{"operation":"document","citation":"07-0031","title":"West-Mark — Hazardous Materials Safety Interpretation","source_type":"guidance","agency":"Pipeline and Hazardous Materials Safety Administration","status":"guidance","official":true,"published_on":"2008-04-29","effective_on":null,"summary":"07-0031 response to West-Mark concerning 178.337, 178.345.","machine_formats":{"json":"https://regulus.evalyn.ai/document/phmsa-interpretation-07-0031.json","markdown":"https://regulus.evalyn.ai/document/phmsa-interpretation-07-0031.md"},"app_url":"https://regulus.evalyn.ai/document/phmsa-interpretation-07-0031","source_url":"https://www.phmsa.dot.gov/sites/phmsa.dot.gov/files/legacy/interpretations/Interpretation%20Files/2007/070031.pdf","body":"<<<PAGE 1>>>\n\nU.S. Department\nof Transportation\nPipeline and Hazardous\nMaterials Safety\nAdministration\nAPR 2 9 2008\n1200 New Jersey Avenue, SE\nWashington, D.C. 20590\nMr. Gary Spoelstra\nChief Engineer\nWest-Mark\nP.O. Box 100\nCeres, California 95307\nRef. No.: 07-003 1\nDear Mr. Spoelstra:\nThis is in response to your January 10,2007 letter requesting clarification of the Hazardous\nMaterials Regulations (HMR; 49 CFR Parts 17 1-1 80) applicable to cargo tanks. Your\nquestions are based on an interpretation issued in 1993, in which we specified that DOT 400\nseries tanks could be designed without considering weld efficiencies less than 100% and still\nmeet the requirements in the HMR. You state that Section XI1 of the ASME Code, which we\nwill be incorporating into the HMR, will invalidate the 1993 interpretation by mandating the\nuse of full design stress at 70% joint efficiency on a large population of tanks. The result of\nthis would generate heavier tanks, a situation not in keeping with the present regulations if not\nproperly addressed. Specifically, you ask for us to allow a 20% increase in allowable\ncompressive and tensile stress for longitudinal bending in cargo tanks when considering the\nextreme case of .7G as specified in 4 178.337-3(c)(2)(iii)(C) for MC 331 cargo tanks and\nparagraphs (c)(2)(iii)(C) and (c)(2)(iv)(B) of 5 178.345-3 for DOT 400 series cargo tanks.\nBased on the information provided, we have determined that it is acceptable to use the long\nstanding ASME Section VIII criteria in UG-23(d) of a 20% increase in allowable stress for\ncertain conditions. For DOT 400 series cargo tanks, the allowable compressive and tensile\nstress may be increased 20% when analyzing longitudinal bending in cargo tanks when\nconsidering the extreme load case of .7G as specified in fj 178.345-3 (c)(2)(iii)(C) and\n(c)(2)(iv)(B). We will be addressing this issue in a future rulemaking.\nPlease note that although ASME UG-23(d) may be an appropriate alternative criterion to use\nin the analysis of certain loading conditions for other cargo tank specifications, we are\nlimiting your request to that which is directly related to the co-operative research effort\n\n<<<PAGE 2>>>\n\nbetween DOT and industry for 400 series cargo tanks and the supporting documentation\nprovided in your letter.\nI hope this information is helpful. If you have further questions, please do not hesitate to\ncontact this office.\ni at tie L. Mitchell\nChief, Regulatory Review and Reinvention\nOffice of Hazardous Materials Standards\n\n<<<PAGE 3>>>\n\nP. 0. BOX 100\nCeres, California 95307\nPhone (209) 537-4747\nFax (209) 537-1 753\nU. S. Department of Transportation\nResearch and Special Programs Administration\n400 Seventh St. NW\nWashington, DC 20590-000 1\nJan, 10-07\nAttention: Stan Staniszewski, Office of Hazardous Materials Technology\nSubject: Request for Interpretation of Cargo Tank Rules\nDear Stan,\nThis letter is a request to modify the dynamic loads for which DOT 33 1 and 400 series Cargo Tanks must\nbe designed. Specifically the request is to allow the use of a 20% stress increase when analyzing DOT 33 1 and 400\nseries tanks considering a .7G vertical load \"extreme\" dynamic force increase for these tanks. The history behind\nthis request is somewhat complicated. and will be explained in the following paragraphs.