MHIIIIIHH

5

~25 ":2

'3
1;
TH

A STUDY OF BRIDGE STRESSES
BY PHOTO-ELASTICITYA ?

Thesis for thc Degree of B. S.   I
' - R." A Briggs
' 1937

 

 

 

 

h A h .L
a . .4 - ‘6‘ ~
5 . . ._ r r a. . . r. p

. N 0 WHO“ Av‘ p ..Q. '4. u ‘

Lls’uivo

 

A Study of Bridge Stresses

By Photo-Elasticity

A Thesis Submitted to

The Faculty of
MICHIGAN STATE COLLEGE

of

AGRICULTURE AND APPLIED SCIENCE

1"“. { "a
' D

S I 4
. r A r
\ V -- .5}

WA ‘U
R voBriggB

Candidate for the Degree of

Bachelor of Science

June 1937

THESE

 

CONTENTS

Page
Introduction ......................... I
Chapter I. General Theory of Photo-Elasticity ------- 1
Chapter II. Description of Apparatus ------ . ------ 7
Chapter III. Stress Investigation --------------- 24
Conclusion - - ---------------- - ....... 53

10831.8

INTRODUCTION

When it was mentioned that a subject for a thesis should be
considered Photo-Elasticity was one of the first things thought
of. This was probably brought about by the fascination eXperienced
in the study of Polarized Light in a Physics course. This led to
an investigation of the possibility of such a subject. It was
immediately apparent, however, that this tepic was impossible for‘
two reasons.
(1) The cost of Photo-Elastic apparatus was found
to be anywhere from $300.00 up.
(2) There were no experiments or investigations
published or available in this subject that
could be readily understood without pre-
liminary study.
However, in the latter part of 1936 two events resurrected the
hepes and crystallized the possibility of Photo-Elastic investigations.
(1) A new efficient method of Polarization by
means of an ineXpensive piece of apparatus.
(2) By the publication of "Treatise of Photo-
Eiasticity" by Coker & Filon, two English-
men who for some years have done extensive
study on this subject.

- Using this new Polarizing method and by studying the Coker &
Filon Treatise it was decided the apparatus could be built at a
small cost and investigation carried on in the five or six weeks
allotted during the Spring term for thesis work. By using the

apparatus built for this thesis simple problems in tension and

compression could be easily determined. It takes only a slight
addition to this apparatus to solve more intricate problems, such
as tracing the lines of principal stress. However, investigation

of this kind will be left to some other student.

II

CHAPTER I

General Theomy of Photo-Elasticity

"Photo-Elasticity is the science which deals with the effects
of stress upon light traversing transparent material." In apply-
ing this subject to engineering we determine stresses from the
optical effects caused by Polarized Light traversing these trans-
parent materials. It is apparent, therefore, that we understand
what Polarized Light is. we cannot jump headlong into a definition
without discussing the essentials of light itself. E

Light is a disturbance, believed to be electromagnetic in
character, which is prepagated in empty space, or in transparent
materials, with a finite velocity. .An elementary source of light
is one that may be treated as a point from which a disturbance
traverses outward. If the medium.is homogeneous the velocity of
the light will depend only in the direction in which it is moving.
If, however, the medium is IsotrOpic the wave-velocity will be the
same in all directions and the wave-surface becomes a sphere. Ex-
amples of this are water, glass, vacuum, etc. If, however, the
medium happens to be a crystal the wave-surface is two-sheeted,
that is, the light wave splits up into two rays both of which become
polarized. Examples of this can be seen in Iceland Spar, Mica, etc.
It is easily realized that as the light leaves the elementary source
it is vibrating in all Azimuths this is known as common or unpolarized
light. This new brings us to a definition of Polarized Light.

Polarized Light is light in which the light-vector is throughout
parallel to a fixed direction, that is, the light is all vibrating
in the same plane and this plane is called the Plane of Polarization.
The angle that it makes with a fixed plane through the wave—nonmal

is the Azimuth of Polarization.

