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STRESS DISTRIBUTION
as show by

POLARI 2le LIGHT

A Report Submitted to the Faculty
of the
MICHIGAN STeTE COLLrJGE

of Agriculture and Applied Science

BY

x

0,
Arthur w? Lynch

i
g .
.‘\ d\’
‘b

Candidate for the Degree

01’ 1/

Bachelor of Sci. ence

June 1929

TABIE OF C ONTJSNT S

EmRT I
Introduction. .
PIRT II
Theory of Light .
PART III
Polarization I
PART IV
Study of Stress a
PART V

Stress analysis by the use of Polarized
Light

PART VI

Conclusion

1-033.371

Page

16

Acknowledgement is hereby made for the
help of Prof. c.u. Cade of the Civil dugineering
Dept. in the preparation and study of this thesis.

-1—
Part1...

Introduction.

The distribution of stress and the de-
termination of stresses set up in structures by
the application of external and internal forces are
questions of primary importance to the engineer.
We find an immense variety of problems arising from
what seems a comparatively simple structure. Picture
the stresses set up in the cylinder wall of an in-
ternal combustion engine. It is subjected to the
pressure produced by explosion, variable heat strains,
and internal stresses of unknown application. Our
knouledge is deficient in the condition of loading of
any number of problems. But to those‘who are familiar
with the method of solution of fixed arches, and other
non-statical problems, it is unnecessary to multiply
instances where ample scape for investigation exists.

The experimental research of the physicist and
the investigation of the mathematician are the au-
thority upon which most of our structural design now
hinges. Mechanical measurements can be made, based
on the partially true theory that stress is pro-
portional to strain, but this must, of its nature,
take in length, breadth, and thickness. If the stress
varies from point to point, as it does in a large
marjority of cases, mechanical measurements can give

no positive conception of conditions.

-2-

The mathematician comes nearer to a true
analysis, but this is only true in simple structures.
Consider the action of the supporting beam of‘an
airplane wing. Reduction of weight necessitates a
minimum cross-section at every point. There is a
uniform thrust upuard over the wing. (Fig.1) The beam
is usually supported at the body end and by a brace
attached a little past mid-way. It will be seen that
as the stress increases the deflection increases,
which again increases the stress, and by our present
methods a series of approximations is our nearest
approach to solution. fiven in simple structures we
find assumptions being made which warrant the advance-
ment of a more accurate method.

In the study of measuring'stress from point to
point in a structure it is found that particles of a
transparent medium have a rotational effect on
polarized light proportional to their state of stress.
Polarized light had been studied since 1669 but was
not used in the determination ofsitress until Brewster
and Pnaf. &.G. Coker recently experimented on its
effectiveness. .

The problem of stress analysis by the use of
polarized light is gradually turning from experimental
physics to an engineering method. The effect will be
that the model of the structure, whether it is an arch

bridge or the frame-work of a giant airplane, will be

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-3-

subJected as nearly as possible to the natural con-
ditions which produce the maximum stresses and the
resulting distribution of strain read directly under
polarized light.

It is to be noted that studies have been made
successfully of practical problems by the photo-
elastic method by Prof. Coker of fingland, M. Mesnagsr
of France, the General ilectric Co., the Bureau of
Aeronautics of the Navy Dept., and several others.

Prof. Coker, as a result of extended research
and persistent study has perfected an arrangement of
polarizer and analyser such that a quantitative study
can be made of objects of such complex stress relations
as a cement briquette. H. Hesnager constructed a glass
model of a reinforced concrete bridge, since con-
structed over the Rhone at Balms, from which he de-
termined the distribution ofsatress in the structure
and the points of maximum danger.

A more complicated arrangement was made at
h.I.T. when the Bureau ofSAeronautics constructed to
scale a miniature model of the Shenandoah entirely in
celluloid. This model was subjected to conditions
representative of those Which the giant balloon would
undergo during storms or other indefinite conditions
of the air. Although a quantitative measurement in
celluloid is as yet a difficult matter, the navy Dept.
hopes that these experiments will be of highly

commensurable value in the design of airships, and will

- 4 -

aid in preventing the repetition of disasters similar
to those occuring in recent years.

Prof. Heynans, in charge of the experiment, states:
"By this photo-elastic method we can look into the
vast and intricate net work of the dirigible and see
exactly that is going on when she is laboring. We can
see how she is carrying and distributing the load. as
have made an analysis of the Shenandoah, shoeing ex-
actly how the stresses are taken up by the members of
the frame and wires. When we hear of new forces which
the ship must meet in its ventures overhead we can try
them out on the model here at TechnoIOgy."