\nOriginally MC 300 series cargo tanks were required to be designed for static load conditions. When the\nrules were revised to accommodate DOT 400 series tanks where dynamic loads of up to .7G (the most extreme and\nso labeled) were superimposed on the static loads, the regulations stated that design would be in accordance with the\nASME Code Section VIII which required weld joint efficiencies of 70% if welds were not tested non-destructively\n(x-rayed or ultrasonically inspected). The critical stresses were midspan longitudinal cmpression and tensile stresses\nin bending particularly in compression due to the thin walls This mandated that such tanks would have heavier\nwalls than the MC 300 tanks for a large number of tanks. Accordingly, in 1993, DOT issued an interpretation that\nDOT 400 series tanks could be designed without considering weld efficiencies less than 100% and still meet the\nregulations. As long as the population of these tanks was under only DOT regulation, the interpretation was valid.\nHowever, there will be a special Section XI1 of the ASME Code covering the structural design of all cargo tanks\nwhich DOT will incorporate into its regulations by reference. This will mandate the use of full design stress at 70%\njoint efficiency on a large population of tanks and cause them to be heavier, a situation not in keeping with being\ntransparent to present regulations if this request is not honored.\nIn 2002, a long light gage cargo tank of DOT 4071412 type equipped with accelerometers was over-the-\nroad tested and the data analyzed harmonically to see what equivalent static load increases replicated the summation\nof the dynamic forces on the tank. A report on this test is attached. This was done as a cooperative project between a\ngroup of cargo tank manufacturers and DOT. It was found that the worst case equivalent dynamic condition\nconservatively stated was .42G, not .7G and that tanks designed by the new criterion with 100% joint efficiency\nwere as safe or safer than MC 300 tanks as well as the enormous population of food grade tanks of lighter\nconstruction, many of which remain in service for 30 years or more. It was also found that only one of 102 measured\nevents in the test achieved this transitory load increase so it is not a common dynamic condition.\nThe present interpretation allowing 100% joint efficiency is incompatible with ASME standards, To\nachieve the necessary relief, it is proposed that DOT allow a stress increase of 20% ( the same increase allowed for\nwind and seismic forces in Section VIII) when using the extreme dynamic load factor of .7G. This can be\nincorporated into Section XI1 and assure transparency for this case. This also deals positively with the lesser but still\nsignificant problem of tensile overstress when using 70% joint efficiency.\nWe request that DOT issue an interpretation allowing a 20% increase in allowable compressive and tensile\nstress for longitudinal bending in cargo tanks when considering the extreme case of .7G. The applicable parts of the\nregulations are 49CFR178.337-3(c) (2)(C) for MC 331 tanks and 49CFR178.345-3(c)(2)(iv)(B) and (iii)(C) for DOT\n400 series tanks.\nwww.west-mark.com\nSTAINLESS STEEL o ALUMINUM o MILD STEEL FADRICATIOW\nTRANSPORT TANKS Q PRESSURE VESSELS o PLANT EQUIPMENT\nFlWE TRUCK APPARATUS\n\n<<<PAGE 4>>>\n\nSince MC331 tanks have the same extreme design load conditions as 400 series tanks, such an\ninterpretation might be applicable to them. We don't build MC331 tanks and defer to those building such tanks to\nrecommend the same interpretation for them.\nWe hope this request is adequate for its intended purpose and await your action.\nMonty Ward P.E.\nRTL Inc.\nGary Spoelstra\nChief Engineer\nW est-Mark\n\n<<<PAGE 5>>>\n\nREPORT ON CARGO TANK ROAD TEST\nThis report describes the road tests of a 6700 gallon 12 gauge (.105\") type 304 stainless steel semi\ncargo tank performed from Jan. 20 to Jan. 23, 2003 and its results. This test was performed under a joint\nprogram funded by the Cargo Tank Manufacturers' Association and the U. S. Department of Transportation\n(P. 0. TRS56-02-P-70045). The purpose of the test was to determine the vertical accelerations of a typical\ntype DOT4071412 tank when subjected to dynamic loads caused by various kinds of roads and road\nobstructions likely to be encountered in service. The important feature of the testing was to do a harmonic\nanalysis of the test data to frnd out how each harmonic contributed to the structural loads experienced by\nthe tank. The present DOT regulations contain G factors (gravity factors) that specification tanks must\nmeet. It is known that the structural effects of all the harmonics are not additive in creating stresses in the\ntank. There have been similar analyses on manufactured housing and tank trailers and such investigations\nshould be done on liquid carrying trailers to get a more complete picture of the dynamic load situation.