1、Study to Establish Relations for the Relative Strength of API 650 Cone Roof Roof-to-Shell and Shell-to-Bottom Joints API PUBLICATION 937-A AUGUST 2005 Study to Establish Relations for the Relative Strength of API 650 Cone Roof Roof-to-Shell and Shell-to-Bottom Joints API PUBLICATION 937-A AUGUST 200
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15、sted revisions are invited and should be submitted to the Standards and Publications Department, API, 1220 L Street, NW, Washington, DC 20005, standardsapi.org. TABLE OF CONTENTS 1. INTRODUCTION1 2. SAFEROOF2 3. TANK RESPONSE TO OVER-PRESSURIZATION 3 3.1 EMPTY TANK (NO BUCKLING) .4 3.1.1 Zero Intern
16、al Gauge Pressure .4 3.1.2 Balanced Uplift Pressure.6 3.1.3 Roof-to-Shell Joint Failure Pressure .8 3.1.4 Shell-to-Bottom Joint Failure Pressure .12 3.2 FULL TANK (NO BUCKLING) 13 3.2.1 Zero Internal Gauge Pressure .13 3.2.2 Balanced uplift Pressure15 3.2.3 Roof-to-Shell Joint Failure Pressure .17 3
17、.2.4 Shell-to-Bottom Joint Failure Pressure .18 3.3 EMPTY TANK (WITH BUCKLING)20 3.3.1 Roof-to-Shell Joint Failure Pressure .20 3.4 SUMMARY OF RESPONSES .23 4. FAILURE MODES24 4.1 ROOF-TO-SHELL JOINT FAILURE .24 4.2 SHELL-TO-BOTTOM JOINT FAILURE DUE TO YIELDING OF SHELL .25 4.3 FAILURE OF SHELL-TO-B
18、OTTOM JOINT WELD.25 4.4 FAILURE OF BOTTOM PLATE WELDS.26 4.5 FAILURE OF ATTACHMENTS DUE TO UPLIFT26 4.6 FRACTURE.26 5. SUPPORTING ANALYSES .27 5.1 DESIGNS USED FOR ANALYSIS 27 5.1.1 Tank Size Study27 5.1.2 Roof Slope Study28 5.1.3 Roof Thickness Study .30 5.1.4 Roof Attachment Study.30 5.1.5 Bottom
19、Thickness Study .30 5.1.6 Yield Stress Variation Study 30 5.2 STATIC LARGE DISPLACEMENT, ELASTIC CALCULATIONS31 5.2.1 Tank Size Study32 5.2.2 Roof Slope Study39 5.2.3 Roof Thickness Study .40 5.2.4 Roof Attachment Study.41 5.2.5 Bottom Thickness Study .42 5.2.6 Yield Stress Variation Study 43 5.3 DY
20、NAMIC ELASTIC-PLASTIC CALCULATIONS46 5.3.1 Slow Ramp Analyses using FMA-3D .47 5.3.2 Combustion Analyses using FMA-3D48 5.4 DISCUSSION OF RESULTS.50 6. PROPOSED DESIGN CRITERIA.51 7. DESIGN CHANGES THAT ENABLE SMALL TANKS TO MEET NEW CRITERIA55 8. MISCELLANEOUS ITEMS FOR CONSIDERATION 56 9. CONCLUSI
21、ONS 57 10. REFERENCES58 11. ACKNOWLEDGEMENTS59 A. APPENDIX: SIMPLIFIED DESIGN CALCULATIONS60 A.1 EFFECTIVE STRESS 60 A.2 UPLIFT PRESSURE60 A.1.1 Empty Tank 60 A.1.2 Full Tank60 A.3 ROOF-TO-SHELL JOINT FAILURE PRESSURE 61 A.4 SHELL-TO-BOTTOM JOINT FAILURE PRESSURE .61 A.5 UPLIFT RADIUS .62 A.6 UPLIFT
22、 DISPLACEMENT .63 A.7 CIRCUMFERENTIAL STRESS IN BOTTOM 63 A.8 BOTTOM LAP JOINT FAILURE STRESS64 A.9 APPLICATION OF SIMPLIFIED CALCULATIONS .65 Strength of API 650 Cone Roof Roof-to-Shell and Shell-to- Bottom Joints 1. Introduction This report documents an evaluation of the relative strengths of the
23、roof-to-shell and shell-to-bottom joints in API 650 cone roof tanks. This information is supplied to the American Petroleum Institute as background material for development of design rules that govern frangible roof joints for API 650 tanks. API 650 (American Petroleum Institute, 2001) provides desi
24、gn criteria for fluid storage tanks used to store flammable products. Due to filling and emptying of the tanks, the vapor above the product surface inside the tank may be within its flammability limits. Ignition of this vapor can cause sudden over-pressurization and can lead to the catastrophic loss
25、 of tank integrity. To prevent shell or bottom failure, the rules in API 650 are intended to ensure that the frangible roof-to-shell joint fails before failure occurs in the tank shell or the shell-to-bottom joint. Failure of the frangible roof-to-shell joint provides a large venting area and reduce