It is important today to bring to the general
notice of the engineer the possibilities of this system,
and thus to insure its quiet development and advance to
practicability. Our effort in this thesis will be
twofold: to substantiate by experiment a few ideas on
the practical use of colorimetric effects: and to pro-
duce a cross-pollination of ideas on the subject,
presented in such a manner as to be easily understandable
to the average engineer to whom it is of importance.

No attempt will be made to derive a mathematical back-
ground, and little emphasis will be placed on the

theoretical history of the subject.

.- 5 -
Part 110
Theory of Light.

The average individual knows little of the“
nature of light. whether he sees things or how he
sees them interests him only in its ultimate com-
pletion. that he does see them. However, because of
its relation to our subject, we will delve a little
more into the theory of this great blessing. The
Greeks elaborated several theories of vision.
Democritus held that vision was caused by the pro-
jection of particles from the object into the pupil
of the eye, while muclid advanced the strange doctrine
of ocular beams, according to which the eye itself sends
out something which causes vision as soon as it meets
semething else emanated by the object.

During the time of Galileo most study’was placed
on the action of light until Huygens in 1678 advanced
the wave theory. This theory gained ground until Newton

threw his weight in favor of the corpuscular theory.
He based his reasoning upon his experiments in spectra
and straight line transmission of light, and so great
was the respect of the scientific world fer his opinions
that for nearly a century this theory that we now
consider false held complete may. Thomas Young in

1804 revived the undulatory'theory, after a century of
neglect, in which he was given support by his contempo
orary, the brilliant Fresnel. Through a storm of

- 5 -

contemptuous criticism from every scientific
publication of the day these men finally succeeded
in gaining recOgnition. The study of polarization
added proof to their deductions, and from then until
the present day the wave theory has given the most
satisfactory explanation of the various phenominal
of light.

For our purpose, then,"we may suppose that light
is a vibratory motion set up in an elastic medium,
called the luminiferous other, which fills all space,
and that the rays of ordinary light are caused by
displacements which are transverse to the directioh
of the beam, and have any azimuth." (Note) Consider an
infinite, all pervading mass of a highly sensitive,
jelly like substance. Consider then a particle vi-
brating in this mass. It would cause condensaticns
and rarefactions in the medium which would proceed in

all directions as a wave transverse to the direction
of projection, and which would eventually die out.

Consider now an object made up of an immense
amount of these particles all vibrating and jostling
about at once. It will be seen that they would send
out waves of every imaginable length all vibrating in
different planes but all transverse to the general beam
in every direction. Thus we have built up a ray of
light acting in all azimuths and consisting of waves of
different length travelling at the same velocity. It

is evident that the more violent the agitation, and

(Note) Coker angr 1911

-7-

the greater the number of particles the farther the
disturbance will travel.
as will next consider an.explanation of some of
the various light phenomenad.as sufficient substantia-
tion of’the theory for our article. It is commonly
understood that light travels in a straight line. That
is that while passing through a homegenous medium of
constant density it does not very or curve from the
direction of ray. Therefore, if we allow light from a
source at an infinite distance, which would show the
rays of light to be parallel, to enter a darkened.room
through a small opening it will cast a spot of light
of size equal to the hole on the Opposite wall.
Likewise the shadow of a sphere on a board perpendicular
to the ray should be the same size as the sphere. It
is noted, however, that the shadow of the sphere is
smaller than the object and.that the spot of light is
slightly larger than the hole. This condition is called
dispersion and it is explained that a ray of light
bends lightly around a corner when passing an edge. The
enumbra, or partially shaded part of the shadow, is
caused by these rays which have been bent in slightly.
Conditions under which visual light differed from
normal.wsre noticed by the early Greeks. They first
considered the problem of why the sun appeared to be
larger at the horizon. It was noticed that color was
produced similar to a rainbow when sun light was sub-
jected to certain conditions. Before these conditions

can be further considered it is necessary to define

-3-

and illustrate two terms.

When a ray of white light strikes a glass
grating there is reflected to the eye a complete
rainbow of colors varying from red to violet. This
is called the spectrum and the phenomena of its form-
ation under these conditions is called diffusion.
than light passes from one medium into another of
different density the rays of light are bent in pro-
portion to the difference in density of the media or
the difference in rigidity, or both. This is known as
refraction, and the angle thru which they are bent as
the angle of refraction.

