Yield Strength $\backslash (\backslash$sigma y$=345\backslash$mathrm$\{$MPa$\}\backslash )$

Tensile Strength $\backslash (\backslash$sigma $\backslash$mathbf$\{\backslash$sigma$\}=414\backslash$mathrm$\{$MPa$\}\backslash )$

Exercise $1$

For the structure in the figure:

$1.$ Find the reactions at the external supports and the normal force in the elastic element.

$2.$ Find the dimension $"\backslash ($ b $\backslash )".\backslash ($ b$=(\backslash$mathrm$\{$mm$\})\backslash )$

$3.$ Calculate the deformation of the rod.

You will use the equations of Statics to find the Horizontal and Veritcal ractions at the external support.

After you have to use the equation which hels you find the Normal Force in the elastic element. This means that ycu have to make the sum of the moments towards the support point. The only unknown will be the tension on the elastic element.

After finding the tension at the elastic element you have to write the Condition of Strength. The mechanical characteristic of the materials are given. Is given as well the coefficient of safety. The dimension b will be in mm $.$ It cannot be for example $3\mathrm{.}7$ mm $.$ It has to be $4.$

From $1$ to $10$ can be $1,2,3,4,5,6,7,8,9,10.$

From $10$ to $20$ can be $\backslash (10,12,14,15,16,18,20\backslash )$

From $10$ to $1000$ it will be every $5$ millimeters. And over $100$ every $10.$

Therefore, you cannot have a dimension $67$ mm but either $65$ or $70.$

You cannot have a dimension $213$ mm but either $210$ or $220.$

After you have to find the deformation of the rod in milimmeters. Should be a small number. Please be carefull when using the units.

$\backslash [$

$\backslash$Delta l$=\backslash$frac$\{$N l$\}\{$E A$\}$

$\backslash ]$

$\backslash (\backslash$Delta l $\backslash )-$ Deformation of the Rod

N $-$ Normal Force

$1-$ Length of the Rod

E $-$ Modul of Elasticity for the Rod Material

A $-$ Aria of the Cross Section of the Rod