26、s the pressure in the tank. Although the criteria in API 650 function well for large tanks, small tanks designed to the API 650 rules have not always functioned as intended. Morgenegg, 1978, provides a description of a 20 foot diameter by 20 foot tall tank in which the shell-to-bottom failed. Other
27、such failures have been noted by API, providing the incentive for this study. As presently written, the API 650 rules do not address the strength of the shell-to-bottom joint directly. Instead, the present rule is intended to ensure that the roof-to-shell joint fails at a pressure lower than that re
28、quired to lift the weight of tank. It is assumed that with no uplift, the shell-to-bottom joint will not have significant additional loads and that failure of the shell-to-bottom will be avoided. A study of roof-to-shell joint failure (Swenson, et al., 1996) showed that for large tanks, the roof-to-
29、shell joint did indeed fail before tank uplift, but that for smaller tanks uplift would occur before roof-to-shell joint failure. Since uplift occurs for small tanks, this increases the possibility of shell-to-bottom joint failure. The purpose of this study is to investigate the relative strengths o
30、f the roof-to-shell and shell-to-bottom joints, with the goal of providing suggestions for frangible roof design criteria applicable to smaller tanks. 1 Strength of API 650 Cone Roof Roof-to-Shell and Shell-to- Bottom Joints 2. SafeRoof The calculations in this report were made using the SafeRoof co
31、mputer program (Lu and Swenson, 1994). SafeRoof was developed to design and analyze storage tanks with frangible roof joints. The program is the result of a research program into frangible joint design, sponsored by the American Petroleum Institute and the Pressure Vessel Research Council. SafeRoof
32、includes design, analysis, and post-processing modules. In the design module, the user can input tank parameters and SafeRoof will develop a design following API 650 guidelines. This design can either be accepted or modified. The user can then analyze the stresses and displacements in the tank at pr
33、essures corresponding to selected tank failure modes. The analysis can be coupled to a combustion/joint failure analysis. The pressures at each failure mode can be used to help evaluate safety of the tank due to overload pressures. The original version of SafeRoof used a static, large displacement,
34、elastic finite element model. As part of this project, version 2.0 was extended to incorporate the capability to perform dynamic, large displacement, elastic-plastic analyses of tank response. This capability is based on the FMA-3D code (FMA, 2004). Version 2.1 includes the capability to approximate
35、 circumferential buckling in the roof and floor. Buckling is approximated by reducing the circumferential stiffness of the roof (or floor) finite elements by a factor of 10 in the elements in which compressive circumferential stresses are detected. Based on beam flange buckling practice, buckling ef
36、fects are not included within a distance of 32 times the roof (or floor) thickness from the joint. In addition, for buckling of the floor, the floor must have uplifted from the supporting foundation.2 Strength of API 650 Cone Roof Roof-to-Shell and Shell-to- Bottom Joints 3. Tank Response to Over-Pr
37、essurization Before discussing the general results for the study, it is important to examine in detail the response of an oil storage tank to over-pressurization, based on previous work (Swenson et al., 1996). A tank with a 30 foot diameter and a 32 foot height will be discussed as a representative
38、tank. The tank parameters are given in Figure 3-1. Figure 3-1: Design of representative 30 foot diameter tank This design was done using the SafeRoof program (Lu and Swenson, 1994). This program follows API 650 rules to design the tank. The maximum fluid level is assumed to be 31 feet, with a specif
