(a) determine the maximum tensile stress, the maximum compressive stress, and the maximum shear stress; and (b) show the stresses determined in Part (a) on properly oriented stress elements (e.g., see Fig. 4.14).

Consider a metal bar of length L, cross-sectional area A, and Young's modulus Y. When a tension force F is applied to the bar, it causes an extension AL. Model the material as a cubic lattice, where the atoms lie at the corners of the cubes and are connected by springs with equilibrium length x. Calculate the force constant k of the atomic springs by deriving expressions for (1) the number of atoms in any cross-sectional area, (2) the number of atoms in a single chain of length L, (3) the microscopic extension Ax between atoms, (4) the tensile force f between atoms, (5) write f = kAr and show that k = Yr, (6) calculate the value of k for a typical metal such as aluminum, for which Y = 70 GN/m² and x = 0.4 nm.

A disk between vertebrae in the spine is subjected to a shearing force of 600 N. Find its shear deformation, taking it to have the shear modulus of 1X10 N/m. The disk is equivalent to a solid cylinder 0.700 cm high and 4.00 cm in diameter.

Find the elongation of a rod made of aluminum and copper under a tension of 5.8×103 N. The dimensions of the rod are R=0.5 cm, LAl=10.5 m, LCu=5.5 m (Young moduli are 7.0×1010 Pa for Al and 11×1010 Pa for Cu)