SD160 Fall Protection Rough Concept Calc
\(200\ lbs\ =\ 90.72\ kg\)
\(Force\ =\ mass\ \cdot\ gravity\)
\(F\ =\ 90.72\ kg\ \cdot\ 9.81\ \frac{m}{s^2}\)
\(F\ =\ 889.06\ N\)
Moment of Inertia of the tube
0.03175m square tubing, 0.0021m thick
\(I\ \left(Moment\ of\ Inertia\right)\ =\ \frac{\left(b_{outside}h_{outside}^3\right)\cdot\left(b_{inside}h_{inside}^3\right)}{12}\)
\(I\ =\ \frac{\left(0.03175\ meters\ \right)^4\ -\left(0.02964\ meters\ \right)^4}{12}\ \)
\(I\ \ =\ 2.04\ \cdot\ 10^{-8}\ m^4\)
Max Stress in the tube
Longest unsupported tubing distance = 0.41m
\(σ_{\max}\ =\ \frac{FL_{\max}}{I}\cdot\frac{h}{2}\)
\(σ_{\max}\ =\ \frac{889.06\ N\ \cdot\ 0.41\ m}{2.04\ \cdot10^{-8}\ m^4}\cdot\ \frac{0.03175\ m}{2}\)
\(σ_{\max\ }=\ 2.83\ \cdot\ 10^8\ Pa\)
\(\ \ \ \ \ \ \ \ \ =41,190\ psi\)
\(σ_{ultimate\ tensile,\ ANSI\ 1008\ steel}\ =\ 50,000\ psi\)