Structural Analysis: RHIC Dummy Magnet End Volume

Analyst: Rudy Alforque, 5/19/95
E-Mail: rudy@bnl.gov

Problem Description:

1. Determine if the end volume design of the dummy 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: 14 in.
  • Thickness: 0.375 in.
  • Material: St. Stl. 304
  • Yield Point, Sy: 30,000 psi
  • Design Stress Intensity, Sm: 20,000 psi
• Inner Shell:
  • Outside Diameter: 3.75 in.
  • Thickness: 0.25 in.
  • Material: St. Stl. 316
  • Yield Point, Sy: 30,000 psi
  • Design Stress Intensity, Sm: 20,000 psi
• End Plates:
  • Diameter: 13.5 in.
  • Thickness: 1.00 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 Tesca 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 values to satisfy item 1 are as follow:

• Outer Shell, SS304: 1.5Sm = 30,000psi;
• Inner Shell, SS316: 1.5Sm = 30,000psi;
• End Plate, 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 values to satisfy item 2 are as follow:

• Outer Shell, SS304: 0.8Sy = 24,000psi
• Inner Shell, SS316: 0.8Sy = 24,000psi
• End Plate, SS304L: 0.8Sy = 20,000psi

Hence, a finite element model was developed using ANSYS5.1 and the resulting stress intensities at critical locations were compared to the corresponding limiting values as described above.

Note: Although, the pressure load in the model, during the initial run, was 325 psi, the stresses at other pressures were calculated by applying the appropriate scale factor, since all the finite elements in the model were linear, elastic axisymmetric elements.

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

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

 ELEMENT TYPE    1 IS PLANE42      AXI. STRUCTURAL SOLID          INOPR 
  KEYOPT(1-12)=    0  0  1    0  0  0    0  0  0    0  0  0       0

 CURRENT NODAL DOF SET IS  UX    UY  
  AXISYMMETRIC MODEL


 RELEVANT MATERIAL PROPERTIES: 
 -----------------------------

 MODULUS OF ELASTICITY (psi):
 PROPERTY TABLE EX    MAT=   1  NUM. POINTS=  2
   TEMPERATURE     DATA    TEMPERATURE     DATA    TEMPERATURE     DATA    
    -9999.0     0.28400E+08  9999.0     0.28400E+08
 
 POISSON'S RATIO:
 PROPERTY TABLE NUXY  MAT=   1  NUM. POINTS=  2
   TEMPERATURE     DATA    TEMPERATURE     DATA    TEMPERATURE     DATA    
    -9999.0     0.30000      9999.0     0.30000    
 
 SHEAR MODULUS (psi):
 PROPERTY TABLE GXY   MAT=   1  NUM. POINTS=  2
   TEMPERATURE     DATA    TEMPERATURE     DATA    TEMPERATURE     DATA    
    -9999.0     0.12500E+08  9999.0     0.12500E+08

 DENSITY (lbs/cu. in.):
 PROPERTY TABLE DENS  MAT=   1  NUM. POINTS=  2
   TEMPERATURE     DATA    TEMPERATURE     DATA    TEMPERATURE     DATA    
    -9999.0     0.29000      9999.0     0.29000    
---------------------------------------------------------------------------

 Solid model summary:

                             Largest       Number      Number
                              Number      Defined     Selected
 Keypoints . . . . . . . . .     33           33           33
 Lines . . . . . . . . . . .     51           51           51
 Areas . . . . . . . . . . .     15           15           15
 Volumes . . . . . . . . . .      0            0            0

 Finite element model summary:

                             Largest       Number      Number
                              Number      Defined     Selected
 Nodes . . . . . . . . . . .   2943         2943         2943
 Elements. . . . . . . . . .   2712         2712         2712

 Element types . . . . . . .      1            1         n.a.
 Real constant sets. . . . .      0            0         n.a.
 Material property sets. . .      1            1         n.a.

 Coupling. . . . . . . . . .      0            0         n.a.
 Constraint equations. . . .      0            0         n.a.
 Master DOFs . . . . . . . .      0            0         n.a.
 Dynamic gap conditions. . .      0            0         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. . . . . . . . . . .    27
 Constraints on keypoints. . . . . . . . .     0
 Constraints on lines. . . . . . . . . . .     6
 Constraints on areas. . . . . . . . . . .     0

 Forces on nodes . . . . . . . . . . . . .     0
 Forces on keypoints . . . . . . . . . . .     0

 Surface loads on elements . . . . . . . .   209
 Surface loads on lines. . . . . . . . . .     5
 Surface loads on areas. . . . . . . . . .     0

 SURFACE LOADS ON ALL SELECTED LINES:
  -----------------------------------

    LINE   LOAD LABEL       VALI         VALJ          VAL2I        VAL2J
      2      PRES          325.0        325.0         0.0000E+00   0.0000E+00
      6      PRES          325.0        325.0         0.0000E+00   0.0000E+00
     14      PRES          325.0        325.0         0.0000E+00   0.0000E+00
     28      PRES          325.0        325.0         0.0000E+00   0.0000E+00
     33      PRES          325.0        325.0         0.0000E+00   0.0000E+00
-----------------------------------------------------------------------------

Fig. 1: FEA MODEL:

RESULTS:

• Max. Stress Intensity at P=275 psi:
  • Outer Shell(@Loc#2), SS304: Max. SI = 19,160 psi < 1.5Sm = 30,000psi;
  • Inner Shell(@Loc#1), SS316: Max. SI = 18,216 psi < 1.5Sm = 30,000psi;
  • End Plate(@Loc#1), SS304L: Max. SI = 17,333 psi < 1.5Sm = 25,050psi;
• Max. Stress Intensity at P=316 psi:
  • Outer Shell(@Loc#2), SS304: Max. SI = 22,016 psi < 0.8Sy = 24,000psi;
  • Inner Shell(@Loc#1), SS316: Max. SI = 20,932 psi < 0.8Sy = 24,000psi;
  • End Plate(@Loc#1), SS304L: Max. SI = 19,917 psi < 0.8Sy = 20,000psi;

Fig. 2: STRESS INT. @ LOC. #1 (P=325 psi):

Fig. 3: STRESS INT. @ LOC. #2 (P=325 psi):