A \(1800\,\mathrm{N}\) tensile force acts on cross-sectional area \(6.0\times10^{-4}\,\mathrm{m^2}\). Find the normal stress.

A \(1.8\,\mathrm{m}\) tie extends by \(0.72\,\mathrm{mm}\). Find the tensile strain.

A compressive force of \(900\,\mathrm{N}\) acts on area \(3.0\times10^{-4}\,\mathrm{m^2}\). Find the stress magnitude and state whether it is tensile or compressive.

A rod has length \(1.5\,\mathrm{m}\) and tensile strain \(4.0\times10^{-4}\). Find its extension.

A shear force of \(600\,\mathrm{N}\) acts on area \(2.0\times10^{-3}\,\mathrm{m^2}\). Find the shear stress.

A rectangular block of height \(0.20\,\mathrm{m}\) is sheared sideways by \(0.50\,\mathrm{mm}\). Find the shear strain.

Two rods carry the same tensile force. Rod A has twice the cross-sectional area of rod B. Compare their normal stresses and explain the physical meaning.

A circular wire of diameter \(1.2\,\mathrm{mm}\) carries \(150\,\mathrm{N}\). Find the tensile stress and compare it with a yield stress of \(180\,\mathrm{MPa}\).

A vertical cable supports a load \(P\). The cable has two equal-length sections in series: the upper section has area \(2A\), the lower section has area \(A\). Derive the stress in each section, state the assumption about internal force, and interpret which section controls yielding.

A tensile member has cross-sectional area \(A(x)=A_0(1+\alpha x/L)\) for \(0\le x\le L\), with \(\alpha>0\), and carries axial force \(F\). Derive \(\sigma(x)\), find the maximum stress, and give the symbolic no-yield condition for yield stress \(\sigma_y\). State assumptions and interpret the role of \(\alpha\).