APPENDIX: STRUCTURAL CIRCULAR POINT CALCULATION

Assuming a structurally bonded point fixing as a flat circular plate bonded with a sealant interlayer of constant thickness to a substrate. Forces might act in a point of the center line with a certain distance to the bonding interface. An addi­tional torsion momentum can be considered around the center axis (as shown in Fig. 25). The sealant is considered to be an ideal elastomer, i. e., to be fully incompressible corresponding to a Poisson ratio of 0.5.

The following nomenclature and units are used for the parameters in the formulas below:

D (mm): diameter of the structural point fixing plate

d (mm): distance of bonding interface from the point, where forces are attacking

E (MPa): elastic modulus (Young’s modulus) of the sealant

e (mm): origin thickness of structural sealant layer

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FIG. 25—Forces acting on a bonded circular point fixation.

F (N): tension force acting in normal direction along center axis G (MPa): shear modulus of the sealant

Q (N): tangential force acting parallel to the bonding interface M (Nm): torsion momentum around the center axis r (mm): radius of the structural point fixing plate (r = D/2) t (mm): distance of rotation point form edge fi (rad or deg): angle of inclination k (mm/mm): engineering strain (k = 1 + De/e)

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Calculation of Sealant Tension Stress and Elongation Caused by Normal Load F Acting on Its Own

The force F acting along the center axis creates a tension stress (engineering stress) in the sealant, which, assuming a homogenous stress distribution, can be expressed as follows:

F

p • r2

This tension stress results in an elongation of the sealant (increase in sealant thickness), which for the case of the linear stress model can be expressed as follows:

Calculation of Sealant Shear Stress and Displacement Caused by Tangential Load Q

The force Q acting on a point along the center axis causes shear stress in the sealant, which, assuming a homogenous distribution, can be expressed as follows:

Q

p r2

The resulting displacement of the structural point in the direction of Q then is given by Eq A4