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| Based on Budynas.R, et al. Shigley's Mechanical Engineering Design, McGraw-Hill (2011) 9th Ed. P.192 | ||
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| Based on Budynas.R, et al. Shigley's Mechanical Engineering Design, McGraw-Hill (2011) 9th Ed. P.192 | ||
At impact the kinetic energy is equal to the strain energy:
\frac{1}{2}k\delta^2 = W(h+\delta)
Solving for beam deflection $(\delta)$:
\delta = \frac{W}{k}+\frac{W}{k}\left(1+\frac{2hk}{W}\right)^{1/2}
where:
h = \frac{v_{f}^2 - v_{i}^2}{2g};k = \frac{48EI}{l^3}
The force at impact can then be determined to be:
F = k\delta