Newton stated that "light is not similar or
homOgeneal, but consists of difform rays some of which
are more refrangible than others." Thus, in the case
of refraction we may have the formation of a spectrum.
This phenomena, then, explains the apparent change in
shape of an object projecting from air into water, the
large appearance of the sun at the horizon, and also
the spectrum formed by light transmitted through a glass
prism. We will not consider the theory of this action,
but will turn to subjects whose bearing on the subject

is more immediate.

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- g -
Part Ills
Polarization.

There is no need to go further into the history
of the discovery and develOpment of polarization. a
peculiar prOperty, known as double refraction, was
found to he possessed by certain bodies of’aelotropic
structure, due to their molecular arrangement. If we
take a Rhombohedral crystal of Iceland Spar, or Calcite,
Fig. 3 we will find the refracted light broken into an
ordinary and extraordinary ray. This natural crystal,
which has the power of double refraction, is bounded
by six parallelograms having angles of 101°55' and
78°6'. If light passes through this crystal parallel
to the axis of symmetry the ordinary’and extraordinary
rays coincide. This is called the cptical axis.

In passing a ray of light through a crystal of
tourmaline the ordinary ray'was found to be absorbed
and the extraordinary ray, only, transmitted. This
ray has the peculiar property of only vibrating in one
plane. In other words it is Polarized.

let us consider this phenomena, there is really
no difficulty to its conception. We have said that a
ray of ordinary light consisted of displacements
transverse to the direction of the ray'and.having any
azimuth. It is reasonablé to suppose that a wave could
be selected from this having only one azimuth if the

others could be cut out.. The situation is snaIOgous to

- 10 -

a rope (Fig. 2) which is being shaken in such a
manner as to cause a nondescript series of waves to
progress donn its length. If a block(a)is placed
over the rope with a vertical slot in it only those
waves whose transverse motion were vertical would be
allowed to pass through. we then have displacements
in one known azimuth. If we place a second block (b)
with the slot in a direction perpendicular to that in
block(a)no vertical wave motion can pass through. we
have now set up an apparatus for the production, de-
tection, and the determination of direction of a.
polarized wave motion. If an Optical setup block(a)
would be called the polarizer and block (b) the analyser.

Certain substances have the property of rotating
this plane of polarization. The anmunt of this
rotation can be detected by the position of the analyser
winch allows no light to pass through, as compared to
its position in a similar circumstance when the
polarized light was not passed through the substance.
This fact has been used largely in ¢hemical analysis,
and recently in the determination ofsatress.

A convenient arrangement of apparatus for obtaining
plane polarized light is the modified form of a crystal
of Iceland Spar devised by Nicol in which the rhomb is
out along plane A B (Fig. 4) ehd the cut surfaces, after
being polished, are cemented together aith Canada

Balsam, which has a refraction index between that of the

 

 

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- 11 -

ordinary and extraordinary ray. Thereby 0 is got rid
of by internal reflection at the out surfaces, aid
only the extraordinary ray is transmitted.

It is also noted that transparent substances
polarize nearly all the light reflected from their
surfaces uhen light is caused to enter them at a certain
angle (known in Optics as the polarizing angle of the
medium in question.) Thus if we cover the back of two
glass plates with a light absorbing substance, such
as a mixture of lamp-black and turpentine, and cause
light to strike the first at an angle of about 45°
(the polarizing angle of glass) most of‘the light will
be absorbed by the lamp-black on the back of the glass
but a portion of it will be reflected and polarized at
the surface. If as non cause this polarized light to
strike the second plate at the same angle as have set
up a polarizer and analyser between which quite large
specimens can be examined. If the light is monochro-
matic light and dark lines till be obtained. If shite
light is used a succession of spectra uill appear,
varying uith the strain produced in the specimen.

Of these methods, for our experiments, as have
chosen an arrangement of glass reflectors shown and
illustrated in Fig. 5 and 6. We considered these as
offering the most convenience, with the least difficulty
of construction. An explanation of the set up sill be
found with the illustrating figures. shite light

I88 used, propagated by'twelve incandescent lamps, and

knee passed through a shite asbestos paper before striking

the polarizer.

