Joints flexible

The energy balance approach is generally the most applicable to flexible joints, since away from the crack tip the adhesive or substrates may not exhibit linear-elastic behaviour and so the stress intensity factor is invalid. Of course, in those cases where linear-elastic behaviour is observed then either approach may in principle be adopted. Essentially, to obtain an expression for the value of the adhesive fracture energy, Gc, for a particular geometry requires a solution to the left-hand side of Equation 7.3 to be deduced. 

If no other external work is done the input energy (i) must be balanced by those of (ii), (iii) and (iv) giving  

If the strain in the tab can be neglected, for example if (i) the peel forces are very low or (ii) a fabric- or plastic-backed rubbery adhesive or a relatively thick plastic or metallic substrate is the peeling member, then  

More recently Andrews and Stevenson [71] have expressed these equations as  

Other geometries have also been developed to determine Gc for rubbery adhesives and include a cone-test specimen [69], a torsion test which results in mode III failure [66] and the adherence of spheres to rubbers [77-80]. 

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Figure 1.5 Placement of successive polymer segments connected by perfectly flexible joints. In (a), the ith and (i + l)th bond can be moved through angles 0 and 6 so that carbon 3 can lie anywhere on the surface of a sphere. In (b), the pattern is illustrated for a longer portion of chain.

A flexible Joint may also htive to connect two non-aligned sections of current-carrying conductors, which may also be different in configuration and size (Figure 29.10). They may therefore be longer than an expansion... 

The purpose of a flexible joint is thus to make an electrical connection and to absorb the busbar s expansion and vibrations of the generator or the transformer and to prevent transmission of these vibrations to the bus system and mounting structure. 

Expansion joint A flexible joint in a run of pipework or ductwork that allows expansion or contraction. 

Somewhat surprisingly, a 2 1 styrene ly more flexible than polystyrene itself (9 ) 7 styrene (SMMS) units evidently constitute flexible joints which permit an overall freedom of motion despite local constraints at SMS units. The greater length of the C-S bond compared to that of the C-C bond (0.180 vs. 0.154 nm) may also contribute. 

An alternative route to implement local MC moves is provided by the literature on (inverse) kinematics, such as on control systems for robotic arms composed of flexible joints [27,87]. Here, the problem is transformed to either a set of linear equations [27] or finding the roots of a high-order polynomial [87] at comparable computational expense. One of the benefits of such an approach is the ability to introduce arbitrary stiff segments into the loop, that is, the degrees of freedom used for chain closure do not have to be consecutive. Conversely,... 

Random-coil sequences left in a predominantly helical chain can be a cause of flexibility of the molecular rod unless they are too short, and will lead to deviations of the shape-dependent properties of the molecule from those expected for rigid rod. Too short a random-coil sequence may not act as a flexible joint partly because of hindered rotations of the single bonds contained... 

The physical significance of 2 in Equation (73) is somewhat harder to define. At first glance it appears to be the length of the repeating unit, about 0.25 nm for a vinyl polymer. We must remember, however, that the derivation of Equation (73) assumed that the coil was connected by completely flexible joints. Molecular segments are attached at definite bond angles, however, so an actual molecule has less flexibility than the model assumes. Any restriction on the flexibility of a joint will lead to an increase in the dimensions of the coil. The effect of fixed bond angles on the dimensions of the chain may be incorporated into the model as follows. 

Control of flexible joints and fragile devices in hazardous service... 

Fig. 3. The contact area in the aiP2 subunit interface showing the switch and flexible joint regions of the hemoglobin molecule. [Adapted from Dickerson and Geis (1983) illustration copyright by I. Geis].

Finally, the dotted curve in Fig. 13 traces the relation between v and vs for rigid prolate ellipsoids of revolution [see Peterlin (16) or Frisch and Simha (6 )] with axial ratio proportional to molecular weight. This curve lies very far from those for flexible molecules except for very low values of the axial ratio p. This seems to exhaust the available information of the type represented by Fig. 13. In connection with the behavior of DNA and perhaps other naturally occurring macromolecules, it would be interesting to have calculations for rods with one or two or at most a small number of flexible joints, such as might correspond to almost completely helical structures [see Section III D]. In spite of the absence of theories for this and possibly other relevant molecular models, it is often possible to arrive at useful indications of conformation by comparing the experimental data with Fig. 13. 

Flexible or expansion joints in piping should be eliminated wherever possible. Flexible joints and expansion joints are any corrugated or flexible transition devices designed to minimize or isolate the effects of ... 

Flexible joints should not be used as a correction for piping errors or to correct misalignment. 

Swing lines made up of pipe with flexible joints and provided with a counterbalance is the preferred method of transferring hazardous chemicals into or from a tank vehicle. Hoses, no matter how thoroughly reinforced, have lower pressure capability and are easily damaged in use. Rupture of transfer hose is a not uncommon cause of employee injury or spill of product. Metallic tubing with braided exterior has admirable qualities, but a sharp bend, particularly near the end, causes weakening and failure, which is often neglected before the failure. 

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