That is, the additional member moments or curvatures are a small percentage of the results given by a first-order analysis. Conveniently, in many circumstances the additional response induced from second-order effects is small enough to be neglected. All structures feel second-order effects, no matter how lightly loaded. Second-order analysis is a more physically accurate representation of the structure. Considering equilibrium on the deformed structure (known as second-order analysis) will, in general, produce greater member moments and curvatures than for the equivalent first-order situation. The way I like to think of this is "what happens when you consider equilibrium on the deformed structure rather than the undeformed structure, and what you need to do if there is a significant difference between the two". Section 10.10 is entitled "Slenderness Effects in Compression Members". After all, a machine can't draw its own conclusions if logic is missing. The process of implementing a new design code within software is a good litmus test for the clarity of the code content. As a developer of concrete design software I must convert the instructions given in ACI 318 to automated computer processes. This is not a topic that is easy to convey but I believe ACI has made a great stride in clarifying their intent for the engineer in the latest edition of the 318 code. Section 10.10 covers second-order effects in the analysis and design of members resisting axial/flexural loads. I would like to commend ACI on their rework of Sections 10.10 through 10.13 in ACI 318-05, the result of which is a single Section 10.10 in ACI 318-08 that, in my opinion, reads much more clearly than previous editions of the 318 document.
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