By Pocius A.V., Dillard D.A.
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Additional info for Adhesion science and engineering
For built-up or laminated beams, illustrated in Fig. 10, these stresses may be carried through mechanical fasteners such as nails, bolts, and rivets, through discrete or continuous welds, or through adhesives joining the components. These load-transferring components allow the individual beams to act together as a single beam rather than as a combination of flexible, independent beams. This composite action is of critical importance in obtaining lightweight, efficient structural elements. A. Dillard 20 V Y 7 _I- 3 v 2 bh =-- transverse shear stress y - distance from neutral axis V - applied lateral shear load b - width of beam h - depth of beam b Fig.
For the case of torsion of circular tubes bonded to tubes or shafts, similar relationships are found involving the second polar moments of area of the individual tubes . Extensions to materials reinforced with fibers or even to steel-reinforced concrete are possible. The load is transferred from the reinforcing fiber to the surrounding material through a shear lag process that has been modeling in a variety of ways depending on the boundary conditions and the assumptions made [45,46]. Chapter 16 will provide additional details on these applications to fiber-reinforced systems.
The upper and lower adherends are denoted by 1 and 2, respectively. Each adherend has a Young’s modulus Ei and a thickness ti. The adhesive has a shear modulus of G and a thickness of h. The joint length is L, as shown in Fig. 12a. Solving this statically indeterminate problem involves the equilibrium equations based on a differential element as shown in Fig. 12a: d ~= ~ -21 - dx &I 1 -- -t, t, dx the kinematic expressions t2 t2 6 dx h’ and the constitutive relationships di3 y=- -=&1-&2, SI = g ~ / E i , ~2 =dEz, Y =t/G, (13) where 01 and ~ 7 2are the axial stresses in the upper and lower adherends, respectively, SI and ~2 are the corresponding axial strains, and 8 represents the relative horizontal displacement between the upper and lower adherend across the bondline; each is a function of position, x, along the length ofthe bond.