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The ASME Boiler & Pressure Vessel Code (BPVC) is an American Society of Mechanical Engineers (ASME) standard that regulates the design and construction of boilers and pressure vessels. These are real world working standards developed for safety of vessels which were developed long time ago after several accidents and causalities were happened. It is common pool for every vessel designers as well as manufacturer across the world. As time passes, the vessel no longer simpler but the complexity in terms of size & shape, welding connections, materials are being observed. Furthermore, stress assessment thorough finite element analysis tool are developed and being used which allows to see stresses inside the vessel components. Nowadays, Finite element analysis is no longer a magical tool which were used earlier only in research labs. Many industries have developed FEA software’s which are being used for design validations & optimizations. Though the vessel calculations are performed with FEA software’s, but analyzing the stresses found in the pressure vessel is still difficult task. It needs skills to identify high stress locations and justify the results, furthermore the pressure vessel validation is performed with respect to ASME guidelines. FEA tools gives different types of stresses in vessel which have different safety implications. This blog article explains, how the stress linearization tool works to separate various stresses like membrane, bending & peak. Stress classification Line: A Stress Classification Line or SCL is a straight line running from the inside to outside of a vessel. It is perpendicular to both inside and outside surfaces of the vessel. In FEA, stresses are calculated at nodal points and SCL is passing through these nodes. Thus, SCL tool takes stresses at each and every point along path and segregates into different stress components like, membrane stress, bending stress, membrane plus bending, peak and total stresses. These membrane and bending stresses are developed on cross sections through the thickness of a component. These sections are called stress classification planes (SCPs). SCPs are flat planes that cut through a section of a component. Figure 1 presents the SCL & SCP on nozzle shell junction component. [caption id="attachment_187" align="aligncenter" width="328"] Figure 1: Stress Classification Line & Stress Classification Plane[/caption] Membrane Stress: Membrane stresses are nothing but average stress across the thickness. Membrane stresses are always positive and it is difficult to predict whether they are positive or negative as magnitude are provided but directions are missing. Bending Stress: Bending stress is the linearly varying stress through the thickness, which is difference in stresses from inside to outside surface. Membrane + Bending: As name suggest, these stresses are sum of membrane and bending stresses. Peak stress: These stresses are highest stress found along the SCL. This is also always positive but not necessarily higher than the membrane + bending number. Peak stress is usually used to determine the fatigue life of the components at respective SCLs. Stress Categorization and Limits as Per ASME: If you are doing stress assessment as per ASME, ASME VIII-2 chart Figure 5.1 provides the stress categorization and their respective allowable limits. Here, stresses are further categorized as primary general membrane, primary local membrane, primary bending, secondary membrane plus bending and peak stresses. This table provides guides for maximum stresses allowed at various different locations. It is used by most of vessel engineer and analyst to predict the component pass or fail judgment. Though the stress category are clearly mentioned in the chart but it is difficult to interpret the stresses will lie in which category? As we know that membrane stress is average stress but if you refer this table 5.1 of ASME, you might confuse with the terminology and allowable limits used and hence the codes experience and correct judgments are needed to qualify the components. Refer Figure 2 for stress categorization and their limits as per table 5.1 of ASME section VIII-2. [caption id="attachment_188" align="aligncenter" width="300"] Figure 2: Stress Categorization and Equivalent Stress Limits[/caption] Primary Stress: A normal or shear stress developed by the imposed loading which is necessary to satisfy the laws of equilibrium of external and internal forces and moments. The basic characteristic of a primary stress is that it is not self-limiting. Primary stresses which considerably exceed the yield strength will result in failure or at least in gross distortion. General primary membrane equivalent Stress (Pm): This stresses are found away from junction and are compared with directly with allowable limits. Local primary membrane equivalent Stress (PL): This stresses are assumed to be at critical locations like junctions, supports, sudden change in cross section, other geometric irregularity, etc. and are compared with SPL (1.5*S). Limits are higher for local membrane due to fact of, additional stresses will come due to irregular sections. Primary bending Stress (Pb) For example, for a vessel subject to internal pressure with an elliptical head; Pm equivalent stresses occur away from the head to shell junction, and PL and equivalent stresses occur at the junction. Secondary stress: A normal stress or a shear stress developed by the constraint of adjacent parts or by self-constraint of a structure. The basic characteristic of a secondary stress is that it is self-limiting. Local yielding and minor distortions can satisfy the conditions that cause the stress to occur and failure from one application of the stress is not to be expected. Examples of secondary stress are a general thermal stress and the bending stress at a gross structural discontinuity. Peak Stress: The basic characteristic of a peak stress is that it does not cause any noticeable distortion and is objectionable only as a possible source of a fatigue crack or a brittle fracture. Examples of peak stress are: the thermal stress in the austenitic steel cladding of a carbon steel vessel, the thermal stress in the wall of a vessel or pipe caused by a rapid change in temperature of the contained fluid, and the stress at a local structural discontinuity.

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