FE Mechanical Exam Flashcards

Q: How many questions are on the FE Mechanical exam?

The FE Mechanical exam has 110 multiple-choice questions delivered as a computer-based test at Pearson VUE. The total appointment is 6 hours, including a tutorial and a 25-minute scheduled break, leaving 5 hours 20 minutes of actual testing time. An on-screen searchable NCEES FE Reference Handbook is provided, and only NCEES-approved calculators (Casio FX-115, TI-30X, TI-36X, HP 35s) are permitted.

Q: What is the FE Mechanical pass rate?

NCEES reported an approximately 65% first-time pass rate for FE Mechanical in early 2026. Pass rates are higher for candidates who test within 12 months of graduating from an EAC/ABET-accredited program. NCEES does not publish a fixed numeric cut score; results are reported pass/fail using psychometric equating across exam forms.

Q: Which content areas have the most questions on FE Mechanical?

The largest NCEES FE Mechanical knowledge areas are Dynamics/Vibrations, Fluid Mechanics, Thermodynamics, and Mechanical Design and Analysis at 10-15 questions each. Statics and Mechanics of Materials are each 9-14 questions, and Heat Transfer is 7-11 questions. There are 15 knowledge areas in total.

Q: How much does the FE Mechanical exam cost?

The NCEES FE exam fee is $225, payable directly to NCEES. State licensing boards may charge additional application or processing fees depending on jurisdiction. Each retake attempt also costs $225 plus any board fees.

Q: How long should I study for FE Mechanical?

Most candidates spend 150-300 hours of focused preparation over 2-4 months. The single most important resource is the NCEES FE Reference Handbook — practice every problem with the on-screen handbook open to build lookup speed, since handbook navigation pace determines exam timing more than memorization.

Question 1

Free-Body Diagram (FBD)

Accepted Answer

An isolated sketch of a body showing every external force, reaction, and applied moment acting on it. Build the FBD before searching for a formula — most FE statics errors come from an incomplete model, not difficult algebra.

Question 2

2D Static Equilibrium Equations

Accepted Answer

A planar body is in equilibrium when ΣFx = 0, ΣFy = 0, and ΣM = 0. These three independent equations solve up to three unknown reactions. Take moments about a point that eliminates unknown reactions to solve fastest.

Question 3

Truss Determinacy Check (m + r = 2j)

Accepted Answer

A planar truss is statically determinate when members m plus reactions r equal twice the joints (m + r = 2j). If satisfied, equilibrium alone solves member forces; the method of joints writes two equations per pin.

Question 4

Parallel-Axis Theorem

Accepted Answer

Moment of inertia about any axis equals the centroidal value plus the area times the squared offset distance: I = Ī + Ad². Essential for composite-section problems; the handbook supplies Ī for standard shapes.

Question 5

Impending-Slip Friction

Accepted Answer

Static friction opposes impending motion and only reaches its maximum value μₛN at the point of impending slip. Below that, friction is whatever value equilibrium requires — not automatically μₛN.

Question 6

Kinematics vs. Kinetics

Accepted Answer

Kinematics describes motion (position, velocity, acceleration) without reference to forces. Kinetics connects that motion to the forces and moments causing it. Identify which is asked before choosing equations.

Question 7

Constant-Acceleration Equations

Accepted Answer

Use v = v₀ + at, s = s₀ + v₀t + ½at², and v² = v₀² + 2a·Δs ONLY when acceleration is actually constant. Applying them to variable-acceleration motion is a classic FE trap.

Question 8

Work-Energy vs. Impulse-Momentum

Accepted Answer

Use work-energy (W = ΔKE) when forces act through distances and time is not central. Use impulse-momentum (ΣF·Δt = Δ(mv)) when forces act over time or collisions are involved.

Question 9

Newton's Second Law for Rotation

Accepted Answer

For rigid-body rotation about the mass center, ΣM = Iα, where I is the mass moment of inertia and α is angular acceleration. Keep radians, angular speed, and torque units consistent.

Question 10

Single-DOF Vibration Characteristics

Accepted Answer

Most FE vibration questions reduce to identifying natural frequency (ωn = √(k/m)), damping ratio, transmissibility, or resonance. Resonance occurs when forcing frequency approaches the natural frequency.

Question 11

Axial Stress and Deformation

Accepted Answer

Axial normal stress is σ = P/A; elastic axial deformation is δ = PL/(AE). Connected or constrained members become compatibility problems where deformations must be matched.

Question 12

Bending (Flexure) Stress

Accepted Answer

σ = Mc/I, maximum at the extreme fiber, where M is the moment at the section, c the distance to the fiber, and I the section's moment of inertia about the bending axis. Get a moment diagram or correct handbook case first.

