A hollow cylindrical shaft with an outer diameter of $80$ mm and an inner diameter of $60$ mm is subjected to a bending moment of $900$ Nm and a torque of $700$ Nm$.$ Calculate the maximum 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 $0\mathrm{.}5$ meters and a wall thickness of $20$ mm is subjected to an internal pressure of $6$ MPa. Determine the hoop stress and longitudinal stress in the wall of the vessel. A simply supported beam with a span of $4\mathrm{.}5$ meters is subjected to a uniformly distributed load of $2\mathrm{.}5$ kN$/$m$.$ Calculate the maximum bending moment, shear force, and deflection at the midpoint of the beam if the beam has a rectangular cross$-$section of $150$ mm by $300$ mm$.$ A steel rod with a diameter of $40$ mm and a length of $2\mathrm{.}5$ meters is subjected to an axial tensile load of $50$ kN$.$ Determine the elongation of the rod, given that the modulus of elasticity of steel is $210$ GPa. A cantilever beam of length $2$ meters is subjected to a point load of $15$ kN at its free end. Compute 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 $1500$ rpm$.$ Determine the centrifugal force acting on a mass of $0\mathrm{.}25$ kg located at the edge of the plate. A rectangular plate with a width of $300$ mm and a length of $600$ mm is subjected to an axial tensile load of $100$ kN$.$ Calculate the stress and strain in the plate if the thickness is $15$ mm$.$ A cylindrical shaft with a diameter of $65$ mm is subjected to a torque of $1800$ Nm$.$ Determine 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 $8$ mm and a mean coil diameter of $80$ mm has $20$ active coils. Calculate the stiffness of the spring and the maximum shear stress in the wire when a load of $300$ N is applied. A simply supported beam with a span of $8$ meters is subjected to a point load of $20$ 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 $5$ 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 $140$ mm by $70$ mm and the modulus of elasticity of steel is $210$ GPa.

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