What do FE Mechanical practice problems actually look like?

Mostly multiple choice with 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. NCEES also uses alternative item types (multiple correct answers, point-and-click, drag-and-drop and fill-in-the-blank), each scored right or wrong with no partial credit.

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 exam 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 exam. 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: electrical fundamentals, DC and AC circuits, motors and generators. That is more than Ethics or Engineering Economics (4-6 each) and the same 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. Practice 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 FE Mechanical practice problems and then traced every wrong option in all three, nine distractors in total. None of them is a random number or an arithmetic slip. Each one comes from a single mishandled term, constant or quantity, with everything else done right. That is why re-reading the equation does not save you.

Updated October 6, 2026 · by the FE → 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 four 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, but it is harder to transcribe, and it offers more places to lose exactly one thing.

A single mishandled term still produces a believable number. Across the three problems below, six 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 a third of it. Nothing about them looks wrong on the page.
Some wrong answers come from a correct formula fed one number wrongly. On the plane-wall problem the outside face is at −4 °C; drop that minus sign and you get 640 W, a believable heat loss. 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; the elastic section modulus bh²/6, not the plastic bh²/4; the minus sign on the von Mises cross term. None of that is a gap in understanding. It is recall under time pressure.
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 practice 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 has four terms under the square root, 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:
Figure — drag or pinch to move around
1. 74.3 MPa
2. 82.3 MPa
3. 95.8 MPa
4. 108 MPa
Show the answer & worked solution
Answer: B.82.3 MPa
The FE Handbook's distortion-energy theory (Mechanical Engineering — Static Loading Failure Theories, p. 452) gives the effective (von Mises) stress for a biaxial state as $\sigma'=\sqrt{\sigma_x^2-\sigma_x\sigma_y+\sigma_y^2+3\tau_{xy}^2}=\sqrt{80^2-(80)(30)+30^2+3(25)^2}=\sqrt{6775}$ = 82.3 MPa. Distractors: dropped the factor $3$ on the shear term ( $+\tau_{xy}^2$ ), 74.3 MPa; dropped the cross term $-\sigma_x\sigma_y$ (used $\sigma_x^2+\sigma_y^2+3\tau_{xy}^2$ ), 95.8 MPa; and added the cross term ( $+\sigma_x\sigma_y$ ) instead of subtracting it, 108 MPa.

What the distractors teach

σ′ = √(80² − 80·30 + 30² + 3·25²) = √6775 = 82.3 MPa. Every wrong option is the same formula copied with one term wrong. Drop the −σxσy cross term and you get 95.8 MPa; add it instead of subtracting and you get 108. Leave the 3 off the shear term and you get 74.3. All four options sit within a factor of 1.5 of each other, 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 each wrong answer gets one quantity wrong, and two of them get the temperature difference wrong.

2
medium
A. Conduction, convection, radiation, transient & heat exchangers
A brick wall 200 mm thick with thermal conductivity $k=0.8$ W/(m·K) has a face area of 10 m². In steady operation its inside surface is at $T_1=20$ °C and its outside surface at $T_2=-4$ °C. The rate of heat loss through the wall is most nearly:
Figure — drag or pinch to move around
1. 640 W
2. 960 W
3. 1500 W
4. 11900 W
Show the answer & worked solution
Answer: B.960 W
The temperature difference across the wall is $T_1-T_2=20-(-4)=24$ K (a difference is the same in °C and K), and $L=0.2$ m. Conduction through a plane wall (FE Reference Handbook 10.6 p. 209): $\dot Q=\dfrac{kA\,(T_1-T_2)}{L}=\dfrac{0.8\cdot10\cdot24}{0.2}=960$ W. Distractors: dropped the minus sign of the outside temperature, taking $\Delta T=20-4=16$ K (640 W); built the resistance as $kL/A$ instead of the handbook's $R=L/(kA)$ , putting the conductivity where a resistivity belongs ( $A\Delta T/(kL)=1500$ W); and converted only the inside temperature to kelvin, $\Delta T=293-(-4)=297$ K (11900 W), where converting both faces, or neither, gives the same 24 K.

