Please solve these exercises in as much detail as possible with drawing$\mathrm{.}2\mathrm{.}2$ At the critical point of a design element the displayed stresses ${}_x,$

${}_y$ and ${}_{xy}$ were determined $($values in $\frac{N}{m}{m}^2).$ Determine with the help of

Mohr's Circle and analytically the extreme values of normal stress ${}_{\text{m}\text{a}\text{x}}$ and

${}_{\text{m}\text{i}\text{n}}$ of shear stress $|{|}_{\text{m}\text{a}\text{x}}$ and their orientation relative to the $x-$axes and

the stresses ${}_x^{**}$;${}_y^{**}$ and ${}_{xy}^{**}$ at an angle of $=60!$ What are the equivalent

stresses ${}_{\text{e}\text{q}\text{N}}($Tensile Stress Hypothesis$),{}_{\text{e}\text{q}\text{s}}($Shear Stress Hypothesis$),$

${}_{\text{e}\text{q}\text{v}\text{m}}($van Mises Criterion$)?$

$3\mathrm{.}1$ Calculate the the elongation $L,$ the width change $b,$ the height change $h,$ the coss section

change $A,$ and the volume change $V$ of rod $1$ in exercise $1\mathrm{.}1.(L_1=500mm,S_1=15kN,b=20mm,$

$s=10mm,$ Elasticity Modulus $E=210000\frac{N}{m}{m}^2,$ Poisson's number $v=0\mathrm{.}3)$

$3\mathrm{.}2$ Three steel rods $,$

$E=210000\frac{N}{m}{m}^2)$ are mounted $a)$ in series and b$)$ parallel. Calculate the

forces $F_i$ and the compression stresses ${}_p$ inside the rods and the

displacement $u$ of the acting point of force $F=3600N.$

$3\mathrm{.}3$ Stress calculations at a critical point of an design element made of steel

$($Elasticity Modulus $E=210000\frac{N}{m}{m}^2,$ Poisson's number $v=0\mathrm{.}3,$ shear modulus

operating temperature is $T=25C$ higher than the environmental temperature.

Wanted are the rel. elongations ${}_x,{}_y,{}_z,$ and the shear angle $.$

$4\mathrm{.}1$ A M$20$ screw is fastened using a two lever socket wrench at a torque of

$M_t=400Nm.$ Determine the lever length a for a driving force of $F=250N,$ the