Discontinuity stress

Appendix 4 gives definitions and rules for stress analysis for shells, flat and formed heads, and tube sheets, layered vessels, and nozzles including discontinuity stresses. Of particular importance are Table 4-120.1, Classification of Stresses for Some Typical Cases, and Fig. 4-130.1, Stress Categories and Limits of Stress Intensity. These are veiy useful in that they clarify a number of paragraphs and simphfy stress analysis. 

Other factors which promote brittleness are geometrical discontinuities (stress concentrations) and aggressive environments which are likely to cause ESC (see Section 1.4.2). The absorption of fluids into plastics (e.g. water into nylon) can also affect their creep rupture characteristics, so advice should be sought where it is envisaged that this may occur. 

It can be seen by examination of equations 13.7 and 13.9, that for equal stress in the cylindrical section and hemispherical head of a vessel the thickness of the head need only be half that of the cylinder. However, as the dilation of the two parts would then be different, discontinuity stresses would be set up at the head and cylinder junction. For no difference in dilation between the two parts (equal diametrical strain) it can be shown that for steels (Poisson s ratio = 0.3) the ratio of the hemispherical head thickness to cylinder... 

Where the vessel wall will be at a significantly higher temperature than the skirt, discontinuity stresses will be set up due to differences in thermal expansion. Methods for calculating the thermal stresses in skirt supports are given by Weil and Murphy (1960) and Bergman (1963). 

Where the vessel wall will be at a significantly higher temperature than the skirt, discontinuity stresses will be set up due to differences in thermal expansion. The British Standard BS 5500 requires that account should be taken of the thermal discontinuity stresses at the vessel to skirt junction where the product of the skirt diameter (mm), the skirt thickness (mm), and the temperature above ambient at the top of the skirt exceeds 1.6 X 10 (mm °C). Similar criteria are given in the other national codes and standards. Methods for calculating the thermal stresses in skirt supports are given by Weil and Murphy (1960) and Bergman (1963). 

Figure 9-33a shows the predicted shear stress as a function of strain for the initial foam orientation depicted in Fig. 9-32. The stress grows continuously until at y = 1.15 a T1 reorganization occurs which brings the cell structure back to its starting state, and the stress jumps back to zero. Thereafter, the stress history repeats itself. Similar periodic stress patterns and stress jumps have been predicted for the three-dimensional tetrakaidecahedron foam model (Reinelt 1993). If the initial orientation is rotated through an angle of r/12 with respect to that shown in Fig. 9-32, the stress history also has jumps, but is aperiodic (see Fig. 9-33b). Aperiodic behavior is the norm, and periodic stress histories occur only for special initial orientations (Kraynik and Hansen 1986). These unsteady, discontinuous stress...

Strictly speaking, a wave in a continuous medium is a propagating surface of discontinuity. The propagation involves the motion of such a surface. In the present context, we are concerned with the propagation of discontinuous stress and strain waves. That implies the propagation of discontinuities in the first derivative of the displacement. Waves of this type are... 

Small molecular mass liquid crystals do not respond to extension and shear stress. Liquid crystalline polymers may exhibit a high elastic state at some temperature due to the entanglements. However, the liquid crystalline network itself is an elastomer, showing rubber elasticity. In the presence of external stress, liquid crystalline networks deform remarkably and then relax back after the release of stress. The elasticity of liquid crystalline networks is more complicated than the conventional network, such as the stress induced phase transition, the discontinuous stress-strain relationship and the non-linear stress optical effect, etc. 

T >TC, e.g., T/Tc> = 1.02, an external stress induces a phase transition accompanied by spontaneous extension. The discontinuous stress-strain relationship and an associated critical point are observed. 

In years past, the ellipsoidal dished head was so much more available than the hemispherical dished head that the hemispherical head was limited primarily to small-diameter vessels. But vessel closure manufacturers have increased the nimiber of dies stocked for hemispherical head production and these are now becoming more widely used. If it were not for the cost of forming, the engineer would usually choose the hemispherical closure for the top head of a tall vertical vessel since it has the least weight and the lowest discontinuity stresses and is therefore the strongest. 

Discontinuity stresses are only considered as secondary stresses if their extent along the length of the shell is limited. Division 2 imposes the restriction that the length over which the stress is secondary is tyRmt. Beyond this distance, the stresses are considered as primary mean stresses. In a cylindrical vessel, the length VR, t represents the length over which the shell behaves as a ring. 

Vessel sections of different thickness, material, diameter, and change in directions would all have different displacements if allowed to expand freely. However, since they are connected in a continuous structure, they must deflect and rotate together. The stresses in the respective parts at or near the juncture are called discontinuity stresses. Discontinuity stresses are necessary to satisfy compatibility of deformation in the region. They are local in extent but can be of... 

Since discontinuity stresses are self-limiting, allowable stresses can be very high. One example specifically addressed by the ASME Code, Section VIII, Division 1, is discontinuity stres.ses at cone-cylinder intersections where the included angle is greater than 60°. Para. l-5(e) recommends limiting combined stresses (membrane -t- discontinuity) in tile longitudinal direction to 4SE and in the circumferential direction to 1..5SE. 

ASME Code, Section VIII, Division 2, limits the combined stress, primary membrane and discontinuity stresses to 3Sn, where S, is the lesser of %Fy or U.T.S., whichever is lower. 

There are two major methods for determining discontinuity stresses ... 

See References 2, Article 4—7 6, Chapter 8 and 7, Chapter 4 for detailed information regarding calculation of discontinuity stresses. 

Toriconical transitions are advisable to avoid the high discontinuity stresses at the junctures for the following conditions ... 

Assume effects of radial loads as additive to those due to internal pressure, even though the loadings mav be in the opposite directions. Although conservative, they will aecount for the high discontinuity stresses immediately adjaeent to the lugs. 

Cone-cylinder intersections are areas of high discontinuity stresses. For this reason the ASME Code requires reinforcement at each junction and limits angle a to 30° unless a special discontinuity analysis is performed. This procedure enables the designer to take into account combinations of loads, pressures, temperatures, and materials for cones where a is less than or equal to 30° without performing a discontinuity analysis and fulfill all code requirements. 

The local stresses as outlined herein do not apply to local stresses due to any condition of internal restraint such as thermal or discontinuity stresses. Local stresses as defined by this section are due to external mechanical loads. The mechanical loading may be the external loads caused by the thermal growth of the attached piping, but this is not a thermal stress For an outline of external loeal loads, see Categories of Loadings in Chapter 1. 

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