What the distractors teach

The outside face is at −4 °C, so the difference is 20 − (−4) = 24 K; drop that minus sign and you get 640 W. Build the thermal resistance like an electrical one, R = kL/A, with the conductivity where a resistivity belongs, and you get 1500 W. Convert only the inside temperature to kelvin and you get 11,900 W. Remember that last one: a temperature difference is the same in K and °C, so convert both temperatures or neither. The right answer is 0.8 × 10 × 24 / 0.2 = 960 W.

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:
Figure — drag or pinch to move around
1. 10 MPa
2. 15 MPa
3. 40 MPa
4. 60 MPa
Show the answer & worked solution
Answer: D.60 MPa
Maximum bending stress (Mechanics of Materials — Stresses in Beams): $\sigma=\dfrac{Mc}{I}$ , with the centroidal $I=\dfrac{bh^3}{12}=\dfrac{(50)(100)^3}{12}=4.167\times10^{6}\ \text{mm}^4$ and $c=h/2=50\ \text{mm}$ , which for a rectangle is $\sigma=\dfrac{6M}{bh^2}$ . With $M=5\ \text{kN·m}=5\times10^{6}\ \text{N·mm}$ : $\sigma=\dfrac{6(5\times10^{6}\ \text{N·mm})}{(50\ \text{mm})(100\ \text{mm})^2}=60$ MPa. Distractors: used $I=bh^3/3$ , the area table's moment of inertia about the BASE, instead of the centroidal $bh^3/12$ (¼ of the true stress); dropped the factor 6 (used $\sigma=M/bh^2$ ); and divided by the plastic section modulus $Z=bh^2/4$ instead of the elastic $S=bh^2/6$ (two-thirds of the true stress).

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. Lose the factor of 6 altogether and you get 10. Divide by the plastic section modulus bh²/4 instead of the elastic bh²/6 and you get 40, two-thirds of the truth. 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 at 10 to 15 questions each (Dynamics, Fluid Mechanics, Thermodynamics, and Mechanical Design and Analysis), 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, central tendency and dispersion, expected value, regression and curve fitting.	4–6
Ethics and Professional PracticeCodes of ethics, public health and safety, intellectual property, societal considerations.	4–6
Engineering EconomicsTime value of money, cost types, economic analyses such as break-even and life cycle.	4–6
Electricity and MagnetismElectrical fundamentals, DC and AC circuits, motors and generators. The area mechanical candidates are most likely to skip entirely, and it outweighs Ethics or Engineering Economics on its own.	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-energy and impulse-momentum, free and forced vibrations.	10–15
Mechanics of MaterialsShear and moment diagrams, stress transformations and Mohr's circle, deformations, combined loading, column buckling, statically indeterminate systems.	9–14
Material Properties and ProcessingProperties, stress-strain and phase diagrams, heat treating, corrosion, failure mechanisms, manufacturing processes.	7–11
Fluid MechanicsFluid properties and statics, continuity and energy, internal and external flow, compressible flow, pump and fan performance.	10–15
ThermodynamicsProperties, energy transfers, cycles, mixtures, psychrometrics, combustion.	10–15
Heat TransferConduction, convection, radiation, transient processes, heat exchangers.	7–11
Measurements, Instrumentation, and ControlsSensors and transducers, feedback control and block diagrams, dynamic system response, measurement uncertainty.	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, outweighs Ethics or Engineering Economics (4 to 6 each). 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?: Mostly multiple choice with 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. NCEES also uses alternative item types (multiple correct answers, point-and-click, drag-and-drop and fill-in-the-blank), each scored right or wrong with no partial credit.
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 exam 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 exam. 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: electrical fundamentals, DC and AC circuits, motors and generators. That is more than Ethics or Engineering Economics (4-6 each) and the same 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. Practice 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, including beam reactions, pipe continuity, a loaded voltage divider, specific heat, capital recovery and 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, so confirm current specifics at ncees.org. Independent study resource; not affiliated with, endorsed by, or sponsored by NCEES.