WRC107

1.关于各频段的范围及米制分类：无线电频谱应细分为九个频段，按照下表以递增的整数列示。

因频率单位为赫兹（Hz），所以频率的表达方式应为：– 3 000 kHz以下（包括3 000 kHz），以千赫（kHz）表示；– 3 MHz以上至3 000 MHz（包括3 000 MHz），以兆赫（MHz）表示；– 3 GHz以上至3 000 GHz（包括3 000 GHz），以吉赫（GHz）表示。

但是，如果遵守这些规定会导致严重困难，例如在进行频率通知及登记、频率表或有关注1：“频段N”（N = 频段序号）从0.3 ×10N Hz 至3 ×10N Hz。

注2：词头：k = 千（103），M = 兆（106），G = 吉（109）。

[I]LK0224[Q]我国无线电频率划分表划分给业余业务使用的最接近Ku波段卫星电视广播频率的频带10-10.5GHz，属于无线电频谱的下列频带（波段）：[A]超高频（厘米波）[B]特高频（分米波）[C]极高频（毫米波）[D]甚高频（米波）解析：3~30GHz为超高频，SHF。

[I]LK0226[Q]我国无线电频率划分表划分给业余业务使用的最高频带为241GHz-250GHz，属于无线电频谱的下列频带（波段）：[A]极高频（毫米波）[B]超高频（厘米波）[C]至高频（丝米波或亚毫米波）[D]特高频（分米波）解析：30~300GHz为极高频，EHF。

[I]LK0215[Q]我国无线电频率划分表划分给业余业务使用的1,800kHz-2,000kHz属于无线电频谱的下列频带（波段）：[A]MF[B]HF[C]VHF[D]LF解析：300~3000kHz为中频，MF。

2.Q短语（*为必须记忆）QRA 电台何台QRB 电台间之距离QRG 告之正确频率QRH 频率是否变动QRI 发送音调QRJ 能否收到QRK 信号之可解度QRL 电台忙碌/工作中*QRM 电台受他台干扰*QRN 电台受天电干扰*QRO 增加发射功率*QRP 减低发射功率*QRQ 请发快点*QRS 请发慢点*QRT 电台关机*QRU 电台已无事可再谈*QRV 电台已准备工作QRW 利用频率呼叫或通知QRX 约会下次*QRY 通信轮流号码QRZ 是谁呼叫*QSA 信号强度如何*QSB 信号衰退*QSD 敲键有缺陷QSI 无法在发射中切入QSK 在发射中切入QSL 确认通信/电报抄收收据/交换通联卡*QSN 在频率上收听到QSO 无线电通信/直接联络*QSP 转告、转报*QSR 频率上重复呼叫QSS 工作频率QSU 在此频率发送回答QSV 某频率发送一系列VQSX 在某频率发送、收听QSY 更改频率*QSZ 重复发送每字及词QTH 所在地*QTQ 以国际简码通信QTR 正确时间QTS 以呼号发送进行调整QTV 在某频率占住QTX 维持通信到通知止QUA 有关某电台消息QUM 重新开始正常工作3.发射类别（class of emission）归纳：（1）CW报发射：A1A（2）单边带话发射：J3E（3）单边带话传输的RTTY发射：F2B（4）单边带话传输的PSK31发射：G2B（5）调频话：F3E[I]LK0127[Q]发射类别（class of emission）是指用标准符号标示的某发射的一组特性，例如主载波调制方式，调制信号，被发送信息的类型以及其他适用的信号特性。

