# Column Design Essay examples

Compression Members

Version 2 CE IIT, Kharagpur

Lesson 27

Slender Columns

Version 2 CE IIT, Kharagpur

Instructional Objectives:

At the end of this lesson, the student should be able to: • • • • • • • • define a slender column, give three reasons for its increasing importance and popularity, explain the behaviour of slender columns loaded concentrically, explain the behaviour of braced and unbraced single column or a part of rigid frame, bent in single or double curvatures, roles and importance of additional moments due to P- Δ effect and moments due to minimum eccentricities in slender columns, identify a column if sway or nonsway type, understand the additional moment method for the design of slender columns, apply

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10.27.2 Concentrically Loaded Columns

It has been explained in Lessons 22 to 26 that short columns fail by reaching the respective stresses indicating their maximum carrying capacities. On the other hand, the slender or long columns may fail at a much lower value of the load when sudden lateral displacement of the member takes place between the ends. Thus, short columns undergo material failure, while long columns may fail by buckling (geometric failure) at a critical load or Euler’s load, which is much less in comparison to that of short columns having equal area of cross-section. The buckling load is termed as Euler’s load as Euler in 1744 first obtained the value of critical load for various support conditions. For more information, please refer to Additamentum, “De Curvis elasticis”, in the “Methodus inveiendi Lineas Curvas maximi minimive proprietate gaudentes” Lausanne and Geneva, 1744. An English translation of this work is given in Isis No.58, Vol.20, p.1, November 1933. The general expression of the critical load Pcr at which a member will fail by buckling is as follows: Pcr = π2EI /(kl)2 where E is the Young’s modulus I is the moment of inertia about the axis of bending, l is the unsupported