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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Stiffness of bolt, kb		106lb/in
Stiffness of bolted members, km		106lb/in
X-section area of threaded portion of bolt, AT		in2
External load on bolted members, P		lb
Bolt strength, Sproof		lb/in2
Endurance limit of bolt material, Se		lb/in2
Ultimate tensile strength of bolt material, Sut		lb/in2
Yield strength of bolt material, Sy		lb/in2

Joint type

Permanent   Disassemblable

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OUTPUT   VARIABLES   &   GRAPHS

STIFFNESS	Values	Units
♦ Joint constant, C
♦ Bolt preload, Fpreload		lb
♦ Load factor, nload
♦ Factor-of-safety against separation, nseparation
♦ Alternating stress on bolt, σa		lb/in2
♦ Alternating strength of bolt, Sa		lb/in2
♦ Fatigue factor-of-safety, nfatigue
♦ Mean stress on bolt, σm		lb/in2
♦ Factor-of-safety against yielding, nyield

Bolted Connection Under Static And Fatigue Loading.

Consider a preloaded bolt joint clamping two members as shown. The stiffness of the members and of the bolt are known, for example using calculators Bolt & Nut Joint: Stiffnesses of components or Cap Screw Joint: Stiffnesses of components . The system is subjected to an external tensile force P, which is carried partly by the bolt and partly by the mating members. The resulting stresses and various factors-of-safety are be estimated via the equations below:

where
     C = joint constant
     k_b = stiffness of bolt
     k_m = stiffness of members
     S_proof = bolt strength
     F_proof = bolt's proof force
     F_preload = bolt's preload force
     f = bolt's preload factor = 0.9 (permanent joint), = 0.75 (disassemblable joint)
     P = external force applied to bolt and members assembly
     n_load = factor-of-safety of bolt relative to the applied load
     n_separation = factor-of-safety against separation, i.e. net force on members is zero
     σ_a = alternating stress on bolt
     σ_m = mean stress on bolt
     n_fatigue = factor-of-safety of bolt relative to fatigue strength
     n_yield = factor-of-safety of bolt relative to yield strength

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 8.
• Hicks TG; Mechanical Engineering Formulas, Pocket Guide; McGraw Hill, New York, 2003.
• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002.