管道应力分析基础理论管道应力分析主要包括三方面内容：正确建立模型、真实地描述边界条件、正确地分析计算结果。

所谓建立模型就是将所分析管系的力学模型按一定形式离散化，简化为程序所要求的数学模型，模型的真实与否是做好应力分析的前提条件。

应力分析的根本问题就是边界条件问题，而体现在工程问题上就是约束（支架）、管口等具体问题的模拟，真实地描述这些边界条件，才能得到正确的计算结果。

要想能够熟练而正确地分析结果，首先会正确设计支吊架，有一定的相关理论知识如工程力学，流体力学，化工设备及机械等，另外需在一定时间内不断摸索，总结出规律性的问题。

第一章管道应力分析有关内容·§1.1 管道应力分析的目的进行管道应力分析的问题很多CAESARII解决的问题主要有：1、使管道各处的应力水平在规范允许的范围内。

2、使与设备相连的管口载荷符合制造商或公认的标准（如NEMASM23，API610 API617等标准）规定的受力条件。

3、使与管道相连的容器处局部应力保持在ASME第八部分许用应力范围内。

4、计算出各约束处所受的载荷。

5、确定各种工况下管道的位移。

6、解决管道动力学问题，如机械振动、水锤、地震、减压阀泄放等。

7、帮助配管设计人员对管系进行优化设计。

§1.2 管道所受应力分类1.2.1 基本应力定义轴向应力（Axial stress）：轴向应力是由作用于管道轴向力引起的平行管子轴线的正应力，：S L＝F AX/A m其中S L＝轴向应力MPaF AX＝横截面上的内力NA m＝管壁横截面积mm2=π（do2-di2)/4管道设计压力引起的轴向应力为S L＝Pdo/4t轴向力和设计压力在截面引起的应力是均布的，故此应力限制在许用应力[σ]t范围内。

弯曲应力（bending stress）：由法向量垂直于管道轴线的力矩产生的轴向正应力。

S L=M b c/I其中：M b=作用在管道截面上的弯矩N.mC－从管道截面中性轴到所在点的距离mmI－管道横截面的惯性矩mm4=π(d o4－d l4）/64当C达到最大值时，弯曲应力最大S max=M b R0/I= M b/Z弯曲应力在断面上是线性分布的,截面最外端应力达到最大时，其它地方仍处于弹性状态，故应力限制在1.5[σ] 之内。

