Appendix a - Notation

7/26/2019 Appendix a - Notation

1/20

OCT 97

PCI BRIDGE DESIGN MANUAL APPENDIX A

CORRESPONDING CORRESPONDING

AASHTO AASHTO

LRFD STANDARD

SYMBOL DESCRIPTION SPECIFICATIONS SPECIFICATIONS

A area of cross section of stringer or beam A (4.6.2.2.1)

A constant

A maximum area of the portion of the supporting surface A (5.10.9.7.2) that is similar to the loaded area and concentric with itand does not overlap similar areas for adjacent anchoragedevices

A effective tension area of concrete surrounding the flexural A (5.7.3.4) A (8.16.8.4)tension reinforcement and having the same centroid asthat reinforcement, divided by the number of bars orwires; when the flexural reinforcement consists of severalbar sizes or wires, the number of bars or wires shall becomputed as the total area of reinforcement divided bythe area of the largest bar or wire used

Ab net area of a bearing plate A b (5.10.9.7.2)

Ac area of core of spirally reinforced compression member Ac (5.7.4.6) A c (8.18.2.2.2)measured to the outside diameter of the spiral

Ac total area of the composite section

Ac area of concrete on the flexural tension side of the member

Acs cross-sectional area of a concrete strut in strut-and-tie Acs (5.6.3.3.1) model

Acv area of concrete section resisting shear transfer A cv (5.8.4.1) A cv (8.16.6.4.5)

Ag gross area of section A g (5.5.4.2.1) A g (8.1.2)

Ag gross area of bearing plate A g (5.10.9.7.2)

Ah area of shear reinforcement parallel to flexural tension Ah (5.13.2.4.1) A h(8.15.5.8,reinforcement 8.16.6.8)

Ao area enclosed by centerlines of the elements of the beam C4.6.2.2.1

Aps, As* area of prestressing steel A ps (5.5.4.2.1) A s

* (9.17)

APT transverse post-tensioning reinforcement

As area of non-prestressed tension reinforcement A s (5.5.4.2.1) A s (9.7, 9.19)

As total area of vertical reinforcement located within thedistance (h/5) from the end of the beam

As area of compression reinforcement A s (5.7.3.1.1) A s (9.19)

Asf steel area required to develop the compressive strength of A sf (9.17)the overhanging portions of the flange

Ask area of skin reinforcement per unit height in one side face Ask (5.7.3.4) A sk (8.17.2.1.3)

NOTATION


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AASHTO AASHTO

LRFD STANDARD


Asr steel area required to develop the compressive strength of A sr (9.17-9.19)the web of a flanged section

Ass area of reinforcement in an assumed strut of a Ass (5.6.3.3.4) strut-and-tie model

Ast total area of longitudinal mild steel reinforcement Ast (5.6.3.4.1) A st (8.16.4.1.2,8.16.4.2.1)

At area of one leg of closed transverse torsion reinforcement At (5.8.3.6.2)

Av area of transverse reinforcement within a distance s Av (5.8.2.5) A v (9.20)

Avh area of web reinforcement required for horizontal shear

Avf area of shear-friction reinforcement A vf (5.8.4.1) A vf (8.15.5.4.3)

Avf total area of reinforcement, including flexural Avf (5.10.11.4.4) reinforcement

Av-min minimum area of web reinforcement

a distance from the end of beam to drape point

a depth of equivalent rectangular stress block a (5.7.2.2) a (8.16.2.7, 9.17.2)

a lateral dimension of the anchorage device measured a (5.10.9.6.2)

af distance between concentrated load and face of support af (5.13.2.5.1)

av shear span, distance between concentrated load and face av (5.13.2.4.1) a v (8.15.5.8,of support 8.16.6.8)

B constant

B buoyancy B (3.22)

BR vehicular braking force BR (3.3.2)

b the lateral dimension of the anchorage device measured b (5.10.9.6.2) parallel to the smaller dimension of the cross-section

b width of bottom flange of the beam

b effective flange width

b width of beam b (4.6.2.2.1)

b width of compression face of member b (5.7.3.1.1) b (8.1.2)

b width of pier or diameter of pile b (3.18.2.2.4)

b width of web of a flanged member b (9.1.2)

bv, be effective web width of the precast beam bv (5.8.2.7)

