iNDENT REMOVAL AND EVALUAHON KN
LUMENUM
SPRENKLER ERREGATEON TUNNG

this for {in Dam of M. S.
MICHIGAN STATE COLLEGE

Daie Ear! Kirk
1954

This is to certify that the

thesis entitled

Indent Removal and Evaluation
in Aluminum Sprinkler Irrigation Tubing

presented hg

Dale E. Kirk

has been accepted towards fulfillment
of the requirements for

__I‘L§n__ degree in Agriculinral

Engineering

V

Major professor

Date May 171 19511

0469

 

INDENT REMOVAL AND EVALUATION IN ALUMINUM

SPRINKLER IRRIGATION TUBING

By

Dale Earl Kirk

“

A THESIS

Submitted to the School of Graduate Studiee of Michigan
State College of Agriculture and Applied Science
in partial fuliillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of.Agricultural Engineering
1951+

ACKNOWLEDGEMENTS

The author wishes to express his sincere thanks
to Professor E. H. Kidder for his inspirational supervision
and continued ready help in this investiaation.

He is also indebted to Professor A. w. Farrall and
his staff as a whole for making materials, equipment, and
facilities available for this study. A special word of
thanks is extended to hr. James Cawood and his staff in the
research laboratory for their c00peration in the development
and construction of test equipment.

The writer expresses his appreciation to Dr. V. D.
Baten in the department of Mathematics for his generous assis-
tance in laying out much of the eXperimental procedure.

To Dr. L. E. Malvern and other members of the depart-
ments of Applied Mechanics and Mechanical Engineering is
extended a word of thanks for their patient council and con-
structive suggestions.

Grateful acknowledgement is due to Mr. Douglas Harvey
and Mr. Don Seble in the department of Mechanical Engineering
who made special test equipment available for parts of this

study.

cg

J
c:
c:
P
CD

TABLE OF

INTRODUCTION . . . .
REVIEW OF LITERATURE .
OBJECTIVES . . . .
EVALUATION OE'HILRAULIC
Scope of the Study
Equipment . . . .
Procedure . . . .

Results . . . .

D

L

O .3," ER

CONTEBTS

DEVELOPMENT OF MEANS FOR SATISFACTORY

DETERMINATION CF RECOVERY OR

Diametral Recovery

Hydraulic Recovery

I O

0 O O
O O O O O O
O O O O O O
O O O O O 0
O O O O O O
O O O O O O
O O O O O O

ENT REMOVAL

EFFICIENCY OF REPAIR .

Bending Strength Recovery

SUMMARY AND CONCLUSIONS
LITERATURE CITED. . . .

LIST OF TABLES
Table

I. U. S. Production of Aluminum Sprinkler System
Irrigation Tubing . . . . . . . . . . . . . .

II. Gage Pressures to Produce Yield and Ultimate
Stress in Aluminum Tubing . . . . . . . . . .

III. K and m from General Friction Equation H = KQm

Determined by Method of Least Squares . . . .

IV. Friction Head Values Computed From Equation
Constants in Table III . . . . . . . . . . .

Va. Load at PrOportional Limit on L.5 Foot Span of
Three-inch Outside Diameter Aluminum Tubing
with Third Point Loading . . . . . . . . . .

Vb. Force to Create Bending Moment at PrOportional
Limit Analysis of Variance of Bending Tests .

VIa. Maximum Combined Load in Pounds on h.S Foot
Span of Three-inch Aluminum Tubing with
Third Point Loading . . . . . . . . . . . .

VIb. Combined Force to Create Maximum Bending
Moment Analysis of Variance of Bending Tests.

Page

22

37

37

A?

FIGULE
l. Specially constructed quick couplar using a
round rubber belt . . . . . . . . . . . . . . .
2. A test section of tubing with couplers, manometer,
and C-Clamp taps O O O O O O O O O O O O O O O O
3. Dented section under test . . . . . . . . . . . .
h. Heir and stilling basin . . . . . . . . . . . . .
5. Laboratory type hydraulic press . . . . . . . . .
6. Five sections dented in 0.6 increments . . . . .
7. Truck exerting 1360 pounds on test section . . .
8. Tractor exerting thO pounds on test section. . .
9. Highway-type scale used for determining wheel
l-eigllts e e e e e e e e o e e e e e e e e e e e
10. Two types of plugs used for sealing the ends .’.
11. End of tubing showing the groove impressions left
by the end plug 0 O I O O O 0 O O O O O O O 0 O
12. Diametral recovery curve for section number
three 0 I O O O O O O O O O O O O O O O O O O
13. Diametral recovery curve for section number

15.
16.
17.
18.

twelve . . . . . . . . . . . . . . . . . . . .
Tractor-dented section number twelve . . . . . .
Section number twelve with 100 pounds pressure .
Section number twelve with 200 pounds pressure .
Section number twelve with LOO pounds pressure .

Section number twelve with 700 pounds pressure .

27
28
28
29
29
3o

Figure

19. Section number twelve after the residual kink
has been removed . . . . . . . . . . . . . . .

20. Curve showing relationship of friction head and'
rate of flow for tubing section number ten . .

21. Six sections crushed by tractor rear wheel for
bending test . . . . . . . . . . . . . . . .

22. Same six sections after straightening . . . . .

23. Wooden plugs shown with saddle-type contact

21;.

25.

List of Figures

bIOCks O O O O O O O O O O O O O O O O O O O

Tubing sample bent to near the point of buckling
in a universal testing machine . . . . . . . .

Curve showing comparative bending strength for
pipe number one . . . . . . . . . . . . . . .

Curve showing comparative bending strength for
pipenumbertwo...............

The twelve sections of tubing after being
buckled in the bending test . . . . . . . . .

.Page

30
35

to
to

141

1.2
1+3

Ab.

INTRODUCTION

Sprinkler-type irrigation with the use of portable,
surface pipe has been practiced on a commercial scale in
various parts of the United States since the early 1930's
(10). Until after World War II various types of steel
surface pipe were used. Steel boiler tubing was used
to a limited extent in the earlier installations, but
Sthe greater share of the pipe was either spiral or straight
seam welded steel with wall thicknesses from 16 to 10
gage. Protection against rusting was generally provided
by galvanizing, although some tubing was asphalt coated.
While this tubing was much lighter than standard pipe
of comparable diameter, it was still quite resistant to
damage from denting and kinking. Deterioration was
generally due to rusting of the base metal where the pro-
tective zinc or asphalt had been loosened or lost.

