Approximate Amplification Factors for Second-Order Effects

One method for approximating the influences of second-order effects (Art. 3.46) is through the use of amplification factors that are applied to first-order moments. Two factors are typically used. The first factor accounts for the additional deflection and moment produced by a combination of compressive axial force and lateral deflection S along the span of a member. It is assumed that there is no relative lateral translation between the two ends of the member. The additional moment is often termed the PS moment. For a member subject to a uniform first-order bending moment Mnt and axial force P (Fig. 3.93) with no relative translation of the ends of the member, the amplification factor is

2. For compression members subject to transverse loading between supports, Cm  1.0.
The second amplification factor accounts for the additional deflections and moments that are produced in a frame that is subject to sidesway, or drift. By combination of compressive axial forces and relative lateral translation of the ends of members, additional moments are developed. These moments are often termed the Pdelta moments. In this case, the moments Mlt determined from a first-order analysis are amplified by the factor

Hence the moments from a second-order analysis when lateral translation of the ends of the member occurs may be approximated by


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