To: All WRC Subscribers and purchasers of WC 537 From: WRC Publication Staff Date: Friday, August 19, 2011 Subject: WRC Bulletin 537 Errata The following errata have been reported.Page Section/Table/Figure DescriptionDate Corrected 6August 1965 ForewordCorrect range for beta from 0.375 to 0.55/31/201116 3.4 Page number for nondimensional curves for spherical shells shouldbe page 43 5/31/201125 4.4.1 Page number for nondimensional curves for cylindrical shells shouldbe page 91 5/31/201139 Table 5Table 5 – for computation of Nø/(P/Rm) currently states 3C or 4C,should only State 3C – Note Figure 3C is properly labeled. 6/1/2011 39 Table 5Table 5 – for computation of Nx/(P/Rm) currently states 3C or 4C,should only State 4C – Note Figure 4C is properly labeled 6/1/2011 51 Curve Fit Table forSP-1 Incorrect column name in last column currently shows My shouldshow Ny7/5/2011 54,55 Figure SP-3 and Curve Fit TableIncorrect range for right side axis for NiT(RmT)1/2/Mcosq6/21/201174,75 Figure SM-3 and Curve Fit Table Curve fit for data was adjusted to prevent negative values for Y withinvalid range for X 7/22/201186 Figure SM-9 Adjusted the placement of the labels for Nx and My for easier reading 7/22/201189 Curve Fit Table forSM-10 Equation shown is not the equation used to calculate the curve fit6/21/2011101 Figure 4A and CurveFit TableMissing figure and table2/28/2011118 Figure 3B Title is incorrect should be longituidinal moment not circumferential 5/31/2011120 Figure 4B Title is incorrect should be longituidinal moment not circumferential 5/31/2011128, 129Figure 1C-1 Original and Curve Fit Table Incorrect range for Y4/4/2011130, 131 Figure 1C-1 Extrapolated and Curve Fit Table Incorrect range for Y 4/4/2011 184Figure B-2Incorrect values for x axis8/19/2011If you have any further questions,please send an email to subscribers@ . If any additional errata items are reported, this file will be updated. Please check/wrc/BULLETIN%20537_Errata_pages.pdf for any updates.The Welding Research Council, Inc.WRC 537Local Stresses in Spherical and Cylindrical Shells Due To External Loading5FOREWORDTo WRC Bulletin 107, March 1979 Update of August 1965 Original VersionWelding Research Council Bulletin No. 107 has been one of the most widely used bulletins ever published by WRC. The original bulletin was published in August 1965. Since that time, a revised printing was issued in December 1968; a second revised printing was issued in July 1970; a third revised printing was released in April 1972; and a June 1977 reprint of the third revised printing was issued. As sometimes happens with publications of this type, some errors were detected and then corrected in subsequent revised printings.In this March 1979 Revision of Bulletin 107, there are some additional revisions and clarifications. The formulations for calculation of the combined stress intensity, S, in Tables 2, 3, and 5 have been clarified. Changes in labels in Figures 1C-1, 2C-1, 3C , and 4C have been made and the calculated stresses for Model "R" in Table A-3 and Model "C-l" in Table A-4 have been revised accordingly. The background for the change in labels is given in a footnote on p. 66.Present plans call for a review and possible extension of curves to parameters which will cover the majority of openings in nuclear containment vessels and large storage tanks. Plans are to extend /R T from 300 to 600 and to extend /d D range from 0.003 to 0.10 for the new /R T range, review available test data to establish limits of applicability, and develop some guidance for pad reinforcements.Long range plans are to review shell theory in general, and Bijlaard's method in particular. The goal is to extend the /R T up to 1200 for a /d D up to 0.1. This will include large deflection theory and other nonlinear effects. In addition, available computer programs will be studied in hope of developing one which will be an appropriate supplement to Bijlaard's method. Finally, a review will be made of limit loads related to large /R T and small /d D .J.R, Farr, Chairman PVRC Design DivisionThe Welding Research Council, Inc.WRC 5376Local Stresses in Spherical and Cylindrical Shells Due To External LoadingFOREWORDTo WRC Bulletin 107, August 1965 Original VersionSeveral years ago, the Pressure Vessel Research Committee sponsored an analytical and experimental research program aimed at providing methods of determining the stresses in pressure vessel nozzle connections subjected to various forms of external loading. The analytical portion of this work was accomplished by Prof. P. P. Bijlaard of Cornell University, and was reported in References 1 to 8 inclusive. Development of the theoretical solutions involved a number of simplifying assumptions, including the use of shallow shell theory for spherical vessels and flexible loading surfaces for cylindrical vessels. These circumstances limited the potential usefulness of the results to /i i d D , ratios of perhaps 0.33 in the case of spherical shells and 0.25 in the case of cylindrical shells. Since no data were available for the larger diameter ratios, Prof. Bijlaard