Studies in Yield-limited Design

Case study 1 elastic design aaaterials for springs 

The argument, at its simplest, is as follows. The primary function of a spring is that of storing elastic energy and - when required - releasing it again. The elastic energy stored per unit volume in a block of material stressed uniformly to a stress a is  

It is this that we wish to maximise. The spring will be damaged if the stress o exceeds the yield stress or failure stress 0, the constraint is ct Uy. So the maximum energy density is 

Torsion bars and leaf springs are less efficient than axial springs because some of the material is not fully loaded the material at the neutral axis, for instance, is not loaded at all. Consider - since we will need the equations in a moment - the case of a leaf spring. 

Even leaf springs can take many different forms, but all of them are basically elastic beams loaded in bending. A rectangular section elastic beam, simply supported at both ends, loaded centrally with a force , deflects by an amount 

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In the design of an industrial scale reactor for a new process, or an old one that employs a new catalyst, it is common practice to carry out both bench and pilot plant studies before finalizing the design of the commercial scale reactor. The bench scale studies yield the best information about the intrinsic chemical kinetics and the associated rate expression. However, when taken alone, they force the chemical engineer to rely on standard empirical correlations and prediction methods in order to determine the possible influence of heat and mass transfer processes on the rates that will be observed in industrial scale equipment. The pilot scale studies can provide a test of the applicability of the correlations and an indication of potential limitations that physical processes may place on conversion rates. These pilot plant studies can provide extremely useful information on the temperature distribution in the reactor and on contacting patterns when... 

It is doubtful that a majority of receptors will ever be isolated and purified to the level of the nicotinic acetylcholine receptor. Even then some important characteristics that the receptor exhibits when embedded in the membrane surrounded by its various ancillary protein and lipid components are lost. Thus studying drug interactions with such receptor isolates will yield limited, possibly erroneous, information to the drug designer. Effects resulting from such interactions on cells, tissues, or organs cannot be evaluated. 

Finally, the results for the partial oxidation of propane are rather frustrating, as after two decades of intense study, the yields to acrylic acid have not been enhanced. In fact, the highest yield to acryUc acid in both the open and patent literature indicates a limit to the maximum yield which can he obtained, as specifically reported by Muller. This is a consequence of the Umitations of the reaction network in consecutive steps, with propylene as the primary reaction product, as indicated in Fig. 24.6. Accordingly, mayhe we should design catalysts by considering the model of -butane selective oxidation over VPO catalysts (Fig. 24.8), in which the olefinic intermediate was not desorhed and acrylic acid was directly formed as the primary reaction product. In this sense, new crystalline strucmres could be required in which active sites for propane activation and those for propylene oxidation were near enough to directly transform the propylene intermediate into acrylic... 

The critical characteristic on each component was analysed, calculated from the analysis and the value obtained was plotted against the process capability indices, Cpk and Cp, for the characteristic in question. See Appendix V for descriptions of the 21 components analysed, including the values of Cp and Cp from the SPC data supplied. Note that some components studied have a zero process capability index. This is a default value given if the process capability index calculated from the SPC data had a mean outside either one of the tolerance limits, which was the case for some of the components submitted. Although it is recognized that negative process capability indices are used for the aim of process improvement, they have little use in the analyses here. A correlation between positive values (or values which are at least within the tolerance limits) will yield a more deterministic relationship between design capability and estimated process capability. 

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