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FE Other Disciplines practice problems: breadth, no depth

This is the only FE exam that will ask you a statics question and a chemistry question in the same sitting. FE Civil and FE Mechanical have statics and no chemistry at all; FE Chemical has chemistry and no statics. FE Other Disciplines has both, plus industrial hygiene and basic electrical engineering, and no depth section anywhere. Here are three real problems from three of those worlds.

· by the FE to PE Prep team

110

Questions

5h 20m

Exam time

14

Knowledge areas

None

Depth sections

What a no-depth exam actually demands

Candidates often choose this exam because no named discipline fits their degree or their work, and then prepare for it as though it were a lighter version of one. It is not lighter. It is wider, and wide costs differently.

  • Nothing carries you. On a depth exam, strength in your specialism covers weakness elsewhere. Here the three mechanics areas — statics, dynamics and strength of materials — are 9 to 14 questions each, exactly equal, and fluid mechanics is bigger than any of them. There is no block large enough to hide a weakness behind.
  • Two areas are outside most engineers’ training entirely. Chemistry at 5–8 and Safety, Health and Environment at 6–9 are not asked of FE Civil, FE Mechanical or FE Electrical candidates at all. Together they are up to 17 questions — more than the whole of Mathematics.
  • The handbook search is harder here. You will jump between chapters that share nothing, under three minutes a question. On a depth exam you live in two or three sections; on this one you visit fourteen.
  • The clock is the same as every other FE. The appointment is 6 hours, 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 is under three minutes each, covering the read, the lookup and the check.

Three real problems

One from statics, one from chemistry, one from industrial hygiene — three subjects that share nothing, which is the point. These are drawn from our free FE Other Disciplines set. Try each before opening the solution, and read the distractor notes.

1. Support reaction on a beam with two kinds of load

Statics runs to 9–14 questions here, the same as Dynamics and the same as Strength of Materials. This is the most ordinary problem in the subject, and it is worth watching what the exam does with an ordinary problem.

  1. 1
    medium
    A. Force systems, equilibrium, trusses, friction & area properties
    A simply-supported beam of span L=6L=6 m carries a uniform load w=4w=4 kN/m over its entire length plus a point load P=12P=12 kN located 2 m from the left support (A). The pin reaction at A is most nearly:
    Loaded beam schematic with its supports and applied loadsw = 4 kN/mP = 12 kNRARBa = 2 mL = 6 m
    1. 32 kN
    2. 18 kN
    3. 20 kN
    4. 16 kN
    Show the answer & worked solution

    Answer: C.20 kN

    ΣM about B: RA=P(La)L+wL2=12(4)6+462=20R_A=\dfrac{P(L-a)}{L}+\dfrac{wL}{2}=\dfrac{12(4)}{6}+\dfrac{4\cdot6}{2}=20 kN. Distractors: the entire distributed load assigned to A instead of half (+wL+wL, giving 32 kN), the point-load moment arm taken as aa instead of (La)(L-a) — moments summed about the wrong support — yielding RB (16 kN), and the point load split evenly regardless of its position (P/2P/2, giving 18 kN).

What the distractors teach: The two loads have to be handled differently and every wrong answer treats one of them as if it were the other. Give the whole uniform load to A rather than half of it and you get 32 kN. Sum moments about the wrong support and you compute the far reaction instead: 16 kN. Split the point load evenly regardless of where it actually sits — P/2 rather than P(L−a)/L — and you get 18 kN. That last one is the dangerous one, because splitting a load in half is right for the UDL and wrong for the point load, in the same problem.

2. pH of a strong acid

Here is the part of this exam that surprises people. Chemistry carries 5–8 questions on FE Other Disciplines — and neither FE Civil nor FE Mechanical nor FE Electrical asks a chemistry question at all. If you came to this exam from a mechanical or civil background, this is unfamiliar ground worth an hour.

