Pressure Vessel Lifting Lugs

Journal of Pressure Vessel Technology

Design Innovations

Proposed Design Criterion for Vessel Lifting Lugs in Lieu of ASME B30.20 Dennis K. Williams Sharoden Engineering Consultants, P.A. P.O. Box 1336, 1153 Willow Oaks Trail, Matthews, NC 28106-1336 e-mail: [email protected] This paper describes a method for evaluating the structural adequacy of various lifting lugs utilized in the erection and up righting of large pressure vessels. In addition, the analysis techniques are described in detail and design guidelines for vessel lifting are tendered. The statutory and provincial regulations in both the United States and the province of Alberta, Canada are also reviewed and discussed with respect to the too often utilized phrase “factor of safety” (FOS). The implied implications derived from the chosen FOS are also outlined. A discussion is presented as to the applicability of the ASME safety standard B30.20 entitled, “Below the Hook Lifting Devices” (1999, ASME, New York) and as to the severe shortcomings of the safety standard in its attempt to delve into the design of lifting devices, especially when applied to lifting lugs on large and heavy-weight pressure vessels. Exemplar lugs on vessels are defined and the finite element analyses and closed form Hertzian contact problem solutions are presented and interpreted in accordance with the proposed design criteria. These results are compared against the very limited design information contained within ASME B30.20. Suggestions for the revision and applicability of the safety standard are presented and discussed in light of the examples and technical justification presented in the following paragraphs. In addition, the silence of this safety standard on the very large contact stresses that are well known to exist between a lifting pin and clevis type geometry is also discussed. Because of the limited number of repetitive loading cycles that vessel lifting lugs actually experience during the service life of a vessel, a recommendation is made to either clearly exclude vessel lifting lugs from the scope of ASME B30.20 or to specifically include a separate design and analysis section within this standard to properly address the mechanical and structural design issues applicable to pressure vessel lifting lugs. 关DOI: 10.1115/1.2716439兴

Introduction The basic approach of the current study is to first define the mode of failure against which any design criteria and/or standard Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received January 23, 2006; final manuscript received September 7, 2006. Review conducted by David Raj. Paper presented at the 2002 ASME Pressure Vessels and Piping Conference 共PVP2002兲, Vancouver, British Columbia, Canada, August 5–9, 2002.

326 / Vol. 129, MAY 2007

must try to protect during the design phase of a vessel lifting lug. Second, the approach selects a failure criteria from those commonly discussed in the literature, such as maximum shear stress theory, maximum octahedral shear stress theory, and maximum principal stress theory, that most closely matches the mode of failure defined in the first step of the basic approach. Third, the method adopts an “achievable” factor of safety based on the chosen failure theory from step two of the approach and applies the FOS against the respective “failure” stress. Finally, a well-defined design criterion for vessel lifting lugs is outlined based on the basic approach presented herein and applied to the statutory and provincial regulations contained within 29CFR1926 共OSHA regulations兲 关1兴 and the Occupational Safety and Health Act of the Province of Alberta, Canada 关2兴. The purpose of this paper is to provide technical insight into the applied mechanics evaluation of an exemplar pressure vessel lifting lug and proposed design criteria in lieu of the limited “design” requirements contained within ASME B30.20 关3兴. The current work is restricted to the evaluation of the lug in the vicinity of the lifting pin. The subject lifting lug of this paper is one whose design load capacity is 700 metric tons 共⬃1,544,000 lbf兲. This load capacity is not uncommon in the petroleum refinery industry for a number of specialty types of ASME B&PV Code, Section VIII 关4兴 reactor vessels. On many project designs, there are at least two types of imposed design bases for the lifting and handling equipment. The first of these design bases is an internally generated or self-imposed design basis. The second of these design bases is one that may be classified as externally generated design basis. For purposes of this discussion, “internal” and “external” refer to an organization within the design engineering organization 共hence internal兲 or to an outside authority having jurisdiction 共hence external兲. The internal design basis for the lifting lug can further be defined by either internally generated design and analysis criteria or by externally generated codes and safety standards. The internally generated criteria most often attempt to define an “allowable” set of component stresses that restrict the computed bending, bearing, and shear stresses within the lifting lug critical sections as determined by both experience and empirical data. Although there are no uniform set of criteria among the numerous engineering design professionals throughout the U.S. and Canada, it is this author’s experience that one guideline, which is often quoted, is the limitation of the bending stress to one third of the yield strength of the lug material 共assuming a one-piece forged design兲. The additional component stresses and the associated allowable stressess vary widely across-the-board, depending on the particular design engineering group and their given experience. The externally generated or imposed “design” standard on lifting lugs often falls on the limited criteria contained within the ASME safety standard B30.20 关3兴 entitled, “Below the Hook Lifting Devices.” This paper addresses the “fallback” position employed by many engineering organizations in attempting to utilize the “design” criteria contained therein and the inherent pitfalls of such a practice, particularly when applied to large lifting lugs for pressure vessels. The second major group of design basis criteria originates from

