Stress, allowable

For a very long cylindrical vessel without stiffeners, the following equation gives the theoretical value for the maximum pressure that can be used without collapse of the vessel. 

External pressure that by theory will cause collapse, psia Modulus of elasticity of shell, psi Poisson s ratio (usually about 0.3 for steel) 

For steel in which Poisson s ratio is 0.3, equation 4-5 reduces to 

Equation 4-6 is the classical theoretical relationship for long thin cylinders under external pressures. These theoretical values for collapsing pressure are based on considerations of perfect geometry and perfect uniformity in the shell material. In any actual vessel, the idealized condition cannot be obtained and it was found that the collapse of commercial tubing and pipe occured at a critical pressure, approximately 27% less than the theoretical critical pressure. Using a safety factor of 4 for equation 4-5 we obtain 

Equations 4-5, 4-6 and 4-7 apply to long, cylindrical vessels under external loads without reinforcement against coUapse. You can increase the maximum allowable external pressure by placing stiffeners circumferentially on the vessel 

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Division 2. With the advent of higher design pressures the ASME recognized the need for alternative rules permitting thinner walls with adequate safety factors. Division 2 provides for these alternative rules it is more restrictive in both materials and methods of analysis, but it makes use of higher allowable stresses than does Division 1. The maximum allowable stresses were increased from one-fourth to one-third of the ultimate tensile stress or two-thkds of the yield stress, whichever is least for materials at any temperature. Division 2 requkes an analysis of combined stress, stress concentration factors, fatigue stresses, and thermal stress. The same type of materials are covered as in Division 1. 

Supports. The spaciag of supports is governed by the hot allowable stress of the piping materials stabiUty, ia the case of large-diameter thin-wall pipe deflection to avoid sagging or pocketing and the natural frequency of the unsupported length to avoid susceptibiUty to undesirable vibration. 

Code-allowable stresses are conservative with respect to stmctural failure that occurs when the limit load is reached, ie, the load that results when component deflections and distortions have destroyed its serviceabiUty. The limit load is generally reached when the stresses throughout a main portion of the component cross section exceed the material yield strength (29). 

For the above, the total allowable stress range (for 7000 cycles or less) is as follows ... 

Tank Shell. Another example of where thickness is set by minimums for fabricabihty but not for strength is in small-diameter tanks. For example, a water storage tank built using a steel of an allowable stress of 20,000 psi (138 mPa), 9 ft (3 m) in diameter by 21-ft (7-m) high, requires a shell thickness to resist hoop stress of only 0.023-in. (0.58-mm) thick. However, if built to API Standard 650, the shell would be fabricated at least 0.1875-in. (4.76-mm) thick. The code requires this thickness so that when fabrication, welding, and tolerances are considered, a tank of acceptable quaUty and appearance meeting the requirements of most services in most locations is provided. 

D, the tank diameter and the shell material allowable stresses. This 1-ft (0.305-m) equation is slightly conservative. For tanks over 200 ft (61 m) in... 

Elastic Behavior. Elastic deformation is defined as the reversible deformation that occurs when a load is appHed. Most ceramics deform in a linear elastic fashion, ie, the amount of reversible deformation is a linear function of the appHed stress up to a certain stress level. If the appHed stress is increased any further the ceramic fractures catastrophically. This is in contrast to most metals which initially deform elastically and then begin to deform plastically. Plastic deformation allows stresses to be dissipated rather than building to the point where bonds break irreversibly. 

Sa metals, excluding factor E, or bolt design stress Allowable stress range for MPa Idp/im (ksi)... 

Plastic Pipe In contrast to other piping materials, plastic pipe is free from internal and external corrosion, is easily cut and joined, and does not cause galvanic corrosion when coupled to other materials. Allowable stresses and upper temperature limits are low. Normal operation is in the creep range. Fluids for which a plastic is not suited penetrate and soften it rather than dissolve surface layers. Coefficients... 