At the end of World War .II the war-born aluminum
reduction and extrusion plants began producing an ex-
truded thin-wall aluminum tubing which rapidly became the
dominant material used for sprinkler irrigation. The
rapid increase in the production of aluminum irrigation

tubing can be seen from the figures in Table I.

TABLE I

U. S. PRODUCTION OF ALUMINUM SPRINKLER IRRIGATION TUBING (l3)

 

 

 

Year Miles of Tubing Year Miles of Tubing
191+6 230 1950 Laoo
1947 uoo 1951 4800
19A8 2000 1952 7000
1949 2300 1953 9000

 

 

The availability of production potential in the field
of aluminum products at the close of the war was a very
timely stimulus to the expansion of the sprinkler irriga-
tion practice. The advantages of sprinkler irrigation
under many conditions had already been well demonstrated
in many parts of the United States but the labor involved
in moving the heavier steel tubing was a dominant factor
in deterring farmer acceptance of this method of water ap-
plication. The light weight and apparent general corrosion
resistance of extruded aluminum tubing made it a compara-
tively ideal material and its application brought about
a very rapid expansion in the acreage covered annually by
sprinkler irrigation.

Future expansion should not be hampered by material
shortages since aluminum is the third most abundant mater-

ial on the earth's crust (2).

Virtually all the aluminum sprinkler tubing produced
prior to 1952 was extruded and designated as alloy bBS-Tb.
Since 1952 at least one manufacturer in the state of Wash-
ington has been marketing a fabricated welded tubing from
a harder alloy which is somewhat more resistant to field
damage.

Due to the lower stiffness of aluminum and the thin-
ness of the tubing wall, aluminum irrigation tubing is
much more susceptible than steel to field damage in the
form of dents and kinks. With a modulus of elasticity
and a density each approximately one-third that of steel,
the deflection of an empty section of aluminum tubing
supported at the ends will be approximately equal to the
deflection of a steel tube of the same dimensions. When
loaded with water the deflection of the aluminum is much
greater.

The types of damage most common are dents due to
radial impact and kinks due to excessive bending. Much
of the serious damage from dents is caused by accidentally
driving over the tubing with automobiles, trucks, tractors
and other farm implements. Dents of various sizes occur
when the sprinkler systems are left in the field with
horses or cattle. Smaller dents are often incurred in the

handling of the tubing when moving from one irrigation set

to the next. A large dent or flattened area will cause
the pipe to kink or be off-set unless the ends are re-
strained.

Damage due to kinking may occur also when long sec-
tions loaded with water are lifted abruptly or are allowed
to drop and strike a support at one or both ends with no
support near the center.

These various indents in the original shape of the
tubing always cause some change in the normal pattern of
flow of water through it. More apparent to the farmer
is the inconvenience of handling kinked sections or sec-
tions sufficiently dented to cause a bend or an offset in
the tube. These sections tend to twist in the hands when
carried, will not lie in the prOper position for coupling,
and will not stack up well with the other sections in a
moving wagon or truck rack.

A repair may be effected by cutting out the damaged
section and fitting a new coupler to one of the cut ends.
This repair is expensive and leaves two shorter sections
which are again a problem to handle with the other uniform
length sections. For a three inch diameter line the cost
of a coupler is approximately equivalent to the cost of
six to ten feet of tubing.

PersOnal interviews with representatives of two west

coast regional distributors of irrigation tubing indicated

their cognizance of the dent problem. Their attempts to
repair dented sections employed exterior malleting of the
tube while a projectile-shaped mandrel or "mouse" was
forced against the dent on the inside. This process is
slow and costly and necessarily involves excessive bending
and stretching of the metal near the regions malleted.

From random field observations, tears and cracks in
the tubing were very uncommon. It was believed that this
type of damage could best be handled by cutting out the
damaged portion and installing a coupler. In a few cases
repair by welding might be practical where aluminum welding
service is available. This type of repair is not practical
on the average farm.

The major problem in restoring damaged tubing to its
full degree of usefulness involved the repair of sections

damaged by dents and kinks or hands.

REVIEW OF LITERATURE

The deformation of circular cylindrical shells within
the elastic limits of the material has been analyzed by
Timoshenko (15) for concentrated diametral loading as well
as for the general case of deformation. His analysis em-
ploys the theory of inextensional deformation of the center
line of the shell cross sections. This theory, credited to
Lord Rayleigh, by Hermes (8) assumes that the strain along
an axial line is zero at a point equidistant from the ends
of the shell, and that shear across this line at this point
is also negligible. Hermes used electrical resistance
strain gages to check the strains in steel tubing subjected
to concentrated diametral loading. His measurements taken
along an axial line 900 from the point of loading showed
reasonable conformance with the inextensional theory of
right circular cylindrical shells. While this inextensional
theory method of analysis may be used to predict strains
along the shell when it is loaded within the elastic limits
of the material, it appears to be of little value in pre-
dicting other than border strains when deflections have
entered the plastic range.

Timoshenko (It) discusses the buckling of thin cylin-

drical shells under the action of uniform external lateral

pressure and various types of axial loading including
eccentric loading to induce bending. While the buckling
failure appeared to result in damage similar to that
inflicted by a straight edged tool impressed tangentially
to the tube, no mention was made of the equivalent exter-
nal force or energy involved in making such an indentation.
No references were found that treated the problem of pre-
dicting the amount of elastic and plastic deformation of
a thin-walled cylinder under a concentrated load or the
amount of force required to restore the metal back to its
original position.

Partial yielding and plastic flow is discussed by
Nadai (12) for thick-walled hollow cylinders subjected to
internal pressures. His discussion of the yielding of
a die-cast aluminum tube under internal pressure gives
an indication of the general behavior of the metal stressed
slightly beyond the yield stress in a smoothly generated
cylinder but is of little value in predicting internal
pressures required to restore a dented cylinder to its
original shape.