later supplied data, at the urging of the design engineers, for the values of 0.375β= and0.50 (/i i d D , ratios approaching 0.60) for cylindrical shells, as listed on page 12 of Reference 10.In so doing, Prof. Bijlaard included a specific warning concerning the possible limitations of these data, as follows: "The values for these large loading surfaces were computed on request of several companies. It should be remembered, however, that they actually apply to flexible loading surfaces and, for radial load, to the center of the loading surface. It should be understood that using these values for the edge of the attachment, as was recommended for small loading surfaces, may be unconservative.''Following completion of the theoretical work, experimental work was undertaken in an effort to verify the theory, the results of which were published in References 17 and 18. Whereas this work seemingly provided reasonable verification of the theory, it was limited to relatively small /i i d D ratios-0.10 in the case of spherical shells and 0.126 in the case of cylindrical shells. Since virtually no data, either analytical or experimental, were available covering the larger diameter ratios, the Bureau of Ships sponsored a limited investigation of this problem in spheres, aimed at a particular design problem, and the Pressure Vessel Research Committee undertook a somewhat similar investigation in cylinders. Results of this work have recently become available emphasizing the limitations in Bijlaard 's data on cylindrical shells, particularly as it applies to thin shells over the "extended range " (page 12 of Reference 10).Incident to the use of Bijlaard's data for design purposes, it has become apparent that design engineers sometimes have difficulty in interpreting or properly applying this work. As a result of such experience, PVRC has felt it desirable that all of Bijlaard's work be summarized in convenient, "cook-book" form to facilitate its use by design engineers. However, before this document could be issued, the above mentioned limitations became apparent, presenting an unfortunate dilemma, viz., the test data indicate that the calculated data are partially inadequate, but the exact nature and magnitude of the error is not known, nor is any better analytical treatment of the problem available (for cylinders).Under these circumstances, it was decided that the best course was to proceed with issuing the "cook-book," extending Bijlaard's curves as best we can on the basis of available test data. This decision was based on the premise that all of the proposed changes would be toward the conservative (or "safe") side and that design engineers would continue to use Bijlaard 's extended range data unless some alternative were offered. The following paper is therefore presented in the hope that it will facilitate the use of Bijlaard's work by design engineers. Every effort has been made to point out any known limitations in the work and to explain the exact nature of the changes which have been made to Bijlaard's original curves and data; however, users are warned that the resulting work is not necessarily adequate for all cases. It is the hope of the Subcommittee that additional theoretical work can be undertaken to provide more adequate data on various phases of this problem.F. S.G. Williams, ChairmanPVRC Subcommittee on Reinforced Openings and External LoadingsThe Welding Research Council, Inc.WRC 537Local Stresses in Spherical and Cylindrical Shells Due To External Loading153.3.2 Stresses Resulting From Overturning Moment,M3.3.2.1Radial Stresses (x σ)a) STEP 1. Using the applicable values of *,,U and ρϒ, read off the dimensionless membrane force()/xN M from the applicable curve which will be found in one of the following figures:Figure SR-3 or SM-1 to SM-10, inclusive.b) STEP 2. By the same procedure used in STEP 1 above, read off the value of dimensionless bendingmoment ()/M M from the applicable curve. This value will be found in the same figureused in STEP 1.c) STEP 3. Using the applicable values of ,,m M R and T , calculate the radial membrane stress()/x N Tby:x N T ⎞=⎝(12) d) STEP 4. By a procedure similar to that used in STEP 3, calculate the radial bending stress()26xMT, thus:26x M T ⎞=⎝ (13) e) STEP 5. Combine the radial membrane and bending stresses by use of the general stress equation(paragraph 2) together with the proper choice of sign (see Table 1); i.e.,26x x x nb N MK K T Tσ=± (14) 3.3.2.2Tangential Stress (y σ)Follow the five steps outlined in 3.3.2.1, using the same figure to obtain ()/y N Mand()/MM used to obtain ()/x N T P and ()/x M P .It follows that:yN T ⎛⎞=⎝⎠(15) 26yM T ⎛⎞=⎝⎠ (16) 26y yy nbN M K K T Tσ=± (17)The Welding Research Council, Inc.WRC 53716Local Stresses in Spherical and Cylindrical Shells Due To External Loading3.3.3Stresses Resulting From Torsional Moment, T MIn the case of a round attachment (such as a pipe), torsional moment is assumed to induce pure shear stresses, so that shear stress ()τ in the shell at the attachment-to-shell juncture is given by:202Tyx xy M r Tττπ==(18) If only shear stresses are being considered, it is to be noted that the equivalent stress intensity is twice the above calculated shear stress.In the case of rectangular attachments, torsional moment produces a complex stress field in the shell. Acceptable methods of analyzing this situation are not available at this time. If the designer has reason for concern, the problem should be resolved by testing in accordance with established code procedures. 