Kirsch equations

The Kirsch equations describe the elastic stressesaround the hole in an innite plate in one directional ten-sion. They are named after Ernst Gustav Kirsch.

1 ResultLoading an innite plate with circular hole of radius awith stress , the resulting stress eld is:rr =

2

1 a2r2

+ 2

1 + 3a

4

r4 4a2

r2

cos 2

=2

1 + a

2

r2

2

1 + 3a

4

r4

cos 2

r = 21 3a4r4 + 2a

2

r2

sin 2

2 References Kirsch, 1898, Die Theorie der Elastizitt und die

Bedrfnisse der Festigkeitslehre. Zeitschrift desVereines deutscher Ingenieure, 42, 797807.

1

2 3 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

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