12 - chapter12

Chapter 12Bridge Design Manual - 2002 Detail Design of Bridges and Structures

Ethiopian Roads Authority 2-1

12 DETAIL DESIGN OF BRIDGES AND STRUCTURES

12.1 GENERAL

These detail design recommendations deal only with culverts, retaining walls, and small andmedium size bridges of certain types. Other types or larger bridges should be designedaccording to Chapter 3: Load Requirements.

Detail design shall be made either according to the empirical methods in Chapter 13:Approximate Methods of Analysis (based on Ref. 1) or any other refined design methods, aslong as they follow accepted static and general design rules.

Loads, force effects and minimum requirements stated in Chapter 3: Load Requirementsshall be used for the detail design.

Construction Loads: In addition to the loads specified in Chapter 3: Load Requirements, allthe appropriate construction loads, such as construction live load from machinery and otherequipment, segment unbalance, etc., shall be considered. Construction loads and conditionsfrequently determine section dimensions and reinforcing and/or prestressing requirements insegmentally constructed bridges. It is important that the designer shows these assumedconditions in the contract documents.

Forms are placed in appropriate sections of the text for checklists in the design of variouspiles, piers, abutments, slabs, girders, frame bridges, masonry arch bridges, prestressedsuperstructure, and bearings. A final Form 12-12 at the end of the chapter gives a checklistfor the basic steps in the design of concrete bridges. Worked examples of detailed design aregiven in the appendix.

12.2 NOTATIONS

The following notations have been used in the recommended methods of calculation:

Acp = total area enclosed by outside perimeter of concrete cross-section (mm2)Ag = gross area of section (mm2)Ao = area enclosed by the shear flow path, including area of holes therein, if any

(mm2)A′s = area of compression reinforcement (mm2)As = area of non-prestressed tension reinforcement; area of reinforcing steel (mm2)As-BW = area of steel in the band width (mm2)As-SD = total area of steel in short direction (mm2)At = area of one leg of closed transverse torsion reinforcement (mm2)Av = total area of steel (mm2)Av = area of shear reinforcement within a distance s (mm2)Av = area of transverse reinforcement within a distance s (mm2)

Chapter 12Detail Design of Bridges and Structures Bridge Design Manual - 2002

Page 12-2 Ethiopian Roads Authority

b = design width, usually taken as 1.0 (mm)bc = perimeter of slabbo = perimeter of the critical section (mm)B = footing dimensionB’ = reduced footing dimensionBc = outside width of culvert (mm)Bd = horizontal width of trench (mm)bv = effective web width taken as the minimum web width within depth dv (mm)Cd = coefficient for trench installationsc = the distance from the extreme compression fiber to the neutral axis (mm)d = depth of slab or footingde = effective depth from extreme compression fiber to the centroid of the tensile

force in the tensile reinforcement (mm)dv = effective shear depth (mm)D = pile width (mm)eB = eccentricity parallel to dimension B (mm)eL = eccentricity parallel to dimension L (mm)E = equivalent width (mm)f2b = stress corresponding to M2b (MPa)f2s = stress corresponding to M2s (MPa)f’c = compressive strength of concretefc = factored stressfcp = 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)

fpe = effective stress in the prestressing steel after losses (MPa)fr = modulus of rupture of concretefy = yield strength of reinforcement (MPa)Fe = soil-structure interaction factor for embankment installationsFt = soil-structure interaction factor for trench installationsg = acceleration of gravity (m/s2)H = depth of backfill; notional height of earth pressure diagram; height of soil face

(mm)Hs = depth of embedment of pile socketed into rocki = backfill slope angle (DEG)I = importance categoryIe = effective moment of inertiaIg = gross moment of inertiakap = dimensionless bearing resistance coefficientkh = horizontal acceleration coefficient (DIM)kh = humidity factorks = size factorkv = vertical acceleration coefficient (DIM)K = effective length factor to compensate for rotational and translational boundary

conditions other than pinned ends


Ethiopian Roads Authority Page 12-3

l = unbraced length (mm)L = footing dimensionL = span length (mm)L’ = reduced footing dimensionL1 = modified span length taken equal to the lesser of the actual span or 18 000 (mm)M = moment (Nmm)M2b = Moment on compression member due to factored gravity loads that results in no

appreciable sidesway, calculated by conventional first order elastic frameanalysis, always positive (Nmm).

M2s = Moment on compression member due to factored lateral or gravity loads thatresults in no sidesway, ∆, greater than lu/500, calculated by conventional firstorder elastic frame analysis, always positive (Nmm).

Ma = maximum moment in a component at the stage for which deformation iscomputed (N-mm)

Mc = factored momentMcr = cracking moment (N-mm)Mu = moment from factored loads (Nmm)NL = number of design lanesP = load (N)Pc = the length of the outside perimeter of the concrete section (mm)Pe = Euler buckling load (N)Pu = factored axial load (N)QR = factored uplift resistance (N)Qs = nominal uplift capacity due to shaft resistance (N)qp = nominal end bearing resistance of piles driven into rock (MPa)qu = average uniaxial compression strength of the rock core (MPa)r = minimum radius of gyration (mm)R = reduction factor for longitudinal force effectss = effective span length; spacing of stirrups (mm)S = spacing of transverse reinforcementSd = spacing of discontinuities (mm)t = drying time (Days)t = thickness (mm)td = width of discontinuities (mm)Tcr = torsional cracking moment (Mnn)Tn = nominal torsional resistanceTr = factored torsional resistanceTu = factored torsional moment (Mnn)Vc = shear strength (N)Vc = nominal shear resistance, concreteVn = nominal shear resistance (N)Vp = vertical component of prestressing force (N)VP = component in the direction of the applied shear of the effective prestressing

force, positive if resisting the applied shear (N)Vr = factored shear resistance (N)



Vs = shear resistance, steelVu = factored shear force, in section (N)W = physical edge-to-edge width of bridge (mm)W1 = modified edge-to-edge width of bridge taken equal to the lesser of the actual

width or 18 000 mm for multi-lane loading, or 9000 mm for single lane loading(mm)

WE = total unfactored earth load (N/mm)Weff = effective width of footingyt = distance from the neutral axis to the extreme tension fiber (mm)α = angle of inclination of transverse reinforcement to longitudinal axis, also taken as

the angle between a strut and the longitudinal axis of a member (DEG)αo = bedrock acceleration coefficientβ = slope of wall to the vertical, negative as shown in Figure 12-5 (DEG)β = factor indicating ability of diagonally cracked concrete to transmit tensionβc = ratio of long side to short side of the rectangle through which the concentrated

load or reaction force is transmittedγs = density of backfill (kg/m3)γ = density of soil (kg/m3)δ = angle of friction between soil and abutment (DEG)∈sh = strain due to shrinkageθ = angle of shear resistance; arc tan (kh /(I - kv)) (DEG)θ = angle of inclination of diagonal compressive stresses (DEG)θ = angle of crack, usually 45°θ = skew angle (DEG)ϕ = resistance factors; angle of friction of soil (DEG)ϕu = resistance factor for uplift capacity