3.3.4 Stresses Resulting From Shear Load, V Bijlaard has proposed 14 that shear force()V can be assumed transmitted to the shell entirely bymembrane shear force. Therefore, stresses in the shell at the attachment-to-shell juncture can be approximated as follows:3.3.4.1 Round Attachment0sin xy V(refer to Figure 1)r T τθπ=(19)3.3.4.2 Square Attachment1(90270)4xy V at and c Tτθ==°° (20)3.3.5 Stresses Resulting From Arbitrary LoadingIn the general case, all applied loads and moments must be resolved (at the attachment-shell interface) in the three principal directions; i.e., they must be resolved into components 1212,,,,,T P V V M M and M . If one then proceeds in the manner previously outlined, membrane, bending and shear stresses can be evaluated at eight distinct points in the shell at its juncture with the attachment. These eight points are shown in the sign convention chart, Table 1.The numerous stress components can be readily accounted for, if a scheme similar to that shown in Table 2 and 3 is adopted. In using this scheme, it is to be noted that the Maximum Shear Theory has been used to determine equivalent stress intensities. Also, it is to be noted that evaluation of stresses resulting from internal pressure has been omitted.Test work conducted by PVRC has shown that stresses attenuate rapidly at points removed from the attachment-to-shell juncture, the maximum stress frequently being located at the juncture.* However, in the general case of arbitrary loading, one has no assurance that the absolute maximum stress intensity in the shell will be located at one of the eight points considered in the above discussion.3.4 List Of Nondimensional Curves For Spherical ShellsThe nondimensional curves for solid and hollow attachments in spherical shells is shown on page 43 .*Under certain conditions stresses may be higher in the nozzle wall than they are in the vessel wall. This possibility is most likely if the nozzle opening in not reinforced or if the reinforcement is placed on the vessel wall and not on the nozzle.The Welding Research Council, Inc.WRC 537Local Stresses in Spherical and Cylindrical Shells Due To External Loading254.3.5.2 Rectangular Attachment14cx V c Tφτ=(50) 24Lx V c Tφτ=(51) 4.3.6 Stresses Resulting From Arbitrary LoadingIn the general case, all applied loads and moments must be resolved (at the attachment-to-shell interface) in the three principal directions; i.e., they must be resolved into components ,,,,,c L c L T P V V M M and M . If one then proceeds in the manner previously outlined (e.g., paragraph 4.3.1.1), membrane, bending and shear stresses can be evaluated at eight points in the shell at its juncture with the attachment. These eight points are shown in the sign convention chart, Table 4.4.4 Nondimensional Curves For Cylindrical ShellsThe nondimensional curves which follow constitute, in general, a replot of Bijlaard's data to a semilog scale in order that certain portions of the curves can be read with greater facility. Those portions of the curves which are taken directly from Bijlaard's work are shown as solid curves; those portions of the curves which have been modified on the basis of recent experimental data, as discussed in Appendix A, are shown as dotted curves.In the case of longitudinal moment loading and axial loading (thrust), two sets of curves are shown for the bending components of stress-one set applying to the longitudinal axis, and the other applying to an area of maximum stress off the axes of symmetry (longitudinal moment), or to the transverse axis (thrust). In the latter case, a portion of the original curves has been deleted in order to emphasize that the curves should not be used beyond the limits indicated. This was done because the available data indicated that the "outer limits" of the curves were appreciably unconservative, with no feasible manner to "correct" them (as explained in Appendix A).In the case of longitudinal moment , the exact location, of the maximum stress cannot be defined with certainty, but Figure A-14 will provide an estimate of its location (considering that the location of maximum stress under internal pressure and longitudinal moment was essentially the same on IIT model "C-1," as shown on Figures A-2 and A-3). It should also be noted that, to the best of our knowledge, the curves for "maximum stresses off the axes of symmetry" (Figures 1B-1 and 2B-1) would apply only to the case of a round, flexible nozzle connection; it is conceivable that a similar effect might apply to a rigid square or rectangular attachment, for which the shell at the outer edges of the attachment might take a greater part of the load than that portion of