It was mentioned before that as light traverses a crystal
there is two distinct wave-fronts. The waves corresponding to
these two wave-fronts, which travel with different velocities,
are always Plane-Polarized in definite directions depending on
the directions of the wave-normal and the nature of the crystal.
These two directions are always perpendicular and are known as
the Polarizing Axes.

It was discovered by Sir David Brewster in 1816 that as a
transparent Isotropic material is subjected to stress it behaves
like a temporary crystal. Since his day the laws of this phenomenon
have been investigated by many men who instigated the following laws.

(1) The directions of polarization corresponding
to a given wave-normal are along the direct-
ions of principal stress in the wave-front.

(2) If, P,'Q are the principal stresses in the
wave-front, np , nq the refractive indices
of the waves polarized in the directions of
P, Q reapectively no the refractive index
of the unstrained materials, and R the normal

stress across the wave-front.

Np - N0 01 Q + Cg (P s R)

Nq - N0 = 01 P + Cg (Q + R)
The coefficient C1, Cg are termed the Stress Optical coefficients.
If P a 0, so that the plate is under a simple tension Q, the wave
is then polarized in the directions of the tension.

It is also found that these laws hold for considerable amount

of stress, generally exceeding the elastic limit.

Since polarized light is the essential in this study it must
be understood that there are various methods of producing this
kind of light.
(1) Glass Spar Prism
(2) Nicol's Prism
(3) Reflection
(4) Transmission Polarizer (Pile of Plates)
(5) By use of the Polaroid (A trade name)
The last one of these is the method that will be used in the
apparatus. A brief discussion might be in order on the physical
properties of the Polarbid.
It was discovered that if a certain liquid chemical compound
was allowed to evaporate, long slender crystals were formed. These
crystals were microscOpic in size, in fact, they could not be seen
at a magnification of 1100 times. Using these facts as a bases the
following things were then done. The crystals were forms on,a mem-
brane of gelatine and were then automatically parallel aligned by
merely stretching this gelatine in Opposite directions. The crystals
were then held in this position on the gelatine by clamping the entire
mass between two plates of glass. This piece of apparatus then has
the pr0perty of passing polarized light only, and is better than
98% efficient. The Polarizing Axes of these polarizers are plainly
marked by the manufacturer.
We now come to what is known as a PolariscOpe. If we take two
of these Polaroids and place them in a beam of light with their
polarizing axes parallel the light would pass completely through both

(except the small amount that is lost by reflection, absorption, etc.)

but as their axes are turned so as to become perpendicular

the field becomes dark and no light can be seen except that which

is passed by the translucency of the crystals. In this position
the two Polaroids become a Plane-PolariscoPe and is the type of
Polarisc0pe that is used in this thesis. If light is polarized

by one of these Polaroids and viewed by another as in the above

case the first one is known as a Polarizer and the second is known
as an Analyzer. In the case of such a Plane-PolariscOpe the kind
of light is relatively unimportant. It would be, however, if we
were solving more intricate problems, such as tracing the lines

of principal stress in which case it would be necessary to use

Mica Quarter wave Plates but as we are solving problems dealing

only with simple tension and compression a white source of light

is all that is necessary. Much better results, however, are obtained
in these simple problems by making the light rays as nearly parallel
as possible.

As to the choice of tranSparent material to be used in our
investigations there are certain considerations which have to be
born in mind:

(1) It must be easily worked and shaped.

(2) It must be sensitive.

(3) It must be fairly rigid.

(4) It must have only a small amount of creep.

(5) It must be free from initial double refraction.
(6) It must be transparent and absent of color.

(7) It must not be too expensive.

Of the four materials that could be used namely glass, celluloid,
bakelite and gelatine the second one holds nearest to the desired
oualities. It is available in large sheets and can be bought for
31.20 per lb. at the time of writing. The l/S inch material used
in this thesis was found to be very satisfactory.