Experimental determination of the behavior of copper
tubing subjected to various combinations of internal pres-
sure and axial loading are given by Espey (5). His inves-
tigation of the various load conditions showed that a thin-

walled tube subjected either to "pure“ internal pressure

(plane strain) or to balanced biaxial tension will fail

by instability at a considerably smaller circumferential
strain than the longitudinal strain which occurs on

necking of a tensile test Specimen made from the same metal.
A tube subjected to pure internal pressure will become
unstable at only approximately one half of the circumfer-
ential strain as a tube subjected to pure longitudinal
tension. His results further indicated that the longitudi-
nal strain at which a circumferential neck occurs should
decrease as the internal pressure superimposed on the lon-
gitudinal tension increases.

While experimental work may have been reported in
various trade literature, the only references found in the
formal literature which dealt directly with indent re-
moval was an article in Engineer (3). The article described
a machine which employed a tapered plug fitted to a piston
with a ten-inch stroke. Dents were removed from light
alloy tubes or spools by forcing the plug through the

tubes by pneumatic power.

OBJECTIVES

The objectives about which this study centered
are listed as follows:

1. Evaluate the hydraulic power losses in aluminum
Sprinkler irrigation tubing due to dents.

2. Develop means for satisfactory dent removal.

3. Determine the extent of recovery or efficiency
of the dent removal method. This involved a
study of the recovery of both hydraulic charac-
teristics and recovery of the strength of the
tube in bending.

EVALUATION OF HYDRAULIC POWER LOSSES
Scope of the Study

Observations of hydraulic power losses were limited
to three-inch tubing. This is the size commonly used for
lateral lines in sprinkler irrigation. Since these lines
are moved once or twice each day they are the most suscep-
tible to damage from handling. The flow rates observed
ran from 39 gpm to 229 gpm which covered the range of flow
rates consistent with sound engineering design practice

as indicated by Gray (7) for this size tubing.

Equipment

A steady supply of water was obtained with a four-inch
turbine type pump rated at 250 gpm when discharging against
a 22 foot head. The pump discharged directly into a three
and one-half foot length of four-inch standard pipe which
was in direct alignment with the sections to be tested.
Attachment to the test section was made by use of two
specially designed couplers. These couplers were made
to permit rapid and easy attachment of the test sections.
They also tightly sealed the ends of badly oblated sections
aS'well as sections retaining their circular shape. The

seal was formed by placing a four and one-half inch long

11

by one-quarter inch diameter rubber sewing machine belt
over the tubing near each end as shown in Figure 1.

As the tubing was forced into the tapered socket
in one end of the coupler the rubber belt was rolled
and compressed between the tube and the coupler forming
a tight, flexible seal. Longitudinal thrust on the
couplers due to water pressure was taken up by a light
chain Which was hooked to the fittings at each end of the
tube. C-type clamps fitted with a nipple and a rubber
gasket seal were used to attach the manometer hoses to the
sections being tested. A closed-top or inverted U-tube mano-
meter using water as the indicator fluid was used for check-
ing static differential heads up to 42 inches. The general
coupler, U-tube, and C-clamp arrangement is shown in Figure 2.
For heads beyond 42 inches a mercury Uetube manometer was
used as shown in Figure 3. The 90° V-notch weir shown in

Figure A was used for determining rates of flow.

Procedure

Dented tubing samples for the hydraulic study were
obtained by crushing five foot long sections of three inch
diameter tubing in a small hydraulic press and by driving
over them with tractors and trucks. The hydraulic press

was fitted with a die-block with a one-eighth inch radius

l2

 

Fig. l.

Specially constructed quick coupler using

a round rubber belt between mating sections
for a seal.

 

 

1
Fig. 2. A test section of tubing with couplers,
manometer, and C-clamp taps in place. The

tie chain was used for taking coupler end
thrust.

13

 

Fig. 3. Dented section under test. the the use of
the mercury manometer in the foreground for
measuring the higher friction heads.

I
‘ c

_.«r

f

 

.4... _A77 -~'

.Fig. h. Weir and stilling basin used for determining
rates of flow through test section.

1h

leading edge. This block was placed to form an impression

in the tubing at right angles to its longitudinal axis as
shown in Figure 5. For the shallower dents, the impression
left by this edge roughly simulated a buckling failure of

the tubing due to excessive bending load. A denting series
consisted of five test sections each impressed a progressive-
ly greater amount with the die block as shown in Figure 6.
Load and deflection data were taken at suitable increments
while the sections were being dented.

Random samples of sections damaged by field equipment were
obtained by driving over the test sections placed on a concrete
floor. Figures 7 and 8 show the truck and one of the trac-
tors used for denting or crushing the sections. The total
denting force or weight of the wheel was measured by a high-

way scale as shown in Figure 9.

 

 

Fig. 5. Laboratory type hydraulic press used with one-
eighth inch radius die block for transverse denting series.
An 870 pound force was required to make this dent.

 

Fig. 6. Five sections dented in 0.6 inch increments
with one-eighth inch radius die block.

 

Fig. 7. Truck exerting 1360 pounds on test section.

16

 

Fig. 8. Tractor exerting thO pounds on test section.

 

 

Fig. 9. Highway-type scale used for determining wheel
weights.

17

A standard test length of h.§ feet between manometer
tap holes was selected for all test sections. For the
tapping of pipes which have a much greater wall thickness
Addison (1) suggests that a 3/32 inch tap hole is as small
as can usually be recommended. He further states, however,
that ideally the hole should be of the smallest diameter
that will not get choked and that will not impose excessive
damping. A one-sixteenth inch diameter hole was used and
the burrs were carefully removed after drilling.

With the test section coupled to the pump, the clamps
were fitted over the tap holes and the hoses scavenged to
prevent errors in static head readings due to air inclusion.
This was done by partially Opening the pump discharge valve
and allowing the water to run freely through the hoses
which were disconnected from the manometer. When the mer-
cury Uetube was required, the hoses were completely drained
and air was used as the medium over the manometer fluid.
Care was taken to run the water through each section of alu-
minum tubing in the same direction each time it was tested.
This was done for two reasons. First, the turbulent flow
pattern past the damaged area could possibly result in
greater friction head in one direction than in the other.
Secondly, the static head readings from the tap holes could
be affected by the direction of flow if the hole directions

or hole edges were slightly irregular.