\nDESCRIPTION OF TEST: - The test was performed on a newly built fifth wheel double rear axle semi\ntank 64\" diameter by 480\" long transported by a standard h c k . The tank lacked its normal insulated jacket\nso that it could be instrumented easily. Four accelerometers were placed on the tank unit, one each at the\nforward end, the middle and the rear end of the tank and one on the front rear axle. The accelerometers\nwere connected to a recording system which could be tumed on and off to gather data at significant times\nduring the test. The tank was fully loaded with water up to within 1% of its maximum legal carrying\ncapacity of 80, 000 lbs ( including tractor unit) and run twice over a predetermined route on public roads\nnear Norco, California and data was recorded for the following road conditions:\na) Relatively smooth asphalt road\nb) Gravel road (unpaved)\nc) Rough paved road with numerous potholes which were driven over and not avoided.\nd) Paved road with a steel plate barrier equivalent to a railroad crossing.\ne) Double dip paved intersection.\nThe same test was done for a half full tank and an empty tank so that a representative amount of data was\nobtained. The half load test was particularly severe in that the tank was a single compartment with no\ninternal baffles to damp out sloshing.\nThe data from the test runs was analyzed by computer (a Fourier analysis) to develop the\naccelerations associated with the various harmonics. The most extreme of the runs were analyzed for each\nload condition. Six runs at differing road conditions for each load condition were analyzed and the G\nfactors for each harmonic up to the ninth were determined for each accelerometer. Also the overall root\nmean square (RMS) value for each run was determined so that G factors for other tests could be compared.\nA report from Wyle Labs is attached to this report, which includes all the data runs analyzed, and some\ninformation on the instrumentation and computer analysis they did.\nThe certified gross vehicle weights (GVW) for the three test conditions were as follows: full load\n79740 lb, half load 53240 lbs, and empty 24220 lbs. These weights include the tractor and running gear.\nThe main area of interest is the loads on the tank itself. The light weight of the tank is assumed to be 5000\nlbs uniformly distributed. This gives an assumed uniformly distributed load for the full tank of 60.52 kips,\nfor the half full tank 34.02 kips, and for the empty tank 5 kips. Certified GVW's do not include the weight\nof the driver and other occupant. There were two people in the truck during the test. This added about 500\nlbs to the GVW's.\nAnalysis of Test Results - The results of the test indicated that there were two obvious natural\nfrequencies for the dynamic response of the tank trailer assembly during every test run. It appears that the\ntank assembly on two sets of elastic supports is a two degree of freedom system with the tank acting as a\nrigid body. A check of expected natural frequencies indicate that, for the full load condition, the most\nimportant one, the lowest natural frequencies for the two degree of freedom system are around 1-2.5HZ and\nfor the tank itself vibrating as a uniform beam 30-60HZ. For the full load condition, the two lowest natural\nfrequencies were 1.48HZ and 2.14HZ for the most severe shock. For other lesser shocks, the values varied\nslightly but were within a fairly narrow range. The tank experienced Root Mean Square (RMS)\naccelerations of up to 1.3G excluding the static weight of the tank, which is higher than the DOT\nRegulation 49CFR178.345-3 maximum of .7G vertical acting alone and .35G acting both vertically and\nhorizontally (when resolved amounting to .395G). According to the physics of sinusoidal harmonic motion,\n\n<<<PAGE 6>>>\n\nthe deflection associated with each mode of vibration varies in proportion to the G value for each mode\ndetermined by Fourier (Harmonic) analysis divided by the square of the mode number. This means that the\neffect of a total G force on tank stresses must take into account the contribution of each mode of vibration.