Primary stress bending

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. 

Primary general bending stress, P/,. Primary bending stresses are due to sustained loads and are capable of causing collapse of the vessel. There are relatively few areas where primary bending occurs ... 

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 primary stress intensity in the ASME Boiler and Pressure Vessel Code is intended to prevent uncontrolled plastic deformation and to provide a nominal factor of safety on the ductile burst pressure. These limits are based on the principles of limit design. The material is assumed to be elastic-perfectly plastic. For a straight bar in tension, a load producing yield stress, Sy, results in a collapse. If it is loaded in bending, collapse does not occur until the yield moment has been increased by the shape factor of the section. 

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

An optimum layout is arrived at, based on the requirement of flexibility to accommodate thermal expansion and the availability of space in the cold pool and compactness. The optimized layout consists of a short straight portion connected to a single curvature bend having a radius equal to 945 mm (1.5 times diameter). Stress analysis has been carried out for an internal pressure of 0.8 MPa and seismic loads imposed at the nozzle in the horizontal direction (peak value of 20 t under SSE). Analysis shows that the maximum Pm and (Pm+Pb) values are 76 and 80 Mpa, respectively, for the pipe wall thickness of 8 mm. These values are less than the primary stress limits of RCC-MR, 104 and 156 Mpa respectively. Considering the possible wall thinning during fabrication of the pipe bend, a plate thickness of 10 mm is used for the manufacture of the pipes, ensuring the minimum requirement of the wall thickness of 8 mm after fabrication. 

The SMI, SM2, and SMS output parameters are section bending moments in the piping about the. three local element axes (x, y, z). These three output parameters are taken from the ABACUS output and used in ASME B PV Code Section III Div I - NB piping limit equations. The primary and the primary plus secondary stress range limits are evaluated for this anaiysis. The primary stress limit is evaluated for the pressure only load case for the cases listed in Table 9-32. The primary plus secondary stress limit is a limit on the stress intensity range. This requires a stress state at each end of the range. The range used to evaluate the limit is ... 

The Code establishes allowable stresses by stating in Para. UG-23(c) that the maximum general primary membrane stress must be less than allowable stresses outlined in material sections. Further, it states that the maximum primary membrane stress plus primary bending stress may not exceed 1.5 times the allowable stress of the material sections. In other sections, specifically Paras. l-5(e) and 2-8, higher allowable stresses are permitted if appropriate analysis is made. These higher allowable stresses clearly indicate that different stress levels for different stress categories are acceptable. 

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. 

Peak stress, F. Peak stresses are the additional stresses due to stress intensification in highly localized areas. They apply to both sustained loads and self-limiting loads. Tliere are no significant distortions associated with peak stresses. Peak stresses are additive to primary and secondary stresses present at the point of the stress conc-entration. Peak stresses are only significant in fatigue conditions or brittle materials. Peak stresses are sources of fatigue cracks and apply to membrane, bending, and shear stresses. Examples are ... 

Primary bending stress in head, Note Primary bending stress is maximum at the center of the head. 

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. 

With most typical sandwich constructions, the faces provide primary stififhess under in-plane shear stress resultants (Nxy), direct stress resultants (N, Ny), and bending stress resultants (Mx, My) (Figure 7.48). Also as important, the adhesive and the core provide primary stiffness under normal direct stress resultants ( z), and transverse shear stress resultants (Q, Qy). Resistance to twisting moments (T, TyJ that is important in certain plate configurations, is improved by the faces. Capacity of faces is designed not to be limited by either material strength or resistance to local buckling. 

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