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Chapter 9Bridge Design Manual - 2002 Reinforced Concrete

Ethiopian Roads Authority Page 9-1

9 REINFORCED CONCRETE

9.1 SCOPE

Designs should be based on the material properties cited herein.

In these Design Specifications, the compressive strength of concrete, f′c, is determined fromtests on 150 mm cylinders at the age of 28 days in accordance with the Ethiopian Standards.It is common practice that the specified strength be attained 28 days after placement. Othermaturity ages shall be assumed for design and specified for components, which will receiveloads at times appreciably different than 28 days after placement.

The Ethiopian Building Code Standards (Ref. 1) shall be used as a compliment to theseSpecifications, unless otherwise stated herein.

9.2 NOTATIONS

A = area of concrete having the same centroid as the principal tensile reinforcement andbounded by the surfaces of the cross-section and a straight line parallel to theneutral axis, divided by the number of bars or wires (mm2)

Ab = area of bar or wire (mm2)Ac = area of core measured to the outside diameter of the spiral (mm2)Acp = total area enclosed by outside perimeter of concrete cross-section (mm2)Ag = gross area of concrete section (mm2)Aps = area of prestressing steel (mm2)As = area of reinforcement (mm2)Ast = total area of longitudinal reinforcement (mm2)At = area of one leg of closed transverse torsion reinforcement (mm2)Ao = area enclosed by the shear flow path, including area of holes therein, if any (mm2)d = distance from compression face to centroid of tension reinforcement (mm)dc = depth of concrete measured from extreme tension fiber to center of bar or wire

located closest theretodb = diameter of bar or wire (mm)ex = eccentricity of the applied factored axial force in the X direction, i.e.= Mux/Pu (mm)ey = eccentricity of the applied factored axial force in the Y direction, i.e= Mux/Pu (mm)Ec = the modulus of elasticity of concrete (MPa)Es = modulus of elasticity of longitudinal steel (MPa)f′c = compressive strength of concrete at 28 days (MPa)fc = factored torsional moment (Nmm)fctk = characteristic tensile strength (MPa)fctm = characteristic cylinder compressive strength (MPa)ff = stress range (MPa)fmin = minimum live load stress resulting from the fatigue load combination specified in

Table 3-2, combined with the more severe stress from either the permanent loads orthe permanent loads, shrinkage, and creep induced external loads; positive iftension, negative if compression (MPa)

Chapter 9Reinforced Concrete Bridge Design Manual - 2002

Page 9-2 Ethiopian Roads Authority

fpc = compressive stress in concrete after prestress losses have occurred either at thecentroid of the cross-section resisting transient loads or at the junction of the weband flange where the centroid lies in the flange (MPa)

fpu = specified tensile strength of prestressing steel (MPa)fr = modulus of rupture (MPa)fsa = tensile stress in the mild steel reinforcement at the service limit statefy = specified yield strength of reinforcing bars (MPa)fyh = specified yield strength of spiral reinforcement (MPa)H = average relative humidity at the site (%)Ig = moment of inertia of gross concrete section about centroidal axis (mm4)Is = moment of inertia of longitudinal steel about the centroidal axis (mm4)K = effective length factorkc = factor for the effect of the volume-to-surface ratio of the component (see Figure 9-1)kf = factor for the effect of concrete strength (see Equation 9.2)lc = compression development length for lap splice (mm)ld = tension development length for lap splice (mm)ldb = basic tension development length for deformed bar (mm)lhb = basic tension development length for hooked bar (mm)lu = unbraced length (mm)Ml = smaller end momentM2 = larger end momentMc = magnified factored momentMr = factored flexural resistanceMux = factored applied moment about the X-axis (Nmm)Muy = factored applied moment about the Y-axis (Nmm)pc = length of the outside perimeter of the concrete section (mm)Pe = Euler buckling loadPn = nominal axial resistance, with or without flexure (N)Pr = factored axial resistance, with or without flexure (N)Prx = factored axial resistance determined on the basis that only eccentricity ey is present (N)Prxy = factored axial resistance in biaxial flexure (N)Pry = factored axial resistance determined on the basis that only eccentricity ex is present (N)Pu = factored applied axial force (N)r = radius of gyration (mm)r/h = ratio of base radius to height of rolled-on transverse deformations; if the actual

value is not known, 0.3 shall be usedt = maturity of concrete (Days)tI = age of concrete when load is initially applied (Days)Tcr = torsional cracking moment (Nmm)Tn = nominal torsional resistance (Nmm)Tr = factored torsional resistance (Nmm)Tn = nominal shear resistance (N)Tr = factored shear resistance (N)Z = crack width parameter (N/mm)βd = ratio of maximum factored permanent load moments to maximum factored total

load moment; always positive



γc = density of concrete (kg/m3)θ = angle of crack, usually 45°.ρmin = ratio of tension steel to gross areaϕ = resistance factor (see Table 9-7)ψ = creep coefficient

9.3 CONCRETE

9.3.1 GENERAL

Recommended grade of concrete and corresponding specified strengths are shown in Table 9-1 for both cylinder and cube strengths. Classes of concrete corresponding to these grades areshown in Table 9-2.