\nIt is incorrect to take an RMS acceleration reading fiom a dynamic test of a tank and apply it directly to the\nmass of the tank to obtain forces, moments and stresses without doing a harmonic analysis so that the\ncontribution of each vibration mode can be computed separately and added in a logical manner to obtain\nrealistic stresses in the tank. In doing this, the phase of each mode must be considered as well. Odd modes\nhave maximum deformations 90 degrees out of phase fiom even modes and this must be considered as an\ninteraction rather than simply adding them all together.\nAnalyses of extreme data obtained fiom the several test runs have been performed. One such\nanalysis is presented below. It represents the highest G value (1.2626 RMS) and occurred in the middle of\nthe tank when going over a steel plate laid over a ditch on a paved road at approximately 40mph.\nMode No. Freq (HZ)\n1 1.48\n2 2.96\n3 4.44\n4 5.93\n5 7.4 1\n6 8.89\n7 10.37\n8 11.85\n9 13.33\nTotals\nOdd G ~ / n ' Even G G / ~ I\n.4117 .4117\n.0618 .0135\n.0245 ,0027 Total Values\n.0128 .0008 GmS=l .262\n.0121 .0004\n.3482 .0097 Odd G + Even G = 1.3563\n.I897 .0039\n.I467 .0023 Odd ~ / n ' + Even ~ / n ' = .4288\n.I478 .0018\n.7858 .4203 .5705 .0283\nMode No. Frecl (HZ)\n1 2.14\n2 4.27\n3 6.4 1\n4 8.95\n5 10.69\n6 12.82\n7 14.56\n8 17.10\n9 19.24\n10 2 1.37\nTotals\nOdd G ~ / n ' Even G ~ / n ~\n,0477 .0477\n.0193 .0048\n.0022 .0002 Total Values\n.lo40 .0065 GmS=l .262\n.0978 .0039\n.5902 .0164 Odd G + Even G = 1.0862\n.I121 .0023\n.0550 .0009 Odd ~ / n ~ + Even ~ / n ~ = .0834\n.0367 .0005\n.0242 .0002\n.2965 .0546 ,7857 ,0288\nThere were six runs each of data for three tank loading conditions, full load (60,520 Ib), half load\n(34,020 lb), and empty (5,000 lb). There were three accelerometers on top of the tank and one on a rear\naxle. On the tank, they were mounted at the forward end, middle and aft ends and, except for two runs over\na smooth road, there were two obvious natural frequencies analyzed. For a reasonably rigid body such as\nthe tank, mounted on springs at its ends, it is a two degree of freedom system from an analytical standpoint.\nThis means that one should expect two major natural frequencies for vertical motion which was the case.\nOne of the frequencies is for translation up and down and the other is rotation of the tank about a transverse\nhorizontal axis. As a result of all this, there were 102 G value spectra recorded and analyzed. The axle\naccelerometer was analyzed but was recorded as a basis of comparison to other possible dynamic tests\nwhere accelerometers might have been used. The measured overall root mean square (RMS) G values for\nthe tank and axle were as follows:\nLoad Condition Tank Min Val Tank Max Val Axle Min Val Axle Max Val\nFull Load (60.52K) .192G 1.290G .824G 4.152G\nHalf Load (34.02K) .196G 2.6886 .586G 5.6226\nEmpty (5.00K) .39 1 G 1.245G 1.516G 3.4726\n\n<<<PAGE 7>>>\n\nThe half full tank, having no interior swash plates or baffles and being 40 feet long, experienced\nappreciable sloshing which may have increased the G values from those of the other two load conditions\nwhich had no sloshing.\nA harmonic analysis was made of each run at each frequency for a total of 102 analyses. The G\nfactor for each mode was divided by the square of the mode number to obtain the contribution of each\nmode to the total G factor to be used in structural design. These contributions were added together in two\nseparate groups, odd modes in one group and even modes in the other. For the vast majority of runs, ten\nmodes were included. The logic for this is that, for the eleventh mode, the measured G factor for that mode\nmust be divided by 121, the square of the mode number, to obtain its contribution to the total effect. Since\nits effect is less than one percent of its measured value, it and higher modes can be ignored in this type of\nanalysis. The summations of odd and even modes were combined by squaring each of them, adding them\nand taking the square root to obtain an overall G factor to be used in design. The ratio of this G factor to the\ntotal RMS G factor was also computed for each case. The distribution of these G factors was as follows for\nall cases analyzed:\nOverall G factor OG to .I G .lG to .2G .2G to .3G .3G to .4G Over .4G Total\nNo. of Values 67 19 9 5 2 102\nIn range\nThe two highest G values were ,44496 ( on the half full tank) and .42 15G (on the full tank). The\n.4449G value when multiplied by the ratio of full load weight to half load weight gives a value of .2501G\nfor the equivalent full load G force applied to