NOTATION


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AASHTO AASHTO

LRFD STANDARD


bv width of cross section at the contact surface being bv (5.8.4.1) bv (9.20)investigated for horizontal shear

bw width of a web of a flanged member bw (5.7.3.1.1) bw (8.15.5.1.1)

bw width of web adjusted for the presence of ducts bw ( 5.8.2.5)

C stiffness parameter = K(W/L) C (3.23.4.3)

C centrifugal force in percent of live load C (3.10.1)

Ca creep coefficient for deflection at time of erection due to loads applied at release

Cu ultimate creep coefficient Cu ultimate creep coefficient for concrete at time of

application of the superimposed dead loads

CE vehicular centrifugal force CE (3.3.2)

CF centrifugal force CF (3.22)

CR creep CR (3.3.2)

CT vehicular collision force CT (3.3.2)

CV vessel collision force CV (3.3.2)

C (t,to) creep coefficient at a concrete age of t days

c cohesion factor c (5.8.4.1)

c vehicular braking force

c distance from extreme compression fiber to neutral axis c (5.7.2.2) c (8.16.2.7)

D parameter used in determination of load fraction of D (3.23.4.3)wheel load

D prestressing steel elongation

D a constant that varies with bridge type and geometry

D width of distribution per lane

D dead load D (3.3.2) D (3.22)

DC dead load of structural components and nonstructural DC (5.14.2.3.2) attachments

DD downdrag DD (3.3.2)

D.F. fraction of wheel load applied to beam D.F. (3.28.1)

DFD distribution factor for deflection

NOTATION


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AASHTO AASHTO

LRFD STANDARD


DFM distribution factor for bending moment

DFm live load distribution factor for moment

DFV distribution factor for shear force

DL contributing dead load DL (3.1)

DW dead load of wearing surfaces and utilities DW (3.3.2, 5.14.2.3.2)

d distance from extreme compressive fiber to centroid of the d (9.1.2)pretensioning force

d depth of beam or stringer d (4.6.2.2.1) d precast beam depth

d distance from extreme compressive fiber to centroid of the d (9.1.2)reinforcing but not less than 0.8h . In negative momentsection, the reinforcement is assumed to be located at themid-height of the slab. For computing horizontal shearstrength of composite members, d should be the distancefrom extreme compression fiber to centroid of tensionreinforcement for entire composite section.

db nominal diameter of a reinforcing bar or wire db (5.10.2.1) db (8.1.2)

db nominal diameter of prestressing steel db (5.10.2.1) D (9.17, 9.27)

dc thickness of concrete cover measured from extreme dc (5.7.3.4) dc (8.16.8.4)tension fiber to center of bar or wire located closest thereto

de distance between the center of exterior beam and interior de (4.6.2.2.1) edge of curb or traffic barrier

de effective depth from extreme compression fiber to the de (5.7.3.3.1) centroid of the tensile force in the tensile reinforcement

dext depth of the extreme steel layer from extreme compression fiber

di depth of steel layer from extreme compression fiber

dp distance from extreme compression fiber to the centroid dp (5.7.3.1.1) of the prestressing tendons

ds distance from extreme compression fiber to the centroid ds (5.7.3.2.2) dt (9.7, 9.17-9.19)of the non-prestressed tensile reinforcement

dv effective shear depth dv (5.8.2.7)

ds distance from extreme compression fiber to centroid of ds (5.7.3.2.2) d (8.1.2)compression reinforcement

NOTATION


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AASHTO AASHTO

LRFD STANDARD


d" distance from centroid of gross section, neglecting the d" (8.1.2)reinforcement, to centroid of tension reinforcement

E earth pressure

E width of slab over which a wheel load is distributed E (3.24.3)

Eb the modulus of elasticity of the bearing plate material Eb (5.10.9.7.2)

Ec modulus of elasticity of concrete Ec (5.4.2.4) Ec (3.26.3, 8.7.1)

Eci modulus of elasticity of concrete at transfer Eci (5.9.5.2.3a)

Eeff effective modulus of elasticity Eeff (C5.14.2.3.6)

Ep, Es modulus of elasticity of pretensioning reinforcement Ep (5.4.4.2) Es (9.16.2.1.2)

Es modulus of elasticity of non-pretensioned reinforcement Es (5.4.3.2) Es (3.26.3, 8.7.2)

Ec* age adjusted effective modulus of concrete for a gradually

applied load at the time of release of prestressing

EH horizontal earth pressure load EH (3.3.2)