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Fig. 1 Lifting-lug geometry

an outside source and most often takes the form of regulatory requirements defined by federal, state, and/or provincial authorities having jurisdiction. For the purposes of this paper, only the regulations imposed in the U.S. and the Province of Alberta, Canada are discussed, although the subject discussion is one that has universal implications. This becomes even more apparent as fabricators across the globe are providing ASME Code 关4兴 pressure vessels intended for installation in both the U.S. and Canada. The specific design lifting requirements imposed by the U.S. Department of Labor, 29CFR1926 共OSHA regulations兲 关1兴 are outlined and the implementation of a 5 to 1 “factor of safety” 共FOS兲 is also explored. Finally, the Provincial Regulations contained within the Occupational Safety and Health Act of the Province of Alberta, Canada 关2兴 are also reviewed and discussed with further interpretation of a very specific five-to-one factor of safety on the ultimate tensile strength of the chosen lug material. The analysis of the 700 metric ton lifting lug is conducted in two separate manners. The first is the analysis and prediction of the contact stresses, the general stress field within the critical sections of the lug, and the associated contact area between a close tolerance fitting lifting bolt/pin utilizing the techniques presented by Timoshenko and Goodier in the Theory of Elasticity 关5兴 and summarized for direct application by Young 关6兴. The lug geometry itself is a simple clevis type design of uniform thickness as shown in Fig. 1. The second analysis utilizes the finite element method to analyze the effects of the contact stresses within the lug and also utilizes the calculated results to serve as a basis for the proposed lug design criteria. The proposed lug design criteria must achieve two goals. The first is to ensure a safe and practical design. The second is to provide a design that is in full compliance with the defined regulatory requirements defined herein. The technical bases for achieving this two-fold objective are outlined in the paragraphs that follow.

ASME B30.20: Below the Hook Lifting Devices ASME B30.20 had its beginning in December 1916, when an eight-page Code of Safety Standards for Cranes was presented to the annual meeting of the ASME. Because of changes in design, advancement in techniques, and the general interest of labor and industry in safety, an American National Standards Committee was formed under the joint sponsorship of ASME and Naval Facilities Engineering Command 共ASME 关3兴兲. According to the foreword provided within ASME B30.20 关3兴, the Standard presents a coordinated set of rules that may serve as a guide to government and other regulatory bodies responsible for the “guarding and inspection” of the equipment falling within its scope. Furthermore, the foreword to the referenced ASME Standard 关3兴 urges administrative and regulatory agencies to “consult the B30 Committee” prior to rendering decisions on disputed points. The foreJournal of Pressure Vessel Technology