the tank. Clearly the full load G factor is a greater load on the\ntank.A conservative design approach would be to take the .42 15G and add .02G to it for shock effects, that\nis, effects of modes past the tenth mode. This would result in a maximum G factor for design of .45G. The\npresent regulation maximum is .7G based presumably on a total RMS G value of .7G. For the particular\ncase in question, the tank RMS value was 1.2626 or 80 % more than .7G. Factoring the .45G down by the\nratio .7/1.262 gives approximately .25G. It would appear that the worst case design factor of .45G is\nultraconservative and would be a low cycle fatigue situation at best occurring perhaps twice a day for a\ntank life of 20years operating every day. This amounts to 14,610 times in the tank life, a low number for a\nfatigue case. With this number of cycles, fatigue should not be a factor for designs based on normal\nallowable stresses. In fact it might be reasonable to allow the 20 % stress increase for the worst case\nstructural design for DOT 400 series tanks.\nThe theoretical natural frequency of the loaded tank on end supports was computed to be about\n40HZ. This is about 25 times more than the lowest natural frequency of the loaded tank on its suspension.\nThe suspension acts as a dynamic vibration or shock absorber because its stiffness is so much lower than\nthe tank itself. That this is true is indicated by an analysis of the higher frequency spectrum of the same\nload case analyzed above where the total RMS G value was 1.262. The results are as follows:\nMode Frea(HZ)\nOdd G Odd ~ / n ' Even G Even ~ / n '\n1 38.50\n.0506 .0506\n2 72.99\n.0075 ,0019 Totals\n3 109.49\n.0037 .0004 G,,,= 1.262\n4 149.98\n.0114 .0007 Odd G + Even G=. 1006\n5 182.48\n.0108 .0004 Odd ~ / n ' + ~ v e n ~/n'=.0544\n6 218.97\n.0 10 1 ,0003 ( ( ~ d d ~ / n ' ) ' + ( ~ v e n ~/n')').~=.05 16\n7 255.47\n.0029 .0001 (Above is 4.09% of G-3\n-~~..,\n8 29 1.96 ,0016 .OOOO\nTotals .0680 ,0515 .0326 .0029\nThese results c o n f m that the suspension acts as a dynamic vibration absorber for the higher\nfrequency shocks liable to excite flexural vibration of the tank on its supports. The test tank was long and\nthin. Flexural natural frequencies would be higher for most other tanks which are shorter and thicker.\n\n<<<PAGE 8>>>\n\nSummaw of Test Results: - The test results indicate the following:\na) G factors used for establishing dynamic loads on highway tanks should not be based directly\non overall G factors obtained from accelerometers mounted on tanks.\nb) It is necessary to do a harmonic analysis on accelerometer data used to establish practical\nallowable stress values for dynamic load conditions on highway cargo tanks.\nc) The magnitude of present dynamic load G factors may be too conservative as presently\napplied to tank design and should be evaluated based on harmonic analysis of the data used to\ndetermine them.\nd) As required by DOT Regulations, ASME specified values for allowable longitudinal\ncompressive stresses in highway tanks appear to be too conservative and may not take into\naccount the fact that tanks under maximum longitudinal compressive stress are full of product\nand have positive internal pressure which would reduce their tendency to buckle over tanks\nwith external pressure. This is substantiated by the large number of MC 306 and 307 tanks as\nwell as food grade tanks which continue to perform satisfactorily in service even though\nsome, as the tank used in this test, do not even meet the longitudinal compressive stress\nrequirements under the static load condition with no dynamic loads at all.\ne) Evidence indicates that the most severe dynamic stress conditions occur rarely enough so that\nfatigue may not be a factor in design for them.\nf) In severe dynamic load cases, the test tank was overstressed in longitudinal bending, primarily\nbecause of the 70 percent joint efficiency requirement of the Regulations. The major\ncomponent of longitudinal tensile bending stress in a long and thin tank comes fiom the\nlongitudinal bending moment, not fiom the membrane stress. It may be desirable to ignore the\njoint efficiency factor where longitudinal bending stress is over 213 of the maximum total\nlongitudinal tensile stress.