12.3 SEISMIC DESIGN METHODS

Seismic methods are outlined in section 3.19: Earthquake Effects. The Ethiopian BuildingCode Standard (EBCS), Vol. 8 “Design of Structures for Earthquake Resistance” (Ref. 2)shall be used as a compliment for seismic design of bridges in the country. The “importancecategory” (I) for bridges should be set to I = 1.4. Other load factors and coefficients are givenin section 3.3: Load Factors and Combinations and in section 3.19: Earthquake Effects.

Seismic zones 1 2 3 4AASHTO (Ref. 1) (αo)

EBCS (Ref. 2) (αo)

≤0.09

≤0.03

≤0.19

≤0.05

≤0.29

≤0.07

≥0.29

≤0.10

Table 12-1 Comparison between Bedrock Acceleration Coefficients

As shown in the Table 12-1, zones 1 to (and including) zone 3 in EBCS correspondapproximately to zone 1 in the AASHTO (Ref.1), meaning that few special precautions have



to be considered for common bridge types. Only for special substructures and large orsensitive bridge types in EBCS zone 4, seismic design should be performed according tosection 3.19: Earthquake Effects or any generally recognized method of seismic design thatmight be accepted by ERA. The bedrock acceleration ratios above should be compared.Regarding the limits of the zones see Figure 3-9.

SETTLEMENT CALCULATION METHODS

The most common method used in Ethiopia is shown in the Ethiopian Building CodeStandard, Vol. 7, “Foundations,” Chapter 6.6.3 Estimation of Settlements in theServiceability Limit State (Ref. 3). It can also be recommended for bridges of small andmedium size. However for certain silty soils or deep cohesive soils, as well as for largebridges, more exact methods are recommended. There are at least three methods where thesoil under the footing is divided into 8 or more strata to a depth, z, under the footing z = 4*Weff ; where Weff is the effective width of the footing, and the compression of each strata iscalculated with its specific properties.

12.4 FOUNDATIONS

12.4.1 EFFECT OF LOAD ECCENTRICITY

For loads eccentric to the centroid of the footing, a reduced effective area, B' x L', within theconfines of the physical footing shall be used in geotechnical design for settlement or bearingresistance, as indicated in Figure 12-1. The design bearing pressure on the effective area shallbe assumed to be uniform. The reduced effective area shall be concentric with the load.

Figure 12-1 Reduced Footings Dimensions

L



The reduced dimensions for an eccentrically loaded rectangular footing shall be taken as:

B′ = B – 2eB (12.1)L' = L - 2eL (12.2)

where: eB = eccentricity parallel to dimension B (mm)eL = eccentricity parallel to dimension L (mm)

Footings under eccentric loads shall be designed to ensure that:• The factored bearing resistance is not less than the effects of factored loads, and• For footings on soils, the eccentricity of the footing, evaluated based on factored loads, is

less than 1/4 of the corresponding footing dimension, B or L.

For structural design of an eccentrically loaded foundation, a triangular or trapezoidal contactpressure distribution based on factored loads shall be used.

For footings that are not rectangular, similar procedures should be used based upon theprinciples specified above.

For purposes of structural design, it is usually assumed that the bearing pressure varieslinearly across the bottom of the footing. This assumption results in the slightly conservativetriangular or trapezoidal contact pressure distribution.

For footings that are not rectangular, the reduced effective area is always concentricallyloaded and can be estimated by approximation and judgment.

12.4.2 SPREAD FOOTINGS

Provisions herein shall apply to the design of isolated footings, combined footings andfoundation mats. The Ethiopian Building Code Standard, Vol.7 “Foundations,” Chapter 6(Ref. 3) deals with shallow foundations.

Class A concrete is generally used for most elements of structures, except when another classis more appropriate, and specifically for concrete exposed to saltwater. Class B concrete isused in footings, massive pier shafts, and gravity walls.

In sloped or stepped footings, the angle of slope or depth and location of steps shall be suchthat design requirements are satisfied at every section. Circular or regular polygon-shapedconcrete columns or piers shall be treated as square members with the same area, for locationof critical sections for moment, shear and development of reinforcement in footings.

Where an isolated footing supports a column, pier or wall, the footing shall be assumed toact as a cantilever. Where a footing supports more than one column, pier or wall, the footingshall be designed for the actual conditions of continuity and restraint.



Flexure

The critical section for flexure shall be taken at the face of the column, pier or wall. In thecase of columns that are not rectangular, the critical section shall be taken at the side of theconcentric rectangle of equivalent area. For footings under masonry walls, the criticalsection shall be taken as halfway between the center and edge of the wall.

Moment at any section of a footing shall be determined by passing a vertical plane throughthe footing and computing the moment of the forces acting on one side of that vertical plane.

In one-way footings and two-way square footings, reinforcement shall be distributeduniformly across the entire width of the footing. The following guidelines apply to thedistribution of reinforcement in two-way rectangular footings:

• in the long direction, reinforcement shall be distributed uniformly across the entire widthof footing,

• in the short direction, a portion of the total reinforcement as specified by Equation 12-3below, shall be distributed uniformly over a band width equal to the length of the shortside of footing and centered on centerline of column or pier. The remainder ofreinforcement required in the short direction shall be distributed uniformly outside of thecenter band width of footing. The area of steel in the band width shall satisfy thefollowing equation:

As-BW = As-SD( 2 ) (12.3)β+1

where: β = the ratio of long side to short side of footingAs-BW = area of steel in the band width (mm2)As-SD = total area of steel in short direction (mm2)

Shear

Critical Sections: In determining the shear resistance of slabs and footings in the vicinity ofconcentrated loads or reaction forces, the more critical of the following conditions shallgovern:• one-way action, eg. longitudinal to the bridge, with a critical section extending in a plane

across the entire width and located at a distance taken at either:• "d", the overall depth of the slab or footing, from the face of the concentrated load or

reaction area, or from any abrupt change in slab thickness where the load introducescompression in the top of the section, or

• at the face of the concentrated load or reaction area where the load introducestension in the top of the section.

