Volume XX: Sresses in Pressure Vessels - Part 2


The scope of this presentation is to present basic information and understanding of the ASME code for the design of pressure vessels for the chemical and process industry as applicable in the United States and most of North and South America. For more information about our productsheavy plate & custom fabrication services or fabrication capabilities contact us today! 



Design Temperature

The temperature that a system is designed to maintain (inside) or operate against (outside) under the most extreme conditions.

Primary Stress and Secondary Stress

The pressure vessel codes define two important ‘classes’ of stress. A primary stress is related to mechanical loading directly and satisfies force and moment equilibrium. Primary stress that exceeds the yield stress by some margin will result in failure. By contrast, secondary stresses are those arising from geometric discontinuities or stress concentrations. For an increasing external load, at any point, both primary and secondary stresses increase in proportion to this load, until the yield point is reached. But secondary stresses are termed self-limiting by the ASME code: that is, once the yield point has been passed locally around the stress concentration, the direct relationship between load and stress is broken, due to the reduced post-yield stiffness of the material. This is in contrast to primaries (sometimes termed ‘load controlled’ stresses) that will continue to increase in overall magnitude, in direct proportion to the applied load, irrespective of the shape of the stress-strain curve, until failure.

In a region away from any discontinuities, only primary stress will arise. The secondary stress cannot arise alone however - at a discontinuity, the secondary stress will be superimposed on the underlying primary stress. It is worth pointing out the distinction made between primary and secondary stress in the pressure vessel codes is broadly similar to that made between net section and peak stresses identified in the British Standards for the assessment of fabricated structures, as described in previous articles.

General Primary Membrane Stress

A membrane stress is the component of normal stress which is uniformly distributed and equal to the average value of stress across the thickness of the section under consideration. A primary stress is a normal stress or shear stress developed by the imposed loading which is necessary to satisfy the simple laws of equilibrium or external and internal forces and moments. A general primary membrane stress is one which is so distributed in the structure that no redistribution of load occurs as a result of yielding.

Restated in plain English, general primary membrane stress is the average stress through the thickness in a cylinder, head, or cone away from structural discontinuities due to mechanical loads such as internal pressure, dead weight, or wind loads. When you calculate the required thickness of a cylinder or dished head using Code rules, you are in essence limiting the general primary membrane stress in the component to the allowable tensile stress limit. If you transpose the equation to solve for stress, you would be calculating the general primary membrane stress.

When we say away from discontinuities we are talking about areas of high local stresses such as nozzle-to-shell or cone-to-cylinder junctions [see sketch below]. It is recognized in Section VIII-1 that high localized discontinuity stresses may exist in vessels constructed to this standard. These stresses are not directly calculated but are controlled to a safe level consistent with experience through design rules and mandatory fabrication details [e.g., opening reinforcement calculations, minimum 3:1 transition taper at head-to-shell joints, minimum weld sizes for nozzle attachments].

Allowable Stresses

The Code-allowable stresses are determined by the ASME Subcommittee on Materials and are listed in ASME Section II, Part D of the B&PV Code. The basic rules for acceptance of new materials are contained in the “Guideline on the Approval of New Materials under the ASME Boiler and Pressure Vessel Code” (found in Section II, Part D, Appendix 5).

The allowable stresses of carbon steel material are based on properties data provided to the Subcommittee from at least three heats of the material. The properties that must be included are the tensile and yield strengths at 100ºF (38ºC) intervals from room temperature to 100ºF (38ºC) above the maximum intended use temperature. Also, if the material is expected to be used in the time-dependent temperature range (that is, creep), creep rate and stress rupture data must be included starting at approximately 50ºF (10ºC) below the temperature at which the time-dependent properties might govern to 100ºF (38ºC) above the maximum use  temperature. Duration of at least 6000 hours is required for the creep rupture tests.

The basis for the allowable stresses can vary in different Codes, although the bases are generally the same for most power plant applications. Recent changes to the safety factor in the B&PV Code have resulted in increased allowable stresses (the safety factor based on tensile strength was reduced from 4 to 3.5). Although different Codes might have different requirements for the allowable stresses, the criteria used to establish the allowable stress for the Code’s Tables 1A and 1B are shown in Table 1-100 of Appendix 1 of ASME Section II, Part D.

These criteria follow:

• (1/3.5) x the tensile strength at temperature (2YS/3)

• (2/3) x the yield strength at temperature (TS/3.5)

• A percentage of the creep rupture strength dependent on the testing period.

The data are used to develop trend curves. Each of these values (TS/3.5, 2YS/3, and the creep strength value) is plotted against the temperature, and the lowest value is the allowable stress for that material and that temperature. See Figure 1 below for an example plot for SA-516 Gr. 65.



