Ime len $56$:$\frac{3}{\text{:}}32$

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A circular shaft has a diameter $D=40mm$ and a length $L=1\mathrm{.}5m$ and is made of structural steel with elastic perfectly plastic behavior $95\mathrm{.}98$ GPa and $ty=120$MPa $).$ The shaft fixed at one end and subjected to a torque $T$ at the other end. The angle of twist is measured between the ends as $=0\mathrm{.}2$rad.

a$)$ Calculate the yield shear strain $yy.$

b$)$ Calculate the maximum shear strain ymax.

c$)$ Determine the radius py to the elastic$-$ plastic boundary. $$

d$)$ Determine the torque T$.$ If the member has yielded and then unloaded.

e$)$ Determine the residual shear stress at $=5mm.$

$\backslash$table$[[0\mathrm{.}001667$ rad $0\mathrm{.}0016774$ rad $0\mathrm{.}002$ rad $00\mathrm{.}0015$ rad $0\mathrm{.}00225$ rad$],[0\mathrm{.}002667$ rad $0\mathrm{.}001333$ rad $0\mathrm{.}004$ rad $0\mathrm{.}002$ rad $0\mathrm{.}002667$ rad$]]$

$12\mathrm{.}5026mm,12\mathrm{.}5806mm$

$12\mathrm{.}5026$ mm

$8\mathrm{.}3351$ mm

$16\mathrm{.}6701$ mm

$15$ mm

$11\mathrm{.}25$ mm

$\mathrm{.}16\mathrm{.}875$ mm

$2\mathrm{.}5171$ kN$.$m

$2\mathrm{.}0426kN.m$

$0\mathrm{.}17138kN.m$

$2\mathrm{.}6323kN.m$

$2\mathrm{.}2927$ kN$.$m

$2\mathrm{.}3981$ kN$.$m

$106\mathrm{.}6667$ MPa

$86\mathrm{.}6667$ MPa

$53\mathrm{.}33$ MPa

$80.$MPa

$120$ MPa