2. Benchmark solutions

2.1. Calculation method used for reference solutions: analytical

On section \((A,B)(0<\theta <\frac{\pi }{2})\), we have:

\(N=\frac{F}{2}\mathrm{cos}\theta\), \(\mathrm{Vy}=-\frac{F}{2}\mathrm{sin}\theta\), \({M}_{z}=-\frac{\mathrm{FR}}{2}(1-\mathrm{cos}\theta )+\Gamma\).

On section \((B,C)(\frac{\pi }{2}<\theta <\pi )\), we have:

\(N=-\frac{F}{2}\mathrm{cos}\theta\), \(\mathrm{Vy}=\frac{F}{2}\mathrm{sin}\theta\), \({M}_{z}=-\frac{\mathrm{FR}}{2}(1+\mathrm{cos}\theta )+\Gamma\).

By using the law of behavior relating \(M\) to the rotation of the normal and taking into account that the latter is zero in \(A\) and in \(B\), we have:

\({\int }_{0}^{\frac{\pi }{2}}Md\theta =0\),

from where: \(\Gamma ={M}_{A}={M}_{C}=\frac{\pi -2}{2\pi }FR\)

2.2. Benchmark results

Domestic efforts for \(\theta \mathrm{=}0°\) and \(90°\).

2.3. Uncertainty about the solution

Analytical solution.

2.4. Bibliographical references

1. Report no. 2314/A from the Aerotechnical Institute « Proposal and implementation of new test cases lacking the validation of Aster beams »