Determine the location e of the shear center, point O, for the thin-walled member having the cross section shown. The member segments have the same thickness t.
Question 7.64: Determine the location e of the shear center, point O, for ...
Summing moments about A ,
e P=b F_{1} \text{(1)}
I=\frac{1}{12}(t)\left(h_{1}\right)^{3}+\frac{1}{12}(t)\left(h_{2}\right)^{3}=\frac{1}{12} t\left(h_{1}^{3}+h_{2}^{3}\right)
q_{1}=\frac{P\left(h_{1} / 2\right)(t)\left(h_{1} / 4\right)}{I}=\frac{P h_{1}^{2} t}{8 I}
F_{1}=\frac{2}{3} q_{1}\left(h_{1}\right)=\frac{P h_{1}^{3} t}{12 I}
From Eq. (1),
e=\frac{b}{P}\left(\frac{P h_{1}^{3} t}{12 I}\right)= \frac{h_{1}^{3} b}{\left(h_{1}^{3}+h_{2}^{3}\right)}
= \frac{b}{1+\left(h_{2}/h_{1}\right)^{3}}
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