854

THE COLLIERY GUARDIAN.

April 17, 1914.

FACTOR OF SAFETY.*

By C. E. Stromeyer.

The expression “factor of safety” was adopted by the
engineers of the early days of the last century, when
structures in iron were novelties, in order to inspire
confidence in those who were going to use them. It
may also have been hoped that a competition amongst
engineers for high factors of safety would conduce to
safety ; at any rate, Sir William Fairbairn at one time
seems to have advocated a factor of safety of seven.
The public, however, refused to be made judges in
technical matters, and preferred to rely on the expert
knowledge of engineers, amongst whom the expression
“ factor of safety ” then merely meant “ measure of
our ignorance.” In those early days our ignorance was
truly great, for materials could not be tested, and the
mathematical treatment of many engineering subjects
was still in its infancy, but now, although much progress
has been made in both directions, we engineers in
England still cling to the expression “ factor of safety,”
though on the Continent the somewhat more expressive
term “ permissible working pressure ” is now commonly
used. The one term glosses over the fact that we do
not, for instance, know definitely what is the ratio
between safe working stress and ultimate tenacity, and
the other term merely states that engineers refuse to be
guided by laboratory tests and have by experience fixed
on certain stresses as being safe. Both expressions
hide the fact that the mathematical formulae used by
engineers are of the crudest, and do not correctly
determine the actual stresses produced by external
forces. They also hide the fact that these external forces
are sometimes very imperfectly known, and they hide
the fact that even when using the most carefully tested
materials, and handling them with the greatest care in
the workshops, there is always a chance of a flaw or a
brittle locality, which may cause failure.

It is impossible to deal with all these points and make
out a list, as it were, of the subjects about which we are
ignorant, but a brief survey will not be out of place
before dealing with the important question of possible
defects in steel and iron.

Consider the case of a rivet, which is subjected to a
steadily increasing shearing stress. The intensity of
this stress will be distributed over its section in the
form of a paraboloid of rotation, and the maximum
stress at the centre of the section is then seen to be
double the mean stress. Supposing the limit of elas-
ticity for shear to be 8 tons per square inch, then this
limit will be reached when the mean stress exceeds

4	tons per square inch. This maximum stress of 8 tons
should not be exceeded under safe working conditions,
but engineers only refer to the average stress, and
compare this with the ultimate shearing stress in the
rivet of, say, 20 tons, which, before rupture, is, of
course, uniformly distributed over the section, and they
fondly imagine that, as the ratio between the average
elastic stress of 4 tons, and the ultimate plastic stress of
20 tons is as 1 to 5, they are working with a factor of
safety of 5, whereas, in reality, this factor is made up of
50 per cent, of mathematical convenience, and 50 per
cent, of ignorance as to the true value of the elastic
limit, which, judging by recent fatigue experiments, is
much lower than was at one time imagined.

When straining a beam up to its elastic limit of, say,
10 tons per square inch, the maximum elastic stress is
expressed by the formula S = 6 M 1 :b h2, whereas when
this limit is passed and ultimate stress of, say, 30 tons
approached, this stress is expressed by the formula

5	= 4 M 2 : b 7i2, and the ratio of the ultimate to elastic
moment is M 2 : M1 = 30 X 6 :10 X 4 = 4’5, which, by
most engineers, is looked upon as being the factor of
safety, whereas the real factor is 30 : 10 = 3. Thus, in
the one case the ratio between ultimate strength and
limit of elasticity is doubled in order to arrive at factor
of safety ; in the other case it is only increased 50 per
cent. These two examples (and many more could be
adduced) justify the Continental practice of using the
term “ permissible stresses ” when associated with
particular engineering formulae.

