Strength of Materials | Beam Stress Deflection
Mechanics and Machine Design, Equations and Calculators

Springs of rubber bonded to metal are made in a wide variety of configurations. The rubber is usually in shear and, because of the high internal damping, such springs are used for limiting vibrations.

Cylindrical shear spring with axial load applied design equations and calculator, load P

Symbols used:
D_o = Outside diamater of rubber bushing, (mm, in)
D_i = Inside diamater of rubber bushing, (mm, in)
P = Loading Force, (N, lbs)
h = Rubber thickness, (mm, in)
G = Shear modulus

Design equations:

Maximum Shear Stress τ_m = P / π h D_i
Deflection y = [ P / ( 2 π h G ) ] ln ( D_o / D_i )
where G = shear modulus.

Modulus and strength of rubber
G = 0.3 to 1.2MPa
E = 0.9 to 3.6 MPa
Allowable shear stress = 0.2 to 0.4 MPa
Deflection limited to 10% to 20% of free height.