,

Mr. Richard C. Luther , Fermi National Accelerator Lab 2 October 23, 1986'-

TABLE 1. REDUCED SHELL THICKNESS, CENTRAL CALORIMETER

Shell Original Revised Vessel Segment Thickness Thickness

~ Vacuum Outer Cylinder 5/8" 5/8" (a) L Inner Cylinder 1/4" 1/4,,{b) Formed Heads 5/8" 1/211

Argon Inner Cylinder 7/16" 3/8"

Th1c ness maintained for area replacement at nozzles. Thickness maintained due to minimal benefit potential.

-------~...----------------~

-. •

Mr. Richard C. Luther October 23. 1986Fermi National Accelerator Lab 3

The limits on out-of-roundness and deviation from specified shape for cylindrical vessels, per Article UG-80, are intended to maintain not less than 80 Dar§ent of the nominal strength. They are based on a beam-column analogy.\ ,} The limits applied to spherical shells and formed heads are intended to maintain not less than 60 percent of the nominal strength.

Results

The review showed that the revised shell thicknesses provide adequate safety against collapse under the design conditions. These results are shown in Table 2. The inner and outer cylindrical shells of the vacuum vessel were determined to possess minimum SF >2. The vacuum vessel formed head was determined to possess a minimum SF = 1.9, which meets or exceeds the level set by the CGA rules. The inner cylinder of the argonvessel was determined to possess a SF = 2.4 under a maximum deviation condition. The method used to calculate safety factors was necessarilyconservative. Therefore, the SF = 2.4 should be acceptable.

Methods

Battelle critically reviewed the supporting documents provided byFermi lab. These consisted of hand calculations optimizing the shell thicknesses of the vacuum vessel outer cylinder, inner cylinder and formed heads, and the argon vessel inner cylinder. The calculations were checked for correctness of assumptions and numerical results. As requested byFermi lab, a marked-up copy of the calculations with comments is providedin Attachment 1.

Battelle then performed calculations to establish the safety factors in effect for the revised design. The collapse pressures were calculated using accepted design formulas, and adjusted for inherent safety factors. The new safety factors were then calculated as the ratio of collapse pressures to applied pressures. The reductions in these safety factors were then estimated for the maximum deviations from design shape. described below. These calculations are provided as Attachment 2.

Article UG-16(c) (3) limits mill undertolerance on plate thickness to the smaller of 0.01 inch or 6 percent of the design plate thickness. In all cases, the O.OI-inch limit controlled. This value was considered in all calculations making use of a shell thickness.

Article UG-80(a) (3) addresses permissible out-of-roundness, or ovality, for cylindrical shells. For vessels operating under internal or external pressure, the difference between maximum and minimum inside diameters, AID in Table 2, is limited to 1 percent of the nominal diameter. The critical pressure in the ovalized condition was calculated using an equation from Reference (6). This equation is discussed in Attachment 2.

-..

Mr. Richard C. Luther Fermi National Accelerator Lab 4 October 23, 1986

TABLE 2. FACTORS OF SAFETY IN ~EYISED DESIGN

Vessel Shell

Segment Nominal

SF UG_80(a)

AID Minimum

SF Minimum

SF UG-Sl

SF sF'

Vacuum Outer Cylinder 5.7 2.02S" 5.4 0.625" 32.6" 2.2 NA NA NA NA Inner Cylinder 3.0 0.600· 2.S5 0.25" 20.6" 2.25 NA NA NA NA Formed Heads 2.5 NA NA NA NA NA 2.550" 2.2 1.275" 1.9

Argon Inner Cylinder 3.0 0.644" 2.75 0.2S1" 22.S 2.4 NA NA NA NA

( a) Alf-minimum safety factors include the maximum mill undertolerance on platethickness of 0.01 inch.

·.

Mr. Richard C. luther Fermi National Accelerator lab 5 October 23, 1986

Vessels operating under external pressure are also limited by UG-80(b) (3)in deviation from specified shape, as measured by circular templates over a reference chord length. The allowable deviation was considered to result in a locally shallow shell, with increased radius of curvature. The critical pressure was calculated for a cylindrical shell with the increased radius. This is more conservative than the beam-column analogy on which the tolerances are based.

Article UG-81(3) addresses tolerances for formed heads. The inner surface of dished heads may not deviate outside the specified shape by more than 1.25 percent of the vessel diameter, nor "Inside by more than S/8-percent of the diameter. Knuckle radii may not be less than as specified. Although the Central Calorimeter heads are not of a conventional configuration, these limits should be considered applicable. The outside deviation from shape was treated as an increase in radius. The inside deviation was treated as a local shallowness. The critical pressures were than calculated using the curved panel model perReferences (2) and (7). The knuckles were also evaluated, using the Shield and Drucker formula per References (2) and (8), but were found not to be governing. Detailed explanations are contained in Attachment 2.

