GATE ME key terms

The critical axial compressive load at which a slender ideal column becomes unstable and bows sideways, equal to pi squared times flexural rigidity divided by effective length squared.

Effective length of a compression member divided by its least radius of gyration; a large value means a thin column that fails by buckling rather than by yielding.

Square root of the second moment of area divided by cross-sectional area; it measures how far material is spread from the centroid and sets column buckling resistance.

The equivalent pinned-end span of a column that reproduces the buckling load of the actual end conditions, obtained by multiplying actual length by a support-dependent factor.

Integral of area times squared distance from an axis, quantifying a section's resistance to bending about that axis; also called moment of inertia of area.

Normal stress in a beam computed as bending moment times distance from the neutral axis divided by second moment of area; maximum at the outermost fibre.

Line in a beam cross-section where longitudinal bending stress is zero and which passes through the centroid for elastic bending under pure moment.

Graphical construction plotting normal stress on one axis and shear stress on the other, letting you read principal stresses and maximum shear stress for a stress state.

Normal stress acting on a plane where shear stress vanishes; the three principal stresses of a general state are eigenvalues of the stress tensor.

Equivalent scalar stress from distortion energy theory, combining principal stresses into one value compared against yield strength for ductile materials under multiaxial loading.

Tresca yield criterion stating that ductile yielding begins when the largest shear stress reaches the value at yield in simple tension, i.e. half the yield strength.

Stress amplitude below which a ferrous material survives an effectively infinite number of cycles without fatigue failure, determined from an S-N curve.

Ratio of peak local stress near a hole, notch or fillet to the nominal stress in the same section; it raises fatigue risk where geometry changes abruptly.

Number of independent inputs needed to define a mechanism's configuration, given by Gruebler's or Kutzbach's criterion using links, joints and their types.

Criterion for a four-bar linkage stating that the shortest link can fully rotate only if the sum of shortest and longest links is at most the sum of the other two.

Dimensionless ratio of inertial to viscous forces in a flow, equal to density times velocity times length divided by dynamic viscosity; it predicts laminar or turbulent behaviour.

Ordered fluid motion in parallel layers without macroscopic mixing, occurring at low Reynolds number and giving parabolic velocity profiles in fully developed pipe flow.

Four times the flow cross-sectional area divided by wetted perimeter; it lets circular-pipe correlations be applied to non-circular ducts and open channels.

Dimensionless ratio of convective to conductive heat transfer at a surface, equal to heat transfer coefficient times characteristic length divided by fluid thermal conductivity.

Dimensionless ratio of momentum diffusivity to thermal diffusivity of a fluid, indicating how quickly velocity and temperature profiles develop relative to each other.

Dimensionless group comparing buoyancy forces to viscous forces in free convection, formed from thermal expansion coefficient, temperature difference and characteristic length cubed.

Ratio of internal conduction resistance to external convective resistance of a solid body; small values justify the lumped capacitance assumption for transient cooling or heating.

Transient heat transfer simplification treating a body as uniform in temperature, valid for Biot number below about 0.1, giving exponential decay toward ambient temperature.

Ratio of actual thermal efficiency to the maximum reversible efficiency possible between the same reservoirs; it measures how close a device approaches ideal performance.

Maximum useful work obtainable from a system as it reversibly comes to equilibrium with a specified dead-state environment; destroyed by irreversibilities such as friction and unrestrained heat transfer.

Pressure a flowing fluid would reach if brought to rest isentropically; equals static pressure plus dynamic pressure for incompressible flow.

Increase in yield strength caused by dissolved solute atoms distorting the crystal lattice and impeding dislocation motion; larger size mismatch gives stronger effect.

Line defect in a crystal along which atoms are out of registry; its motion produces plastic slip, so obstacles to dislocation movement raise strength.

Empirical equation showing yield strength rises with the inverse square root of grain size, because grain boundaries block dislocation pile-ups and slip transmission.

Solid-state transformation in which one solid phase on cooling forms two different solid phases simultaneously at a fixed composition and temperature, as in pearlite formation.

Controlled reheating of quenched martensitic steel to restore toughness by allowing carbon to precipitate, trading some hardness and strength for ductility.

Network of pouring basin, sprue, runner and ingate that delivers molten metal into a mould cavity while controlling fill rate, turbulence and slag entrapment.

Reservoir of molten metal in a casting mould that feeds shrinkage as the casting solidifies, designed to freeze after the section it supplies.

Empirical relation stating solidification time is proportional to the square of volume-to-surface-area ratio of a casting, used to size risers and compare freezing order.

Approximate threshold, near 0.3 to 0.5 of absolute melting point, above which cold-worked metal forms new strain-free grains and loses its work hardening.

Relation between cutting speed and tool life of the form speed times life to the power n equals a constant, where n depends on tool and workpiece material.

Relative ease with which a material can be cut, judged by tool wear rate, cutting forces, surface finish and chip form under given machining conditions.

Longest sequence of dependent activities in a project network, which fixes the minimum project duration and has zero total float.

Amount of time an activity can be delayed without delaying project completion, computed as latest finish minus earliest finish in a network schedule.

Standard deviation of a data set divided by its mean, expressing relative dispersion as a dimensionless fraction useful for comparing groups with different scales.

Probability model for the number of rare independent events in a fixed interval, defined by a single mean rate parameter equal to its variance.

Scalar that, multiplied by a nonzero vector, gives the same result as applying a square matrix to that vector; roots of the characteristic equation.

Number of linearly independent rows or columns; it determines whether a linear system has a unique solution, none, or infinitely many.

Identity equating the volume integral of the divergence of a vector field to the closed-surface integral of its normal component, used to convert between surface and volume forms.

Vector of partial derivatives of a scalar field, pointing in the direction of steepest increase and perpendicular to level surfaces.

Quantitative aptitude question type asking whether the given statements are enough to answer a question, without requiring the actual numerical answer.