Question F12.4: If the beam is subjected to a shear force of V = 20 kN, dete......
If the beam is subjected to a shear force of V = 20 kN, determine the maximum shear stress in the beam.
Step-by-Step
Consider two vertical rectangles and two horizontal rectangles.
\begin{aligned} I=2[ & \left.\frac{1}{12}(0.03)\left(0.4^{3}\right)\right]+2\left[\frac{1}{12}(0.14)\left(0.03^{3}\right)\right. \\ & \left.+0.14(0.03)\left(0.15^{2}\right)\right]=0.50963\left(10^{-3}\right) \mathrm{m}^{4} \end{aligned}
Take the top half of area.
Q_{\max }=2 y^{\prime}{ }_{1} A_{1}^{\prime}+y_{2}^{\prime} A_{2}^{\prime}=2(0.1)(0.2)(0.03)
+(0.15)(0.14)(0.03)=1.83\left(10^{-3}\right) \mathrm{m}^{3}
\tau_{\max }=\frac{V Q_{\max }}{I t}=\frac{20\left(10^{3}\right)\left[1.83\left(10^{-3}\right)\right]}{0.50963\left(10^{-3}\right)[2(0.03)]}=1.20 \mathrm{MPa}
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