Problem $1$:

Solve step by step using legible handwriting, if you wish you can use python. Explaining

the transformation matrices, and writing the formulas.

The truss shown in the figure is made up of $3$ elements of linear elastic material with

elasticity modulus $E=2^{**}{10}^8,$ whose cross sections are constant.

a$)$ Using the stiffness method, determine the Force $F$ applied at node $3$ so that the

displacement of that point is $d_{{?}_{?}}0\mathrm{.}05$mmi,$0\mathrm{.}15mmj.$

b$)$ For the previously obtained force F$,$ calculate the reactions of the structure in global

coordinates.

b$)$ Axial force at any given moment.

D$)$ Nodal displacements in global coordinates.

Answers

vec$(F)=(37\mathrm{.}4553$vec$(i)-178\mathrm{.}4199$vec$(j))kN$

$\{[F{x}_1$

$F{Y}_1$

$F{x}_2$

$F{Y}_2]\}=\{[47\mathrm{.}0549$

$39\mathrm{.}4838$

$-84\mathrm{.}5102$

$138\mathrm{.}9361]\}kN$