Grades of Concrete C25 C30 C40 C50 C60

Fck (150 mm cylinders, MPa) 20 24 32 40 48

fck (200 mm cubes, MPa) 21 25 34 42 50

fck (150 mm cubes, MPa) 25 30 40 50 60

Table 9-1 Grades of Concrete and Characteristic Cylinder and Cube CompressiveStrength, fck

Class Permissible Grades of ConcreteIII

(C20)(C20)

C25-

C30-

C40-

C50-

C60-

Table 9-2 Grades and Classes of Concrete

Class I concrete is generally used for all elements of structures, except when another class ismore appropriate, and specifically for concrete exposed to saltwater. Class II concrete is usedin footings, pedestals, massive pier shafts, and gravity walls.

Concrete strengths above 50 MPa (150 mm cylinders) shall be used only when physical testsare made to establish the relationships between the concrete strength and other properties.Concrete with strengths below 20 MPa at 28 days (150 mm cylinders) should not be used instructural applications.The specified compressive strength for prestressed concrete shall not be less than 30 MPa.

Regarding tensile strength see subheading Characteristic Tensile Strength below.



9.3.2 COEFFICIENT OF THERMAL EXPANSION

The coefficient of thermal expansion should be determined by the laboratory tests on thespecific mix to be used. In the absence of more precise data, the thermal coefficient ofexpansion shall be taken as:• for normal density concrete: 10.8 x 10-6/oC, and• for low-density concrete: 9.0 x 10-6/oC

The thermal coefficient of normal density concrete can vary between 5.4 to 14.4 x 10-6/oC,with limestone and marble aggregates producing the lower values, and chert and quartzite thehigher.

9.3.3 SHRINKAGE AND CREEP

Values of shrinkage and creep, specified herein, shall be used to determine the effects ofshrinkage and creep on the loss of prestressing force in bridges other than segmentallyconstructed ones. These values in conjunction with the Moment of Inertia shall be used todetermine the effects of shrinkage and creep on deflections.

The shrinkage coefficients shall be assumed to be 0.0002 after 28 days and 0.0005 after oneyear of drying.

Shrinkage of concrete can vary over a wide range from nearly nil if continually immersed inwater to in excess of 0.0008 for either thin sections made with high shrinkage aggregates orfor sections which are not property cured.

The creep coefficient shall be estimated as:

6.0i

6.0i118.0

ifci)tt(0.10

)tt(t

120

H58.1kk5.3)t,t(

−+−

��

��

� −=ψ − (Ref. 2) (9.1)

for which: kf = 62 (9.2)42+f′c

where: H = average relative humidity at the site (%)kc = factor for the effect of the volume-to-surface ratio of the component, Figure 9-1

below.kf = factor for the effect of concrete strength (from Equation 9.2 above)t = maturity of concrete (Days)tI = age of concrete when load is initially applied (Days)f′c = specified compressive strength at 28 days (MPa)

Creep is influenced by the same factors as shrinkage, and also by: magnitude and duration ofthe stress, maturity of the concrete at the time of loading, and temperature of concrete.



Figure 9.1 Factor kc for Volume to Surface Ratio

Creep shortening of concrete under permanent loads is generally in the range of 1.5 to 4.0times the initial elastic shortening, depending primarily on concrete maturity at the time ofloading.

9.3.4 DESIGN PROPERTIES (MODULUS OF ELASTICITY, POISSON'S RATIO, MODULUS OF RUPTURE)

In the absence of more precise data, the modulus of elasticity, Ec, for concrete with densitiesbetween 1440 and 2500 kg/M3, shall be taken as:

c5.1

cc f043.0E γ= (9.3)

where: γc = density of concrete (kg/m3)f′c = specified cylinder strength of concrete (MPa)

For normal density concrete with γc = 2 400 kg/m3 , Ec shall be taken as:

cc f4800E = (9.4)

Poisson's ratio shall be assumed as 0.2. For components which are expected to be subject tocracking, the effect of Poisson's ratio shall be neglected.

The modulus of rupture (fr) in MPa, for normal density concrete, shall be taken as:

cr 'f63.0F = (9.5)



9.3.5 CHARACTERISTIC TENSILE STRENGTH

The Characteristic Tensile Strength refers to the axial tensile strength as determined by testsin accordance with standards issued or approved by the Quality and Standardization Authorityof Ethiopia. It shall be determined by either using the Ethiopian Standards, ASTM C900-94"Standard Test Method for Pullout Strength of Hardened Concrete", or the split tensilestrength method in accordance with AASHTO T198 (ASTM C496-90) "Standard Method forSplitting Tensile Strength of Cylindrical Concrete Specimens.

The Characteristic Tensile Strength may also be determined from the characteristic cylindercompressive strength as:

fctk =0.7 fctm ; (9.6)Where fctm =0.3 fck

2/3 (see Table 9.3 below) (9.7)

Grades of Concrete C20 C25 C30 C40 C50 C60fctm

fctk

1.91.3

2.21.5

2.51.7

3.02.1

3.52.5

4.02.8

Table 9-3 Grades of Concrete and Values of fctk and fctm

9.4 REINFORCEMENT

9.4.1 GENERAL

Reinforcing bars, deformed wire, cold-drawn wire, welded plain wire fabric and weldeddeformed wire fabric shall conform to the materials standards as specified herein.

Reinforcement shall be deformed, except that plain bars or plain wire may be used for spirals,hoops and wire fabric. Bars < Ø 10 mm should not be used for cast-in-place structures.

The nominal yield strength shall be the minimum as specified for the grade of steel selected,except that yield strengths in excess of 520 MPa shall not be used for design purposes. Barswith yield strengths less than 270 MPa shall be used only with the approval of ERA. Tensilerequirements are as indicated in Table 9-4.