the shell adjacent to the longitudinal centerline. However, we know of no direct evidence to support such an assumption.4.4.1 List Of Nondimensional Curves For Cylindrical ShellsThe list of nondimensional curves for cylindrical shells is shown on page 91.4.5 Limits On ApplicationWhere relatively large attachments are considered, or when situations are encountered that deviate considerably from the idealized cases presented herein, the designer should refer to paragraph A.3 in Appendix A and to the original references to ascertain the limitations of applicability for the procedure used. However, there are a few generalizations that can safely be made regarding vessel and attachment geometry.The Welding Research Council, Inc.WRC 53726Local Stresses in Spherical and Cylindrical Shells Due To External Loading4.5.1 External Radial LoadStresses are affected very little by the ratio of shell length to shell radius ()/m l R . Therefore, no restriction is made on the point of load application except in very extreme cases. The curves included in this report are for an /m l R ratio of 8, which is sufficient for most practical applications. On the basis of data presented in Bibliographical Reference 2, results based on an /m l R ratio of 8 will be slightly conservative for lesser values of /m l R ratio and unconservative for greater values of /m l R ratio. However, the error involved does not exceed approximately 10% of all /m l R values greater than 3, which should be sufficiently accurate for most calculations. Since for lesser values of /m l R , the results are conservative, no restriction will ordinarily be necessary on /m l R ratio or the point of load application. For extreme cases or for "off center" loading, one may make corrections by use of the curves presented on page 8 of Bibliographical Reference 2, if desired.Results are not considered applicable in cases where the length of the cylinder ()l is less than its radius()m R . This applies either to the case of an open ended cylinder or closed ended cylinder where thestiffness is appreciably modified from the case considered.4.5.2 External MomentResults are applicable in the case of longitudinally off center attachments (a more usual case) provided that the attachment is located at least half the shell radius ()0.5m R from the end of the cylinder.4.5.3 Attachment StressesThe foregoing procedure provides one with a tool to find stresses in the shell, but not in the attachment. Under certain conditions, stresses may be higher in the attachment than they are in the vessel. For example, in the case of a nozzle, it is likely that the stresses will be higher in the nozzle wall than they are in the vessel wall if the nozzle opening is unreinforced or if the reinforcement is placed on the vessel wall and not on the nozzle.5 ACKNOWLEDGMENTThe authors wish to acknowledge the significant contributions made by J. B. Mahoney of Applied Technology Associates Inc. and M. G. Dhawan of the Bureau of Ships during the preparation of this paper. In addition, the comments received during the review of this document by the members of the PVRC Subcommittee on Reinforced Openings and External Loadings are deeply appreciated.6 REFERENCES1. Bijlaard, P. P., "Stresses from local Loadings in Cylindrical Pressure Vessels," Trans. A.S.M.E., 77,805-816 (1955).2. Bijlaard, P. P., "Stresses from Radial Loads in Cylindrical Pressure Vessels," Welding Jnl., 33 (12),Research Supplement, 615-s to 623-s (1954).3. Bijlaard, P. P., "Stresses from Radial Loads and External Moments in Cylindrical Pressure Vessel,"Ibid., 34 (12). Research Supplement, 608-s to 617-s (1955).4. Bijlaard, P. P., "Computation of the Stresses from Local Loads in Spherical Pressure Vessels orPressure Vessel Heads," Welding Research Council Bulletin No. 34, (March 1957).5. Bijlaard, P. P., "Local Stresses in Spherical Shells from Radial or Moment Loadings," Welding Jnl., 36(5), Research Supplement, 240-s to 243-s (1957).6. Bijlaard, P. P., "Stresses in a Spherical Vessel from Radial Loads Acting on a Pipe," Welding ResearchCouncil Bulletin No. 49, 1-30 (April 1959).7. Bijlaard, P. P., "Stresses in a Spherical Vessel from External Moments Acting on a Pipe," Ibid., No. 49,31-62 (April 1959).The Welding Research Council, Inc.Table 5 Continued – Computation Sheet for Local Stresses in Cylindrical ShellsWRC 537Local Stresses in Spherical and Cylindrical Shells Due To External Loading 39The Welding Research Council, Inc.WRC 53740Local Stresses in Spherical and Cylindrical Shells Due To External LoadingTable 6 – Radial Load PTable 7 – Circumferential Moment c M12/ββγc K for θ c K for M φc xK for M c C for N φ c x C for N0.2515 1.09 1.31 1.84 0.31 0.4950 1.04 1.24 1.62 0.21 0.46 100 0.97 1.16 1.45 0.15 0.44 300 0.92 1.02 1.17 0.09 0.46 0.515 1.00 1.09 1.36 0.64 0.7550 0.98 1.08 1.31 0.57 0.75 100 0.94 1.04 1.26 0.51 0.76 300 0.95 0.99 1.13 0.39 0.77 215 (1.00) (1.20) (0.97) (1.7) (1.3)100 1.19 1.10 0.95 1.43 1.12 300 --- (1.00) (0.90) (1.3) (1.00) 415 (1.00) (1.47) (1.08) (1.75) (1.31)100 1.49 1.38 1.06 1.49 0.81 300 --- (1.27) (0.98) (1.36) (0.74)Note: The values in parenthesis determined by an approximate solution.