How to design a pressure vessel considering loads other than Pressure

Many years ago, when the first boilers and pressure vessels were put into service, and when people realized the danger involved in their operation, the national governments of the main industrial countries started to issue rules for their design, fabrication and inspection. Of course the most important problem at that time was to avoid an explosion caused by internal pressure, also considering the change in material properties due to high temperature. If we look at any one of the national standards existing 50 years ago, their size was certainly much smaller than the present editions of the same standards. About Pressure Vessel Design, there were only some simple formulae for the calculation of cylindrical shells and domed ends, while very few of them considered more complex components like main flanges and heat exchanger tubesheets. Although some of them warned the user about the need to consider in the design also loads other than pressure, very few of them gave practical rules to take these loads into account. Of course the evolution of all these regulations was aimed to increase safety on one side, and to reduce costs on the other side. To achieve this goal different directions were followed: to improve material technology, in order to have a better control on material properties; to develop new materials with higher characteristics; to improve NDT controls on welds, in order to increase reliability of all pressure vessel joints; and finally to make more precise calculations, refining the engineering approach in order to improve the calculation models and to consider all the possible loading situations, caused by pressure and by other loads, thus having the possibility to reduce the safety factors and, as a consequence, the thicknesses and the weights. Although the national Pressure Equipment standards existing in the different countries have given a different priority to these directions (American standards relying more on weight and thickness, European standards relying more on a greater amount of NDT and welding qualifications), the evolution of all the pressure equipment rules was similar in all the industrialized countries. An important contribution to this process was given in Europe by the coming into force (2002) of the PED (=Pressure Equipment Directive). From a superficial examination of this document one should come to the conclusion that its basic philosophy (to consider as binding only the Essential Safety Requirements and not the detailed standards used to translate them into more precise prescriptions) is a sort of deregulation: all standards are acceptable (with a slight preference given to the Harmonized EN Standards, which should guarantee a certain “Presumption of Conformity” to the PED of the pressure equipment concerned). But the reality is completely different: in fact the basis of the PED is the Risk Analysis, which the Manufacturer is obliged to carry out for any kind of pressure equipment, and for which he is fully responsible. In other words, according to the PED there is no detailed standard which can relieve the Manufacturer’s responsibility to design and fabricate his product considering all the possible situations to which it could reasonably be subject during its foreseeable lifetime: therefore all the possible loads, not only pressure, but also weight, wind, snow, earthquake, thermal stresses, loads transmitted from adjoining structures and so on. But this new approach is causing a series of practical problems, that we will try to explain in the following. Many of the loads other than pressure have been dealt with in other regulations: own weight, “live” weight (that is the weight that might also be present, however not necessarily, or not necessarily at its maximum possible value: for example,  the weight of workers walking on a platform);  the weight of the snow (that may be there in Winter time, but certainly not in Summer); the force caused by wind pressure (that is occasionally present); the seismic acceleration (only exceptionally present), etc. These loads have been extensively dealt with in the rules for civil structures (buildings), which also were subject to continuous improvements and modifications. In fact, before the PED, another directive came into force in Europe: the Directive about Construction Products. Also this directive, as the PED, has generated a series of harmonized standards, the so called “Eurocodes” (EN 1990 to EN 1998). However the philosophy on which the Eurocodes are based (differently from what happened for the pressure equipment rules) is not the same in Europe and in the United States: in fact in USA either the ASCE (=American Society of Civil Engineers) or the IBC (=International Building Code) standards consider the traditional approach of Structural Engineering (comparison between an actual stress and an allowable stress), while the Eurocodes use the method of the “partial safety factors“, that is to split the safety factor into two different components: the first one to be applied to the design load (different for each load category), the second one to be applied to a significant material property (different for the different materials). Therefore the first problem that we have in Europe is to combine the philosophy normally used by all the Pressure Equipment standards with the philosophy normally used by the standards dealing with building and structures. The problem is further complicated by the presence in many European countries of different national Annexes of the Eurocodes, which in many cases are also binding by law: these national rules sometimes give an interpretation of the Eurocodes which may be slightly different in the different countries. An attempt to integrate the Eurocodes with EN Pressure Equipment standards is the one contained in the Unfired Pressure Vessel standard EN 13445 part 3, Annex B (Design by Analysis using the so called “Alternative Route”, i.e. the limit analysis). The philosophy of Annex B is the same of the Eurocodes, therefore based on the method of the partial safety factors: however the corresponding values  are not always in compliance with the values given by the Eurocodes. The same philosophy of Annex B has recently been considered also in the new Clause 22 (“Tall vertical Vessels”) of the same standard, issued, for the first time, in the 2014 edition of EN 13445.3. A second problem is given by the need to combine with each other the different loads. This problem (never considered in the Pressure Equipment standards, which are usually dealing with the pressure load only) becomes important when also other loads are acting together with pressure, particularly (as already explained above) when these loads may or may not be present, or may be present with variable values. The presence and the intensity of the variable loads must therefore be considered with a probabilistic approach: if one of them is present with the maximum possible intensity, the probability to have also the contemporary presence of the other variable loads at their maximum possible intensity is certainly negligible. Just to make an example, if a distillation tower has a platform with a nominal loading capacity of 250 kg/m2 and is located in an area where the maximum wind pressure is 1400 N/m2, it is not reasonable to consider the possibility of the