Report:09

                       Slender Column Test for different end condition

Objective:
-To determine Euler load /critical load /buckling load of slender columns through experiment.
-To determine Euler crippling load /critical load /buckling load of slender columns
theoretically from Euler formula for slender columns.
-To compare the experimental critical load and theoretical critical load.
-To draw column strength curves (both experimental plot & theoretical plot).

Apparatus:
Digital slide calipers, Column testing apparatus, Steel scale, electronic balance, support system
and computer.

Significance:
This experiment provides fundamental knowledge on slender column and its behaviour, test
procedure, testing machine, Euler’s critical load for pined and fixed ended columns etc.

Specimen:
Steel column.

Theory:
The term column is frequently used to describe a vertical member, whereas the word strut is
occasionally used in regard to inclined bars. The vertical members of a building frame or any
structural system which carry mainly compressive loads are called as columns. The compression
member of a truss is called strut. The common feature of the columns and struts is such that they
are subjected to compressive forces. A compression member is generally considered to be
column when its unsupported length is more than 10 times its least lateral dimension.
The design of columns presents a problem; some of the reasons are:
1. There is no definite demarcation point between a column that is relatively short and a
compression block that is relatively tall.
2. Although a column is, for practical purpose, a straight, homogeneous compression
member, it is never made theoretically perfect. Any deviation in its alignment, lack of
homogeneity, or presence of internal stresses will act as a source of bending and possible
ultimate collapse.3. The inability to apply perfectly axial load causes slight eccentricities to be imposed upon
the column that may contribute markedly on its bending tendency and possible ultimate
collapse.
4. The character and magnitude of the end restraint of ordinary columns may vary greatly.

Classification of column:
The classification of structural column may be classified in three categories, they are as follows:
(a) Long column
(b) Intermediate column
(c) Short column

Eular’s Theory for Axially Loaded Elastic Long Column:
The type of failure of columns due to excessive displacement is called buckling failure. The
buckling load depends upon the slenderness ratio of the column, length of the column and also
on the end conditions. Leonard Euler (1707-1783), a Swiss mathematician was first to derive
theoretical expression for buckling load.
Assumtion are the theory-
(a) The material of the column is homogeneous, isotropic and elastic; and thus obeys
Hooke’s law.
(b) The cross-section of the column is uniform throughout its length.
(c) The column is initially straight and is loaded axially.
(d) The column fails by buckling alone.
(e) The self weight of the column is negligible.
(f) The formula is applicable for only long slender column (the length of the column is very
large as compared its cross-sectional dimension) (i.e. it is not applicable for short and
intermediate column).
(g) The shortening of the column, due to direct compression (being very small), is neglected.

Procedure:
i) At first, measure the geometric dimensions of the column.
ii) Then place the column in the testing apparatus between the end supports.
iii) Apply the compressive load axially.iv) Record the critical buckling load from the display.
v) Perform the test for all support conditions.

Sample Calculation:
Calculate slenderness ratio, critical loads, and critical stresses for different support condition.
Graph:
1. Combined graphs of experimental Pcr vs. K and theoretical Pcr vs. K.
2. Combined graphs of experimental Pcr vs. KL and theoretical Pcr vs. KL.
3. Combined graphs of experimental critical stress σcr vs. slenderness ratio, KL/r and
theoretical critical stress σcr vs. slenderness ratio, KL/r.

Result:
According to the method.

Discussion:
The slender column test is a fundamental experiment in structural engineering used to study the
buckling behavior of columns under different loading conditions. The findings from this
experiment provide valuable insights into the stability and failure mechanisms of slender
columns, which are crucial for the design and construction of various structures.