Shear spring

Fig. 58 The rheological model of a polymer fibre consists of a series arrangement of an elastic tensile spring representing the chain modulus, ec, and a shear spring, g(t), with viscoelastic and plastic properties representing the intermolecular bonding...

Understanding of the mechanism of creep failure of polymeric fibres is required for the prediction of lifetimes in technical applications (Northolt et al., 2005). For describing the viscoelastic properties of a polymer fibre use is made of a rheological model as depicted in Fig. 13.103. It consists of a series arrangement of an "elastic" spring representing the chain modulus ech and a "shear" spring, yd with viscoelastic and plastic properties... 

In the first case [P t) is known], let us consider a standard solid that is viscoelastic in shear (spring in parallel with a Maxwell element) but elastic in compression. By assuming a step input, we obtain in the usual way... 

Erom the definition of the shear spring constant k of a laminated rubber/ steel spring, expressing the force F and deflection x in terms of shear stress and shear strain of the composite, we obtain... 

Fig. 21. Schematic presentation of the mechanical model of an oriented and crystalline fiber a chain spring in series coupling with a shear spring...

Fig. 19.7 Hysteretic model for axial (steel and concrete) and shear springs, (a) Steel spring, (b) Concrete spring, (c) Shear spring...

Regarding the shear springs, it is assumed that shear has no effects on the axial force and bending interaction. The hysteretic model for the shear spring is assumed to be multi-linear model, as shown in Fig. 19.7c, where Q is shear force and y the deflection of the shear wall due to shear deformation. The value of the shear force and deflection at cracking and yielding can be calculated according to the formulations proposed by the Architectural Institute of Japan. 

Figure 5. Schematic presentation of the model for elastic extension of a fibre a serial arrangement of a "chain spring" and a "shear spring".

If we now assume that the interfacial zone between the membrane and the elastic substrate is modelled by a "shear spring", then the integral equation expressing the displacement continuity becomes [6] (Figure 1)... 

Some results comparing solutions that correspond to various adherend and interface models discussed in this section are shown in Figure 1 where h3=0 and h3 0 refer to the "ideal interface" and "shear spring models, respectively (see [4] and [6]). 

More recently, Crisafulli and Carr (2007) proposed a new macromodel in order to represent, in a rational but simple way, the effect of masonry infill panels. The model is implemented as a four-node panel element which is connected to the frame at the beam-column joints. Internally, the panel element accounts separately for the compression and shear behavior of the masonry panel using two parallel struts and a shear spring in each direction. This configuration allows an adequate consideration of the lateral stiffness of the panel and of the strength of masonry panel, particularly when a shear failure along mortar joints or diagonal tension... 

Seismic Vulnerability Assessment Reinforced Concrete Structures, Fig. 15 Shear spring in series model using... 

The second theoretical approximation of Goland and Reissner is applicable to metal-to-metal adhesive bonded joints, whereas the first approximation assumes the joint to the monolithic. By treating the adhesive layer as an infinite number of shear springs and an infinite number of tension/compression springs in the y direction (a description first explicitly used by Cornell, 1953), soluble differential equations, assuming plane strain, to describe both the shear stress (t3x) and the normal stress (o-3y) distributions can be derived. 

This model treats the adherend as a rigid bar and the adhesive as continuous shear spring, which is based on the assumption that the adherends are so stiff that they do not deform and only the adhesive deforms as it is so soft, as shown in O Fig. 24.4a. In this model, the adhesive shear stress uniformly distributes within the adhesive and is given by ... 

Volkersen (1938) proposed a shear lag model, in which the adherend was modeled as a rod undergoing axial or longitudinal deformation only and the adhesive as a continuous shear spring. As shown in O Fig. 24.4b, the equilibrium and constitutive equations for adherends 1 and 2 are ... 

Figure 8 (Left) Force spectroscopy Shear forces between poly(ethylene propylene) end functionalized with a zwitterionic group (PEP-X) brush-bearing surfaces at separation D=7.0 0.4nm. Upper trace, applied lateral motion (AXo) of top mica surface lower trace, shear force fs transmitted to the lower mica surface. The horizontal broken line represents the midpoint between the shear forces on the back and forth cycles, and is therefore the position of zero shearforce when the shear springs are unbent. Inset (i) illustrates the chain configuration in the initial force rise regime a- b. Inset (ii) illustrates the relaxation of a chain following cessation of the applied motion at point d (lower trace) the thick part is as yet unrelaxed, while the thin part has relaxed by arm retraction. (Right) The variation of the plateau normalized shearforce (kinetic normalized friction force, fnin IR, in units of pN m" ) with sliding velocity. Vs, taken from traces as on the left. The cartoons indicate schematically the effect of the self-regulation mechanism on the interpenetration zone S (see also Section 2.24.3.5). Adapted from Tadmor, R. Janik, J. Fetters, L. J. Klein, J. Phys. Rev. Lett. 2003, 91,115503. ...

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