A solid cylindrical shaft is subjected to a bending moment of $400$ Nm and a torque of $250$ Nm$.$ Determine the principal stresses and the maximum shear stress at a point on the surface of the shaft. A flat plate with an elliptical hole in the center is subjected to an axial tensile load. If the plate is made of aluminum with a yield strength of $300$ MPa, calculate the maximum stress concentration factor and the stress at the edge of the hole. A rectangular beam is simply supported at both ends and subjected to a uniformly distributed load. Calculate the maximum bending stress and the deflection at the midpoint of the beam. A steel rod of $15$ mm diameter is subjected to a tensile load of $20$ kN$.$ Determine the elongation of the rod if the length of the rod is $1\mathrm{.}5$ meters and the modulus of elasticity of steel is $210$ GPa. A cantilever beam with a length of $1\mathrm{.}5$ meters is subjected to a point load at its free end. Determine the slope and deflection at the free end of the beam. A thin$-$walled cylindrical pressure vessel with a radius of $0\mathrm{.}6$ meters and a wall thickness of $12$ mm is subjected to an internal pressure of $1\mathrm{.}5$ MPa. Calculate the hoop stress and the longitudinal stress in the wall of the vessel. A solid circular shaft of diameter $45$ mm is subjected to a torque of $900$ Nm$.$ Calculate the shear stress and the angle of twist per meter length of the shaft. A simply supported beam with a span of $5$ meters is subjected to a point load at the midpoint. Determine the maximum bending moment, shear force, and deflection at the midpoint. A rectangular plate with a width of $150$ mm and a length of $300$ mm is subjected to a uniform axial tensile load. Calculate the stress and strain in the plate if the load is $70$ kN and the thickness of the plate is $6$ mm$.$ 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. A helical spring made of steel wire with a diameter of $4$ mm and a mean coil diameter of $40$ mm has $8$ active coils. Calculate the stiffness of the spring and the maximum shear stress in the wire when a load of $120$ N is applied. A cylindrical pressure vessel with a closed end is subjected to an internal pressure of $4$ MPa. If the vessel has an inner radius of $0\mathrm{.}25$ meters and a wall thickness of $15$ mm$,$ calculate the hoop stress, longitudinal stress, and radial stress in the wall of the vessel. A rectangular beam with a width of $40$ mm and a height of $80$ mm is subjected to a bending moment of $1500$ Nm$.$ Determine the maximum bending stress and the location of the neutral axis. A steel rod with a diameter of $25$ mm and a length of $1$ meter is subjected to a torque of $450$ Nm$.$ Calculate the shear stress and the angle of twist per meter length of the rod. A circular disk with a radius of $0\mathrm{.}08$ meters is rotating at a speed of $800$ rpm$.$ Determine the centrifugal force acting on a small mass of $0\mathrm{.}08$ kg located at the edge of the disk. A rectangular plate with a width of $180$ mm and a length of $360$ mm is subjected to a uniform axial compressive load. Calculate the critical buckling load and the factor of safety against buckling if the plate has a thickness of $9$ mm and is simply supported along its edges. A cylindrical shaft with a diameter of $30$ mm and a length of $0\mathrm{.}8$ meters is subjected to a bending moment of $400$ Nm and an axial compressive load of $15$ kN$.$ Determine the principal stresses and the maximum shear stress at a point on the surface of the shaft. A simply supported beam with a span of $6$ meters is subjected to a uniformly distributed load. Calculate the maximum bending moment, shear force, and deflection at the midpoint of the beam. A steel rod with a diameter of $20$ mm and a length of $1\mathrm{.}2$ meters is subjected to an axial tensile load of $25$ kN$.$ What is machine learning