BEM PCE Civil & Structural flashcards

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

Average end area method

Earthwork volume formula V = L(A1 + A2)/2, where A1 and A2 are cross-sectional areas at the two stations separated by distance L. Approximate but standard for roadway cut and fill quantities.

Prismoidal correction

Refines average end area volumes using V = L(A1 + 4Am + A2)/6, where Am is the mid-section area. Required when ground changes markedly between stations or for large irregular sections.

Degree of curve (arc)

Central angle subtended by a 30 m arc (or 100 ft arc in US practice). Related to radius by D = 5729.58/R when R is in feet, or D = 1746.4/R when R is in metres.

Horizontal curve tangent

Tangent length T = R tan(Δ/2), where Δ is the total intersection (deflection) angle. Used to locate the PC and PT from the point of intersection.

Stopping sight distance

Sum of brake reaction distance (0.278 V t) and braking distance V²/(254(f ± G)). Design must provide at least this distance along the roadway for the design speed.

Vertical curve turning point

Location of the high or low point at x = −g1L/(g2 − g1) from the PVC. Valid only when x falls between 0 and L; otherwise the extreme lies outside the curve.

Superelevation equation

e + f = V²/(127R) with V in km/h and R in metres. The term e is the rate of roadway cross slope and f the side friction factor demanded by the curve.

Rational method runoff

Q = CiA estimates peak runoff, where C is a runoff coefficient (0.3–0.95), i is rainfall intensity, and A is the tributary area. Applies to small catchments, generally under about 80 hectares.

Manning pipe capacity

Q = (1/n) A R^(2/3) S^(1/2), with n the roughness coefficient, R the hydraulic radius (area/wetted perimeter), and S the energy slope. Standard for gravity storm and sanitary sewers.

Traffic flow identity

Flow q equals density k multiplied by space mean speed v. Because q = kv, maximum flow (capacity) occurs at the density where the speed–density product peaks.

Relative compaction

Field dry density divided by laboratory maximum dry density for the same soil and compaction energy. Acceptance criteria commonly require 95% standard Proctor or 92% modified Proctor.

Plasticity index

PI = liquid limit minus plastic limit. It measures the range of water content over which a soil behaves plastically; higher PI indicates more clay and greater volume change potential.

Group index formula

GI = (F − 35)[0.2 + 0.005(LL − 40)] + 0.01(F − 15)(PI − 10), where F is percent passing the 0.075 mm sieve. Higher values indicate poorer subgrade quality.

Effective stress principle

Total vertical stress minus pore water pressure, σ' = σ − u. Effective stress controls shear strength, consolidation settlement, and bearing capacity in saturated soils.

Terzaghi bearing capacity

Ultimate bearing capacity for a strip footing: qu = c Nc + q Nq + 0.5 γ B Nγ, with N factors depending on the friction angle. Shape and depth factors modify this for real footings.

Sieve analysis coefficients

Cu = D60/D10 and Cc = D30²/(D10 × D60). A well-graded gravel has Cu ≥ 4 and 1 ≤ Cc ≤ 3; a well-graded sand requires Cu ≥ 6 with the same Cc range.

Nominal moment, singly reinforced

Mn = As fy (d − a/2) with a = As fy/(0.85 f'c b). The lever arm between tension steel and the equivalent rectangular compression block determines the resisting moment.

Tension-controlled strain limit

A section is tension-controlled when the net tensile strain in the extreme tension steel at nominal strength is at least 0.005. Such sections permit a strength reduction factor φ of 0.90 for flexure.

Balanced reinforcement ratio

ρb = 0.85 β1 (f'c/fy) × [0.003/(0.003 + εy)], where εy = fy/Es. It corresponds to simultaneous concrete crushing and steel yielding at nominal strength.

Minimum beam reinforcement

As,min ≈ max(0.25√f'c/fy, 1.4/fy) × bw × d in SI units, providing ductility so a beam does not fail abruptly when cracked moment capacity is exceeded.

Concrete shear strength Vc

Nominal concrete shear resistance of about 0.17 λ √f'c bw d (SI, in newtons), with λ = 1.0 for normal-weight concrete. Shear design factor φ is 0.75.

Stirrup spacing equation

s = Av fy d / Vs, where Vs = Vu/φ − Vc. Av is the total area of stirrup legs crossing the shear plane and d is the effective depth of the section.

Long-term deflection multiplier

λΔ = ξ/(1 + 50ρ'), where ρ' is the compression steel ratio and ξ depends on the sustained load duration. Multiplies the immediate deflection due to sustained loads.

Euler buckling load

Pcr = π²EI/(kL)², where k depends on end restraint (0.5 fixed-fixed, 0.7 fixed-pinned, 1.0 pinned-pinned, 2.0 cantilever). Governs slender column capacity.

Steel tension rupture limit

Nominal rupture strength is Fu Ae, with Ae = U An. The shear lag factor U accounts for non-uniform stress when not all element area is connected.

Plastic moment capacity

Mp = Fy Zx, where Zx is the plastic section modulus. Represents the full plastic hinge moment of a compact steel section with adequate lateral bracing.

Unbraced length limits

Lp = 1.76 ry √(E/Fy) is the limiting unbraced length for full plastic moment; Lr is the length beyond which elastic lateral-torsional buckling governs. Capacity reduces between them.

Fillet weld throat

Effective throat equals 0.707 times the weld leg size for a 45° fillet. Nominal strength is Rn = 0.6 FEXX times the throat area and weld length.

Bolt shear strength

Rn = Fnv Ab per shear plane, where Ab is the nominal bolt area. Threads in the shear plane reduce Fnv relative to threads excluded. Bearing must also be checked.

Strength load combination

1.2D + 1.6L + 0.5(Lr or S or R). Dead load is factored 1.2 and live load 1.6; roof live, snow, and rain loads enter at 0.5 when not the principal variable load.