39、ic gravity of 0.95. The material is ASTM A36, with a minimum yield strength of 36,000 psi, a modulus of 30E6 psi, and a Poissons ratio of 0.25. In this example, the minimum yield strength was used, however, the typical yield strength should be used for design calculations. The design has four course
40、s with a thickness of 0.1875 inch. The top angle faces radially outward, with an angle width of 2 inches and a thickness of 0.1875 inches. The roof is welded to the top angle at a distance of 1 inch outside the radius of the tank. The slope of the roof is 0.75 inches in 12 inches. The bottom thickne
41、ss is 0.25 inches. The tank is assumed to rest on sand, with a ringwall foundation. The stiffness of the sand is assumed to be 250 lb/sq. in/in and the stiffness of the foundation is assumed to be 1,000 lb/sq. in/in. The inner radius of the ringwall is 3 Strength of API 650 Cone Roof Roof-to-Shell a
42、nd Shell-to- Bottom Joints 14.5 ft. The weight of the roof and tank shell is calculated to be 28,400 lbs. This does not include any deadweight due to stairways or other attachments. As will be discussed, the roof-to-shell and shell-to-bottom joints act in circumferential compression at their respect
43、ive failure pressures. This can lead to circumferential buckling of the roof near the roof-to-shell joint. The same buckling can occur at the shell-to-bottom joint, although to a lesser extent. If buckling occurs, it reduces the participation of the roof in carrying the compressive load at the joint
44、. This leads to a lower calculated failure pressure than if buckling is not taken into account. This will be discussed for the case of an empty tank. 3.1 Empty Tank (no buckling) We will first examine the response of the empty tank to four cases: Zero internal gauge pressure The pressure required to
45、 just cause uplift of the tank The pressure at failure of the roof-to-shell joint The pressure at failure of the shell-to-bottom joint These results are based on the elastic, large deformation, static finite element analysis in SafeRoof. Results for inelastic, large deformation, dynamic analyses are
46、 similar and are presented later in this report. 3.1.1 Zero Internal Gauge Pressure At zero internal gauge pressure and for an empty tank, the only load is the weight of the tank. As shown in Figure 3-2, there is little displacement except at the foundation. Figure 3-3 shows a detail of this displac
47、ement, which has a value of -0.005 inch directly under the tank shell. A plot of the equivalent stress (which can be used to predict onset of yielding), is shown in Figure 3-4. The stress is largest slightly above the shell-to-bottom, however the maximum stress is only 280 psi, so it is very low. 4
48、Strength of API 650 Cone Roof Roof-to-Shell and Shell-to- Bottom Joints Figure 3-2: Tank displacement at zero internal gauge pressure (magnification=100x) Figure 3-3: Detail of displacement of empty tank at foundation (magnification=100x) 5 Strength of API 650 Cone Roof Roof-to-Shell and Shell-to- B
49、ottom Joints Figure 3-4: Middle surface equivalent stress contours in empty tank (min=0 psi, max=280 psi) 3.1.2 Balanced Uplift Pressure Using the SafeRoof program, the pressure needed to just cause uplift of the empty tank (the “balanced uplift pressure” is calculated to be 0.295 psi. The deformed tank shape at this pressure is shown in Figure 3-5. The roof has lifted off the rafters and the displacement at the bottom of the shell is zero. The equivalent stresses shown in Figure 3-6 show that the peak stress is now at the roof-to-shell joint. However, th
