Normal stresses

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Normal stresses#

The bending moment gives a linear normal stress distribution:

\[\sigma^{(M)} = \frac{M_{z}z}{I_{zz}}\]

Combining with normal stress due to extension gives the stress formula:

\[\sigma(z) = \frac{N}{A} + \frac{M_{z}z}{I_{zz}}\]

This is treated in chapter 4.4 and 4.5 of the book Engineering Mechanics Volume 2 (Hartsuijker and Welleman, 2007).

When there is bending in both the \(xz\) plane and \(xy\) plane, the general stress formula is obtained:

\[\sigma(y,z) = \frac{N}{A} + \frac{M_{y}y}{I_{yy}} + \frac{M_{z}z}{I_{zz}}\]

This is treated in chapter 4.8 of the book Engineering Mechanics Volume 2 (Hartsuijker and Welleman, 2007).

Exercises#

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