m10l27 - Module 10 Compression Members Version 2 CE IIT...

Module
10
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- effect and
moments due to minimum eccentricities in slender columns,
Δ
• identify a column if sway or nonsway type,
• understand the additional moment method for the design of slender
columns,
• apply the equations or use the appropriate tables or charts of SP-16 for
the complete design of slender columns as recommended by IS 456.
11.27.1 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 l
ex
/D and l
ey
/b less than twelve are designated as short and otherwise, they
are slender, where l
ex
and l
ey
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:
(i) the development of high strength materials (concrete and steel),
(ii) improved methods of dimensioning and designing with rational and
reliable design procedures,
Version 2 CE IIT, Kharagpur

(iii) innovative structural concepts – specially, the architect’s expectations
for creative structures.
Accordingly, this lesson explains first, the behaviour of slender elastic
columns loaded concentrically. Thereafter, reinforced concrete slender columns
loaded concentrically or eccentrically about one or both axes are taken up. The
design of slender columns has been explained and illustrated with numerical
examples for easy understanding.
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.