# Strength of Materials: Narrow Rectangular Cross-Sections

A narrow cross-sectional beam is a rectangular beam that has a width that is much greater then its thickness. Since the cross-section is not circular the stress will vary on the outside. Which can be seen in the stress profile below. Notice also that the higher stress concentration is located at the end in the center where there would normally be zero stress for a circular profile.

To calculate the stress and angle of twist equations 1 thru 3 would be used.

(1)

(2)

(3)

## Rectangular Cross-Section

At some point the rectangular cross-section can no longer be considered narrow. When that happens equation 4 and 5 would be used to calculate the stress and polar moment of inertia, while equation 2 would still be used to calculate the angle of twist.

(4)

(5)

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