Practice Problems: Stress Analysis
Question 1
A mechanical engineer is designing a pressure vessel for an industrial application. The cylindrical vessel has an internal diameter of 48 inches and a wall thickness of 0.5 inches. The vessel is subjected to an internal pressure of 800 psi. Using thin-walled pressure vessel theory, what is the hoop stress in the vessel wall?
(a) 19,200 psi
(b) 38,400 psi
(c) 9,600 psi
(d) 28,800 psi
Question 2
A structural engineer is analyzing a simply supported steel beam with a rectangular cross-section. The beam has a width of 6 inches and a height of 12 inches. It spans 20 feet and carries a uniformly distributed load of 2,000 lb/ft. What is the maximum bending stress in the beam?
(a) 8,333 psi
(b) 10,417 psi
(c) 12,500 psi
(d) 6,944 psi
Question 3
A design engineer is evaluating a solid circular shaft that transmits 150 hp at 1,200 rpm. The allowable shear stress for the shaft material is 8,000 psi. What is the minimum required shaft diameter to ensure safe operation?
(a) 1.75 inches
(b) 2.15 inches
(c) 1.95 inches
(d) 2.35 inches
Question 4
A manufacturing engineer is analyzing a steel bracket subjected to a tensile load of 25,000 N. The bracket has a through-hole with a diameter of 20 mm drilled through its center. The plate width is 80 mm and the thickness is 12 mm. What is the maximum tensile stress at the net section?
(a) 34.7 MPa
(b) 26.0 MPa
(c) 41.7 MPa
(d) 52.1 MPa
Question 5
A pressure vessel engineer is designing a spherical tank with an internal diameter of 3 meters and a wall thickness of 25 mm. The tank will operate at an internal pressure of 2.5 MPa. What is the hoop stress developed in the vessel wall?
(a) 37.5 MPa
(b) 75.0 MPa
(c) 50.0 MPa
(d) 25.0 MPa
Question 6
A mechanical engineer is analyzing a cantilever beam with a length of 8 feet. The beam has a rectangular cross-section of 4 inches wide by 8 inches deep. A concentrated load of 5,000 lb is applied at the free end. What is the maximum bending stress in the beam?
(a) 11,250 psi
(b) 22,500 psi
(c) 16,875 psi
(d) 28,125 psi
Question 7
A component designer is evaluating a steel pin in double shear. The pin diameter is 0.75 inches and it supports a total load of 18,000 lb. What is the average shear stress in the pin?
(a) 20,372 psi
(b) 10,186 psi
(c) 15,279 psi
(d) 25,465 psi
Question 8
A mechanical engineer is designing a hollow circular shaft with an outer diameter of 100 mm and an inner diameter of 80 mm. The shaft is subjected to a torque of 8 kN·m. What is the maximum shear stress in the shaft?
(a) 72.8 MPa
(b) 54.6 MPa
(c) 91.0 MPa
(d) 36.4 MPa
Question 9
A structural engineer is analyzing a steel column with a solid circular cross-section of 6 inches diameter and a length of 15 feet. The column is pinned at both ends and made of steel with E = 29,000 ksi. What is the critical buckling load using Euler's formula?
(a) 246 kips
(b) 328 kips
(c) 164 kips
(d) 410 kips
Question 10
A pressure vessel engineer is analyzing a cylindrical pressure vessel with an internal radius of 500 mm and wall thickness of 15 mm. The vessel is subjected to an internal pressure of 3.0 MPa. What is the longitudinal stress in the vessel wall?
(a) 50 MPa
(b) 100 MPa
(c) 75 MPa
(d) 25 MPa
Question 11
A machine designer is evaluating a steel bolt subjected to an axial tensile load of 12,000 lb. The bolt has a nominal diameter of 0.75 inches and the tensile stress area is 0.334 in². What is the tensile stress in the bolt?
(a) 27,500 psi
(b) 35,928 psi
(c) 16,000 psi
(d) 42,735 psi
Question 12
A structural engineer is designing a beam with an I-shaped cross-section. The beam has a moment of inertia of 850 in⁴ and the distance from the neutral axis to the extreme fiber is 10 inches. The beam is subjected to a bending moment of 425,000 lb-in. What is the maximum bending stress?
(a) 3,750 psi
(b) 5,000 psi
(c) 4,250 psi
(d) 6,500 psi
Question 13
A mechanical engineer is analyzing a component under biaxial stress state. The principal stresses are σ₁ = 80 MPa and σ₂ = 30 MPa. Using the maximum shear stress theory (Tresca criterion), what is the maximum shear stress in the component?
(a) 40 MPa
(b) 25 MPa
(c) 55 MPa
(d) 50 MPa
Question 14
A design engineer is evaluating a rectangular beam with width b = 150 mm and height h = 300 mm. The beam is subjected to a maximum shear force of 75 kN. What is the maximum shear stress in the beam cross-section?
(a) 1.67 MPa
(b) 2.50 MPa
(c) 1.11 MPa
(d) 3.33 MPa
Question 15
A mechanical engineer is analyzing a state of plane stress where σₓ = 60 MPa, σᵧ = 20 MPa, and τₓᵧ = 15 MPa. What is the magnitude of the maximum principal stress?
(a) 66.1 MPa
(b) 54.7 MPa
(c) 72.0 MPa
(d) 48.3 MPa
Question 16
A structural engineer is designing a fixed-fixed beam with length L = 6 meters carrying a uniformly distributed load of 15 kN/m. What is the maximum bending moment in the beam?
(a) 45 kN·m
(b) 67.5 kN·m
(c) 90 kN·m
(d) 33.75 kN·m
Question 17
A mechanical engineer is evaluating a cast iron component under combined loading with a tensile stress of 50 MPa and a compressive stress of -30 MPa acting on perpendicular planes. The shear stress is zero. Using Mohr's circle analysis, what is the radius of Mohr's circle?
(a) 40 MPa
(b) 20 MPa
(c) 30 MPa
(d) 10 MPa
Question 18
A pressure vessel engineer is analyzing a thin-walled cylindrical tank with an internal pressure of 1,200 psi, internal diameter of 36 inches, and wall thickness of 0.375 inches. What is the ratio of hoop stress to longitudinal stress in the vessel?
(a) 1.5
(b) 2.0
(c) 1.0
(d) 0.5
Question 19
A machine designer is analyzing a welded connection where a force of 50 kN is applied at an eccentricity of 200 mm from the centroid of a weld group. The polar moment of inertia of the weld group about its centroid is 2.5 × 10⁶ mm³. What is the maximum torsional shear stress at a point 100 mm from the centroid?
(a) 400 MPa
(b) 200 MPa
(c) 600 MPa
(d) 800 MPa
Question 20
A structural engineer is designing a steel plate connection with three bolts in a line. Each bolt has a diameter of 0.875 inches. The connection transfers a tensile load of 60,000 lb. Assuming equal load distribution, what is the tensile stress in each bolt?
(a) 33,333 psi
(b) 42,105 psi
(c) 28,947 psi
(d) 52,632 psi