• two-way action, eg. longitudinal and transverse to the bridge, with a critical sectionperpendicular to the plane of the slab and located so that its perimeter, bc, is a minimum,but not closer than 0.5d to the perimeter of the concentrated load or reaction area,



• where the slab thickness is not constant, critical sections located at a distance notcloser than 0.5d from the face of any change in the slab thickness and located suchthat the perimeter, bc, is a minimum.

For one-way action, the shear resistance of the footing or slab shall satisfy the generalrequirements for shear.

For two-way action for sections without transverse reinforcement, the nominal shearresistance,Vn in (N), of the concrete shall be taken as:

(12.4)

where: βc = ratio of long side to short side of the rectangle through which the concentratedload or reaction force is transmitted

bo = perimeter of the critical section (mm)dv = effective shear depth (mm)

Where the factored shear force, in section, Vu > ϕVn (see Figure 12-2), shear reinforcementshall be added such that Vn = Vc+ Vs in compliance with Nominal Shear Resistance withangle θ taken as 45o.

If a haunch has a rise-to-spanratio of 1:1 or more where therise is in the direction of theshear force under investigation,it shall be considered an abruptchange in section and thedesign section shall be taken as"d" into the span with “d” takenas the depth past the haunch.

Vu = factored shear force, in section (N)M = moment (Nmm)P = load (N)H = horizontal load (N)W = weight (N/mm)Fr = field reaction (N/mm)

Figure 12-2 Example of Critical Sections for Shear in Footings

vocvocc

n dbfdbf33.0

17.0V ′′��

��

�

β−= ≤



For two-way action for sections with transverse reinforcement, the nominal shear resistance,in N, shall be taken as:

Vn = Vc + Vs ≤ 0.504 f′c *bo dv (12.5)

for which: Vc = 0.166 f′c *bo dv , and (12.6)

Vs = Av fy dv / s (12.7)

For the development of shear reinforcement in slabs and footings, the provisions above shallapply.

If shear perimeters for individual loads overlap or project beyond the edge of the member,the critical perimeter bo should be taken as that portion of the smallest envelope of individualshear perimeter which will actually resist the critical shear for the group under consideration.

12.4.3 PILED FOUNDATIONS

General design

Calculation of piled footings for bridges follow the same rules as buildings. Therefore theEthiopian Building Code Standard, Vol.7 “Foundations”, Chapter 7: Pile Foundations (Ref.3) can be used. The special requirements for bridges in section 6.3 Foundations: Footings onPiles should however be considered.

All loads resisted by the footing, and the weight of the footing itself, shall be assumedtransmitted to the piles. Piles installed by driving shall be designed to resist driving andhandling forces. For transportation and erection, 1.5 times the self-weight of a precast pileshould be considered for the design.

Any portion of a pile, where lateral support adequate to prevent buckling may not exist at alltimes, shall be designed as a column.The points or zones of fixity for resistance to lateral loads and moments shall be determinedby an analysis of the soil properties.

Concrete piles shall be embedded into footings or pile caps, as specified below. Anchoragereinforcement shall consist of either an extension of the pile reinforcement or the use ofdowels. Uplift forces or stresses induced by flexure shall be resisted by the reinforcement.The steel ratio for anchorage reinforcement shall not be less than 0.005 and the number ofbars shall not be less than four. The reinforcement shall be developed sufficiently to resist theforce 1.25 fy As.

For the design of footings, unless the use of special equipment is specified to assure precisiondriving of piles, it shall be assumed that individual driven piles shall be out of plannedposition in a footing by either 150 mm or one quarter of the pile diameter, and that the centerof a group of piles shall be 75 mm from its planned position. For pile bents, the contractdocuments may require a 50 mm tolerance for pile position, in which case that value should



be accounted for in the design.Splices in concrete piles shall develop the axial, flexural, shear and torsional resistance of thepile. Details of splices shall be shown in the contract documents.

If possible piles in tension should be avoided, although this is sometimes not possible in highabutments. Piers should preferably be designed symmetrically so that the center of rotation ofthe entire pile group will be below the bearings.

Required pile penetration should be determined based on the resistance to vertical and lateralloads and the displacement of both the pile and the subsurface materials. In general, unlessrefusal is encountered, the design penetration for any pile should be not less than 3000 mminto hard cohesive or dense granular material and not less than 6000 mm into soft cohesiveor loose granular material.

Where a portion of a pile lies inside the critical section, the pile load shall be considered tobe uniformly distributed across the width or diameter of the pile, and that portion of the loadwhich is outside the critical section shall be included in the calculation of shear on thecritical section.

If a large diameter pile is subjected to significant flexural moments, the load on the criticalsection shall be adjusted by considering the pile reaction on the footing to be idealized as thestress distribution resulting from the axial load and moment.

Piling design (driven piles)

The calculations shall be made in the order presented in Form 12-1.

Skin friction pile group may have total strength limit bearing capacity considerable greaterthan or less than the sum of the bearing capacity of each pile.

Tip bearing pile group usually has the total strength limit bearing capacity equal to the sumof the bearing capacity of each pile. Tip bearing piles are usually assumed to behave likeelastic compressed members loose hinged into the pile footing. The settlement of the groupis usually very small and need not to be calculated for the common types of bridges.

Usually batter piles are used to resist horizontal forces. If the piles penetrate frictionmaterial or certain types of over-consolidated clays the side bearing stability shall be used,but then the horizontal displacement should be calculated as well.

The pile group of abutment and piers should be designed so that the rotation center is abovethe bearings.

If the Soil Investigation Report indicates downdrag (negative skin friction), especially fortip bearing piles this case must be considered. To minimize the downdrag there are differentmethods to be used:• a tip with larger area than the pile itself, combined with• asphalt dipped or painted on the surface of the pile• preboring of a hole before inserting the asphalt painted pile itself.



FORM 12-1: CHECKLIST FOR PILING DESIGN (DRIVEN PILES)

1. List all acting vertical and horizontal forces.

2. Assume a number of piles and their batter.

3. Calculate the resultant roughly by the lever rule method (moment equation through thebottom edge of the pile cap).

4. Check that the tension in the piles is limited otherwise increase the batter of the piles.5. Check the approximate compression force in each pile and optimize the number ofpiles.

6. Calculate the center of the pile group7. Merge all the piles with the same batter and distance from the centerline in stacks.8. Calculate the distance of the resultant exactly9. Check the rotational center point

10. Calculate the moment of inertia at the center of rotation11. Calculate the pile forces in each pile by the lever method (moment equations)12. Table the result, check that every pile is not different from the assumed value.13. If downdrag is given in the Soil Investigation Report, add the downdrag (= negativeskin friction) to the pile load.