It is not necessary to go deeply into the subject
of polarization, nor to mathematically prove our
statements. It is sufficient at present to describe
certain effects uhich can be used to advantage in the
solution of problems. For many experiments circularly
polarized light is used. This is usually obtained by
passing plane polarized light through quarter-nave
plates. Their effect is to produce to beams of equal
amplitude, vibrating at right angles, and differing
in phase. This retards the nave motion in such a say
as to cause the plane of polarization to move forward
with a motion similar to a screw, each nave turning
through a definite angle. If a Babinet's compensator
is used either elliptically or circularly polarized
light may be produced, depending on the part of the
compensator passed through.

Our interest now turns to a study of stress, and
we will leave polarized light until we take up its
application to stress analysis, and its peculiar action

when passed through a strained, transparent specimen.

- 15 -
Part IV
A Study of Stress.

The force exerted upon one body by another at
a surface of contact is called the stress between
the bodies. If then, we consider a single body as
out by an imaginary plane there‘uould be forces set
up at this plane knonn as the internal stresses of
the body. If the forces are such that the particles
of the body are pushed together at the imaginary
surface this is knonn as a compressive stress. If
the forces tend to pull the portions apart it is called
tensile stress. Compressive stress at the surface of
two bodies in contact is called bearing stress.
Intensity of stress is spoken of in terms of the area
concerned and the total stress. Thus we have lbs./eg.
in.ordynes /sg.cm, or like units.

Since every body has a certain amount of elasticity
it follows that wherever stress exist deformation must
take place. The body is elongated or compressed de-
pending on whether the stress in tensile or compressive.
A deformation which remains after the stress is removed
is called a set. It is of interest to note that only
up to the last point nhere no set is obtained is the
stress cansidered preportional to the strain. This
point is called the elastic limit of the material and,
after this condition of stress is reached, if more is

applied, the strain increases out of pooportion to the

.1;-

stress and some set remains. By mechanical or
mathematical methods it has been impossible to de-
termine this point accurately due to the influence of
time and the gradualness with winch the first set
comes on.

in the study of a simple beam it till be seen
that tension is affected along the bottom and com-
pression along the top. This is easily seen by the
may in nhich the particles tend to pull apart or push
together. Between these stresses there exists a neutral
plans. If a beam is twisted a stress called tortdon is
produced. all stresses in any structure whatsoever
can be reduced to these types. The stress in any member
consists of tension, compression, or tortion, or-a
combination of these. The identity of the type of
stress is easily determined if the conditions of load-
ing and the distribution from known points are under-
stood. In photo-elastic work a strain in the material
registers the same color regardless of type, showing
only the amount and lecation of the strain. It is
necessary therefore to identify the types at some
easily determined point of the structure and by means
of the neutral planes and points of nosatress follow
them through.

A number of assumptions are made in the
mathematical determination of stress. Up to a certain
point of excessive loading it is assumed that stress
is proportional to strain, and up to this point it is

held that any plans section perpendicular to the axis

-15-

of moments before loading remains a plane section
when stressed. The general.theory of stress is
limited by the elastic limit and.the ordinary theory
is further limited to symmetric bending. There is a
ratio of definite relation between shear'and.monent,
but the distortion caused by tension or compression
is not in accordance, as far as our medium is
concerned, with the distortion caused by the same ratio
of lbs./sq. in. in shear.

The elements entering into the relations set up
in the Bending Mom. equation of stress are the load
and the beam, with the span considered as common to
the load and the been. In shear the section of the
beam and the applied external forces are the controlling

elements.

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562‘ was produced x'n ffie beam.

- 15 -
Part V.
Stress Analysis by the Use of
. Polarized Idght

The colorimetric or photo-elastic method of
testing materials determines the stress produced
upon a particle at any point. It shows, then, the

total or resultant strain upon that particle. For
‘ example, in mechanics, we consider any section of
a loaded simple beam as affected by two principle
stresses: one normal to the section and the other
acting along the section. In a vertical section we
have the stress normal produced by the moment of the
loading and the stress vertical produced by the shear
of the support. In the Optical determination of this
stress the coloration representing its intensity
would be seen in a line passing through the ppint
at an angle in proportion to the ratio of shear to
moment at the point.

An analogy may be made here between these lines
of coloration and the contour lines of surface
mapping. It is found that these lines are continuous
and must either form a closed figure or run off the
edge of the specimen. The reasoning of this fact
needs no demonstration as it is in direct accordance
with that of contour lines and is very simple.

It is also to be noted that the shape of the line

of intensity through any point never changes although

- 17 -

its color does as the load is applied or removed.