EQ earthquake EQ (3.3.2) EQ (3.22.1)

EQ equivalent static horizontal force applied at the center EQ (3.1)of gravity of the structure

ES earth surcharge load ES (3.3.2)

EV vertical pressure from dead load of earth fill EV (3.3.2)

e eccentricity of the strands at h/2

e eccentricity of strands at transfer length

e correction factor for distribution e (4.6.2.2.1)

e eccentricity of a lane from the center of gravity of the e (4.6.2.2.2d) pattern of girders

e the eccentricity of the anchorage device or group of e (5.10.9.6.3)

devices, with respect to the centroid of the cross-section,always taken as positive

e difference between eccentricity of pretensioning steel at midspan and end span

ec eccentricity of the strand at the midspan

ee eccentricity of pretensioning force at end of beam

eg distance between the centers of gravity of the basic eg (4.6.2.2.1) beam and deck

NOTATION


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AASHTO AASHTO

LRFD STANDARD


ep eccentricity of the prestressing strands with respect to the centroid of the section

Fb allowable tensile stress in the precompressed tensile zone at service loads

Fb allowable bending stress Fb (2.7.4.2)

Fcj force in concrete for the j th component

FR friction FR (3.3.2)

Fpi total force in strands before release

F reduction factor F (5.8.3.4.2) f stress

fD sum of dead load bending stresses

f(L+I) live load plus impact bending stress

fb concrete stress at the bottom fiber of the beam

fb average bearing stress in concrete on loaded area f b (8.15.2.1.3,8.16.7.1)

fc extreme fiber compressive stress in concrete at service loads f c (8.15.2.1.1)

fc specified compressive strength of concrete at 28 days, fc (5.4.2.1) f c (8.1.2)unless another age is specified

fca concrete compressive stress ahead of the anchorage devices fca (5.10.9.6.2)

fcds average concrete compressive stress at the c.g. of the f cds (9.16)prestressing steel under full dead load

fcgp concrete stress at the center of gravity of pretensioning fcgp (5.9.5.2.3a) f cir (9.16)tendons, due to pretensioning force at transfer and theself-weight of the member at the section of maximumpositive moment

fci compressive strength of concrete at time of initial prestress fci (5.9.1.2) f ci (9.15)

fct average splitting tensile strength of lightweight fct (5.8.2.2) f ct (9.1.2)aggregate concrete

(fc )t compressive strength of concrete at t days

fcu the limiting concrete compressive stress for design by fcu (5.6.3.3.1) strut-and-tie model

fd stress due to unfactored dead load, at extreme fiber of f d (9.20)section where tensile stress is caused by externallyapplied loads

NOTATION


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OCT 97



AASHTO AASHTO

LRFD STANDARD


ff fatigue stress range in reinforcement f f (5.5.3.2) f f (8.16.8.3)

fmin algebraic minimum stress level in reinforcement f min (5.5.3.2) f min (8.16.8.3)

fn nominal concrete bearing stress f n (5.10.9.7.2)

fpb compressive stress at bottom fiber of the beam due to prestress force

fpc compressive stress in concrete (after allowance for all fpc(C5.6.3.5) f pc (9.20)prestress losses) at centroid of cross section resistingexternally applied loads or at junction of web and flangewhen the centroid lies within the flange (In a compositemember, fpc is resultant compressive stress at centroid of

composite section, or at junction of web and flange whenthe centroid lies within the flange, due to both prestressand moments resisted by precast member acting alone.)

fpe effective prestress after losses f pe (5.6.3.4.1) f se

fpe compressive stress in concrete due to effective prestress f pe (9.20)forces only (after allowance for all prestress losses) atextreme fiber of section where tensile stress is caused byexternally applied loads

fpi initial stress immediately before transfer

fpj stress in the prestressing steel at jacking f pj (5.9.3)

fpo stress in the prestressing steel when the stress in the fpo (5.8.3.4.2) surrounding concrete is 0.0

fps average stress in prestressing steel at the time for which the fps (C5.6.3.3.3) nominal resistance of member is required

fpt stress in prestressing steel immediately after transfer fpt (5.9.3)

fpu, fs ultimate strength of prestressing steel f pu (5.4.4.1) f s (9.15, 9.17)

fpy yield point stress of prestressing steel f py (5.4.4.1) f y* (9.15)

