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:
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:
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 
 Mounting
type TA,TC,CA,CB,MP3,MP1, 


The force produced by a double acting hydraulic piston on the rod side can be expressed as
F_{1} = (π (d_{2}^{2}  d_{1}^{2}) / 4) P_{1} (1)
where
F_{1} = rod pull force (lb, N)
d_{1} = rod diameter (in, m)
d_{2} = piston diameter (in, m)
P_{1} = pressure in the cylinder (rod side) (lf_{f}/in^{2 }(psi), N/m^{2} (Pa))
The force produced opposite the rod can be expressed as
F_{2} = (π d_{2}^{2 }/ 4) P_{2} (2)
where
F_{2} = rod push force (lb, N)
P_{2} = pressure in the cylinder (opposite rod) (lf_{f}/in^{2 }(psi), N/m^{2} (Pa))
Rod pushing force for hydraulic cylinders are indicated below:
Rod pulling force for hydraulic cylinders are indicated below:
The selection of a piston rod for thrust (push) conditions requires the following steps to be carried out:
1. Determine the type of cylinder mounting style and rod end connection to be used. Consult the Stroke Factor table and determine which factor corresponds to the application.
2. Using this stroke factor, determine basic length from the equation:
Basic Length = Net Stroke x Stroke Factor
( The Piston Rod Selection Chart, below, is prepared for standard rod extensions beyond the face of the gland retainer. For rod extensions greater than standard’ add the increase to the stroke to arrive at the basic length’)
3. Find the load imposed for the thrust application by multiplying the full bore area fo the cylinder by the system pressure, or by referring to the Push and Pull Force charts.
4. Using the Piston Rod Selection Chart below, look along the values of ‘ basic length ’ and ‘ thrust ‘ as found in 2. and 3. above, and note the point of intersection.
The correct piston rod size is read from the diagonally curved line labeled ‘Rod Diameter‘ above the point of intersection.
Long Stroke and Stop Tubes
When considering the use of long stroke cylinders, the piston rod should be of sufficient diameter to provide the necessary column strength.
For tensile(pull)loads, the rod size is selected by specifying standard cylinders with standard rod diameters and using them at or below the rated pressure.
For long stroke cylinders under compressive loads, the use of stop tubes should be considered, to reduce bearing stress. Selection of a stop tube is described.
Given that the load and operating pressure of the system are known, and that a piston rod size has been estimated taking account of whether the rod is in tension(pull) or compression (push), then the cylinder bore can be selected.
If the piston rod is in compression, use the ‘Push Force’ table below.
If the cylinder envelope dimensions are too large for your application increase the operating pressure, if possible, and repeat the exercise.
If the piston rod is in tension, use the ‘Deduction for Pull Force’ table. The procedure is the same but, due to the reduced piston surface area resulting from the piston rod, the force available on the ‘pull’ stroke will be smaller, To determine the pull force.
If this force is not large enough, go through the process again but increase the system operating pressure or cylinder diameter if possible. If in doubt, Our design engineers will be pleased to assist.