AASHTO M31 M Grade Grade 300 Grade 420 Grade 520

Equiv. European bars B500B Ks60(Old AASHTO M31 Grade) (40) (60) (75)Tensile strength, min. MPa 500 620 690Yield strength, min. Mpa 300 420 520

Table 9-4 Tensile Requirements for Reinforcement Bars



Where ductility is to be assured or where welding is required, steel conforming to therequirements of ASTM A706M, Low Alloy Steel Deformed Bars for ConcreteReinforcement, or similar weldable European Steel, should be specified.

Reinforcement shall be deformed, except that plain bars or plain wire shall be used for spirals,hoops and wire fabric. Bars < ∅10 mm should not be used for cast-in-place structures.

The Ethiopian Iron and Steel Foundry in Akaki and Zuquala Steel Rolling Mill Enterprises inDebre Zeit manufacture up to 400 MPa deformed bars with diameters ∅6 - ∅32 mm.

9.4.2 DESIGN PROPERTIES

Water/Cement Ratio ≤0,40 ≤0,45 ≤0,50SITUATION COVER (mm) COVER (mm) COVER (mm)Direct exposure to salt water 80 100 120Cast against earth (i.e. Bottom offootings)

60 75 90

Exterior other than above 40 50 60Interior other than above (i.e. hollowstructures)• Up to ∅35 Bar• ∅45 and ∅55Bars

3240

4050

4860

Bottom of cast-in-place slabs• Up to ∅35 Bar• ∅45 and ∅55Bars

2540

2550

3060

Precast soffit form panels 20 20 24Precast Reinforced Piles• Non-corrosive environments• Corrosive environments

3260

4075

4890

Precast Prestressed Piles 40 50 60Cast-in-place Piles• Non-corrosive environments• Corrosive environments- General- Protected• Shells• Auger cast, tremie concrete or slurryconstruction

40

60604060

50

75755075

60

90906090

Table 9-5 Cover for Unprotected Main Reinforcing Steel (mm)

The modulus of elasticity, Ec, of bars and undeformed wires shall be assumed as 200 000MPa.



Minimum cover to main bars, including bars protected by epoxy coating, shall be 25 mm.Minimum Cover to ties and stirrups may be 12 mm less than the values specified in Table 9-5for main bars, but shall not be less than 25 mm (not less than 20 mm for Precast soffit formpanels).

Concrete Cover for unprotected prestressing and reinforcing steel for the actual water-cementratio shall not be less than as specified in Table 9-5 above, unless otherwise specified herein.Concrete cover and placing tolerances shall be shown in the contract documents and/or at thedetail drawings.

Cover for pretensioned prestressing strand, anchorage hardware and mechanical connectionsfor reinforcing bars or post-tensioned prestressing strands shall be the same as for reinforcingsteel.

Cover for metal ducts for post-tensioned tendons shall not be less than:

• that specified for main reinforcing steel,• one-half the diameter of the duct, or• that specified in Table 9-5.

Protective Coatings: Protection against chloride-induced corrosion shall be provided byepoxy coating or galvanizing of reinforcing steel, post-tensioning duct and anchoragehardware and epoxy coating of prestressing strand.

9.4.3 DEVELOPMENT (CUT OFF) AND SPLICES OF REINFORCEMENT:

Development of Reinforcement

Positive Moment Reinforcement: At least one-third of the positive moment reinforcement insimple-span members, and one fourth the positive moment reinforcement in continuousmembers, shall extend along the same face of the member beyond the centerline of thesupport. In beams such extension shall be no less than 150 mm.

Negative Moment Reinforcement: At least one-third of the total tension reinforcementprovided for negative moment at a support shall have an embedment length beyond the pointof inflection not less than:

• the effective depth of the member,• 20 times the nominal diameter of bar, and• 0.0625 times the clear span.

Deformed Bars and Deformed Wire in Tension: The tension development length, ld, shall notbe less than the product of the basic tension development length, ldb, as specified herein, andthe modification factor or factors, as specified below. The tension development length shallnot be less than 300 mm, except for lap splices and in development of shear reinforcementbelow.


Ethiopian Roads Authority -9

The basic tension development length, ldb in mm shall be taken as:

• for ∅ 35 bar and smaller............................ cl

yb f/fA02.0 but not less than: 0.06 db fy

• for ∅ 45 bars .............................................................................................. cl

y f/f25

• for ∅ 55 bars ............................................................................................ cl

y f/f34

• for deformed wire ................................................................................ cl

yb f/fd36.0

where: Ab = area of bar or wire (mm2)fy = specified yield strength of reinforcing bars (MPa)f'c = specified compressive strength of concrete at 28 days (MPa)db = diameter of bar or wire (mm)

Modification Factors which increase ld : The basic development length, ldb, shall bemultiplied by the following factor or factors as applicable:• for top horizontal or nearly horizontal reinforcement, so placed that more• than 300 mm of fresh concrete is cast below the reinforcement................................. 1.4• for bars with a cover of db or less, or with a clear spacing of 2db or less .................... 2.0

Modification Factors which Decrease ld: The basic development length, ldb, modified by thefactors as specified above, shall be multiplied by the following factors, where:• reinforcement being developed in the length under consideration is spaced laterally not

less than 150 mm center-to-center, with not less than 75 mm clear cover measured in thedirection of the spacing ............................................................................................ 0.8

• anchorage or development for the full yield strength of reinforcement is not required, orwhere reinforcement in flexural members is in excess of that required by analysis(As required) / (As provided)

Deformed Bars In Compression: The development length, ld, for deformed bars incompression shall not be less than either the product of the basic development length asspecified herein and the applicable modification factors as specified below (Modificationfactors) or 200 mm.

