Calculate the minimum radius that the piston must have so that it does not deform plastically under the indicated load 2) Calculate the contraction in the length of the bar when the load is applied

To manufacture a piston with a circular cross section, an alloy steel bar is required whose length is fixed and has a value of 35 cm and must withstand a compression load of 5.2 tons. For its design, a safety factor of 4/5 is suggested with respect to the yield stress. The shear modulus for that alloy is 80 GPa.

To know the resistance of this steel alloy, a compression test was carried out on a specimen of the same material, from this test the data table of stress against engineering deformation shown was obtained.

1) Calculate the minimum radius that the piston must have so that it does not deform plastically under the indicated load
2) Calculate the contraction in the length of the bar when the load is applied