Question F12.8: The boards are bolted together to form lhe built-up beam. If......
The boards are bolted together to form lhe built-up beam. If the beam is subjected to a shear force of V = 20 kN, determine the maxin1wu spacing s of the bolts to the nearest mm if each bolt has a shear strength of 8 kN.
Step-by-Step
Consider two large rectangles and two side rectangles.
I=2\left[\frac{1}{12}(0.025)\left(0.3^{3}\right)\right]+2\left[\frac{1}{12}(0.05)\left(0.2^{3}\right)+0.05(0.2)\left(0.15^{2}\right)\right] =0.62917\left(10^{-3}\right) \mathrm{m}^{4}
Top center board is held onto beam by the top row of bolts.
Q=y^{\prime} A^{\prime}=0.15(0.2)(0.05)=1.5\left(10^{-3}\right) \mathrm{m}^{3}Each bolt has two shearing surfaces.
\begin{aligned} & q_{\text {allow }}=2\left(\frac{F}{s}\right)=\frac{2\left[8\left(10^{3}\right)\right]}{s}=\frac{16\left(10^{3}\right)}{s} \\ & q_{\text {allow }}=\frac{V Q}{I} ; \quad \frac{16\left(10^{3}\right)}{s}=\frac{20\left(10^{3}\right)\left[1.5\left(10^{-3}\right)\right]}{0.62917\left(10^{-3}\right)} \\ & s=0.3356 \mathrm{~m}=335.56 \mathrm{~mm} \end{aligned}Use s=335 \mathrm{~mm}
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