2. Benchmark solution#

2.1. Reference quantities and results#

Arrow to \(B\) next \(Z\)	Arrow to \(B\) next	Arrow to next \(Y\)
\({\delta }_{z}=\frac{{F}_{z}\mathrm{.}{L}^{3}}{2E{I}_{y}}\)	\({\delta }_{y}=\frac{{F}_{y}\mathrm{.}{L}^{3}}{2E{I}_{z}}\)

Stress at a point \(C\) with coordinates \(({v}_{y},{v}_{z})\) of the section of the beam

\[\]

: label: EQ-None

sigma =frac {N} {S} +frac {{M} _ {y}} {{I} _ {y}}}mathrm {.} {v} _ {z} -frac {{M} _ {z}} {{z}} {{I} _ {z}}mathrm {.} {v} _ {y}

from where:

\(\sigma =\frac{N}{S}-\frac{3E\mathrm{Lo}}{{L}^{3}}({\delta }_{y}{v}_{y}+{\delta }_{z}{v}_{z})\) [éq2.1-1]

[1] « Project M7-01-72. Elasto-plastic behavior of beams. New approach. » Note HM77 /01/140/A.