$1.$ A beam of rectangular cross$-$section $60$ mm $100$ mm is subjected to an axial tensile load of $60000$ N$.$ If the material of the beam fails in simple tension at a stress of $150$ N$/$mm$2$ determine the maximum shear force that can be applied to the beam section in a direction parallel to its longest side using the Tresca and Von Mises theories of elastic failure.