FE Mechanical key terms

A single force that produces the same translational effect on a body as all the individual forces acting on it combined. Found by vector addition of force components, usually resolved into x and y directions.

The tendency of a force to rotate a body about a point or axis, equal to force times perpendicular distance from the point to the force's line of action. Sign convention must be stated.

Two parallel forces of equal magnitude, opposite direction, and non-collinear lines of action. A couple produces pure rotation with zero net force, so its moment is the same about every point in the plane.

A sketch isolating one body and showing every external force and moment acting on it, including reactions, weights, and applied loads, with supports replaced by their reaction components. Basis for writing equilibrium equations.

The condition in which a body has zero translational and rotational acceleration. For a planar rigid body this requires the sum of forces in x and y and the sum of moments about any point to each equal zero.

A classification of a structure based on whether its support reactions can be found from equilibrium equations alone. Determinate structures have exactly as many unknown reactions as independent equilibrium equations.

A framework of slender members connected at joints assumed to be frictionless pins, loaded only at joints. Under these assumptions each member carries only axial force, either tension or compression.

A truss analysis technique applying force equilibrium at each pin joint in turn, starting where at most two member forces are unknown, to solve for all member axial forces.

A truss member carrying no axial load under the given loading, identified by inspection at a joint where only two non-collinear members meet with no external load, or three members where two are collinear.

The geometric center of a line, area, or volume, found by first moments of length, area, or volume divided by total length, area, or volume. For a uniform body it coincides with the center of gravity.

A tangential resistance force at contacting surfaces that opposes relative motion or its tendency. Static friction can reach a maximum proportional to the normal force; kinetic friction is roughly constant during sliding.

The description of motion in terms of position, velocity, acceleration, and time, without reference to the forces causing the motion. Includes rectilinear, curvilinear, and rotational motion descriptions.

The study of motion accounting for the forces and moments that produce it, using Newton's second law, work-energy methods, or impulse-momentum methods to relate forces to changes in motion.

The two components of acceleration for a particle on a curved path. Tangential acceleration changes speed and equals the rate of change of velocity magnitude; normal acceleration changes direction and equals speed squared divided by radius of curvature.

The inward-directed acceleration of a body moving on a circular path at constant speed, of magnitude speed squared divided by path radius. It arises from a net inward force such as tension or gravity.

The velocity of one body as observed from a moving reference frame attached to another body, equal to the vector difference of their absolute velocities. Essential for analyzing connected or contacting moving parts.

For a rigid body in planar motion, the point about which the body appears to rotate at a given instant, having zero velocity at that moment. Locating it lets you relate velocities of points through angular velocity.

A statement that the net work done by all forces on a body equals its change in kinetic energy. Useful when forces vary with position or when time is unknown but displacement is known.

A statement that the linear impulse of the net force over a time interval equals the change in linear momentum of the body. Useful when forces act over short times or when displacement is unknown.

A measure of a body's resistance to angular acceleration about a specified axis, equal to the integral of mass times squared distance from the axis. Depends on the axis location and mass distribution.

The distance from an axis at which a body's entire mass could be concentrated to give the same moment of inertia about that axis. Equals the square root of moment of inertia divided by mass.

A relation giving the moment of inertia about any axis parallel to an axis through the centroid: the centroidal value plus mass (or area) times the squared distance between the axes.

A geometric property of a cross section equal to the integral of squared distance from a reference axis over the area, measuring resistance to bending. Often called second moment of area.

A cross-sectional property equal to the area moment of inertia about the centroidal axis divided by the distance from that axis to the extreme fiber. Used to compute maximum bending stress.

Normal stress in a beam caused by an internal bending moment, distributed linearly from zero at the neutral axis to a maximum at the extreme fiber. Computed as moment times distance from neutral axis divided by moment of inertia.

The line in a beam cross section where bending stress is zero and which passes through the section centroid for elastic bending. Fibers on one side are in tension, the other in compression.

Stress acting parallel to a material surface, arising from transverse shear forces, torsion, or direct shear. In beams it is largest at the neutral axis and zero at the free surfaces for transverse loading.

Twisting of a member caused by an applied torque about its longitudinal axis. Shear stress varies linearly with radial distance from the axis and is largest at the outer surface for a circular shaft.

