There is a structure composed of multiple beams that support distributed and concentrated loads. The beams are made of a specific material, and it has been observed that some of them are experiencing excessive deformations and, in some cases, failures. The objective is to determine the maximum stress present in the beams that are experiencing problems, to evaluate their load capacity and design solutions to avoid future failures.

Problem Data:

$1.$ Structure geometry:

$-$ Total length of the structure: L $=10$ meters.

$-$ Cross section of the beams: Rectangular, with dimensions $20$ cm wide and $40$ cm high.

$-$ Arrangement of the beams: There are three beams equidistant from each other, $3\mathrm{.}33$ meters apart.

$2.$ Material properties:

$-$ Beams material: Structural steel.

$-$ Modulus of elasticity of steel E: $200$ GPa.

$-$ Elastic limit of steel $250$ MPa.

$-$ Ultimate strength of steel $400$ MPa.

$-$ Concentrated load: P $=50$ kN $($applied at the midpoint of the beam$).$

$-$Safety factor FS: $1\mathrm{.}5($a safety margin of $50\%$ is desired$).$