14. If skin friction piles, calculate the long-term settlement of the entire pile group.(Usually the initial settlement of cohesion piles is neglected). If tip bearing piles, thesettlement usually corresponds to the compression of the piles.

15. Note: Usually the pile group needs design checking after the piling due tomisplacements, broken piles, wrong batter, etc.

Date: ................................ Designer Date: ..................... Responsible Engineer

........................................................................................................................................................................


-12 Ethiopian Roads Authority

Piles Bearing on Rock:

The resistance factor for the tip resistance of piles bearing on rock shall be taken asspecified in section 6.3 Limit States and Resistance Factors. The same applies for the axialresistance obtained from the pile driving analyzer, where:• pile width exceeds 290 mm, and• rock discontinuity spacing exceeds 300 mm, and• unfilled discontinuity thickness is less than 6.4 mm, or• discontinuities filled with soil or rock debris are less than 25 mm wide

The nominal unit end bearing resistance, qp, of piles driven to rock, in MPa, shall be takenas:

qp = 3quKapd (12.8)

for which:

(12.9)

d = 1 + 0.4Hs/D < 3.4

where: qu = average uniaxial compression strength of the rock core (MPa)Kap = dimensionless bearing resistance coefficient from the formula above.Sd = spacing of discontinuities (mm)td = width of discontinuities (mm)D = pile width (mm)Hs = depth of embedment of pile socketed into rock taken as 0.0 for piles resting on

top of bedrock (mm)

When this method is applicable, the rocks are usually so sound that the structural capacitywill govern the design.

Uplift shall be considered when the force effects, calculated based on the appropriatestrength limit state load combinations, are tensile. When piles are subjected to uplift, theyshould be investigated for both resistance to pullout and structural ability to resist tensionand transmit it to the footing.

The uplift resistance of a single pile shall be estimated in a manner similar to that forestimating the skin friction resistance of piles in compression. Factored uplift resistance QR,in N, shall be taken as:

QR = ϕQn = ϕu Qs (12.10)

Where: Qs = nominal uplift capacity due to shaft resistance (N)ϕu = resistance factor for uplift capacity

The factored load effect acting on any pile in a group shall be estimated using the traditionalelastic strength of materials procedure for a cross-section under thrust and moment. The

))S/t(3001(*10/)D/S3(K dddap ++=



cross-sectional properties should be based on the pile as a unit area. The resistance factorsfor axial tension are lower than those for compression. One reason for this is that piles intension unload the soil; this reduces the overburden effective stress and hence the uplift skinfriction resistance of the pile.

12.5 RETAINING WALLS

12.5.1 GENERAL

The design of retaining walls is usually made by classic soil pressure theory, similar to thatof abutments. In earthquake zone 4 however, it might be necessary to check sliding by theManonobe-Okabe method (Ref. 4) given later in this chapter.

Usually the stability /overturning, lateral sliding and bearing resistance failure should bechecked in the strength limit state. Excessive displacement shall be checked in the servicelimit state.

12.5.2 GRAVITY WALLS (STONE MASONRY)

See also following subchapter on masonry abutments.

Stone masonry retaining walls are designed as gravity walls, usually using Masonry Class B(see Technical Specifications). The methods used are general for all similar structures. TheEthiopian Building Code Standard, Vol. 7 “Foundations”, Chapter 8: Retaining Structuresand in particular subchapter 8.6.3 Foundation Failure of Gravity Walls of that document(Ref. 3), are recommended. The Live Load Surcharge according to section 3.20: EarthPressure should be applied, if the retaining wall is close to the traffic.

Class B concrete is usually used in gravity walls and footings. Usually the stability/overturning, lateral sliding and bearing resistance failure should be checked in the strengthlimit state. Excessive displacement shall be checked in the service limit state.

12.5.3 CANTILEVERED RC WALL DESIGN

The cantilevered retaining wall design usually is a tedious iteration problem. Therefore it ismost suited for computers. There are a few commercial programs available at present but adesigner could also prepare his own EXCEL-sheet. If possible, the Standard Detail DrawingManual-2002(No. RW-1 for RC Cantilever Retaining Walls with 2-6 m height) should beused.

Regarding the initial settings of dimensions, for common types of soil the footing width shallbe set to 0.6-0.8 of the height, and depending on the soil bearing capacity, the toe should be0.2-0.3 of the total footing. If the heel is too short, a "shear wall" is needed under the footingto resist sliding. In other words, if the safety factor of sliding is not obtained, the heeldimension should be increased, and if the safety factor of overturning too low, then the toe



should preferably be increased. For practical reasons the top of the wall shall not be less than0.2 m. The backfill should be granular or of stone, whichever is available at the site.

Generally, Class A concrete is used for RC retaining walls and Class B concrete is used forconcrete gravity walls and footings.

Regarding loads, the temperature and shrinkage deformation effects and the earthquake loadsshould also be applied. For stability computations, the earth loads shall be multiplied by themaximum and/or the minimum load factors given in section 3.3: Load Factors andCombinations. Structural failure, lateral sliding, stability /overturning and bearing resistancefailure shall be checked in the strength limit state. Excessive displacement shall be checkedin the service limit state.

In the general case of a cantilever retaining wall where the downward load on the heel islarger than the upward reaction of the soil under the heel, the critical section for shear in thefooting is taken at the back face of the stem.

A worked example of a concrete retaining wall design is given in the appendix.

12.6 CULVERTS

12.6.1 GENERAL

One of the most common types of culvert is a simple supported reinforced concrete slab ontwo or three masonry walls. In this case the bearings shall be made only of a layer of bitumenfelt on top of concrete shelves cast on the stone masonry. The design should however beaccording to simple statics as a bridge with the loads from section 3.3: Load Factors andCombinations, with the following exceptions:• Expansion joints need not to be considered.• For buried structures with more than 0.6 m fill, earthquake forces in all zones shall be

omitted.

12.6.2 DESIGN OF RC CULVERTS

General

Buried structures shall be designed so that no movement of any part of the structure willoccur as a result of scour. In areas where scour is a concern, the wingwalls shall be extendedfar enough from the structure to protect the structural portion of the soil envelopesurrounding the structure. For structures placed over erodible deposits, a cutoff wall or scourcurtain, extending below the maximum anticipated depth of scour or a paved invert, shall beused. The footings of structures shall be placed not less than 600 mm below the maximumanticipated depth of scour.

Uplift shall be considered where structures are installed below the highest anticipated



groundwater level. To satisfy this provision, the dead load on the crown of the structureshould exceed the buoyancy of the culvert, using load factors as appropriate.