Closure

As stated above, the review of the revised Central Calorimeter shell designs showed that the level of risk of collapse under the design conditions appears to be acceptable. A marked-up copy of Fermilab's calculations, with comments, is provided in Attachment 1, and Battelle's calculations are provided in Attachment 2. This letter report completes the scope of work under our contract.

If you have any questions or comments, please call me at (614) 424-4662. Battelle looks forward to supporting Fermilab's engineering programs in the future.

Yours truly,

Michael Rosenfeld Mechanics Section

MR:bkb

Attachments (2)

cc: l. O. Vonasch, Jr. G. Mu1ho11 and

----------------... .. ~-...~-- ..

c

. . •

Mr. Richard C. Luther Fermi National Accelerator Lab 6 October 23, 1986

References

1. Rosenfeld, M. J. and Saffell, B. F., "Design Review of the D-Zero Cryostats", Final Report to Fermilab, June 26, 1986.

2. Luther, R. D., 00 Calculations, June 19, 1986.

3. ASME Boiler and Pressure Vessel Code, Section VIII, Rules for Construction of Pressure Vessels, Division 1, 1983 Edition with Addenda through Winter, 1985.

4. Jawad, M. H. and Farr, J. R., Structural Analysis and Design of Process Equipment, 1984.

5. Windenburg, D. F., "Vessels Under External Pressure", in Pressure Vessel and Piping Design: Collected Papers 1927-1959. ASME. 1960.

6. Timoshenko. S•• Strength of Materials, Part II, Third Edition. 1976.

7. Roark. R. J., Formulas for Stress and Strain, Fourth Edition, 1965.

8. Shield, R. T. and Drucker, D. C•• "Design of Thin-Walled Torispherical and Toriconical Pressure Vessel Heads". ASME Transactions, Journal of Applied Mechanics, June, 1961.

• •

•

ATTACHMENT 1

ANNOTATED FERMILAB 00 CALCULATIONS

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· ,

Annotations for Attachment 1

1. Actual SF = 3.0 for ASHE design of cylindrical vessels operating under external pressure. The apparent SF =1.5 for CGA-341.

2. A = 0.230 x 10-3• This is in the elastic buckling range, therefore calculate B = AE/2 = 3220.

3. Weld area = 0.0313 in2• 4. Propertie~ for ll-1/2 x 1-112 x 1/4 are A =0.69, Y = 1.353, ~y =

0.934, Ad = 0.151, all multiplied by 2. Total As = 10.06 in • -35. t + All = 0.538, B = 2133, A = 0.152 x 10 , Is = 13.6.

6. tr = 0.361 inch.

7. Bending stress varies with 1/t2• For t = 5/8 inch, sm = 6650 psi, sb = 5425 psi, so

ty = (3g~~~ + ~3~~8~0 ) x 0.625 = 0.404 inch 8. Inasmuch as SF = Pcr/Pa and Pcr = f(t

3),

the true SF = (0.50/0.458)3 x (30/15) = 2.6.

9. t = [product] 1/3.

10. At S = 211, Stress Intensity SI = 13.94 ksi. 11. The limit 4SE applies to longitudinal 10ca1 2membrane plus bending stress. The bending stress varies with lit. At S = 201, for t = 5/8

inch, longitudinal sm = 1421 pSi, sb = 7708 psi, so

_ (1421 ~ 7708 ) .t 4SE - 48,880 + 48,880 x 0.625 =0.266 lnch

Also, maximum SI = 13.94 ksi, so tSI = 0.290 inch.

12. Review of the local stresses in the inner knuckle calculated in the NONlIN runs indicates that the stress intensification for the inverted knuckle 1s at least 3 times greater than for a "nonnal" 6 percent knuckle on a 60-inch-diameter cylinder. This is a result of two factors:

(a) As pOinted out in this calculation, the included tangent angles of the knuckle result in a greater effective l = 132.5 inches instead of the 87.75 inch design value. This results in a stress intensification of around 1.7.

(b) Review of the longitudinal stresses in the inner cylinder from the NONlIN runs shows that the annular head applies an

(b) Review of the longitudinal stresses in the inner cylinder from the NONLIN runs shows that the annular head applies an axial load to the inner cylinder through the knuckle equal to twice that of the applied pressure.

The use of L = 132.5 inches is correct. However, in solving for tcr with SF = 2, the required value of Pcr = 15 x 2 x 2 = 60 psi. This results in tcr = 0.366 inch~

13. The writer does not concur that a knuckle thickness of 1/4 inch is adequate. However, the final thickness chosen, equal to 1/2 inch, is adequate.

14. For A = 0.338 x 10-3, buckling is in the elastic range. Therefore, calculate B = AE/2 = 4732, so Pa = 36.5 pSi. This is an acceptablevalue, by engineering judgement.

~--

ATTACHMENT 2

SAFETY FACTOR CALCULATIONS

FOR REVISED CENTRAL CALORIMETER

SHELL THICKNESSES

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