Question

Consider four identical circular Euler columns under a compressive axial load with a) one end fixed and the other pinned (or hinged or simply-supported), b) both ends fixed, c) both ends pinned (or hinged or simply-supported), d) one end fixed and the other free. What are the buckling loads Pcr for each one and which one is the strongest against buckling? Given are: the length L of the column and bending rigidity EI, ?

Answer 1

Critical Buckling load of the column whose Bending rigidity is EI and Length is L, is given by the equation,

  

Where, = Effective length of the column ( It depends on the end condition of the column. )

As equation shows, Critical Bucking load of column is directly proposnal to modulus of rigidity ( E ) and Minimum moment of inertia of the column cross- section. Critical buckling load is inversely proposnal to the square of the effective length of column.

Now, Buckling load equation for different four end conditions of the column is shown below.

(1) One end fixed and other is hinged or simply supported

for this end condition of the column of length L ,

Effective length

So, Critical Bucking load,

So,   

(2) Both end fixed

for this end condition of the column of length L ,

Effective length

So, Critical buckling load,

So,

(3) Both ends pinned or hinged or simply supported

for this end condition of the column of length L ,

Effective length

So, Critical buckling Load,  

(4) One end fixed and other end free

for this end condition of the column of length L ,

Effective length  

So, Critical buckling load,

So,   

Now, Critical buckling load gives the value at which column will tends to Buckle or tends to bend sideways.

So, Small critical bucking load indicated that column will buckle for a small value of compressive loadso it is a Weak Column and High value of critical buckling load indicates that column can resist high value of compressive load without buckling so it is konwn as strong column.

Now, Comparing Critical Buckling load equations for above four cases, Highest critical buckling load value will be case 2 where both ends of the column is fixed. So, For Column whose both ends are fixed will be the strongest against the buckling.