Mechanical Design and Analysis is 10-15 questions on the FE Mechanical exam, tied for the largest knowledge area. It is also the most distinctly mechanical part of the paper: nothing equivalent appears on FE Civil.
Every question here is downstream of something else. The stress comes from mechanics of materials, the material limit comes from material properties, and the loading comes from statics. Study it last and it takes half the time.
Exam weight: NCEES lists Mechanical Design and Analysis at 10-15 questions of the 110-question FE Mechanical exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Mechanical Design and Analysis
The specification covers stress analysis of machine elements, failure theories and failure prevention, deformation and stiffness, pressure vessels and piping, bearings, power screws, power transmission, joining methods, manufacturability, quality and reliability, and components such as springs, gears, clutches and brakes.
Failure theories are the backbone: maximum shear stress and distortion energy for ductile materials, and fatigue analysis using the endurance limit with stress concentration and surface factors. Expect a thin-walled pressure vessel hoop and longitudinal stress calculation, a bolted joint sized against a load, and a gear or belt drive ratio.
5 Free Mechanical Design and Analysis Practice Problems
Each mechanical design problem below comes from the FEExamClick FE Mechanical question bank, with worked solutions, and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — Springs
A helical compression spring has a spring rate of 25 N/mm and a free length of 80 mm. If the spring is compressed to a length of 56 mm, the compressive force (N) is most nearly:
Answer: B) 600
Refer to the Springs section (p. 436) in the Mechanical Engineering chapter of the FE Reference Handbook.
\(F = k \times \delta = 25 \times (80 - 56) = 25 \times 24 = 600\) N
Problem 2 — Quality and reliability
Components A and B are in parallel (redundant), and that parallel block is in series with Component C. If \(R_A\) = \(R_B\) = 0.90 and \(R_C\) = 0.95, the system reliability is most nearly:
Answer: A) 0.941
Refer to the Machine Design section in the Mechanical Engineering chapter of the FE Reference Handbook.
Parallel: \(R_{AB} = 1-(1-0.90)(1-0.90) = 1-0.01 = 0.99\)
Series with C: \(R_{sys} = 0.99 \times 0.95 = 0.9405\)
Problem 3 — Components (hydraulic, pneumatic, electromechanical)
A double-acting hydraulic cylinder has piston diameter 100 mm and rod diameter 40 mm at system pressure 15 MPa. The retraction force (kN) is most nearly:
Answer: D) 98.9
Refer to the Machine Design section in the Mechanical Engineering chapter of the FE Reference Handbook.
Retraction force uses annular area:
\(F = p \times \frac{\pi}{4}(D^2-d^2) = 15 \times \frac{\pi}{4}(100^2-40^2) = 15 \times 6{,}597 = 98{,}960\) N \(\approx 99.0\) kN
Problem 4 — Bearings
A ball bearing operates at 900 rpm and carries an equivalent radial load of 6 kN. The bearing must last at least 5,000 hours. The minimum required basic dynamic load rating C (kN) is most nearly:
Answer: C) 39
Refer to the Bearings section (p. 437) in the Mechanical Engineering chapter of the FE Reference Handbook.
Convert to millions of revolutions:
\(L_{10} = 60 \times n \times L_h / 10^6 = 60 \times 900 \times 5{,}000 / 10^6 = 270\) Mrev
\(C = P \times L_{10}^{1/3} = 6 \times 270^{1/3} = 6 \times 6.463 = 38.8\) kN
Problem 5 — Manufacturability (limits, fits)
An ISO 40H7/g6 fit has hole = 40.000/40.025 mm and shaft = 39.991/39.975 mm. The minimum clearance (mm) is most nearly:
Answer: D) 0.009
Refer to the Machine Design section in the Mechanical Engineering chapter of the FE Reference Handbook.
Minimum clearance = \(D_{min} - d_{max} = 40.000 - 39.991 = 0.009\) mm.
Using the FE Reference Handbook for Mechanical Design and Analysis
This section is the widest in the handbook and the easiest to get lost in, so navigate by component rather than by concept. If the question names a spring, a bearing, a bolt or a gear, search that word directly. Two relationships worth locating before exam day are the thin-walled pressure vessel stresses and the distortion energy expression for combined loading, because they appear more than any other formulas in this area.
Four Mistakes That Cost Points
- Swapping hoop and longitudinal stress. In a thin-walled cylinder hoop stress is twice the longitudinal stress. Getting them the wrong way round produces a factor-of-two error, and both values sit on the answer list.
- Applying a ductile failure theory to a brittle material. Maximum shear stress and distortion energy describe ductile yielding. Brittle materials call for a maximum normal stress or a Mohr-based criterion, and the exam tests whether you notice which material you were given.
- Using ultimate strength directly as the fatigue limit. The endurance limit is a fraction of ultimate strength, then reduced further by surface finish, size, loading and stress concentration factors. Skipping the modifying factors gives an unconservative answer that is deliberately offered.
- Ignoring stress concentration at a discontinuity. A hole, fillet or keyway raises local stress by the concentration factor, and it matters most in fatigue. Computing nominal stress and stopping there is the most common fatigue error.
Frequently Asked Questions
How many mechanical design questions are on the FE Mechanical exam?
NCEES specifies 10-15 questions from Mechanical Design and Analysis out of 110. It is tied with Dynamics, Fluid Mechanics and Thermodynamics for the heaviest area on the exam.
Which failure theory should I use?
Read the material first. For ductile materials use maximum shear stress for a conservative result or distortion energy for a more accurate one; the question usually names which it wants. For brittle materials use a maximum normal stress criterion. Choosing the theory is often the entire question.
How much fatigue analysis is tested?
Enough to require the endurance limit and its modifying factors, not enough to require a full cumulative-damage analysis. Know how to get from ultimate strength to a corrected endurance limit, and how stress concentration enters that chain.
Should I study this area first or last?
Last. It builds directly on statics, mechanics of materials and material properties, so studying it before those means relearning their content inside harder problems. Once the three feeder areas are solid, this area is mostly about knowing which criterion applies.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Mechanics of Materials practice problems — 9-14 questions on the exam
- FE Mechanical Material Properties and Processing practice problems — 7-11 questions on the exam
- FE Mechanical Statics practice problems — 9-14 questions on the exam
Done with mechanical design? Browse every knowledge area from the free FE Mechanical practice problem hub, see what the full bank covers on the FE Mechanical exam prep page, or plan your schedule with the FE study timeline. Or test yourself against the clock with the free FE Mechanical practice exam: 20 timed questions in the CBT format.