of bending,
                                                                           M 
                                                                     −
                                                                   .
                                                              C = 06 04 .    1                       (5.7)
                                                                m
                                                                           M 
                                                                           2
                                      where M 1 and M 2 , calculated from a first-order analysis, are the smaller and larger moments,
                                      respectively, at the ends of that portion of the member unbraced in the plane of bending under
                                      consideration. M 1 /M 2 is positive when the member is bent in reverse curvature, negative when
                                      it is bent in single curvature.
                                    • For beam-columns subjected to transverse loading between supports, the value of C m may be
                                      determined either by analysis or taken conservatively as 1.0.
                                    P e1  = elastic critical buckling load of the member in the plane of bending, kips (N)
                                                                      π 2 EI
                                                                  P =                                  (5.8)
                                                                  e1
                                                                      ( KL) 2
                                                                       1
                                    ΣP e2 = elastic critical buckling resistance for the story determined by sidesway buckling analy-
                                    sis, kips (N)
                                    • For moment frames where sidesway buckling effective length K 2 factors are determined for the
                                      columns, the following equation may be used:
                                                                  e2 ∑
                                                               ∑ P =     π 2 EI
                                                                        ( KL) 2                       (5.9a)
                                                                          2

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