\nRecommendations: - There are two kinds of recommendations emanating fiom this project. One is\nsuggested changes to existing regulations and the other is additional projects that might be useful. The\nrecommendations consider the dynamic load test results as well as the experience with the very thin wall\ntank used in the test and the stresses it experienced in the conduct of the testing.\nThe recommended changes to regulations are:\na) Change the G factors for dynamic loads fiom .35G to .25G in vertical direction for dynamic load\ncases with combined acceleration, deceleration, and .2G lateral loads ( The .2G lateral load is\nprobably due to centrifugal force and not vibration and should remain as it is).(49CFR178.345-\n3(c)(l)(iii)(B) &(C))\nb) Change the G factor for maximum vertical load to .45G instead of .7G and do not consider this\nload subject to fatigue because it occurs so seldom. (49CFR178.345-3(c)(2)(iii)(B) & (C) and\n49CFR178.345-3(c)(2)(iv)(A) &(B))\nc) For longitudinal bending in tension, allow the weld efficiency factor of .7 to be 1 .OO for the\nbending portion of the total stress and keep the .7 factor for the membrane stress as required by the\nASME Code. (New item 49CFR178.345-3(b)(3)). Review with ASME.\nd) Ask ASME to revisit its latest work on compressive stress in bending of cylindrical shells to\naccount for the case where there is internal pressure in the vessel combined with longitudinal\nbending. In discussions with those who did the work for ASME resulting in UG-23 and Code Case\n2286, it appears that the cases considered were for external pressure combined with longitudinal\nbending, an entirely different condition than obtains in a loaded cargo tank where bending stresses\nare maximum.\nRecommendations for further work are:\na) Run road tests similar to this one on a wider variety of highway, rail and intermodal tanks, such as\nLPG tanks, cryogenic tanks with jackets, non-cylindrical DOT 406 tanks, and heavier DOT\n40714 12 tanks with different suspension systems and configurations (truck mounted tanks, pull\ntrailers and semi tanks) to get a broader spectrum of data to analyze.\nb) Develop standard procedures for analyzing accelerometer readings fiom dynamic tests to establish\nreasonable parameters for developing design load factors using the additional data fiom a). This\n\n<<<PAGE 9>>>\n\nc) d) would consider impact or shock loads in addition to vibratory loads. They would also consider as\nwell the effect of different suspension systems on mitigating such loads on the tanks.\nRun some tests and do analyses to establish lateral force limits for highway cargo tanks. Lateral\nloads on these tanks are usually limited by overturn considerations, not by vibratory or shock\nforces.\nStudy thin wall long tanks to establish safe and realistic design parameters and stresses for them.\nThere is ample evidence fiom the service history of large numbers of MC 300 series tanks and\nnon-hazardous food grade tanks to indicate that safe tanks can be built with less critical and\nexpensive high alloy material.\nSome of these recommendations overlap in certain areas but can be dealt with usually as separate\nprojects.\nAcknowledaements: - This project was a cooperative effort of industry and government. The\nfollowing companies, institutions and individuals contributed to its success: Gary Spoelstra and West-Mark\nsupplied the tank, the tractor unit that hauled it and the driver, Bob Ramos. Wyle Laboratories, Norco, CA\nprovided the accelerometers, the recording equipment and the harmonic analysis of the data. Ron\nMcCarthy, Dan Cook and Tom Balfi-y of Wyle were very helpful. Tom Rogers, P. E. of Container\nTechnology, Lubbock, TX took time out from his regular business and contributed to the success of the test\nand in the analysis of the results. Thompson Tank Inc. (Dave Thompson Sr. and Dave Thompson Jr.)\nprovided video and photographic equipment. Kurt Van Diest and his staff supplied and disposed of the test\nwater. Weld-It (Ray Schaffer), Paramount Tank (Howard Grey) and Beall Tank provided fbnding and\naccounting services. U. S. Department of Transportation provided funding for the project and Stan\nStaniszewski handled the project a on the government side and got it underway on the government side.\nRTL Inc represented by M. R. Ward, P. E. supervised the test and wrote the report. The Cargo Tank\nManufacturers' Association, whose membership includes Beall, Paramount Tank, Thompson Tank and\nWest-Mark, sponsored the industry portion of the project.