Copyright
Thomas J Kiernan.

Predictions of the collapse strength of three HY-100 steel shperical hulls fabricated for the oceanographic research vehicle Alvin online

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Online LibraryThomas J KiernanPredictions of the collapse strength of three HY-100 steel shperical hulls fabricated for the oceanographic research vehicle Alvin → online text (page 2 of 2)
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18



Horizontal

Adjustment

Holes



lamps



Vertical

Adjustment

Screw




Horizontal
Pivot Point



Ames Dial Gage



Adjustable Arm



\



PSD- 311 754
Figure 11 - Instrument Used in Measuring Departures from Sphericity



19



the instrument is designed to measure the distance from a central point
inside the sphere to any point on its inside surface. This central point
should coincide closely with the center of the sphere. It is possible to
take the readings obtained from the instrument and then, utilizing the
high-speed computer facilities of the Applied Mathematics Laboratory at the
Model Basin, to calculate the theoretical location of the center of the
sphere relative to the actuaJ. position of the instrument. Departures from
sphericity may then be calculated by a computer relative to the theo-
retical center of the sphere. This was not done for the ALVIN spheres
since it was possible to locate the instrument with sufficient accuracy
(within 0.050 in.) by taking readings on the Ames dial gage and adjusting
the position of the instrument by means of the vertical adjustment screw
and the horizontal adjustment holes shown in Figure 11. Small variations
between the theoretical center of the sphere and the position of the in-
strument would have a negligible effect on the local curvature over a
criticcil arc length. The instrument can rotate 350 deg about the horizontal
pivot points, and the adjustable arm can rotate 180 deg about the vertical
pivot point.

Over 1200 measurements were taken on each hull to ensure that at
least five readings were taken over a critical arc length. Additional
readings were taken in the areas of the welds to locate points of maximum
deviations. The Ames dial gage was calibrated for each hull by the use of
inside micrometers. Deviations were then measured and computed relative to
the nominal inside radius.

RESULTS OF MEASUREMENTS

Measured deviations from the nominal inside radius are plotted in
the form of contour maps in Figure 12. Inward deviations are plotted as
minus contours. The radial scale used in all drawings is constant. The
solid circles in the figures represent a complete hemisphere, and the radial
scale may be determined by measuring the diameter of this circle. This
measured diameter represents one-half the inside circumference of the
sphere. This is done for accuracy in analyzing the data. As is the case
with the problem of mapping, however, the scale in all other directions
varies, depending on the distance from the center of the plot and the

20



Figure 12 - Deviations from Sphericity""




Figure 12a — Huii Number 1, Inside View Looking Forward

NOTE: Contours are plotted in intervals of 5 mils. Minus
contours indicate inward deviations, i.e., -10 indicates distance
from center of sphere is 39.630 in. For local geometry in areas
marked by Roman Numerals, see Table 1.

*The surface enclosed by the solid circle shown represents a hemisphere unfolded into
flat surface whose radial scale remains constant.



21




Figure 12b — Hull Number 1, Inside View Looking Aft



22




Figure 12c — Hull Number 2, Inside View Looking Forward



23




Figure 12d — Hull Number 2, Inside View Looking Aft



24




Figure 12e — Hull Number 3, Inside View Looking Forward



25




Figure 12f — Hull Number 3, Inside View Looking Aft



26



orientation with the radial direction. The location of the penetration
and girth welds are shown in Figure 13 to the same scale as the contour

plots o

DISCUSSION

To determine the maximum loca]. radius of curvature, it is necessary
to obtain the maximum out-of-roundness A over a critical arc length. This
value may be obtained using the contour maps (Figure 12) and the scales
presented in Figure 14. These scales have been drawn to overcome the
mapping problem. Each scale contains two curves; the inner curve covers an
arc length of 16.6 in., the outer curve an arc length of 19.4 in. The
critical arc length may be calculated by Equation [10]. Assuming a thick-
ness of 1.33 in. and a ratio R-, /R of lo05, the critical, arc length is 18.0
in., which is midway between the curves presented in Figure 14. Areas of
maximum out-of-roundness may be determined by placing Figure 14 over Figure
12 and rotating the scal-es . The values for the deviations from sphericity

6 and fi (see Figure 4) are determined across any "diameter" of a scale
at a point midway between the two curves. The deviation 5 is determined
at the center of each scale. The location of points with relatively large
values of out-of-roundness A may be found in this manner.

