Transverse shearing stresses

Composite materials typically have a low matrix Young s modulus in comparison to the fiber modulus and even in comparison to the overall laminae moduli. Because the matrix material is the bonding agent between laminae, the shearing effect on the entire laminate is built up by summation of the contributions of each interlaminar zone of matrix material. This summation effect cannot be ignored because laminates can have 100 or more layersi The point is that the composite material shear moduli and G are much lower relative to the direct modulus than for isotropic materials. Thus, the effect of transverse shearing stresses. 

Study of transverse shearing stress effects is divided in two parts. First, some exact elasticity solutions for composite laminates in cylindrical bending are examined. These solutions are limited in their applicability to practical problems but are extremely useful as checl oints for more broadly applicable approximate theories. Second, various approximations for treatment of transverse shearing stresses in plate theory are discussed. 

The treatment of transverse shear stress effects in plates made of isotropic materials stems from the classical papers by Reissner [6-26] and Mindlin [6-27. Extension of Reissner s theory to plates made of orthotropic materials is due to Girkmann and Beer [6-28], Ambartsumyan [6-29] treated symmetrically laminated plates with orthotropic laminae having their principal material directions aligned with the plate axes. Whitney [6-30] extended Ambartsumyan s analysis to symmetrically laminated plates with orthotropic laminae of arbitrary orientation. 

The transverse shearing stress distribution is then approximated... 

Figure 6-23 Transverse Shear Stress Distribution along...

Now recognize an apparent contradiction in classical plate theory. First, from force equilibrium in the z-direction, we saw transverse shear forces and Qy must exist to equilibrate the lateral pressure, p. However, these shear forces can only be the resultant of certain transverse shearing stresses, i.e.. 

However, these transverse shearing stresses were neglected implicitly when we adopted the Kirchhoff hypothesis of lines that were normal to the undeformed middle surface remaining normal after deformation in Section 4.2.2 on classical lamination theory. That hypothesis is interpreted to mean that transverse shearing strains are zero, and, hence, by the stress-strain relations, the transverse shearing stresses are zero. The Kirchhoff hypothesis was also adopted as part of classical plate theory in Section 5.2.1. 

We can reexamine the beam problem to determine the distribution of the transverse shearing stress -c z- know that the resultant of -c z is V which we obtain from Equation (D.7), i.e.,... 

Accordingly, we find it difficult to determine the distribution of the transverse shearing stress in a beam, much less in a plate. Procedures for determining the approximate transverse shear stress distribution in plates are described in Section 6.5.2. 

The primary structural role of the face/core interface in sandwich construction is to transfer transverse shear stresses between faces and core. This condition stabilizes the faces against rupture or buckling away ftom the core. It also carries loads normally applied to the panel surface. They resist transverse shear and normal compressive and tensile stress resultants. For the most part, the faces and core that contain all plastics can be connected during a wet lay-up molding or, thereafter, by adhesive bonding. In some special cases, such as in a truss-core pipe. 

With most typical sandwich constructions, the faces provide primary stififhess under in-plane shear stress resultants (Nxy), direct stress resultants (N, Ny), and bending stress resultants (Mx, My) (Figure 7.48). Also as important, the adhesive and the core provide primary stiffness under normal direct stress resultants ( z), and transverse shear stress resultants (Q, Qy). Resistance to twisting moments (T, TyJ that is important in certain plate configurations, is improved by the faces. Capacity of faces is designed not to be limited by either material strength or resistance to local buckling. 

The transverse shear stress through the melt will be equal through the thickness and will be proportional to the applied rotation rate for a constant viscosity. Polymer melts are not ideal fluids (i.e., Newtonian and constant temperature), so in actual conditions, the transverse shear rate will not be constant through the thickness of the extrudate between the cylinder walls, but this is a good approximation. 

In the GHS model, the no-slip condition is assumed between the mold surface and the charge surface layer. Hence, the transverse shear stress across the narrow gap between the mold surfaces is the dominant factor that drives material flow, and the in-plane stresses are negligible. The material flow configuration is illustrated in Fig. 3.28. 

The tangential transverse shear stress at any point on a section on both sides of the stiffener is ... 

T - transverse shear stress y - distance from neutral axis V - applied lateral shear load b - width of beam at section Q - 1 moment of area of partial section I - 2" moment of area... 

Fig. 9. When subjected to lateral shear loads, transverse shear stresses are required within the beam to allow buildup of axial stresses associated with changing bending moment.

Fig. 2.15 Cylinder in pure torsion, a element free body stress state, b brittle behavior with helicoidally failure, c and d ductile failure activated by either longitudinal or transverse shearing stress...

The American engineer A. M. Wahl has shown that the combined effect of curvature of the wire and transverse force results in a transverse shear stress that is not exactly given by the second term of the above equations. The complete equation for the maximum stress in a coil spring may be calculated as... 

Adams and Peppiatt [60] have considered the problem of the in-plane transverse stresses and to ascertain the magnitude of such stresses they have used experimental models and analytical and finite-element analyses solutions of the Volkersen theory, but in three dimensions. They demonstrated that Poisson s ratio strains generated in the substrates cause shear stresses, T13, in the adhesive layer and tensile stresses, 0-33, in the substrate acting transverse to the direction of the applied load, but in the plane of the joint. For metal-to-metal joints the transverse shear stress, has a maximum value of about one-third of the maximum longitudinal shear stress, ri2(max), and this occurs at the corners of the overlap. This, therefore, enhances the shear stress concentration which exists at this point due to the effects described above. Bonding substrates of dissimilar stiffness produces greater stress concentration in the adhesive than when similar substrates are employed. 

The diagrams for transverse shear stresses across the thickness of two five-ply packages, loaded with more prolonged impulses, are presented in Fig, 6, The division was as follows = 30 6 sublayers making up a layer. 

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