$1$ Beams & trusses $(8$ points$)$

A commonly used streetlight arrangement is shown in Figure $1.$ Assuming fixed nodes, approximate the vertical

displacement, $d,$ of the lamp for the $2$ different configurations:

Considering only the tubes $($shown in blue$)$ without the tie $($shown in red$)$;

With the tie.

The weight of the structural elements can be neglected. Given the differences between the stiffness, the

masonry wall can be directly considered infinitely rigid.

Figure $1$: Streetlight

Solution :

Configuration $1,d-3\mathrm{.}23mm$

Configuration $2,d-0\mathrm{.}175mm$