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e S P -1The Welding Research Council Inc.F i g u r e S P - 2 S t r e s s e s i n S p h e r i c a l S h e l l D u e t o a R a d i a l L o a d P o n N o z z l e C o n n e c t i o n0.01N xN yx (M A X )y (MA X )The Welding Research Council Inc.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e S P -2The Welding Research Council Inc.F i g u r e S P -3 – S t r e s s e s i n S p h e r i c a l S h e l l D u e t o a R a d i a l L o a d P o n N o z z l e C o n n e c t i o nThe Welding Research Council Inc.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e S P -3The Welding Research Council Inc.F i g u r e S P -4 – S t r e s s e s i n S p h e r i c a l S h e l l D u e t o a R a d i a l L o a d P o n N o z z l e C o n n e c t i o n0.01N xN yM x(M A X )The Welding Research Council Inc.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e S M -2The Welding Research Council Inc.F i g u r eS M-3 – S t r e s s e s i n S p h e r i c a l S h e l l D u e t o O v e r t u r n i n g M o m e n tM o n a N o z z l e C o n n e c t i o nThe Welding Research Council Inc.r R TC u r v e F i t C o e f f i c i e n t s f o r F i g u r e S M -3The Welding Research Council Inc.F i g u r eS M-4 – S t r e s s e s i n S p h e r i c a l S h e l l D u e t o O v e r t u r n i n g M o m e n tM o n a N o z z l e C o n n e c t i o n0.010.10.1N xM yN y (M A X )M x (MA X )The Welding Research Council Inc.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e S M -8The Welding Research Council Inc.F i g u r eS M-9 – S t r e s s e s i n S p h e r i c a l S h e l l D u e t o O v e r t u r n i n g M o m e n tM o n a N o z z l e C o n n e c t i o nThe Welding Research Council Inc.r R TC u r v e F i t C o e f f i c i e n t s f o r F i g u r e S M -10The Welding Research Council Inc.The Welding Research Council, Inc.THIS PAGE INTENTIONALLY LEFT BLANKC u r v e F i t C o e f f i c i e n t s f o r F i g u r e 3A – E x t r a p o l a t e dThe Welding Research Council Inc.F i g u r e 4A – M o m e n t()2/cmN MR φβ D u e t o a n E x t e r n a l C i r c u m f e r e n t i a l M o m e n t c M on a C i r c u l a r C y l i n d e r – O r i g i n a lThe Welding Research Council Inc.βC u r v e F i t C o e f f i c i e n t s f o r F i g u r e 4A – O r i g i n a lThe Welding Research Council Inc.i g u r e 1B – M o m e n t()/L m M M R φβ D u e t o a n E x t e r n a l L o n g i t u d i n a l M o m e n t LMo n a C i r c u l a r C y l i n d e r (S t r e s s o n t h e L o n g i t u d i n a l P l a n e o fS y m m e t r y ) – O r i g i n a lβThe Welding Research Council Inc.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e 2B -1 – E x t r a p o l a t e dThe Welding Research Council Inc.F i g u r e 3B – M e m b r a n e F o r c e()2/LmN MR φβ D u e t o a n E x t e r n a l L o n g i t u d i n a l M o m en t LMo n a C i r c u l a r C y l i n d e r – O r i g i n a lβThe Welding Research Council Inc.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e 1C – E x t r a p o l a t e dWRC Bulletin 537Local Stresses in Spherical and Cylindrical Shells Due To External Loading127The Welding Research Council Inc.F i g u r e 1C -1 – B e n d i n g M o m e n tx M PD u e t o a nE x t e r n a l R a d i a l L o a d P o n a C i r c u l a r C y l i n d e r (L o n g i t u d i n a l A x i s ) – O r i g i n a l WRC Bulletin 537128Local Stresses in Spherical and Cylindrical Shells Due To External LoadingThe Welding Research Council Inc.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e 1C -1 – O r i g i n a lWRC Bulletin 537Local Stresses in Spherical and Cylindrical Shells Due To External Loading129The Welding Research Council Inc.F i g u r e 1C -1 – B e n d i n g M o m e n tx M PD u e t o a nE x t e r n a l R a d i a l L o a d P o n a C i r c u l a r C y l i n d e r (L o n g i t u d i n a l A x i s ) – E x t r a p o l a t e d 0.10.5WRC Bulletin 537130Local Stresses in Spherical and Cylindrical Shells Due To External LoadingThe Welding Research Council Inc.C u r v e F i t C o e f f i c i e n t s f o r F i g u r e 1C -1 – E x t r a p o l a t e dWRC Bulletin 537Local Stresses in Spherical and Cylindrical Shells Due To External Loading131The Welding Research Council Inc.F i g u r e 2C – B e n d i n g M o m e n tx M PD u e t o a nE x t e r n a l R a d i a l L o a d P o n a C i r c u l ar C y l i n d e r (T r a n s v e r s e A x i s ) – O r i g i n a l WRC Bulletin 537132Local Stresses in Spherical and Cylindrical Shells Due To External LoadingThe Welding Research Council Inc.The Welding Research Council, Inc.WRC 537Local Stresses in Spherical and Cylindrical Shells Due To External Loading183B.6 FiguresFigure B-1 – Stepped BarThe Welding Research Council, Inc.WRC 537184Local Stresses in Spherical and Cylindrical Shells Due To External Loading00.050.100.150.200.250.300.35Scale BScale A0.51.01.52.02.53.03.5S t r e s s C o n c e n t r a t i o n F a c t o r , KRatio of Fillet Radius to Shellor Nozzle Thickness (r/T, 2r/d n , or 2r/h)5.04.03.02.01.51.0Figure B-2 – Stress Concentration Factors for D d >>。

