Adhesive-beam model

Goland and Reissner (1944) proposed an adhesive-beam model for the single lap joint shown in O Fig. 24.5a, in which a two-parameter elastic medium and Euler beams are used to model the adhesive and adherends, respectively. 

O Figures 24.9 and O 24.10 illustrate distributions of the shear and peel stresses for the composite SLJ predicted by the linear adhesive-beam model based on the Euler beam theory and the nonlinear adhesive-beam model based on the Timoshenko beam theory, respectively. 

In O Figs. 24.9 and O 24.10, the same edge moment factor at = 9 calculated using O Eq. 24.33 is used for both models. Figure 24.9 shows that there are slight differences in values of shear stress predicted by the linear adhesive-beam model based on the Euler beam theory and the nonlinear adhesive-beam model based on the Timoshenko beam theory. However, there exist significant differences in the adhesive peel stress for the two models as shown in Fig. 24.10, including peak values and distribution patterns. 

When the maximum stresses are determined and the allowable stresses are calibrated, failure criteria based on continuum mechanics can be used to predict adhesive joint failure. When the failure criteria in Eqs. 24.56a-c are used to predict joint failure, it is found (Adams 1989 Gleich et al. 2001 da Silva et al. 2006) that the failure trend for different adhesive thickness predicted by the adhesive-beam models proposed by Goland and Reissner (1944) is different from that of the experimental results. In theory, the maximum stresses increase with decreasing adhesive thickness. However, failure load decreases with increasing the adhesive thickness when it is relatively thick, such as fa > 0.1 mm. 

Three methods of mode partition may be used for fracture of adhesive joints (Femlund and Spelt 1991) the local method based on the stress singular field (Hutchinson and Suo 1992), the global method based on the beam theory (Williams 1988), and the method using the adhesive edge stresses based on the adhesive-beam model (Fernlund and Spelt 1991). 

Analytical approaches for adhesively bonded structures are presented in this chapter. Stress analysis for adhesively bonded joints is conducted using the classical adhesive-beam model and the other adhesive-beam models. Closed-form solutions of symmetric joints are presented and analytical procedures of asymmetric and unbalanced joints are discussed. Load update for single lap joints is investigated in detail. Numerical results calculated using the classical and other formulations are illustrated and compared. It is shown that the nonlinear adhesive-beam model based on the Timoshenko beam theory provides enhanced results compared to the linear adhesive-beam model based on the Euler beam theory for adhesively bonded composite structures. Analytical solutions of energy release rates for cohesive failure and delamination are presented, and several failure criteria are reviewed and discussed. 

Linear adhesive-Euler-beam model Pl Mk + t) 2cikMk + 1 ak Fti -2Mk)... 

Nonlinear adhesive-Timoshenko-beam model Pi A<0 [2akMk + Ft-, (1 - rk2)]Pa ccoth... 

Inelastic electron tunneling spectroscopy has been shown to be a useful method for the study of chemisorption and catalysis on model oxide and supported metal catalyst systems. There are in addition a number of proven and potential applications in the fields of lubrication, adhesion (48), electron beam damage (49,50), and electrochemistry for the experimentalist who appreciates the advantages and limitations of the technique. 

Although the model is frequently used to identify contributions of ambient VOCs from different sources [83], it has not been widely used for source apportionment of indoor VOCs. Won et al. [84], recently used the model to show that wall adhesive, caulking, I-beam joist and particleboard were the dominant sources of 24 indoor VOCs that were measured from a newly constructed building. However, similarities in the signatures of the various sources were observed. Such high correlations (collinearity) among measured chemical species could lead to large uncertainties in the estimated source contributions [83]. 

Corporation (Golden, CO). The reactor, 1.22m wide by 2.44 m, consisted of a fiberglass-reinforced plastic I-beam frame. A transparent fluoropolymer film, treated to accept adhesives, formed the front and back windows of the reactor. The film windows were attached to the reactor frame with foam tape coated on both sides with an acrylic adhesive. The catalyst, titanium dioxide (Degussa P25), was coated onto a structured, perforated polypropylene tubular packing commonly used in oil-water separators. The Ti02 was suspended in water as a slurry and sprayed onto the tubular supports with a new paint sprayer until the supports were opaque. Fluid modeling of airflow flnough the reactor showed that a 5.1 cm PVC manifold, located at the inlet and outlet of flie reactor, would provide an even flow distribution. Small (0.6 cm) holes, drilled into flie manifold at one inch intervals, provided the even flow distribution required for efficient contact of the contaminated air with the catalyst. 

In order that the bipartite beam should attain the higher bending strength as compared to a glulam beam of the same size and wood quality, the theoretical models indicate that the adhesive layers must exhibit a very special load-bearing behaviour. The adhesive manufacturer was able to produce some adhesive layers (like 027-2 in Fig. 7) which attained the requisite load-bearing behaviour for the ideal elastic adhesive layer. However, he was not quite able to fully attain the behaviour required for the ideal plastic adhesive layer. We decided to perform further tests with two selected adhesive layers (009-05 and 13-1 in Fig. 7), which came close to the desired performance needed for the ideal-plastic adhesive layer. There was a need to estimate the performance of bipartite beams with these adhesive connections. A programme based on the Excel solver function was developed to calculate the beam behaviour for these and other adhesive layers as follows. 

Verify the calculation models which had predicted improved bending performances for the bipartite beams with the optimized adhesive layers. 

The calculation model by integration (Section 2.4) had predicted the existence of an optimal span for the bipartite beam with adhesive layer 027. The mean values listed in Table 5 confirm that the maximum bending resistance is attained at a span of exactly 4 m increasing the span to 4.3 m or reducing it to 3.7 m leads to a reduced bending resistance. 

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