Structural Analysis: RHIC D0 Magnet End Volume

Analyst: Rudy Alforque, 8/23/95
E-Mail: rudy@bnl.gov

Problem Description:

1. Determine if the end volume design of the D0 magnets, at the given design pressure (275 psi), meets the criteria specified by the Boiler and Pressure Vessel Code, Sec. VIII, Div. 2, Appendix 4, Mandatory: Design Based on Stress Analysis.
2. Determine if the end volume is structurally sound enough to withstand the pneumatic test pressure of 316 psi; This value is 1.15 times the design pressure of 275 psi as specified in Article T-4, B&PV Code, Sec. VIII-2.

Parameters:

• Vessel Design Pressure: 275 psi
• Pneumatic Test Pressure: 316 psi
• Outer Shell:
  • Outside Diameter: 15.5 in.
  • Thickness: 0.375 in.
  • Material: St. Stl. 304L
  • Yield Point, Sy: 25,000 psi
  • Design Stress Intensity, Sm: 16,700 psi
• End Plates:
  • Diameter: 13.5 in.
  • Thickness: 1.50 in.
  • Material: St. Stl. 304L
  • Yield Point, Sy: 25,000 psi
  • Design Stress Intensity, Sm: 16,700 psi

Solution Approach:

The failure criterion specified in the B&PV Code is the Maximum Shear Stress Theory which is often called as the Tresca criterion. It states that failure of the material subject to multi-axial stress occurs when the maximum shearing stress at any point reaches the value of the shearing stress at failure in a simple tension or compression test on the same material. Accordingly, it can be formulated as Stress Intensity, Sint = max{abs|S1-S2|, abs|S2-S3|, abs|S1-S3|} = Yield Point, Sy, where S1, S2, S3 are the principal stresses.

The Code, however, stipulates that the calculated stress intensity should be within specified limiting values, instead of the material yield point, Sy, as indicated above. In our case, based on Table AD-150.1, & Fig. 4-130.1 of Appendix 4 of the B&PV Code VIII-2, in order to satisfy item 1 in the problem description above, with the design pressure of 275 psi, the calculated stress intensity at any point on the end volume should not exceed 1.5Sm. With the values of Sm shown under Parameters above, the limiting value to satisfy item 1 is:

• SS304L: 1.5Sm = 25,050psi;

On the other hand, Item 2 can be satisfied by showing that the calculated stress intensity at the given test pressure (316 psi) does not exceed 80% of the yield point, Sy, of the material. This stipulation is specified by AD-151, & AD-151.2 of the B&PV Code VIII-2. With the values of Sy shown under Parameters above, the limiting value to satisfy item 2 is:

• SS304L: 0.8Sy = 20,000psi

Hence, a finite element model was developed using ANSYS5.1. In order to account for the effect of the three holes on the endplate due to the helium pipes and the beam tube, a 3-D shell model was developed using element type SHELL43. This element has six degrees of freedom at each node: translations, and rotations in the nodal x, y, and z axes.

The resulting stress intensities at critical locations were compared to the corresponding limiting values as described above. Please note that the pressure load that was applied to the model was rounded off to 320 psi.

Structural Analysis: RHIC D0 Magnet End Volume 
-----------------------------------------------

M O D E L   I N F O R M A T I O N:
----------------------------------


 LIST ELEMENT TYPES FROM    1 TO    1 BY    1

 ELEMENT TYPE    1 IS SHELL43      4-NODE STRUCTURAL SHELL        INOPR 
  KEYOPT(1-12)=    0  0  0    0  0  0    0  0  0    0  0  0       0

 CURRENT NODAL DOF SET IS  UX    UY    UZ    ROTX  ROTY  ROTZ
  THREE-DIMENSIONAL MODEL


 RELEVANT MATERIAL PROPERTIES: 
 -----------------------------
  EX   =  0.28400E+08
  NUXY =  0.30000    
  GXY  =  0.12500E+08
  ALPX =  0.84507E-05
  DENS =  0.29000    
  KXX  =  0.78000    
  C    =  0.12000    
---------------------------------------------------------------------------
  Solid model summary:

                             Largest       Number      Number
                              Number      Defined     Selected
 Keypoints . . . . . . . . .     58           58           58
 Lines . . . . . . . . . . .     98           98           98
 Areas . . . . . . . . . . .     40           40           40
 Volumes . . . . . . . . . .      0            0            0

 Finite element model summary:

                             Largest       Number      Number
                              Number      Defined     Selected
 Nodes . . . . . . . . . . .   1839         1839         1839
 Elements. . . . . . . . . .   1744         1744         1744

 Element types . . . . . . .      1            1         n.a.
 Real constant sets. . . . .      2            2         n.a.
 Material property sets. . .      1            1         n.a.

