# Comparison of merchant-rankine approach against second-order plastic analysis for steel frames

 Author: Wang, Hongbo Title: Comparison of merchant-rankine approach against second-order plastic analysis for steel frames Degree: M.Sc. Year: 2010 Subject: Hong Kong Polytechnic University -- DissertationsStructural frames -- Mathematical models.Structural design -- Data processing.Plastic analysis (Engineering)Steel, Structural Department: Dept. of Civil and Structural Engineering Pages: ix, 88 leaves : ill. (some col.) ; 31 cm. InnoPac Record: http://library.polyu.edu.hk/record=b2360440 URI: http://theses.lib.polyu.edu.hk/handle/200/5734 Abstract: This dissertation presents a study on two non-linear approaches to obtain the ultimate collapse load factors for steel frames. One is called Merchant-Rankine approach which is empirical formula associated with the elastic critical load factor and plastic collapse load factor while the other is named Second-order analysis which is used much more popular recently. Linear analysis was the main analysis type for structural design in the past due to the simplification of it. However, the actual behaviour of a structure under loading condition is non-linear and complicated, engineers started to find more accurate analysis methods to replace the conventional linear analysis several decades ago. Although the Merchant-Rankine formula is simple enough for even hand calculation and can attain an approximation of ultimate collapse load factor, its limitations become more evident with the high speed development of constructions of which the empirical approach can not fulfil all the requirements. Several important factors are not considered and covered in this method, such as residual stress, initial imperfection and the sway effect. Also, the derivation of the empirical formula is still hard nowadays. On the other hand, a relatively new and practical approach named second-order analysis based on the simulation of deformed structure under external loading has been applied in many huge projects. In this new method, second-order effects including the P-Δ effect, P-δ effect, member and geometric imperfections are considered directly during analysis, so several parameters that need to assume in traditional methods (i.e. effective length, moment amplification factor) are unnecessary. The safety of a structure is directly checked by the section capacity along the length of every member, and there is no need to check every member in a structure. Conceptually, the second-order analysis designs a structure by modelling accurately its true behaviour, instead of making use of empirical formula for individual member check. It is readily available for design application of realistic structures, and it will initiate a revolution in the practical design of steel structures.

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