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costs and quantities of a few principal items, such as clearing, sanita-
tion, excavation, temporary works, construction camp, masonry, earth
fill, spillway, moving structures, moving highways, moving railways,
etc. In arriving at fair values, commissions and Courts are not in
the habit of disallowing sums which have been prudently and wisely
expended in the construction of used and useful utility property;
instead, their problem is to isolate the reasonable from the limitless
conjectures of experts and from the flowery arguments of attorneys
who seek to inflate the much-abused term "value."

The remarks of the last paragraph apply equally well to several
other specific examples set forth by the Committee. The instances
of the Pennsylvania and New York Central Terminals, on page 1365,
are very similar to the aforesaid dam examples. There is little doubt
in the writer's mind that excellent cost data are available for the
recently-constructed I^ew York terminals. Why is it necessary to dis-
regard the actual original cost of these terminals and turn to a
conjectural reproduction thereof? Opponents to the reproduction
theories will answer that the underlying reason lies in the possibility
of claiming inequitable increments in the railway's capital account.
Advocates of the reproduction theories will answer that the purpose
is to arrive at present value; and then the deluge of arguments of
what constitutes value soon creates mire sufficient to obscure the
original issue.

The next example cited by the Committee is that of a certain
highway crossing a railroad track. For the sake of brevity, the
Committee's statement (page 1366) relating thereto is reproduced, as
follows :

"One illustration brought to the attention of the Committee is
a case of a highway which originally crossed a steam railroad at a
very acute angle, making a dangerous crossing to both railroad and



1616 DISCUSSION ON VALUATION OF PUBLIC UTILITIES

Mr. public. At its own expense the railroad acquired land parallel with
McCann. j^g q^-^^ changed the course of the road for several hundred feet and
made a right-angled crossing. It was argued that, 'in case of repro-
duction, all other property remaining as at present', the highway would
be in its new location and would not have to be reproduced. On this
basis, many items which the owner of a railroad or other public utility
was compelled to pay for might be cut out of an appraisal. But the
highway would be in its original place were it not for the act of the
railroad, and would have to be moved by any railroad, building
presently, if the existing road had not been built; the evidence of the
necessity, however, having been destroyed in the doing. The cost was
a proper cost, capable of historic proof; and the Committee believes
that it should be included as a cost in the estimate of reproduction."

If the writer understands this last illustration correctly, the cost of
the old highway crossing (which had grown inadequate to meet modern
traffic condition, and was dangerous), should be charged against the
railway's accrued depreciation fund, created for the purpose of replac-
ing equipraent, structures, and other property as it wears out, grows
obsolescent, and becomes inadequate. The actual cost, borne by the
railway, of the new and re-aligned highway crossing should be placed
in the capital account of the carrier; and such an item would appear
in simple terms in an original-cost appraisal, without theorization of
what may have happened during a process of reproduction.

It seems needless to dwell further on the several instances wherein
the Committee advises departure from the strict reproduction theory
and recommends the historical modification thereof. The writer regrets
that the Committee did not see fit, in each of the examples, to point
out wherein the original-cost method would establish more convincing
equities before a tribunal in a valuation proceedings.

Before leaving the Committee's specific examples of application of
a reproduction theory, attention is called to the stone bridge piers, in-
stanced on page 1373 of the report, and to similar examples following.
Certain abutments of a railroad bridge, built of stone masonry at a
cost-to-reproduee of from $12 to $16 per cu. yd., in accordance with
the road's practice for the previous 10 years, would now be built with
concrete at a cost of from $7 to $11 per cu. yd. The Committee's con-
clusion, as to this and similar examples, is that the precise existing
structure should be appraised at its reproduction cost, and that the only
departures (page 1374) from such a rule are the cases where, due to
obsolescence of existing machinery, it is absolutely absurd to pursue
this method to its ultimate conclusion. Once again comment is forth-
coming to the effect that the Committee's recommendations result in an
adherence to the strict reproduction theory whenever the value to be
derived therefrom enhances the original cost of an item of property;
but, if the strict theory does not establish sufficiently high values, it
would seem that the Committee's idea is to modify the theory. If a



DISCUSSION ON VALUATION OF PUBLIC UTILITIES 1617

theory can be modified in one place, there should be no great objection Mr.
to a reasonable modification at another place. Unfortunately, multi-
tudinous modifications of the strict theory result in individual theories
of each and every appraiser. The writer, in the instance of the masonry
abutments referred to, would call attention to the equities of appraisal
at the original cost of the structure, regardless of what similar stone
masonry is costing to-day, and regardless of the present-day cost of
better concrete abutments.