fr the modulus of rupture of concrete f r (5.4.2.6) f r (9.18,

8.15.2.1.1)

fs allowable stress in steel, but not taken greater than 20 ksi

fs tensile stress in reinforcement at service loads f s (8.15.2.2)

fsa tensile stress in the reinforcement at service loads f sa (5.7.3.4)

fse effective final pretension stress

fsi effective initial pretension stress

fsu* stress in prestressing tension steel at ultimate load f su

*

NOTATION


8/20



AASHTO AASHTO

LRFD STANDARD


ft extreme fiber tensile stress in concrete at service loads f t (8.15.2.1.1)

ft concrete stress at top fiber of the beam for the non-composite section

ftc concrete stress at top fiber of the slab for the composite section

ftg concrete stress at top fiber of the beam for the composite section

fy specified yield strength of non-prestressed conventional fy (5.5.4.2.1), fy (8.1.2), fyreinforcement fy(5.7.3.1.1) (9.19), f sy (9.19,

9.20)fyh specified yield strength of transverse reinforcement f yh (5.7.4.6)

g A factor used to multiply the total longitudinal response of the bridge due to a single longitudinal line of wheelloads in order to determine the maximum response ofa single girder

g distribution factor g (4.6.2.2.1)

H average annual ambient mean relative humidity, percent H (5.4.2.3.2) RH (9.16.2.1.1)

H height of wall H (A13.4.2)

h overall thickness or depth of a member h (5.8.2.7) h (9.20)

hc total height of composite section

hf compression flange thickness hf (5.7.3.1.1) hf (8.1.2)

I moment of inertia about the centroid of the Ig (5.7.3.6.2) I (9.20)non-composite precast beam

Ic moment of inertia of composite section

Icr moment of inertia of cracked section transformed Icr (5.7.3.6.2) Icr (8.13.3)to concrete

Ie effective moment of inertia Ie (5.7.3.6.2) Ie (8.13.3)

Ig moment of inertia of the gross concrete section about the Ig (5.7.3.6.2) Ig (3.23.4.3,centroidal axis, neglecting reinforcement 8.1.2, 9.20)

Is moment of inertia of reinforcement about centroidal axis Is (5.7.4.3) Is (8.1.2)of member cross section

IC ice load

ICE ice pressure ICE (3.22.1)

IM vehicular dynamic load allowance IM (3.6.1.2.5) I (3.8.2)

NOTATION

OCT 97


9/20

OCT 97



AASHTO AASHTO

LRFD STANDARD


J gross St. Venant torsional constant of the precast member J (4.6.2.2.1) J (3.23.4.3)

K a non-dimensional constant

K effective length factor for compression members K (5.7.4.1) k (8.16.5.2.3)

K factor used for calculating time-dependent losses

K wobble friction coefficient K (5.9.5.2.2b) K (9.16)

Kg longitudinal stiffness parameter K g(4.6.2.2.1) K (3.23.4)

Kr factor used for calculating relaxation loss occurs priorto transfer

k factor used in calculation of distribution factor for k (4.6.2.2) multi-beam bridges

k factor used in calculation of average stress in pretensioning steel for Strength Limit State

k live load distribution constant for spread box girders k (3.28.1)

kc product of applicable correction factors = kla (kh) (ks)

kc a factor for the effect of the volume-to-surface ratio kc (5.4.2.3.2)

kcp correction factor for curing period

kf a factor for the effect of concrete strength k f (5.4.2.3.2)

kh correction factor for relative humidity k h (5.4.2.3.3)

kla correction factor for loading age

ks product of applicable correction factors = kcp (kh) (ks)

ks correction factor for size k s (5.4.2.3.3)

L length in feet of the span under consideration for positive L (3.8.2.1)moment and the average of two adjacent loaded spansfor negative moment

L Overall beam length or design span

L span length measured parallel to longitudinal beams

L length of the loaded portion of span from section under consideration to the far reaction when computing sheardue to truck loads.

