ESE CE Prelims flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Degree of static indeterminacy

For a plane rigid frame it equals 3m + r − 3j, where m is member count, r reaction components, j joints. For a plane truss it is m + r − 2j. Positive values indicate redundant forces beyond equilibrium.

Kinematic indeterminacy

The number of independent joint displacements that must be restrained to make the structure non-swaying. Count three per plane rigid joint, two per truss joint, and one per roller direction. It governs the size of stiffness-method equations.

Distribution factor

Ratio of a member's rotational stiffness (4EI/L for fixed far end, 3EI/L for pinned) to the sum of stiffnesses of all members meeting at the joint. Used in moment distribution to apportion unbalanced moment.

Carry-over factor

Fraction of an applied joint moment transferred to the far end of a member. It equals 0.5 when the far end is fixed and 0 when the far end is pinned, forming the basis of the moment-distribution iteration.

Euler buckling load

Critical axial load for a slender column, Pcr = π²EI/(KL)², where K depends on end conditions (0.5 to 2.0). Valid only when the slenderness ratio exceeds the elastic limit value.

Effective length factor K

Multiplier converting actual column length to equivalent pinned-ended length. Values are approximately 0.5 fixed-fixed, 0.7 fixed-pinned, 1.0 pinned-pinned, and 2.0 for a cantilever column.

Limiting neutral axis depth

The xu/d ratio at which the concrete reaches its ultimate strain simultaneously with steel yielding. It is 0.53 for Fe 415, 0.48 for Fe 500, and 0.46 for Fe 550 steel, defining the singly reinforced limit moment.

Balanced section

A reinforced concrete section in which concrete crushing and steel yielding occur simultaneously. It gives the maximum moment a singly reinforced section can resist; adding more tension steel makes the section over-reinforced and brittle.

Minimum shear reinforcement

Required stirrup provision when nominal concrete shear strength governs: Asv/(b·sv) must be at least 0.4/(0.87 fy). It prevents sudden brittle shear failure and controls diagonal cracking in beams.

Nominal cover requirements

Minimum concrete cover to reinforcement depends on exposure and member: typically 20 mm for slabs, 25 mm for beams, 40 mm for columns, and 50 mm for footings, with higher values for moderate or severe exposure.

Terzaghi bearing capacity equation

Ultimate bearing capacity for a strip footing is qu = cNc + qNq + 0.5γBNγ. Shape factors modify the cohesion and width terms for square and circular footings. Factors Nc, Nq, Nγ depend on the friction angle.

Net safe bearing capacity

The allowable pressure in excess of the existing overburden at foundation level. It equals (qu − γDf)/FOS, and the gross safe value adds γDf back. Used to size footings against shear failure.

Immediate settlement

Elastic compression of soil under a loaded footing, computed as Si = qB(1 − μ²)If/Es. It occurs during construction, is largest in saturated sands, and is separate from consolidation settlement in clays.

Consolidation settlement

Time-dependent compression of saturated clay as pore water drains. For normally consolidated soil, Sc = (Cc·H/(1 + e0))·log10((σ0 + Δσ)/σ0). Preconsolidated clays use the recompression index until the preconsolidation pressure.

Liquefaction

Loss of shear strength in loose saturated sands when cyclic loading raises pore pressure to equal effective stress. Assessed using standard penetration resistance and plasticity; mitigated by densification, drains, or replacement.

Effective stress principle

Total stress equals effective stress plus pore water pressure: σ = σ' + u. Only effective stress controls soil shear strength and compression. Lowering the water table increases effective stress and causes settlement.

Mohr-Coulomb shear strength

Soil shear strength is τ = c' + σ'·tan φ', where c' is effective cohesion and φ' the effective friction angle. Drained tests give effective parameters; undrained tests give total stress parameters with φu = 0.

Rankine active earth pressure

Lateral pressure coefficient Ka = (1 − sin φ)/(1 + sin φ) = tan²(45° − φ/2). Active pressure at depth z is Ka·γ·z minus cohesion effects; passive coefficient Kp is the reciprocal.

Manning equation

Open-channel mean velocity V = (1/n)·R^(2/3)·S^(1/2), with R = A/P and S the bed slope. Roughness n ranges near 0.013 for concrete and 0.030 for natural channels.

Most efficient channel section

The trapezoidal or rectangular geometry giving maximum discharge for a given area and roughness. For a trapezoid this occurs when the hydraulic radius equals half the depth and the half top width equals the sloping side length.

Critical depth

Depth at which specific energy is minimum for a given discharge. In a rectangular channel yc = (q²/g)^(1/3), where q is discharge per unit width. Flow is supercritical when depth is below yc.

Hydraulic jump

Rapid transition from supercritical to subcritical flow with energy loss. Conjugate depths follow y2/y1 = 0.5(√(1 + 8Fr1²) − 1), and the head loss equals (y2 − y1)³/(4y1y2).

Froude number

Ratio Fr = V/√(gD), where D is hydraulic depth. Fr < 1 is subcritical, Fr = 1 critical, and Fr > 1 supercritical. It governs channel flow regime and jump formation.

Chezy formula

Velocity in open channel V = C√(RS), where C is the Chezy coefficient, R hydraulic radius, S bed slope. Manning's n relates to C through C = R^(1/6)/n. Used for uniform flow computation.

Stadia distance formula

For inclined sights, horizontal distance D = 100·s·cos²θ plus instrument constants, where s is staff intercept and θ the vertical angle. Vertical component is 100·s·sinθ·cosθ plus constants.

Curvature and refraction correction

Curvature correction is 0.0785 D² metres with D in kilometres; refraction is about one-seventh of it. Combined correction is −0.0673 D², subtracted from leveling readings to correct for Earth curvature.

Traverse closing error

Vector sum of latitude and departure misclosures, e = √(ΣL² + ΣD²). Relative precision equals e divided by total traverse perimeter, expressed as 1 in perimeter/e. Adjusted by Bowditch or transit rule.

Contour interval

Vertical distance between successive contour lines, chosen as maximum elevation difference divided by the number of contours. Smaller intervals suit flat terrain and detailed design; larger intervals suit steep, small-scale maps.

Bending moment diagram ordinate

For a simply supported beam with a point load, maximum moment PL/4 at midspan. For uniformly distributed load w, maximum is wL²/8. Moment is maximum where shear crosses zero.

Slope-deflection equation

Member end moment expressed as M = (2EI/L)(2θnear + θfar − 3Δ/L) plus fixed-end moments. It forms the stiffness method basis for continuous beams and frames with joint translation.

Shear strength of concrete

Nominal shear stress τc depends on percentage tension steel and concrete grade, tabulated in design codes. Design shear τv = Vu/(bd) must not exceed τc,max; excess requires larger section or stirrups.

Plastic section modulus

For a steel section, Zp = Ac·ȳc + At·ȳt about the equal-area axis. Plastic moment Mp = fy·Zp; shape factor = Zp/Zelastic, about 1.5 for a rectangle and 1.14 for a wide-flange beam.