Axial stresses

Upwind Total stress = Bending stress + Axial stress -... 

Up wind Total stress = Axial stress - Radial stress... 

Mechanical and Electrical Stress. With reference to mechanical stress, axial and radial deformations are of potential concern. Excessive axial elongation is largely prevented by the conductor which serves as an... 

The current way to characterize the mechanical behaviour of soils or rocks consists in the study of the experimental load-displacement curve (F-d) or of the deviatoric stress-axial strain one (q-e). Local internal measurement (in the confining cell) of specimen axial displacement have been performed in order to exclude bedding errors at both ends of the specimen in contact with porous discs. In addition we can also use an external axial measurement to measure the piston axial displacement. In order to have a better precision axial displacement are measured using three miniature LVDT transducers, mounted at 120° from each other. The transducers are glued on the neoprene membrane in order to measure axial displacement in the central part of the specimen (figure 2). 

In order to understand the thermomechanical cycle of the syntactic foam under different test conditions better, the test results are presented in both 3-D and 2-D format. Typical 2-D axial stress-time and temperature-time curves for the foam confined by the nylon liner, programmed at 79 °C, and under 60% pre-strain level, and fully confined shape recovery are shown in Figure 3.29. Typical 3-D axial stress-axial strain-ternperamre thermomechanical cycles for the syntactic foam at a programming ternperamre of 71 °C, pre-strain level of 30%, and fully confined shape recovery are shown in Figure 3.30. Typical 3-D axial stress-axial strain-time behaviors at a programming temperature of 79 °C, pre-strain level of 30%, and fully confined shape recovery are shown in Figure 3.31. 

Fig. 1.47 Stress-strain plots obtained from the uniaxial/triaxial compression tests of SiC-N specimens (tr —axial stress, —axial strain, Si—lateral strain, —volumetric strain), a without confining pressure b confining pressure of 350 MPa [33], With kind permission of Professor Brannon...

Table 14.2 Peak stress, axial stress at 10% and 20% axial strain, and peak stress increase for sandy silt reinforced with one-pass carpet and fibrillated polypropylene fiber...

Musculoskeletal problems are injuries that may be a consequence of an accident at work. Therefore, this study revealed that the vast majority of workers at the shop, shown more symptoms of pain or discomfort in the area of the back and cervical region. In many work tasks performed daily, the column is maintained in stress (axial rotation) which becomes a factor conductive to situations of low back pain and degenerative lesions of the disks (Bolonha, et al., 2012). 

Coincident with the formation of a neck is the introdnction of a complex stress state within the neck region (i.e., the existence of other stress components in addition to the axial stress). As a consequence, the correct stress (axial) within the neck is slightly lower than the stress computed from the applied load and neck cross-sectional area. This leads to the corrected curve in Figure 6.16. 

When a stress equal to cr is applied to a fiber having just this critical length, the stress-position profile shown in Figure 16.7a results—that is, the maximum fiber load is achieved only at the axial center of the fiber. As fiber length I increases, the fiber reinforcement becomes more effective this is demonstrated in Figure 16 Jb, a stress-axial position profile for l>l, when the applied stress is equal to the fiber strength. Figure 16.7c shows the stress-position profile for I <... 

The axial stress is the only stress component which can be determined directly from measurement data. Hence, we have the boundary-value problem with equations (27), (29)-(31) and the boundary conditions (34)-(36). 

Let us assume that stress gradient in axial direction is present but smooth. Then we can use a perturbation method and expand the solution of equation (30) in a series. The first term of this expansion will be a solution of the plane strain problem and potential N will be equal to zero. The next terms of the stress components will contain potential N also. 

In integrated photoelasticity it is impossible to achieve a complete reconstruction of stresses in samples by only illuminating a system of parallel planes and using equilibrium equations of the elasticity theory. Theory of the fictitious temperature field allows one to formulate a boundary-value problem which permits to determine all components of the stress tensor field in some cases. If the stress gradient in the axial direction is smooth enough, then perturbation method can be used for the solution of the inverse problem. As an example, distribution of stresses in a bow tie type fiber preforms is shown in Fig. 2 [2]. 

Fig.4 Relation of reflective echo height F/B and axial compressive stress a (pseudo-bonding)...

The F/B of (a) decreases about 1 8dB in the maximum as the axial compressive stress is loaded, and is constant during an... 

Fig. 2. (a) Closed-end condition (b) open-end condition (4). The stress in the axial direction of a cylinder sealed under closed-end conditions is given by... 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

CompoundShrinka.g e. In its simplest form (Fig. 8a) compound shrinkage consists of machining the inner radius of an outer component I, (Qp so that it is smaller than the outer radius of an inner component II, The difference between the two is known as the radial interference 5. To assemble the cylinders, outer component I is heated and/or inner component II cooled so that the outer component can be sHpped over the inner as shown in Figure 8b. When the temperature of the assembly returns to ambient, a compressive stress (pressure) is generated across the interface which simultaneously compresses the inner and expands the outer component and, in so doing, displaces radius (r/j by Uj and radius ( jj by U, Unfortunately, it is difficult to carry out this operation without setting up stresses in the axial direction (32). 

The radial interference, 5, necessary to achieve pressure P may be calculated from the radial displacements Uj and Ujj generated during assembly, assuming that the shrinkage is carried out without generating an axial stress in either component. 

Probably the largest compound vessels built were two triple-wall vessels, each having a bore diameter of 782 mm and a length of 3048 mm designed for a pressure of 207 MPa (30,000 psi). These vessels were used by Union Carbide Co. for isostatic compaction unfortunately the first failed at the root of the internal thread of the outer component which was required to withstand the end load (40). A disadvantage of compound shrinkage is that, unless the vessel is sealed under open-end conditions, the end load on the closures has to be resisted by one of the components, which means that the axial stress in that component is high. 

Thermal Stresses. When the wak of a cylindrical pressure vessel is subjected to a temperature gradient, every part expands in accordance with the thermal coefficient of linear expansion of the steel. Those parts of the cylinder at a lower temperature resist the expansion of those parts at a higher temperature, so setting up thermal stresses. To estimate the transient thermal stresses which arise during start-up or shutdown of continuous processes or as a result of process intermptions, it is necessary to know the temperature across the wak thickness as a function of radius and time. Techniques for evaluating transient thermal stresses are available (59) but here only steady-state thermal stresses are considered. The steady-state thermal stresses in the radial, tangential, and axial directions at a point sufficiently far away from the ends of the cylinder for there to be no end effects are as fokows ... 

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