Can anyone help with this Impact problem? It does not seem very difficult but I am having trouble putting all the parts together.
Thanks,
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$\begingroup$ Can you describe what your formulas calculate? The last two in particular should be described. $\endgroup$– JohnHoltzCommented Apr 6, 2021 at 3:34
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3 Answers
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This problem involves the concepts of "conservation of mass" and "conservation of energy".
Due to impact, the static deflection has no bearing on this matter. You need to find the force (static + impact) that causes the beam to fail.
Assume the beam will fail by flexural (moment), then you can solve this problem by the Energy Method: Potential Energy (m x g x h') = Work Energy (Me)
From the given dimension (w, t), and the failure stress (Su), find the limiting moment Me, then solve for h', which is the total distance travelled, including the static deflection.
You can also solve the equivalent impact force, F' = Me/L, and check for deflection.
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It seems you use the formula for simply supported beam, the cantilever static deflection is as the question already states:
$$ \delta_{static} = \frac{mgL^3}{3EI}=\frac{50*1^3}{3*207* 10^{-11}*2.66*10^{-7}}=29.6*10^{-6}m $$
Now you can plug this into:
$$F_c=(50kg)(1+ \sqrt{1+\frac{2h}{29.6*10^{-6}m}} \quad )$$
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Its just a matter of using the right formulas and algebraically finding an equation that will leave you with 1 unknown. In this case it is h.