Possibly it will not be amiss to cite here a pertinent criticism made
by the late John M. Eshleman, formerly Lieutenant Governor of Cali-
fornia, and once President of the California Railroad Commission, in
an address* delivered before a conference held \inder the auspices of
The Utilities Bureau, at Philadelphia, in November, 1915 :

«* * *_ "jij^g inconsistency of adapting the historical method
with reference to some elements and rejecting it with reference to some
others need only be mentioned. Why it is that the committee of presi-
dents of the railroads of the United States should concern themselves
with hidden costs of some elements of the properties of the railroads
and forget all about hidden or other costs of lands and properties that
have appreciated, is beyond my comprehension.

"I really seriously wonder at the logic of those who urge that cost
shall ever have anything to do with this question unless they admit it
has everything to do with it, and I marvel at their regard for the
simplicity of public authority when they urge that original cost shall
always be used even in their reproduction theory when it will give them
more than present cost to reproduce, and at the same time utterly
repudiate costs of lands and similar properties when sxich costs are less
than the market value now obtained. I do not for a moment contend
that the work of the engineers in making inventories, and, if you please,
in fixing unit prices is not very important. But holding, as I do, that
where government is dealing with monopoly it of necessity must deprive
such monopoly of the power of taking all that it can get from its
patrons, I am driven to conclude that government must determine as
a substitute what the agency ought to take, and in determining what
the agency ought to take, the safest and most just guide is what the
agency has sacrificed and what service it has performed for the public.

That the original-cost method possesses merit in valuation proceed-
ings is shown by such facts as (1) a more or less general adoption by
regulatory State commissions of original-cost as a perfectly legitimate
line of inquiry to shed light on property values, (2) the recognition by
Congress of original cost as one of the methods to be pursued in the
valuation of the nation's railroads, (3) the National Association of
Railway Commissioners' unanimous insistence that original cost be
considered in the Interstate Commerce Commission's valuation of com-
mon carriers' properties, and (4) Court decisions supporting the posi-
* The Utilities Magazine, 1-10-11.



McCann



1618 DISCUSSION ON VALUATION OF PUBLIC UTILITIES

Mr. tion of the Supreme Court of the United States in Smyth v.
Ames (cited by the Committee). No judicial authority, moreover, is to
be cited to show that an estimate of tlie cost of reproducing the prop-
erty (with or without deduction for accrued depreciation), is the sole
and only guide to a reasonable and adequate valuation of a utility
property for rate-making purposes. On the contrary, the inconsistencies
of the reproduction method have been scored time and again. It is
only recently that the Supreme Court of the United States, in the
Des Moines Gas Case, repudiated the reproduction method when applied
to what, in valuation work, is commonly termed "undisturbed paving."
In addition to those steadfast older commissions and their represent-
atives, who have given due and just weight to the actual original-cost
methods, it is noteworthy that many a recent author is outspoken in
recommending the sacrifice of the investor as the measure of fair value,
particularly fair value as a rate base. (Cf. Whitten and Hayes, supra.)
A recent engineering contribution is "Public Utility Rates," by Mr.
Harry Barker, Associate Editor of Engineering News, wherein the
author (at pages 37 and 38) states:

"Present tendency seems to be to give more and more weight to
figures of investment and investors' sacrifice in determining rate-basis
worth. With the general imposition of proper accounting systems
figures of investments and sacrifice can be more completely secured than
in the past so that a better basis for value by investment can be estab-
lished. Where regulation has been longest established, there invest-
ment has greatest weight; it is not unreasonable to expect that in the
course of time the entire country may accept the theory. * * *"

