From my days working aerospace, I have the following equations that came from a DoD/NASA Adv. Composites Design Guide, dated July 1983:
 
For single lap shear joints:
 
1/K = [ (t1 + t2)^2 ] / (Eb * D^3)   +   3.72 * [ 1 / (t1*E1) + 1 / (t2*E2) ]
 
For double lap shear joints:
 
1/K = [ (t1 + t2/2)^2 ] / (2 * Eb * D^3)   +  [ 2 / (t1*E1) + 1 / (t2*E2) ]
 
Where:
 
K = lateral stiffness of the fastener/joint
Eb = modulus of elasticity of the bolt
D = bolt diameter
t1 = thickness of outer plate
E1 = longitudinal modulus of elasticity of the outer plate
t2 = thickness of inner plate
E2 = longitudinal modulus of elasticity of the inner plate
 
 
For the axial stiffness of a fastener, I usually use K = EA/L
 
Greg
 
----- Original Message -----
From: [log in to unmask] href="mailto:[log in to unmask]">Muge Coker
To: [log in to unmask] href="mailto:[log in to unmask]">[log in to unmask]
Sent: Tuesday, November 21, 2000 12:57 PM
Subject: fastener stiffness representation



Hi!

I was wondering if anyone can give me some tips or point me to some references
on estimating stiffness coefficients for springs that represent fasteners in
finite element models.  To be more specific, if there are 3 springs between two
coincident nodes, one for each translational DOF, how would one go about
estimating the stiffness coefficients for these springs?   Thank you in advance.

M. Coker