A hollow cylindrical shaft with an outer diameter of $100$ mm and an inner diameter of $80$ mm is subjected to a bending moment of $1200$ Nm and a torque of $1000$ Nm$.$ Determine the principal stresses, maximum shear stress, and von Mises stress at a point on the surface of the shaft. A thin$-$walled cylindrical pressure vessel with an outer radius of $0\mathrm{.}45$ meters and a wall thickness of $10$ mm is subjected to an internal pressure of $8$ MPa. Calculate the hoop stress and longitudinal stress in the wall of the vessel. A simply supported beam with a span of $7$ meters is subjected to a uniformly distributed load of $4$ kN$/$m$.$ Compute the maximum bending moment, shear force, and deflection at the midpoint of the beam if the beam has a rectangular cross$-$section of $250$ mm by $500$ mm$.$ A steel rod with a diameter of $50$ mm and a length of $2$ meters is subjected to an axial tensile load of $70$ kN$.$ Calculate the elongation of the rod, given that the modulus of elasticity of steel is $210$ GPa. A cantilever beam of length $2\mathrm{.}2$ meters is subjected to a point load of $20$ kN at its free end. Determine the slope and deflection at the free end of the beam. A circular plate with a radius of $0\mathrm{.}35$ meters is rotating at $2500$ rpm$.$ Calculate the centrifugal force acting on a mass of $0\mathrm{.}4$ kg located at the edge of the plate. A rectangular plate with a width of $400$ mm and a length of $800$ mm is subjected to an axial tensile load of $150$ kN$.$ Determine the stress and strain in the plate if the thickness is $25$ mm$.$ A cylindrical shaft with a diameter of $85$ mm is subjected to a torque of $2200$ 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 $10$ mm and a mean coil diameter of $100$ mm has $30$ active coils. Compute the stiffness of the spring and the maximum shear stress in the wire when a load of $400$ N is applied. A simply supported beam with a span of $6\mathrm{.}5$ meters is subjected to a point load of $25$ kN at the midpoint. Calculate the maximum bending moment, shear force, and deflection at the midpoint of the beam. A steel column with a length of $7$ 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 $180$ mm by $90$ mm and the modulus of elasticity of steel is $210$ GPa.

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