Zick Method Adaptation for Horizontal Cylindrical …

1 REV. CHIM. (Bucharest) 62 No. 5 2011 Method Adaptation for Horizontal Cylindrical Vessels ( )Asymmetrically Supported on Three Saddle Supportswith Support SettlementsALEXANDRU POPA*, EUGENIU SOVARELP etroleum-Gas University of Ploiesti, Mechanical and Electrical Engineering Faculty, 39 Bucuresti, Bvd., 100880, Ploiesti, paper presents a way of using the zick Method for the design of the Horizontal Cylindrical vesselsupported in three points. The effect of the settlements has been considered taking into account the PD5500-2009 hypothesis used and the results of the calculations reached the conclusion thatthe bounded of a Cylindrical vessel is not recommended to be made in three : Horizontal Cylindrical vessel supported on three saddle supports, settlements, zick methodIn a previous paper [1], there was presented the wayZick Method had been extended to the supported on three saddle supports withoutsupport settlements, as described under the BritishStandards 5500 - 2003 [2].

2 Hereunder, we intend to consider also the effect ofsupport settlements on the status of stresses in therecipient stressesThe supported on three saddle supports, as treatedin the Beam Theory, are once statically undetermined. Tocalculate the bending moment on the intermediarysupport, the Equation of the Three Moments forcontinuous beams shall be applied [3, 4].In case of support settlement, either due to the variablesettlement of the foundation land, or due to faulty executionof works, it is necessary to consider these settlements inthe equation of the three moments [4].Equation of the Three Moments* the support settlements, the equation of thethree moments (as per assumption of constant thicknessof the Cylindrical shell) becomes as follows:where:where:m21 and m23 are the uniformly distributed load w forthe segment between supports 1-2 and 2-3;v1, v2, v3 settlements in the supports 1, 2, 3;E longitudinal elasticity module of the recipient shell;I = r2t moment of inertia of the meaning of the other units is deducted from bending moment M4 on the support 2 can becalculated by using equation (2).

3 Using this value and making elementary calculations, itis possible to determine reactions W1, W2 and W3 by makinguse of the following equations (fig. 2b): (2)(6)(5)(4)(3)(7)(8)(9)Fig. v1, v2 and v3 are the settlements in the three supports(fig. 1), the equation of the three moments has to becompleted with the following member: (1)The modelling of supported on three saddlesupports, compliant with the schematization proposed byL. P. zick for supported on two saddle supports, ispresented in figure 2 (equivalent of the scheme in in paper [2]). As far as possible, the notations werekept similar to those in PD 5500 2009 [2].REV. CHIM. (Bucharest) 62 No. 5 2011 shear forces T1RT, T2LT, T2RT and T3LT shall be calculatedby using the equations below:The extreme bending moments M3' and M3' ,corresponding to the intervals between supports 1-2 and2-3 respectively, are calculated according to the followingequations:StressesThe Adaptation of zick Method , as per the designformulae provided in the British Standards 5500 2009[2], to the analysed case requires the highlighting of thechanges in the equivalent equations for two supports.

4 Weshall observe the order provisioned in the stress against the maximum momentbetween supportsThere shall be selected the maximum value of thebending moment M3' and M3' . Stresses f1 and f2 shall bedetermined by replacing this value of the bending momentM3 in the equations ( ) and ( ) from 5500 2009 [2].Longitudinal stress against the saddle supportsThere will be selected the highest value of the bendingmoments M4 , M4 and M4 .If this value corresponds to the bending moments onend supports (M4 , M4 ), then the possibility of shellreinforcement by heads (ends) may be considered (if A1/A2 r / 2).Stresses f3 and f4 shall be calculated by replacing thehighest value chosen for moment M4 from the equations( ) and ( ) from 5500 2009 [2].

5 For coefficients K1 and K2 [4], the following equationsshall be used:A1,2 >r/2 or for the intermediate supportFig. 2.(10)(11)(12)(13)(14)(15)(16)REV. CHIM. (Bucharest) 62 No. 5 2011 [4]: (19)Angle is in sexagesimale shear stressThere shall be selected the highest absolute value ofthe shear forces T1RT, T2LT, T2RT and T3LT, determined usingthe equations (10) .. (13) and it shall be noted as the way of setting up the equation of thetangential shear stress under paper [5], equation ( )from [2] becomes: (20)For the other cases mentioned under 5500 2009[2], the same equations shall be used, taking into accountthat the highest value W1, W2 or W3, determined accordingto equations (7).

