Knowledge area 8 of the FE Mechanical exam: 9–14 of the 110 questions. The subtopics NCEES lists, how they are tested and worked practice problems with solutions.
110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.
Or start the free Mechanics of Materials drillFrom the NCEES FE Mechanical CBT exam specifications, knowledge area 8.
Mechanics of materials questions are short stress and deformation calculations: axial, torsion, bending, transverse shear, thermal, combined stress and column buckling. Know which formula applies to which loading and keep units consistent; the Reference Handbook section on mechanics of materials lists the beam deflection cases and the stress formulas.
On exam day the relationships you need are in the Reference Handbook section on Mechanics of Materials. The handbook is the only reference allowed, so practice finding each formula in it rather than memorizing a separate sheet.
Work each problem with your calculator and the handbook, then open the solution.
Problem 1 · Deformations
A steel cantilever 2.0 m long carries a 5 kN point load at its free end. Use E = 200 GPa and I = 8.0 × 10⁶ mm⁴. Neglecting self-weight, the tip deflection is most nearly:
Answer: C: 8.33 mm
For an end-loaded cantilever δ = PL³/(3EI) = 5000(2.0)³/[3(200 × 10⁹)(8.0 × 10⁻⁶)] = 0.00833 m = 8.33 mm. Note I = 8.0 × 10⁶ mm⁴ = 8.0 × 10⁻⁶ m⁴.
Deformations · Reference Handbook: Mechanics of Materials
Problem 2 · Stress transformations and Mohr's circle
Select all that apply.
For a general state of plane stress analyzed with Mohr's circle, which of the following statements are true? Select all that apply.
Answer: A: The shear stress on the principal planes is zero; B: The planes of maximum in-plane shear stress are oriented 45° from the principal planes; D: The sum σx + σy is the same for every rotated orientation of the element
Principal planes lie where the circle crosses the σ axis, so their shear stress is zero. Maximum shear is at the top and bottom of the circle, 90° on the circle and therefore 45° on the element from the principal planes, and the normal stress there is the center value (σx + σy)/2, which is zero only in special cases. σx + σy is an invariant equal to twice the center coordinate. Mohr's circle angles are double the physical rotation.
Stress transformations and Mohr's circle · Reference Handbook: Mechanics of Materials
Problem 3 · Stress and strain caused by shear
A rectangular steel bar used as a short beam is 60 mm wide and 200 mm deep. At a section where the vertical shear force is 18 kN, the maximum transverse shear stress is most nearly:
Answer: C: 2.25 MPa
For a rectangle the maximum shear stress at the neutral axis is τ = VQ/(Ib) = 3V/(2A) = 1.5(18,000 N)/(0.060 × 0.200 m²) = 2.25 MPa. The average V/A = 1.50 MPa underestimates the peak by a third.
Stress and strain caused by shear · Reference Handbook: Mechanics of Materials
Problem 4 · Shear and moment diagrams
A simply supported beam spans 6 m between supports A and B. A single 40 kN point load acts 2 m from support A. Neglecting self-weight, the maximum absolute shear force in the beam is most nearly:
Answer: C: 26.7 kN
Summing moments about B: R_A(6) = 40(4), so R_A = 26.67 kN and R_B = 13.33 kN. The shear diagram is +26.7 kN from A to the load and −13.3 kN from the load to B, so the maximum shear is 26.7 kN. The 13.3 kN option is the smaller reaction; the larger reaction is always at the support nearer the load.
Shear and moment diagrams · Reference Handbook: Mechanics of Materials
More FE Mechanical practice problems from every knowledge area
Sit the full exam under the real clock
110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.
Or start the free Mechanics of Materials drillThe NCEES FE Mechanical specification lists 9–14 questions on Mechanics of Materials, out of 110. Every examinee gets the same number per knowledge area.
Shear and moment diagrams; Stress transformations and Mohr’s circle; Stress and strain caused by axial loads; Stress and strain caused by bending loads; Stress and strain caused by torsional loads; Stress and strain caused by shear; Stress and strain caused by temperature changes; Combined loading; Deformations; Column buckling; Statically indeterminate systems.
In the NCEES FE Reference Handbook, which appears on screen during the exam: the Mechanics of Materials section. Practice with your free copy from MyNCEES so you know where each relationship sits.
Original independent practice questions written to the published NCEES exam specifications. Not affiliated with or endorsed by NCEES (National Council of Examiners for Engineering and Surveying).