Allowable stresses must be obtained from the applicable Code. The allowable stresses are subject to change because they are a function of the safety factor used in the applicable Code and of the properties of the material specification (which are also subject to change). There are also differences in the temperature limits for the materials. Due to the fact that the strength requirements and the pressure-temperature tables of the standards are subject to change, particular attention should be paid to the edition reference of the material specification or referenced standard. Prior to referencing a later edition, the Code committees review these changes and adjust the allowable stresses accordingly.

Maximum Allowable Tensile Stresses

The maximum allowable stress is the maximum unit stress permitted in a given material used in the vessel. The maximum allowable tensile stress values permitted for different materials are given in ASME Section II-D. A listing of these materials is given in the following tables, which are included in Subsection C of ASME Section VIII-1. Subsection C contains the requirements pertaining to classes of materials. For materials identified as meeting more than one material specification and/or grade, the maximum allowable tensile stress value for either material specification and/or grade may be used provided all requirements and limitations for the material specification and grade are met for the maximum allowable tensile stress value chosen.


Maximum Allowable Compressive Stresses

The maximum allowable longitudinal compressive stress to be used in the design of cylindrical shells or tubes, either seamless or butt welded, subjected to loadings that produce longitudinal compression in the shell or tube shall be the smaller of the following values:

1. The maximum allowable tensile stress value

2. The value of Factor B determined by the following procedure where

E =      modulus of elasticity of material at design temperature. The modulus of elasticity to be used shall be taken from the applicable materials chart in Section II-D, Subpart 3 (Interpolation may be made between lines for intermediate temperatures)

Ro =     outside radius of cylindrical shell or tube

t =        the minimum required thickness of the cylindrical shell or tube

The joint efficiency for butt welded joints shall be taken as one. The value of B shall be determined as follows:

Step 1. Using the selected values of t and R, calculate the value of Factor A using the following formula:


Step 2. Using the value of A calculated in Step 1, enter the applicable material chart in Section II-D, Subpart 3 for the material under consideration. Move vertically to an intersection with the material/temperature line for the design temperature. Interpolation may be used between lines for intermediate temperatures. If the tabular values in Subpart 3 of Section II-D are used, linear interpolation or any other rational interpolation method may be used to determine a B value that lies between the two adjacent tabular values for a specific temperature. Such interpolation may also be used to determine a B value at an intermediate temperature that lies between two sets of tabular values, after first determining B values for each set of tabular values.

In cases where the value at A falls to the right of the end of the material/temperature line, assume an intersection with the horizontal projection of the upper end of the material/temperature line. If tabular values are used, the last (maximum) tabulated value shall be used. For values of A falling to the left of the material/temperature line, see Step 4.

Step 3. From the intersection obtained in Step 2, move horizontally to the right and read the value of Factor B.

This is the maximum allowable compressive stress for the values of t and Ro used in Step 1.

Step 4. For values of A falling to the left of the applicable material/temperature line, the value of B shall be calculated using the following formula:



If tabulated values are used, determine B as in Step 2 and apply it to equation in Step 4.

Step 5. Compare the value of B determined in Steps 3 or 4 with the computed longitudinal compressive stress in the cylindrical shell or tube, using the selected values of t and Ro. If the value of B is smaller than the computed compressive stress, a greater value of t must be selected and the design procedure repeated until a value of B is obtained that is greater than the compressive stress computed for the loading on the cylindrical shell or tube.

Wall Thickness

The wall thickness of a vessel shall be determined such that, for any combinations of loadings listed in UG-22 that induce primary stress and are expected to occur simultaneously during normal operation of the vessel, the induced maximum general primary membrane stress does not exceed the maximum allowable stress value in tension (See exception for combination of earthquake loading, or wind loading with other loadings). Except where limited by special rules, such as those for cast iron in flanged joints, the above loads shall not induce a combined maximum primary membrane stress plus primary bending stress across the thickness that exceeds 1½ times the maximum allowable stress value in tension. It is recognized that high localized discontinuity stresses may exist in vessels.

Earthquake and Wind Loadings

For the combination of earthquake loading, or wind loading with other loadings, the wall thickness of a vessel shall be determined such that the general primary membrane stress shall not exceed 1.2 times the maximum allowable stress permitted. This rule is applicable to stresses caused by internal pressure, external pressure, and axial compressive load on a cylinder. Earthquake loading and wind loading need not be considered to act simultaneously.

Localized Discontinuity Stresses

The primary plus secondary stresses at discontinuities shall be limited to SPS, where SPS = 3S, and S is the maximum allowable stress of the material at the temperature. In lieu of using SPS = 3S, a value of SPS = 2SY may be used where SY is the yield strength at the temperature, provided the following three conditions are met:

  1. The allowable stress of the material is not governed by time-dependent properties as provided in Table 1A or 1B of Section II-D;
  2. The room temperature ratio of the specified minimum yield strength to specified minimum tensile strength for the material does not exceed 0.7; and
  3. The value of SY at temperature can be obtained from Table Y-1 of Section II-D.


1. ASME Boiler & Pressure Vessel Code, Section VIII, Division 1


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