6 (9), shall be used for stressThere shall be selected the highest value of reactionsW1, W2 or W3, which shall be used instead of the reactionoccurring in the equations corresponding tocircumferential stress in Chapter in 5500 2009 [2].Considering the specifications expressed by zick in the1971 edition of the paper [5] (page 964), the followingequation will be used for L: (21)Consequently, the stresses f6 ..f8 shall be calculated bythe same equations from the normative PD 5500-2009 [2].Verification of effective stresses as against to theallowable values shall be done in the same manner as inthe exampleThe goal of the example is to analyse the effect of thesettlements in the bending moments from the supports ofa Horizontal Cylindrical vessel bounded on three supports(the values M4' , M4' and M4' from the figure 2 ).

7 The calculus scheme of the vessel is presented in thefigure the weight of the recipient and of the hydrostatic testfluid are considered, an uniform pressure w = N/mm is numerical calculations have been performed bothwith classical Method of strength of materials and withfinite elements Method (FEM).In order to analyse the effect of the settlements for themiddle support a vertical displacement ( 2=5 mm) hasbeen ANSYS program has been used and the cylindricalvessel has been meshed in 32 PIPE finite following cases have been analysed:- Cylindrical vessel supported in 3 points without anysettlements;- Cylindrical vessel supported in 3 points with somesettlements of 5 and 10 mm for the middle supports;- Cylindrical vessel supported in 3 points with somesettlements of 5 and 10mm for one of the end supports;- Cylindrical vessel supported only in 2 points (withoutthe middle support).

8 - Cylindrical vessel supported in 2 points (without an endsupport) After analysing the above mentioned cases thefollowing results have been obtained:- the bending moments from the end supported points(because of the equal length of the cantilevers) have thevalues: M4'= M4' = - x 108 N. mm; - the values of the bending moments from the middlesupported point, when a vertical settlement (0,-5,+5,-10,+10)mm for the middle support has been considered,are presented in table 1. The values of the bending(17)(18)Fig. 1 REV. CHIM. (Bucharest) 62 No. 5 2011 from the middle supported point for the samevalues of the settlements have been considered (for anend support) and are presented in the table 1; - if the middle support is eliminated the bending momentfrom the middle point has the value M3= x 109 ,the vertical displacement from this point being only ;- the fraction between the bending moments frommiddle point in the case that the tank is supported only intwo points(at the ends) and the bending moment from thesame middle point in the case that the tank is supported inthree points (without any settlements) has the value.

9 - in the hypothesis that an end support is eliminated thebending moment in the middle supported point has thevalue: M4' = x a situation is not recommended to be used indesign The situation of bounded the Horizontal Cylindrical vesselin three supported points is not recommended because ofpossible settlements that have the disadvantage ofconducing at the middle support to high values of thebending moments (tables 1 and 2),Table 2 The analysed Cylindrical vessel had a high enoughbending rigidity in order to be supported only in two POPA AL., Adaptarea metodei zick pentru recipientele cilindriceorizontale( )sprijinite asimetric pe trei suporturi- Lucrarilestiintifice ale simpozionului international multidisciplinar Universitaria SIMPRO 2005 Mecanica si rezistenta , 14-15 Octombrie2005 Universitatea din Petrosani, Ed Universitas,Petrosani p.

10 402. ** PD 5500:2009 Specification for Unfired Fusion Welded PressureVessel-British Standards Institution-section andMounting for Horizontal ,N., Rezistenta materialelor, Editura didactica si pedagogica,Bucuresti, ,V. Mecanica teoretica si rezistenta Materialelor, si pedagogica, Bucuresti, , , Stresses in Large Horizontal Cylindrical Pressure Vesselson Two Saddle Suports- Welding, Journal Research Supplement , 30 ,1951 , p 435s- 446s,republished in Pressure Vessel and Piping Design Collected Papers (1927-1959) , ASME, New York 1960, p 556-566 ,revised in 1971,republished in Pressure Vessel and Piping Design andAnalysis , ASME, New York, 1972 , p 959 Manuscript received.