A bar having a square cross section of 30 mm by 30 mm is 2 m long and is held upward. If it has a mass of 5 kg/m, determine the largest angle θ measured from the vertical, at which it can be supported before it is subjected to a tensile stress along its axis near the grip.
Question 8.77: A bar having a square cross section of 30 mm by 30 mm is 2 m...
A=0.03(0.03)=0.9\left(10^{-3}\right) \mathrm{m}^{2}
I=\frac{1}{12}(0.03)\left(0.03^{3}\right)=67.5\left(10^{-9}\right) \mathrm{m}^{4}
Require \sigma_{A}=0
\sigma_{A}=0=\frac{P}{A}+\frac{M c}{I}
0=\frac{-98.1 \cos \theta}{0.9\left(10^{-3}\right)}+\frac{98.1 \sin \theta(0.015)}{67.5\left(10^{-9}\right)}
0=-1111.11 \cos \theta+222222.22 \sin \theta
\tan \theta=0.005 ; \quad \theta=0.286^{\circ}
Related Answered Questions
A=\frac{\pi}{4}\left(0.75^{2}\right)=0.4417...
The location of the neutral surface from the cente...
Support Reactions: Referring to the free-body diag...
A=\frac{\pi}{4}\left(0.03^{2}\right)=0.225 ...
Segment A B :
\left(\sigma_{\max }\r...
Equation of Equilibrium: The absolute pressure dev...