A solid cylindrical shaft with a diameter of $70$ mm is subjected to a bending moment of $800$ Nm and a torque of $600$ Nm$.$ Calculate the principal stresses, maximum shear stress, and the equivalent von Mises stress at a point on the surface of the shaft. A thin$-$walled cylindrical pressure vessel with an outer radius of $0\mathrm{.}4$ meters and a wall thickness of $18$ mm is subjected to an internal pressure of $5$ MPa. Determine the hoop stress and longitudinal stress in the wall of the vessel. A simply supported beam with a span of $6$ meters is subjected to a uniformly distributed load of $1\mathrm{.}5$ kN$/$m$.$ Compute the maximum bending moment, shear force, and deflection at the midpoint of the beam, assuming a rectangular cross$-$section with a width of $120$ mm and a height of $240$ mm$.$ A steel rod of $30$ mm diameter and $2$ meters length is subjected to an axial tensile load of $40$ kN$.$ Calculate the elongation of the rod given that the modulus of elasticity of steel is $210$ GPa. A cantilever beam of length $1\mathrm{.}5$ 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 $1800$ 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 $250$ mm and a length of $500$ mm is subjected to a tensile load of $90$ kN$.$ Determine the stress and strain in the plate if the thickness is $12$ mm$.$ A cylindrical shaft with a diameter of $55$ mm is subjected to a torque of $1400$ 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. Calculate 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 $7$ meters is subjected to a point load of $15$ kN at the midpoint. Determine the maximum bending moment, shear force, and deflection at the midpoint of the beam. A steel column with a length of $4$ meters is pinned at both ends and subjected to a compressive load. Determine 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.

Explain the concept of a digital twin