In this thesis the method of actually making a measurement
of tension or compression in a piece of transparent material is
by a system first suggested by‘Werthein but was actually deve10ped
by E.G.Coker.

A tension test piece is cut from the same plate as the specimen.
This piece is subjected to a pull in such a manner that the tension
in the material can be determined. This test piece shall be referred
to as a Coker compensator. The method of actually mounting and deter-
mining the tension in this test piece will be explained later in the
paper. It is first necessary, however, to understand what happens
in such a system. If the specimen is subjected to a tension Q in
any direction the compensator is set with its Plane parallel to that
of the specimen. and its axes is set perpendicular to the line of
stress. The Polarizing Axes of the specimen and the compensator are
then in the same directions, but the wave which is accelerated in
one case is retarded in the other. If then the compensator and the
specimen are placed in a Plane-PolariscOpe the stress in the specimen
will be the same as the stress in the compensator when extinction
in the light field is obtained.

Since the tension in the compensator is known this,is, therefore,

a direct means of determining stress. It may be, though, that the

Specimen happens to be in compression; in this case the axes of
the compensator must be set parallel, instead of perpendicular,
to the line of stress. If the Specimen is under two perpendicular
P, Q, the compensator axes must be parallel to that stress (tension
being positive) which is algebraically least. In the case of simple
tension or compression the stress will be measured by the formula
Q = T/bo do-

T . The total pull on the test piece.

b0 u The width of the central part of the test piece.

do a The thickness of the central part of the test piece.
Knowing the dimensions of the Specimen, the total stress in it can
be determined.

The advantages of such a compensator are very great. In the
first place, it gives the stress, or the stress difference, directly,
and does not require a preliminary determination of the Optical
coefficient of the material. In the second place, the observations
are independent of wave-length, or of Photo-Elastic diSpersion,
and may be taken in any kind of light.

In solving for the stresses P and Q it will appear at once by
trial in which of the two possible directions extinction can be
obtained. This last is to be used only if the specimen is under

two perpendicular stresses.

CHAPTER II

Description of Apparatus

The idea for this apparatus was obtained in Coker &
Filon's Treatise but as the book gave only a general explan-
ation the details had to be worked out as they arose. The
apparatus more or less is built around the compensating piece
which will be described below.

A celluloid strip was cut to a general shape by means of
a ceping saw, which, incidentally, was found to adapt itself
very well to the material. The final and desired dimensions
were obtained by the use of sandpaper and a micrometer. Holes
were then drilled approximately six and a half inches apart.
on the centerline of the piece. This last is very important
because if the holes are not on the centerline, uneven stresses
would be introduced and the final results untrue. As .093 inch
celluloid was used and as the strip was made one inch wdde, the
cross sectional area was .093 square inches. This area is
capable of standing a tension of 150# without undue defermation.

Logically then, this leads us to the holders for this piece

which will be described on the next page..

This paragraph will describe the holder on one end and
will refer to illustration #1.

Holes (B) were drilled in the plates (C) the same size
as the hole in the celluloid. Dowels were then fitted to
these holes so that they could be removed by tapping them
lightly with a hammer. The size of the plates are approxi-
mately 1-1/2" x 1-1/4" x 1/8" and are separated by the bar
(D). Holes were drilled in the plates and the bar so they
could be held together by nuts and bolts (E) as shown. Be-
fore assembling a hole was drilled and tapped at (F), the

purpose of which will be eXplained later.

 

Illustration #1

10

The references made in this description will refer to
illustration #2, which is the fastening of the other end
of the test piece. In this, the plates (A) are doweled
tightly to the separating block (B). This block was drilled
and tapped at (c) to take a s/s" belt, also holes were drilled
at (D) 9/16" in diameter. The purpose of the holes at (C)
and (D) will be explained on page 14. The dimensions of the
plates (A) are 3" x l-l/A" x l/B” while those of block (B)
are 6" x 3/!" x S/A". This completes a description of the
holders preper, but the one must be fastened to a steel ring

which will be eXplained next.