word concludes with the protective remark that, “revisions 关to the Standard兴 do not imply that previous editions were inadequate.” Within the Introduction to the ASME Standard 关3兴, the Standards Committee states that they fully realize the importance of proper design factors. In addition, the Standards Committee states that, “关they兴 will be glad to receive criticisms of this Standard’s requirements and suggestions for its improvement, especially those based on actual experience in application of the rules” 关3兴. The purpose of this paper is to explore the “design” requirements contained in the Standard 关3兴 and to provide an exemplar of the application of the suggested rules and some well defined and quantitative criticisms of the Standard. Within the scope of ASME B30.20 关3兴 is the “construction” of lifting devices. Some engineers interpret the 700 metric tons lifting lug under consideration to fall within the scope of the subject Standard 关3兴. Although Chapter 20-1 entitled “Structural and Mechanical Lifting Devices” 关3兴 does not specifically categorize the lifting lug under consideration, many design organizations cite this chapter for use as a design guideline or requirement. In particular, paragraph 20-1.1.1 entitled “General Construction,” outlines the “design” requirements for a lifter as follows: “The load bearing structural components of a lifter shall be designed to withstand stresses imposed by its rated load plus the weight of the lifter, with a minimum design factor of three, based upon yield strength of the material, and with stress ranges that do not exceed the values given in ANSI/AWS D14.1 [7] for the applicable conditions” [3]. Before proceeding, there are several observations that must be highlighted concerning the preceding design requirement. First, the placement of a “design requirement” under the heading of “Construction” is not consistent with the organization of many other ASME Codes and Standards 关4兴 in that design criteria are clearly labeled as such and are also segregated from the construction 共i.e., fabrication兲 requirements. Second, the design requirement contained within the referenced Standard 关3兴 only gives the engineer a very vague idea 共at best兲 as to which particular computed stresses must be compared against essentially the material’s yield stress divided by three. Third, the choice of an “allowable” stress of sorts by the Standard 关3兴 that is based on yield implies some sort of “failure criteria” that would preclude the initiation of yielding within the lug material when subjected to its maximum rated load. Fourth, the selection of a yield based failure criteria would most likely also imply that the anticipated failure mode would be one of a ductile nature 共of course assuming the selection of a linear, elastic, homogeneous, and isotropic lug material兲. Fifth, the utilization of a large capacity vessel lifting lug will typically only be subjected to a very limited number of “lift cycles,” as once the vessel is moved from the fabricator’s shop and uprighted in the field, it generally is there for the remainder of its intended design life. Finally, the subject design problem clearly involves contact stresses between a shackle pin and a clevis hole, which obviously implies very large contact stresses that are highly localized, which are not addressed by this or any other standard known to this author. It is these implications in combination with other regulatory requirements that are explored in some detail in the paragraphs that follow.

OSHA Rigging Equipment Regulations in the United States The U.S. Department of Labor, through the regulations specified by its Occupational Health and Safety Administration 共OSHA兲, specifies the general safety requirements for rigging equipment for material handling. Throughout the U.S. Code of Federal Regulations 共CFR兲, numerous references are made to slings, wire rope, hooks, shackles, and other forms of material handling and other forms of lifting equipment 关1兴. In particular, the regulations that are of most importance during the uprighting and lifting of a pressure vessel are found in Title 29, Part 1926, MAY 2007, Vol. 129 / 327

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Subpart 251 entitled “Rigging Equipment for Material Handling” 关1兴. This and other OSHA Regulations may now be easily found on the Internet at URL http://www.osha.gov. Although there are numerous similarities between ASME B30.20 关3兴 and 29CFR1926.251 关1兴 regarding the inspection of the lifting equipment 共including, but not limited to lifting lugs兲 prior to use, there exists a striking difference in the “design” criteria for the handling devices. The OSHA requirements specifically define that the safe working loads of shackles and “specific identifiable products” be designed with a “safety factor of not less than 5,” although the safety factor is not explicitly defined therein 关1兴. The FOS of 5 is repeatedly echoed throughout this and other OSHA Regulations regarding handling equipment. As in the proceeding section, there are several observations that must be discussed concerning the preceding design requirement. First, the OSHA design requirement 关1兴 gives the engineer no suggestion or proposal as to which particular computed stresses must be compared against essentially the material’s ultimate tensile stress divided by five. This assumes that the failure load, however, is proportional to the ultimate tensile failure stress 共or vice versa兲 in the application of the FOS as recommended by Boresi et al. 关8兴. Second, the choice of an “allowable” stress of sorts by the Regulation 关1兴, which is based on what is assumed to be a FOS of 5 applied to the ultimate tensile strength, implies some sort of “failure criteria” that would be based on a predominant component stress or computed maximum principal stress when subjected to its maximum rated load. Third, the selection of an ultimate tensile strength based failure criteria would most likely also imply that the anticipated failure mode would be one of a brittle nature 共even though the lug material is most assuredly classified as a ductile material under ordinary loading conditions兲. Fourth, similar to the parley on ASME B30.20, the utilization of a large-capacity vessel lifting lug will typically only be subjected to a very limited number of lift cycles, for the reasons previously cited. Finally, the subject design problem clearly involves contact stresses between a shackle pin and a clevis hole, which obviously implies very large contact stresses that are highly localized, which are not addressed by this or any other regulation known to this author.