\n\n<<<PAGE 10>>>\n\nAppendix B - Tank Flexural Vibration\nA long semi trailer cargo tank has many modes of vertical vibration. Firstly it vibrates as a rigid\nbody mounted on springs at its ends as essentially a two degree of freedom system. The primary modes\nhave fiequencies on the order of 1 to 3HZ for each degree of freedom. In addition, the tank itself can\nvibrate flexurally with infinite degrees of freedom with the primary mode having a frequency of 20 to\n100HZ, an order of magnitude higher than the rigid body modes. The tank used in the test was 40 feet long\nmade of stainless steel. It was filled with water as the simulated payload. If a filled tank is subject to a\nshock exciting vibration, the shock wave travels at the speed of sound both through the tank shell and\nthrough the liquid. The speed of sound in steel is about 16,000 Wsec and in water is about 4800 Wsec. A\nshock wave, if undamped, would take .005 seconds to travel the length of the tank and return in the shell\nand.0167 seconds in the water. This is equivalent to frequencies of 200HZ and 60HZ respectively. The tank\nsupports are about 35 feet apart. For a tank traveling at 60 mph, the time interval between shocks\nemanating from the same bump in the road would be about .4 seconds apart, equivalent to a frequency of\nabout 2.5HZ. If traveling at 30 mph, the frequency would be about 1.25HZ, approximately in the primary\nmode range of the tank as a rigid body on springs. It is then possible that for a certain resonant speed, the\ntwo shocks would supplement each other and cause a more severe rigid body response than if they were not\nresonant. When driving on a smooth road such as a freeway, the travel speed would be in the 60 mph range,\nwhile on a rougher road, the speed would be more likely to be in the resonant range. When the travel speed\nis less the shock is less which would tend to reduce the magnitude of the shock. The kinetic energy created\nby a shock is probably roughly proportional to the square of the speed so that half speed would result in one\nquarter the shock. Two shocks in resonant sequence would at worst double the energy of one shock so\ntravel speed may have more effect than bump severity.\nThe road test measured accelerations at three points on the tank. It did not measure deformations\nor deflections. Stress in the tank is proportional to the deformation or deflection, not to the acceleration so\nit is necessary to convert acceleration to deflection for each mode of oscillation. The relationship is derived\nas follows:\nFor harmonic motion, deflection is X=Asin(pt) where X is deflection, A is maximum\namplitude, t is time and p is twice pi times the natural frequency in Hertz (cycles per second). If the\ndeflection formula is differentiated twice, the result is the acceleration namely X =-Xp 2\nThe deflection and hence the stress for each mode of vibration is proportional to the acceleration divided by\nthe square of the mode number. A shock response can be divided into modes starting from the primary\nmode by doing a Fourier analysis of the accelerometer trace for a particular point on the tank. The first\nmode is the primary frequency, the second mode is twice the primary frequency and so on. The higher the\nmode the more complete and accurate is the analysis of accelerations. However, since the effect on stress is\ninversely proportional to the inverse square of the modal frequency, the effect of the tenth mode is only one\nhundredth of that for the first mode for the same magnitude of acceleration, a negligible effect. Normally\nthe first few modes have the largest accelerations and the higher modes have the lowest so it is reasonable\nto ignore the highest modes. There is a further factor in harmonic analysis. The maximum amplitudes for\nthe odd modes are close together and the amplitudes of the even modes are located away from those of the\nodd modes. This means that odd and even modes should be considered independently in harmonic analysis.\nThe procedure followed in this report is to sum the odd mode values of acceleration, divide by the mode\nnumber squared, sum those for the even modes and combine them by taking the square root of the sum of\ntheir squares. This is a conservative approach. In almost all cases the odd modes are predominant as might\nbe expected.\n\n<<<PAGE 11>>>\n\nCUL w< 5FnOSS rnIkf--f''5\nb ( 1 ~ 6 ' ~ C~MPMWLVE B W D I W L WCULATZCIN SHEET RTL I ~ c .\nSHfiET rVo.-. or\n-JOB NO. BY CKD DATE I ) \\ 0 \\ 0 7 REV___, RATE:","truncated":false,"body_characters":30055}