18

The formula for discharge over a 900 V—notch sharp-
crested weir is given by King (11) as Q 3 2.52H‘2'li7 where
Q is given in cubic feet per second and H is in feet of
head. Barr(h) listed the formula as Q = 2.h8H2'u8 for the
same type weir. Differences in the equation constants
result from differences in smoothness of the weir face and
shape of the approaching channel. Since these conditions
will be somewhat different in every case, each weir should
be individually calibrated for most accurate results. Data
taken by Gillette (6) on the M.S.C. Agricultural Engineering
Department weir were used to calculate a discharge formula
as Q = 2.15H2'32. The formula was used in the form Q = 96SH2°32
where Q,was given in gallons per minute. The weir zero was
determined by clamping a temporary hook gage near the weir
and adjusting it with a carpenter level until it was at the
same elevation as the bottom of the weir notch. The tank
was then.filled to the level of the temporary hook gage and
the reading on the vernier scale noted when the permanent
hook gage in the stilling well was adjusted to the water
level.

A minimum of five sets of readings were taken for de-
termining;the friction characteristics of each test section.
A minimum of ten minutes was allowed between each valve
setting and.the time of reading to allow the flow system

to reach an equilibrium.

Results

Due to the limited number of samples used and the
method of selecting these samples, it could not be assumed
that the observations recorded were representative of a
normally distributed pepulation of values. The values
observed in the study did, however, appear to cover
the range of restrictions to flow that might conceivably
be encountered in the field for three inch tubing.

Sections number three and twelve were taken as being
representative of the maximum damage that might possibly
be tolerated by the farmer. A rate of flow of 170 gallons
per minute was taken as a typical maximum rate of flow for
three inch tubing consistent with good irrigation system
design practice. System operation was assumed to be twenty
hours per day and thirty days per month. With an overall
pump and motor efficiency of fifty percent and a power cost
of $0.02 per kilowatt hour, the additional power cost per
month per dent was found to be $0.275 per month for a dent
of number three order and a $0.23 per month for a dent of
number twelve order. These costs wereon the basis of no

relief of restriction when operating pressure was applied.

DEVELOPEEHT UP MEANS FOR SATISFACTORY DENT REMOVAL

The requirements for any methods or equipment deve10ped
for the removal of dents were set down as follows:
1. Must be adaptable to various lengths and diameters
of tubing.
2. Must accommodate various types of loose and rigid
couplers.
3. The ends of the tubing can not be restrained since
longitudinal movement is required for straightening.
h. Equipment must be sufficiently portable to be readily
carried to the farm.
5. The maximum cost of repair must be much less than
the cost of a repair coupler for a damaged section.
The portability factor virtually eliminated the use of
any outside restraining form that might be employed with
either a mechanical expansion or hydraulic eXpansion of the
tube from the inside. From the standpoint of simplicity,
the hydraulic expansion method without a restraining form
appeared to meet the best requirements set down above.
Hydraulic radial expansion of monotube gun barrels be-
yond the elastic limit without restraining forms is practiced
by the United States Navy for pre-stressing the outer wall
metal against the inner wall metal. Upon firing, this results

21

in much less tube eXpansion since a greater thickness of
metal is subjected to a more nearly uniform stress. Hy-
draulic radial expansion against an outer forming shell is
used in the steel industry in the final forming of large
sizes of fabricated steel tubing.

To determine the maximum pressures that might be used
on aluminum tubing, the yield and ultimate pressure values
were computed. The yield and ultimate stress values of
alloy 63S-T6 aluminum are listed as 31,000 and 35,000 pounds
per square inch respectively by Hoyt (11). Since the yield
strength value was based on two percent permanent elongation
or set, a value of 30,000 pounds per square inch was chosen
for calculating internal pressures within the elastic limit.
The computed pressures to produce these stresses in a thin
walled cylinder are listed for the various sizes of tubing
in Table II. The values were computed from the equation

P = ZSt
D

where P is the gage pressure in pounds per square inch
S is the mean circumferential stress in pounds
per square inch
t is the wall thickness in inches

D is the inside diameter in inches.

TABLE II
GAGE PRESSUHES TO PhUUICE YIELD AND ULTIMATE
STRESS IN ALUMINUM TUBING

 

‘- -. —

Nominal V‘Wall Inside Pressure to Pressure to

 

 

Tubing Thickness Diameter cause 30,000 cause 35,000
Size 0.D. lb per sq in lb per sq in
stress, stress
in. in. in. lb/sq. in. lb/sq. in.
2 0.050 1.900 1579 18h2
2.5 0.050 2.b00 1250 1&58
0.050 2.900 103h 1207
i 0.050 3.900 769 897
a 0.054 3.892 862 971
A 0.062 3.876 9 0 1120
5 0.052 .896 667 7A3
5 0.062 u.876 3 890
6 0.062 5.876 33 739
7 0.072 6.856 630 7 5
8 0.083 7.83u 636 732
8 0.098 7.812 722 882
9 0.094 8.812 6%0 7%7
10 0.109 9.782 6 9 7 0

 

 

For three inch diameter tubing the gage pressures should
be restricted to less than 1000 pounds per square inch if the
tubing is not to be permanently enlarged. The force on each
end plug at this pressure would be 6636 pounds or more than
three and one fourth tons. Corrosion of the metal with use,
variation in wall thickness in manufacturing, and Espey's
findings were factors considered in determining maximum
working pressures to use for dent removal.

The requisites of the hydraulic expansion method for

repairing Sprinkler tubing include a ready water source, a

23

set of prOper end plugs, an accurate pressure gage, a small-
volume high-pressure pump, and miscellaneous fittings.

The most critical item in the hydraulic expansion
method is the and plug design. The main requisites of such
a design were listed as follows:

1. Fast and easy to install and extract.

2. Should not damage the tubing.

3. Near perfect water seal.

L. Feed water in and out rapidly.

5. Provide for complete scavenging of air from the

tubing.

