2. Benchmark solution#

2.1. Calculation method used for the reference solution#

_images/Object_7.svg

The ruin of the beam occurs when there are plastic joints at points \(A\), \(D\) and \(E\) (figure b). The static equilibrium of the left half of the beam makes it possible to determine the limit pressure (figure c)

_images/Object_8.svg

=>

_images/Object_9.svg

where:

\({q}_{L}\) represents the limit pressure

\({M}_{p}\) represents the plastic moment (

_images/Object_10.svg

)

The appearance of the first plastic dot on the outer fiber of the beam takes place at points \(A\) and \(D\), the other fibers being in an elastic regime. The elastic limit pressure is

_images/Object_11.svg

.

2.2. Benchmark results#

Pressure limit \({q}_{L}\mathrm{=}39166.67N\mathrm{/}m\)

2.3. Uncertainties about the solution#

Analytical solution

2.4. Bibliographical references#

  1. WILLIAM A. NASH: Theory and Problems of Strength of Material, Schaum’s Outline Series, 2/Ed, Mc GRAW - HILL