A material has \(Y=150\,\mathrm{GPa}\) and yield stress \(300\,\mathrm{MPa}\). Find the yield strain in the linear elastic model.

Define plastic deformation in one sentence.

A part has yield stress \(240\,\mathrm{MPa}\) and safety factor \(3.0\). Find the allowable working stress.

A \(18\,\mathrm{kN}\) tensile load is carried by a material with yield stress \(360\,\mathrm{MPa}\) using safety factor \(2.5\). Find the minimum area from yield alone.

A material is loaded elastically to stress \(80\,\mathrm{MPa}\). Its Young modulus is \(160\,\mathrm{GPa}\). Find the elastic strain.

A stress-strain graph is linear up to \(\sigma_y\), then no longer follows the original line. Which stress is associated with first permanent deformation: yield stress or ultimate stress?

A specimen is loaded to stress below yield and then unloaded. Explain what happens to its strain and why.

A material with \(Y=100\,\mathrm{GPa}\) is loaded to total strain \(3.0\times10^{-3}\). On unloading, it follows slope \(Y\) from a maximum stress of \(200\,\mathrm{MPa}\). Find the permanent strain.

A rod of area \(A\) and length \(L\) is loaded to force \(F_{\max}\) beyond yield. At maximum load its measured total strain is \(\epsilon_{\max}\), and unloading is linear with slope \(Y\). Derive the permanent extension after unloading, state assumptions, and interpret the special case \(F_{\max}/A=Y\epsilon_{\max}\).

A tensile member must carry load \(F\), remain below yield stress \(\sigma_y\) with safety factor \(S\), and extend by no more than \(\delta_{\max}\) over length \(L\) with Young modulus \(Y\). Derive the symbolic minimum area and state which constraint controls in each parameter regime.