2. Benchmark solution#

2.1. Calculation method#

Travel in \(B\)

Single pull \({u}_{x}\mathrm{=}\frac{{F}_{x}L}{ES}\)
Pure flex \({u}_{z}\mathrm{=}\mathrm{-}\frac{{M}_{y}{L}^{2}}{2E{I}_{y}}\) \({\theta }_{y}\mathrm{=}\frac{{M}_{y}L}{E{I}_{y}}\)
Pure flex \({u}_{y}\mathrm{=}\frac{{M}_{z}{L}^{2}}{2E{I}_{z}}\) \({\theta }_{z}\mathrm{=}\frac{{M}_{z}L}{E{I}_{z}}\)

Maximum stress in \(A\)

Single pull \({\sigma }_{x}\mathrm{=}\frac{{F}_{x}}{S}\)
Pure flex \({\sigma }_{x}\mathrm{=}\mathrm{-}\frac{{M}_{y}}{\frac{2{I}_{y}}{h}}\)
Pure flex \({\sigma }_{x}\mathrm{=}\mathrm{-}\frac{{M}_{z}}{\frac{{\mathrm{2I}}_{z}}{b}}\)

Fashion 1: \({f}_{1}\mathrm{=}\frac{3.516}{2{L}^{2}\pi }\sqrt{\frac{\mathit{EI}}{\rho S}}\)

Mode 2: \({f}_{2}\mathrm{=}\frac{22.0345}{2{L}^{2}\pi }\sqrt{\frac{\mathit{EI}}{\rho S}}\)

Dot	\(\mathit{DX}\)	\(\mathit{DY}\)	\(\mathit{DZ}\)
\(B\)	\(8.3333\mathrm{\times }{10}^{\mathrm{-}5}\)	\(1.6667\mathrm{\times }{10}^{\mathrm{-}4}\)	\(\mathrm{-}2.5\mathrm{\times }{10}^{\mathrm{-}4}\)

Analytical solution.