Blast-Resistant Highway Bridges: Design and Detailing Guidelines (2010)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

141 Ac = area of concrete core (in.2) Ag = gross cross-sectional area (in.2) As = area of longitudinal reinforcement (in.2) Ash = area of transverse reinforcement (in.2) Av = area of shear reinforcement within a distance s (in.2) b = effective width of cross section (in.) c = concrete clear cover (in.) Cage = age of concrete (months) d = effective depth of cross section (in.) db = nominal diameter of reinforcing bar (in.) dv = effective moment arm (in.) D = diameter or width (in.) Dcore = diameter or width of concrete core (in.) Dr = diameter or width passing through longitudinal reinforcement (in.) DIF = dynamic increase factor Es = steel modulus of elasticity (ksi) fdu = dynamic ultimate strength of reinforcing bars (psi) fdy = dynamic yield strength of reinforcing bars (psi) fu = ultimate strength of reinforcing bars (psi) fy = yield strength of reinforcing bars (psi) f 'c = specified compressive strength of concrete at 28 days (psi) f 'dc = dynamic compressive strength of concrete (psi) Fe = force applied to a single-degree-of-freedom system hc = core dimension of column in the direction under consideration (in.) H = charge height above ground surface HT = height of triple point above ground surface ir = unit positive normal reflected impulse (psi-ms) is = unit positive incident impulse (psi-ms) IBEL = BEL equivalent impulse (psi-ms) Ix = moment of inertia (in.4) ke = stiffness of a single-degree-of-freedom system KA = age increase factor for concrete KE = strength increase factor for concrete and steel L = height of column (in.) Lo = column height between supports (in.) Lw = wavelength of positive phase (ft) L I S T O F V A R I A B L E S

mo(x) = mass per unit length of a member Me = mass of a single-degree-of-freedom system Mn = nominal moment capacity (kip-ft) MP = plastic moment capacity (kip-ft) P = applied load (lb) PBEL = BEL equivalent uniform pressure (psi) Po = ambient atmospheric pressure (psi) Pr = peak positive normal reflected pressure (psi) Ps = peak incident overpressure at Mach front (psi) Pso = peak positive incident pressure (psi) R = standoff, distance between center of blast source and target (ft) s = center-to-center spacing or pitch of transverse reinforcement (in.) S = section modulus (in.3) Sx = distance from nearest free edge to point of interest (ft) tA = time of arrival (s) tBEL = BEL duration (ms) tc = clearing time (s) to = positive phase duration (s) to – = negative phase duration (s) Us = shock front velocity (ft/s) Vbase = maximum shear at base (lb) Vc = nominal shear strength provided by concrete (lb) VN = nominal shear strength (lb) Vs = nominal shear strength provided by steel (lb) w = charge weight parameter wo = maximum magnitude of assumed blast load shape applied to a member wo(x) = assumed blast load shape applied to a member W = charge weight of explosive WTNT = charge weight of explosive (lb equivalent TNT) z = standoff distance parameter Z = scaled standoff (ft/lb1/3) Zx = plastic section modulus (in.3) α = angle of incidence (degrees) γv = average shear strain across section γc = concrete unit weight (lb/ft3) δ = displacement Δelastic = displacement at the elastic limit (in.) Δmax = maximum displacement of a member (in.) Δ(x) = displaced shape of a beam θ = support rotation (degrees) θSBEDS = SBEDS support rotation (psi) µ = flexural ductility ratio µSBEDS = SBEDS flexural ductility (psi-msec) ρs = volumetric reinforcement ratio ρL = longitudinal reinforcement ratio φ(x) = normalized displaced shape of a beam 142