Using the hull thickness measurements presented in P'igure 10 and
the curves presented in Figure 5, further refinements can be made in
determining the critical, arc length. A sample calculation sheet is shown

in Figure 15. Values of A . h , and R, /R were determined for several locations

a 1

on each of the three hulls. Some of these values are shown in Table 1„
The maximum ratio of R /r for the three hulls was 1.05. This demonstrates
the accuracy with which these hulls were fabricated and provides a guide-
line for reasonable tolerances for similarly fabricated steel vehicles.
For example. Figure 5 indicates that a steel hull 2 3/4 in. thick and an
out-of-roundness A of 0.107 in. would also have a ratio R, /R of 1.05 o It
is important to remember that the out-of-roundness is defined over a critical
arc length „

The collapse depths of the three ALVIN pressure hulls were cal-
culated using a critical local geometry„ A minimum ratio of hull thickness



27



Figure 13 - Location of Penetrations and Girth Welds




Figure 13a — Inside view looking forward



*The surface enclosed by the solid circle shown represents a hemisphere unfolded into a
flat surface whose radial scale remains constant.



28




Figure 13b — Inside view looking aft



29




Figure 14 - Arc Length Scales

*The surface enclosed by the solid circle shown represents a hemisphere unfolded into a
flat surface whose radial scale remains constant.

Figure 14 is also reproduced on transparent film for use as an overlay on Figure 12
and enclosed in a back-cover pocket.



30



TABLE 1
Local Geometry of the Three ALVIN Pressure Hulls



Hull


Location


h
a


R^/R




(See Figure 12)


(See Figure 10 )




1


I


1.35


1.04




II


1.36


1.03




III"


1.32


1.05




IV


1.35


1.05




V


1.35


1.04




VI


1.35


1.05


2


I


1.34


1.03




II


1.33"'"


1.03




-X-

III


1.34


1.04




IV


1.34


1.03




V


1.36


1.03




VI


1.34


1.03


3


I


1.33


1.03




II


1.34


1.04




III


1.35


1.04




IV


1.34


1.04




V


1.32


1.03




VI


1.34


1.04


Location of minimum value of h /K,




""Assumed thickness; no values given.





31



(h ) to outside local radius (R, ) was obtained for each pressure hull,
a ±Q

The local geometries for these critical areas are presented in Table 2.

Using these values of h and R-, in Equations [8] and [9], the collapse
a 1q

depths pg were calculated. The results of these calculations indicate

that Hulls No. 1, 2, and 3 will collapse at depths of 15,800, 16,100, and

15,100 ft, respectively. The lower collapse depths for Hull No. 3 may be

attributed to its relatively low yield strength (see Figure 8).

A high degree of confidence can be placed on these collapse depths

for a number of reasons. First and primarily, the shape of the hull has

been measured accurately. Previous tests have indicated that the collapse

strength of a spherical shell can be predicted accurately if the critical

local geometry is known. Second, the analysis presented in this report is

conservative for stable shells; i.e., for those shells whose empirical

inelastic buckling pressure is considerably lower than the classical

elastic buckling pressure. The average ratio of p' to p' for the three

E 1

ALVIN hulls is approximately 0.20 (see Table 2). Figure 5 indicates that
the analysis is conservative in this range. The reason for this is that a
Poissons ratio of 0.3 was used in the plastic range and the three-dimensional
Hencky-Von Mises effect of the pressure was neglected. In addition,
buckling coefficients higher than 0.84 are possible. Third, the effect of
secondary moments, which are not considered in the analysis, is negligible.
This is shown by the experimental results plotted in Figure 3 which indicate
that even for clamped edges, the effect of secondary moments is very slight
for stable shells with 9 values of 2.2 or greater.

The viewing port and access hatch inserts should not adversely
affect the collapse strength of the pressure hulls. Reference 8 reports
tests of two 0.286-scale hemispherical models of ALVIN, each penetrated by
a single viewing port. Strains were measured on the penetration insert as
well as on the adjacent portion of the spherical shell. These strains and
the calculated experimental stresses in and around the penetration inserts
indicated that the design of the penetration inserts was adequate.



Obviously this confidence would be destroyed if significant changes
occur in the shape of the hulls due to any additional penetrations or welding.

32



TABLE 2

Critical Local Geometry and Calculated Collapse
Depths for the Three ALVIN Pressure Hulls



Hull


h
a


\


>

Pi
psi


Pe

psi


' / '

Pe/pi


Collapse
Depth

K
ft


1
2
3


1.32
1.34
1.32


43.0
42.6

42.2


34,200
36,000
35,600


7000
7160
6710


0.20
0.20
0.19


15,800
16,100
15,100



33



Figure 15 - San^ile Calculation Sheet for Determining Ratio

of R /R



2.2



Equation [10] L^ = ^ f^^



Assume



h^ = 1.33 and R^/r = 1.05



Then L — 18.0 in. (Midway between curves)



Pfull No. 1 - Location I (See Figure 12a)




25 deg Scale

Inner curve covers arc length of 16.6 in.
Outer curve covers arc length of 19.4 in.



A =



a + "c



2 - «g (see Figure 4)



A = " ^^ ~ ^Q - (_ 54) = 42 mils = 0.042 in.



