What do FE Mechanical practice problems actually look like?

Multiple choice, four options, usually phrased 'most nearly', and the options sit close enough that you cannot eliminate them by inspection. Many carry a figure: a stress element, a free-body diagram, a wall section, a beam. NCEES gives 110 questions in a 6-hour appointment, of which 5 hours 20 minutes is exam time, so the working time per question is under three minutes once you allow for reading, a handbook lookup and a check.

How many questions are on each FE Mechanical topic?

The specification allocates 10-15 questions each to Dynamics, Kinematics and Vibrations; Fluid Mechanics; Thermodynamics; and Mechanical Design and Analysis. Statics and Mechanics of Materials get 9-14 each, Material Properties and Processing and Heat Transfer 7-11 each, Mathematics 6-9, Electricity and Magnetism and Measurements, Instrumentation and Controls 5-8 each, and Probability and Statistics, Ethics and Professional Practice, and Engineering Economics 4-6 each. The ranges sum to between 100 and 153 across the 14 areas against an exam of 110, so no single sitting hits every maximum.

How much of the FE Mechanical exam is thermal?

More than any single named area. Thermodynamics carries 10-15 questions and Heat Transfer another 7-11, so together the thermal sciences account for 17 to 26 of the 110 — larger than the biggest individual block on the paper. That pairing is ours rather than an NCEES grouping, but the question counts are theirs, and it is worth knowing before you decide Heat Transfer is a minor topic you can skim.

Is there electrical content on the FE Mechanical exam?

Yes, and it is the area mechanical candidates most often skip. Electricity and Magnetism is allocated 5-8 questions — charge and current, circuits, power and work, magnetic fields. That is the same size as Ethics and Engineering Economics combined, and about as many marks as Measurements, Instrumentation and Controls. Writing it off is one of the cheapest ways to lose points on this exam.

What reference material do you get on the FE Mechanical exam?

The exam is closed book with an electronic reference: the NCEES FE Reference Handbook is supplied on-screen as a searchable PDF, and you cannot bring your own copy or any outside material. Practise with the searchable PDF rather than a printed one — finding an equation under time pressure is its own skill, and the on-screen search behaves nothing like flipping pages.

FE Mechanical practice problems: one dropped factor

We worked three real FE Mechanical problems and then checked every wrong option in all three — nine distractors in total. Not one of them is a random number, and not one is an arithmetic slip. Every single one is the correct formula with exactly one term mishandled. That is what this exam does to you, and it is why re-reading the equation does not save you.

Updated August 31, 2026 · by the FE to PE Prep team

110

Questions

5h 20m

Exam time

Knowledge areas

17–26

Thermal sciences

Why one dropped factor is fatal

FE Mechanical formulas are long. Von Mises has five terms under a square root. Fourier's law has four quantities and a division. Bending stress hides a cube and a factor of six inside a section property. A longer formula is not harder to understand — it is harder to transcribe, and it offers more places to lose exactly one thing.

A single dropped term still produces a believable number. Across the three problems below, five of the nine wrong answers land within a factor of two of the right one, and on the von Mises problem all three sit within 17% of it. Nothing about them looks wrong on the page.
Some wrong answers are not wrong quantities — they are the right value of something else. Omit the area from Fourier’s law and you have correctly computed a heat flux in W/m² for a question that asked for a rate in watts. Re-reading the formula will never flag that, because the formula was never misremembered.
The constants are where it goes. bh³/12 not bh³/3; c = h/2 not h; the factor 3 on the shear term, and the square on it. None of that is understanding — it is recall under time pressure, and it is most of the marks.
The clock is tighter than the appointment. Six hours sounds generous, but only 5 hours 20 minutes is exam time; the rest is a nondisclosure agreement, a tutorial and a scheduled break. Across 110 questions that leaves under three minutes each, covering the read, the lookup and the check.

Three real problems

One each from Mechanical Design and Analysis, Heat Transfer and Mechanics of Materials. These are drawn from our free FE Mechanical set. Try each before you open the solution — and read the distractor notes, because on this exam the wrong answers are the lesson.

1. Von Mises stress at a critical point

Mechanical Design and Analysis is one of the four largest blocks on this exam, and the distortion-energy criterion is its signature calculation. The formula is printed in the handbook. It also has five terms, and that is the whole difficulty.

1
medium
A. Machine-element stress, failure theories, springs & deflection
At the critical point of a loaded machine element the plane-stress components are $\sigma_x=80\,\text{MPa}$ , $\sigma_y=30\,\text{MPa}$ , and $\tau_{xy}=25\,\text{MPa}$ (see the stress element). The distortion-energy (von Mises) effective stress is most nearly:
1. 82.3 MPa
2. 95.8 MPa
3. 74.3 MPa
4. 70.5 MPa
Show the answer & worked solution
Answer: A.82.3 MPa
$\sigma'=\sqrt{\sigma_x^2-\sigma_x\sigma_y+\sigma_y^2+3\tau_{xy}^2}=\sqrt{80^2-(80)(30)+30^2+3(25)^2}=82.3$ MPa. Distractors: dropped the cross term $-\sigma_x\sigma_y$ (used $\sigma_x^2+\sigma_y^2+3\tau^2$ ); used $3\tau_{xy}$ instead of $3\tau_{xy}^2$ (shear left un-squared); and dropped the factor $3$ on the shear term ( $+\tau_{xy}^2$ ).