The basic development length, ldb, for deformed bars in compression shall not be less than:

or,f

fd24.0l

cl

ybdb = (9.8)

ldb = 0.044 db fy (.9.9)

where:fy = specified yield strength of reinforcing bars (MPa)fl

c = specified compressive strength of concrete at 28 days,unless another age is specified (MPa)



db = diameter of bar (mm)

Modification Factors: The basic development length, ldb, shall be multiplied by applicablefactors, where:• anchorage or development for the full yield strength of reinforcement is not required, or

where reinforcement is provided in excess of that required byanalysis .................................................................................... (As required) / (As provided)

• reinforcement is enclosed within a spiral composed of a bar of not less than 6 mm indiameter and spaced at not more than a 100 mm pitch..................................................... 0.75

Bundled Bars: The development length of individual bars within a bundle, in tension orcompression, shall be that for the individual bar, increased by 20% for a three-bar bundle andby 33% for a four-bar bundle. For determining the Modification factors for tensiondevelopment length above, a unit of bundled bars shall be treated as a single bar of a diameterdetermined from the equivalent total area.

Standard Hooks in Tension: The development length, ldh, in mm, for deformed bars in tensionterminating in a standard hook shall not be less than:• the product of the basic development length lhb, as specified in Equation 9.10, and the

applicable modification factor or factors, as below• 8.0 bar diameters, or• 150 mm.Basic development length, lhb, for a hooked bar with yield strength, fy not exceeding 400MPa shall be taken as:

cl

bhb

f

d100l = (9.10)

where: db = diameter of bar (mm)f'c = specified compressive strength of concrete at 28 days, unless another age

specified (MPa)

Modification factors: Basic hook development length, lhb , shall be multiplied by thefollowing factors as applicable, where:• reinforcement yield strength exceeds 400 MPa ...............................................fy / 400• anchorage or development of full yield strength is

not required, or where reinforcement is provided inexcess of that required by analysis .................................(As required) / (As provided)

Lap Splices of Reinforcement in Tension

The length of lap for tension lap splices shall not be less than either 300 mm or the followingfor Class A, B or C splices (see Table 9-6):

Class A splice ....................................................................................................... 1.0 ld

Class B splice ....................................................................................................... 1.3 ld

Class C splice ....................................................................................................... 1.7 ld



The class of lap splice required for deformed bars and deformed wire in tension shall be asshown in Table 9-6.

Percent of As Spliced with Required Lap LengthRatio of(As as provided)(As as required)

50 75 100

≥ 2 A A B< 2 B C C

Table 9-6 Classes of Tension Lap Splices

The tension development length, ld, used as a basis for calculating splice lengths shouldinclude all of the modification factors specified in this subchapter.

Splices in Tension Tie Members

A tension tie member is assumed to have:• An axial tensile force sufficient to create tension over the cross-section, and• A level of stress in the reinforcement such that every bar is fully effective.

Examples of members that shall be classified as tension ties are arch ties, hangers carryingload to an overhead supporting structure, and main tension components in a truss.

Splices of reinforcement in tension tie members shall be made only with either full-weldedsplices or full mechanical connections. Splices in adjacent bars shall be staggered not lessthan 750 mm apart.

Splices of Reinforcement Bars in Compression

The length of lap, lc, for compression lap splices shall be ≥ 300 mm or as follows:

• If fy ≤ 420 MPa then: lc = 0.073m fy db, or (9.11)

• If fy > 420 MPa then: lc = m(0.13 fy – 24) db (9.12)

for which:• Where the specified concrete strength, f′c is less than 21 MPa. ......................m = 1.33• Where ties along the splice have an effective area not less than 0.15% of the product of the

thickness of the compression component times the tie spacing .....................m = 0.83• With spirals................................................................................ ..................... m = 0.75• In all other cases.................................................................................................m = 1.0

where: fy = specified yield strength of reinforcing bars (MPa)db = diameter of bar (mm)



The effective area of the ties is the area of the legs perpendicular to the thickness of thecomponent, as seen in cross-section.

9.4.5 FLEXURAL REINFORCEMENT

Flexural Reinforcement General

Critical sections for development of reinforcement in flexural members shall be taken atpoints of maximum stress and at points within the span where adjacent reinforcementterminates or is bent.

Except at supports of simple-spans and at the free ends of cantilevers, reinforcement shall beextended beyond the point at which it is no longer required to resist flexure for a distance notless than:

• the effective depth of the member,• 15 times the nominal diameter of bar, or• 1/20 of the clear span.

Continuing reinforcement shall extend not less than the development length, ld, beyond thepoint where bent or terminated tension reinforcement is no longer required to resist flexure.

No more than 50% of the reinforcement shall be terminated at any section, and adjacentbars shall not be terminated in the same section.

Tension reinforcement may also be developed by either bending across the web in whichreinforcement lies and terminating the reinforcement in a compression area and providing thedevelopment length ld to the design section, or by making it continuous with thereinforcement on the opposite face of the member.

Minimum Reinforcement

Unless otherwise specified, at any section of a flexural component, the amount of prestressedand non-prestressed tensile reinforcement shall be adequate to develop a factored flexuralresistance, Mr, at least equal to the lesser of:

• 1.2 times the cracking strength determined on the basis of elastic stress distribution and

the modulus of rupture cl

r f63.0f = of the concrete or

• 1.33 times the factored moment required by the applicable strength load combinationsspecified in Table 3-2.

