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Appendix D NOTATION AND SI CONVERSION FACTORS
D.1 NOTATION The following notation is used in this manual: A B Cf COVX
C&M D Dbottom Dtop DL e E fact fnom F Fa Fb Fb5%LEL Fy
= projected wind area (ft2) = response term in calculating the wind force, F = shape factor (force, or drag, coefficient), ASCE Manual 74 (ASCE 1991) = coefficient of variation, measure of variability of the structural strength (X = R) or other paraeter of interest (for example, X = P, O); defined as the standard deviation divided by the mean value. = loads produced by construction and maintenance operations = outer diameter of steel pole = diameter at bottom (groundline) of pole = diameter at top of pole = dead loads, such as weights of bare wires, hardware, insulators, and supporting structures = base of the natural logarithm = 2.718282 = exposure factor in calculating the wind force, F = actual bending stress = allowable bending stress = wind force, in pounds = allowable (failure) bending stress of multisided steel pole (Eqs. B-1 and B2) = allowable (failure) bending stress for round steel pole (Eqs. B–3 and B–4) = 5% LEL bending stress = yield stress of steel
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RELIABILITY-BASED DESIGN OF UTILITY POLE STRUCTURES
FA
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G
H I50, I75 Itop K K kN kv Kz L LEL
LL
1n[ ] LTL
m[ . ] mP M
= variability in strength property introduced during fabrication = gust response factor as described in the forthcoming edition of ASCE Manual 74 (ASCE 2002) or National Electric Safety Code, C2-2002 (NESC) (IEEE 2002) for wires and structures = effective height in calculating Kz (ft) confidence level factors, nonparametric PDF (Table 4-1) = moment of inertia at top of pole = distance from the mean of a normal population to a target LEL in units of standard normal deviations (Eq. 4-4) K factor derived to provide confidence ξ that the sample LEL will be less than or equal to the target value of the parent population (Table 4-1) = log-normal factor relating mean strength to nominal 5% LTL (Eqs. 4-8, 4-9) = factor used in calculating the wind force F = velocity pressure exposure coefficient = distance from groundline to centroid of horizontal loads on pole = lower exclusion limit of distribution identifies the upper limit on a prescribed portion of the low tail of the distribution. For example, 5% of the area under a probability distribution function will lie below the 5% LEL and 95% will lie above it. = legislated loads, which are any set of minimum loadings specified by law for the particular service area of the line; the most common of these are the NESC district loadings with the appropriate NESC overload and strength factors (IEEE 2002). = natural logarithm (base e) = lower tolerance limit (of a strength property). The LTL strength is an estimate of the LEL strength for a finite sample size. The LTL is associated with a confidence value that it is less than or equal to the corresponding population LEL. For example, the 5% LTL of pole strength with 50% confidence calculated using a small sample has a 50% probability of being smaller than the population 5% LEL = mean of variable in the subscript [ . ] = mean of professional factor, P = variability of strength property attributed to material variability
Reliability-Based Design of Utility Pole Structures
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Appendix D: Notation and SI Conversion Factors
Mnom M5%LEL MOE N O
= = = = =
P
=
Pcr PDF
= =
Q50
=
QRP
=
R Re
= =
Rm Rn
= =
S Sact Snom s SL
= = = = =
t
=
T/D
=
95
nominal moment capacity 5% LEL bending moment modulus of elasticity number of specimens in a sample variability in strength property introduced by other effects such as deterioration, design error, and environmental risk. These effects must be combined to give an estimate of the pole strength variability. professional factor representing the accuracy of a strength predictive model critical buckling load of pole probability density function. Parametric or nonparametric function used to represent frequency of occurrence over a representative range of values of a random variable. loads produced by the wind velocity V50 or combinations of ice and wind that have a 50-year (approximate) return period (RP) loads similar to Q50, except that they have an RP-year return period resistance or strength of a component or a structure e% lower exclusion limit of strength, corresponding to the strength level for which there is an e% probability that a given pole or structural component will be less than or equal; thus, (100 − e)% of the poles or components exceed this strength level. mean strength nominal or characteristic strength of a component, calculated using an approved design guide, defined as the 5% lower exclusion limit (LEL), or as estimated by the 5% lower tolerance limit (LTL), at a specified confidence (e.g., 50% or 75%). section modulus actual section modulus nominal section modulus sample standard deviation security loads such as anticascading loads that will result in a structure with sufficient strength to limit the consequences of failures from weather-related or accidental events plate thickness of steel pole side or steel pole tube transmission and distribution
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RELIABILITY-BASED DESIGN OF UTILITY POLE STRUCTURES
= 3-s gust wind velocity with a 50-year return period (RP) VL = total vertical load on pole (Appendix A.9) w = width each side (flat) of steel pole section = reliability index. (See Eq. 1-1.) = load factor applied to the load effect Q50 under consideration CM = the load factor applied to all the loads in Eq. 2-3 = scale parameter for the Weibull distribution function (Eq. 4-10) = proportion (decimal value) of the range of values in a parent population included in a sample of N specimens = mean of the natural logarithms of the data points µ = standard deviation of the natural logarithm of the data points = assurance (%) that the range of values in a sample will encompass a prescribed portion of the parent population = standard deviation for normal probability distribution function R = standard deviation of strength = strength (or resistance or capacity) factor. The φ takes into account variability in material, dimensions, workmanship, and the uncertainty inherent in the equation used to calculate Rn as a predictor of the true strength of the component. It can also be used to coordinate the strengths of components and subsystems by adjusting their reliabilities. Procedures for selecting φ are provided in this document. LL = a strength factor to use with legislated loads (this factor is to be obtained from the appropriate code documents). 0 = location parameter for the Weibull distribution function (Eq. 4-10) = coefficient of variation of the strength data (R/Rm) = slope or shape factor for the Weibull distribution function (Eq. 4-10) [ . ]m = mean of variable [ . ]
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V50
Reliability-Based Design of Utility Pole Structures
Appendix D: Notation and SI Conversion Factors
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D.2 SI CONVERSION FACTORS 1 ft 1 ft-lb 1 in. 1 pound (lb) 1 lb/ft 1 lb/ft2 (psf) 1 lb mass/ft3 (pcf) 1 mile per hour (mph)
= = = = = = =
0.305 meter (m) 1.36 m-N 25.4 millimeters (mm) 4.45 newtons (N) 14.6 N/m 47.8 pascals (Pa) (N/m2) 0.016 gram/cubic centimeter (g/cc)
= 0.45 meter/s (m/s)
To convert temperature, θ, from °F to °C, Τ (°C) = 5/9 [Τ(°F) − 32 °F].
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