Structural Analysis: LHC Magnet, D4A (Rev. 4)

Analyst: Rudy Alforque, 4/15/01
E-Mail: rudy@bnl.gov

I. General

This revision is a study of the shell response to the test pressure when there is no more void between the shell and yoke, i.e. h₂ = 0 in the basic geometry shown in rev. 3.

(Please see Rev. 3 for reference)

II. FEM Model:

(Please see Rev. 3 for reference)

The relevant material properties used in the model are:

1. Shell, SS304L
   • Young's Modulus, E = 0.193x10⁶ MPa (28x10⁶ psi),
   • Poisson's ratio, mu = 0.3,
   • Ultimate Strength, Su = 483 MPa (70 Ksi) (Table 1A, Part D, BPV Code Sec. VIII)
   • Yield Point, Sy = 172 MPa (25 Ksi) (Table 1A, Part D, BPV Code Sec. VIII)
   • Max. Allowable Stress, Sa = 112 MPa (16.3 Ksi) (Table 1A, Part D, BPV Code Sec. VIII)
   • Design Stress Intensity, Sm = 115 MPa (16.7 Ksi) (Table 2A, Part D, BPV Code Sec. VIII)
   • Parameter, 1.5kSm = 173 MPa (where k = 1)
2. Yoke, Iron
   • Young's Modulus, E = 0.207x10⁶ MPa (30x10⁶ psi),
   • Poisson's ratio, mu = 0.3.

III. Loads:

Case 1: Response of the coldmass shell to a test pressure of 2.38 MPa (345 psi). This internal pressure was applied on the inner surface of the shell. It was assumed that the coldmass was in a stress-free state before the application of this pressure, i.e. all residual stresses due to the forming and welding of the shell around the yoke had been fully relieved. Other loads, aside from the test pressure, should be analyzed separately, and appropriately combined with the results given here.

IV. Boundary conditions:

Symmetry boundary conditions are imposed at the horizontal and vertical midplanes.
For more details, see the following plot :

• Fig.1: Case 1: FEM Model, Full View

V. Structural Analysis: Results

Please note the following while viewing the graphics below.

1. Results for Case 1 were generated with the results coordinate system set to the global cylindrical system (Rsys=1) which has its origin at the true center of the cold mass shell. Hence, the displacements, Ux, refer to radial deformations.
   • Fig.2a: Case 1, Radial Displacements
   • Fig.2b: Case 1, Stress Intensity
     Based on ASME BPV Code, Sec. VIII, Div. 2, the max. combined general and local primary membrane stress intensity should be less than 1.5kSm = 173 MPa (See material properties for SS304L, above).