The provisions for shrinkage and temperature reinforcement later in this chapter shall apply.

For components containing no prestressing steel, the minimum reinforcement provision hereinshall be considered satisfied if:



ρmin ≥ 0.03 f′c/ fy (9.13)

where: ρmin = ratio of tension steel to gross areaf′c = specified concrete strength (MPa)fy = yield strength of tension steel (MPa)

In T-beams where the web is in tension, the determination of the actual mild steel ratio, ρ, forcomparison with the requirement of Equation 9.13 shall be based on the width of the web.

Control of Cracking by Distribution of Reinforcement

The provisions specified herein shall apply to the reinforcement of all concrete components,except that of deck slabs designed according to empirical design methods in which tension in

the cross-section exceeds clf5.0 at the applicable service limit state load combination

specified in Table 3-2.

All reinforced concrete members are subject to cracking under any load condition, includingthermal effects and restraint of deformations, which produces tension in the gross section inexcess of the cracking strength of the concrete. Locations particularly vulnerable to crackinginclude those where there is an abrupt change in section and intermediate post-tensioninganchorage zones.

Provisions specified, herein, are used for the distribution of tension reinforcement to controlflexural cracking in beams.

From the standpoint of appearance, many fine cracks are preferable to a few wide cracks. Thebest crack control is obtained when the steel reinforcement is well distributed over the zone ofmaximum concrete tension. Several bars at moderate spacing are more effective in controllingcracking than one or two larger bars of equivalent area.

Components shall be so proportioned that the tensile stress in the mild steel reinforcement atthe service limit state, fsa does not exceed:

fsa = Z ≤ 0.6 fy (9.14)(dc A)1/3

where: dc = depth of concrete measured from extreme tension fiber to center of bar or wirelocated closest thereto; for calculation purposes, the thickness of clear cover usedto compute dc shall not be taken to be greater than 50 mm

A = area of concrete having the same centroid as the principal tensile reinforcementand bounded by the surfaces of the cross-section and a straight line parallel to theneutral axis, divided by the number of bars or wires (mm2); for calculationpurposes, the thickness of clear concrete cover used to compute A shall not betaken to be greater than 50 mm

Z = crack width parameter (N/mm)



Except as specified below for cast-in-place reinforced concrete box culverts, the quantity Z inEquation 9.14 shall not exceed 30 kN/mm for members in moderate exposure conditions, 23kN/mm for members in severe exposure conditions, and 17.5 kN/mm for buried structures.The quantity Z shall not exceed 23 000 for the transverse design of segmental concrete boxgirders for any loads applied prior to the attainment of the full nominal concrete strength.

Extensive laboratory work involving deformed reinforcing bars has confirmed that the crackwidth at the service limit state is proportional to steel stress. However, the significantvariables reflecting steel detailing were found to be the thickness of concrete cover and thearea of concrete in the zone of maximum tension surrounding each individual reinforcing bar.

Using a value of 30 kN/mm in the numerator of Equation 9.14 corresponds to a limitingsurface crack width of about 0.4 mm.

There appears to be little or no connection between surface crack width and corrosion.Thicker or additional cover for reinforcement will result in greater surface crack widths.These wider surface cracks are not detrimental to the corrosion protection of thereinforcement. In applying Equation 9.14, the actual clear cover should be used where theclear cover is ≤ 50 mm. Where the actual clear cover is > 50 mm, a value of 50 mm should beused for calculation purposes related to Equation 9.14. Additional cover shall be regarded asadded protection.

For cast-in-place reinforced concrete box culverts, the quantity Z in Equation 9.14 shall notexceed:

Z = 27 500 / β (9.15)

for which: β = 1 + dc / 0.7d (9.16)

where: d = distance from compression face to centroid of tension reinforcement (mm)

Bonded prestressing steel shall be included in the calculation of A, in which case the increasein stress in the bonded prestressing steel beyond the decompression state calculated on thebasis of a cracked section or strain compatibility analysis shall not exceed the value of fsa

determined from Equation 9.14.

The basic derivation of the crack control parameter, Z, includes an assumption that a typicalratio of the distance from the neutral axis to the location of the crack at the concrete surfacedivided by the distance from the neutral axis to the centroid of the tensile reinforcing, β, is1.2, which is a typical value for reinforced concrete beams. However, cast-in-place reinforcedconcrete box culvert sections may have a range of β ratios from about 1.1 for thick slabs toabout 1.6 for thin slabs. Thus, the variation in the β ratio for typical box culvert sections isgreater than the range of β values for typical reinforced concrete beams. Equation 9.15 wasderived to take into account the variation in β for reinforced concrete box culverts.



Where flanges of reinforced concrete T-girders and box girders are in tension at the servicelimit state, the flexural tension reinforcement shall be distributed over the lesser of:• The effective flange width, or• A width equal to 1/10 of the average of adjacent spans between bearings.

If the effective flange width exceeds 1/10 the span, additional longitudinal reinforcement,with area of not less than 0.4 percent of the excess slab area, shall be provided in the outerportions of the flange.

Distribution of the negative reinforcement for control of cracking in T-girders should be madein the context of the following considerations:• Wide spacing of the reinforcement across the full effective width of flange may cause

some wide cracks to form in the slab near the web.• Close spacing near this web leaves the outer regions of the flange unprotected.

The 1/10 of the span limitation is to guard against an excessive spacing of bars, withadditional reinforcement required to protect the outer portions of the flange.

