Determine the variation in the depth d of a cantilevered beam that supports a concentrated force P at its end so that it has a constant maximum bending stress \sigma_{\text {allow }} throughout its length. The beam has a constant width b_{0}.
Question 11.35: Determine the variation in the depth d of a cantilevered bea...
Section properties:
I=\frac{1}{12} b_{0} d^{3} ; \quad S=\frac{I}{c}=\frac{\frac{1}{12} b_{0} d^{3}}{\frac{d}{2}}=\frac{b_{0} d^{2}}{6}Maximum bending stress:
\sigma_{\text {allow }}=\frac{M}{S}=\frac{P x}{b_{0} \frac{d^{2}}{6}}=\frac{6 P x}{b_{0} d^{2}}\quad(1)At x=L, \quad d=h
\sigma_{\text {allow }}=\frac{6 P L}{b_{0} h^{2}}\quad(2)Equating Eqs (1) and (2),
\frac{6 P x}{b_{0} d^{2}}=\frac{6 P L}{b_{0} h^{2}}d=h \sqrt{\frac{x}{L}}
Related Answered Questions
Moment Function: As shown on FBD (b).
Section Prop...
Support Reactions: As shown on the free-body diagr...
Support Reactions: As shown on the free-body diagr...
Moment Functions: Considering the moment equilibri...
Section Properties:
I=\frac{1}{12} b t^{3} ...
I=\frac{\pi}{4}\left(c^{4}-0.0075^{4}\right...
Section just to the left of point C is the most cr...
The critical moment is at B.
M=\sqrt{(473.7...
Maximum resultant moment
M=\sqrt{1250^{2}+2...