WE Symbols Sep07

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WE 0 Contents v7 13 Sep 07 for web .doc 17-Sep-07 Page 2 of8

Symbols and abbreviations used in this publication

Symbol Definition

IxI Absolute value ofx

1/r Curvature at a particular

sectionA Cross-sectional area;

Accidental action

A Site altitude, m (snow)

A Altitude of the site in metresabove mean sea level (wind)

A, B, C Variables used in thedetermination oflim

Ac Cross-sectional area ofconcrete

Act Area of concrete in that partof the section that iscalculated to be in tensionjust before the formation of

the first crackAd Design value of an accidental

action

AEd Design value of a seismicaction

Ak Area enclosed by the centrelines of connecting wallsincluding the inner hollowarea (torsion)

Ap Area of prestressing steel

Aref Reference area of thestructure or structuralelement (wind)

As Cross-sectional area of

reinforcementAs,min Minimum cross-sectional area

of reinforcement

As,prov Area of steel provided

As,req Area of steel required

As1 Area of reinforcing steel inlayer 1

As2 Area of compression steel (inlayer 2)

Asl Area of the tensilereinforcement extending atleast lbd + dbeyond thesection considered

AsM (AsN) Total area of reinforcementrequired in symmetrical,rectangular columns to resistmoment (axial load) usingsimplified calculation method

Ast Cross-sectional area oftransverse steel (at laps)

Asw Cross-sectional area of shearreinforcement

Symbol Definition

Asw Area of punching shearreinforcement in one

perimeter around the columnAsw,min Minimum cross-sectional area

of shear reinforcement

Asw,min Minimum area of punchingshear reinforcement in oneperimeter around the column

a Distance, allowance atsupports

a Axis distance from theconcrete surface to the centreof the bar (fire)

a An exponent (in consideringbiaxial bending of columns)

a Projection of the footing from

the face of the column or wallab Half the centre-to-centre

spacing of bars (perpendicularto the plane of the bend)

al Distance by which the locationwhere a bar is no longerrequired for bending momentis displaced to allow for theforces from the truss modelfor shear. (Shift distance forcurtailment)

am Average axis distance (fire)

asd Axis distance (in fire) from thelateral surface of a member to

the centre of the barav Distance between bearings or

face of support and face ofload

a1, b1 Dimensions of the controlperimeter around anelongated support (punchingshear)

b Overall width of a cross-section, or flange width in a Tor L beam

b Breadth of building (wind)

be Effective width of a flat slab(adjacent to perimetercolumn)

beff Effective width of a flange

beq (heq) Equivalent width (height) ofcolumn = b (h) for rectangularsections

bmin Minimum width of web on T, Ior L beams


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Symbol Definition

bt Mean width of the tensionzone. For a T beam with theflange in compression, onlythe width of the web is takeninto account

bw Width of the web on T, I or L

beams. Minimum widthbetween tension andcompression chords

by, bz Dimensions of the controlperimeter (punching shear)

Ce Exposure coefficient (snow)

Ct Thermal coefficient (snow)

c1, c2 Dimensions of a rectangularcolumn. For edge columns, c1is measured perpendicular tothe free edge (punching shear)

calt Altitude factor (wind)

cd Dynamic factor (wind)

cdir Directional factor (wind)

ce,flat Exposure factor (wind)cf Force coefficient (wind)

cmin Minimum cover, (due to therequirements for bond, cmin,bor durability cmin,dur)

cnom Nominal cover. Nominal covershould satisfy the minimumrequirements of bond,durability and fire

cpe (External) pressure coefficient(wind)

cpe,10 (External) pressure coefficientfor areas > 1 m2 (wind)

cpi Internal pressure coefficient

(wind)cprob Probability factor (wind)

cseason Season factor (wind)

cscd Structural factor (wind)

cs Size factor (wind)

cy, cx Column dimensions in plan

D Diameter of a circular column;Diameter

d Effective depth to tensionsteel

d2 Effective depth tocompression steel

dc Effective depth of concrete in

compressiondeff Effective depth of the slab

taken as the average of theeffective depths in twoorthogonal directions(punching shear)

dl A short length of a perimeter(punching shear)

E Effect of action; Integrity (infire); Elastic modulus

Symbol Definition

Ec, Ec(28) Tangent modulus of elasticityof normal weight concrete at a

stress ofc = 0 and at 28 days

Ec,eff Effective modulus of elasticityof concrete

Ecd Design value of modulus of

elasticity of concreteEcm Secant modulus of elasticity of

concrete

Ed Design value of the effect ofactions

EI Bending stiffness

Es Design value of modulus ofelasticity of reinforcing steel

Exp. Expression

EQU Static equilibrium

e Eccentricity

e2 Deflection (used in assessingM2 in slender columns)

ei Eccentricity due to

imperfectionsepar Eccentricity parallel to the

slab edge resulting from amoment about an axisperpendicular to the slab edge(punching shear)

ey, ez Eccentricity, MEd/VEd along yand z axes respectively(punching shear)

