Table Of Content,
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special Faculty Committee is accepted by
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the Graduate School of the
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University of Wyoming
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in partial fulfillment of the requirements
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for the degree of I
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Dean of the Graduate School.
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THE PHOTOELASTIC M ETHO D OF STRESS ANALYSIS
A PPLIED TO STRU CTURAL FRAMES
by
H arry M . John
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A Thesis
Submitted to the DepartmEent of
C ivil Engineering and the Graduate School
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of the University of Wyoming in P artial
Fulfillm ent of ReqEuirements for the Degree of
M aster of Science
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University of Wyoming
Laram ie, Wyoming
June, 1950
LIBRARY
THE
UNIVERSITY OF WYOMING
&ARAMIE
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UMI Number: EP21073
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tisb&rd Lujas
ACKNOW LEDGM ENTS
The w riter wishes to express his sincere appreciation to
D r. H. S. Sweet, Assistant Professor of C ivil Engineering, for
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his assistance in the preparation of the working plan, review of
the m anuscript, and encouragement at all stages of the investi
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gation. G rateful acknowledgment is also due M r. H. P. Davis,
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Associate Professor of M echanical Engineering, for making avail
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able the facilities of the Foundry and Machine Shop of the Mechanical
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Engineering Departm ent, and to D r. J. K. Wood, Assistant P ro
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fessor of Physics, and M r. Jack Chatelain, Instructor in Physics,
for their assistancPe and advice on photography, and for placing the
% Photo Laboratory of the Physics Departm ent at the disposal of the
w riter.
H. M . J.
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TABLE OF CONTENTS
Chapte r Page
I. IN TR O D U C T IO N ................................................................................................. 1
II. HISTORICAL R E V IE W ................................................................................... 3
HI. T H E O R Y ................................................................................................................... 10
Principal S tre s s e s ................................................W.................................. 10
Plane Polarized L ig h t......................................................................... 13
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Double R e fra c tio n .................................................................................. 14
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C ircularly Polarized L ig h t................................................................ 14
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Crossed Quarter P la te s .................................................................... 15
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The Standard C ircular P o la ris c o p e ......................................... 16
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Tem porary Double Refraction - Stress Pattern . . . . 21
Stress-Optic L a w ...................................................................................... 23
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Is o c lin ic s ........................................................................................................ 24
Application of the Photoelastic M e th o d ................................ 28
IV . EQ UIPM EN T AND M A T E R IA L S ............................................................ 30
Optical B ench............................................................................................... 30
Loading F ra m e ........................................................................................... 33
Observation Equipm ent......................................................................... 35
M illing E q u ip m e n t.................................................................................. 37
M a te ria ls ........................................................................................................ 37
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Chapter Page
V. PRO CEDURE.......................................................................................................... 40
Calibration of M aterial .................................................................... 40
Model P re p a ra tio n .................................................................................. 48
Photographing the Stress P a tte rn .............................................. 55
Isoclinic S ketching.................................................................................. 59
VI. PRACTICAL, A P P L IC A T IO N S ................................................................. 62
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Simply Supported B e a m ...................................................... 62
C entrally Loaded Restrained B e a m ......................................... 70
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Parabolically Haunched B e a m ....................................................... 77
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Single Story Rigid F ra m e.................................................................... 80
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Hinged-Base F r a m e ............................................................................. 87
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V II. CONCLUSIONS ................................................................................................ 91
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B IB L IO G R A P H Y .................................................................................................................. 94
SELECTED REFPERENCES ....................................................................................... 97
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LIST OF FIGURES
Figure Fage
1. Norm al Stresses on Elem ent Free from S h ear............................. 11
2. Principal Planes Oriented at Angle 0 with Planes Sub
jected to Norm al and Shear Stresses.............................................. 11
3. Production of C ircularly Polarized L ig h t....W...................................... 15
4. Effect of Two Crossed Quarter-W ave P la te s ................................. 16
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5. Schematic Arrangem ent of Elem ents to Produce
C ircularly Polarized L ig hIt..................................................................... 17
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6. Schematic Diagram s of Optical Transform ations in a
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Standard Polaris cope Produced by Simple Crystal
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Plates of D ifferent T hickn esses........................................ 20
7. Sketch of a Doubly Refracting Simple Plate of Linearly
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Varying T h ickn ess...................................................................................... 21
8. Variation in Intensity of Light at a Point in a Model as
Load is Increased............................................................................: . . 22
9. Effect of Doubly-Refracting M aterial on Plane-
Polarized White L ig h t.............................................................................. 26
10. Elem ent on Free Boundary of Simple B eam .................................... 28
11. Standard C ircular Polaris cope ............................................................... 31
12. Plane P o la risco p e ............................................................................................... 32
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Figure Page
13. Polaroid and Q uarter-w ave Plate in M ountings............................ 34
14. Lead W eights............................... ......................................................................... 36
15. End M ill ............................................................................................... 38
16. Dimensions for Tension Calibration M em b er............................ 41
17. Stress Patterns of Tension Specimen under Increasing
L o a d ................................................................................................................. 42
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18. Stress-Fringe Curve for C R -3 9 .....................................................................45
19. Loading Arrangem ent for Pure Bending . ' • . . . . 47
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20. Stress Pattern of Beam in Pure B e n d in g .................................. . 49
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21. Machining S et-u p .......................V........................................................................ 52
22. Stress Pattern in Tension Specim en................................................. 57
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23. Sim ply Supported B e a m ................................................• ......................... 62
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24. Stress Pattern of Sim ply Supported Beam Carrying
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Concentrated Load at M id -s p a n .................................................. 64
25. Isoclinics for Sim ply Supported B e a m ............................................. 66
26. Stress Trajectories for Sim ply Supported B e a m ................. 66
27. Curves of (p - q) and Orientation of Principal Planes . . 67
28. Distribution of V ertical Shear Stress in Simply
Supported B e a m ...................................................................................... 68
29. Sketch of Restrained Beam Showing Dimensions of Beam
and Plate in Which It was Cut ................................ 71
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Figure Page
30. Stress Pattern of Restrained Beam of Constant Section . 72
31. Stress Pattern at Left End of Constant Depth
Restrained B e a m .............................................................................. 74
32. Stress Pattern at Center of Constant Depth Restrained
B e a m ......................................................................................................... 74
33. Isoclinics for Centrally Loaded Restrained B eam .......... 75
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34. Flexural Stresses in Restrained Beam of Constant Depth. 76
35. Sketch of Parabolically Haunched Beam Showing
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Dimensions of Beam and Plate in Which It was Cut . . 78
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36. Stress Pattern of Parabolically Haunched B e a m .......... 79
37. Flexural Stresses in Parabolically Haunched Beam . . . . 81
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38. Sketch Showing Dimensions of Rigid Fram e Model . . . . 82
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39. Application of Load to Single Story Rigid F ra m e .......... 83
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40. Stress Pattern of Single Story Rigid Fram e 84
41. Flexural Stresses in Single Story Rigid F ra m e .............. 86
42. Stress Pattern of Hinged-Base Fram e with Fillets
at Knees ........................................................................................................ 88
43. Stress Pattern of Hinged-Base Fram e with Fillets
R e m o v e d ........................................................................................................ 90
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