Question 13

Torsional Shear Stress (Circular Shaft)

Accepted Answer

τ = Tr/J, where J = πd⁴/32 for a solid circular shaft. Formula applies directly to circular sections; noncircular sections need the handbook's specific relationships, not this one.

Question 14

Euler Critical Buckling Load

Accepted Answer

Pcr = π²EI/(KL)². Effective-length factor K: 1.0 pinned-pinned, 0.5 fixed-fixed, 2.0 fixed-free. Buckling uses the weak-axis (smallest) moment of inertia.

Question 15

Mohr's Circle

Accepted Answer

A graphical stress-transformation tool giving principal stresses and maximum shear from a known stress state. It transforms an existing state — it is not a new free-body diagram or equilibrium problem.

Question 16

Shear-Moment Diagram Slope Relationships

Accepted Answer

The slope of the shear diagram equals the distributed load (dV/dx = −w); the slope of the moment diagram equals the shear (dM/dx = V). Maximum moment occurs where shear crosses zero.

Question 17

Hydrostatic Pressure

Accepted Answer

Pressure in a static fluid changes with elevation only: p = γh = ρgh. Velocity and pipe-loss ideas do not belong in a static-fluid model — choosing flow equations for a static problem is a frequent FE error.

Question 18

Continuity Equation (Incompressible)

Accepted Answer

For incompressible steady flow, Q = A₁V₁ = A₂V₂. Halving pipe diameter quarters the area and quadruples the velocity. Mass flow rate is ṁ = ρQ.

Question 19

When to Use Simple Bernoulli

Accepted Answer

Use the simple Bernoulli equation ONLY when flow is steady, incompressible, along a streamline, with negligible losses and no shaft devices. Otherwise use the full mechanical-energy equation with head-loss and pump/turbine terms.

Question 20

Reynolds Number

Accepted Answer

Re = ρVD/μ = VD/ν, the ratio of inertial to viscous forces. Pipe flow is laminar below Re ≈ 2,100 and turbulent above Re ≈ 4,000. It governs friction-factor selection in pipe-loss problems.

Question 21

Darcy-Weisbach Head Loss

Accepted Answer

Major pipe friction loss is h_f = f·(L/D)·(V²/2g), where f is the Darcy friction factor (Re- and roughness-dependent). Minor losses scale with velocity head and can dominate short systems with valves and fittings.

Question 22

NPSH (Net Positive Suction Head)

Accepted Answer

The margin of suction-side pressure above the fluid's vapor pressure. NPSH questions are cavitation-avoidance questions: available NPSH must exceed required NPSH, not ordinary pump-power problems.

Question 23

Closed System vs. Control Volume

Accepted Answer

Define the boundary first. A closed system has no mass crossing it (use internal energy U). A control volume allows mass flow (use enthalpy h in steady-flow energy balances).

Question 24

Quality (Saturated Mixture)

Accepted Answer

Quality x is the mass fraction of vapor in a saturated liquid-vapor mixture (0 ≤ x ≤ 1). It is defined ONLY in the two-phase region — never assign quality to compressed liquid or superheated vapor.

Question 25

Ideal Gas Law Requirements

Accepted Answer

PV = mRT requires ABSOLUTE pressure and ABSOLUTE temperature. Using gauge pressure or Celsius/Fahrenheit in gas-law ratios is one of the most common FE thermodynamics traps.

Question 26

Thermal Efficiency vs. COP

Accepted Answer

Thermal efficiency (η = W_net/Q_in) applies to heat engines. Coefficient of performance applies to refrigerators and heat pumps and can exceed 1. Do not interchange them between cycle types.

Question 27

Carnot (Second-Law) Limits

Accepted Answer

Maximum possible efficiency between two reservoirs is η = 1 − T_cold/T_hot, using ABSOLUTE temperatures (K or R). Carnot efficiency and Carnot COP cannot be computed from Celsius or Fahrenheit differences.

Question 28

Power Cycle Identification

Accepted Answer

Otto, Diesel, and Brayton FE items often use air-standard ideal-gas relations; Rankine and vapor-compression cycles require property-table states. Name each component (compressor, heat addition, expander, heat rejection) before solving.

Question 29

Three Modes of Heat Transfer

Accepted Answer

Conduction (Fourier: q = kA·ΔT/L) through a material, convection (Newton's cooling: q = hA·ΔT) between surface and fluid, and radiation (q ∝ εσAT⁴) between surfaces. Choose the mode before calculating.

Question 30

Thermal Resistance Network

Accepted Answer

Model conduction and convection as resistances in series/parallel (R_cond = L/kA, R_conv = 1/hA), then q = ΔT/ΣR. The fastest FE method for composite walls, cylinders, and combined boundaries.

