A cylindrical pressure vessel with an inner radius of $0\mathrm{.}4$ meters and a wall thickness of $12$ mm is subjected to an internal pressure of $5$ MPa. Determine the hoop stress and longitudinal stress in the wall of the vessel. A solid circular shaft with a diameter of $60$ mm is subjected to a combined bending moment of $700$ Nm and a torque of $600$ Nm$.$ Calculate the principal stresses and the maximum shear stress at a point on the surface of the shaft. A simply supported beam with a span of $3$ meters is subjected to a uniformly distributed load of $3$ kN$/$m$.$ Find the maximum bending moment, shear force, and deflection at the midpoint of the beam if the beam has a rectangular cross$-$section of $120$ mm by $240$ mm$.$ A steel rod of $30$ mm diameter and $1\mathrm{.}8$ meters length is subjected to an axial tensile load of $50$ kN$.$ Calculate the elongation of the rod if the modulus of elasticity of steel is $210$ GPa. A cantilever beam with a length of $1\mathrm{.}5$ meters is subjected to a point load of $10$ kN at its free end. Determine the slope and deflection at the free end of the beam. A circular disk with a radius of $0\mathrm{.}25$ meters is rotating at $1000$ rpm$.$ Calculate the centrifugal force acting on a mass of $0\mathrm{.}2$ kg located at the edge of the disk. A rectangular plate with a width of $150$ mm and a length of $300$ mm is subjected to a tensile load of $75$ kN$.$ Determine the stress and strain in the plate if the thickness is $10$ mm$.$ A cylindrical shaft with a diameter of $40$ mm is subjected to a torque of $800$ Nm$.$ Calculate the shear stress and the angle of twist per meter length of the shaft. A helical spring made of steel wire with a diameter of $7$ mm and a mean coil diameter of $70$ mm has $15$ active coils. Determine the stiffness of the spring and the maximum shear stress in the wire when a load of $250$ N is applied. A simply supported beam with a span of $6$ meters is subjected to a point load of $15$ kN at the midpoint. Find the maximum bending moment, shear force, and deflection at the midpoint of the beam. A steel column with a length of $3$ meters is pinned at both ends and subjected to a compressive load. Calculate the critical load and the factor of safety against buckling if the column has a rectangular cross$-$section of $120$ mm by $60$ mm and the modulus of elasticity of steel is $210$ GPa. What is data modelling.