Free FE Mechanical Exam Flashcards

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.