9.4.6 SHRINKAGE AND TEMPERATURE REINFORCEMENT

Reinforcement for shrinkage and temperature stresses shall be provided near surfaces ofconcrete exposed to daily temperature changes and in structural mass concrete. Temperatureand shrinkage reinforcement shall be added, so that the total reinforcement on exposedsurfaces is not less than that specified herein.

The spacing of stress- relieving joints should be considered in determining the area ofshrinkage and temperature reinforcement. Surfaces of interior walls of box girders need notbe considered to be subject to daily temperature changes.

Components less than 1200 mm thick: Reinforcement for shrinkage and temperature shall bein the form of bars, welded wire fabric or prestressing tendons. For bars or welded wire fabric,the area of reinforcement in each direction shall not be less than:

As ≥ 0.75 Ag/fy (9.17)

Where: Ag = gross area of section (mm2)fy = Specified yield strength of reinforcing bars (MPa)

Shrinkage and temperature reinforcement shall not be spaced farther apart than either 3.0times the component thickness or 450 mm.

For solid structural concrete walls and footings, bar spacing shall not exceed 300 mm in eachdirection on all faces, and the area of shrinkage and temperature steel need not exceed:

Σ Ab = 0.0015 Ag (9.18)Where: Ab = minimum area of bar (mm2)



9.5 PRESTRESSING STEEL/POST-TENSIONING STEEL

If prestressing tendons are used as steel for shrinkage and temperature reinforcement, thetendons shall provide a minimum average compressive stress of 0.75 MPa on the grossconcrete area in the direction being considered, based on the effective prestress after losses.Spacing of tendons should not exceed 1800 mm. Where the spacing is greater than 1400 mm,bonded reinforcement shall be provided.

9.6 LIMIT STATES

Structural components shall be proportioned to satisfy the requirements at all appropriateservice, fatigue, strength and extreme event states.

Prestressed and partially prestressed concrete structural components shall be investigated forstresses and deformations for each stage that shall be critical during construction, stressing,handling, transportation, and erection, as well as during the service life of the structure ofwhich they are part.

Stress concentrations due to prestressing or other loads, and restraints or imposeddeformations shall be considered.

9.6.1 SERVICE LIMIT STATE

Actions to be considered for concrete at the service limit state shall be cracking (if the tension

exceeds clf5.0 ) deformations, and concrete stresses.

The cracking stress shall be taken as the modulus of rupture (Equation 9.5).

9.6.2 FATIGUE LIMIT STATE

Fatigue need not be investigated for concrete deck slabs in multi-girder applications.

In regions of compressive stress due to permanent loads and prestress, fatigue shall beconsidered only if this compressive stress is less than twice the maximum tensile live loadstress resulting from the fatigue load combination as specified in Table 3-2 in combinationwith the provisions of section 3.10: Fatigue Load.

Where consideration of fatigue is required, the stress range shall be determined using thefatigue load combination as specified in Table 3-2.

The section properties for fatigue investigations shall be based on cracked sections where thesum of stresses, due to unfactored permanent loads and prestress, and 1.5 times the fatigue

load is tensile and exceeds clf*25.0 .

Reinforcing Bars: The stress range in straight reinforcement resulting from the fatigue loadcombination, specified in Table 3-2, shall not exceed:



ff = 145 - 0.33 fmin + 55 ( r/h) (9.19)

where: ff = stress range (MPa)fmin = the minimum live load stress resulting from the fatigue load combination

specified in Table 3-2, combined with the more severe stress from either thepermanent loads or the permanent loads, shrinkage, and creep induced externalloads; positive if tension, negative if compression (MPa)

r/h = ratio of base radius to height of rolled-on transverse deformations; if the actualvalue is not known, 0.3 shall be used

9.6.3 STRENGTH LIMIT STATE

The strength limit state issues to be considered shall be those of strength and stability.Factored resistance shall be the product of nominal resistance, and the resistance factor inTable 9-7 below:

Resistance Factors, Conventional Construction: Resistance factor ϕ:• For flexure and tension of reinforced concrete ................................0.90• For flexure and tension of prestressed concrete................................1.00• For shear and torsion:

Normal density concrete ...................................................................0.90Low-density concrete........................................................................0.70

• For axial compression with spirals or ties.........................................0.75• For bearing on concrete ...................................................................0.70• For compression in strut-and-tie models ..........................................0.70• For compression in anchorage zones:

Normal density concrete ..................................................................0.80Low-density concrete.......................................................................0.65

• For tension in steel in anchorage zones ..........................................1.00• for resistance during pile driving .....................................................1.00

Table 9-7 Resistance Factors

For compression members with flexure, the value of ϕ shall be increased linearly to the valuefor flexure as the factored axial load resistance, ϕ*Pn decreases from 0.10 f′c Ag → to 0.

9.6.4 EXTREME EVENT LIMIT STATE

The structure as a whole, and its components, shall be proportioned to resist collapse due toextreme events, specified in Table 3-2, as shall be appropriate to its site and use.