What the distractors teach: Every wrong option is the same formula with exactly one term mishandled, and none of them sits more than 17% from the right answer. Drop the cross term −σxσy and you get 95.8. Leave the shear un-squared, using 3τ where the formula wants 3τ², and you get 70.5. Keep τ² but lose the factor of 3 in front of it and you get 74.3. Three different single-term slips, three plausible stresses, and nothing about any of them looks wrong on the page.

2. Steady conduction through a plane wall

Fourier's law for a plane wall is the simplest equation in heat transfer — four quantities and one division. It is worth doing slowly anyway, because one of the wrong answers is not a wrong number at all.

2
medium
A. Conduction, convection, radiation, transient & heat exchangers
A plane wall of thermal conductivity $k=0.8$ W/m·K has a face area $A=10$ m² and thickness $L=0.2$ m, with its two faces held at a temperature difference $\Delta T=20$ K. By Fourier's law, the steady rate of heat conduction through the wall is most nearly:
1. 1600 W
2. 80 W
3. 800 W
4. 160 W
Show the answer & worked solution
Answer: C.800 W
Fourier's law: $q=\dfrac{kA\,\Delta T}{L}=\dfrac{0.8\cdot10\cdot20}{0.2}=800$ W. Distractors: used half the thickness — the distance to the mid-plane — in the denominator ( $kA\Delta T/(L/2)$ , which doubles the rate); dropped the area $A$ (reported the heat flux $k\Delta T/L$ as a rate); and omitted the thickness entirely ( $kA\Delta T$ , as if $L=1$ m).

What the distractors teach: Drop the area and you compute kΔT/L = 80, which is the heat flux in W/m². That is a correct quantity, correctly calculated, answering a question about rate in watts — and no re-reading of the formula will flag it, because nothing in the formula was misremembered. The other two are geometry: use half the thickness, the distance to the mid-plane, and the rate doubles to 1600; omit the thickness entirely, as though L were 1 m, and you get 160. Check what your answer is a rate of before you check the arithmetic.

3. Maximum bending stress in a rectangular section

Mechanics of Materials runs to 9–14 questions. This one collapses to σ = 6M/bh² if you know the section properties cold, and the distractors are a tour of the ways not to.

3
medium
A. Stress & strain, bending, torsion, transformation, buckling & failure
A beam of solid rectangular cross-section, width $b=50\,\text{mm}$ and depth $h=100\,\text{mm}$ , carries an internal bending moment $M=5\,\text{kN}\cdot\text{m}$ . The maximum bending (flexural) stress is most nearly:
1. 120 MPa
2. 10 MPa
3. 15 MPa
4. 60 MPa
Show the answer & worked solution
Answer: D.60 MPa
$I=\dfrac{bh^3}{12}=4166667\,\text{mm}^4$ , $c=h/2=50\,\text{mm}$ ; $\sigma=\dfrac{Mc}{I}=\dfrac{6M}{bh^2}=\dfrac{6(5\times10^6)}{(50)(100)^2}=60$ MPa. Distractors: used $I=bh^3/3$ instead of $bh^3/12$ (¼ of the true stress); used $c=h$ instead of $h/2$ (twice the stress); and dropped the factor 6 (used $\sigma=M/bh^2$ ).

What the distractors teach: All three wrong answers come from the section, not the loading. Use I = bh³/3 instead of bh³/12 and the stress drops to a quarter of the truth: 15 MPa. Use c = h rather than h/2 and it doubles to 120. Lose the factor of 6 altogether and you get 10. The bending moment is handled correctly in every one of them. On this exam the arithmetic is rarely what fails — the constants buried in a section property are.

Where the 110 questions come from

NCEES publishes how many questions come from each of the fourteen knowledge areas. Four are tied at the top — Dynamics, Fluid Mechanics, Thermodynamics and Mechanical Design and Analysis, at 10 to 15 questions each — with Statics and Mechanics of Materials just behind at 9 to 14.

