Comparison of the Approximate and Exact Second Order Elastic Analysis Methods in Relation with Eurocode 8’s interstorey drift sensitivity Coefficient (θ) limit
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Date
2018-11
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Addis Ababa University
Abstract
Stability of structures is a major issue that must be checked at the first stage of the design. It is
the ability of a structure to keep its equilibrium position after being disturbed by external actions.
One of the parameters used to check the stability of structures in code of practices is a second
order effect. The Eurocode families, Eurocode-2 and Eurocode-8 set the criteria for neglecting
second order effect by considering different parameters into account. In the EC8 approach to the
second order effect, inerstory drift sensitivity coefficient θ is the most important quantity
governing the analysis. The code allows to neglect the second order effect if θ is less than 0.1
and to use an amplification factor (1/1- θ) if θ does not exceed 0.2. It restricts the value of θ not
to exceed 0.3.
The second order effect is the phenomenon of additional force and moments produced by the
vertical load acting on the laterally deformed structure. Second order elastic analysis can be
evaluated in one of the two methods, approximate and “exact” second order elastic analysis
method. The accuracy limit of approximate second order elastic analysis method is illustrated by
comparing the results of the two methods in relation to the limit of interstory drift sensitivity
coefficient θ.
The procedure is done in two cases using simple elastic portal frames. In case I axial load is
applied only on the weak column of the frame, and in case II the load is applied on both strong
and weak columns. In both cases five portal frames with a different relative stiffness value of
columns are used to study the effect of the relative stiffness of columns on the bracing action of
strong column. These frames clearly show cases where the validity of the basic assumption
behind the approximate methods becomes uncertain.
The results of the investigation reveal that, the approximate method gives relatively good results
up to the value of θ=0.3 in the case of supported sway column. After this point, the P-δ effect,
which is neglected by the approximate method, becomes very high and the supported sway
column deflects in an elastic failure mode which is very different from the basic assumption of
approximate method. As a result, the approximate method becomes less accurate for θ values
greater than 0.3 compared to the “exact” one.
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Keywords
Elastic Analysis Methods, Eurocode 8’, Coefficient (θ) limit