1、Evaluation of Design Criteria for Storage Tanks With Frangible Roof Joints API PUBLICATION 937 APRIL 1996 American Petroleum Institute 1220 L Street, Northwest Washington, D.C. 20005 11 (1) API publications necessarily address problems of a general nature. With respect to particular circumstances, l
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7、uarterly by API, 1220 L Street, N.W., Washington, D.C. 20005. Copyright s 1996 Welding Research Council Inc. American Petroleum Institute EVALUATION OF DESIGN CRITERIA FOR STORAGE TANKS WITH FRANGIBLE ROOF JOINTS Daniel Swenson, Co-Investigator Don Fenton, Co-Investigator Zhi Lu, Graduate Research A
8、ssistant Asif Ghori, Graduate Research Assistant Joe Baalman, Graduate Research Assistant Mechanical Engineering Department Kansas State University Manhattan, KS 66506 API PUBLICATION 937-APRIL 1996 American Petroleum Institute 1220 L Street, Northwest Washington, D.C. 20005 Q FOREWORD American Petr
9、oleum Institute (API) provides standards for the design, construction and inspection of storage tanks. One of the family of design standards, API 650-Welded Steel Tanks for Oil Storis the target of the research addressed by this Bulletin. API 650 includes, among other important design provisions, cr
10、iteria governing the design of frangible rooIjoi#s for w for tanks with diameters of 35 to 60 feet, 2 by 2 by 1/4 inches; for larger tanks 3 by 3 by % inches. Section 3.10.2.2: Roof plates shall have a minimum nominal thickness of 3/16 inch (permissible ordering basis-7.65 pounds per square fool of
11、plate, 0.180- inch plate, or 7-gauge sheet). Section 3.10.2.3: Roof plates of supported cone roofs shall not be attached to the supporting mem- bers. Section 3.10.2.5: Basic criteria for frangible roof joints are given in this section. Section 3.10.2.5 states that for a frangible joint, the top angl
12、e may be smaller than that specified in Section 3.1.5.9. 2 Frangible Roof Joints CONCRETE FWNOATION 114 ItK SlNGlE LAP 25 -0 NOM OIAMETER Fig. 2.2-Overall layout of typical tank Section 3.10.2.5.1: The continuous fillet weld be- tween the roof plates and the top angle can not exceed %s inch. The slo
13、pe of the roof at the top-angle attachment can not exceed 2 inches in 12 inches. Section 3.10.2.5.3: The cross-sectional area at the roof-to-shell junction should not exceed: 0.153 W A = 30,800 tan 0 where, A = Area resisting the compressive force, in square inches, W = Total weight of the shell and
14、 any framing (but not roof plates) supported by the shell and roof, in pounds, 8 = Angle between the roof and a horizontal plane at the roof-to-shell junction, in degrees. Section 3.10.4.1: Roof plates shall be welded on the top side with continuous full-fillet welds on all seams. The size of the ro
15、of-to-top angle weld shall be inch or smaller if so specified on the purchase order. Section 3.10.4.2: The slope of the roof shall be 3/4 inch in 12 inches, or greater if specified by purchaser. (Note: Section 3.10.2.5 limits maximum slope to 2 inches in 12 inches.) Section 3.10.4.5: Rafters shall b
16、e spaced so that at the outer edges their center shall be not more than 6.28 feet apart. Spacing on inner rings shall not be less than 5% feet. Appendix F.2.2.1: When the construction of the compression ring conforms to but does not exceed the minimum requirements of Item e of 3.1.5.9, 3.10.2, and 3
17、.10.4, the frangible characteristic of the ring is retained, and additional emergency venting devices are not required. (Note: The Appendix F requirement to conform to 3.1.5.9 (Item e) is not consistent with Section 10.3.2.5 which allows compression ring area to be reduced for frangible joints.) App
18、endix F.4.1: Maximum design pressure is given by: where, P = internal design pressure, in inches of water, D = tank diameter, in feet, th = nominal roof thickness, in inches. Appendix F.4.2: The maximum design pressure, limited by uplift at the base of the shell, shall not exceed: 0.245W 0.735M P, =
19、 - D2 + 8th - D3 (2.2.3) where, M = wind moment, in foot-pounds. Note: the wind moment term was not in the Eighth Edition of API 650 (API, 1988). Appendix F.5.1: Where the maximum design pres- sure has already been established (not higher than Frangible Roof Joints 3 Frangible Roof Joints that permi
20、tted by F.4.2 or F.4.3), the total required given in Appendix F and are shown in Figure 2.4. As compression area at the roof-to-shell junction may be the roof lifts due to internal pressure, it applies an calculated from the following: inward radial force on the compression area. The compression are
21、a calculations in Figure 2.4 allow the D2(P - 8th) A = (2.2.4) designer to calculate the area available to resist this 30,80O(tan 0) compressive force. Appendix F.5.6: Failure can be expected to occur when the stress in the compression ring area reaches the yield point, as given by: Pf = 1.6P - 4.8t
22、h (2.2.5) where Pf = calculated failure pressure, in inches of water. In addition to the rules given above, only certain configurations of joint design are allowed. These are 2.3 Derivation of API 650 Rules In the above section, the rules that govern frangible joint design were listed as facts. To t
23、ruly understand the rules, it is necessary to understand the intent and derivation of the rules. In this section, we re-derived the API 650 rules to make clear the assumptions on which they are based. The intent is stated in Section 3.10.2.5.1, where, if Neutral axis of amgle , Detail a Detail b Det
24、ell o Detall d Detail e Detail f Detall g max max Detall h Detail I r, = thickness of angle leg. wh = maximum width of participating roof. rb = thickness of bar. = 0.3(Rr). or I2 inches, whichever is less. r, = thickness of shell plate. R, = inside radius of tank shell. rh = thickness of roof plate.
