Strength
Determination of the maximum axial force for two pieces joined by adhesive can easily be determined using two equations that can be derived from the geometry of the problem by breaking the axial force component into a tensile force and shear force normal and parallel to the scarf joint. Shear strength is assumed to be equal to σ/2. The following equations need to be adjusted if the shear strength is greater than σ/2. The two equations that give a maximum axial force are F=σ/sin(α)^2 and F=σ/sin(2α) where α is the angle from the horizontal to the joint. Both should be evaluated for a given problem and the smaller F of the two is the magnitude of the maximum allowable axial force. The first equation accounts for failure in tension. The second equation accounts for failure in shear. Some special angles should be noted or the graphs of two equations should be compared on the same plot. The joint is weakest at α=90° due to tension limits and 45° due to shear limits. However, α=45° will be stronger than α=90° if shear strength is greater than σ/2. The joint is strongest between these two angles at 63.4°. The joint becomes stronger than 63.4° at 25.4°. At a shallow enough angle, strength of the joint continues to increase and failure will occur anywhere in the two pieces, possibly outside of the joint.
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