_A_ ^ 0.042
ha ~ 1.33



= 0.032



1.04 (See Figure 5)



From Figure 10 h =1.35
a



Assume



\M



1.04



L = 18.0" A = 0.042
c



0.042



0.031



ha 1.35

R^/R = 1.04 (Agrees with assumed value)



34



Normally these stresses were less than the membrane stresses in the
spherical hiill. Any mismatch which might occur on the three prototype
hulls would cause very local bending stresses in an area reinforced by the
increased thickness of the penetration insert. Since these stresses are
normally less than the membrane stresses or are very local, they should not
adversely affect the strength of the hulls.

Throughout the analysis, reference has been made to available
stress-strain curves. It has been assumed that the stress-strain curves
presented in Figure 8 are representative of the material used in the hull.
As additional data becomes available, they should be compared with the data
used in this analysis. If significant differences are reported from other
sources the predicted collapse depths can easily be adjusted using the
geometry presented in Table 2 and Equations [8] and [9]. It should be
mentioned that preliminary data on the weld material indicate that the
strength of the welds may be 5 percent lower than that of the hull material.
In view of the stability of these hulls, it is not felt that this would
affect the collapse of these spheres since this is a very local effect.

Although the results of this analysis differ little from the
results obtained using the nominal geometry of the spherical pressure
hulls, it should be eitphasized that this is only because the hulls have
been fabricated so accurately. For example, if the hull had been built
to an out-of-roundness tolerance of ±l/8 in., the collapse depths for the
three hulls would range from 12,600 to 13,400 ftT Further, if normal
boiler code tolerances of ±1 percent of the outside diameter were obtained
in fabrication this range would be reduced even further, that is, the
collapse depths would range from 6000 to 6400 ft. Thus the effect of
neglecting initial imperfections and the inqjortance of determining the
exact shape of spherical pressure hulls is evident.



"For these calculations it is assumed that the maximum allowable out-of-
roundness A (0.25 in. and 1.64 in.) occurs over the critical arc length.



35



SUMMARY AND CONCLUSIONS

1. On the basis of measured deviations from sphericity, hull thickness
measurements made by the fabricators and material stress-strain curves
available at this time, collapse depths of the ALVIN Pressure Hulls No. 1,

2, and 3 were calcialated as 15,800, 16,100, and 15,100 ft, respectively.

2. The maximum local radius of curvature for the three hulls was only 5
percent greater than the nominal radius.

3. Local geometry and not nominal geometry must be used to determine the
collapse strength of a spherical shell. The collapse strength of a
spherical shell with the same geometry as ALVIN, fabricated to boiler code
tolerances may be as low as 40 percent of the strength which was predicted
for the ALVIN spheres.



ACKNOWLEDGMENTS

The author is indebted to CDR Lasley of the Office of Naval Re-
search for his interest in this project. The cooperation of Mr. H. E. Froelich
of Litton Industries, Messrs. J. W. Mavor and J. B. Walsh of the Woods Hole
Oceanographic Institution and representatives of Hahn and Clay is
appreciated. Thanks are also due to Mr. M. A. Krenzke who directed this
project and contributed to the work described in this report and to
Mr. R. M. Charles who designed the measuring instrument and obtained the
measurements on the ALVIN pressure hulls.



36



REFERENCES

1, Office of Naval Research Letter 0NR:466:WWL:mjh of 30 July 1963
to David Taylor Model Basin.

2o Timoshenko, S., "Theory of Elastic Stability/' McGraw-Hill
Book Co., Inc. New York (1936).

3. Krenzke, M. A., "Tests of Machined Deep Spherical Shells under
External Hydrostatic Pressure," David Taylor Model Basin Report 1601
(May 1962).

4. Krenzke, M. A., "The Elastic Buckling Strength of Near-Perfect
Deep Spherical Shells with Ideal Boundaries," David Taylor Model Basin
Report 1713 (Jul 1963).

5. Krenzke, M. A. and Kiernan, T. J. "Tests of Stiffened and Un-
stiffened Machined Spherical Shells under External Hydrostatic Pressure,"
David Taylor Model Basin Report 1741 (Aug 1963).

6. Krenzke, M. A. and Kiernan, T. J., "The Effect of Initial Im-
perfections on the Collapse Strength of Deep Spherical Shells," David
Taylor Model Basin Report 1757 (in preparation).

7. Kiernan, T. J., "The Buckling Strength of Segmented HY-80
Steel Hemispheres," David Taylor Model Basin Report 1721 (in preparation).

8. Bynum, D. J. and DeHart, R. C, "Experimental Stress Analysis of
a Model of the ALVIN Hull," Southwest Research Institute Report (Apr 1963).



37



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2

Online LibraryThomas J KiernanPredictions of the collapse strength of three HY-100 steel shperical hulls fabricated for the oceanographic research vehicle Alvin → online text (page 2 of 2)