Abstract
Elliptical notches in rectangular beams under pure bending are examined photoelastically. Stress-concentration factors due to a single elliptical notch are obtained for wide ranges of 2a/h andd/h, where 2a, d, andh are the width of notch, depth of notch, and depth of beam, respectively. In particular, the geometries of the optimum elliptical notches producing the least stress concentrations are obtained. Almost the whole elliptical boundary of these notches are stressed to the same peak, which indicates that these notches will probably produce the least stress concentrations among all notches, elliptical or nonelliptical.
The graphs herein will enable the designers to find the stress-concentration factors of elliptical notches and to pick out the geometry of the optimum notch which will give the least stress concentration for any given values of 2a/h andd/h.
Stresses and the stress-concentration factors at the bottom of the beam opposite the notch are also obtained. These stresses, though smaller in magnitude, are of an opposite sign to the peak stress at the notch. For brittle materials, a smaller tensile stress may be more critical than a large compressive stress; therefore, these stress-concentration factors are also given.
Similar content being viewed by others
Abbreviations
- a :
-
semimajor axis of ellipse
- b :
-
semiminor axis of ellipse
- d :
-
depth of notch
- h :
-
depth of beam
- k :
-
stress-concentration factor
- M :
-
bending moment
- t :
-
width
- k :
-
stress-concentration factor at the notch
- k 1 :
-
stress-concentration factor at the bottom of the beam opposite the notch
- σ max :
-
maximum stress at the elliptical notch
- σ nom :
-
nominal stress at the net section
- σ1 :
-
stress at the bottom of the beam opposite the notch
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tsao, C.H., Ching, A. & Okubo, S. Stress-concentration factors for semielliptical notches in beams under pure bending. Experimental Mechanics 5, 19A–22A (1965). https://doi.org/10.1007/BF02323214
Issue Date:
DOI: https://doi.org/10.1007/BF02323214