6. Must work past all types of couplers.

7. Light weight.

8. Inexpensive.

9. Parts replaceable.

The two plugs, which were used, both embodied the same
principle of operation but were of different type construction
as shown in Figure 10. These plugs had been developed for
‘preliminary investigation previous to the formation of this
project. They were composed of a steel body with a slotted,
tapered hole which received a tapered bronze expansion core.
The core was fitted to an internal threaded drive for forcing
it into the plug body. As the core was forced into the
body, the segments of steel about the slotted tapered hole
expanded radially against the inside of the tubing. The
tubing was restrained from expanding by the use of an

21;

 

I

 

 

————— ,

Fig. 10. Two types of plugs used for sealing the
ends of three inch diameter tubing.

adjustable band or clamp on the outside. Water was admitted
through a pipe in the center of one plug and air scavenged
out through a pipe in the center of the other plug. A
riser nipple bled off the air from the pocket formed near
the top of the tubing as it was filled with water. The seal
was made on each plug by a rubber cup which fit against the
plug body. To insure positive expansion of the rubber cap
against rough or slightly misshapened tubing, a steel mush-
room.core was fitted inside the cup to serve as an expander.
This expander could be controlled from outside the tubing
whenever the CUp failed to seat itself readily.

The plugs used were constructed in only the three inch

size and generally satisfied quite well the mechanical

25

requirements previously set down. Their cost of construction
was undetermined but it was believed that the general type

of design changes which must always take place in adapting

an experimental model to volume production would result

in a satisfactory manufacturing cost. In preliminary de-
structive tests of tubing the plugs held pressures up to

1100 pounds per square inch. For three inch tubing with a
2.9 inch inside diameter this meant resisting an axial load
of 7267 pounds force. To obtain sufficient wall friction

to withstand this force, the threadlike grooves on the

outer surface of the plug body segments were embedded slight-
ly into the inside surface of the tubing as seen in Figure ll.
These groove impressions were only a few thousandths of an

inch deep and not considered detrimental to the tubing.

 

 

IWig. 11. End of tubing showing theygroove impressions
left by the end plug.

26

DEThnmIJATIOJ 0b hLUOVth 05 EFFICILNUI 0s REPAIR

The efficiency of the hydrostatic radial expansion
method of repair was checked in three ways. First, the
extent of recovery of the original tubing diameter was
noted for several random types of dents. Second, the ex-
tent of recovery of the original hydraulic friction char-
acteristics was measured. Third, a replicated experiment
was set up for determining the extent of recovery of the

original bending strength of the tubing.

Diametral Recovery

Diametral recovery was observed on the transverse
dent or kink series shown in Figure 6 and also on repre-
sentative samples damaged by the truck wheel and the trac-
tor wheel. The measurements taken represented the minimum
setting which would allow an outside caliper to pass across
any part of the dented area as the tubing was being straight-
ened. Figures 12 and 13 plotted from the hydrostatic ex-
pansion data show the typical recovery pattern as hydraulic
pressure is applied. For transverse dents or kinks com-
plete recovery of the original outside diameter was not

possible without the use of localized forces such as might

M/m'm um Ca/iper O u/s/de

D/ame fer; in Inches

h)

\

C)

 

 

27

 

DIAMETRAL RECOVERY or
3 EC r/ozv NUMBER THREE UNDER

H VDA’OS 7/! no A 0.4 D/NG

I I j J

 

0

200 400 600 600
Pressure in /b/.sq /'/7

Fig. 12. Diametral recovery curve for section

.Aflhnhflnmnv Clahkxw' (Duvsflde

/'/7 inches

£9/va7e/e/y

0»

h:

\

h—

 

01

number three.

Pressure Reliaffia; _ __ _ _ _ _ i

    
 

DIAMETRAL RECOVERY OF
SEC T/ON NUMBER ELEVEN UNDER

H YDROS TA 77C 1. GAD/N6

I l 1 J
200 400 600 500
Pressure in lb/sq in

Fig. 13. Diametral recovery curve for section

number twelve.

 

Fig. 1A. Tractor-dented section number twelve shown
with hand-operated water pump and pressure
gage before pressure was applied.

 

 

 

 

 

 

LFig. 15. Section number twelve with 100 pounds per
square inch pressure applied.

 

 

 

3?»..41_, :r$_
-- - we“: a”-..
I "i ' ‘ flit-"w -;

‘5
. ~ ,
_ b .2
,~~‘J-“..}\, . I . -' .

-«

 

Fig. 16. Section number twelve with 200 pounds per
square inch pressure applied.

 

 

Fig. 17. Section number twelve with 400 pounds per
square inch pressure applied.

20

 

 

 

Fig. 18. Section number twelve with 700 pounds per square
inch pressure applied. the the slight amount of
residual kink or offset as shown by the gage stick
held along the t0p edge of the tubing

 

Fig. 19. Section number twelve after the residual kink
has been removed under pressure by use of the
bending bar shown in the background.

be obtained by malleting against a mandrel placed inside
the tubing. Flatter types of dents with less severe bending
at the edges were recovered virtually one hundred percent.
Hydraulic expansion brought the dent out as shown in the
series represented in Figure 14 through Figure 18. The
slight offset or kink left as shown in Figure 18 was elim-
inated by the use of the crudely improvised bending bar
shown in the background in Figure 19. By applying the
bending bar and creating a bending moment on the tube while
it was under a pressure of 700 psi, the metal on the convex
or outer side of the bend could be stressed rather easily
beyond the elastic limit without danger of buckling the
metal on the concave side. This reduction of the bending
moment required to permanently deform the tubing can be

seen from the following computations:

S I
_U-

bending moment in pound inches

M

where M

(0

stress on extreme fiber in pounds per square inch
I_: moment of inertia of the tubing about its
neutral axis in inches”
C 3 distance from neutral axis to extreme fiber
in inches.
Taking:

I: I (Du-d4)
61+

Ft)

 

-.- _Z'[__ (3.001% — 2.9014)
61+
= 0.50; in.“
S = 30,000 pounds per square inch yield stress
0 = 1.5 inches
Then:
M = LiOJQOOIHgéOAL)

10,080 inch pounds
By subjecting the tubing to an internal pressure of 700
pounds per square inch, the extreme fibers were prestressed

axially as shown below.

