Aluminium Design and Construction John Dwight

11.4.11 Resistance calculations for bonded joints
Resistance calculations are needed in the earlier stages of design, even
when a bonded joint is going to be eventually validated by testing.
Such calculations pose problems because:
1. The stress transmitted by the adhesive is non-uniform, with peak
values at critical points.
2. The adhesives used with aluminium are not generally ductile enough
to allow redistribution of these peak stresses.
3. The shear strengths quoted for adhesives are only typical. Also they
are based on the standard lap-test which is not ideal (Section 11.4.6).
When a joint is to be checked by calculation, the basic requirement is
that the peak shear stress q1 transmitted by the adhesive, under factored
loading, should satisfy:
(11.26)
where p v is the limiting shear stress for the adhesive and � m the material
factor. The determination of suitable values for the three quantities
involved is considered below.
(a) Stress arising (q1 )
The load transmitted by a bonded joint can be transverse or longitudinal,
or a combination thereof. In each case, the adhesive is stressed in shear.
The mean value q of the shear stress in the adhesive can usually be
found using conventional engineering formulae. But this is not the same
as the peak value q1 which is what matters. Figure 11.19(a) shows the
typical stress variation in a simple lap joint with peak stresses at the
ends. For a simple joint of this kind, the difference between q1 and q is
considerable and not to be ignored, since the adhesives used are not
generally ductile enough to allow full redistribution to occur. One outcome
of this is that little advantage is gained by increasing the length l of
such a joint beyond a certain point.
The situation can be improved by tapering the aluminium, which
reduces the peakiness of the stress pattern (Figure 11.19(b)). Modifying
the joint in such a way can reduce the peak stress to a value much
closer to the mean, provided the taper is correctly designed.
The determination of q1 and the design of the taper (if used) is typically
achieved by employing an elastic finite-element program, although a
simpler analysis is possible in some cases. An essential input to such
calculations is the shear-flexibility of the adhesive, which is a function of
its shear modulus G and the glue-line thickness tg . In assuming a suitable
value for the latter, it is important to realize that the ‘peakiness’ of the
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