2. Benchmark solution

2.1. Calculation method used for the reference solution

The calculation of the critical discharge load is given in detail in [bib1].

\({P}_{\mathrm{cr}}={\gamma }_{2}\frac{\sqrt{E{I}_{y}C}}{{L}^{2}}\)	critical spill load
with \(C=\mathrm{GJ}\)	torsional stiffness
\(J=((b-2{h}_{1}){h}_{2}^{3}+2a{h}_{1}^{3})\)	torsional constant [bib2]
\({C}_{1}E{I}_{y}\frac{{b}^{2}}{2}\)	warping stiffness corresponding to an I-beam

Digital application:

\(C=8578.515{\mathrm{N.m}}^{2}\)

\(\mathrm{C1}=5516.8{\mathrm{N.m}}^{4}\)

\(\frac{{L}^{2}C}{{C}_{1}}=6.22\)

The value of \({\gamma }_{2}\) depends on the \(\frac{{L}^{2}C}{{C}_{1}}\) ratio. In our case \({\gamma }_{2}\) is equal to 8.617. This value is taken from an array given in [bib1]. Which gives us \({P}_{\mathrm{cr}}=104797.82N\)

2.2. Benchmark results

Critical discharge load and associated mode.

2.3. Uncertainties about the solution

Analytical solution

2.4. Bibliographical references

1. S.P. TIMOSHENKO, J.M. GERE: Elastic Stability Theory, Second Edition, DUNOD 1966.

2. S.P. TIMOSHENKO: Material Strength, Volume 2: DUNOD 1968.