Application of Second-Order Elastic Analysis in LRFD: Research to Practice

The AISC Load and Resistance Factor Design Specification,1 states, "In structures designed on the basis of elastic analysis, Mu may be determined from a second-order elastic analysis using factored loads." At the present time, a designer who wishes to use this type of analysis has many choices of methods, all of which may be termed "secondorder elastic." This paper compares and contrasts several of the current most commonly used methods (B1/B2 approaches and a number of P-Delta approaches) to matrix analysis approaches based on stability function and geometric stiffness formulations. The matrix approaches are comprehensive in that they account for both P-d and P-D effects and place essentially no constraints on the manner in which the structure is modeled for analysis. As these approaches increasingly become available in commercial software, they will provide a powerful facility for the analysis and design of ordinary as well as irregular and complex three-dimensional structures. In the last twenty to twenty-five years, a large amount of research has been devoted to the nonlinear elastic and inelastic analysis of frame structures. In parallel with the development of more sophisticated analysis methods, the speed, memory capacity, and advanced graphics capabilities of personal and workstation computers continue to increase each year. The capabilities of these new machines have made it possible to employ analysis and design techniques that in the recent past were generally impractical for most engineering firms. As an example, for certain types of building systems, it is now commonplace to perform a three-dimensional linear elastic analysis which accounts for the interaction between shear walls and various other types of structural framing. With each new generation of personal computers and workstations, there are fewer and fewer constraints on analysis technique and size of the analysis model.