25、 R2 = length of the normal to the roof, measured from the r, = thickness of thickened plate in shell. vertical centerline of the tank. tv, = maximum width of participating shell. = RJ(sin 6). = 0.6 ($3 Note: All dimensions and thicknesses shown are in inches. Fig. 2.4-Permissible details of compress
26、ion rings (from API 650) Frangible Roof Joints the frangible joint rules are met “. . . the joint may be considered to be frangible and, in case of excessive internal pressure, will fail before failure occurs in the tank shell joints or the shell-to-bottom joint. Failure of the roof-to-shell joint i
27、s usually initiated by buck- ling of the top angle and followed by tearing of the 3/16 inch continuous weld of the periphery of the roof plates.“ Although it is true that buckling initiates the actual failure of the joint, buckling follows yielding of the compression ring, and it is the yielding of
28、the compression ring that is used as the basis for API 650 rules. Figure 2.5 shows the equilibrium forces (per unit circumference) on the compression ring. The weight of the plates, the pressure acting on this region, and the are aseumed and ne- Fig. 2.6-Top view of eqolibriurn forces on compression
29、 ring glected. The forces consist of a downward force, caused by stresses in the shell, and an inward force, caused by stresses in the roof. The roof force can be separated into vertical and radial components. The force in the compression ring F, is equal to the Equilibrium in the vertical direction
30、 gives: compression stress u, times the compression area A: - Fcomp Qo=H Fcomp f- RP (2.3.1) Fmmp = ucompA. (2.3.4) = Fahell = 2 Substitutingequations (2.3.2) and (2.3.3) into (2.3.4), V RP gives: Hz- tang-2tan8 (2.3.2) RH A=- - R2P (2.3.5) where, %Om, 2%“,ptan0 V = Vertical component of roof force
31、per unit circumference, Fshell = Force in shell per unit circumference, H = Horizontal component of roof force per unit circumference, P = Internal pressure in the tank, R = radius of the tank. Equilibrium of the compression force in the ring and the horizontal force, as shown in Figure 2.6, gives:
32、v Joint I Fahell Assuming yielding occurs when the bottom is about to uplift, then equation (2.3.5) can be written as: where W is the total weight of the shell. Equation (2.3.6) is the basis of the area inequality rule. From this equation follow the remaining equa- tions given in API 650 for frangib
33、le roofs. To avoid uplift of the bottom, considering a factor of safety n = 1.6 and neglecting wind moment, the maximum design pressure and the weight of shell are related by (Note: in API 650, the unit of P is inches of water, and the density of the roof plates is about 8 times of that of water): S
34、ubstituting W in equations (2.3.6) into (2.3.7) we have: 8Aufield tan 8 P = nD2 + 8pwaterth. (2.3.8) Assume a compressive yield stress of 32,000 psi (as described in Appendix F, Section F.6), substitute into equation (2.3.8), and convert units by 1 inch of wa- ter = 0.03606 psi, gives the equation f
35、or calculating Fig. 2.5-Side view of equilibrium forces on compression ring maximum design pressure as stated in API 650 F.4.1 6 Frangible Roof Joints (neglecting the wind moment term): loaded by a shearing force at the edge. Internal pressure, bending moments, and the effect of large 30,800A tan 8
36、P = + 8th. (2.3.9) displacement are all neglected in the analysis. D2 2.4.1 Derivation of W, For a long cylindrical shell submitted to the action of a shearing force Qo, as If the design Pressure (PI has been estab- shown in Figure 2.7, the governing differential equa- lished, equation (2.3.9) can b
37、e inverted to obtain the tion is: total required area expression as in API 650 F.5.1: (P - 8th)D2 A= 30,800 tan 8 Modifying (2.3.9) by equating the maximum uplift where, force by pressure P, to the weight of the shell gives: p4 = 3(1 - v2) 0.25.rrD2(Pm, - 8pWat,th) = W. (2.3.11) R2h2 Rearranging equ