Pipe structures and footings for buried structures shall be investigated for bearing capacityfailure and erosion of soil backfill by hydraulic gradients.

Design criteria, as specified in the ERA Drainage Design Manual-2002, Chapter 7:Culverts, section 7.3: Design Criteria for hydraulic design considerations, shall apply. Seealso ERA Standard Detail Drawings-2002, Chapter 6: Box Culvert and Slab CulvertDrawings for standard single and multiple box culverts.

Design

RC Cast-In-Place and Precast Box Culverts: The provisions herein shall apply to thestructural design of cast-in-place and precast reinforced concrete box culverts and cast-in-place reinforced concrete arches with the arch barrel monolithic with each footing.

These structures become part of a composite system comprised of the box or arch culvertstructure and the soil envelope.

Precast reinforced concrete box culverts shall be manufactured using conventional structuralconcrete and forms, or they shall be machine-made with dry concrete and vibrating form pipemaking methods.

Loads and Live Load Distribution: Loads and load combinations specified in Table 3-1 shallapply. Live load shall be considered as specified in section 3.10: Live Loads. Distribution ofwheel loads and concentrated loads for culverts with less than 600 mm of cover shall betaken as specified for slab-type superstructures. Requirements for bottom distributionreinforcement in top slabs of such culverts shall be placed in the secondary direction in thebottom of slabs as a percentage of the primary reinforcement for positive moment. Forprimary reinforcement parallel to the traffic:

(12.11)

Where s = effective span length (mm).

For primary reinforcement perpendicular to traffic:

(12.12)

Distribution of wheel loads to culverts with 600 mm or more of cover shall be as specified insection 3.8: Gravity Loads/Distribution of Wheel Loads through Earth Fills.

The dynamic load allowance for buried structures shall conform to section 3.9: LiveLoads/Buried Components.

%50s1750 ≤

%67s3840 ≤



Modification of Earth Loads for Soil-Structure Interaction: In lieu of a more refinedanalysis, the total unfactored earth load, WE, in N/mm, acting on the culvert shall be takenas:

• For embankment installations:

WE = g Fe γsBcH*10-9 (12.13)

in which: Fe =1 + 0.20 H (12.14)Bc

• For trench installations:

WE = g FtγsBcH*10-9 (12.15)

in which: (12.16)

where: g = acceleration of gravity (m/s2)Fe = soil-structure interaction factor for embankment installation specified hereinBc = outside width of culvert (mm)H = depth of backfill (mm)Ft = soil-structure interaction factor for trench installations specified hereinγs = density of backfill (kg/m3)Bd = horizontal width of trench (mm)Cd = a coefficient specified in Figure 12-3

Fe shall not exceed 1.15 for installations with compacted fill along the sides of the boxsection, or 1.40 for installations with uncompacted fill along the sides of the box section.

For wide trench installations where the trench width exceeds the horizontal dimension of theculvert across the trench by more than 300 mm, Ft shall not exceed the value specified for anembankment installation.

Precast Box Structures: At all cross-sections subjected to flexural tension, the primaryflexural reinforcement in the direction of the span shall be not less than 0.2% of the grossconcrete area. Such minimum reinforcement shall be provided at the inside faces of wallsand in each direction at the top of slabs of box sections having less than 600 mm of cover.

Where the fabricated length exceeds 5 m, the minimum longitudinal reinforcement forshrinkage and temperature should be in conformance with section 9.1: Concrete.

If the height of the fill is ≤ 600 mm, the minimum cover in the top slab shall be 50 mm forall types of reinforcement.

ec

2dd

t FHB

BCF ≤=



Figure 12-3 Coefficient Cd for Trench Installations

Where welded wire fabric is used, the minimum cover shall be the greater of three times thediameter of the wire or 25 mm.

Shear in Slabs of Box Culverts: The provisions for shear and torsion in general shall applyunless modified herein. For slabs of box culverts under 600 mm or more fill, shear strengthVc shall be computed by:

(12.17)

but: Vc shall not exceed 0.332 f′c b de (12.18)

where: As = area of reinforcing steel (mm2)de = effective depth from extreme compression fiber to the centroid of the tensile

force in the tensile reinforcement (mm)Vu = shear from factored loads (N)Mu = moment from factored loads (Nmm)b = design width usually taken as 1.0 (mm)

eue

euscc bd*

MbddVA32

f178.0V ��

��

� +=



For single cell box culverts only, Vc for slabs monolithic with walls need not be taken lessthan

(12.19)

and Vc for slabs simply supported need not be taken less than

(12.20)The quantity

Vude/Mu ≤ 1.0 (12.21)

where Mu is the factored moment occurring simultaneously with Vu at the sectionconsidered. For slabs of box culverts under less than 600 mm of fill and for sidewalls, theprovisions for shear and torsion in general and in slabs and footings shall apply.

12.6.3 DESIGN OF RC PIPES

Generally the detail design of Reinforced Concrete Pipes should be avoided due to theprevalence of manufactured pipes. Precast Concrete Pipes shall meet the requirements ofthe Technical Specifications.

It should be noted that “Bedding Classes,” also referred to as “Standard Installations,” shallbe as indicated in the ERA Standard Detail Drawings-2002.

12.7 SUBSTRUCTURES FOR RC BRIDGES

12.7.1 GENERAL

Regarding earthquake design within Zone 4, see the following subsection of that title.

Creep Coefficient

The creep coefficient shall be estimated as in section 9.3 Reinforced Concrete/Shrinkage andCreep.

Shrinkage

In the absence of more accurate data, the shrinkage coefficients shall be assumed to be0.0002 after 28 days and 0.0005 after one year of drying. When mix-specific data are notavailable, estimates of shrinkage and creep shall be made using the provisions below.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.

Shrinkage is affected by aggregate characteristics and proportions, average humidity at the

ecbdf25.0 ′

ecbdf207.0 ′



bridge site, water/cement ratio, volume to surface area ratio of member, and duration ofdrying period.

For moist cured concretes, devoid of shrinkage-prone aggregates, the strain due toshrinkage, ∈sh, at time t, shall be taken as:

(12.22)

where: t = drying time (Days)ks = size factor (see Figure 12-4)kh = humidity factor specified in Table 12-2 below

If the moist-cured concrete is exposed to drying before five days of curing have elapsed, theshrinkage as determined in equation above should be increased by 20%.

12.7.2 PIERS (MASONRY, WALLS, FRAMED, COLUMNS)

Design schedules for the most common three types of piers are presented here. Class Aconcrete is generally used for all elements of structures. Class B concrete is used in footings,massive pier shafts, and gravity walls.

