Question 2.12: Several short pieces of timber are to be glued together end-......
Several short pieces of timber are to be glued together end-to-end to form a single longer piece of timber. Figure 1 shows a simple diagonal splice joint. The glue that is to be used in the splice joint is 50% stronger in shear than in tension. Is it possible to take advantage of this higher shear strength by selecting a splice angle θ such that the magnitude of the average shear stress on the joint is 50% higher than the average normal stress? If so, what is the appropriate angle?
Plan the Solution The stresses on an oblique plane are given by Eqs. 2.29 and plotted in Fig. 2.34. From Fig. 2.34 it appears that the answer is, Yes, the cut should be somewhere between 50° and 60° (or between -50° and -60°)
σ_n = \frac{N}{A_n} = σ_x \cos^2 θ\tau_{nt} = \frac{V} {A_n} = -s_x cos θ sin θ (2.29)
We want to determine a splice angle θ_s such that |\tau _{nt}(θ_s)| = 1.5σ_n(θ_s) Therefore, from Eqs. 2.29 we have
1.5(σ_x \cos^2 θ_s)= \pm σ_x \cos θ_s \sin θ_sor
\tan θ_s = \pm 1.5Therefore, the shear stress exceeds the normal stress by 50% on planes oriented at
θ_s = \pm 56.3°Review the Solution When θ = 0 we get no shear stress on the splice joint. Therefore, a “long” splice, like one at \pm 56.3°, makes sense as a splice on which shear stress predominates over normal stress. The stresses for these two cases are illustrated in Fig. 2.