38、ation (2.3.11) and converting units to inches of water gives the equation in API F.4.2 less the wind moment term which is new in the API 650 ninth edition: 0.245W P, = - D2 + 8th. (2.3.12) If the area A satisfies equation (2.3.6), then the uplift pressure P, is also the calculated failure pressure,
39、Pf. From equation (2.3.7), the relation between Pf and the design pressure P is: w = lateral displacement, R = radius of the shell, h = thickness of the shell, P = internal pressure, D = flexural rigidity. The general solution can be written as (Timoshenko, and Woinowsky-Krieger, 1959): w = e-PX(c3
40、cos px + c4 sin px). (2.4.2) Using the boundary condition of zero moment at the end of the shell: or, in terms of inches of water: d2w - = pe-PX(c3 cos px + c4 sin px) Pf = 1.6P - 4.8th. (2.3.14) dX2 This is identical to equation API 650 F.6. - 2p2d-Px(-c3 sin px + c4 cos px) The above derivations a
41、re based on using static + P2e-PX(-c3 cos px - c4 sin px) equilibrium and the original geometry to calculate the inward force on the compression ring due to roof lifting. The resulting equations demonstrate that the (e) = 0 = - 2p2e-Pc4 basis of the inequality rule is to ensure that yielding dX2 x=o
42、 of the compression ring will occur before uplift of the c4 = 0. (2.4.3) bottom. Yielding and subsequent loss of stiffness are expected to cause buckling of the compression ring, followed by gross deformation of the roof, shell, and associated failure of the roof-to-shell weld. As dis- cussed in Sec
43、tion 5.2 and 5.3, our testing confirms that this is the mode in which failure occurs. 2.4 Derivation of W, and Wh in API 650 Design Rules Section 2.3 demonstrated that the objective of the inequality rule is to ensure that yielding of the compression ring will occur before uplift of the bot- tom. Th
44、e area of the compression ring is determined using Wc, the maximum width of participating shell, and Wh, the maximum width of the participating roof. To verify the validity of the rules, it is necessary to know the basis for the derivations of W, and Wh. As shown below, Wc and Wh can be derived from
45、 linear approximations of cylindrical and conical shells Fig. 2.7-A long shell with edge shear loading Frangible Roof Joints 7 Thus: 1.2 d2w - = p2e-Pxc3 cos px + 2p2e-PXc3 sin px dX2 d3w - = 2c3p3e-PX(cos px - sin px). dX3 (2.4.5) Under the shearing force Qo at the edge where x = 0: Fig. 2.8-Change
46、 of circumferential force along meridian Assuming Poissons ratio = 0.3 gives: The solution for the given problem is then: The circumferential force per unit length of meridian (compression) is: This is the formula given by API 650. Thus, the value 0.6 in API 650 arises from considering the shear for
47、ce acting on a shell and finding the distance for the resulting circumferential stress to drop to /3 of the maximum value. 2.4.2 Derivation of Wh. Consider a complete cone shown in Figure 2.9. Define: Ehw No=- R EhQo =- 2Rp3D e-Px cos fix where E is the Youngs modulus. The circumferential stress can
48、 be written as: The maximum value of compression stress is located at the edge of the shell where x = 0, and is given by: where th is the thickness of the cone and v is Poissons ratio. Then: u0 = uO,e-PX cos px (2.4.11) A plot of normalized force as a function of px is plotted in Figure 2.8. If one
49、considers Wc to be the region where the circumferential stress is equal or greater than 1/3 of the maximum value, its length can be evaluated: 1 e-PWc cos pWc = g Fig. 2.9-A complete cone loaded by edge moment and forces Frangible Roof Joints The linear governing differential equation for the cone can be written as (Timoshenko and Woinowsky- Krieger, 1959): where the Qy is the shearing force per unit circumfer ence. The solutions in terms of Kelvins functions have the form: where ber2 and bei2 are second order Kelvins func- tions and the prime denot
