Page 169 - Aircraft Stuctures for Engineering Student

6.1 Euler buckling of columns 153

P

posit ion
I
- I
I F
Displaced
posit ion

P

Fig. 6.1 Definition of buckling load for a perfect column.

there can be no sudden bowing or buckling. We therefore require a precise definition
of buckling load which may be used in our analysis of the perfect column.
If the perfect column of Fig. 6.1 is subjected to a compressive load P, only
shortening of the column occurs no matter what the value of P. However, if the
column is displaced a small amount by a lateral load F then, at values of P below
the critical or buckling load, PCR, removal of F results in a return of the column to
its undisturbed position, indicating a state of stable equilibrium. At the critical
load the displacement does not disappear and, in fact, the column will remain in
any displaced position as long as the displacement is small. Thus, the buckling load
PCR is associated with a state of neutral equilibrium. For P > PCR enforced lateral
displacements increase and the column is unstable.
Consider the pin-ended column AB of Fig. 6.2. We assume that it is in the displaced
state of neutral equilibrium associated with buckling so that the compressive load P
has attained the critical value PCR. Simple bending theory (see Section 9.1) gives

or

Fig. 6.2 Determination of buckling load for a pin-ended column