Alberta Safety and Health Act Requirements The Province of Alberta, Canada, through the regulations specified by its Occupational Health and Safety Act, Regulation 448/83 关2兴, specifies the general safety requirements for rigging equipment for material handling. Similar to the OSHA Regulation 关1兴 previously discussed, within the Alberta Regulation 关2兴, numerous references are made to slings, wire rope, hooks, shackles, and other forms of material handling and other forms of lifting equipment. In particular, the regulations that are of most importance during the up-righting and lifting of a pressure vessel are found in Part 8, entitled, “Rigging,” paragraph 139 关2兴. This and other Alberta Regulations may now be easily found on the Internet at URL http://www.gov.ab.ca Once again, there are numerous similarities between ASME B30.20 关3兴, 29CFR1926.251 关1兴, and Alberta Regulation 448/83 关2兴 共AR 448/83兲 regarding the inspection of the lifting equipment 共including, but not limited to lifting lugs兲 prior to use. The Alberta Regulation, however, begins to define the “design” criteria of the handling devices more specifically than the OSHA regulations and takes on a different basis for the FOS than even ASME B30.20 关3兴. AR 448/83 requirements specifically state that the maximum safe working load of rigging or rigging equipment must not “exceed…20% of the ultimate breaking strength of the weakest component of the rigging.” As with the OSHA regulations, a FOS of 5 appears and is repeatedly echoed throughout this Regulation 关2兴 regarding handling equipment. The pertinent observations that must be discussed concerning the preceding design requirement are as follows. The design requirement 关2兴 gives the engineer the latitude to formulate a failure 328 / Vol. 129, MAY 2007

criteria based on the “ultimate breaking strength,” which suggests at least an ultimate tensile strength divided by five allowable stress. Again however, this assumes that the failure load is proportional to the ultimate tensile failure stress in the application of the five-to-one FOS. Second, the choice of an “allowable” stress of sorts by the Regulation 关1兴 that is based on what is assumed to be a FOS of 5 applied to the ultimate tensile strength implies some sort of “failure criteria” that would be based on a predominant component stress or computed maximum principal stress when subjected to its maximum rated load. Third, the selection of an ultimate tensile strength based failure criteria would most likely also imply that the anticipated failure mode would be one of a brittle nature. Fourth, similar to the discussion on ASME B30.20, the utilization of a large capacity vessel lifting lug will typically be subjected to only a very limited number of lift cycles, for the reasons previously cited. Finally, as with all the other regulations and standards previously cited, the very large contact stresses, which are highly localized, are not addressed by this regulation as well.