L loaded length of span L (5.7.3.1.2) L (3.8.2)

LL, L live load LL (3.3.2) L (3.22)

L total length of prestressing steel from anchorage to anchorage

NOTATION


10/20

OCT 97



AASHTO AASHTO

LRFD STANDARD


Lc critical length of yield line failure pattern Lc (A13.4.2)

LF longitudinal force from live load LF (3.22)

LS live load surcharge LS (3.3.2)

Lr intrinsic relaxation of the strand

ld development length

lt transfer length

lu unsupported length of compression member lu (5.7.4.1) lu (8.16.5.2.1)

Mb unfactored bending moment due to barriers weight

Mc flexural resistance of cantilevered wall

MCIP unfactored bending moment due to cast-in-place topping slab

Mconst unfactored bending moment due to construction load

Mcr moment causing flexural cracking at section due to Mcr (5.7.3.6.2) Mcr (8.13.3, 9.20)externally applied loads

Mcr* cracking moment Mcr

* (9.18)

MD unfactored bending moment due to diaphragm weight

Md bending moment at section due to unfactored dead load

Md/nc non-composite dead load moment Md/nc (9.18)

Mf unfactored bending moment due to fatigue truck per beam

Mg unfactored bending moment due to beam self-weight

MLL unfactored bending moment due to lane load per beam

MLL+I unfactored bending moment due to live load + impact

MLT unfactored bending moment due to truck load with

dynamic allowance per beamMmax maximum factored moment at section due to externally Mmax(9.20)

applied loads

Mn nominal flexural resistance Mn (5.7.3.2.1) Mn (9.1.2)

Mn/dc non-composite dead load moment at the section

Mr factored flexural resistance of a section in bending Mr (5.7.3.2.1)

Mservice total bending moment for service load combination

NOTATION


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OCT 97



AASHTO AASHTO

LRFD STANDARD


MS unfactored bending moment due to slab and haunch weights

MSDL unfactored bending moment due to super-imposed dead loads

MSIP unfactored bending moment due to stay-in-place panel

Mu factored moment at section Mn Mu (C5.6.3.1) Mu (9.17, 9.18)

Msw moment at section of interest due to self-weight of the member plus any permanent loads acting on themember at time of release

Mws unfactored bending moment due to wearing surface

Mx bending moment at a distance (x) from the support

m material parameter

m stress ratio = (f y / 0.85 )

N group number N (3.22.1)

Nb, NB number of beams Nb (4.6.2.2.1) NB (3.28.1)

NL number of traffic lanes NL (4.6.2.2.1, NL (3.23.4)3.6.1.1.1)

NL number of traffic lanes

Nu applied factored axial force taken as positive if tensile

Nuc factored axial force normal to the cross section, occurring Nuc (5.13.2.4.1) Nu (8.16.6.2.2)simultaneously with Vu to be taken as positive fortension, negative for compression; includes effects oftension due to creep and shrinkage

n modular ratio of elasticity - Es/Ec n (5.7.1) n (8.15.3.4)

P concentrated wheel load P (3.6.1.2.5)

P live load intensity P (C3.11.6.2)

P live load on sidewalk P (3.14.1.1)

P load on one rear wheel of truck P (3.24.3)

P Diaphragm weight concentrated at quarter points

Pc permanent net compression force Pc (5.8.4.1)

Peff effective post-tensioning force

Pi total pretensioning force immediately after transfer

Pn nominal axial load strength at given eccentricity Pn (5.5.4.2.1) Pn (8.1.2)

NOTATION


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AASHTO AASHTO

LRFD STANDARD


Pn nominal axial resistance of strut or tie Pn (5.6.3.2)

Pn nominal bearing resistance Pn (5.7.5)

Pnx nominal axial load strength corresponding to Mnx, with Pnx (8.16.4.3)bending considered in the direction of the x axis only

Pny nominal axial load strength corresponding to Mny, with Pny (8.16.4.3)bending considered in the direction of the y axis only

Pnxy nominal axial load strength with biaxial loading Pnxy (8.16.4.3)

Po nominal axial load strength of a section at 0.0 eccentricity Po (5.7.4.5) Po (8.16.4.2.1)

Ppe total pretensioning force after all losses Ps prestress force before initial losses

Ps design jacking force

Pse effective pretension force after allowing for all losses

Psi effective pretension force after allowing for the initial losses

Pr factored bursting resistance of pretensioned anchorage zone provided by transverse reinforcement

PT factored axial resistance of strut or tie Pr (5.6.3.2)

PT factored bursting resistance of pretensioned anchorage t Pr (5.10.10.1) zone provided by transverse reinforcemen

