Stresses at Two-Dimensional Corners for Various Force Distributions

Author: Brahtz, John Henry Augustus

Year: 1932

Degree: Dissertation (Ph.D.)

Advisor: von Kármán, Theodore

Committee Member: Unknown, Unknown

Option: Aeronautics

DOI: 10.7907/4QRC-A816

Abstract

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.

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