F1 Factor to account for flangedsections (deflection)

F2 Factor to account for brittlepartitions in association withlong spans (deflection)

F3 Factor to account for servicestress in tensile reinforcement(deflection)

F Action

Fbt Tensile force in the bar at thestart of the bend caused byultimate loads

Fc (Fs) Force in concrete (steel)

Fcd Design value of the concretecompression force in thedirection of the longitudinalmember axis

Fd Design value of an action

FE Tensile force in reinforcementto be anchored

FEd Compressive force, designvalue of support reaction

Fk Characteristic value of anaction

Frep Representative action (= Fk

where = factor to convertcharacteristic torepresentative action)


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Symbol Definition

FRs Resisting tensile force in steel

Fs Tensile force in the bar

Ftd Design value of the tensileforce in longitudinalreinforcement

Ftie,col Horizontal tie force, column to

floor or roof (kN)Ftie,fac Horizontal tie force, wall to

floor or roof (kN/m)

Ftie,int Internal tie tensile force

Ftie,per Peripheral tie tensile force

Fwd Design shear strength of weld,design value of the force instirrups in corbels

fbd Ultimate bond stress

fc Compressive strength ofconcrete

fcd Design value of concretecompressive strength

fcd,pl Design compressive strength of

plain concretefck Characteristic compressive

cylinder strength of concreteat 28 days

fck, cube Characteristic compressivecube strength of concrete at28 days

fcm Mean value of concretecylinder compressive strength

fct,d Design tensile strength of

concrete (ctfct,k/c)

fct,eff Mean tensile strength ofconcrete effective at the timecracks may be first expectedto occur.fct,eff=fctm at the appropriateage

fct,k Characteristic axial tensilestrength of concrete

fctm Mean value of axial tensilestrength of concrete

fct,0.05 5% fractile value of axialtensile strength of concrete

fct,0.95 95% fractile value of axialtensile strength of concrete

fcvd Concrete design strength inshear and compression (plain

concrete)fsc Compressive stress incompression reinforcement atULS

ft Tensile strength ofreinforcement

ft,k Characteristic tensile strengthof reinforcement

fyd Design yield strength oflongitudinal reinforcement,Asl

Symbol Definition

fyk Characteristic yield strengthof reinforcement

fywd Design yield strength of theshear reinforcement

fywd,ef Effective design strength ofpunching shear reinforcement

fywk Characteristic yield strengthof shear reinforcement

Gk Characteristic value of apermanent action

Gk,sup Upper characteristic value of apermanent action

Gk,inf Lower characteristic value of apermanent action

gk Characteristic value of apermanent action per unitlength or area

Hi Horizontal action applied at alevel

H Height of building (wind)

h Overall depth of a cross-section; Height

have Obstruction height (wind)hdis Displacement height (wind)hf Depth of footing; Thickness of

flange

hH Vertical height of a drop orcolumn head below soffit of aslab (punching shear)

h0 Notional size of cross-section

hs Depth of slab

I Second moment of area ofconcrete section

I Insulation (in fire)

i Radius of gyration

K MEd/bd2fck. A measure of the

relative compressive stress ina member in flexure

K Factor to account forstructural system (deflection)

K Value ofKabove whichcompression reinforcement isrequired

Kr Correction factor for curvaturedepending on axial load

K Factor for taking account ofcreep

k Coefficient or factorkc Coefficient allowing for the

nature of the stressdistribution within the sectionimmediately prior to crackingand for the change of thelever arm as a result ofcracking (minimum areas)

l Clear height of columnbetween end restraints


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Symbol Definition

l Height of the structure inmetres

l (or L) Length; Span

l0 Effective length (of columns)

l0 Distance between points ofzero moment

l0 Design lap lengthl0,fi Effective length under fire

conditions

lb Basic anchorage length

lbd Design anchorage length

lb,eq Equivalent anchorage length

lb,min Minimum anchorage length

lb,rqd Basic anchorage length

leff Effective span

lH Horizontal distance fromcolumn face to edge of a dropor column head below soffit ofa slab (punching shear)

ln Clear distance between the

faces of supportsls Floor to ceiling height

lx, ly Spans of a two-way slab in thex and y directions

M Bending moment. Momentfrom first order analysis

M Moment capacity of a singlyreinforced section (abovewhich compressionreinforcement is required)

M0,Eqp First order bending moment inquasi permanent loadcombination (SLS)

M01

, M02

First order end moments atULS including allowances forimperfections

M0Ed Equivalent first order momentincluding the effect ofimperfections (at about midheight)