A cross-sectional property equal to the integral of squared radial distance from an axis over the area, measuring resistance to torsion. For a circular section it equals the sum of two perpendicular area moments of inertia.

A plot of engineering stress versus engineering strain from a tension test, revealing elastic modulus, yield strength, ultimate strength, and ductility. The elastic region is linear for many metals up to the proportional limit.

The linear relation between stress and strain in the elastic range, with the constant of proportionality being the elastic modulus in tension or the shear modulus in shear. Valid only below the proportional limit.

The stress at which a material begins to deform permanently, often defined by a 0.2 percent offset method for metals lacking a distinct yield point. A key allowable-stress basis in design.

The negative ratio of lateral strain to axial strain for a material under uniaxial loading. Typical metals fall near 0.3; the value approaches 0.5 for nearly incompressible materials such as rubber.

The ratio of a material's failure-level stress to the allowable working stress, or of failure load to design load. It accounts for uncertainty in loads, material properties, and analysis methods.

An engineer's duty to hold public safety, health, and welfare paramount, practice only within competence, be objective and truthful, and avoid conflicts of interest. Codified in many engineering society codes of ethics.

A situation in which personal, financial, or other interests could improperly influence professional judgment. Engineers must disclose such situations and remove or manage the influence before acting.

The licensed engineer's formal certification that work was performed under their responsible charge and meets applicable standards. Applying a seal to work outside one's competence or control is an ethics violation.

The principle that a sum of money available today is worth more than the same sum later because it can earn interest. Basis for comparing cash flows occurring at different times.

Interest computed on both the original principal and previously accumulated interest, so the balance grows geometrically over time. The effective annual rate exceeds the nominal rate when compounding occurs more than once per year.

The equivalent value today of a future cash flow or series of cash flows, found by discounting each amount at a chosen interest rate. Used to compare alternatives on a common time basis.

The sum of discounted cash inflows minus discounted cash outflows for a project at a specified rate. A positive value indicates the project earns more than the required rate of return.

The interest rate at which a project's net present value equals zero, making discounted benefits equal discounted costs. Compared against a minimum attractive rate of return to accept or reject a project.

The systematic allocation of a tangible asset's cost over its useful life for accounting or tax purposes, such as straight-line or declining-balance methods. It is not a cash flow itself.

The mean is the arithmetic average of a data set; the standard deviation measures typical spread about that mean as the square root of variance. Together they describe the center and dispersion of a distribution.

A symmetric, bell-shaped continuous probability distribution defined by its mean and standard deviation. About 68 percent of values fall within one standard deviation of the mean and about 95 percent within two.

A result stating that the sampling distribution of the sample mean approaches a normal distribution as sample size grows, regardless of the population's shape, provided observations are independent and variance is finite.

A range of values, computed from sample data, that is expected to contain an unknown population parameter with a stated probability over repeated sampling. Width shrinks as sample size or confidence level changes.

A procedure comparing sample evidence against a null hypothesis using a test statistic and a chosen significance level. A p-value below the significance level leads to rejecting the null hypothesis.

In hypothesis testing, a Type I error rejects a true null hypothesis, while a Type II error fails to reject a false null hypothesis. Their probabilities trade off against each other for a fixed sample size.

Counting rules for selecting items from a group. Permutations count arrangements where order matters; combinations count selections where order does not, and are always fewer for the same group size.

Basic relations for combining event probabilities, including the addition rule for unions and the multiplication rule for intersections. Mutually exclusive events cannot occur together; independent events do not affect each other's probability.

The probability distribution of the number of successes in a fixed number of independent trials, each with the same success probability. Defined by trial count and success probability.

The instantaneous rate of change of a function with respect to a variable, interpreted geometrically as the slope of the tangent line. Used to find maxima, minima, and rates in engineering models.

The accumulation of a function over an interval, interpreted as signed area under a curve. The definite integral gives totals such as work, mass, or centroid coordinates from distributed quantities.

The process of finding the input values that maximize or minimize a function, typically by setting its derivative to zero and checking second-derivative or boundary conditions for the type of extremum.

Fitting a straight line to paired data by least squares, minimizing the sum of squared vertical deviations. The slope estimates change in the response per unit change in the predictor.