 

Illustration #2

11

12

Two 5/16" holes were then drilled diametrically Opposite
on a steel ring (A),illustration #5,the dimensions of which
are the following: internal diameter 3", 1/2" wide and l/B"
thick. A bolt (B) was then inserted in the one hole and screwed
into the holder described on page . This then eXplains the
purpose of the hole in the holder mentioned on that page. In
the other hole another bolt (B) was placed and by the use of
a nut the ring was tightened securely to the block (D), in which
a hole was drilled for this purpose. The dimensions of this
block are 7” long and 3/4" square. Holes were drilled at (E)
3/16" in diameter for a purpose that will be explained on the
next page. Two of these blocks were made of the same size and

shape.

 

Illustration #5

13

14

In order to form a single unit of all the parts described
on the preceeding pages it was necessary to make two more pieces
in the machine shOp. Two 1/2" drill rods 18” long were drilled
and tapped 1" deep on each end so as to take a 3/16" bolt.

The parts so far described were then assembled and mounted
on an oak board by means of the bolts at (A) illustration #4.
The block and holder at (B) are free to move along the rods
which act as guides. The purpose of the bolt (C) is to enable
the user to screw the holder downward and thus create a tension
in the test piece. A hole was cut in the mounting board so as
to allow the light to pass through the test piece. It is nec-
essary to rotate the apparatus around this hole for purposes
which will be explained later. To do this a cast iron ring 6"
in diameter was obtained and by drilling three holes equally
spaced and parallel to the axes of the ring, it is bolted to
the back of the mounting board and around the hole. Illustration
#5 shows this ring in its pr0per place. Before a support for the
apparatus is explained it is necessary to complete the details of

the apparatus itself which will be done next.

 

 

 

Illustration #4

 

 

Illustration #5

15

16

Illustration #6 shows one of the most important parts
of the apparatus and upon what the accuracy of the determin-
ationsdepend. This is the "scale" or the "balance" whose
Operation works on the deformation of the steel ring. The
wheels in this "balance" were obtained from an old clock
while the rest of the parts were made. A multiplying arm (A)
was cut out roughly, filed to the final shape, and mounted
on an axle. A connecting arm (B) was then out out and fitted
between the multiplying arm and the wheel (C). This wheel
also multiplies the movement through the wheel (D) on which a
pointer will later be placed. A spring (E) holds the multi-
plying arm against the bolt head and thus always makes the
pointer return to zero. This mechanism was mounted between
two metal plates (bottom one shown) which are held apart at
the prOper distance by the four brass columns (F). It is held
apart from the ring, except at the point where it touch. the
bolt head, by clamping it under the block (G). Illustration
‘#7 shows how the apparatus was clamped in a vice and arranged
with a hanger so the balance could be calibrated by applying
5# weights one at a time. This completes the apparatus and

the support will be described.

17

 

 

Illustration #6

18

 

 

 

Illustration -25“?

19

Illustration #8 shows the support for the compensator
apparatus. The wood blocks, around the hole in the middle
upright, were put there so the cast iron ring, mentioned on
the preceeding page, could revolve on them. The uprights are
held in place by angle irons obtained from the local hardware
store. The purpose of the two outside uprights are to form
a support for the 360° calibrated metal discs which are holders
for the five centimeter Polaroids.

It might be apprOpriate at this time to mention where
these Polaroids were obtained. They were purchased from the
Polarizing Instrument Company, 8 west 40th Street, New York City
for the price of five dollars each ($5.00). Quarter wave Plates
for more intricate investigations can be obtained from the same
firm at the same price and size. Illustration #9 shows the two

Polaroids with their axes perpendicular.

 

Illustration #8

20

 

Psi!

 

Il lustration £9

21

Illustration #10 shows the complete apparatus set up
and ready for operation. The flash-light is Operated from
the regular power line by the use of a small transformer.

A flash-light with a focusing beam was used so a beam.of
light as nearly parallel as possible could be obtained. As
the apparatus is set the Polaroid nearest the light is the
Polarizer and the other the Analyzer. All that is needed
now is a model structure in which to determine the stresses.

this will be discussed in chapter III.

