Buckling
Buckling without side loading

Special problems to do with stability occur when cylinders with long stroke lengths are used.
For the purpose of calculation these cases are divided into areas:

 Non elastic buckling loads (Tetmajer’s calculation) and
 Elastic or Hook’s buckling loads (its critical limiting load is determined by Euler’s equation)

In hydraulic cylinder Euler’s calculation is basically the calculation used, as the piston rod may usually be considered to be a slender strut (negligible diameter).

Buckling load and operation load are then calculated as follows:

Buckling load K= ………In N (1)
i.e. the rod buckles under this load
Max. operating load F = K/S In N (2)
Sk = free buckling length in mm
E = modulus of elasticity (2.1 x 10 * for steel ) in N/mm ㎟
J = moment of inertia for circular cross-section in mm* …..
S = safety factor (3.5)

The length to be used as the free buckling length may be determined from the Euler loading cases (see table 4). In order to simplify the calculation the stiffening due to the cylinder tube is ignored. This provides the required safety margin in standard cylinders, the installation position of which is usually not known, in order to cater for any superimposed bending loads..

Table 4: Euler’s loading cases

Euler’s loading case	Case 1 One end free, one end rigidly connected.	Case 2 (Basis case) Two ends pivoted.	Case 3 One end pivoted, one end rigidly connected.	Case 4 Two ends rigidly connected.
Illustration
Free buckling length
Installation position for cylinder Note	Mounting type FA,FB,LA,LB, MF3, ME7,MF4,ME8,MS2	Mounting type TA,TC,CA,CB,MP3,MP1, MT4	Mounting type FA,FB,LA,LB,MF3,ME7, MF4,ME8,MS2 Load must be carefully guided, or else possible bracing.	Mounting type FA,FB,LA,LB,MF3,ME7, MF4,ME8,MS2 Not suitable, as bracing is to be expected.