Bending stress secondary

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

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). 

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. 

This procedure determines the bending stress in the stiffener only. The stresses in the vessel shell should be checked by an appropriate local load procedure. These local stresses are secondary bending stresses and should be combined with primary membrane and bending stresses. 

Oblique fractures result from shear stresses, secondary to axial loading. Pure oblique fractures, however, are rare and, more commonly, there is a minor transverse element to the fracture (Fig. 8.4). Such injuries are due to uneven bending. The middle and distal or proximal end of the bone are fixed and the free end is moved. 

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. 

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... 

Q = secondary membrane plus bending stress as defined in Table 8.2... 

Example 10.6. A vessel flange uses 16-2-in. diameter bolts. Flange stress calculations indicate that a flange thickness of r = 4.5 in. is adequate. The bolt circle diameter is C = 22.5 in. Will secondary bending stresses be developed ... 

Because the actual spacing is less than the maximum spacing without a penalty, no secondary bending stresses are developed. ... 

Example 10.7. Suppose a vessel requires 24-2 -in. diameter bolts on a flange that is 5.5 in. thick. What is the maximum bolt circle that will not cause secondary bending stresses The minimum bolt spacing for 2 -in. diameter bolts is 5 m. 

The Cm and (Cm+cfb) values for the first three load cases, as indicated in the Table 1, are the primary membrane (Pm) and primary membrane plus bending stress intensity (Pm+Pb)-(Cm+Cb) for case 4 is primary plus secondary stress intensity (Pm+Pb+Q)-... 

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. 

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