The most common argument against the use of the original-cost
method of valuing public utility properties, aside from the difficulties
alleged to be encountered in securing records of such costs, is that
appreciations in value of property (if such exist) are denied to the
owners thereof. The reproductionists, however, do not point to any rule
of common equity which entitles them first to earn an adequate return
on their investments and then to participate in the profits which accrue
to appreciation ; but they rely on certain judicial passages, which in
themselves are sound, although subject to linguistic abuses when applied
unadvisedly to valuations that are made bases for rate schedules. Under
certain rulings of the Courts, it may be argued that, even though a
utility may steal equipment without being apprehended, and may con-
vert that equipment into used and useful property in the service of the
public, the stolen equipment must receive due recognition in a valua-
tion and rate-making proceeding. Whether or not this view will pre-
vail ultimately, under a continuance of State regulation, is a some-
what debatable question at the present time. A simple case will serve
to illustrate the fallacy of too great weight given indiscriminately to
appreciation in utility property. Assume that an electric plant, in a



DISCUSSION ON VALUATION OF PUBLIC UTILITIES 1619

State where the laws provide for State regulation, costs $100 000, and Mr.
assume, further, that the regulatory body of jurisdiction, after investi- ^^*^*""-
gation at the very start, has fixed rates such as will yield full operating
expenses plus 5% per annum ($5 000) for accruing depreciation and
7% per annum ($7 000) for a fair rate of return. At the end of 5
years, provided no change is made in the electric property, the utility
will have accumulated $25 000 (plus earnings) in a depreciation fund,
and each year will have paid a full and adequate rate of return on the
entire investment. During these 5 years, if perchance the prices of
labor and materials advance so that the estimated reproduction-cost-
new of the identical property at the end of the period, according to
expert appraisers, would be $110 000 (exclusive of betterments and addi-
tions), there will have been an unearned increment, over and above a
fair rate of return, amounting to $10 000 in the value of the property —
equivalent to $2 000 per year, or 2% annually on the original cost. In
other words, a valuation thus made at the end of the said 5 years,
resulting in revised rates being fixed on an estimated reproduction
theory, capitalizes an unearned increment which automatically results
in rendering a 9% rate of return throughout the entire first 5-year
period. What has the utility done or denied to itself in order to deserve
this unearned increment? Is not the public entitled to participate in
the appreciation of property, at least to the extent of not having the
same capitalized against it, to be borne by the rate-payers of the future ?
Carrying the illustration still further, let it be assumed that the esti-
mated reproduction value sinks to $90 000 at the end of 5 years; then
the reverse is true, and the utility each year is deprived of just earnings
equivalent to 2% of the cost of the property. Under such conditions,
would it not be argued that this deprivation of earnings would consti-
tute a confiscation of property ?

Such illustrations are indicative of the public's vital interest in
what is termed "appreciation." It is to be borne in mind that ''depre-
ciation", as applied in valuation work, in no manner is the opposite of
"appreciation." An original-cost valuation, if properly compiled, does
not presume to inflict on a utility the losses occasioned by decreases in
prices of material and labor. An original-cost valuation, however, does
presume to reflect the conditions under Avhich the bargain between a
utility and its consumers was consummated. Under an original-cost
valuation, the public sustains all losses due to the falling ofi^ of prices,
although it participates in gains only to the extent of not having an
unearned increment capitalized against it.

The reproduction theory has its place. It is undoubtedly one evi-
dence of value, and an appraisal predicated on the strict reproduction
theory should be made a part of every rate case; but the reproduction
theory (or some modification thereof), under no circumstances, should
be construed as the sole and only guide to value. Ultimate value for



McCann.



1620 DISCUSSION ON VALUATION OF PUBLIC UTILITIES

Mr. rate-making piirposes is a discretionary exercise of judgment on the
part of those governmental agencies which are empowered by legislative
enactment to regulate public utilities, subject of course to judicial
review should the administrative power be abused.

