Contraction strains

Magnesium alloys have a Young s modulus of elasticity of approximately 45 GPa (6.5 x 10 psi). The modulus of rigidity or modulus of shear is 17 GPa (2.4 X 10 psi) and Poisson s ratio is 0.35. Poisson s ratio is the ratio of transverse contracting strain to the elongation strain when a rod is stretched by forces at its ends parallel to the rod s axis. 

Therefore, before a final wall structure can be selected, it is necessary to conduct a combined strain analysis in both the longitudinal and hoop directions. This analysis will consider thermal contraction strains, the internal pressure, and the pipe s ability to bridge soft spots in the trench s bedding. In order to do this we must know more about the inherent properties of the material we are dealing with that is a structure made up of successive layers of continuous filament-wound fiberglass strands embedded within a plastic matrix. We must know the modulus of the material in the longitudinal direction and the... 

Poisson ratio The ratio of transverse contraction strain to longitudinal extension strain in a stretched bar. The maximum possible value is 0.5 (around 0.5 for rubber, 0.33 for aluminum, 0.28 for common steels, and 0.1-0.4 for polymer foams). 

Because it gives large contraction strains compared with ferritic steels, it is, however, often recommended that large repairs are filled with weld metal of the 18Cr 10Ni type after buttering on to the ferritic steels with 29Cr 9Ni. It must be emphasised that ferritic weld metal should never he deposited on to weld metals of the stainless steel or nickel alloy types. 

As indicated in Figure 3.1, an elongation (or compression) in one direction, due to an axial force, produces a contraction (or expansion) in the lateral direction, i.e., at right angles to the direction of the force. The ratio of the lateral strain to the longitudinal strain is called Poisson s ratio v. It is an important elastic constant. For instance, a tensile stress, (t which produces a tensile strain, in the x-direction will also produce a contractive strain, Sy, in the y-direction, the two being related by... 

When, for example, a load is acting on an elastic body in x direction, it elongates not only in the direction of the acting load, but contracts laterally, as well. Thus, contraction must occur in the transverse y and z directions. Empirically, it was observed that transverse strains are constant fractions of longitudinal extension. The ratio of the lateral contractive strain to the axial strain is called Poisson s ratio , denoted by v and expressed as ... 

The compressive prestress caused by the contraction strain, is to be chosen so that no tangential tensile stresses will occur in the liner during operation. 

Let us consider the latter requirement first. Adhesives usually shrink as they harden. (Inorganic cements are exceptions.) Polymerization, the loss of solvent, even the cooling of a hot-melt may cause the glue line to contract. Strains are set up which induce the adhesive to pull away from the substrate. In addition, strains are produced when the adhesive joint is flexed. Various remedies may lessen the danger of failure from these causes ... 

Poisson s ratio The ratio of the contracting strain in the diameter direction to the elongation strain in the axial direction when a rod is pulled in tension. 

When a fiber is subject to a tensile stress, it does not just deform in the direction of the applied force, but also contracts in directions perpendicular to the force, as shown in Figure 15.2. This phenomenon is called the Poisson effect. Poisson s ratio (v), also called Poisson ratio or Poisson coefficient, is a measure of the Poisson effect. Poisson s ratio is the negative ratio of the transverse contraction strain to longitudinal tensile strain. 

From the tensile test, another important property is measured and that is the Poisson ratio value (t, which is a measure of the contraction strain 8, in the transverse direction when a strain e is applied in the longitudinal direction. Stretching takes place in the load direction but shortening takes place in the other two directions for isotropic materials. 

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