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108

GLOSSARY OF NOTATIONS

A = Earthquake peak ground acceleration. IρM = influence coefficient for . = A0 Cross-sectional area of the stream. K1, K2, = aB Barge bow damage depth. K3, and K4 = Scour coefficients that account for the nose AF = Annual failure rate. shape of the pier, the angle between the direction b = River channel width. of the flow and the direction of the pier, the BR = Vehicular braking . streambed conditions, and the bed material size. = BRa Aberrancy base rate. Kp = Rankine coefficient. = = bx Bias of øx x/xn. KR = Pile flexibility factor, which gives the relative c = Wind analysis constant. stiffness of the pile and soil. C′=Response spectrum modeling parameter. L = Foundation depth. = CE Vehicular centrifugal force. Le = Effective depth of foundation (distance from = CF Cost of failure. ground level to point of fixity). = CH Hydrodynamic coefficient that accounts for the effect LL = Vehicular live load. of surrounding water on vessel collision . LOA = Overall length of vessel. = CI Initial cost for structure. LS = Live load surcharge. = Cp Wind coefficient. max(x) = Maximum of all possible x values. = CR Creep. M = Moment capacity. = cap CT Expected total cost of building bridge structure. M = Moment capacity of column. = col CT Vehicular collision force. M = Design moment. = design CV Vessel collision force. n = Manning roughness coefficient. = D Diameter of pile or column. N = Number of vessels (or flotillas) of type i. = i DC Dead load of structural components and nonstructural PA = Probability of aberrancy. attachments. P = Nominal design force for ship collisions. DD = Downdrag. B P = Base wind pressure. D = KÐS maximum difference between measured B0 n P = Axial force capacity. cumulative probability and expected probability. cap PC = Probability that bridge will collapse given that DW = Dead load of wearing surfaces and utilities. i,k a vessel of type i has collided with bridge e = Height of column above ground level. member k. EH = Horizontal pressure load earth surcharge load. P = Axial capacity of column. E = Modulus of for pile. col p P = Design axial force. EQ = Earthquake. design P = Probability of failure. EV = Vertical pressure from dead load of earth fill. f PG = Geometric probability. E = Wind exposure coefficient. z = f = Location of maximum moment in pile shaft PL Pedestrian live load. = below the soil surface. Pp Passive resultant resisting force of the soil. Psoil = Soil bearing capacity. F0 = Froude number. Q = River flow discharge rate. Fa = Site soil coefficients for short periods. R = Resistance or member capacity. Fapl = Equivalent applied force. RB = Correction factor for impacting barge width. Fi = Equivalent inertial force. RBa = Correction factor for bridge location for vessel FK = Applied force for load type K. FR = Friction. aberrancy. R = Correction factor for current acting parallel to Fv = Site soil coefficient for system with natural period c T = 1 sec. vessel path. R = Correction factor for vessel traffic . FY(Y*) = Cumulative probability = the probability that the D = variable Y takes a value less than or equal to Y*. RH Hydraulic radius. = G = Wind gust factor. Rm Response modification factor. = g = Acceleration caused by . Rxc Correction factor for crosscurrents acting H = Moment arm of applied force. perpendicular to vessel path. HL-93 = AASHTO LRFD design live load. S = Load effect. = IC = Ice load. S0 Slope of the river bed stream. = IIM = Dynamic amplification for live load. Sa Spectral acceleration. = ILL = Live load intensity in terms of HL-93. SC Scour. IM = Vehicular dynamic load allowance. SD1 = Spectral acceleration for a natural period T1 = 1

Ip = Moment of inertia of pile. sec.

IρH = Soil influence coefficient for lateral force. SDs = Spectral acceleration for short period Ts = 0.2 sec. 109

SE = Settlement. y0 = Depth of river flow just upstream of bridge pier SH = Shrinkage. excluding local scour. T = Natural period of the system. ymax = Maximum depth of scour. = t′=Natural period modeling factor. yscour Scour depth. = = T0 = Natural period at which the maximum spectral Z Safety margin RÐS. = acceleration is reached. Z0 Friction length for wind. β = TG = Temperature gradient. target Target reliability index used for calibration. β= T = Natural period at which the spectral acceleration begins Reliability index. s ε= to decrease. Standard error in regression equation. φ= TU = Uniform temperature. Resistance factor. φ = V = Velocity (for wind speed, vessels at impact, or river s Angle of friction for sand. Φ=Cumulative standard normal distribution function. flow). Φ = Unit adjustment parameter = 1.486 for U.S. units V = Wind friction velocity. 0 0 or = 1.0 for SI units. V = Wind velocity above ground level. 10 γ=Specific of sand. VB = Base wind velocity = 160 km/h (100 mph). γk = Load factor for load type K. Vcol = Shear capacity of column. λcyc = Variable representing cyclic effects. VDZ = Design wind velocity at design elevation Z. λeq = Modeling factor for the analysis of earthquake loads. Vx = Coefficient of variation (COV) of x = standard λLL = Live load modeling factor. deviation/mean value. λ = Scour modeling variable. = sc W Weight (for vessel or structure). λ = System factor that represents the capacity of the = sys w Vessel weight modeling variable. “system” to continue to carry loads after failure of first WA = Water load and stream pressure. member. = WL Wind on live load. λV = Statistical modeling for estimating wind speed V. = WS Wind load on structure. µcap = Ductility capacity of a concrete column. = x Vessel collision modeling variable. µspecified = Specified ductility capacity. = øx Mean value of random variable x. νi = Yearly rate of collisions for each vessel (or flotilla) of Xmax,T = Maximum value of variable X in a period of time T. type i. xn = Nominal value of x as specified by design code. σx = Standard deviation of a random variable x. 106

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