2. Benchmark solution#

2.1. Calculation method used for the reference solution#

We ask:

\({k}_{\mathrm{An}}=\frac{{\mathrm{EI}}_{\mathrm{An}}}{{l}_{\mathrm{An}}}\)

with \(n=B,C,D\) or \(E\)

\(\begin{array}{}K={k}_{\mathrm{AB}}+{k}_{\mathrm{AD}}+{k}_{\mathrm{AE}}+\frac{3}{4}{k}_{\mathrm{AC}}\\ {r}_{\mathrm{An}}=\frac{{k}_{\mathrm{An}}}{K}\end{array}\)

with \(n=B,C,D\) or \(E\)

\({C}_{1}=+\frac{{\mathrm{Fl}}_{\mathrm{AD}}}{8}-\frac{{\mathrm{pl}}_{\mathrm{AB}}^{2}}{12}\)

  • Rotation to \(A\):

\(\theta =\frac{{C}_{1}}{\mathrm{4K}}\)

  • Moment in \(A\):

\(\begin{array}{}{M}_{\mathrm{AB}}=+\frac{{\mathrm{pl}}_{\mathrm{AB}}^{2}}{12}+{r}_{\mathrm{AB}}\mathrm{.}{C}_{1}\\ {M}_{\mathrm{AD}}=-\frac{{\mathrm{Fl}}_{\mathrm{AD}}}{8}+{r}_{\mathrm{AD}}\mathrm{.}{C}_{1}\\ {M}_{\mathrm{AE}}={r}_{\mathrm{AE}}\mathrm{.}{C}_{1}\\ {M}_{\mathrm{AC}}={r}_{\mathrm{AC}}\mathrm{.}{C}_{1}\end{array}\)

2.2. Benchmark results#

Value of rotation and moments in \(A\).

2.3. Bibliographical references#

  1. Guide VPCS - 1990 edition.