Classical Contact Stress Evaluations The problem presented by the design of a vessel lifting lug is first and foremost one created by the Hertzian contact of a lifting pin 共supported by a shackle in this case兲 with that of the lifting hole in a clevis-type lifting lug. The resulting stresses of the greatest magnitude are indeed those created by the pressure exerted by the pin on the clevis over a limited area of contact. The Hertzian contact stress problem is treated and discussed in detail in Boresi 关8兴 共Chap. 14兲, Timoshenko 关5兴 and Young 关6兴. It is these contact stresses that are not, however, addressed in any of the Standards or Regulations previously discussed in the preceding paragraphs of this paper 关1–3兴. The only plausible justification for the silence by these Standards and Regulations on the obvious existence of the contact stresses may be as explained in the following by Boresi 关8兴: “Most load resisting members are designed on the basis of stress in the main body of the member, that is, in portions of the body not affected by the localized stresses at or near a surface of contact between bodies. In other words, most failures (excessive elastic deflection, yielding, and fracture) of members are associated with stresses and strains in portions of the body far removed from the points of application of the loads.” Appendix A contains a sample calculation for the 700 metric ton lifting lug contact stress evaluation. The geometric and material properties are defined within the calculation proper. The chosen material for the lifting lug is ASME 508 Grade 3 Class 2 with an ultimate tensile strength of 90,000 psi and yield strength of 65,000 psi. The lifting lughole diameter is 8.543 in. within which a pin diameter of 8.460 in. must be inserted. The thickness of the lifting lug is 11.50 in. The relatively simple evaluation of the contact stresses contained in Appendix A is not applicable close to the edges where the contact boundary begins. This sharp interface area can produce highly localized stresses in excess of 100,000 psi 关8兴 for the 700 metric tons loading under consideration. The depths at which the effects of the contact stresses are significant range from the surface of contact 共for the maximum principal stress兲 to an approximate depth of 1.6 in. 共for the maximum shear stress and the maximum octahedral shearing stress兲. Nevertheless, the results of the contact stress evaluation contained in Appendix A reveal at least two important pieces of information. The first is that the average contact stress for the loading, geometry, and materials of construction defined herein are ⬃40,000 psi. Keeping in mind that this is a compressive stress and that when compared to a yield strength of at least 65,000 psi, this is far below those levels of bearing and/or compressive stress allowed within other ASME Codes 关4兴. The second important piece of information is the calculated width of the assumed rectangular contact area. For the subject design, this width is calculated to be ⬃4.35 in., which Transactions of the ASME

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Fig. 2 Lifting-lug finite element mesh

equates to a half angle from top dead center of ⬃30 deg for the contact area. This value is and can be utilized in a more detailed finite element analysis of the lifting lug and represents the angular dimension over which the lifting load may be applied.

Classical Failure Theories and the Mystery of the Ulimate Factor of Safety Clearly in the design and analysis of a lifting lug for a vessel that weighs 700 metric tons, the engineer must have an exceptional understanding of the possible ways by which the lug may fail to perform its function. In determining the possible modes of failure, the engineer must also establish the failure criteria by which the design will be judged. In the present study, the modes of failure for the lug must include not only the common static causes, such as bending, shear, and bearing, but also the effects of a dynamic or shock loading due to the lift itself. It is this consideration of a potential dynamic load 共generated as a result of the sudden loss of tension in a cable or sling兲 that drives the need for some form of a FOS to be employed to the applied static load or resulting computed stress. Furthermore, the selection of a failure criteria for the lifting lug must be predicated based on this dynamic load consideration and not the initiation of yield per se, as the lug will only be utilized a very few number of times in its design life 共i.e., certainly no more than ten times兲. As will be shown, it is not only the mere specification of a single FOS but also the failure criterion that determines the ultimate factor of safety of a given lifting lug design. Boresi 关8兴 states, “There is considerable but not necessarily conclusive evidence…that when a member fails by general yielding at ordinary temperatures, the significant quantity associated with the failure is shearing stress.” Two of the most widely utilized failure criteria that address general yielding include the maximum shearing stress 共Tresca’s criterion兲 and the maximum octahedral stress 共von Mises criterion兲 theories. A third criterion to be considered is the maximum principal stress theory of failure 共Rankine’s criterion兲. Before proceeding, however, the engineer must remember that in a uniaxial state of stress, the critical “failure” values for each of the defined theories are achieved simultaneously in a simple tensile test. Journal of Pressure Vessel Technology

Tresca’s criterion states that inelastic action in any point in a part initiates when the computed maximum shearing stress reaches one-half of the material’s yield strength. Although the maximum shear stress failure theory is best suited for ductile material behavior in which relatively large shearing stresses are developed 关8兴, for the problem at hand, the maximum shearing stress would be limited to no more than 32,500 psi prior to the application of any FOS. The maximum octahedral shear stress failure theory states that inelastic action in any point in a part initiates when the computed octahedral shearing stress reaches 0.471 times the material’s yield strength. In many ductile materials utilized within the pressure vessel industry, the octahedral shearing stress criterion predicts the initiation of yield better and with less conservatism than does the Tresca criterion. For the problem at hand, the maximum octahedral shearing stress would be limited to no more than 30,641 psi prior to the application of any FOS. The maximum principal failure theory is one that may be easily employed to establish either the initiation of yield for a brittle material or one that may be employed to establish a guard against fracture through the use of the ultimate tensile strength 共UTS兲 and an imposed FOS. In fact, even though the chosen material for a vessel lifting lug should be one of high ductility and possess good impact properties, the failure mechanism due to a sudden acceleration 共i.e., a dynamic load兲 in most cases will be one of a brittle nature. Therefore, Rankine’s criterion, when modified to utilize the UTS, provides both an easy to use criterion and one that is consistent with the expected mode of failure. For the problem at hand, the maximum principal stress would be limited to 90,000 psi divided by the chosen FOS. This also implies that the minimum principal stress must be addressed as a separate matter. This is because the failure mode that must be guarded against is one, first and foremost, that would be tensile in nature and tend to open any preexisting cracks in the lifting lug material.