SD = §
where
Sp 3 prestress in pounds per square inch
P 3 total axial force acting in pounds
A = cross section area of stressed metal in
square inches.
Taking:

P I (pressure) (projected area)

(700) Hide)
T

2
(700) (m (2.9)
1:

A62u pounds

- _7_r_(D2 - de)
A

:>
u

Then:

sp = “32%!

9976 pounds per square inch tensile prestress

This prestress reduced the required bending moment as

shown below.

M - (30,000 - 9970) (0.50t)
1.5

3 6728 inch pounds
10,080 - 6728 = 3352 inch pound reduction of necessary
bending moment.
Besides giving this reduction of 33 percent in the neces-
sary bending moment, the prestress in tension further pro-
tected the convex side from buckling under the compressive

stresses as the bending bar was applied.

Hydraulic Recovery

The same equipment and procedure used in determining
hydraulic power losses due to denting were used in deter-
mining the extent of hydraulic recovery after the sections
were straightened.

Resistance to the flow of water in pipes may be ex-

pressed in the general equation

H = K QT

‘L’

.-

where
H is the friction head in feet of water
K is an empirical constant which includes pipe
length and diameter

Q is the rate of flow in gallons per minute

m is an empirical constant.
{M'taking the logarithm of both sides of the equation, the
exponent, m, may be expressed as a coefficient of the logarithm

of Q.

Log H Log KQm

8 Log K - Log Q?

Log K - mLog Q'

Thus by plotting the logarithms of the values of the equation
on rectangular coordinates or by plotting the values directly
on logarithmic paper the locus should describe a straight
line.

The observations for friction head and rate of flow of
the various sections of tubing were plotted on logarithmic
paper. Figure 20 is a sample of the plot for one section.
The constant, m, which becomes the slope of the line when
the data is plotted on logarithmic coordinates, may be
taken directly from the curve. Since the logarithm of one is
zero, the ordinate value at an abscissa value of one on log-
arithmic coordinates correSponds with the zero intercept

value of the curve on rectangular coordinates. Thus, the

fn feef

FF/C f/on Head

35

F/Q/C 770M C URL/F 3
Ft”?
/.0 SECWO/‘v’ /VO. TEN

05.

04.

O.
3r

02.

O./

 

 

0.08

0% I I L I I l I 4 I j
30 4o 50 70 /00 200 300

Fare 07’ F/ow fn 9/0/77

F18. 20. Curve showing relationship of friction head
and rate of flow for tubing section number

ten.

value of H may be read directly irom the curve at an

abscissa value of one on logarithmic coordinates.

For the range of large flow rates and small friction
heads involved, however, the value of H determined graph-
ically would have to be obtained by projecting the line
past two cycles on the logarithmic paper. Since this
would greatly magnify any error made in choosing a line
through the plotted points, the method of least squares
of logarithms was used for determining the equation con-
stants.

The exponent m was determined for each tubing section

for each treatment by the following formula:

m = nZ(log 9105»; H) - (210g Q) (210g H)
nzdog 0) - (2 log 0)?

 

where n - number of observations of H and Q.
The values of K were determined by taking the antilog of the
value found by the following formula:
LongzlogH -m ElogQ
n n
Table III shows the emperical friction constants ob—
tained from the above equations for the tubing before it

was damaged and after it was damaged and straightened.

37

TABLE III

R AJD m PROM cEiLkAL FRICTION EQUATION H = KQm
DETERMINED BY METHOD OF LEAST SQUARES

W

Pipe Treatment

 

 

Section

No. Original Dented Straightened
xxlo-h m xx10’4 m Kx10’4 m

1 0.747 2.1020 1.840 1.9217 3.332 1.7993

2 fi.597 1.79L3 2.730 1.884L 2.915 1.8 7L

i .347 1.7SLL 5.308 1.872% L.031 1.7 22
2.333 1.8997 15.230 2.00

5 0.807 2.10L8 31.L10 2.05 3

7 1.121 2.0107 1.450 2.2580 1.007 2 .0L37

9 2.7 0 2.7153 2 .029 1.8817 1.52 1.9521

10 2.%68 1.8778 10. 200 1.7012 1.83 1.9255

11 2. 2 1 .873A 2 .529 2.3201

12 1.05 2 .03L5 5. 810 1.832u 1.237 1.9992

 

To give a clearer picture of the comparative friction

of tubing sections under various treatments, a sample.fric-
tion head value was computed from the above tabulated data
for each h.5 foot test section. Each friction head was

computed on the basis of 150 gallons per minute water flow

and was listed in inches of water as shown in Table IV.

TABLE IV

FRICTION hLAD VALUES COMPUTED IROM EQUATION
CONSTANTS IN TKBLE IIMI

”m-“ -— -w-” --. l -"M

Computed Friction Head at 150 Gallons
Per Niinute, in Inches of Water

 

 

 

 

Section Original Dented Straightened
% ”“’ §.§% 2.§9 2.3g2
3 22 57 8: 5% 317 E
i ltd? 5%2226
? 2.021 11.83L 5.821
9 2.75, 2.5.% Mg
ii Siggb 232130
12 2.830 S.g45 2.772

D
I

\u

A single classification analysis of variance showed
that there was no significant diffcmncc between the friction

values ohtaihed for the original and the straightened sections.

Bending Strength Recovery

For any method of dent removal to be acceptable it
should effectively restore the damaged tubing to near its
original strength. Restoration of shape and hydraulic
characteristics should not be considered sufficient if the
reclaimed section must be given favored treatment in the
field to prevent kinking at the originally damaged area.

A replicated eXperiment was set up for determining bend—
ing strength recovery of tubing sections damaged by a trac-
tor wiwel. TWO grOUps of six samples each were used in the
experiment. Each sample consisted of a section of new,
three inch O.D. aluminum tubing five feet long.