Similar remarks apply to what might be called external
forces, about which the mathematics as used by engineers
are often far from comprehensive. Most engineering
text-books demonstrate that a load which is applied
suddenly results in a stress which is twice as great as
that which a gradually increasing load will produce, and
engineers seem to rely on this one demonstration for
their practice of assuming that stresses due to live loads
are twice as great as those due to steady loads. This is
merely a mathematical convenience for average con-
ditions, for it ignores the fact that the expression is
only true if the load is a weight. The suddenness of the
steam admission into a cylinder, and the suddenness of a
gas explosion, do not double the stresses in the cylinders,
pistons and rods beyond what they would be under a
steady pressure of the same intensity; and, on the other
hand, the sudden application of pressure which occurs
when two elastic bodies collide leads to much severer
stresses than double the static one. If each case were
dealt with on its merits the estimated stresses would
often be much intenser than the customary rules make
them out to be, and the factor of safety would be found
to be much lower than was believed. Then, however,
the very legitimate conclusion could be drawn that if
certain structures are safe with these comparatively low
factors, other structures for which improved mathe-
matics show large factors might be reduced in
dimensions.

The term factor of safety also covers our ignorance
of the real properties of materials and their behaviours
when stressed. Much has been done in the past by the
introduction of quality tests and the use of testing
machines, but much yet remains to be done before even

* Read before the Staffordshire Iron and Steel Institute’
March 28, 1914.

engineers can take the initial step of defining how many
chances there are for and against occasional failures.
As there seems to be some misapprehension on this
probability question, it will be well to refer to it briefly.

Let it be assumed that a piece of steel were placed
before us of which the average test results show that it
breaks down at 15 tons. Assume also that there is a
chance that the chemical composition is not quite what
it should be, that the casting temperature and sub-
sequent heatings may have affected the grain, and that
initial strains have not been entirely removed, &c.
Separate these various possibilities into, say, 10 influ-
ences, of which each one will affect the elastic limit
by ± 1 ton, then there are 210 = 1,024 possible com-
binations and the chance that all the five adverse
circumstances will combine together and result in a low
breakdown point of 15 — 5 = 10 tons per square inch is
one in 1,024. There is also this one chance that the
breakdown point will be 15 4~ 5 = 20 tons. Against
this there are 252 chances that its value will be equal to
the average of 15 tons and 672 chances, or 67 per cent.,
that the breakdown point will be between 14 and 16 tons
per square inch, &c. Suppose now that nine tests
have been made of this material, then the results will
very likely be as follows :—One of 13 tons, two of
14 tons, three of 15 tons, two of 16 tons, and one of
17 tons. Most engineers would accept the average
result of 15 tons and apply a factor of safety without
looking into the distribution of the test results, but
the more correct procedure would be to say: These
nine tests indicate that if we were to make 1,024 tests,
one of these would give a limit of only 10 tons per
square inch, and in order to be safe we must not depend
on a higher value. If, with another lot of steel, the test
results should be as follows ::—One of 14, two of 14J,
three of 15, two of 15 J, and one of 16, then the conclusion
to be drawn would be that there is a chance of one failure
occurring at 12| tons. On the other hand, if the test
results were to be more scattered, say, one test of 11
tons, two of 13, three of 15, two of 17, and one of 19,
the conclusion should be drawn that one failure per
thousand tests is likely to occur at 5 tons per square
inch, and this should be the permissible maximum stress.
It will thus be seen that the habit of engineers to accept
average results might with advantage be replaced by the
one adopted by astronomers, chemists and others who,
when stating average results, also add a ± quantity
which indicates the probable average error. To be of
value in this respect laboratory test results should
indicate not the probable mean error, but the maximum
one, which is, of course, outside the limits of the
extremest tests. Then, however, much of our uncer-
tainty would be removed, and the factor of safety might
be correspondingly reduced. Unfortunately, engineers
can do little with regard to defining the nature and
extent of possible errors except it be by carefully
recording all cases of unexpected failures or wonderful
endurances, and it must be left to the metallurgist to
unravel the details.