PL pedestrian live load PL (3.3.2)

p fraction of truck traffic in a single lane p (3.6.1.4.2)

p As /bd, ratio of non-prestressed tension reinforcement p (9.7, 9.17-9.19)

p As /bd, ratio of compression reinforcement p (9.19)

p* As*/bd, ratio of prestressing steel p* (9.17, 9.19)

pc outside perimeter of the concrete section pc (5.8.2.1)

ph perimeter of the centerline of the closed transverse torsion ph (5.8.3.6.2) reinforcement

Q first moment of inertia of the area above the fiber being considered

Q statical moment of cross sectional area, above or below the Q (9.20)level being investigated for shear, about the centroid

Q total factored load Q (3.4.1)

q generalized load q (3.4.1)

NOTATION


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AASHTO AASHTO

LRFD STANDARD


qi specified loads qi (3.4.1)

R reaction on exterior beam in terms of lanes

R rib shortening R (3.22)

Ru flexural resistance factor

Rw total transverse resistance of the railing R w (A13.4.2)

r radius of gyration of cross section of a compression member r (5.7.4.1) r (8.16.5.2.2)

r/h ratio of base radius to height of rolled-on transverse r/h (5.5.3.2) deformations

S coefficient related to site conditions for use in determining S (3.10.5) seismic loads)

S surface area of concrete exposed to drying

S shrinkage S (3.22)

S spacing of beams S (3.23.3, 3.28.1)

S effective span length of the deck slab S (3.25.1.3)

S width of precast member S (3.23.4.3)

Sb noncomposite section modulus for the extreme fiber of Sb (9.18)

section where the tensile stress is caused by externallyapplied loads

Sbc composite section modulus for extreme bottom fiber of the precast beam, Ic/ybc

Sc composite section modulus for the extreme fiber of section Sc (9.18)where the tensile stress is caused by externally applied loads

St section modulus for the extreme top fiber of the non-composite precast beam

Stc composite section modulus for top fiber of the slab, Ic/(n)(ytc)

Stg composite section modulus for top fiber of the precast beam, Ic/ytg

Su ultimate free shrinkage strain in the concrete adjusted for member size and relative humidity

S(t,to) shrinkage strain at a concrete age of t days

SE settlement SE (3.3.2)

SF stream flow pressure SF (3.22)

NOTATION

OCT 97


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OCT 97



AASHTO AASHTO

LRFD STANDARD


SH shrinkage SH (3.3.2, S (3.22)5.14.2.3.2)

SR fatigue stress range

s spacing of shear reinforcement in direction parallel to the s(5.8.4.1) s (9.20)longitudinal reinforcement

s effective deck span s (3.25.1.3)

s length of a side element s (C4.6.2.2.1)

s spacing of rows of ties s (5.8.4.1)

T collision force at deck slab level T mean daily air temperature T (C3.9.2.2)

Tburst the tensile force in the anchorage zone acting ahead of the Tburst (5.10.9.6.3) anchorage device and transverse to the tendon axis

Tcr torsional cracking resistance Tcr (5.8.2.1)

Tn nominal torsion resistance Tn (5.8.2.1)

TT factored torsional resistance provided by circulatory Tr (5.8.2.1) shear flow

Tu factored torsional moment Tu (C5.6.3.1)

TG temperature gradient TG (3.3.2, C4.6.6)

TU uniform temperature TU (3.3.2)

t thickness of web

t thickness of an element of the beam

t time in days t (5.4.2.3.2)

t average thickness of the flange of a flanged member t (9.17, 9.18)

t deck thickness t (3.25.1.3)

tf thickness of flange

ti age of concrete when load is initially applied ti (5.4.2.3.2)

tla loading ages in days

ts depth of concrete slab ts (4.6.2.2.1)

to age of concrete in days at the end of the initial curing period

V design shear force at section V (8.15.5.1.1)

NOTATION


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LRFD STANDARD


V variable spacing of truck axles V (3.7.6)

V volume of concrete

Vc nominal shear resistance provided by tensile stresses in Vc (5.8.2.4) V c (9.20, 8.16.6.1)the concrete

Vci nominal shear strength provided by concrete when V ci (9.20)diagonal cracking results from combined shear and moment

Vcw nominal shear strength provided by concrete when V cw (9.20)diagonal cracking results from excessive principal tensilestress in web

Vd shear force at section due to unfactored dead load V d (9.20)

Vi factored shear force at section due to externally applied V i (9.20)loads occurring simultaneously with Mmax

