A Caltech Library Service

Stresses at Two-Dimensional Corners for Various Force Distributions


Brahtz, John Henry Augustus (1932) Stresses at Two-Dimensional Corners for Various Force Distributions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4QRC-A816.


This paper deals with the stress distribution under plain strain in a corner of any angular magnitude, i.e., a plane with an angular incision or notch.

The Introduction contains a brief statement of the method employed by Dr. Theodor von Karman in his exact treatment of a beam in bending (Aachen Abhandlungen, Heft 7, 1927).

In Part I a generalization of this method is outlined which is applicable to the corner for any force distribution over the straight boundaries. Solutions are found in the 3/4-plane for:
1. Concentrated load at any point of the straight boundaries.
2. Uniform distribution between the vertex and a point of the boundary.
3. Linear distribution in the same region.
4. Superposition of 2 and 3.

Certain stresses are determined and plotted and shown to be infinite at the vertex for partial loadings of the boundaries.

In Part II an alternate method is given to obtain a solution for case 1.

The discussion points out the very interesting paradox that stresses may be finite for certain continuous loadings, but become infinite if a portion of the load is removed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Aeronautics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • von Kármán, Theodore
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1932
Record Number:CaltechETD:etd-09062007-140731
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3365
Deposited By: Imported from ETD-db
Deposited On:11 Sep 2007
Last Modified:03 Oct 2019 23:25

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page