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Stress-concentration factors for multiple semielliptical notches in beams under pure bending

Within range of parameters investigated, the stress-concentration factor for beams with multiple semielliptical notches is found to be 15 to 37 percent less than that for multiple semicircular notches

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Abstract

Uniformly spaced semielliptical notches in rectangular beams under pure bending are examined photoelastically. Minimum stress-concentration factors, produced by multiple elliptical notching of beams, are obtained for wide ranges of notch width, semiminor elliptical axis, notch depth, notch pitch and depth of beam. In particular, the geometries of the optimum elliptical notch producing the least stress concentration are obtained for a practical range of parameters. Stress-concentration factors for beams with multiple semi-elliptical notches are compared to those for beams with single semielliptical notches and to those for beams with semicircular notches. The maximum reduction of stress-concentration factor for beams with multiple semielliptical notches is to approximately 37 percent of the stress-concentration factor for beams with single semielliptical notches. Within the range of parameters investigated, the stress-concentration factor for beams with multiple semielliptical notches was 15 to 37 percent less than that for multiple semicircular notches.

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Abbreviations

a :

semimajor axis of ellipse

2a :

notch width or major axis of ellipse

b :

semiminor axis of ellipse

d :

depth of notch

h :

depth of beam

k :

stress-concentration factor

M :

bending moment

p :

pitch or spacing of notches

t :

thickness of beam

σ max :

maximum stress at the elliptical notch

σ nom :

nominal stress at the net section

References

  1. Nishioka, K., andHisamitsu, N., “On the Stress Concentration in Multiple Notches,”J. Appl. Mech.,29 (3),575–577 (September 1962).

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  2. Durelli, A. J., Lake, R. L., and Phillips, E., “Stress Distribution in Plates under a Uniaxial State of Stress, with Multiple Semicircular and Flat-Bottom Notches,” Proceeding of the First National Congress of Applied Mechanics, Amer. Soc. Mech. Engrs., 309–315 (1952).

  3. Tsao, C. H., Ching, A., andOkubo, S., “Stress-concentration Factors for Semielliptical Notches in Beams under Pure Bending,”Experimental Mechanics,5 (3),19A-23A (March 1965);also TDR-169(3230-11) TN-16, Aerospace Corporation (October 1963).

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Authors and Affiliations

  1. Aerospace Corporation, El Segundo, Calif

    A. Ching & S. Okubo

  2. California State College at Long Beach, USA

    C. Tsao (Associate Professor of Mechanical Engineering)

Authors
  1. A. Ching
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  2. S. Okubo
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  3. C. Tsao
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Additional information

Investigation reported in this paper was supported by the United States Air Force under Contract No. AF 04(695)-1001.

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Ching, A., Okubo, S. & Tsao, C. Stress-concentration factors for multiple semielliptical notches in beams under pure bending. Experimental Mechanics 8, 19N–24N (1968). https://doi.org/10.1007/BF02326348

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  • DOI: https://doi.org/10.1007/BF02326348

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