Confining our attention to steel, the first problem
should be the determination of a correlation between the
chemical constituents and the physical properties of
this metal. In each new edition of my work on marine
boilers, I endeavour to fill up certain blanks in a skeleton
table in which chemical impurities are compared with
the following properties of steel:—Tenacity, elongation,
resistance to impact, pliability when hot, cold, and after
being hardened or tempered, weldability and corrodi-
bility, to which list the following might, with advantage,
be added—fatigue-resisting powers, ageing properties,
and reliability or treacherousness.

As regards tenacity the following formula will give
the tenacity of mild steel to within about ± 2 tons per
square inch 19’75 + 25 (CC2) + 11’5 Si + 30 P + 205 N
+ 36’5 AS + 9’5 S.

Here the several letters stand for the percentage of
the respective chemical elements.

It will be seen that nitrogen has a much greater effect
than carbon in increasing the ultimate tenacity, and
unfortunately, too, it is even much more powerful in
making mild steel brittle and treacherous. This
treacherousness is as yet difficult to define, but, judging
from a large number of failures in practice, so-called
unaccountable failures may be expected to occur when
the percentage of phosphorus, which also causes brittle-
ness, plus five times the percentage of nitrogen, exceeds
0’080 per cent.

This limit is very much exceeded in all Bessemer
steels, nitrogen being more readily absorbed under the
high-pressure conditions of the Bessemer furnace than
under the low ones of the open hearth. Unfortunately a
high temperature, unless it be associated with a vacuum,
will not drive nitrogen out of steel when it has once got
into it, with the result that much of the steel which is
turned out of basic open-hearth furnaces is compara-
tively rich in nitrogen, for in these furnaces the ratio of
scrap to pig is very large, and steel scrap, especially on
the Continent, consists largely of basic Bessemer crop
ends and even whole ingots, or of molten metal.

The British basic open-hearth furnaces use compara-
tively little steel scrap, and their products are compara-
tively free from nitrogen.

Percentages of Nitrogen and Phosphorus in Various
Steel Samples.

Percentages.

Sample.	Material.	Phos- phorus.	Nitro- gen.	P + 5N.
H. ...	German acid Bessemer .	.. 0’079 ..	.. 0’0145 .	.. 0’151
LE. ...	„ basic „	.. 0’077 ..	. 0’0185 .	.. 0’169
LF. ...	>> >> >•>	.. 0 067 ..	.. 0’0170 .	.. 0’152
LA. ...	German basic open hearth.	.. 0’017 .	.. 0’0088	... 0’061
LB. ...		.. 0’032 .	.. 0’0106	... 0’085
LC. ...	yy	yy	yy	.. 0 017 ..	.0’0105	... 0*069
LD. ...	yy	yy	„	yy	.. 0’038 .,	.. 0’0123 .	... 0’100
X. ...	British basic open hearth.	...0’033 .	.. 0’0040	... 0’053
z. ...	yy	yy	yy	yy	.. 0’039 .	.. 0’0033	... 0’055
V. ...	„ acid „	„	.	.. 0'045 .	.. 0’0035	... 0’062
w. ...	yy	yy	yy	yy	.. 0’044 .	.. 0’0033	... 0’060

The probability that the nitrogen, which is forced into
the steel in the Bessemer converter, and which is not
removed by subsequent remelting in the open-hearth
furnace, is responsible for so-called inexplicable failures,
is confirmed by the fact that this class of failures is
most frequent in those countries (Germany and America)
where the acid open-hearth furnace is conspicuous by its
absence. Then also during the first two decades of mild
steel, before the basic open-hearth furnace had been
invented, failures of steel shells of boilers never occurred,
whereas since basic steel is being used for shells, occa-
sional explosions occur, the most startling one being
that of the shell of the ss. “ Pahud.”

Treacherous qualities of steel must possess ageing or
maturing properties, their natural condition being one
of brittleness which has been temporarily altered by
heating and rolling; at any rate, steels rich in nitrogen
or phosphorus may behave well in the testing machine,
and fail in the shop, or they may even survive the work-
shop treatment and fail subsequently. My researches
into this subject were as follow:—Samples were injured
by shearing; of these, some were bent at once and
others after waiting (ageing) for a few days, weeks or
months. Generally the old samples were rather more
brittle than the newly-sheared ones. Samples were
also planed on their edges, nicked and bent either at
once or after waiting. They, too, showed ageing effects,
but neither test discriminated between those steels
which had failed in practice and the more reliable
qualities. The ageing effect could be produced rapidly
by simply immersing the samples in boiling water.

