Variables

Description and Units

A, B, C

Coefficients in Ramberg-Osgood stress-strain relationship for stainless steel prestressing strands

A_c

Area of section calculated using the gross composite concrete section properties of the girder and the deck and the deck-to-girder modular ratio, in.²

A_g

Gross area of section, in.²

A_ps

Area of prestressing steel, in.²

A_px

Area of stainless steel prestressing strand no. x, in.²

A_s

Area of nonprestressed tension reinforcement, in.²

a

Shear span or depth on compressive concrete stress block, in.

a/d

Shear span to effective depth ratio

b

Width of the compression face of the member, in.

b_w

Web width or diameter of a circular section, in.

C

Total compressive force, kip

c

Distance from the extreme compression fiber to the neutral axis, in.

COV(P)

Coefficient of variation

d_b

Nominal diameter of strand, a reinforcing bar, or wire, in.

d_e

Effective depth from extreme compression fiber to the centroid of the tensile force in tensile reinforcement, in.

d_px

Distance from the extreme compression fiber to the centroid of stainless steel prestressing strands in layer x, where x is replaced by the row number, with layer 1 being the layer closest to the extreme tension fiber, in.

d_t

Effective depth of the member defined as the distance between the extreme compression fiber and the centroid of the primary longitudinal reinforcement, in.

d_v

Effective shear depth taken as the distance measured perpendicular to the neutral axis, between the resultants of the tensile and compressive forces due to flexure, in.

E

Modulus of elasticity, ksi

E_c

Modulus of elasticity of concrete, ksi

E_p

Modulus of elasticity of stainless steel prestressing strands, ksi

e_pg

Eccentricity of prestressing force with respect to centroid of girder, in.

F

Fabrication tolerances

f′_c

Specified compressive strength of concrete for use in design, ksi

f_cr

Design flexural cracking stress of the hypothetical unreinforced concrete beam consisting of the cover concrete over the inside face of a stack of horizontally curved posttensioned tendons, ksi

f_j

Jacking stress, ksi

f_j,max

Jacking stress capacity, ksi

f_pe

Effective stress in stainless steel prestressing strands after all losses, ksi

f_pt

Stress in prestressing strands immediately after the transfer; taken as not less than 0.55f_py, ksi

f_ps0

Jacking stress of reinforcement, ksi

f_pu

Specified tensile strength of prestressing steel, ksi

f_si

Stress in layer i of the nonprestressed reinforcement, ksi

f_px

Stress in layer x of the stainless steel prestressing strand, ksi

f_t

Direct tensile strength of concrete, ksi

f_pu

Specified tensile strength of prestressing steel, ksi

f_py

Yield strength of prestressing steel, ksi

g_Str.I

Limit state function for the Strength I limit state

h

Overall thickness or depth of member, in.

I_g

Moment of inertia of the gross concrete section about the centroidal axis, neglecting the reinforcement, in.⁴

x

Number of prestressing strands

K

Bulk modulus, ksi; wobble friction coefficient (per ft of tendon)

K_L

Factor accounting for the type of steel taken as 30 for low-relaxation strands and 7.0 for other prestressing steel, unless more accurate manufacturerʼs data are available

L

Span length between supports, in.

l_d

Development length, in.

l_t

Transfer length, in.

M

Sectional moment, kip-in.; material variabilities

M_cr

Cracking moment, kip-in.

M_exp

Experimental moment capacity, kip-in.

M_pred

Predicted moment capacity, kip-in.

M_n

Nominal flexural resistance, kip-in.

M_u

Factored moment at the section, kip-in.

np

Total number of layers of prestressed tension reinforcement

P

Applied force, kip; or professional factor

P_pt

Force in SS strands immediately after transfer, kip

R

Random variable

R_n

Nominal resistance as obtained from the proposed design expression

t

Time, day; average thickness of the bearing plate, in.

T

Total tensile force, kip

V_c

Nominal shear resistance of the concrete, lb.

V_n

Nominal shear resistance, lb.

V_p

Component of prestressing forces in direction of shear force, kip

V_s

Shear resistance provided by shear reinforcement, kip

x

Prestressed reinforcement layer number, starting with 1 closest to the tension face

α₁, β₁

Stress-block factors

β

Reliability index

∆

Deflection, in.

∆f_pF

Loss due to friction, ksi

∆f_pR1

Prestress loss due to relaxation of prestressing strands between time of transfer and deck placement, ksi

ε_cc

Strain in extreme compression fiber at failure (<0.003), in./in.

ε′_c

Strain in concrete corresponding to compression peak stress f′_c

ε_cu

Failure strain of concrete in compression, in./in.

ε_cp

Strain in the concrete adjacent to the SS strand due to prestress, in./in.

ε_F

Stain drop limit for the creep rupture test, in./in.

ε_p

Nominal strain of reinforcement, in./in.

ε_pe

Strain due to effective prestress in the stainless steel prestressing strands, in./in.

ε_fy

Yield strain of the reinforcement, in./in.

ε_pt,net

Net tensile strain, in./in.

ε_pu

Ultimate strain of reinforcement, in./in.

θ

Angle of inclination of diagonal compressive stresses, degrees

κ

Jacking stress level, ksi/ksi; or factor that accounts for the effect of member depth; or section curvature

λ

Concrete density modification factor

λ_P

Professional factor

ξ_GDF

Random variable

µ

Friction factor or mean

ϕ

Resistance factor

Ω_U

Strain reduction factor

Abbreviations and acronyms used without definitions in TRB publications:

A4A

Airlines for America

AAAE

American Association of Airport Executives

AASHO

American Association of State Highway Officials

AASHTO

American Association of State Highway and Transportation Officials

ACI–NA

Airports Council International–North America

ACRP

Airport Cooperative Research Program

ADA

Americans with Disabilities Act

APTA

American Public Transportation Association

ASCE

American Society of Civil Engineers

ASME

American Society of Mechanical Engineers

ASTM

American Society for Testing and Materials

ATA

American Trucking Associations

CTAA

Community Transportation Association of America

CTBSSP

Commercial Truck and Bus Safety Synthesis Program

DHS

Department of Homeland Security

DOE

Department of Energy

EPA

Environmental Protection Agency

FAA

Federal Aviation Administration

FAST

Fixing Americaʼs Surface Transportation Act (2015)

FHWA

Federal Highway Administration

FMCSA

Federal Motor Carrier Safety Administration

FRA

Federal Railroad Administration

FTA

Federal Transit Administration

GHSA

Governors Highway Safety Association

HMCRP

Hazardous Materials Cooperative Research Program

IEEE

Institute of Electrical and Electronics Engineers

ISTEA

Intermodal Surface Transportation Efficiency Act of 1991

ITE

Institute of Transportation Engineers

MAP-21

Moving Ahead for Progress in the 21st Century Act (2012)

NASA

National Aeronautics and Space Administration

NASAO

National Association of State Aviation Officials

NCFRP

National Cooperative Freight Research Program

NCHRP

National Cooperative Highway Research Program

NHTSA

National Highway Traffic Safety Administration

NTSB

National Transportation Safety Board

PHMSA

Pipeline and Hazardous Materials Safety Administration

RITA

Research and Innovative Technology Administration

SAE

Society of Automotive Engineers

SAFETEA-LU

Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005)

TCRP

Transit Cooperative Research Program

TEA-21

Transportation Equity Act for the 21st Century (1998)

TRB

Transportation Research Board

TSA

Transportation Security Administration

U.S. DOT

United States Department of Transportation