Membrane stress secondary

In the stress analysis of pressure vessels and pressure vessel components stresses are classified as primary or secondary. Primary stresses can be defined as those stresses that are necessary to satisfy the conditions of static equilibrium. The membrane stresses induced by the applied pressure and the bending stresses due to wind loads are examples of primary stresses. Primary stresses are not self-limiting if they exceed the yield point of the material, gross distortion, and in the extreme situation, failure of the vessel will occur. 

The thin-wall bellows element should be designed for membrane stresses to conform to code-allowable stresses. The sum of membrane and secondary bending stresses should not exceed 1.5 times the yield stress in order to prevent the collapse of the corrugations caused by pressure. Bellows subjected to external pressure can be analyzed in a manner similar to a cylinder, utilizing an equivalent moment of inertia. The fatigue life can be estimated based on the sum of deflections and pressure stresses as compared to S/N curves based on bellows test data or using the curves in B31.3 Appendix X, Metal Bellows Expansion Joints. Formulas for the stress analysis of bellows are available in the Expansion Joints Manufacturing Association (EJMA) Standards (37). 

Local primary membrane stress, Pl. Local primary membrane stress is not technically a classification of stress but a stress category, since it is a combination of two stresses. The combination it represents is primary membrane stress, P, , plus secondary membrane stress, Qn produced from sustained loads. These have been grouped together in order to limit the allowable stress for this particular combination to a level lower than allowed for other primary and secondary stress apphcations. It was felt that local stress from sustained (unrelenting) loads presented a great enough hazard for the combination to be classified as a primaiy stress. 

Primary local membrane stresses are a combination of membrane stresses only. Thus only the membrane stresses from a local load are combined with primary general membrane stresses, not the bending stresses. The bending stresses associated with a local loading are secondary stresses. Therefore, the membrane stresses from a WRC-lOT-ri pe analysis must be broken out separately and combined with primary general stresses. The same is true for discontinuity membrane stresses at head-shell junctures, cone-cylinder junctures, and nozzle-shell junctures. The bending stresses would be secondary stresses. 

This analysis combines the primary membrane stress due to pressure with the secondary bending stress resulting from the flexure of the nozzle about the hard axis. 

On the other hand, the stresses from the inward radial load could be either a primary stress or secondary stress. It is a primary stress if it is produced from an unrelenting load or a secondary stress if produced by a relenting load. A general primary membrane stress will not redistribute upon yielding, whereas a primary local membrane stress will, and for a secondary stress the load will relax once slight deformation occurs. 

Primary local membrane stress, Pl- A primary local membrane stress is produced either by design pressure alone or by other mechanical loads. Primary local membrane stresses have some self-limiting characteristics like secondary stresses. Since they are localized, once the yield strength of the material is reached, the load is redistributed to stiffer portions of the vessel. However, since any deformation associated with yielding would be unacceptable, an allowable stress lower than a secondary stress is assigned. The ability of primary local membrane stresses to redistribute after the material yields allows for a higher allowable stress but only in a local area. 

The bending stresses associated with a local loading are almost always classified as secondary stresses. Therefore, the membrane stresses from a WRC-107-type analysis must be broken out separately and combined with general primary stresses due to internal pressure, for example. 

Within the context of local primary membrane stress, Pl, as well as secondary stress, Q, the discontinuity effects need not be elaborated. The structural discontinuity can be either gross or local. Gross structural discontinuity is a region where a source of stress and strain intensification affects a relatively large portion of the structure and has a significant effect on the overall stress or strain pattern. Some of the examples are head-to-shell and flange-to-shell junctions, nozzles, and junctions between shells of different diameters or thicknesses. 

The stress classifications for various parts of a pressure vessel are indicated in Table 4.1 and are reproduced from the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code Sections III and VIII. It can be observed that the membrane stress is considered primary for mechanical loads. Eor a number of geometries and loading situations, the bending stress is considered secondary. The bending stress is considered primary when the net section experiences the applied bending moment. 

Guideline 4 establishes the global locations for assessment of stresses, and states that the general primary membrane stress intensity, should be evaluated remote from a discontinuity whereas the primary membrane plus bending stress intensity, Pl + Pb, and primary plus secondary stress intensity, P + Q, should be evaluated at a discontinuity. 

The basic characteristic of secondary stress is that it is self-limiting. Minor yielding will reduce the forces causing excessive stresses. Secondary stress can be divided into membrane stress and bending stress, but both are controlled by the same limit stress intensities. Typical examples of secondary stress are thermal stresses and local bending stresses due to internal pressure at shell discontinuities. 

Primary plus secondary stress intensity. The maximum stress intensity S as based on the primary or local membrane stresses plus the primary bending stress plus the secondary stress (cr m or ctl + (7b -f X) 2) cannot exceed the... 

From Tables 8.1 and 8.2 the maximum allowable local membrane plus secondary stress is equal to... 

Primary stresses, including general primary membrane stress, local primary membrane stress, and primary bending stress Secondary stresses Peak stresses... 

In BWRs, all stresses (pressure difference, hydraulic vibrations, contact pressure of spacers, etc.) are first evaluated and categorized into primary membrane stress, primary bending stress, and secondary stress. The maximum allowable stresses are set for each of these categorized stresses at both normal and abnormal transients. The maximum allowable stresses in the Super LWR fuel rod design are determined similarly. 

Changes in mitochondrial stmcture are very relevant during X-ray induced apoptosis. A few hours after irradiation, a hyperpolarisation of A /m is noticed. This likely represents the attempt to restore the depleted ATP levels, stimulating the oxidative burst of surviving mitochondria. If this secondary oxidative stress overcomes the threshold given by mitochondrial thiols, mitochondrial cardiolipin is oxidized and mitochondrial inner membrane allows the leakage of A /m with the consequent initiation of the execution phase. 

A variety of responses can be initiated by the direct interaction of metals with cellular components. Membrane damage and enzyme inhibition are examples of such a metal effect. Above a certain threshold concentration of metals in the cell, its physiological state is irreversibly changed (Van Assche et al., 1988). This response is reflected by an increase in capacity (activity under non-limiting substrate and coenzyme concentrations) of certain enzymes. This increase in capacity is generally called enzyme induction. These secondary, indirect effects of metals are considered to play an important role in the stress metabolism induced by toxic metal concentrations. 

---