 B O U N D A R Y   C O N D I T I O N   I N F O R M A T I O N ------------------

                                           Number
                                          Defined
 Constraints on nodes. . . . . . . . . . .   388
 Constraints on keypoints. . . . . . . . .     0
 Constraints on lines. . . . . . . . . . .   187
 Constraints on areas. . . . . . . . . . .     0
---------------------------------------------------------------------------
 LIST SOLID MODEL BOUNDARY CONDITIONS (LABEL = LSBC)
 ON ALL SELECTED LINES
---------------------------------------------------------------------------
   LINE                    SURFACE NORMAL AREA
---------------------------------------------------------------------------
        2        SYMMETRY             1
       56        SYMMETRY            21
       57        SYMMETRY            10
       58        SYMMETRY             9
       59        SYMMETRY            29
       60        SYMMETRY            30
       61        SYMMETRY            31
       62        SYMMETRY            32
       63        SYMMETRY            20
       82        SYMMETRY            33
       84        SYMMETRY            33
       86        SYMMETRY            34
       88        SYMMETRY            35
       90        SYMMETRY            36
       92        SYMMETRY            37
       94        SYMMETRY            38
       96        SYMMETRY            39
       97        SYMMETRY            40
       98        SYMMETRY            40
---------------------------------------------------------------------------
   AREA     PRESSURE    SLKCN SLDIR  SLZERO      SLOPE
---------------------------------------------------------------------------
      1       320.          0   0    0.000E+00   0.000E+00
      2       320.          0   0    0.000E+00   0.000E+00
      3       320.          0   0    0.000E+00   0.000E+00
      4       320.          0   0    0.000E+00   0.000E+00
      5       320.          0   0    0.000E+00   0.000E+00
      6       320.          0   0    0.000E+00   0.000E+00
      7       320.          0   0    0.000E+00   0.000E+00
      8       320.          0   0    0.000E+00   0.000E+00
      9       320.          0   0    0.000E+00   0.000E+00
     10       320.          0   0    0.000E+00   0.000E+00
     11       320.          0   0    0.000E+00   0.000E+00
     12       320.          0   0    0.000E+00   0.000E+00
     13       320.          0   0    0.000E+00   0.000E+00
     14       320.          0   0    0.000E+00   0.000E+00
     15       320.          0   0    0.000E+00   0.000E+00
     16       320.          0   0    0.000E+00   0.000E+00
     17       320.          0   0    0.000E+00   0.000E+00
     18       320.          0   0    0.000E+00   0.000E+00
     19       320.          0   0    0.000E+00   0.000E+00
     20       320.          0   0    0.000E+00   0.000E+00
     21       320.          0   0    0.000E+00   0.000E+00
     22       320.          0   0    0.000E+00   0.000E+00
     23       320.          0   0    0.000E+00   0.000E+00
     24       320.          0   0    0.000E+00   0.000E+00
     25       320.          0   0    0.000E+00   0.000E+00
     26       320.          0   0    0.000E+00   0.000E+00
     27       320.          0   0    0.000E+00   0.000E+00
     28       320.          0   0    0.000E+00   0.000E+00
     29       320.          0   0    0.000E+00   0.000E+00
     30       320.          0   0    0.000E+00   0.000E+00
     31       320.          0   0    0.000E+00   0.000E+00
     32       320.          0   0    0.000E+00   0.000E+00
     33      -320.          0   0    0.000E+00   0.000E+00
     34      -320.          0   0    0.000E+00   0.000E+00
     35      -320.          0   0    0.000E+00   0.000E+00
     36      -320.          0   0    0.000E+00   0.000E+00
     37      -320.          0   0    0.000E+00   0.000E+00
     38      -320.          0   0    0.000E+00   0.000E+00
     39      -320.          0   0    0.000E+00   0.000E+00
     40      -320.          0   0    0.000E+00   0.000E+00
---------------------------------------------------------------------------

Fig. 1: FEA MODEL:

RESULTS:

• Max. Stress Intensity at P=275 psi:
  • Outer Shell, SS304L: Max. SI = 15,700 psi < 1.5Sm = 25,050psi;
  • End Plate, SS304L: Max. SI = 14,339 psi < 1.5Sm = 25,050psi;
• Max. Stress Intensity at P=320 psi:
  • Outer Shell, SS304L: Max. SI = 18,269 psi < 0.8Sy = 20,000psi;
  • End Plate, SS304L: Max. SI = 16,686 psi < 0.8Sy = 20,000psi;

  The max. stress intensity on the shell as given above is the max. value of SI when only the outer shell elements are selected. The nodal averaging process only takes into account the nodes of the selected elements and ignores the contribution of the unselected end plate elements. Thus, the max. outer shell stress intensity would be a more conservative estimate of the potential stress around the welded interface between the shell and end plate.

  The max. stress intensity on the endplate occurs at the center hole region. This is consistent with Roark and Youngs formula for a circular plate with simply supported outer edge, and free inner edge. From Table 4, Case 2, (Ref: Formulas for Stress and Strain, 5th Edition, by Roark and Young), @ P=320 psi, the max. stress would be 15,026 psi, and the max. displacement, Uz, is -0.0075 in. In our FEM model with the same load, the max. stress intensity on the end plate is 16, 686 psi, and the max. displacement, Uz, is -0.0069 in.

  

  

  Fig. 2: AVE. NODAL STRESS INTENSITY @ P=320 psi:

  

  

  Fig. 3: OUTER SHELL STRESS INTENSITY @ P=320 psi:

  

  

  Fig. 4: AVE. DISPLACEMENT, Uz, @ P=320 psi:

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