Figure 12-4: Factor ks for Volume-to-Surface Ratio

Average AmbientRelative Humidity %

40 50 60 70 80 90 100

kh 1.43 1.29 1.14 1.00 0.86 0.43 0.00

Table 12-2 Factor kh for Relative Humidity

3hssh 10*51.0

t0.35

tkk −

��

�

�

��

�

�

+−=∈



Masonry Piers shall be designed in the order presented in Form 12-2.

RC Wall Pier Design

The procedure of calculation will follow the schedule presented in Form 12-2 with thefollowing alterations:

• The bending and shear reinforcement shall be calculated also at some points (at least atthe bottom and at the midpoint) of the wall.

• The spalling effect under the bearings should be checked if the bearing plate is small (i.e.steel girders).

• If the stream velocity is high, the pier is high and the water is deep, the load combinationwithout vertical load from the superstructure and the full stream force shall be dangerousand should therefore be checked.

RC Frame Pier Design

Framed piers shall be designed according to the schedule in Form 12-3.

12.7.3 ABUTMENTS (STONE MASONRY, RC CLOSED, RC OPENED)

Abutment seats constructed on modular units shall be designed by considering earthpressures and supplemental horizontal pressures from the abutment seat beam and earthpressures on the backwall. The top module shall be proportioned to be stable under thecombined actions of normal and supplementary earth pressures. The minimum width of thetop module shall be 0.9 m. The centerline of bearing shall be located a minimum of 300 mmfrom the outside face of the top precast module. The abutment beam seat shall be supportedby and cast integrally with the top module. The front face thickness of the top module shallbe designed for bending forces developed by supplemental earth pressures. Abutment beam-seat loadings shall be carried to the foundation level and shall be considered in the design offootings.

The minimum dimensions of RC abutments shall be as follows:Footing : t ≥ 0.3 m; on rock trock ≥ 0.25m, usually ≥ 0.6 mAbutment : frontwall/stem and headwall t ≥ 0.25m, usually ≥ 0.5/0.3 m respectively.Wingwall : t ≥ 0.2m, usually ≥ 0.3 m

Differential settlement provisions shall apply.A design schedule of the most common type of abutment, stone masonry, is shown here.



FORM 12-2: CHECKLIST FOR MASONRY PIERS DESIGN

1. Specify the class of masonry (usually B) and strength of other materials to be used (ifany).

2. Assume some preliminary dimensions. e.g. top width of seat & side batterings. Thesides are to be rounded if the design velocity exceeds 1 m/s and the battering of the sidesusually are chosen as 1:20 upstream and equal downstream, or 1:10 if high watervelocity and high pier.

3. Draw a sketch with the above preliminary dimensions.4. Divide the wall into parts so that it will be simple to calculate the dead load of theparts of the pier and their centroidal distance from an arbitrary selected point, usually atthe toe.

5. Calculate the loads transferred from superstructure to the pier; i.e. dead load, live load,wind loads, longitudinal forces and thermal loads.

6. Calculate the loads directly applied on the pier; i.e. wind load if applicable and streamforce.

7. Calculate the maximum and minimum bearing pressure at the base of pier with theabove loads.

8. Check whether the eccentricity for the maximum bearing pressure is within theallowable range for the type of foundation material.

9. Check if the ground pressure at the base of the wall is less than the allowable bearingcapacity of the founding material.

10. If the bearing pressure at the base of the wall exceeds the allowable bearing capacityof the soil either increase the battering and/or provide a reinforced concrete footing.Revise the dead load of the pier. The final maximum bearing pressure from thesubstructure shall be less than or equal to the allowable bearing capacity of the soil.

11. Check the stability of the pier for overturning. The factor of safety againstoverturning shall usually be greater or equal to 2.0 according to the serviceability limitstage. Sometimes the soil stability regarding circular gliding in friction soil should bechecked in cooperation with the Soil Engineer.

12. Check the stability of the pier for sliding. The factor of safety against sliding shallusually be greater or equal to 1.5 according to the serviceability limit stage.

Note if a RC footing is used the sliding surface is between the concrete and the ground.The surface between the stone masonry and the concrete should be checked for ”shearfriction”. Note that checking of the stone compression strength at the bottom of the pieris usually not necessary, since the stone masonry is stronger than the soil bearingcapacity.If RC footing is provided under the masonry the following order could be applied:13. Calculate the bearing pressure on top and bottom surface of footing14. Calculate the moment per meter of footing at halfway between the middle and edgeof wall



15. Check the adequacy of the footing thickness for flexure and shear.16. Calculate the flexural reinforcement at the four sides of the cantilever.17. Draw a sketch of the final dimensions of the pier cross section with the footingreinforcement (if any)


........................................................................................................................................................................



Form 12-3: Checklist for RC Frame Pier Design

1. Specify the quality of reinforcement steel; concrete used and their strengths2. Assume some preliminary dimensions: i.e. top width of seat/cap depth of cap, columndimensions, footing dimensions3. Draw a sketch with the above preliminary dimensions.4. Calculate the dead load of the parts of the pier and their centroidal distance from anarbitrary selected point, usually the toe of the footing.5. Calculate the load transferred from superstructure to the pier; i.e. dead load, live load,wind loads, longitudinal forces and thermal loads, usually from the bearing design.6. Calculate the loads directly applied on the pier; i.e. wind loads, stream forces, collisionloads (if the river is navigable)7. Calculate the maximum and minimum bearing pressure at the base of pier with theabove loads.8. Check whether the eccentricity for the maximum soil bearing pressure is within theallowable range for the actual type of foundation material.9. Check that the pressure at the base of the footing is less than the allowable bearingcapacity of the founding material.10. If the bearing pressure at the base of the wall exceeds the allowable bearing capacityof the soil either increase the front and/or back battering and/or provide reinforcedconcrete footing. Revise the dead load of the pier. The final maximum bearing pressurefrom the substructure shall be less than or equal to the allowable bearing capacity of thesoil.11. Check the stability of the pier for overturning. The factor of safety againstoverturning shall usually be greater or equal to 2.0 according to the serviceability limitstage.12. Check the stability of the pier for sliding. The factor of safety against sliding shallusually be greater or equal to 1.5 according to the serviceability limit stage.13. Draw a sketch with the loads from superstructure and directly applied on the pier.14. Analyze the frame with the different load conditions.15. Design the pier cap for flexure and shear.16. Design the bracing for flexure and shear (if any)17. Design the columns (Hint: Calculate the moment magnification factor for theslenderness effect, prepare the column interaction curve with the assumed dimension andreinforcement, check if the factored axial load with the simultaneously applied magnifiedmoment is within the column interaction curve.)18. Check the minimum steel ratio of the column reinforcement.19. Design the footing in the longitudinal and transversal direction for flexure; widebeam and punching shear (a circular column should be converted to an equivalent squareone).20. Draw a sketch of the final dimensions of the pier cross section with the footingreinforcement.21. Prepare bar schedule table.

