Answer Happy

Problem 1 (33 points) A way to make artificial diamond is to squeeze carbon atoms under intense pressure: about 725,000 Psi (∼5,000MPa). The intense temperature and pressure bond the carbon atoms to each other in a unique arrangement: one carbon atom to four other carbon atoms. A scientist seeks to invent a method to make diamond applying much lower pressure. In one of his experiments, he uses an environmental bubble that applies stresses in the range of 50−100MPa. The equipment to make the diamond has a component formed by fusing three mutually perpendicular rods A,B,C at their mid-length, and each rod can twist independently. According to the scientist's calculation, this component gets its stresses from 4 external loads, which are applied simultaneously during the experiment. Torsion load on rod A gives: τxy​=23MPa Torsion load on rod B gives: τyz​=26MPa Torsion load on rod C gives: τzx​=21MPa Loading from the environmental bubble gives: σx​=−100MPaσy​=−90MPa,σz​=−97MPa, (a) Determine the principal normal stresses σ1​,σ2​ and σ3​. Use σ1​ to denote the largest principal normal stress, and σ3​ to denote the smallest, i.e., σ1​>σ2​>σ3​. (b) Determine the ultimate strength σu​ of the material that will give a safety factor against fracture of 4.0 when the Maximum Normal Stress Fracture Criterion is used.