contemporary presence of the maximum allowable inside pressure, of a load on the platform equal to its full capacity and of the maximum possible wind pressure. On the contrary, if we really want to take into account the possibility of a platform loaded at 100% of its capacity, it will be necessary to define the “combination coefficients” (values between 0 and 1) for the other variable loads: in other words, the reduction to be attributed to the maximum possible values of the other variable loads, which of course cannot be present at their maximum possible intensity when the load on the platform is at its maximum design value. In the Eurocodes there are tables giving the combination coefficients to be used  in the different cases. In the specific case of Pressure Equipment there is another non pressure load category which may lead to a still worse situation: these are the Local Nozzle Loads. In fact the engineering companies responsible for the piping design usually make the piping calculations after purchasing the vessels: in order to avoid problems when the vessel is built, at the beginning they simply give to the vessel manufacturers a table with the maximum possible values of some load components (usually the axial load and the bending moment, based on the nozzle diameter), however without specifying the direction.  Well, if we now imagine that the distillation tower of the previous example may have about 50 nozzles, and that on each one of them the bending moments and the axial loads are present at their maximum values and are oriented towards the same direction, even supposing that the local stresses at the nozzle connections are acceptable, the total load on the column supports would be totally unrealistic. Moreover, some of the loads other than pressure might have a favourable effect when combined with the other loads: a tower subject to wind is practically loaded by the wind pressure as a cantilever beam subjected to a distributed load and having each cross section shaped as a circular crown: if the cantilever beam is fixed at its base, on each cross section there will be an overall bending moment (decreasing with the height) causing longitudinal tensile stresses on the upwind side (with the risk of gross plastic deformations) and longitudinal compressive stresses (with the risk of buckling) in the downwind side. If we algebraically add these stresses to the longitudinal tensile stresses caused by the inside pressure, the situation upwind will be worse (increase of tensile stresses), but the situation downwind will be better (compressive stresses will decrease or even disappear, thus reducing the risk of buckling): in the first case it is reasonable to give to the inside design pressure its maximum allowable value, while in the second one this value should be reduced, or may be also set to 0. A particular case of variable loads are those usually defined as “exceptional”, particularly seismic loads, that is, those loads that have a very low (however well defined) probability to be present in a reference (conveniently long) “return period”. In case such loads should be present, there should however be the guarantee that they will not affect the stability of the structure in respect of its “ultimate limit state” (one of the new ideas contained in the Eurocodes is the design of a structure in respect of more than one “limit state”).  Such limit states are usually considered in the buildings, where reference is made either to “ultimate limit states” (states causing the collapse of a structure) or to “damage limitation states” (limit states which do not cause the collapse of a structure, but simply a damage condition involving serious limitations of its service capability). In the case of Pressure Vessels, damage limitation states are not generally relevant, therefore only ultimate limit states shall be considered. With reference to the example of a distillation tower containing a dangerous fluid, the seismic design for an ultimate limit state is based on a seismic event which has 5% probability to happen in a return period of 1472 years. According to EN 1990 (Eurocode 0), in a carbon steel vessel a normal operating condition where only the internal design pressure and the weight are present should be evaluated with a partial safety factor of 1,35 applied to both loads, while the partial safety factor to be applied to the material limit property should be 1,00 (1,25 only for the case of fasteners); Annex B of EN 13445.3 gives 1,2 for the load and 1,25 for the material. At the end, this gives a total safety factor of 1,2 x 1,25 = 1,5, that is the customary safety coefficient on the elastic limit at design temperature always used by the great majority of the Pressure Vessel standards, therefore more conservative than the total coefficient obtained with the Eurocode 0 (1,35 x 1,00 = 1,35). For an exceptional (or seismic) condition the combined safety factor of Eurocode 0 is 1,00 x 1,00 = 1,00, while Annex B gives 1,00 x 1,05 = 1,05. The method of the partial safety factors used in the Eurocodes may cause a little bit of confusion for those who are accustomed to use the traditional approach of structural engineering, that is to consider a single safety factor on the material property, thus obtaining an allowable stress (better defined as a nominal design stress in all the European standards) to be compared with the actual stress caused by the design loads. Of course a decrease of the safety factor on the material characteristic with a corresponding increase of the safety factor on the design loads doesn’t make a lot of difference when the behaviour of the structure is fully elastic (all stresses directly proportional to the design loads); however this situation may change when the limit analysis is used. Moreover, an additional remark should be made for the cases where the designer has to consider Non Pressure Loads (such as wind and earthquake) in the context of a specific Pressure Vessel standard: in this case he might have the freedom (particularly for deliveries outside Europe or USA) to choose (or interpret) the standards for civil structures needed in order to take into account the additional loads. Well, it has to be noted that it is absolutely dangerous to mix different standards together. In other words, all the standards used should be considered in their entirety, avoiding the mixture between loads calculated according to one standard with the nominal design stresses given by another standard: this because in each standard the probabilistic considerations used for the definition of the loads are generally tied to the safety factors and the nominal design stresses: a mixture would involve the risk either to be too much on the safe side, or (which is worse) to  give raise to an unsafe structure.   But now let’s stop, without coming too much into details. The logical conclusion is that in Pressure Vessel design considering Pressure together with Non Pressure loads is a critical process, which requires a careful examination particularly for the preparation of the design specifications to be given to the Manufacturer; who, at his turn, must not forget that according to the PED (and this is the main difference with the American philosophy!) he will be fully responsible also for the case where such specifications are prepared by somebody else.  

Dr. Fernando Lidonnici, Convenor of WG53/CEN TC54