22

 

I1 lustration #10

 

23

CHAPTER III

STRESS INVESTIGATIONS

24

In order to get a structure in which there were only tension
and compression members when loaded at the panel points, it was
necessary to use one that was Pin-connected. After investigations
along this line a Pin-connected Pratt Truss Highway Bridge, as de-
signed in Thomson's "Bridges", was used. The Specifications used
in designing the model are as follows:

Length C to C of bearings 120 ft. 3 8 panels of 15'
Depth C to C of chords 3 20 ft.
Length of diagonal web-members 3 V202 - 152 3 25 ft.

Using these values and the reasonable scale I/Z" . 1 ft. the
specifications of the model are as follows:

Length C to C of bearings 60 inches 3 8 panels of 9-1/2"
Depth C to C of'chords : 10 inches
Length of diagonal web-members : lZ-l/B ft.

At first it seems necessary to make the entire bridge of
celluloid if it is to be investigated by Photo-Elasticity, but with
a little reasoning it will be understood that only the bar that is
to be investigated need be of this material. Acting on this prin-
cipal the bridge was completely made of 24 gauge sheet metal. The
tension members were simply strips of the material with pin holes
drilled at the prOper distances. This type of bar would not hold
compression though, so channels were made with the pin holes drilled
on the neutral axes and were found completely satisfactory. These
bars were made 1" across the t0p and the flange fi/s", while l/B"
cotter-pins were used holding the bridge together. Hangers of the
same material were made for applying the loads to the panel points.

In the investigation it was not necessary to test every bar as the

25

bridge was symmetrical. In the actual tests all the tension
members were examined first. The loads were applied 5# at a

time to a total of 15#, beyond this it was found that the cotter-
pins would not stand up. The following procedure was followed

in the investigation; ‘the apparatus was so placed that the light
could shine through the celluloid member and the Polaroids crossed
so the field was dark. If it was a tension member the compensating
piece was set with its axes perpendicular to the bridge member or
rather perpendicular to the line of stress. Then as the bridge

was loaded it was noticed that the field was no longer dark, which
proved there was a stress in the celluloid piece. By means of the
screw a tension was applied to the compensator until the field again
became dark. The "scale" was read at this point and was a direct
measurement of the stress in the member. If,however, the member
was in compression the compensator was set with its axes parallel
to the line of stress and the procedure repeated. Illustration #11
shows the apparatus set up with the bridge model in position, ready
to make an investigation of the celluloid tension member. All the
celluloid bars were made of the same width and thickness as the
compensating piece which was 1" x .093". If desired the unit stress
could have been easily computed from the formula Q n-E—§-—. The
following table gives the computed stresses obtained by solving the
model with the different loads on it. Method of Moments & Shear
were used. The table also gives the stresses obtained by Photo-
Elasticity. It is noticed that the values found by this method are

several pounds more than the computed stresses, this was noticed at

the time the readings were made and by looking at the member through

26

the PolariSCOpe without the bridge being loaded the field was
found light instead of dark like it should have been,proving
that there were stresses produced in the bar by the weight of
the bridge. Unfortunately the "scale" could not be read accur-
ately under such a low stress so an average was taken and it was
found that the stresses obtained are about 4# more than actual.

If this is taken account of the values will be fairly close.

Bar

999

O‘O‘O‘

000

0 CLQoD-n

GO

WWW

D'D‘D‘ manual

3.5
Method of Loading

1 5

2 10

3 15

Method of
Loading

Compression El)
" 2

~ (33
Tension (l)
'1 $2)

I! 3)
Tension (1
fl (2

" (3)
Compression (1)
1! E2)

9‘ 3)
Tension (l
u 2

it 23
Tension 1
a 2

a 3
Compression £1;
" 2

" (5)
Compression 1)
fl 2)

fl 3)
Tension (1)
" (2)
" (3)

Hw*r*

A

 

CI-

9

 

 

d?