This is fundamental. no reason that for a definite
condition or state of loading the distribution of
stress over a beam is preportional to the relative
length, heighth, and breadth. Therefore, as the

load is increased the distribution remaing the same
but the intensity increases in preportion to the

load. as see, then, colors progressing one into
anothers position as the load is changed. If the
variation of strain is increased several bands may
show uhere one was, but they will conform to the shape
of that one, and if a minute study mere made of shades
the original band would have been subdivided along
similar lines. Figure 7 shows a typical coloration of
a simple beam seen under polarized light. Several
spectra appear'within the limits of stress and the
furthest spectrum from the neutral plane indicates

the greatest stress. As the load is increased a
spectra of greater intensity moves touard the position
of one of less intensity. This movement is carried
out over the entire beam, but the general direction

of the lines of stress intensity does not change.

The fact that polarized white light produces
several spectra in accordance with the increase in
intensity of strain in the specimen under observation
suggests a simple and easily denoted denomination of
the amount of strain in a particle. The number of

the spectra could be used for the rougher measurement

and the color for the fractional reading of the first.

-18..

For the purpose of our study in this treatise it

will be sufficient to compute the stresses represented
by the different spectra seen in a stressed beam of
transparent batelite.

.Ne have said that a line of definite coloration
represents a certain intensity of strain, that a
spectrum of coloration represents a certain range of
intensity, and that these lines of color are in
accordance with the resultant lines of stress. It
is now in order that us should give some explanation
of the presence of several spectra over a range of
stress of one type (such as tension or compression.)

Light has a slower velocity in a denser medium.
Therefore, an analogy can be made between the impeded
progress of light through a stressed specimen and a
homogeneous wedge, it being commonly understood that
stress varies the density of a substance.

Consider the wedge ABC (Fig. 8) If a ray of light
from the source D strikes the face AC part of it is
reflected to the eye at a. The rest passes through
the wedge and another part is reflected to the eye
from the face AB. The second portion of the beam has
travelled further before reaching the eye by an amount
equal to twice the thickness of the wedge. Suppose
now that this retaining amounts to one half the have
length of blue light. Then a crest and trough of blue

light strikes the eye simultaneously, interfering with

each other, and the eye sees white light minus the
blue. As the ray strike farther down the wedge the
longer rays reach interference points until white
light minus the red is seen. At some point past this
twice the wave length of blue is reached and.blue
again cancels itself. Thus as the ray is considered
to progress down the wedge a succession of spectra

is produced which might be used for an accurate
measurement of the width at any point.

Applying this anaIOgy to the phenomena of color
bands obtained when a stressed specimen is observed
under polarized light, we find a sudcession of spectra
relative to the distribution and varying intensity of
stress which afford an easy denomination of measure-
ment. The change in color from red £0 red represents
the interference of a definite color in each case and
amounts to the impeding of light that wave length. For
finer measurements it would be necessary to consider
the varying colors in each spectra, but for our
purpose it is sufficient to calibrate and measure by
the number of spectra.

as may then consider a loaded simple beam at the
center to be ana10gous in its interference phenomena
to a wedge. The bottom would be in tension, would
therefore have the least density, would impede the
the progress of light the least, and would be comparable
to the sharp end of the uedge. The top, or compression
side, by the same reasoning would be represented by '

the wide part of the wedge.

 

 

 

Showing aka/73.9 in ou/oloarf Giro/n: . ?
w/f-h load/r23

L No JfI'CJS

rig/”(y gripped beam

 

 

 

 

          
     

 

      
 

  
 

  
   

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/

A '/

r
/

Loose/y grog/090’ beam

Fly IO

Figure 9 and 10 show two small transparent

specimens of babslite with dimensions as shown.

These were tested as cantilever beams, a weight of

one and one-half lbs. being applied at a distance

of 4 1/2 inches from the support. Bar A was held
tightly in the support, while 5hr B nas given enough
compression only to keep it in place while the load
was applied. Due to the coloration of the specimens
and the working conditions of the experiment the

line or location of each spectra is shoun by the three
colors of Red, Green, and Yellow. The location of

the neutral ixis is noted and the position of the

red line of the first, second and third spectra at
various points along the beam. The stress is then
computed mathematically for these points. This sets
up an elementary method of reading the stress directly.
each of these lines represents a definite strain in
the material at all the points it passes through.