The p\sxibility was considered that there might be a
significant difference in the mechanical preperties of the
two thirty-foot long parent sections of tubing from which
the samples were out. To bring out this difierence, if any,
and to compensate for its effect the six samples for each
group were cut from one-half of each thirty-foot parent
section. The six samples in one group were each crushed

in as nearly the same manner as possible by driving a tractor

rear wheel over then. Care was taken to start the tire

tread contact in nearly the same position on each sample

and to drive over each of them at a uniform rate of speed.

he uniformity of the dent pattern obtained can be seen in
figure 21. Each of the dented sections was subjected to 750
pounds per square inch hydrostatic pressure and the residual
offset of approximately 0.2 inch at the center was removed

by the use of the bending bar. The slight residual oblate-
ness of the tube in the dented region was removed by pressing
the tubing between a pair of vise jaws lined with soft lum-
ber. Figure 22 shows the sections ready for the bending test.
The other group of six undented samples was used as a check.
The comparative bending strength of the two groups was meas-
ured by third-point loading in a universal testing machine.
To prevent collapse or premature buckling at the point of
contact of the load, a pair of dumbbell-shaped wooden plugs
was used. Figure 23 shows the wooden plugs and the saddle
blocks which were used at the four points of load contact

in the bending test.

Load and deflection readings were taken at deflection
increments of 0.1 inch for each sample until it buckled.
Figure 2h shows a sample loaded in the testing machine to
near the point of buckling.

Figure 25, plotted from the bending test data, shows
the comparative bending strengths of the three samples of

undamaged tubing and the three samples of damaged and

 

Fig. 21.; Six sections crushed by tractor rear wheel for
bending strength test.

 

 

Fig. 22. Same six sections as shown above after straightening
for bending strength test.

   

Fig. 23.

Fig. 2h.

L

b1

 

Wooden plugs shown with saddle-type contact
blocks for obtaining constant bending moment
near the mid—section of the tubing.

 

 

Tubing sample bent to near the point of buckling
in a universal testing machine. Note the wooden
plugs inserted in the tubing to help prevent
crushi-x.

LOAD VERSUS DEFLECWO/VCURVES

 

FOP P/PE /‘/U/x//EE/? ONE

 

 

/500.
j
77v ree Undamaged
Sec ffons
/200 ..
/ 777 ree Damaged and
A _ Repaired 88C 770 I75
900..
3
5 50d
‘6
Q
0
\l
3004,.
0 1 1 L 4 l
0 0.3 06 0.9 /.2 /.5
De f/ec f/on 07 /'n ches
Fig. 25. Curves showing comparative bending strengths

of three samples of damaged tubing and three
samples of undamaged tubing taken from the
first piece of parent material.

07 /b

Z. 0676/

1+3

LOAD VERSUS OEFLECWO/V CURVES

/5OO

/200 .

900

600

300

 

 

FOR P/PE maxi/755? 7* W

 

 

 

Fig. 26.

D
E)
C)
U - Una/amagec/ Sacha/":5
0 = Damaged and
Repa/red Sec/Vans
L J J L l
0.6 0.9 /.2 . A5 /.8

Def/ecfx'on x'n inc/78$

Curves showing comparative bending strengths
of three samples of damaged tubing and three
samples of undamaged tubing taken from the
second piece of parent material.

Lu

straightened tubing from one of the parent sections. Since
the curves were plotted from the unadjusted data, they do

not all fall through the origin. This displacement was due

to slack in the linkage and the tendency for the various parts
to shift slightly at the initial loading causing the first
displacement reading to be somewhat erratic. It can be seen
from the curves that the bending strength for the damaged
sections was very near the strength of the undamaged sections
up to the proportional limit of each. Beyond the proportional
limit the damaged sections soon buckled while the undamaged
sections were bent into a permanent curve to some extent be-
fore buckling occurred and the strength fell off drastically.
The type of buckling failure can be seen in Figure 27 which

shows all twelve samples after the bending test.

 

 

 
 

 

  
  

j‘.
'7" 4’";
.1 §
‘ a
W:l‘.,
r - ‘

 

4m

   

 

. \k‘
i F‘ .
‘1
x _ - j
. _ 'r _.
,' ‘
-:-.'_ ‘1': : .~'-I
: Ir. ‘
‘ v

V
.' I t
\‘ 0

 

r I
V_ 4’ r |
v '1

Fig. 27. The twelve sections of tubing after being buckled
in the bending test. The six damaged and repaired
sections are in the foreground.

Figure 26 shows apprcximately the same results for the
samples taken from the second parent section of tubing.

There was more dispersian of the loading curves but the
strengths were, in general, again comparable up to the pro-
portional limit of the sample from both treatments.

Table Va shows the maximum loading of each sample within
the proportional limit as taken from the curves and Table Vb
lists an analysis of variance for this data. The analysis
was carried out, primarily, to show whether there was suffi-
cient variation of the loadings within each treatment to make
the data unreliable. The within or error term in the analysis
is clearly insignificant as compared with the effect of the
sample treatment and the sample parentage. Since the mean sum
of squares for interaction was much larger than the mean sum
of squares for variation of the samples within each group,
the former was selected as the preper error term. Due to the
small number of degrees of freedom for the interaction term,
neither the effects of the dent nor the effects of the pipe
showed up as being significant at the five percent level.

Tables VIa and VIb show the data and analysis of vari-
ance for the maximum loadings obtained for the samples. Here
again the error within samples was small compared with the
interaction term. Use of the interaction term with only one
degree of freedom showed the effect of both the denting and

the parentage to be insignificant.

TABLE Va

LOAD AT PROPORTIONAL LIMIT (in pounds) ON h-S FOOT SPAN OF
THREE-INCH OUTSIDE DIAMETER ALUMINUM TUBING
WITH THIRL POINT LOADING

 

 

 

Dented Undented Pipe Totals
""‘ ‘ lbs. lbs. lbs. ‘“
Pipe I 1007 10u0
1000 1010 6057
990 1010
Pipe II 820 897
862 870 507u
7h0 885
Treatment
Totals 5&19 5712 11131,

Grand Total

 

TABLE Vb

FORCE TO CREATE BENDING MOMENT AT PROPORTIONAL LIMIT
ANALYSIS OF VARIANCE OF BENDING TESTS*

 

 

 

 

Source D.F. SS MS F F
5% point

Total 11 98,797
Dent 1 7.15h 7,15u 3.08 161
Pipe 1 80,52t 80,52k 3h.70 161
Interaction l 2,32h 2,32h
Within 8 8,795 1,099

Interaction

Plus within 9 11,119 1,235

* Notations and method of presentation follow examples in
Goulden, Cyril H., "Methods of Statistical Analysis."

