Comparison Of The Approximate And Exact Second Order Elastic Analysis Methods In Relation With Eurocode 8s Interstorey Drift Sensitivity Coefficient () Limit

Stability of structures is a major issue that must be checked at the first stage of the design. It isrnthe ability of a structure to keep its equilibrium position after being disturbed by external actions.rnOne of the parameters used to check the stability of structures in code of practices is a secondrnorder effect. The Eurocode families, Eurocode-2 and Eurocode-8 set the criteria for neglectingrnsecond order effect by considering different parameters into account. In the EC8 approach to thernsecond order effect, inerstory drift sensitivity coefficient θ is the most important quantityrngoverning the analysis. The code allows to neglect the second order effect if θ is less than 0.1rnand to use an amplification factor (1/1- θ) if θ does not exceed 0.2. It restricts the value of θ notrnto exceed 0.3.rnThe second order effect is the phenomenon of additional force and moments produced by thernvertical load acting on the laterally deformed structure. Second order elastic analysis can bernevaluated in one of the two methods, approximate and “exact” second order elastic analysisrnmethod. The accuracy limit of approximate second order elastic analysis method is illustrated byrncomparing the results of the two methods in relation to the limit of interstory drift sensitivityrncoefficient θ.rnThe procedure is done in two cases using simple elastic portal frames. In case I axial load isrnapplied only on the weak column of the frame, and in case II the load is applied on both strongrnand weak columns. In both cases five portal frames with a different relative stiffness value ofrncolumns are used to study the effect of the relative stiffness of columns on the bracing action ofrnstrong column. These frames clearly show cases where the validity of the basic assumptionrnbehind the approximate methods becomes uncertain.rnThe results of the investigation reveal that, the approximate method gives relatively good resultsrnup to the value of θ=0.3 in the case of supported sway column. After this point, the P-δ effect,rnwhich is neglected by the approximate method, becomes very high and the supported swayrncolumn deflects in an elastic failure mode which is very different from the basic assumption ofrnapproximate method. As a result, the approximate method becomes less accurate for θ valuesrngreater than 0.3 compared to the “exact” one.

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