VLL unfactored shear force due to lane load per beam

VLL+I unfactored shear force due to live load plus impact

VLT unfactored shear force due to truck load with dynamic allowance per beam

Vmu ultimate shear force occurring simultaneously with Mu

Vn nominal shear resistance of the section considered Vn (5.8.2.1) V n (8.16.6.1)Vnh nominal horizontal shear strength V nh(8.16.6.5.3,

9.20)

Vp component in the direction of the applied shear of the Vp (C5.8.2.3) V p (9.20)effective pretensioning force, positive if resisting theapplied shear

Vs shear resistance provided by shear reinforcement Vs (5.8.3.3) V s (8.16.6.1, 9.20)

VT factored shear resistance V r (5.8.2.1)

Vu factored shear force at section V u (C5.6.3.1) V u (8.16.6.1, 9.20)

Vuh factored horizontal shear force per unit length of the beam

Vx shear force at a distance (x) from the support

v factored design shear stress v (5.8.3.4.2) v (8.15.5.1.1)

v permissible horizontal shear stress v (9.20)

vc permissible shear stress carried by concrete v c (8.15.5.2)

WS, W wind load on structure WS (3.3.2) W (3.22)

W overall width of bridge W (3.23.4.3)

NOTATION

OCT 97


16/20

OCT 97



AASHTO AASHTO

LRFD STANDARD


W roadway width between curbs W (3.28.1)

WA water load and stream pressure WA (3.3.2)

WL wind load on live load WL (3.3.2) WL (3.22)

w width of clear roadway w (3.6.1.1.1)

w a uniformly distributed load

wb weight of barriers

wc unit weight of concrete w c (5.4.2.4) w c (8.1.2)

wg beam self-weight

ws slab and haunch weights

wws weight of future wearing surface

X distance from load to point of support X (3.24.5.1)

Xext horizontal distance from the center of gravity of the Xext (C4.6.2.2.2d) pattern of girders to the exterior girder

x the distance from the support to the section under question

x horizontal distance from the center of gravity of the x (C4.6.2.2.2d) pattern of girders to each girder

x length of prestressing steel element from jack end to x (5.9.5.2.2b) L (9.16)point x

yb distance from centroid to the extreme bottom fiber of the non-composite precast beam

ybc distance from the centroid of the composite section to extreme bottom fiber of the precast beam

ybs distance from the center of gravity of strands to the bottom fiber of the beam

yt distance from centroid to the extreme top fiber of the

non-composite precast beam

yt distance from centroidal axis of gross section, neglecting yt (5.7.3.6.2) y t (8.13.3, 9.20)reinforcement, to extreme fiber in tension

ytc distance from the centroid of the composite section to extreme top fiber of the slab

ytg distance from the centroid of the composite section to extreme top fiber of the precast beam

Z crack control parameter Z (5.7.3.4)

NOTATION


17/20

OCT 97



AASHTO AASHTO

LRFD STANDARD


Z factor reflecting exposure conditions

angle of inclination of transverse reinforcement to (5.8.3.3) longitudinal axis

angle between inclined shear reinforcement and (5.8.3.3) (8.1.2)longitudinal axis of member

factor used in calculating elastic shortening loss

total angular change of prestressing steel path from jacking (5.9.5.2.2b) (9.16)end to a point under investigation

the angle of inclination of a tendon force, with respect to (5.10.9.6.3)

the centerline of the member

h total horizontal angular change of prestressing steel path h (5.9.5.2.2b) from jacking end to a point under investigation

s angle between compressive strut and adjoining tension tie s (5.6.3.3.3)

v total vertical angular change of prestressing steel path from v (5.9.5.2.2b) jacking end to a point under investigation

factor indicating ability of diagonally cracked concrete to (5.8.3.3) transmit tension (a value indicating concrete contribution)

factor relating effect of longitudinal strain on the shear (5.8.3.3)

capacity of concrete, as indicated by the ability ofdiagonally cracked concrete to transmit tension

b ratio of area of reinforcement cut off to total area of b (5.11.1.2.1) b (8.24.1.4.2)reinforcement at the section

d absolute value of ratio of maximum dead load moment to d (5.7.4.3) d (8.1.2)maximum total load moment, always positive

D load combination coefficient for dead loads D (3.22.1)

L load combination coefficient for live loads L (3.22.1)

