Use a coaxial, linear elastic, n = 1 dual spring model, with load introduced from the support surface. This experiment fixes the assembly preload at 40 kN, independent of the upper friction test; no account is made of embedded losses, temperature changes, or bending.
Φ = cS / (cS + cP) = 0.20
FS = FM + ΦFA;FK = FM − (1 − Φ)FAUnder this stiffness, each increase of 1 kN external load increases the bolt tension by 0.2 kN and decreases the clamping force by 0.8 kN.
u = FA/(cS + cP) u is the additional elongation of the bolt, which is also the compression rebound of the clamped part. When contact closure occurs, it is not the interface gap.
FA,sep = FM/(1 − Φ) = 50 kN. When reaching this boundary, FK = 0,FS = FAThe slider stops here; the separation state after continued loading is not included in this experiment.
This figure explains the basic elastic relationship. The actual load introduction, eccentricity, local separation, and complete strength determination of real connections should be calculated using actual structures and operating conditions.
Illustration and basic relationship reference:NASA 'Fastener Design Manual', Figure 27;GWJ eAssistant,VDI 2230 Joint Diagram。