 

 

 

 

T

"b

E f
1

F

1

5
10
15

(Ll-v
“—ia
q
"-Ta

5 5
10 10
15 15

Measured
Stress

25
48
68

16
29
43

14
19

26
49
73

19
33
52

18
27
43

12
20
27

32
60
90

15
22
32

5
10
15

Stress by
Computation

5
10
15

21.9
43.8
65.7

13.1
26.2
39.3

5.0
10.0
15.0

22.5
45.0
67.5

15.6
31.2
46.8

13.1
26.2
39.3

7.5
15.0
22.5

28.2
56.4
84.6

9.4
1828
28.2

1

1

5
10
15

3.5

27

Method of Measured Stress by

Bar Loading Stress Computation
j Tension (1) 25 22.5

.i " (2 48 45.0

3 " (3) 71 67.5

k Compression (1) 2.5

k " (2) 5.0

k " 3) 12 7.5

1 Compression (l) 35 30.0

1 " (2; 64 60.0

1 " (3. 95 90.0

m Tension (l) 3.1

m " 2) 6.2

m " 3) 13 9.3

n Tension 1) No readings because bar could
n " 2 only take tension. Did not
n " 3) load to get reversal of stress.
0 Tension (1) 33 28.2

o " 2) 62 56.4

o " 3) 89 84.6

p (I) O .0

p 2) o .0

p (3) o .0

29

Results found by this method can be transferred to a large
scale structure very easily. In every case the load applied to
the model must bear a constant ratio 0( to the corresponding load
applied to the full-size. Then the total tension in any bar of
the model is in the ratioa( to the total tension of the corres-
ponding bar of the full-size. It is also possible to work on
another basis and that is to make the width of each bar of the
model prOportional to the cross-section of the correSponding bar
of the full-size. In such a case the relative retardations in
the model are prOportional to the stress-intensities in the full-
size, this then, determines the safety conditions. It can also
be shown that in a great number of problems, such as the one in-
vestigated here, the final results are independent of the differ-
ence between the values of the Moduli of the material. As the I
object of investigation of stresses in transparent models is to
obtain information about the corresponding stresses in a full-
size structure we have then been shown that such a method is
accurate with even such a crude apparatus as described here,

and that with good apparatus the results would be very dependable.

Since the loads increased by even increments the bridge
was loaded (theoretically) at the panel point with l#-weights
and the stresses figured with this load. To get the stresses
with the 5, 10, and 15# loads all that was necessary was to

multiply the stress obtained with unit loads by theta figures.

 

Slide Rule results

 

 

 

 

 

I
2v 3 0
a 3.5 - VaI; 0
V3 3 3.5
A _.
35'
”Z ’V' 5 4 a 16

7x2" 5
5 g 21.9
a - 3.5 x 5 = 4.375 x 10 s 43.8
4 15 I 65.7
5 a 1301
b-3.5x3- 10:262
"" 4 2'63 x 15 2 39 3

C.
b ; 2veo
l - c : 0 5 u 5
c = 1 x 10 a 10
I 15 u 15
253 g 0
b - f z 0 5 = 13.1
150: 5903

31

 

 

 

 

 

 

 

 

 

 

 

 

2v 3 o
305 - 1 " V0 : 0
e _,2.5 x 5 _
—-__-T_ - 3.13
5 n 15.6
:5 3.13 x 10 s 31.2
15 I 4608
2v ,0
__'D 3.5-’1’]. '- g . O 5 - 7.5
: 8-105x10'15.0
e 15 I 2205
6'
4C 9
A a Zn!) :0
1 r? .5 ID -
15C¥ygs\ 3 :2 5653‘: ix4305322.5
35 1} ‘ '3. : O X - X 3 4.5 X 10 : 45.0
I I 4 5.3.67.5
:53 s 0
d ‘ 4-5 = 0 5 s 22.5
d = 405 x 10 I 45e0
15 8 6705
s d l L!
fly“? ‘ ZY-O
e L. '.5.-5-1-l-V1 I 0
“ c 9 \ V1 3 1.5
‘\
A Q;
T b C f )1?er
l l

 

 

5 9 40
1.5 x 5 ‘ '
5 . 6.5 .2802
4 4 L5
3 . .

