Introduction: EXECUTIVE SUMMARY: Many famous scientists have left us much to appreciate and be grateful for their work. If anyone thinks about how much the mysteries of the world are clearer to us today precisely based on what they have left behind. It's amazing how technology and science are moving forward every single day. "Standing on the shoulders of giants." The following task was divided into 3 main parts. 1: Isostatic and Hyperstatic. Isostatics also called determinate systems are those that can allow us to calculate all given unknown forces. Hyperstatic systems, also called indeterminate, are those that do not allow us to calculate all the unknowns using the three equilibrium equations.2: Hooke's Law, Poisson's Ratio and Modulus of Rigidity. Hooke's Law, Poisson's Ratio, and shear modulus (stiffness modulus) all share a common link. They are individually considered equal for a specific material. Hooke's law is formulated as F=kx; Poisson's ratio is formulated as = (lateral strain / axial strain) and the shear modulus is formulated as G= E/(2(1+" " )).3: polar moment of inertia and torsion angle. Determining Systems: (ISO-STATIC) A system is considered statically determined if the support reaction or unknown forces can be calculated from all three forces of the equilibrium equations. The equations can be solved independently. The equations are the following: ∑x forces = 0∑y forces= 0∑ moments around a point= 0Some examples of isostaticity are: cantilever beams, supported beams, arches. Indeterminate Systems: (HYPERSTATIC) :A system is considered statically indeterminate if the unknown forces exceed the number of e...... center of the paper...... proportional to the shear modulus and polar moment of inertia. Below is an example of torsion angle: Torsion velocity: Torsion velocity is formulated as: dφ/dx = T/(G(Ip)) It is directly proportional to torque and inversely proportional to torsional stiffness (G*Ip ). References: Mechanics of Material 8th Edition (RC Hibbeler)Mechanics of Materials pg:52 (James Gere & Barry Goodno)Plastic Engineering Handbook and Production (Volume 2) (Dominik V Rosato, Donald V Rosato, Nick R Schott) PAGE: 1300 -1303Engineering Physics 2nd edition ( K Rajagopal) PAGE: 7-12Mechanics of Material 3rd edition (Roy R Craig Jr)Mechanics of Material 2nd edition SI (Andrew Pytoll and Jaan Musalaas) PAGE: 342Mechanics of Material 8th edition (James M.Gere and Barry J.Goodno)Structural and Stress Analysis Publishers Arnold (THG Megson) PAGE: 158