Criteria for Consideration in the Design and Analysis of Pressure Vessel Lifting Lugs In an effort to more fully understand the stress field within the 700 metric tons lifting lug, a finite element analysis was perMAY 2007, Vol. 129 / 329

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Fig. 3 Stress-intensity contour

formed. The lug geometry was as shown in Fig. 1, and the refined element mesh was as shown in Fig. 2. The base of the lug was fixed against translation in all three coordinate directions, as the elements chosen to model the geometry were a three-dimensional solid with three-degrees of freedom at each node 共i.e., translations in the x, y, and z directions兲. The 700 metric tons load was evenly distributed within a 30 deg half angle from top dead center on each side of the symmetry plane and continued through the thickness of the lifting lug. The chosen contact area was confirmed independently by the calculations presented in Appendix A of this paper, which was previously discussed. Several mesh densities were employed until the stress results converged to within 3% of the more course mesh density. The results of the finite element analysis were decomposed into all of the constituent component stresses. In addition, the results were also reviewed in light of the three failure criteria previously defined and outlined above. The stress contours showing the calculated maximum stress intensities 共i.e., twice the value of the maximum shear stresses兲, the von Mises stresses and the maximum principal stresses are included in Figs. 3–5, respectively. All of the contours reflect a highly concentrated respective combined stress at the geometric discontinuity between the lug hole bore and orthogonal outside surface. This is both attributed to the contact load discontinuity and the reality of the geometric/load combination. This area is very small and is not anticipated to reflect the overall load carrying capacity of the lug, regardless of the failure criterion employed. The calculated maximum shear stress as shown in Fig. 3 is ⬃40,000 psi 共i.e., one-half of the calculated stress intensity兲. When compared to the Tresca criterion allowable stress of onehalf of yield 共i.e., 32,500 psi兲, this represents an overage of ⬃25% without employing any factor of safety. As the distance from the applied contact load increases, the stress contour reveals that an overall maximum shear stress throughout the body of the lifting lug quickly decreases to a value of ⬃13,400– 17,800 psi. In order to fully evaluate the FOS for this criterion, these values must be compared to one-half of the yield, which results in a FOS of as low as 1.82 on the initiation of yield a short distance away from 330 / Vol. 129, MAY 2007

the proximity of the contact load application. It is recognized that the subject lifting lug design would have a much higher load carrying capacity than that predicted by this criterion due to the strain hardening capacity of the chosen forging material. The calculated equivalent stress 共i.e., von Mises兲 as shown in Fig. 4 is ⬃69,194 psi. When compared to the equivalent allowable stress of 1.0 times yield 共i.e., 65,000 psi兲, this represents an overage of ⬃6.5% without employing any factor of safety. As the distance from the applied contact load increases, the stress contour reveals that an overall maximum equivalent stress throughout the body of the lifting lug quickly decreases to a value of ⬃23,100– 30,800 psi. In order to fully evaluate the FOS for this criterion, these values must be compared to the one times yield, which results in a FOS of as low as 2.11 on the initiation of yield a short distance away from the proximity of the contact load application. As before, it is recognized that the subject lifting lug design would have a much higher load carrying capacity than that predicted by this criterion due to the strain hardening capacity of the chosen forging material. The calculated maximum principal stress as shown in Fig. 5 is ⬃53,276 psi. When compared to the equivalent allowable stress of 1.0 times yield 共i.e., 65,000 psi兲, this represents a margin of ⬃18% without employing any factor of safety. As the distance from the applied contact load increases, the stress contour reveals that an overall maximum principal stress throughout the body of the lifting lug quickly decreases to a value of ⬃16,400 psi. In order to fully evaluate the FOS for this criterion, these values may be compared to the one-time yield, which results in a FOS of ⬃3.96 on the initiation of yield. As stated previously however, this is not a good predictor of yield and is most well suited for use with the ultimate tensile strength in this case. Proceeding on this basis, these values must be compared to the UTS, which results in a FOS of ⬃5.49 on the ultimate failure load 共assuming totally elastic response, which is a conservative predictor兲. In contrast, the calculated minimum principal stress, as shown in Fig. 6, is found to be approximately −61,292 psi, which is reflective of the compressive contact stress between the lifting pin and lug hole. Transactions of the ASME

