as an infinite series of extremely thin columns). The formula derived by Euler for long slender columns is given below. To get the mathematical demonstration read: Euler's critical load where , maximum or critical force (vertical load on column), , modulus of elasticity, , smallest area moment of inertia (second moment of area) of the cross section of the column, , unsupported length of column, , column effective length factor, whose value depends on the conditions of end support of the column, as follows. For both ends pinned (hinged, free to rotate), . For both ends fixed, . For one end fixed and the other end pinned, . For one end fixed and the other end free to move laterally, . is the effective length of the column. Examination of this formula reveals the following facts with regard to the load-bearing ability of slender columns. The elasticity of the material of the column and not the compressive strength of the material of the column determines the column's buckling load. The buckling load is directly proportional to the second moment of area of the cross section. The boundary conditions have a considerable effect on the critical load of slender columns. The boundary conditions determine the mode of bending of the column and the distance between inflection points on the displacement curve of the deflected column. The inflection points in the deflection shape of the column are the points at which the curvature of the column changes sign and are also the points at which the column's internal bending moments of the column are zero. The closer the inflection points are, the greater the resulting axial load capacity (bucking load) of the column. A conclusion from the above is that the buckling load of a column may be increased by changing its material to one with a higher modulus of elasticity (E), or changing the design of the column's cross section so as to increase its moment of inertia. The latter can be done without increasing the weight of the column by distributing the material as far from the principal axis of the column's cross section as possible. For most purposes, the most effective use of the material of a column is that of a tubular section. Another insight that may be gleaned from this equation is the effect of length on critical load. Doubling the unsupported length of the column quarters