Buckling of Columns

 

*Example:  A steel, simply-supported, wide flange column, W 10 x 60,  of length, L, is

  subjected to compressive loading P as shown in the figure below.  Let L = 18 ft.  For steel

  E = 30 x 106 psi.  Find the smallest load for column buckling.

 

 

                         

 

 

Strategy:  Calculate the critical load by applying Pcr = n π2EI/L2  .

 

Note:  The critical buckling load depends on the sizes of the moment of inertia and the
buckling mode shape. 

 

From tables for wide-flange beams:      I11  =  341 in4  and  I22 = 116 in4

                                                

Next consider the buckled mode shape.  The mode shape for buckling with no mid-span restraint

 Is a single sine wave.  So  n  =  1.

 

Now the column is free to buckle in any direction.  It will buckle first in the “weakest”

direction.  So select  I22 .

 

         Pcr = Pcr =  π2 (30 x 106)(116) / [(18)(12)2  lb  =  7.36 x 105 lb

 

The figure below shows a top view of the deflected column.

 

                            

 


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