A solid cylindrical shaft with a diameter of $45$ mm is subjected to a bending moment of $500$ Nm and a torque of $400$ Nm$.$ Determine the principal stresses and the maximum shear stress at a point on the surface of the shaft. A thin$-$walled cylindrical pressure vessel with an outer radius of $0\mathrm{.}3$ meters and a wall thickness of $15$ mm is subjected to an internal pressure of $3$ MPa. Calculate the hoop stress and the longitudinal stress in the wall of the vessel. A simply supported beam with a span of $5$ meters is subjected to a uniformly distributed load of $2$ kN$/$m$.$ Determine the maximum bending moment, shear force, and deflection at the midpoint of the beam if the beam has a rectangular cross$-$section of $100$ mm by $200$ mm$.$ A steel rod of $25$ mm diameter and $1\mathrm{.}5$ meters length is subjected to an axial tensile load of $35$ kN$.$ Calculate the elongation of the rod if the modulus of elasticity of steel is $210$ GPa. A cantilever beam of length $1$ meter is subjected to a point load of $8$ kN at its free end. Determine the slope and deflection at the free end of the beam. A circular disk with a radius of $0\mathrm{.}2$ meters is rotating at $1500$ rpm$.$ Calculate the centrifugal force acting on a mass of $0\mathrm{.}15$ kg located at the edge of the disk. A rectangular plate with a width of $200$ mm and a length of $400$ mm is subjected to a tensile load of $60$ kN$.$ Determine the stress and strain in the plate if the thickness is $8$ mm$.$ A cylindrical shaft with a diameter of $50$ mm is subjected to a torque of $1200$ 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 $6$ mm and a mean coil diameter of $60$ mm has $10$ active coils. Calculate the stiffness of the spring and the maximum shear stress in the wire when a load of $200$ N is applied. A simply supported beam with a span of $4$ meters is subjected to a point load of $12$ 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 $2\mathrm{.}5$ 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 $80$ mm by $40$ mm and the modulus of elasticity of steel is $210$ GPa.

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