**Linear Flexibility**C is displacement Δ cause by force P of 1 kg, C=Δ/P. Linear flexibility is expressed in mm/kg.**Rotational Flexibility**C is rotation angle φ (in radians) from bending or rotating moment M of 1 kg*m, C=φ/M. Rotational flexibility is expressed in radian/(kg*m).

**Stiffness** is
the opposite value of flexibility, K=1/C.

**Linear Stiffness**K is reaction P caused by displacement Δ of 1 mm, KC=P/Δ. Linear stiffness is expressed in kg/mm.**Rotational Stiffness**K is moment M caused by rotation φ of 1 degree, K=M/φ. Rotational stiffness is expressed in kg*m/radian.

To input infinite flexibility (zero stiffness), the following should be input:

rotational flexibility equal to 1 radian/(kg*m)

linear flexibility equal to 1000 mm/kg.

Examples:

A rotational bellows has an allowable opening angle of φ=3

^{0}=0.05236 radian; moment at allowable opening angle is М=120 kg*m. Rotational flexibility if φ/М = 0.05236/120 = 0.000436 1/kg*m.An axial expansion joint has an allowable operation deformation of Δ = 25 mm. Axial force at allowable operation deformation is P = 1500 kg. Linear flexibility is Δ/P = 25/1500 = 0.0166 mm/kg.

Expansion joint catalogues give stiffness values for given numbers of waves. Stiffness is the opposite value of flexibility. For example, if expansion joint stiffness is K=50 kg/mm, axial flexibility is C=1/K = 1/50 = 0.02 mm/kg.

The number of waves is often unknown and is determined through analysis. In the case, the expansion joint should be input as completely smooth with a linear flexibility of 1000 mm/kg and rotational flexibility of 1 degree/(kg*m). After analysis deformation, the structure and elastic properties of the appropriate expansion joint are taken from a catalog. Next, a final verification piping analysis is run.

A spiral coil spring, according to OST 108.764.01-80 (revision 09), has an allowable subsidence (operation deformation) of Δ = 70 mm and allowable load (spring compression force for operation deformation) of P=3225 kg. Spring flexibility is Δ/P = 70/3225 = 0.0271 mm/kg.