  1. 2
    medium
    A. Stoichiometry, equilibrium, acids/bases, oxidation-reduction & gas laws
    A strong monoprotic acid is dissolved in water to give [H+]=0.01[\mathrm{H^+}]=0.01 mol/L. Using pH=log10[H+]\mathrm{pH}=-\log_{10}[\mathrm{H^+}], the pH is most nearly:
    1. 4.61
    2. -2
    3. 2
    4. 12
    Show the answer & worked solution

    Answer: C.2

    pH=log10(0.01)=2\mathrm{pH}=-\log_{10}(0.01)=2. Distractors: the minus sign dropped (+log10[H+]=2+\log_{10}[\mathrm{H^+}]=-2); the pOH reported instead (14+log10[H+]=1214+\log_{10}[\mathrm{H^+}]=12, treating the acid as a base); and natural log used in place of log10\log_{10} (ln[H+]=4.61-\ln[\mathrm{H^+}]=4.61).

What the distractors teach: Four options, one definition, and three ways to misapply it. Lose the minus sign and pH becomes −2, which no aqueous solution has. Report pOH instead of pH and you get 12, which is the answer for a strong base. Use the natural log where the definition says log base 10 and you get 4.61, the only distractor that looks like a plausible pH. Note the shape of that: the two wrong answers a chemist would spot instantly are the obvious ones, and the survivor is the one that needs you to have read the definition properly.

3. Eight-hour time-weighted average exposure

Safety, Health and Environment is 6–9 questions, another area unique to this exam among the general FE disciplines. Time-weighted averaging is industrial hygiene rather than engineering analysis, and it rewards reading the question over recalling a formula.

  1. 3
    medium
    A. Industrial hygiene: exposure, radiation, ventilation & gas concentration
    Personal sampling over an 8-hour shift (PEL =100=100 ppm) records 100100 ppm for 2 h, 150150 ppm for 4 h, 5050 ppm for 2 h. The 8-hour time-weighted average (TWA) exposure is most nearly:
    1. 150 ppm
    2. 300 ppm
    3. 113 ppm
    4. 100 ppm
    Show the answer & worked solution

    Answer: C.113 ppm

    TWA=Cititi=1002+1504+5028=9008=112.5\text{TWA}=\dfrac{\sum C_it_i}{\sum t_i}=\dfrac{100\cdot2+150\cdot4+50\cdot2}{8}=\dfrac{900}{8}=112.5 ppm (exceeds the 100 ppm PEL). Distractors: the readings averaged un-weighted (Ci/n\sum C_i/n, ignoring duration); the peak concentration read off as the TWA; and the time-products divided by the NUMBER of readings (Citi/n\sum C_it_i/n) instead of by the 8-hour shift.

What the distractors teach: This is the sharpest distractor set of the three. The un-weighted mean of the three readings comes to exactly 100 ppm — which is also the permissible exposure limit — so the tempting wrong answer reads as “right at the limit, compliant”. The correctly weighted average is 112.5 ppm, over the limit. Getting it wrong does not just cost a mark; it inverts the engineering conclusion. The other two are the peak reading taken as the average, 150, and dividing the time-products by the number of readings rather than by the eight-hour shift, 300.

Where the 110 questions come from

NCEES publishes how many questions come from each of the fourteen knowledge areas. Read it looking for a depth section and you will not find one — that absence is the exam's defining feature.

FE Other Disciplines knowledge areas and question counts, per the NCEES specification effective July 2020
Knowledge areaQuestions
MathematicsAnalytic geometry, calculus, differential equations, numerical methods, vector analysis.8–12
Probability and StatisticsMeasures of central tendency and dispersion, distributions, estimation, comparison of options.6–9
ChemistryPeriodic table, oxidation and reduction, acids and bases, equations and equilibrium. No FE Civil, Mechanical or Electrical candidate is asked any of this.5–8
Instrumentation and ControlsSensors, block diagrams, system response, measurement uncertainty.4–6
Engineering Ethics and Societal ImpactsCodes of ethics, public protection, licensure, intellectual property, professional liability.5–8
Safety, Health, and EnvironmentIndustrial hygiene, exposure limits and time-weighted averages, hazard classification, indoor air, noise.6–9
Engineering EconomicsTime value of money, cost estimation, economic analyses, depreciation.6–9
StaticsResultants, equilibrium, frames and trusses, centroids, moments of inertia, friction.9–14
DynamicsKinematics, mass moments of inertia, force and acceleration, work and energy, vibrations.9–14
Strength of MaterialsStress and strain, shear and moment diagrams, torsion, beams, columns, combined stresses.9–14
MaterialsChemical and physical properties, corrosion, testing, thermal and mechanical processing.6–9
Fluid MechanicsThe largest single area on the exam — and exactly double the FE Civil allocation at both ends of the range. Properties, statics, energy and continuity, pipe flow, pumps, flow measurement.12–18
Basic Electrical EngineeringDC and AC circuits, power, electrical safety, motors and generators, sources.6–9
Thermodynamics and Heat TransferCombined into one area here, where FE Mechanical splits them into two. Properties, laws, cycles, conduction, convection, radiation.9–14