Question 31

LMTD vs. Effectiveness-NTU

Accepted Answer

Use LMTD (log mean temperature difference) when all four terminal temperatures are known. Use effectiveness-NTU when outlet temperatures are unknown but exchanger size or UA is given.

Question 32

Convection Coefficient (h)

Accepted Answer

h is NOT a material property. It depends on flow condition, geometry, fluid properties, and the temperature scale used in the correlation. Treating it like thermal conductivity is a common error.

Question 33

Stress-Strain Curve Properties

Accepted Answer

The curve yields elastic modulus E (initial slope), yield strength, ultimate strength, ductility (elongation), and toughness (area under curve). Brittle materials fail near ultimate with little plastic strain.

Question 34

Material Selection Priorities

Accepted Answer

Start from the service condition: load, temperature, corrosion, weight, wear, manufacturability, and cost. Identify the governing failure mode first, then pick a material/process that controls that risk.

Question 35

Heat Treatment Purpose

Accepted Answer

Controlled heating/cooling (annealing, quenching, tempering) alters microstructure to trade strength, hardness, ductility, and toughness. FE items test which process fits the required property change.

Question 36

Accuracy vs. Precision vs. Resolution

Accepted Answer

Accuracy = closeness to the true value. Precision/repeatability = consistency of repeated readings. Resolution = smallest distinguishable change. Bias is a systematic offset. These are distinct, often-confused terms.

Question 37

Full-Scale Accuracy Specification

Accepted Answer

An accuracy stated as ±% of full scale produces a large RELATIVE error at low readings. A sensor with ±1% FS on a 100-unit range can be ±10% of a 10-unit measurement.

Question 38

Signal Conditioning

Accepted Answer

Processing a raw sensor signal for use: amplification, filtering, isolation, linearization, and analog-to-digital conversion. Each stage matches the transducer output to the data-acquisition input.

Question 39

Transfer Function

Accepted Answer

The ratio of output to input in the Laplace domain assuming zero initial conditions. It models a system's dynamic response and is the basis for block-diagram reduction in FE controls questions.

Question 40

First-Order vs. Second-Order Response

Accepted Answer

First-order systems are characterized by gain and time constant τ. Second-order systems add natural frequency ωn and damping ratio ζ, producing overdamped, critically damped, or underdamped (oscillatory) responses.

Question 41

Feedback Effects and Stability

Accepted Answer

Negative feedback reduces sensitivity to disturbances and steady-state error, but inadequate gain or phase margin can drive the system unstable. Pole locations describe stability and response speed.

Question 42

Bearing L10 Life

Accepted Answer

The rated life (millions of revolutions) that 90% of bearings exceed under a given load. Life is highly load-sensitive via L10 = (C/P)^p, so equivalent load and the life exponent must be handled carefully.

Question 43

Shaft Design Drivers

Accepted Answer

Shaft sizing starts from combined torque and bending, rotational speed, stress concentrations at steps/keyways, and fatigue context. It is one of the largest FE Mechanical knowledge areas.

Question 44

Bolted-Joint Preload

Accepted Answer

A tightened fastener carries an initial tension (preload) that keeps the joint clamped and reduces the bolt's share of external load. FE questions test load path, shear vs. tension, and tensile stress area.

Question 45

Thin-Wall Pressure Vessel Stresses

Accepted Answer

For a thin-wall cylinder: hoop stress σ_h = pr/t and longitudinal stress σ_l = pr/(2t). Hoop stress is twice the longitudinal stress and governs design.

Question 46

Fatigue Failure Factors

Accepted Answer

Cyclic loading can fail a part below its static strength. Endurance limit is reduced by surface finish, size, loading type, temperature, and stress concentration; mean stress shifts the alternating-stress limit.

Question 47

Engineering Economics: Common Basis

Accepted Answer

Present worth, future worth, annual worth, and rate-of-return methods all convert cash flows to one comparable basis. The interest period MUST match the cash-flow period before any factor is applied.

Question 48

Rate of Return Decision Rule

Accepted Answer

Rate of return is the interest rate that sets net present worth to zero. Accept a project when ROR ≥ MARR (minimum acceptable rate of return), or equivalently when NPW ≥ 0 at the MARR.

Question 49

Sample vs. Population Standard Deviation

Accepted Answer

A sample standard deviation divides by (n − 1); a known-population σ divides by n. Choosing the wrong denominator is a classic FE statistics trap, especially on small data sets.

Question 50

Engineer's Paramount Ethical Duty

Accepted Answer

Under the NCEES Model Rules, engineers must hold the safety, health, and welfare of the public above duties to clients, employers, and themselves. In close FE answer choices, public welfare and honest disclosure decide.

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