Date: ................................ Designer Date: ..................... Responsible Engineer........................................................................................................................................................................



Form 12-4: Checklist for Masonry Abutments Design

1. Specify the class of masonry (usually B) and strength of other materials to be used.2. Assume some preliminary dimensions: i.e. top width of seat usually 0.5 m, frontbattering, back battering, etc.3. Draw a sketch with the above preliminary dimensions.4. Calculate the loads transferred from superstructure to the abutment; i.e. dead load, liveload, wind loads, longitudinal forces (breaking force, shrinkage, creep and thermal loads− all transferred through friction forces from bearings).5. Divide the wall into parts to make it simple to calculate the dead load of the parts ofthe abutments and their centroidal distance from an arbitrarily selected point, usuallytaken to be the toe.6. Calculate the active soil earth pressure from back of wall and the passive earthpressure from front of wall. Usually the passive earth pressure is neglected since the frontsoil adjacent to the wall is susceptible for scour, is loose backfill and hence not effectivein developing the resistance, as well as relatively more shallow in depth.7. Calculate the maximum and minimum bearing pressure at the base of abutment withthe above loads.8. Check whether the eccentricity for the maximum bearing pressure is with in theallowable range for the type of foundation material.9. Check if the pressure at the base of the wall is less than the allowable bearing capacityof the founding material.10. If the bearing pressure at the base of wall exceeds the allowable bearing capacity ofthe soil either increase the front and/or back battering and/or provide reinforced concretefooting. Revise the dead load of the abutment. The final maximum bearing pressure fromthe substructure shall be less than or equal to the allowable bearing capacity of the soil.11. Check the stability of the abutment for overturning. The factor of safety againstoverturning ≥ 2.0, according to the serviceability limit stage.12. Check the stability of the abutment for sliding. The factor of safety against slidingshall usually be ≥1.5 according to the serviceability limit stage.

• Note that checking of the stone compression strength at the bottom is usually notnecessary, since the stone masonry is stronger than the soil.

• The battering of the sides usually follow the outer side of the wingwalls.

If RC footing is provided under the masonry the following applies:

13. Calculate the bearing pressure on top and bottom surface of footing.14. Calculate the moment per linear width of footing at the point B/4 (which is halfwaybetween the middle and edge of wall)15. Check the adequacy of the footing thickness for flexure and shear.16. Calculate the flexural reinforcement at the toe and heel cantilever.17. Draw a sketch of the final dimensions of the abutment cross section with the footingreinforcement (if any)

Date: ................................ Designer Date: ..................... Responsible Engineer........................................................................................................................................................................



FORM 12-5: CHECKLIST FOR RC ABUTMENT DESIGN

1. Specify the class of concrete (usually B) and strength of reinforcement steel to be used.28-Day Strength Classes are: 28 Mpa for Concrete A and 17 Mpa for Concrete B.

2. Assume some preliminary dimensions: i.e. top width of seat (usually 0.6 m), thicknessof wall, thickness of footing, etc.

3. Draw a sketch with the above preliminary dimensions.4. Calculate the loads transferred from superstructure to the abutment; i.e. dead load, liveload, wind loads, longitudinal forces (breaking force, shrinkage, creep and thermal loads− all transferred through friction forces from bearings).

5. Divide the wall into parts to make it simple to calculate the dead load of the parts ofthe abutments and their centroidal distance from an arbitrarily selected point (usually thetoe).

6. Calculate the active soil earth pressure from back of wall and the passive earthpressure from front of wall. Usually the passive earth pressure is neglected since thefront soil adjacent to the wall is susceptible for scour, is loose backfill and hence noteffective in developing the resistance, as well as relatively more shallow in depth.

7. Calculate the maximum and minimum bearing pressure at the base of abutment withthe above loads.

8. If piled calculate the pile group according to text. (Usually all rows are battered).9. Check whether the eccentricity for the maximum bearing pressure is within theallowable range for the type of foundation material.

10. Check if the pressure at the base of the wall is less than the allowable bearingcapacity of the founding material.

11. If the soil bearing pressure at the base of wall exceeds the allowable bearing capacityof the soil increase the footing. Revise the dead load of the abutment. The finalmaximum bearing pressure from the substructure shall be less than or equal to theallowable bearing capacity of the soil.

12. Check the stability of the abutment for overturning. The factor of safety againstoverturning ≥ 2.0, according to the serviceability limit stage.

13. Check the stability of the abutment for sliding. The factor of safety against slidingshall usually be ≥1.5 according to the serviceability limit stage.

14. Check the compression strength at the bottom of wall15. Calculate the moment of frontwall (base)/stem at 2-4 points and headwall at base16. Calculate the moment per linear width of footing and check for shear reinforcement.17. Check the adequacy of the footing thickness for flexure and shear.18. Calculate the flexural reinforcement at the toe and heel cantilever.19. Calculate the settlement of the abutment footing.20. Draw a sketch of the final dimensions of the abutment cross section with the footingreinforcement


........................................................................................................................................................................



Masonry Abutments shall be designed as presented in Form 12-4.

The closed reinforced concrete abutment shall be calculated according to the checklistpresented as Form 12-5. Detailed design is similar to that for retaining walls, as presented inthe appendix.

RC Closed and Open Abutment (with counterforts)

Shall be calculated according to the Checklist in Form 12-5. Refer Chapter 5, Section 5.7figure 5-2.

Earthquake Design of Abutments, Retaining Walls, etc.

There is some possibility of damage to bridge abutments due to earthquakes in Ethiopia.Damage is typically associated with fill settlement or slumping, displacements induced byhigh, seismically caused, lateral earth pressures, or the transfer of high longitudinal ortransverse inertia forces from the bridge structure itself.

Movements of freestanding abutments follow the general pattern of outward motion androtation about the top after contact with and restraint by the superstructures. Fill settlementscan be 10 - 15% of the fill height.

Design features of abutments vary tremendously and depend on the nature of the bridge site,foundation soils, bridge span length, and load magnitudes. Abutment types include free-standing gravity walls, cantilever walls, tied back walls, and monolithic diaphragms.Foundation support may use spread footings, vertical piles, or battered piles, whereasconnection details to the superstructure may incorporate roller supports, elastomericbearings, or fixed bolted connections. Considering the number of potential design variables,together with the complex nature of soil abutment superstructure interaction duringearthquakes, it is clear that the seismic design of abutments necessitates many simplifyingassumptions.