f7
‘91

TABLE VIa

MAXIMUM COMBINED LOAD IN POUNDS 0N 9.5 POOT SPAN
0F THRhE-INCH ALUMINUM TUBING NITH THIRD POINT IOADING

.__v

 

 

Dented Undented Pipe Totals
Pipe I 1012 1420
1050 Ikea 7t1u
1063 1t67
Pipe II 98L 1226
1050 12th 6831
1098 1229
Treatment '
Totals 6257 7988 1t,2t5

Grand Total

 

 

TABLE VIb
COMBINED FORCE TO CREATE MAXIMUM BENDING MORENT

‘.L A..—

 

 

 

Source D.F. SS MS F F
5% Point

Total 11 318,117
Dent 1 2h9,696- 2u9,696 8.u2 161
Pipe 1 28,32u 28,32u 0.95 161
Interaction 1 29,701 29,701
Within 8 10,396 1,299.5
Interaction

Plus Within 9 h0.097 u,u55.2

 

 

It should be pointed out, however, that haO the
within term been taken as the error term, the effects of
the dent and parentage would have been significant in both
analyses. The strong effect of the parentage of the source
of tubing from which the samples wer( cut was not antici-
pated in the design of the experiment. Had this been anti-
cipated the experiment might have been modified to cut all
the samples from one forty-foot section of tubing or to cut
pairs of samples from many different sources of tubing.

The analysis of Variance for the experiment as conducted
does point toward two indications which are of importance.
The small within mean sum of squares, (MS), indicated that
the denting procedure, the straightening procedure, and the
loading procedure all resulted in very little dispersion of
data and that they should be capable of fairly accurate re-
production. The large mean sum of squares for the two sources
of tubing or pipe indicated a rather wide variation of some
of the mechanical properties of extruded aluminum tubing from
the same manufacturer. This variation should definitely be
considered if further work of this nature is anticipated.

From the practical standpoint, the bending strength
within the nominal elastic range of undamaged tubing ap-
peared to be a reasonable criteria for comparison. Loading
beyond this point would cause permanent deformation whether

the section was damaged or undamaged. For the type of damage

inflicted in this test series, the repair procedure re-
stored the proportional limit in bending to an average of

5 percent of the value for undamaged tubing.

SUMTTAPIY AYE!) (INCLUSIONS

The use of thin-walled aluminum tubing in sprinkler
irrigation is increasing rapidly as the acreage covered
by this method of irrigation is expanded annually. While
an exact evaluation has not been made of the extent of the
losses of materials and labor due to damage of this tubing
in handling, these losses appear sufficiently significant
for consideration.

Losses of power from pumping water past dents in
sprinkler irrigation tubing appeared from the study to be
' generally too small to be of economic significance. It ap-
pears that the inconvenience of handling a badly mashed
section would generally result in its being pulled out of
service before power losses due to increased friction would
become a problem.

Dents of the type normally caused by running over the
tubing with rubber tired vehicles were removed successfully
by the use of hydraulic radial expansion. By closing the
ends of the tubing with suitable end plugs and applying hydro-
static pressure up to approximately 75 percent of the yield
strength of the tubing, the dents were removed sufficiently
for most practical purposes. Any slight residual kink left

in the section was removed by exerting a bending moment at
the dented section while the tubing was under pressure.

Tubing which had been dented and straightened showed
essentially complete recovery of its original hydraulic
characteristics. Bending strength recovery of dented and
straightened tubing averaged 95 percent recovery up to the
proportional limit of the metal. Bending strength tests
showed that the damaged and straightened sections would
not stand as much pure plastic bending as the undamaged
sections without buckling.

While a cost study of the dent removing procedure was
not a part of this project, it would appear that due to the
limited amount of equipment required, the hydraulic radial
expansion method of repair should be quite economical. A
set of plugs and a small hand pump carried on the pick-up
truck of an irrigation equipment salesman could likely be
used to build customer good will besides netting the salesman
a good wage from the straightening fee charged. With the
cost of a length of three inch tubing, for example, running
from fifteen dollars to thirty dollars depending Upon the
length of the section and the style of COUpler used, there
is an opportunity to show a considerable saving to the far-

mer with a few minutes work on each dented tubing section.

\."1
N

LITERATURE CITED

Addison, Herber. Hydraulic Measurements, John Wiley and
Sons Inc. New York, p. 50, 19L1.

Anderson, Robert J. The Metallurgy of A1uminhm1and Alumi-
numiAlloys. H. C. Baird and Co., Inc., New York, 1925.

Anon. Small Tube Indent Removing Machine. Engineer. 190,
November 2t, 1950, p. 509.

Barr, James. Experiments Upon the Flow of Water Over
Triangular Notches, Engineering, April 8, 15, 1910.

Espey, G. Instability of Thin—Walled Tubes Sub ected
to Internal Pressur . ASME Transactions. 6-, 19L6.

Gillette, Allen K. Unpublished Report of Special Problem
in Michigan State College Agricultural Engr. Dept.

Gray, Alfred S. Sprinkler Irrigation Handbook, Rainbird
Sprinkler Mfg. Corp.,.G1endale, Calif., 1952.

Hermes, R. M. On the Inextensional Theory of Deformation
of a Right Circular Cylindrical Shell. JOurnal of
Applied Mechanics, New York, p. 3&1, Vol. 18, Dec. 1951.

Hoyt, Samuel L. Metal Data, Reinhold Pub. Corp., New
York, 1952.

Israelson, O. W. Irrigation Principles and Practices,
Second Edition, John Wiley and Sons Inc., New York,

p. 141, 1950.

King, H. h. Handbook of Hydraulics, Second Edition,
McGraw Hill Book Co., Inc., New York, p. 93, 1929.

Nadai, Aroad. Plasticity, McGraw Hill Book Co. Inc.,
New York, 1931.

Nuerberger, H. H. Aluminum Company of America, Written
communication.

1h. Timoshenko. 8. Theory of Elastic Stability, McGraw
Hill Book Co. Inc., New York, 1936.

15. Timoshenko, S. Theory of Plates and Shells, McGraw
Hill Book Co. Inc., New York, 19t0.

MICHIGAN STATE UNIVERSITY LIBRAR

mIII IIII III II IIIIIIIII