FE Mechanical knowledge areas and question counts, per the NCEES specification effective July 2020
Knowledge area	Questions
MathematicsAnalytic geometry, calculus, differential equations, numerical methods, linear algebra.	6–9
Probability and StatisticsDistributions, regression and curve fitting, confidence intervals, hypothesis testing.	4–6
Ethics and Professional PracticeCodes of ethics, agreements and contracts, professional liability, public safety.	4–6
Engineering EconomicsTime value of money, cost estimation, economic analyses, depreciation.	4–6
Electricity and MagnetismCharge and current, circuits, power and work, magnetic fields. The area mechanical candidates are most likely to skip entirely — and it is the same size as Ethics and Economics combined.	5–8
StaticsResultants, equilibrium, frames and trusses, centroids and moments of inertia, friction.	9–14
Dynamics, Kinematics, and VibrationsKinematics, friction, particle and rigid-body dynamics, work and energy, natural frequency, resonance, vibration isolation.	10–15
Mechanics of MaterialsShear and moment diagrams, stress transformations and Mohr's circle, deformations, combined stresses, columns, fatigue.	9–14
Material Properties and ProcessingProperties, diagrams and phase relations, thermal processing, testing, manufacturing processes.	7–11
Fluid MechanicsFluid properties and statics, continuity and energy, pipe flow, pumps and turbines, compressible flow.	10–15
ThermodynamicsProperties, energy transfers, cycles, mixtures, psychrometrics, combustion.	10–15
Heat TransferConduction, convection, radiation, transient processes, heat exchangers, boiling and condensation.	7–11
Measurements, Instrumentation, and ControlsSensors and measurement error, system dynamics, control theory, stability.	5–8
Mechanical Design and AnalysisStress analysis of machine elements, failure theories, deformation and stiffness, springs, bearings, gears, joints, pressure vessels.	10–15

Two things in that table are worth acting on. Thermodynamics and Heat Transfer are listed separately, but together they carry 17 to 26 questions — more than any single named area on the exam, which makes treating Heat Transfer as a minor topic an expensive habit. And Electricity and Magnetism, at 5 to 8, is the same size as Ethics and Engineering Economics combined. It is the area mechanical candidates are most likely to skip outright, and it is not small.

For the pass-rate picture alongside this, the companion guide covers it: how hard is the FE Mechanical exam?

Common questions

What do FE Mechanical practice problems actually look like?: Multiple choice, four options, usually phrased 'most nearly', and the options sit close enough that you cannot eliminate them by inspection. Many carry a figure: a stress element, a free-body diagram, a wall section, a beam. NCEES gives 110 questions in a 6-hour appointment, of which 5 hours 20 minutes is exam time, so the working time per question is under three minutes once you allow for reading, a handbook lookup and a check.
How many questions are on each FE Mechanical topic?: The specification allocates 10-15 questions each to Dynamics, Kinematics and Vibrations; Fluid Mechanics; Thermodynamics; and Mechanical Design and Analysis. Statics and Mechanics of Materials get 9-14 each, Material Properties and Processing and Heat Transfer 7-11 each, Mathematics 6-9, Electricity and Magnetism and Measurements, Instrumentation and Controls 5-8 each, and Probability and Statistics, Ethics and Professional Practice, and Engineering Economics 4-6 each. The ranges sum to between 100 and 153 across the 14 areas against an exam of 110, so no single sitting hits every maximum.
How much of the FE Mechanical exam is thermal?: More than any single named area. Thermodynamics carries 10-15 questions and Heat Transfer another 7-11, so together the thermal sciences account for 17 to 26 of the 110 — larger than the biggest individual block on the paper. That pairing is ours rather than an NCEES grouping, but the question counts are theirs, and it is worth knowing before you decide Heat Transfer is a minor topic you can skim.
Is there electrical content on the FE Mechanical exam?: Yes, and it is the area mechanical candidates most often skip. Electricity and Magnetism is allocated 5-8 questions — charge and current, circuits, power and work, magnetic fields. That is the same size as Ethics and Engineering Economics combined, and about as many marks as Measurements, Instrumentation and Controls. Writing it off is one of the cheapest ways to lose points on this exam.
What reference material do you get on the FE Mechanical exam?: The exam is closed book with an electronic reference: the NCEES FE Reference Handbook is supplied on-screen as a searchable PDF, and you cannot bring your own copy or any outside material. Practise with the searchable PDF rather than a printed one — finding an equation under time pressure is its own skill, and the on-screen search behaves nothing like flipping pages.

Build your study plan

Tell us how long you have. We'll budget your hours across every knowledge area using the official NCEES question weights — the heaviest areas get the most time, which is the opposite of how most people study.

Work through seven more

Ten free FE Mechanical problems in total — beam reactions, pipe continuity, a loaded voltage divider, specific heat, capital recovery, normal distributions — each with the full worked solution and every distractor named. No signup.

Try the free FE Mechanical set Explore FE Mechanical

Format, knowledge areas and appointment length are from the NCEES FE Mechanical specification effective beginning with the July 2020 examinations. The per-question time and the pairing of Thermodynamics with Heat Transfer are ours, not NCEES figures. Specifications and fees change over time — confirm current specifics at ncees.org. Independent study resource; not affiliated with, endorsed by, or sponsored by NCEES.