Curiously enough, amongst all the steels tested by me
by bending at a blue heat, those which were rich in
phosphorus or nitrogen failed more readily than others.
This test is not a very convenient one, and could not
be relied upon to discriminate between good and
treacherous steels, but the experience suggests that
some so-called mysterious failures may be due to steels
rich in nitrogen being warmed with heaters before
bending, an operation which may have made these
plates brittle, whereas acid plates would not have
suffered.

At one time injudicious annealing may have been
the cause of unexpected failures, but as this treatment
can be detected by subsequent microscopic examination
it cannot now be called mysterious. On the other
hand, annealing, because it encourages the segregation
of the impurities in steel, may be looked upon as being
an accelerated ageing procedure, and it is more than
probable that one quality of steel may get spoilt under
certain annealing conditions which do no harm to other
qualities. The risk of ageing, in the widest sense of
the term, is particularly great with alloys, and many
engineers object to their use except for special purposes
like bronze bearings, for it is well known that certain
nickel steel alloys, brasses and bronzes may become
absolutely rotten after a time, though there is no
certainty that this will be the case; also it is well
known that the alloys in fusible plugs change their
nature and must be renewed every 12 months. As
some of the alloys possess wonderful physical properties,
it would be a great pity if they were banned because of
occasional failures which remain inexplicable, for the
not very satisfactory reason that they have not been
thoroughly investigated.

It will thus be seen that by interpreting the term
“ factor of safety ” as being a measure of our ignorance,
it has been possible to deal separately with its three
main subdivisions and to show that, although metal-
lurgists have already reduced one of these subdivisions
to vanishing point as regards open-hearth acid steel,
there is still a wide field open to them amongst steel
alloys in which to strive for an equally satisfactory state
of things.

KiiraG EXMIMTIOM.

A New Rule.

A rule has been made by the Board for Mining
Examinations and approved by the Secretary of State,
March 21,1914, under section 9 (2) of the Coal Mines
Act, 1911 (1 and 2 Geo. 5, c. 50), amending the rules
dated July 30, 1912, for the conduct of examinations.

It is provided that the rules for the conduct of
examinations made by the Board on July 30, 1912, and
approved by the Secretary of State on August 1, 1912
shall be amended as follows:—

The following paragraph shall be substituted for the
first paragraph of Bule 6 :—

(6.) Before proceeding to his seat in the examination
room a candidate must lay aside his hat, overcoat,
umbrella, and any book, papers, or appliances the use of
which is not expressly allowed to him. The candidate
shall be allowed to bring with him a drawing scale, slide
rule, protractor, a pair of compasses, parallel rule and set
squares. Apart from such special articles, a candidate
shall be at liberty to take to his place in the examination
room such ordinary appliances as pens, ink, penknife,
chalks and indiarubber ; but the examiner may at his
discretion prohibit the use of any such articles.

Partnerships Dissolved.—The following dissolutions of
partnership have been announced by the London Gazette:—
H. Vanstone and E. Roper, gas and electrical engineersand
furnishing ironmongers, Exchange-street, Norwich, under
the style of Vanstone and Roper; W. Denby and J.
Shackleton, reed heald and wire polishing machine makers
and engineers, Cliff ord-street, Bradford, under the style of
the Bradford Machine Company; A. Lister-Kaye and V. M.
Methold, motor engineers, Mortimer, Berkshire, under the
style of Methold and Lister-Kaye; A. Pressburger, L.
Landau and M. Schleif, steel and iron merchants and
contractors, Fenchurch-avenue, E.C., under the style of
J. Feige and Co., so far as regards M. Schleif.