M0Ed,fi First order moment under fireconditions

M2 Nominal second order momentin slender columns

Med Design value of the appliedinternal bending moment

MEdy, MEdz Design moment in the

respective directionMRdy, MRdz Moment resistance in the

respective direction

m Number of vertical memberscontributing to an effect

m Mass

N Axial force

N Basic span-to-effective-depthratio, l/d, for K= 1.0

Symbol Definition

N0Ed,fi Axial load under fireconditions

NA National Annex

Na, Nb Longitudinal forcescontributing to Hi

NEd Design value of the applied

axial force (tension orcompression) at ULS

NDP Nationally DeterminedParameter(s) as published in acountrys National Annex

n Load level at normaltemperatures. Conservativelyn = 0.7 (fire)

n Axial stress at ULS

n Ultimate action (load) per unitlength (or area)

n0 Number of storeys

nb Number of bars in the bundle

Qk Characteristic value of a

variable actionQk1 (Qki) Characteristic value of a

leading variable action(Characteristic value of anaccompanying variable action)

qk Characteristic value of avariable action per unit lengthor area

qb Basic wind pressure

qp Peak wind pressure

qp(ze) Peak velocity pressure atreference height ze, (wind)

R Resistance; Mechanicalresistance (in fire)

R/A Vertical bearing resistance perunit area (foundations)

RA Reaction at support A

RB Reaction at support B

Rd Design value of the resistanceto an action

RH Relative humidity

r Radius

rcont The distance from thecentroid of a column to thecontrol section outside thecolumn head

rm Ratio of first order end

moments in columns at ULSS, N, R Cement types

SLS Serviceability limit state(s) corresponding to conditionsbeyond which specified servicerequirements are no longermet

s Spacing

s Snow load on a roof


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Symbol Definition

sk Characteristic ground snowload

sr Radial spacing of perimetersof shear reinforcement

st Tangential spacing shearreinforcement along

perimeters of shearreinforcement

T Torsional moment

Ted Design value of the appliedtorsional moment

TRd Design torsional resistancemoment

TRd,max Maximum design torsionalresistance moment capacity

t Thickness; Time beingconsidered; Breadth of support

t0 The age of concrete at thetime of loading

tef,i Effective wall thickness

(torsion)ULS Ultimate limit state(s)

associated with collapse orother forms of structuralfailure

u Perimeter of concrete cross-section, having areaAc

u Perimeter of that part which isexposed to drying

u Circumference of outer edgeof effective cross-section(torsion)

u0 Perimeter adjacent to columns(punching shear)

u1 Basic control perimeter (at 2dfrom face of load) (punchingshear)

u1* Reduced control perimeter atperimeter columns (at 2dfromface of load (punching shear)

ui Length of the controlperimeter under consideration(punching shear)

uk Perimeter of the areaAk(torsion)

uout Perimeter at which shearreinforcement is no longerrequired

V Shear force

VEd Design value of the appliedshear force

VEd,red Applied shear force reducedby the force due to soilpressure less self weight ofbase (punching shear,foundations)

VRd,c Shear resistance of a memberwithout shear reinforcement

Symbol Definition

VRd,max Shear resistance of a memberlimited by the crushing ofcompression struts

VRd,cmin Minimum shear resistance ofmember considering concrete

aloneVRd,s Shear resistance of a member

governed by the yielding ofshear reinforcement

vb Basic wind velocity

vb,0 The fundamental basic windvelocity being thecharacteristic 10 minute windvelocity at 10 m above groundlevel in open country

vb,map Fundamental basic windvelocity from Figure NA.1 m/s

vEd Punching shear stress

vEd Shear stress for sections

without shear reinforcement(= VEd/bwd)

vEd,z Shear stress for sections withshear reinforcement (=VEd/bwz= VEd/bw0.9d)

vRd,c Design shear resistance ofconcrete without shearreinforcement expressed as astress

vRd,cs Design punching shearresistance of concrete withshear reinforcement expressedas a stress (punching shear)

vRd,max Capacity of concrete struts

expressed as a stressW1 Factor corresponding to a

distribution of shear (punchingshear)

We Peak external wind load

Wk Characteristic value of windaction (NB not in theEurocodes and should beregarded as a form ofQk,characteristic value of avariable action)

wk Crack width

wmax Limiting calculated crackwidth

X0, XA, XC,XD, XF, XS

Concrete exposure classes

x Neutral axis depth

x Distance between buildings(wind)

x Distance of the section beingconsidered from the centreline of the support

x, y, z Co-ordinates; Planes underconsideration


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Symbol Definition

xu Depth of the neutral axis atthe ultimate limit state afterredistribution

Z Zone number obtainedfrom map (snow)

z Lever arm of internal forces

z Reference height (wind)ze Reference height for windward

walls of rectangular buildings(wind)

