04-02-2013, 11:29 AM
Compression Members
1Compression.pdf (Size: 919.56 KB / Downloads: 342)
Introduction
Slender and short are the two types of columns classified on the basis of slenderness ratios as mentioned in sec.10.21.5 of Lesson 21. Columns having both lex/D and ley/b less than twelve are designated as short and otherwise, they are slender, where lex and ley are the effective lengths with respect to major and minor axes, respectively; and D and b are the depth and width of rectangular columns, respectively. Short columns are frequently used in concrete structures, the design of such columns has been explained in Lessons 22 to 26, loaded concentrically or eccentrically about one or both axes. However, slender columns are also becoming increasingly important and popular because of the following reasons.
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.
Effective Length of Columns
Annex E of IS 456 presents two figures (Figs.26 and 27) and a table (Table 26) to estimate the effective length of columns in frame structures based on a research paper, “Effective length of column in multistoreyed building” by R.H. Wood in The Structural Engineer Journal, No.7, Vol.52, July 1974. Figure 26 is for columns in a frame with no sway, while Fig.27 is for columns in a frame with sway. These two figures give the values of k (i.e., le/l) from two parameters 21 and ββ which are obtained from the following expression.