Two rows deserve a second look. Fluid Mechanics at 12 to 18 is the largest area on the exam — exactly double FE Civil's allocation at both ends of the range, and more than FE Mechanical's. And Thermodynamics and Heat Transfer are combined into a single 9 to 14 area here, where FE Mechanical splits them into two. Neither of those is what a candidate expects from an exam described as general.

For the pass-rate picture across all seven FE disciplines, the companion guide covers it: how hard is the FE exam?

Common questions

What is on the FE Other Disciplines exam?
Fourteen knowledge areas, all of them general engineering rather than a specialism: mathematics, probability and statistics, chemistry, instrumentation and controls, ethics and societal impacts, safety and health and environment, engineering economics, statics, dynamics, strength of materials, materials, fluid mechanics, basic electrical engineering, and thermodynamics and heat transfer. There is no civil, mechanical or electrical depth section. That is the defining feature of this exam and the reason it suits candidates whose degree or practice does not map onto one of the named disciplines.
How is FE Other Disciplines different from the other FE exams?
It is the only FE exam that asks you statics and chemistry in the same sitting. FE Civil and FE Mechanical have statics but no chemistry area at all; FE Chemical has chemistry but no statics. FE Other has both, plus safety and health and environment, plus basic electrical engineering. It also carries three mechanics areas of exactly equal weight — statics, dynamics and strength of materials at 9 to 14 questions each, 27 to 42 between them.
How many questions are on each FE Other Disciplines topic?
Fluid Mechanics is the largest single area at 12-18 questions. Statics, Dynamics, Strength of Materials, and Thermodynamics and Heat Transfer follow at 9-14 each, then Mathematics at 8-12. Probability and Statistics, Safety and Health and Environment, Engineering Economics, Materials, and Basic Electrical Engineering get 6-9 each; Chemistry and Engineering Ethics and Societal Impacts 5-8 each; Instrumentation and Controls 4-6. The ranges sum to between 100 and 153 across the 14 areas against an exam of 110 questions, so no single sitting hits every maximum.
Why is there so much fluid mechanics on FE Other Disciplines?
It is the largest area on the paper at 12-18 questions, which is exactly double the FE Civil allocation of 6-9 at both ends of the range, and more than FE Mechanical's 10-15. A candidate who moved to this exam expecting a lighter version of a named discipline finds the opposite in fluids. If you are triaging study time, this is the area to protect.
What reference material do you get on the FE Other Disciplines exam?
The exam is closed book with an electronic reference: the NCEES FE Reference Handbook is supplied on-screen as a searchable PDF, and no personal copies or outside material are allowed. Because this exam spans so many subjects, searching the handbook well matters more here than on the depth exams — you will be moving between chapters that have nothing to do with each other, under three minutes a question.

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Work through seven more

Ten free FE Other Disciplines problems in total — pipe continuity, bending stress, a loaded voltage divider, capital recovery, specific heat, normal distributions — spanning as many subjects as the exam does, each with the full worked solution and every distractor named. No signup.

Format, knowledge areas and appointment length are from the NCEES FE Other Disciplines specification effective beginning with the July 2020 examinations. The per-question time and the comparisons drawn against other FE specifications 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.