Angle; Angle of shear links tothe longitudinal axis; Ratio

A A coefficient for use with arepresentative variable actiontaking into account areasupported

1,2,3,

4,5,6

Factors dealing withanchorage and laps of bars

cc (ct) A coefficient taking intoaccount long term effects of

compressive (tensile) load andthe way load is applied

n A coefficient for use with arepresentative variable actiontaking into account number ofstoreys supported

Angle; Ratio; Coefficient

Factor dealing witheccentricity (punching shear)

Partial factor

A Partial factor for accidentalactions,A

G Partial factor for permanentactions, G

Gk,sup Partial factor to be applie3dto Gk,inf

Gk,inf Partial factor to be applied toGk,sup

M Partial factor for a materialproperty, taking account ofuncertainties in the materialproperty itself, in geometricdeviation and in the designmodel used

Q Partial factor for variableactions, Q

C Partial factor for concrete

F Partial factor for actions, Ff Partial factor for actionswithout taking account ofmodel uncertainties

g Partial factor for permanentactions without taking accountof model uncertainties

S Partial factor for reinforcingsteel

Symbol Definition

Ratio of the redistributedmoment to the elastic bendingmoment. Redistribution ratio(1 % redistribution)

c Allowance for deviation madein design, e.g. to allow for

workmanship (BS EN 13760)cdev Allowance made in design for

deviation

p Change in strain inprestressing steel

Ftd Additional tensile force inlongitudinal reinforcementdue to the truss shear model

c Compressive strain in concrete

c2 Compressive strain limit inconcrete for concrete in pureaxial compression or strain inconcrete at reaching maximumstrength assuming use of the

parabolicrectangular stressstrain relationship

c3 Compressive strain limit inconcrete for concrete in pureaxial compression or strain inconcrete at reaching maximumstrength assuming use of thebilinear stressstrainrelationship

cu Ultimate compressive strain inthe concrete

cu2 Ultimate compressive strainlimit in concrete which is notfully in pure axial compression

assuming use of the parabolicrectangular stressstrainrelationship (numericallycu2 = cu3)

cu3 Ultimate compressive strainlimit in concrete which is notfully in pure axial compressionassuming use of the bilinearstressstrain relationship

p(0) Initial strain in prestressingsteel

s Strain in reinforcing steel

u Strain of reinforcement orprestressing steel at maximum

loadud Design limit for strain for

reinforcing steel in tension= 0.9 uk

uk Characteristic strain ofreinforcement (or prestressingsteel) at maximum load

y Reinforcement yield strain

Factor defining effectivestrength (= 1 for C50/60)


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Symbol Definition1 Coefficient for bond conditions

2 Coefficient for bar diameter

Angle; Angle of compressionstruts (shear)

I Inclination used to representimperfections

Slenderness ratio Factor defining the height of

the compression zone (= 0.8for C50/60)

fi Slenderness in fire

lim Limiting slenderness ratio (ofcolumns)

I Snow load shape factor

fi Ratio of the design axial loadunder fire conditions to thedesign resistance of thecolumn at normal temperaturebut with an eccentricityapplicable to fire conditions

Strength reduction factor forconcrete cracked in shear

Reduction factor/distributioncoefficient. Factor applied toGk in BS EN 1990 Exp. (6.10b)

Required tensionreinforcement ratio

Density of air (wind)

Reinforcement ratio forrequired compressionreinforcement,As2/bd

1 Percentage of reinforcementlapped within 0.65l0 from thecentre line of the lap beingconsidered

l Reinforcement ratio forlongitudinal reinforcement

0 Reference reinforcement ratio

fck0.5 103

gd Design value of the groundpressure

s Stress in reinforcement at SLS

s Absolute value of themaximum stress permitted inthe reinforcementimmediately after theformation of the crack

sc(st) Stress in compression (andtension) reinforcement

sd Design stress in the bar at theultimate limit state

su Estimate of stress inreinforcement at SLS(deflection)

Torsional shear stress

(,t0) Final value of creepcoefficient

Symbol Definition

ef Effective creep factor

(t,t0) Creep coefficient, definingcreep between times t and t0,related to elastic deformationat 28 days

Bar diameter

n Equivalent diameter of abundle of reinforcing bars

m Mandrel diameter

Factors definingrepresentative values ofvariable actions

0 Combination value of avariable action (e.g. usedwhen considering ULS)

1 Frequent value of a variableaction (e.g. used whenconsidering whether sectionwill have cracked or not)

2 Quasi-permanent value of a

variable action (e.g. usedwhen consideringdeformation)

Mechanical reinforcementratio =Asfyd/Acfcd 1

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WE Symbols Sep07