In general, we notice that the beam gripped
loosely in the supports follous closely the distribution
of stress assumed in the study of cantilever beams.
The neutral axis is approximately in the'center, the
point of maximum compression is at the lower, outside
corner of the support, compression is quite I611
distributed over the top of the support, and the width
of the spectrum bands in compression and tension are

approximately equal. In the tightly gripped bar,

houevsr, no notice that the tension spectrum bands
are narrower than the compression bands, the neutral
axis is nearer the top, and the change of compression
in the support is distributed to the loser outside
and upper inside corners. This condition was not
universally true, although it uas found to exist in
several cases. It was probably due to an arrangement
'of material such that the shear components overthreu
the general formation of stress lines.

The downward hook in the neutral plane at the
support is common to all the cantilever beams tried
in our experiment. This is due to the combining of
tension.at the top of the beam with compression in
the support. Because a mathematical solution assumes
the lacation of the neutral plane, only bar B will be
examined quanitatively. The computation and locations

of points are below.

 

1‘73 /0

 

 

 

 

 

 

 

Can f1 lgver Beam
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A 3rd 0 0.23 6.7:; 370 /3
5 Id 3— 0.03 5:63 /07 ma
0 and 32'— ” 0.33 3.0 My 513
gm :3 L5 (3 .HflVUfh 7a
a I I «a a’ la aq
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6“ u I’ ?L R -;3
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C and 2 ‘2" 9L 5' ll/ 0
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‘It is evident that the difference in moduli
of elasticity accounts for the lack of coordination
between tension and compression, and shear strain.
If sufficient time were available to measure the
strain by mono-chromatic light in wave lengths
it would be possible, by having specimens in pure
tension and pure shear, to determine the relation
of both and account for the position of every black
line in a simple beam accurately. With our equip-
ment at present, however, quantitative work must

be largely a matter of guessing.

-22..

Fig. 11 shows this Optical effects of a

concentrated load of four lbs. at the center of
a five inch beam of trenSparent bacolite three-
quarter inches deep by 0.24 inches wide. There

is nothing about these lines of stress contrary to
our excepted distribution in like circumstance. we
will, however, on a following page compute the
stress represented by the red lines of the first and
second spectra in tension and compression. This
will act as a check on the results of the study of
the cantilever.

It must here be noted that shear plays a very
appreciable part in the location of stress lines and
cannot be disregarded. It is also noticed that the
strain caused by shear is not proportional to that

caused by moment.

 

 

 

 

 

 

 

Strains around Q ho/e

Fl'j la

- “a -
Fig. 12 shows a simple arrangement for pro-

ducing cantilever moment by compression of the

fingers. Due to the length of the plane AB a section

was seen there which showed no stress. A small hole

was drilled through this section and the beam again

strese=d. Fig. 13 shows the strange coloration

resulting. It is impossible for us to go into a

discussion of the resolution of forces which caused

this action. Two many variables are concerned for a

decision from one experiment. However, these figures

do show the unlimited possibilities of photo-elastic

work. Consider the new facts which might be discovered

a colorimetric test cf the Plate Girder. It may be

urged as an objection that the reactions of these

materials are not similar to those of steel and wood,

but tests on such media as India Rubber and Jelly

have yielded results which contradict this statement.
it.is also known that after the last point of

perfect resilience stress is no longer prcportional

to strain, and after the load is removed some strain,

or set, remaind, Our material, not being highly

elastic, is easily overstressed without breaking. After

the load is removed there can be no stress, yet some

coloration remains. We can conclude from this that

the coloration is due to the strain only. The detection

of set in a structure might be of importance in many

problems.

e. 24 .-
Part “e

Conclusion.

In conclusion as wish to state that, due to
limited time and crudeness of material, this study
was not made uith a physicists accuracy. It is
the purpose of this paper, not to establish laws
or units, but to convey some impression of the real

importance and possibilities of the subject. Great
companies such as the General filectric are interested
in its study and their resources lend to their de-
ductions the distinction_of accuracy. we have
accomplished our purpose if we succeed in producing
a convincing argument fer‘the general study of this

phenomena as an engineering Hethcd.

B IBLIOGRAPHY

Coker - Photo-Elasticity Engr. Jan. 6, 1911.
Coker - Optical Determination of Stress
Phil. Mag. Oct.l910

Mesnager - Determinat ion of Stress Distribution
in a Rein. Concrete bridge over the
Rhone at Balms

L. A. Morrison - Thesis - 1924

Watson - Textbook on Physics

Duff - Textbook on Physics

Houstcun - Treatise on Light

CaJorie - History of Physics

Preston - Theory of Light

 

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