Membrane stress

Internal-pressure design rules and formulas are given for cylindrical and spherical shells and for ellipsoidal, torispherical (often called ASME heads), hemispherical, and conical heads. The formulas given assume membrane-stress failure, although the rules for heads include consideration for buckling failure in the transition area from cylinder to head (knuckle area). 

The analysis of the membrane stresses induced in shells of revolution by internal pressure gives a basis for determining the minimum wall thickness required for vessel shells. The actual thickness required will also depend on the stresses arising from the other loads to which the vessel is subjected. 

This force is resisted by the normal component of the forces associated with the membrane stresses in the walls of the vessel (given by, force = stress x area)... 

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 minimum wall thickness required to resist the hydrostatic pressure can be calculated from the equations for the membrane stresses in thin cylinders (Section 13.3.4) ... 

The minimum wall thickness required can be estimated using the equations for membrane stress derived in Section 13.3.4. For a solid bowl... 

Calculate the maximum membrane stress in the wall of shells having the shapes listed below. The vessel walls are 2 mm thick and subject to an internal pressure of 5 bar. 

The polycarbonate glazing is modeled as a simply supported plate subjected to nonlinear center deflections up to 15 times the pane thickness. Using the finite element solution of Moore (Reference 4), the resistance function is generated for each pane under consideration. Typically, the resistance is concave up, as illustrated for typical pane sizes in Figure 1. This occurs because membrane stresses induced by the stretching of the neutral axis of the pane become more pronounced as the ratio of the center pane deflection to the pane... 

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). 

Ion selective membranes are the active, chemically selective component of many potentiometric ion sensors (7). They have been most successfully used with solution contacts on both sides of the membrane, and have been found to perform less satisfactorily when a solid state contact is made to one face. One approach that has been used to improve the lifetime of solid state devices coated with membranes has been to improve the adhesion of the film on the solid substrate (2-5). However, our results with this approach for plasticized polyvinylchloride (PVC) based membranes suggested it is important to understand the basic phenomena occurring inside these membranes in terms of solvent uptake, ion transport and membrane stress (4,6). We have previously reported on the design of an optical instrument that allows the concentration profiles inside PVC based ion sensitive membranes to be determined (7). In that study it was shown that water uptake occurs in two steps. A more detailed study of water transport has been undertaken since water is believed to play an important role in such membranes, but its exact function is poorly understood, and the quantitative data available on water in PVC membranes is not in good agreement (8-10). One key problem is to develop an understanding of the role of water uptake in polymer swelling and internal stress, since these factors appear to be related to the rapid failure of membranes on solid substrates. 

ADVANCED STRENGTH OF MATERIALS, J.P. Den Hartog. Superbly written advanced text covers torsion, rotating disks, membrane stresses in shells, much more. Many problems and answers. 388pp. 54 x 84. 65407-9 Pa. 8.95... 

Determine the normal and bending stresses, cross-sectional areas near the eye, and assess the acceptability of the results. The normal (or membrane) stress is calculated by the formula... 

Qi Z, Chi S, Namse K, Sokabe M. Activation of a mechanosensitive BK channel by membrane stress created with amphipaths. Mol. Membrane Biol. 2005 22 519-527. 

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