 

32

 

 

 

 

 

 

 

 

 

 

 

B D
:1 K11 _:F 2'? 3 o
a e L- 3.5x9-116-1x3-4x0=0
5' 4c 9 N 51 5 6 3 [5 : 28.2
0: "' " =5.64x10=56.4
A 3 3 3. 4 15 : 8406
t b C i f 3 G 0 \
‘1 ‘ V {H = 0
h 3 5.64 xflo : 56.4
15 8 8406
iv 3 O
3.5-1-1-1-K a O 5 u 2.6
K = .5 I 10 I 500
15 3 705
B J D In F 11$ 2v - 0
1., ,- 3.5-1-1-1- 11 -_- O
as e d K 1! g .5 in compression and
4‘ 9 it can take only tension
so we use the other diagonal
A 3 3 3. , (m)
' 6 IC 5 IE 3 ‘0 I
3.5 I / 2v = o
3..‘5-1--1--1-Vm -.-. O
vm = 05 .
4 5 = 3.1
u :__T_.'5 x 5 : .szséo : 6.2
3 , 5 g 9.3

 

3.5 x 12 - 9 x 1 - 6 x 1 - 3 x 1 - L x 4 = 0

_ - - 5 I 30.0
L842 2 6 3 :61é0;60.o
5 3 9000

 

 

‘ /
' e
v
P

ZV_=O
-O:O
P:0

CON CLUS ION

33

The purpose of this thesis was not to make an investigation
of a full size bridge by Photo-Elastic methods but to show that
it could be done and to build the apparatus necessary to do so.
It has been shown in this thesis that the results obtained in
structure investigation by Photo-Elasticity are reasonably accur-
ate and fairly rapid compared to solving for stresses by calculation.
It is easy to imagine how much quicker the stresses could be found
in complicated frameworks, rigid frames and indeterminate structures
by this method. Not saying, however, that these problems could be
solved with the apparatus built here, but with apparatus that could
be purchased for a not too large sum of money. One instrument in
particular can be bought for about one hundred dollars (8100.00),
this apparatus is called a Soleil-Babinet Compensator and with it
Lines of Stress can be traced, stress differences can be measured
and many other things determined. With such a compensator stresses
in a complicated framework can be read with surprising speed; Coker
& Filon have read as many as one hundred stresses in an hour that
would take a week to determine by calculation. It is obvious then
that the old adage "Good in theory only" is untrue if reference is
made to such a method. All the other apparatus (except the Polaroids
and the size used in this thesis are plenty large) can be built very
easily.

The theory of Photo-Elasticity has been known for many years
but it is only in the last few that the engineer has began to realize
its practical possibilities, and it won't be very long before results

from it will be a dominant factor in structure design. Many schools

already have recognized the need for instruction along this line

if they were to be up to date in their engineering courses. It

has one drawback, however, in that the many Photo-Elastic invest-
igations require much preliminary study that is very complicated.
The result is that to fully understand the subject extra courses

in Mathematics, Physics and Strength of Materials had to be incor-
porated. This then limits Photo-Elastic study to graduate students
or part time instructors but even used by this limited group of
students it keeps the school up to date and a leader in engineering

StUdie S e

   

 

 

.5.

..\‘

.‘I‘

C .
r]; .. .. .. L“ -. ,. 13.. - s L .
hulwmmuw§. i. mi % a ..
a . . .- a . . :1 .

5..

 

 

WACENVOOPD

 

 

 

 

T."

M ll! ('14::

I

N

IHI
“2!!

1

’1‘: "1
HI
lb

rMiC HIGAN STATE UNIVERSIIT{ Ll IRB

H!

”M”