WRC107，WRC297，EN13445在筒体上局部应力计算的比较一、力学模型和适用范围：1、WRC107：- 筒体上的实心圆柱体、矩形附件和方形附件受外加机械载荷；- 球壳上的接管、实心圆柱体和方形附件受外加机械载荷；- 筒体与圆柱体连接结构的适用直径比d/D ≤ 0.5；- 球壳与接管连接结构的适用直径比d/D ≤0.375；注：准确的说不是0.5而是0.496，见WRC107公报。

这个还有筒体直径和璧厚比值的限制：璧厚和球形封头中径的比值≤ 236；璧厚和筒体中径的比值≤230。

但不知道什么原因软件按中都用的是0.5，或者是我看标准不够认真看错了。

HG20583上球壳与接管连接结构的适用直径比d/D ≤0.5，也应该是0.496而不是0.375见WRC107公报，或许我看错了。

2、WRC297：- 筒体上接管受到外加机械载荷；- 接管与筒体的直径比d/D ≤0.5。

3、EN13445中局部应力计算方法，其适用范围：球壳与接管连接结构: 0.001 ≤ de /R ≤ 0.1；筒体与接管连接结构: 1) 0.001 ≤de /D ≤0.1。

二、壳体上薄膜应力的比较：1、WRC107方法：薄壁管结构或接管壁厚与筒体壁厚相当时，膜应力计算结果偏小；仅当接管壁厚大于筒体壁厚时，计算结果才偏安全；2、WRC297方法：不能得到确定的结论，但得到的膜应力或接近，或大于有限元方法的结果；3、EN13445 方法：将有限元方法得到的膜应力除以1.5倍许用应力后与EN13445方法得到的载荷比相比，EN13445方法的结果其安全裕量总是大于有限元方法的结果。

三、壳体上表面应力：1、WRC107方法：-薄壁管结构，该方法的计算结果偏小；-当接管壁厚与筒体壁厚相当或接管壁厚大于筒体壁厚时，在弯矩作用下，计算结果偏安全；- 在轴向力作用下，计算结果也偏小；2、WRC297方法：该方法的计算结果在绝大多数情况下大于有限元方法的结果；3、EN13445 方法：该方法的结果总是大于有限元方法的结果；在弯矩作用工况下，该方法与有限元方法的结果之比有可能大于2.0。