9.7 SHEAR AND TORSION DESIGN

General Requirements: The factored torsional resistance, Tr, shall be taken as:



Tr = ϕTn (9.20)

where: Tn = nominal torsional resistance (Nmm)ϕ = resistance factor from Table 9-7

The factored shear resistance, Vr, shall be taken as:

Vr = ϕVn (9.21)

Where : Vn = nominal shear resistance (N)ϕ = resistance factor from Table 9-7

For normal density concrete, torsional effects shall be investigated where:

Tr > 0.25 ϕ Tcr (9.22)

cl

pcccp

2c

lcr

f328.0

f1)p/A(f328.0T

+= (9.23)

where: fc = factored torsional moment (Nmm)Tcr = torsional cracking moment from the formulae above (Nmm)Acp = total area enclosed by outside perimeter of concrete cross-section (mm2)pc = the length of the outside perimeter of the concrete section (mm)fpc = compressive stress in concrete after prestress losses have occurred either at the

centroid of the cross-section resisting transient loads or at the junction of the weband flange where the centroid lies in the flange (MPa)

ϕ = resistance factor for strength limit state, Table 9-7

The nominal torsional resistance shall be taken as:

S

CotfAA2T

yton

θ= (9.24)

where: Ao = area enclosed by the shear flow path, including area of holes therein, if any(mm2)

At = area of one leg of closed transverse torsion reinforcement (mm2)θ = angle of crack, usually 45°.

9.8 DEFORMATIONS

9.8.1 GENERAL

The provisions of maximum deflection shall be considered. Deck joints and bearings shallaccommodate the dimensional changes caused by loads, creep, shrinkage, thermal changes,settlement, and if appropriate, prestressing.



For more precise determinations of long-term deflections, the creep and shrinkage coefficientsgiven earlier in this chapter should be utilized. These coefficients include the effects ofaggregate characteristics, humidity at the structure site, relative thickness of member, maturityat time of loading, and length of time under loads.

9.8.2 DEFLECTION AND CAMBER

Deflection and camber calculations shall consider dead load, live load, prestressing, erectionloads, concrete creep and shrinkage, and steel relaxation.

For determining deflection and camber, the elastic behavior shall apply.

9.9 COMPRESSION MEMBERS

9.9.1 GENERAL

Unless otherwise permitted, compression members shall be analyzed with consideration of theeffects of:

• Eccentricity,• Axial loads,• Variable moments of inertia,• Degree of end fixity,• Deflections,• Duration of loads, and• Prestressing.

In lieu of a refined procedure, non-prestressed columns with the slenderness ratio,

K * lu / r < 100, (9.25)

where: K = effective length factor (see subchapter 13.6)lu = unbraced length (mm)r = radius of gyration (mm)

shall be designed by the approximate procedure specified below.

The requirements of this subchapter shall be supplemented and modified for structures inSeismic Zone 4.

Provisions shall be made to transfer all force effects from compression components, adjustedfor second order moment magnification, to adjacent components.

Where the connection to an adjacent component is by a concrete hinge, longitudinalreinforcement shall be centralized within the hinge to minimize flexural resistance and shallbe developed on both sides of the hinge.



9.9.2 LIMITS FOR COMPRESSION REINFORCEMENT

The maximum area of prestressed and non-prestressed longitudinal reinforcement for non-composite compression components shall be such that:

08.0fA

fA

A

A

yg

pups

g

s ≤+ (9.26)

30.0fA

fA

cg

pcps ≤ (9.27)

The minimum area of prestressed and non-prestressed longitudinal reinforcement for non-composite compression components shall be such that:

0135.0fA

fA

clfA

fA

yg

pups

g

ys ≥+ (9.28)

where: As = area of non-prestressed tension steel (mm2)Ag = gross area of section (mm2)Aps = area of prestressing steel (mm2)fpu = specified tensile strength of prestressing steel (MPa)fy = specified yield strength of reinforcing bars (MPa)f′c = specified compressive strength of concrete (MPa)fpc = effective prestress (MPa)

According to current ACI codes (Ref. 3), the area of longitudinal reinforcement for non-prestressed non-composite compression components should be not less than 0.01 Ag. Becausethe dimensioning of columns is primarily controlled by bending, this limitation does notaccount for the influence of the concrete compressive strength. To account for thecompressive strength of concrete, the minimum reinforcement in flexural members is shownto be proportional to f′c / fy.. This approach is also reflected in the first term of Equation 9.28.For fully prestressed members, current codes specify a minimum average prestress of 1.6MPa. Here also the influence of compressive strength is not accounted for. A compressivestrength of 35 MPa has been used as a basis for these provisions, and a weighted averagingprocedure was used to arrive at the equation.

The minimum number of longitudinal reinforcing bars in the body of a column shall be 6 ∅16 in a circular arrangement and 4 ∅ 16 in a rectangular arrangement.

For bridges in Seismic Zone 1-3, the minimum area of longitudinal reinforcement shall be thatrequired for a component with a reduced effective area of concrete, provided that both the fullsection and the reduced effective section are capable of resisting the factored loads and thatthe area of reinforcement is not less than 0.7 percent of the gross area of the column.

Where columns are pinned to their foundations, a small number of central bars havesometimes been used as a connection between footing and column.



9.9.3 APPROXIMATE EVALUATION OF SLENDERNESS EFFECTS

These procedures were developed for reinforced concrete columns but are currently used forprestressed concrete columns as well.

For members not braced against sidesway, the effects of slenderness shall be neglected wherethe slenderness ratio, (K * lu / r)< 22.

For members braced against sidesway, the effects of slenderness shall be neglected where:

(K*lu/r)<34-12 (M1/M2),

in which Ml and M2 are the smaller and larger end moments, respectively, and the term(Ml/M2) is positive for single curvature flexure.

