Free FE Mechanical Exam Flashcards

Isolate the body and draw all external forces, support reactions, and applied couples acting on it.

A planar rigid body in equilibrium satisfies ΣFx = 0, ΣFy = 0, and ΣM = 0. Taking moments about the intersection of unknown reaction lines can eliminate those reactions from the moment equation.

For a stable planar pin-jointed truss, m + r = 2j is the count for static determinacy. Check member geometry and reaction directions for stability before relying on the count.

For an area moment of inertia, I = Icentroid + Ad², where the two axes are parallel and d is their perpendicular separation.

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.

Net work over a displacement equals the change in kinetic energy. Net impulse ∫ΣF dt equals the change in linear momentum. For constant force, the impulse is ΣF Δt.

For planar rigid-body motion, the sum of external moments about the mass center equals IGα. IG is the mass moment of inertia about the axis through the mass center normal to the plane.

For a single undamped mass on a linear spring, ωn = √(k/m). Harmonic forcing near this frequency can produce large amplitudes when damping is low.

For a prismatic, linearly elastic member under constant concentric axial force P, average normal stress is P/A and the change in length is PL/(AE).

In elastic bending, stress magnitude at distance y from the neutral axis is |My|/I. The extreme-fiber stress uses the greatest distance c on the side being checked.

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.

For a slender, linearly elastic column, Pcr = π²EI/(KL)². Typical K values are 1 for pinned-pinned, 0.5 for fixed-fixed, and 2 for fixed-free. Check the axis with the lowest buckling load, accounting for both I and end restraint.

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.

With w positive downward and the usual beam sign convention, dV/dx = −w and dM/dx = V. Check smooth zero-shear crossings, boundaries, and load discontinuities for moment extrema.

For a static fluid of constant density, pressure increases by ρgh over a vertical drop h. At depth h below an open free surface, this is the gauge pressure.

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

Use simple Bernoulli along a streamline for steady, incompressible flow with negligible viscous losses and no shaft work. In pipe systems with significant losses or pumps and turbines, include their heads in the mechanical energy balance.

Re = ρVD/μ = VD/ν for pipe flow. Transition depends on disturbances and geometry. A common circular-pipe convention is laminar below about 2,300 and turbulent above about 4,000.

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.

Available NPSH is the absolute total suction head at the NPSH datum minus vapor pressure head. Compare it with the pump’s required NPSH and allow an appropriate margin to reduce cavitation risk.

Mass cannot cross a closed-system boundary. A control volume permits mass flow, and the energy carried by flowing mass includes enthalpy h = u + pv.

Quality x is vapor mass divided by total mass at liquid–vapor saturation. Saturated liquid has x = 0 and saturated vapor has x = 1. Compressed liquid and superheated vapor are outside the quality range.

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.

For reservoirs at absolute temperatures Th and Tc, Carnot heat-engine efficiency is 1 − Tc/Th. Use kelvin or Rankine for both temperatures.

Ideal Otto, Diesel, and Brayton examples often use air-standard ideal-gas relations. For a steam Rankine or vapor-compression cycle, use the working-fluid property tables or diagrams to determine component inlet and outlet states.

Conduction transfers energy through a material. Convection transfers heat between a surface and fluid. For a gray surface, emitted radiant power is εσAT⁴, with T absolute. Net radiation also depends on irradiation.

For steady, one-dimensional heat transfer through a plane layer, Rcond = L/(kA). For radial conduction in a cylindrical layer, use ln(ro/ri)/(2πkL). Surface convection uses Rconv = 1/(hA). Reduce the network, then use q = ΔT/Req.

Use the log mean temperature difference when the terminal temperatures are known, with a correction factor when the flow arrangement requires one. Effectiveness–NTU is useful when outlet temperatures are unknown and UA and heat-capacity rates are given.

The convection coefficient depends on flow, geometry, and fluid properties. Its units are W/(m²·K), while thermal conductivity k has units W/(m·K).

For a tensile test, the initial slope gives E, the peak engineering stress gives ultimate tensile strength, and elongation at fracture indicates ductility. The area under the stress–strain curve to fracture gives energy absorbed per unit volume.

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 concerns closeness to a reference value. Precision concerns agreement among repeated readings. Repeatability is precision under unchanged conditions. Resolution is the smallest distinguishable change.

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.

The time constant controls a standard first-order response. A standard second-order response also depends on natural frequency and damping ratio, with underdamped, critically damped, or overdamped behavior.

Negative feedback can reduce error and sensitivity where loop gain is high. Check closed-loop poles or gain and phase margins because a negative-feedback loop can still become unstable.

Basic rating life L10 is the life that 90% of a population of apparently identical bearings are expected to meet or exceed under specified conditions. In millions of revolutions, L10 = (C/P)ᵖ, with p = 3 for balls and 10/3 for rollers.

Check a loaded shaft for combined bending and torsion, stress concentrations at steps and keyways, fatigue under cyclic loading, and any relevant deflection or critical-speed limits.

Bolt preload creates a clamping force. While the joint remains closed, the increase in bolt tension under external separating load depends on the relative stiffness of the bolt and the clamped members.

For a thin-walled closed-end cylinder under internal pressure p relative to the exterior, hoop stress is pr/t and longitudinal stress is pr/(2t), with r the cylinder radius and t the wall thickness.

Cyclic stress can cause failure below static strength. Surface finish, size, load type, and temperature can alter the endurance strength. Account for stress concentrations and mean stress when checking allowable alternating stress.

Convert cash flows to equivalent values at one date or on a common annual basis. Match the effective interest rate period to the cash-flow interval before applying a factor.

For an independent investment with a conventional cash-flow pattern and a unique IRR, accept if IRR is at least the MARR. This gives the same decision as nonnegative net present worth at the MARR.

Sample variance s² divides the sum of squared deviations from the sample mean by n − 1. Population variance σ² averages squared deviations from the population mean over all n values. Take the square root for standard deviation.

NCEES Model Rules place protection of the public’s health, safety, and welfare first when engineers serve employers or clients.

Use xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ). The derivative at the current estimate must be nonzero.

A definite integral accumulates signed area. For example, integrating velocity over time gives displacement, while integrating speed gives distance.

For the unilateral transform, L{dy/dt} = sY(s) − y(0). Use the initial value before solving the transformed algebraic equation.

Multiply each possible value by its probability and sum the products, E[X] = Σxᵢpᵢ.

Under the NCEES Model Rules, disclose known or potential conflicts that could influence your professional judgment or the quality of your services to your employer or client.

The algebraic sum of currents entering and leaving a node is zero. With incoming currents positive, assign outgoing currents negative signs.

For ideal components at angular frequency ω, inductive reactance is Xₗ = ωL and capacitive reactance magnitude is Xc = 1/(ωC). Their impedances have opposite imaginary signs.

For sinusoidal steady state, real power is Vrms Irms cos φ, where φ is the phase angle between voltage and current. Vrms Irms is apparent power.

Dissimilar metals in electrical contact and exposed to a common electrolyte can form a galvanic couple. The more active metal is typically the anode and corrodes preferentially.