Support spacing must be much closer than for carbon steel. As temperature increases, the allowable stress for many plastic pipes decreases very rapidly, and heat from sunhght or adjacent hot uninsulated equipment nas a marked effec t. Successful economical underground use of plastic pipe does not necessarily indicate similar economies outdoors aboveground. 

When the variation lasts no more than 50 h at any one time and not more than 500 h per year, it is permissible to exceed the pressure rating or the allowable stress for pressure design at the temperature of the increased condition by not more than 20 percent. 

S = basic allowable stress for materials, excluding casting, joint, or structural-grade quahty factors E = quahty factor. The quahty factor E is one or the product of more than one of the following quahty factors casting quality factor Ec, joint quahty factor Ej (see Fig. 10-164), and structural-grade quahty factor E, of 0.92. 

P = internal design pressure or external design pressure S = applicable allowable stress... 

To assure that a system meets these requirements, the computed displacement-stress range Se shall not exceed the allowable stress range [Eqs. (10-93) and (10-94)], the reaction forces [Eq. (10-105)] shall not be detrimental to supports or connected equipment, and movement of the piping shall be within any prescribed hmits. 

TABLE 10 49 Allowable Stresses in Tension for Materials (4/ 13/ 28) Continued)... 

Special note for the sixth edition At diis time, metric equivalents have not been provided for the allowable-stress tables of the piping code B31.3. Tliey may be computed by the following rela-tionsliips ( F - 32) x 9 = C Ibf/iir (stress) x 6.S9.5 x 10 = MPa. 

In shaded areas, allowable-stress values wliich are printed in italics exceed two- tliirds of the expected yield strength at temperature. All odier allowable-stress values in shaded areas are equal to 90 percent of expected yield strength at temperature. See ANSI B31.3. 

For use in code piping at the stated allowable stresses, the tensile and yield strengths listed in these tables must be verified by tensile tests at the mill such tests shall be specified in the purchase order. 

Pressure-temperature ratings of cast and forged parts as published in standards referenced in tliis code section may be used for parts meeting requirements of these standards. Allowable stresses for castings and forgings, where listed, are for use in the design of special components not fnmished in accordance with such standards. 

For welded construction with work-hardened grades, use the stresses for annealed material for welded construction with precipitation-hardened grades, use the special allowable stresses for welded constrnction given in die tables. 

SE values shown in tliis table for welded pipe include the joint quality factor E, for the longitudinal weld as required by Fig. 10-164 and, when applicable, the structural-grade quality factor Es of 0.92. For some code computations, particularly with regard to expansion, dexibility, structural attachments, supports, and restraints, the longihidinal-joint quality factor E, need not be considered. To determine the allowable stress S for use in code computations not ntdizing the joint quality factor E, divide the value SF shown in tliis table by the longitudinal-joint quality factor E, tabulated in Fig. 10-164. 

The allowable stress to be used for tliis gray-cast-iron material at its upper temperature limit of 232 C (450 F) is the same as diat shown in the 204 C (400 F) column. 

The SE values in Table 10-49 are equal to the basic allowable stresses in tension S multiplied by a quality factor E (see subsection Pressure Design of Metallic Components Wall Tliick-ness"). The design stress values for bolting materials are equal to die basic allowable stresses S. The stress values in shear shall be 0.80 times the allowable stresses in tension derived from tabulated values in Table 10-49 adjusted when applicable in accordance widi Note 13. 8tress values in bearing shall be twice those in shear. 

The allowable stress range for displacement stresses and permissible additive stresses shall be as specified in Eqs. (10-93) and (10-94) for systems primarily stressed in bending and/or torsion. For pipe or piping components containing longitudinal welds the basic allowable stress S may be used to determine S. (See Table 10-49, Note 13.)... 

Allowable stress range and permissible additive stresses shall be computed in accordance with Eqs, (10-93) and (10-94),... 

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