The following approximate procedure shall be used for the design of non-prestressedcompression members with (K * lu / r)< 100:

• The design is based on a factored axial load, Pu, determined by elastic analysis and amagnified factored moment, Mc, for approximate methods (see Eq. 12.46 and 12.48).

• The unsupported length, lu, of a compression member is taken as the clear distancebetween components capable of providing lateral support for the compressioncomponents. Where haunches are present, the unsupported length is taken to the extremityof any haunches in the plane considered.

• The radius of gyration, r, is computed for the gross concrete section. For a rectangularcompression member, r shall be taken as 0.30 times the overall dimension in the directionin which stability is being considered. For a circular compression member, r shall betaken as 0.25 times the diameter.

• For members braced against sidesway, the effective length factor, K, is taken as 1.0,unless it is shown by analysis that a lower value shall be used.

• For members not braced against sidesway, K is determined with due consideration for theeffects of cracking and reinforcement on relative stiffness and is taken as not less than1.0.

In lieu of a more precise calculation, EI for use in determining Euler Buckling Load, Pe,where

Pe = π2 E I (9.29)(K*lu)

2

shall be taken as the greater of:

d

ssgc

1

lE5/IEEI

β++= (9.30)

or



d

gc

1

5.2/IEEI

β+= (9.31)

where: Ec = modulus of elasticity of concrete (MPa)Ig = moment of inertia of the gross concrete section about the centroidal axis (mm4)Es = modulus of elasticity of longitudinal steel (MPa)Is = moment of inertia of longitudinal steel about the centroidal axis (mm4)βd = ratio of maximum factored permanent load moments to maximum factored

total load moment; always positiveK = effective length factor (see subchapter 13.6)

For eccentrically prestressed members, consideration shall be given to the effect of lateraldeflection due to prestressing in determining the magnified moment.

For members in structures, which undergo appreciable lateral deflections resulting fromcombinations of vertical load or combinations of vertical and lateral loads, force effectsshould be determined using a second-order analysis.

9.9.4 FACTORED AXIAL RESISTANCE

The factored axial resistance of reinforced concrete compressive components, symmetricalabout both principal axes, shall be taken as:

Pr = ϕ Pn (9.32)

for which:

• For members with spiral reinforcement: Pn = 0.85 [0.85 f′c(Ag-Ast)+fy Ast] (9.33)

• For members with tie reinforcement: Pn = 0.80 [0.85 f′c (Ag - Ast) + fy Ast] (9.34)

where: Pr = factored axial resistance, with or without flexure (N)Pn = nominal axial resistance, with or without flexure (N)f′c = specified strength of concrete at 28 days (MPa)Ag = gross area of section (mm2)Ast = total area of longitudinal reinforcement (mm2)fy = specified yield strength of reinforcement (MPa)ϕ = resistance factor specified in Table 9-7

The values of 0.85 and 0.80 in Equations 9.33 and 9.34 place upper limits on the usableresistance of columns to allow for unintended eccentricity.

9.9.5 BIAXIAL FLEXURE

In lieu of an analysis based on equilibrium and strain compatibility for biaxial flexure,noncircular members subjected to biaxial flexure and compression shall be proportioned usingthe following approximate expressions:



• If the factored axial load is ≥ 0.1* ϕ f′c Ag:

1 = 1 + 1 - 1 (9.35)Prxy Prx Pry ϕPo

for which: Po = 0.85 f′c (Ag – Ast) + Ast fy (9.36)

• If the factored axial load is < 0.10 ϕ f′c Ag:

0.1M

M

M

M

rx

uy

rx

ux ≤+ (9.37)

where: ϕ = resistance factor for members in axial compressionPrxy = factored axial resistance in biaxial flexure (N)Prx = factored axial resistance determined on the basis that only eccentricity ey is

present (N)Pry = factored axial resistance determined on the basis that only eccentricity ex is

present (N)Pu = factored applied axial force (N)Mux = factored applied moment about the X-axis (Nmm)Muy = factored applied moment about the Y-axis (Nmm)ex = eccentricity of the applied factored axial force in the X direction, i.e.= Mux/Pu

(mm)ey = eccentricity of the applied factored axial force in the Y direction, i.e= Mux/Pu

(mm)

The procedure for calculating corresponding values of Mrx and Prx or Mry and Pry can be foundin most texts on reinforced concrete design.

The factored axial resistance Prx and Pry shall not be taken to be greater than the product of theresistance factor, ϕ, and the maximum nominal compressive resistance given by eitherEquations 9.33 or 9.34 above as appropriate.

9.9.6 SPIRALS AND TIES

Where the area of spiral and tie reinforcement is not controlled by:• Seismic requirements,• Shear or torsion, or• Minimum requirements (min. ∅ 10 ties for main reinforcement ≤ ∅ 32)

the ratio of spiral reinforcement to total volume of concrete core, measured out-to-out ofspirals, shall not be less than:

yh

cl

c

gs

f

f1

A

A45.0P �

�

��

� −= (9.38)

where: Ag = gross area of concrete section (mm2)



Ac = area of core measured to the outside diameter of the spiral (mm2)f'c = specified strength of concrete at 28 days (MPa)fyh = specified yield strength of spiral reinforcement (MPa)

REFERENCES

1. Ethiopian Building Code Standards, EBCS-2, “Structural Use of Concrete,” 1995.2. Collins, Michael P., and D. Mitchell. Prestressed Concrete Structures. Prentice Hall:

Englewood Cliffs, New Jersey, 1991.3. ACI Committee 207. Manual of Concrete Practice. ACI 207.2R73. 1973.

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