---

INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Free Length, Lo		in
Mean coil diameter, D		in
Modulus of elasticity, E		106lb/in2
Shear Modulus of elasticity, G		106lb/in2

---

---

OUTPUT   VARIABLES   &   GRAPHS

VARIABLES	End condition constant α	Slenderness ratio λ	Limiting length, L* (in)	Critical deflection, ycr (in)
♦ Supported-Supported
♦ Supported-Hinged
♦ Hinged-Hinged
♦ Supported-Free

Stability of Compression Spring

A cylinderical spring subjected to compressive axial force at it ends can fail (buckle) due to elastic instability. The onset of buckling will depend on the coupling conditions of the two ends of the spring, as well as the net axial displacement. This displacement at which buckling begins is known as the critical deflection and it can be estimated by the following equations:

where
     y_cr = critical deflection to cause buckling
     L_o = unstretched length of the compression spring
     L^* = maximum length of spring
     λ = effective slenderness ratio
     α = end condition dependent constant
     E = modulus of elasticity of spring material
     G = shear modulus of spring material

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 9.
• Hicks TG; Mechanical Engineering Formulas, Pocket Guide; McGraw Hill, New York, 2003, Section 5.
• Moulton A, Grosjean J & Owen G; The Moulton Formulae and Methods - directly usable for calculations in mechanical engineering; Professional Engineering Publishing Ltd, London, UK, 2005.