Chapter 5, Problem 5.5.16P

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
Textbook Problem

# Determine the maximum bending stress emaxdue to pure bending by a moment (M) for a beam having a cross section in the form of a circular core (see figure). The circle has diameter d and the angle ÃŸ = 60Â°. Hint: Use the formulas given in Appendix E, Cases 9 and 15.

To determine

Maximum bending stress, σmaxfor the beam having a cross − section in the form of circular core.

Explanation

Given:

Diameter, d

â€ƒâ€ƒÎ²=60âˆ˜

From the appendix given here:-

â€ƒâ€ƒIy=Ï€r44âˆ’r42(Î±âˆ’abr2+2ab3r4)

â€ƒâ€ƒr=d2

â€ƒâ€ƒÎ±=Ï€2âˆ’Î²

â€ƒâ€ƒa=rsinÎ²

â€ƒâ€ƒb=rcosÎ²

Iy=Ï€d464âˆ’d432(Ï€2âˆ’Î²âˆ’sinÎ²cosÎ²+2sinÎ²cosÎ²)Iy=Ï€d464âˆ’d432(Ï€2âˆ’Î²âˆ’(sinÎ²cosÎ²)(1âˆ’2cos2Î²)</

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