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Fig. 4 Von Mises stress Contour

Again it is recognized that the subject lifting lug design would have a much higher load carrying capacity than that predicted by this criterion due to the reasons previously stated. Based on the results of the detailed finite element analysis of the 700 metric ton lifting lug, the following design criterion is tendered for consideration. First, in an effort to align the chosen failure criterion with the most significant mode of failure 共i.e., from a dynamic load兲, the maximum principal stress failure crite-

ria should be utilized. Although attempts by the ASME B30.20 Safety Standard highlights the use of a one-third yield criterion, there is no single published failure criterion known to this author that can address all of the aspects of the lug design with this method. In this author’s opinion, the simple limitation of a single type of component stress 共for example, a bending stress兲 to some allowable value hardly defines a failure criterion for use in the current or future design of lifting lugs. Furthermore, applying this

Fig. 5 Max principal Stress Contour

Journal of Pressure Vessel Technology

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Fig. 6 Min. Principal Stress Contour

limitation 共i.e., the one-third yield criterion兲 on the compressive stresses present in the contact area, simply does not work nor will it work in a triaxial state of stress. Second, in conjunction with the chosen criterion, the maximum principal stresses should be calculated for the given working load and lug geometry. The load should be distributed over a contact area as determined by either an acceptable contact stress technique such as that presented in Appendix A or by a nonlinear finite element contact stress analysis procedure. The resulting maximum principal stresses in the body of the lug that are located slightly beyond the area of load application should then be compared to an allowable stress value equal to 20% of the UTS of the lug material. This will be consistent with both domestic and Canadian regulations regarding the implementation of a well defined FOS of 5 on fracture and ultimate breaking strength. Finally, the minimum principal stresses should be computed and compared to simply one times the specified minimum yield strength of the lug material. This allowable is consistent with those specified in other ASME Codes 关4兴 and the compressive stresses do not pose the same crack opening hazard found in purely tensile stresses. Utilizing this method of analysis not only achieves a clear utilization of a highly recognized FOS, but also addresses the issue of contact stresses about which the Regulations and Standards identified herein have remained forever silent.

Summary and Conclusions A method for evaluating the structural adequacy of various lifting lugs utilized in the erection and uprighting of large pressure vessels was presented. The analysis techniques were described in detail and design guidelines for vessel lifting lugs were tendered. The statutory and provincial regulations in both the United States and the province of Alberta, Canada, were also reviewed and discussed with respect to the too often utilized phrase “factor of safety” 共FOS兲. Hopefully, the introduction of a clearly defined FOS of 5, when utilized with the maximum principal stress failure criterion, will serve as a constructive criticism to the very limited design criterion given in the current ASME safety standard B30.20 关3兴 entitled, “Below the Hook Lifting Devices” and may 332 / Vol. 129, MAY 2007

be applied to lifting lugs for large and heavyweight pressure vessels in future design standards. Because of the limited number of repetitive loading cycles that vessel lifting lugs actually experience during the service life of a vessel, a recommendation is made to either clearly exclude vessel lifting lugs from the scope of ASME B30.20 关3兴 or to address the design aspects in a separate standard to be developed at a later date. Based on the results presented herein, it is hoped that a more realistic assessment of the failure modes and the proper selection of a failure criterion will be further studied and revised as necessary by the ASME B30.20 Committee, thereby leaving less to chance for the less experienced design engineer of rigging and materials handling equipment.

