Experimental Mechanics

, Volume 18, Issue 9, pp 335–343 | Cite as

Photoelastic analysis of a thick plate with an elliptical hole subjected to simple out-of-plane bending

Three-dimensional photoelasticity was employed to determine the stress distribution and concentration around the periphery of an elliptical hole in a plate subjected to simple out-of-plane bending. The experimental results are correlated with the existing theoretical solutions
  • N. A. Rubayi
  • G. W. Sosropartono


A three-dimensional photoelastic analysis using the stress freezing and slicing techniques was employed to study the stress distribution and the stress-concentration factors around an elliptical hole in a plate of finite thickness. The plate was subjected to simple out-of-plane bending. A special bending device was designed to produce uniform bending moment at the two opposite free edges of the plate. Six plates with various elliptical holes were studied. The stress variation across the plate thickness at the periphery of the elliptical hole was also investigated. The experimental results were correlated with the existing theoretical solutions.


Mechanical Engineer Fluid Dynamics Stress Distribution Plate Thickness Thick Plate 
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\({\left. {\begin{array}{*{20}c} {Q_{xx} } \\ {Q_{yy} } \\ \end{array} } \right\}}\)

shear forces per unit length inX andY directions respectively


plate rigidity


semi axis of ellipse in theX direction


semi axis of ellipse in theY direction


stress-optical coefficient (kPa/fringe/mm)


total plate thickness


stress-concentration factor


applied bending moment (N.m/m)


thickness of calibration specimen


thickness of slice


ratio of axis of ellipse in theY direction to plate thickness


ratio of the semi axes of ellipse


ratio of the semi axis of ellipse in theX direction to plate thickness


angle measured fromX axis




Poisson’s ratio

\(\xi _o\)

boundary of elliptical hole


radius of curvature

\(\sigma _{\eta (max)}\)

tangential stress at η=π/2 (kPa)







\(\left. {\begin{array}{*{20}c} {F_e k_n } \\ {G_e k_n } \\ \end{array} } \right\}\)

modified Mathieu function of the 2nd kind


\(\frac{{Gek'_2 }}{{Gek_2 }}\)

\(M_\eta (\xi _o )\)

bending moment at the edge of the ellipse for any angle η


\(\frac{{M_{max} (\eta = \tfrac{\pi }{2})}}{{M_o }}\)


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Copyright information

© Society for Experimental Mechanics, Inc. 1978

Authors and Affiliations

  • N. A. Rubayi
    • 1
  • G. W. Sosropartono
    • 1
  1. 1.Department of Engineering Mechanics and Materials, School of Engineering and TechnologySouthern Illinois University at CarbondaleCarbondale

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