The Courts have not ruled that reproduction-cost-new (or less depre-
ciation) must be the criterion by which to judge the present value of
utility property for rate-making purjwses; neither have the Courts
stated that such reproduction-cost-new (or less depreciation) is not to
be used, nor that original cost is not to be used. What the Courts have
said is that all these evidences of value are elements to be considered
with other factors in fixing on value for rate-making purposes. When-
ever reproduction advocates turn their attention to bringing forth the
advantages of the original-cost method as earnestly as they have ex-
pounded the reproduction theory, the disadvantages of the reproduction
theory, which make it necessary to resort to original conditions and to
original-cost conceptions, will disappear miraculously in a strict ad-
herence to the actual original cost method of valuation. A fair rate of
return on the actual dollars prudently expended for utility property
that is used in and useful to the rendering of public service are words
that jingle with equity; and it is the writer's opinion that judicial
sanction, supporting the position of commissions respecting original
cost, is not long to be withheld.



AMERICAN SOCIETY OF CIVIL ENGINEERS

INSTITUTED 1852



TRANSACTIONS



Note. — This Society is not responsible for any statement made or opinion expressed

in its publications.



Paper No. 1402

THE DISTRIBUTION OF STRESSES

IN MITERING LOCK-GATES,

WITH SPECIAL REFERENCE TO

THE GATES ON THE PANAMA CANAL



By Henry Goldaiark, M. Am. Soc. C. E.



Synopsis.



This paper is based on an extended study of the laws which govern
the distribution of stresses in different parts of a mitering lock-gate
under service conditions. For reasons mentioned in the paper, the
problem is indeterminate, so that the solution was based on the theory
of elastic work.

A general method of computation is first outlined, which is simple
in principle, though the computations are somewhat laborious. It is
believed to be more complete and accurate than any previously
developed.

An application to several of the lock-gates on the Panama Canal
follows. The resultant loads which are sustained by the different hori-
zontal girders and by the vertical bracing are computed in detail, as
well as the pressures exerted by the gates against the bottom sills.



]622 DISTRIBUTION OF STRESSES IN LOCK-GATES

Some practical conclusions, drawn from the results obtained, are
also given, as a guide for future designs.



General.



Mitering gates have been used in canal locks for several centuries,
and are still the preferred form, to the virtual exclusion of other types.
Tn large modern locks, they are generally built of steel, and are among
the most expensive structures used in hydraulic works. In the interest
of economy as well as safety, therefore, careful designing, based on a
correct determination of the stresses, is a matter of importance.

The problem of finding the stresses in such gates is intricate, and
has been the subject of much investigation in the past. In connection
with the design of the gates for the Panama Canal, the largest yet
built, the writer had occasion to make a rather detailed study of the
subject. It seems proper to put on record some of the results obtained,
especially as American literature on lock-gates is very scanty. It is
believed that the method of calculation used is novel, and is an advance
on previous practice.

The stresses are of two kinds, those due to the weight of the gate
leaf, and those due to water pressure. The former do not affect the
design of the gate seriously, except in the parts which serve to support
it on the foundation, and to connect it to the anchorage in the walls.
They are greatest when the lock chambers are emptied to permit of
inspection and repairs. Their computation is quite simple when the
weight of the metal work is known.

The stresses due to hydrostatic pressure, on the other hand, govern
the dimensions of the principal members, as well as most of the sec-
ondary parts. The external loads in this case, too, are entirely definite,
as well as their points of application, but the stresses they produce are
somewhat indeterminate. This is due, in large part, to the complex
structure of the leaf, which has numerous horizontal and vertical mem-
bers riveted together at their intersections and covered by a continuous
sheathing. The primary fiinction of the different members, in trans-
ferring the hydrostatic load to the masonry, is well defined, but the
rigid connections cause the deflection and, hence, the stress in any



DISTRIBUTION OF STRESSES IN LOCK-GATES 1623

one member to depend, not only on its direct load, but also on other
parts of the gate.

The distribution of the stress, therefore, is complicated, even in
single-leaf gates which span the lock at right angles and support the
water pressure by beam action.