Nomenclature CE D1 D2 E1 E2 KD L P bb p ␯1 ␯2

␴cmax

⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽

material constant for contacting bodies diameter of lifting lug hole diameter of lifting 共shackle兲 pin modulus of elasticity for lifting lug modulus of elasticity for lifting 共shackle兲 pin geometric constant for contacting bodies length of contact; thickness of lifting lug load to be lifted; maximum safe working load width of rectangular contact area load per unit length of contact Poisson’s ratio for lifting lug Poisson’s ratio for lifting 共shackle兲 pin maximum calculated contact stress

Appendix A: A Proposed Design Criterion for Vessel Lifting Lugs in Lieu of ASME B30.20 First, we will evaluate the contact stresses in the lifting lug based upon the one-fifth of the ultimate tensile strength design criteria contained within the Alberta OS&H Act. Lifting Cover Contact Stresses, SA-508 Gr 3 Cl 2. Cylinder in a Cylindrical Socket—Table 33, Case 2c, Formulas for Stress & Strain [6]. Transactions of the ASME

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Width of rectangular contact area: bbª 1.60· 冑p · KD · CE Provides an explanation of Table 33 and the notation used. Diameter of top cylinder:

D2 ª 8.46· in

Poisson’s ratio for the top cylinder:

␯2 ª 0.3

Modulus of elasticity for the top cylinder:

E2 ª 29.7· 106 ·

Diameter of bottom socket:

D1 ª 8.543· in

Poisson’s ratio for the bottom socket:

␯1 ª 0.3

Modulus of elasticity for the bottom socket:

␴cmax ª 0.798·

lbf in2

Length of cylinder:

L ª 11.50· in

1 − ␯21 1 − ␯22 + E1 E2 Load per unit length: CE ª

pª

P L

E1 ª 27.8· 106 ·

KD = 870.768 in CE = 6.337⫻ 10−8

p = 1.342⫻ 105

Journal of Pressure Vessel Technology

p KD · CE

␴cmax = 39354

lbf in2

References

Loading:

D2 · D1 D1 − D2

冑

With the UTS of SA-508 Gr 3 Cl 2 of 90000 psi, this is an acceptable material for the lifting lug. Note: See Timoshenko 关5兴 and Sague 关9兴 for technique and formulas utilized above. 关ASME Paper Lifting Lug.mcd兴

lbf in2 P ª 1.54338⫻ 106 · lbf

KD ª

Stress:

bb= 4.354 in

in2 lbf

lbf in

关1兴 U. S. Department of Labor, Occupational Safety & Health Administration, 2002, Code of Federal Regulations, Title 29, Part 1926, Safety & Health Regulations for Construction, Subpart 251, U. S. Government Printing Office, Washington, DC. 关2兴 Province of Alberta, Canada, 2000, Alberta Regulation 448/83, Occupational Health & Safety Act, Queen’s Printer for Alberta, Edmonton, Alberta, Canada. 关3兴 ASME, 1999, Below-the-Hook Lifting Devices, ASME, New York, ASME B30.20–1999. 关4兴 ASME, 2001, ASME Boiler & Pressure Vessel Code, Rules for Construction of Pressure Vessels, Division 2-Alternate Rules, ASME, New York. 关5兴 Timoshenko, S. P. and Goodier, J. N., 1970, Theory of Elasticity, 3rd ed., McGraw-Hill, New York. 关6兴 Young, W. C., 1989, Roark’s Formulas for Stress & Strain, 6th ed., McGrawHill, New York. 关7兴 AWS, 1997, Specification for Welding Industrial and Mill Cranes & Other Material Handling Equipment, American Welding Society, Miami ANSI/AWS D14.1–1997. 关8兴 Boresi, A. P., Sidebottom, O. M., Seely, F. B., and Smith, J. O., 1978, Advanced Mechanics of Materials, 3rd ed., Wiley, New York. 关9兴 Sague, J. E., 1978, “The Special Way Big Bearings Can Fail,” Mach. Des. 50共21兲, 113–117.

MAY 2007, Vol. 129 / 333

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