A solid cylindrical shaft with a diameter of $90$ mm is subjected to a bending moment of $1000$ Nm and a torque of $800$ Nm$.$ Calculate 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 $0\mathrm{.}6$ meters and a wall thickness of $25$ mm is subjected to an internal pressure of $7$ MPa. Determine the hoop stress and longitudinal stress in the wall of the vessel. A simply supported beam with a span of $5\mathrm{.}5$ meters is subjected to a uniformly distributed load of $3$ 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 $200$ mm by $400$ mm$.$ A steel rod of $35$ mm diameter and $3$ meters length is subjected to an axial tensile load of $60$ kN$.$ Calculate the elongation of the rod, given that the modulus of elasticity of steel is $210$ GPa. A cantilever beam of length $1\mathrm{.}8$ meters is subjected to a point load of $12$ kN at its free end. Determine the slope and deflection at the free end of the beam. A circular plate with a radius of $0\mathrm{.}4$ meters is rotating at $2000$ rpm$.$ Calculate the centrifugal force acting on a mass of $0\mathrm{.}3$ kg located at the edge of the plate. A rectangular plate with a width of $350$ mm and a length of $700$ mm is subjected to an axial tensile load of $120$ kN$.$ Determine the stress and strain in the plate if the thickness is $20$ mm$.$ A cylindrical shaft with a diameter of $75$ mm is subjected to a torque of $2000$ 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 $9$ mm and a mean coil diameter of $90$ mm has $25$ active coils. Compute the stiffness of the spring and the maximum shear stress in the wire when a load of $350$ N is applied. A simply supported beam with a span of $6$ meters is subjected to a point load of $18$ 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 $6$ 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 $160$ mm by $80$ mm and the modulus of elasticity of steel is $210$ GPa.

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