In miter-gates, which act as arches, there are further difficulties.
The first ai'ises from variations in the surface of contact on the miter
and quoin-posts, where the gates bear against each other and against
the hollow quoin. Especially if timber bearing pieces are used, the
exact point at which the reaction acts, is uncertain, so that it is neces-
sary, in the computations, to assume it to have a considerable deviation
from the center of the bearing, in order to obtain the maximum
stresses.

A further difficulty arises from luicertainty as to the pressure
exerted by the gate against its sill. In single-leaf gates this will not
change appreciably after the first adjustment is made. In miter-gates,
however, there are wide variations in the sill reaction at diiferent times,
with corresponding changes in the stresses. This is due to changes in
the length of the leaves arising from variations in temperature, wear
in the contact pieces on the gate posts and sills, and from various
minor causes. Even with careful workmanship and fitting, it is
hardly possible to ascertain the sill pressure exactly, although, as will
be shown later, it is feasible to arrive at limiting values, not likely to
be exceeded in practice.

In this paper, a method of calculation is developed, by which the
sill reaction and the loads on the diiferent horizontal and vertical
girders may be found in a given gate for an assumed hydrostatic load-
ing and various conditions of sill contact. After these loads have been
fixed, the stresses in the diiferent members can be computed without
special trouble. The gates are assumed to be of steel and ''horizontally
framed" with numerous horizontal girders. In the gate with "vertical
framing", which has only two main horizontals, the stresses are more
determinate, and the theory is much simpler.

The problem is first stated in general terms, and a solution is found
applicable to gates of varying dimensions, girder spacing, and cross-
sections. It is then applied to the largest and the smallest of the



1624 DISTRIBUTION OF STRESSES IN LOCK-GATES

Panama gates. Finally, some practical conclusions derived from the
computations are given, as a guide in future designs.

Statement of Problem. — A mitering lock-gate consists of two leaves,
which together support the water pressure due to the difference of head
on the opposite sides of the gate.

If there is no contact at the bottom sill when the gate is closed and
under pressure, the entire hydrostatic load is transferred by arch action
to the side-walls. On the other hand, if the leaves bear against the sill,
the latter will carry a part of the load, the remainder being, as before,
supported by the lock walls.

The proportion of the total load which will go to the sill, in any
given case, depends on the structural arrangement of the gate frame
and the relative adjustment of the gate and sill.

The object of the investigation given herewith was to determine,
for the Panama lock-gates, the pressure of the gates against the sills
for different adjustments, the distribution of the loading between the
several horizontal girders, and the stresses in the vertical framing.

Previous Investigations. — The determination of the laws which
govern the distribution of loading in the horizontal and vertical mem-
bers of mitering-gates has been made the subject of extended studies
by several distinguished engineers in the past.

M. Chevallier* made what was perhaps the first study of this sub-
ject. It included a series of tests with wooden models. The conclu-
sions he drew from his experiments, as to the interaction of horizontal
and vertical members in gate leaves, are in entire accordance with sub-
sequent investigations, and of much interest even now. He gave no
general formulas or rules applicable to the large gates of modern times.

In 1867, M. Lavoinnef published a mathematical investigation
covering the same subject. His method is very complicated, although
applicable only to gates having equal horizontals spaced at equal ver-
tical distances. Owing to these assumptions, and for other reasons,
Lavoinne's formulas are not applicable to large modern gates, in which
the cross-section and spacing vary from the top to the bottom of
the leaf.



* Annales des Fonts et Chaussies for 1850.
t Annales des Fonts et Chaussies.



DISTRIBUTION OF STRESSES IN LOCK-GATES 1625

111 1887, M. Galliot* presented a new mathematical study, making
practically the same assumptions as Lavoinne, but attaining somewhat
simpler results.

In his treatise on "Mitering Lock Gates", published in 1892, First
Lieut, (now Brig.-Gen.) H. F. Hodges, U. S. A., gave a discussion on
vertical i'raming on a somewhat different basis, and deduced valuable



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