1 ratio of depth of equivalent compression zone to depth 1 (5.7.2.2) 1(8.16.2.7,9.17-

9.19)

deflection

beam deflection due to beam self-weight

b+ws deflection due to barrier and wearing surface weights

fcdp change in concrete stress at c.g. of prestressing steel due fcdp (5.9.5.4.3) to all dead loads, except dead load acting at the time theprestressing force is applied

fpA loss in prestressing steel stress due to anchorage set fpA (5.9.5.1)

NOTATION


18/20

OCT 97



AASHTO AASHTO

LRFD STANDARD


fpCR loss in prestressing steel stress due to creep fpCR(5.9.5.1) CR c (9.16)

fpES loss in prestressing steel stress due to elastic shortening fpES (5.9.5.1) ES (9.16)

fpF loss in prestressing steel stress due to friction fpF (5.9.5.1)

fpi total loss in pretensioning steel stress immediately after transfer

fpR total loss in prestressing steel stress due to relaxation of steel fpR (5.9.5.1) CR s (9.16)

fpR1 loss in prestressing steel stress due to relaxation of steel fpR1 (5.9.5.4.4b) at transfer

fpR2 loss in prestressing steel stress due to relaxation of steel

fpR2 (5.9.5.4.4c) after transfer

fpSR loss in prestressing steel stress due to shrinkage fpSR (5.9.5.1) SH (9.16)

fpT total loss in prestressing steel stress fpT (5.9.5.1)

fs total prestress loss, excluding friction fs (9.16)

D deflection due to diaphragm weight

L deflection due to specified live load

LL+I deflection due to live load and impact

LL deflection due to lane load

LT deflection due to design truck load and impact

max maximum allowable live load deflection

p camber due pretension force at transfer

SDL deflection due to barrier and wearing surface weights

slab deflection due to the weights of slab and haunch

strain

cu the failure strain of concrete in compression cu (5.7.3.1.2) ps strain in prestressing steel

s tensile strain in cracked concrete in direction of tension tie s (5.6.3.3.3)

sh concrete shrinkage strain at a given time sh (5.4.2.3.3)

si strain in tendons corresponding to initial effective pretension stress

x longitudinal strain in the web reinforcement on the x (5.8.3.4.2) flexural tension side of the member

NOTATION


19/20

OCT 97



AASHTO AASHTO

LRFD STANDARD


1 principal tensile strain in cracked concrete due to 1 (5.6.3.3.3) factored loads

resistance factor (5.5.4.2.1) (8.16.1.2)

c curvature at midspan

0 curvature at support

load factor (3.22)

* factor for type of prestressing steel * (9.17)= 0.28 for low-relaxation steel= 0.40 for stress-relieved steel

= 0.55 for bars

i load factor i (3.4.1)

p load factor for permanent loading p (3.4.1)

variable load modifier which depends on ductility, (3.4.1) redundancy and operational importance

a correction factor for closely spaced anchorages (5.10.9.6.2)

parameter used to determine friction coefficient and it is (5.8.4.2) (8.15.5.4,related to unit weight for concrete 8.16.6.4)

coefficient of friction (5.8.4.1) (8.15.5.4.3) Poisson's ratio (3.23.4.3)

skew angle

angle of inclination of diagonal compressive stresses (5.8.3.3)

s angle between compression strut and longitudinal axis of s (5.6.3.3.2) the member in a shear truss model of a beam

tension reinforcement ratio - As/bwd, As/bd (8.1.2)

compression reinforcement ratio = As /bd (8.1.2)

* , ratio of pretensioning reinforcement * (9.17, 9.19)

actual actual ratio of nonpretensioned reinforcement

b reinforcement ratio producing balanced strain conditions b (8.16.3.1.1)

min minimum ratio of tension reinforcement to effective min (5.7.3.3.2)

concrete area

v ratio of area of vertical shear reinforcement to area of gross v (5.10.11.4.2)

concrete area of a horizontal section

Abd

s*

NOTATION


20/20



AASHTO AASHTO

LRFD STANDARD


a factor reflects the fact that the actual relaxation is less than the intrinsic relaxation

angle of harped pretensioned reinforcement

(t,ti) creep coefficient - the ratio of the strain which exists t days (t,ti) (5.4.2.3.2) after casting to the elastic strain caused when load p i isapplied ti days after casting

aging coefficient

NOTATION

Documents

Appendix a - Notation