Formulas for Strength Calculations

The ASME Code provides formulas that relate the wall thickness to the diameter, pressure, allowable stress, and weld efficiency. Since they are theoretically sound only for relatively thin shells, some restrictions are placed on their application. Table 18.3 lists these 

TABLE 18.3. Formulas for Design of Vessels under Internal Pressure  

TABLE 18.4. Maximum Allowable Tensile Stresses (psi) of Plate Steels (a) Carbon and Low Alloy Steels 

Specification No. Nominal composition Spec. min. For temperatures not exceeding °F.  

Specification No. Grade Nominal composition Specified minimum tensile strength For temperatures not exceeding F.  

Skirl length POf UG-32,53 fig UW-13 Por UHT-19 Fillet weWs ParUW-t8ond36, 

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However, for metal sulfates with little or no heat treatment, the relative acid strength will be influenced by the property of each cation, involving its tendency to accept an electron, which is closely related to the cation s electronegativity. Tanaka et al. 23) argue that the acid properties of a plain metal sulfate with little heat treatment depend chiefly on the cation electronegativity x%- They proposed the following formula for its calculation ... 

Thus, by employing general formulas for oscillator strengths, results can be obtained which are useful both in practical calculations and in studying the role of correlation effects on transition probabilities. 

Here p is the frequency of plasmon oscillations in a system of free electrons (3.7). The oscillator strengths ft introduced previously differ from the usual fm (see Section IV) in their normalization (Efl, / = 1). A method for calculating the thus defined oscillator strengths from experimental values of e2 is presented in Ref. 89. Since the energy range essential for collective oscillations is ho> < 30 eV, the electrons of inner atomic shells can be disregarded. Thus, the value of ne is determined by the density of valence electrons only, and only the transitions of these electrons should be taken into account in the sum over i in formula (3.15). A convenient formula for calculating the frequencies molecular liquids is presented in ref. 89 ... 

In this section, we have shown that by relating physical parameters from both the liquid and solid states, a formula for calculating the melting temperature of a monatomic solid can be derived. The reasonable agreement between the calculated and observed Tm s for the 31 elements examined, attest to the validity of the formula derived and subsequently the physical model invoked. The strength of the physical model is further enhanced by the logical manner in which the melting temperature dependence on pressure and impurity can be shown. 

With the possibility of an experimental verification at hand it becomes interesting to make this calculation. And here we appreciate the strength of Kramers dispersion formula— for not only is it difficult to check experimentally but the numerical computation is none too simple. For the sums (6) and (6 ) and not the same as those appearing in (4) and (5). 

Also such factors as allowable tensile strengths, weld efficiencies, and possible inaccuracies of formulas used to calculate shell and head thicknesses may be pertinent—that is, the relative uncertainty or error in the function is related hnearly to the fractional uncertainties of the independent variables. For example, take the case of a steam-heated thermosyphon reboiler on a distillation column for which the heat transfer equation is... 

Feret proposed the formula for concrete strength calculation,... 

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