This information is provided as a complimentary service to Granta users and visitors to our website.
Find out more about our materials information management and reference data products 

Buckling of Columns, Panels and Shafts

If sufficiently slender, an elastic column, loaded in compression, fails by elastic buckling at a critical load, Fcrit. This load is determined by the end constraints, of which four extreme cases are illustrated on Fig. A4: an end may be constrained in a position and direction; it may be free to rotate but not translate (or 'sway'); it may sway without rotation; and it may both sway and rotate. Pairs of these constraints applied to the ends of column lead to the five cases shown. Each is characterised by a value of the constant n which is equal to the number of half-wavelengths of the buckled shape.

The addition of the bending moment M reduces the buckling load by the amount shown in the second box. A negative value of Fcrit means that a tensile force is necessary to prevent buckling.

An elastic foundation is one that exerts a lateral restoring pressure, p, proportional to the deflection (p = ky where k is the foundation stiffness per unit depth and y the local lateral deflection). Its effect is to increase Fcrit, by the amount shown in the third box.

A thin-walled elastic tube will buckle inwards under an external pressure p', given in the last box. Here I refers to the second moment of area of a section of the tube wall cut parallel to the tube axis.

Opens in a new window

Figure A2 Buckling of Columns