For freestanding abutments, such as gravity or cantilever walls, which are able to yieldlaterally during an earthquake (i.e., superstructure supported by bearings that are able to slidefreely), the well-established Mononobe-Okabe pseudo-static approach, outlined below, iswidely used to compute earth pressures induced by earthquakes. On the basis of thissimplified approach, recommendations are made for the selection of a pseudo-static seismiccoefficient and the corresponding displacement level for a given effective peak groundacceleration.

Mononobe-Okabe Analysis

The method most frequently used for the calculation of the seismic soil forces acting on abridge abutment is a static approach developed in the 1920s by Mononobe (Ref. 4) andOkabe (Ref. 5). The Mononobe-Okabe analysis is an extension of the Coulomb sliding-



wedge theory, taking into account horizontal and vertical inertia forces acting on the soil.The analysis is further described by Seed and Whitman (Ref. 6), and Richards and Elms(Ref. 7). The following assumptions are made:

1. The abutment is free to yield sufficiently to enable full soil strength or active pressureconditions to be mobilized. If the abutment is rigidly fixed and unable to move, the soilforces will be much higher than those predicted by the Mononobe-Okabe analysis.

2. The backfill is cohesionless, with a friction angle of ϕ.3. The backfill is unsaturated, so that liquefaction problems will not arise.

Equilibrium considerations of the soil wedge behind the abutment, then lead to a value, EAE,of the active force exerted on the soil mass by the abutment and vice versa. When theabutment is at the point of failure, EAE is given by the expression:

EAE = 1 g γ H2 (1 – kv)KAE *10-9 (12.23)2

where the seismic active pressure coefficient KAE is:

(12.24)

where: g = acceleration of gravity (m/s2)γ = density of soil (kg/m3)H = height of soil face (mm)ϕ = angle of friction of soil (DEG)θ = arc tan (kh /(I - kv)) (DEG)δ = angle of friction between soil and abutment (DEG)kh = horizontal acceleration coefficient (DIM)kv = vertical acceleration coefficient (DIM)i = backfill slope angle (DEG)β = slope of wall to the vertical, negative as shown in Figure 12-5 (DEG)

12.7.9 WINGWALLS

The most common type is stone masonry, which could be designed principally in the sameway as abutments according to the design schedule given for stone masonry above.

RC Wingwalls are usually attached to the RC Abutment (as in Figure 5-3) or to the endwall(as shown in Figure 5-4). They shall be calculated either by an approximate method in twopoints or by a refined method using i.e. the integral analysis method.Regarding seismic design in zone 4, see Mononobe-Okabe Analysis above

( )( )

( ) ( )( ) ( )

2

2

2

AEicoscos

sinsin1*

coscoscos

cosK

−

��

��

�

β−θ+β+δθ−ϕδ+ϕ+

θ+β+δβθβ−θ−ϕ=



Figure 12-5 Active Wedge Force Diagram

12.8 SUPERSTRUCTURE FOR RC BRIDGES

12.8.1 CONCRETE GENERAL

Unless otherwise stated, the Ethiopian Building Code Standard, Vol. 2 Structural Use ofConcrete, 1995 (Ref. 8), shall be used.

Flexure

Regarding flexural design see section 9.4: Reinforcement: Flexural Reinforcement.

Shear

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

Vr = ϕVn (12.25)

Vn = nominal shear resistance specified in Equation 12.26 and 12.27 (N)ϕ = resistance factor as specified in section 9.3: Concrete

The shear resistance Vn of a concrete member shall be separated into a component, Vc, whichrelies on tensile stresses in the concrete, a component, Vs which relies on tensile stresses inthe transverse reinforcement, and a component, Vp, which is the vertical component of theprestressing force.

The nominal shear resistance, Vn shall be determined as the lesser of:

Vn = Vc + Vs + VP (12.26)



or

Vn = 0.25 f'c bv dv + VP (12.27)

for which:

(12.28)

and

(12.29)

where: bv = effective web width taken as the minimum web width within the depth dv asdetermined above (mm)

dv = effective shear depth as determined above (mm)s = spacing of stirrups (mm)β = factor indicating ability of diagonally cracked concrete to transmit tension,θ = angle of inclination of diagonal compressive stresses (DEG)α = angle of inclination of transverse reinforcement to longitudinal axis, also

takenas the angle between a strut and the longitudinal axis of a member (DEG)

Av = area of shear reinforcement within a distance s (mm2)VP = component in the direction of the applied shear of the effective prestressing

force, positive if resisting the applied shear (N)

An approximate method – the Sectional Design Model – with β and θ is described in section13.7: Shear- Sectional Design Model.

Torsion

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

Tr = ϕ Tn (12.30)

where: Tn = nominal torsional resistance specified in Equation 5.37 (Nmm)ϕ = resistance factor specified in section 9.1: Concrete

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

Tu > 0.25 ϕ Tcr (12.31)

for which: (12.32)

vvcc dbf083.0V ′β=

s

sin)cot(cotdfAV

vvvs

αα+θ=

c

cp2

c

cpccr

f328.0

f1

P

Af328.0T

′+′=



where: Tu = factored torsional moment (Nmm)Tcr = torsional cracking moment (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)fcp = 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 theweb and flange where the centroid lies in the flange (MPa)

ϕ = resistance factor specified in section 9.1: Concrete

Regions Requiring Transverse Reinforcement: Except for slabs, footings and culverts,transverse reinforcement shall be provided where either:

• Vu > 0.5 0 (Vc + Vp) or (12.33)

• Where consideration of torsion is required by Equation 12.31 above.

where: Vu = factored shear force (N)Vc = nominal shear resistance of the concrete (N)VP = component of prestressing force in direction of the shear force (N)ϕ = resistance factor specified in section 9.1: Concrete

Minimum Transverse Reinforcement: Where transverse reinforcement is required, asspecified above, the area of steel shall not be less than:

(12.34)

where: Av = area of a transverse reinforcement within distance s (mm2)bv = effective web width taken as the minimum web width within the depth dv,

modified for the presence of ducts where applicable, as specified in Equation 12.36below (mm)

S = spacing of transverse reinforcement (mm)fy = yield strength of transverse reinforcement (MPa)

A minimum amount of transverse reinforcement is required to restrain the growth ofdiagonal cracking and to increase the ductility of the section. A larger amount of transversereinforcement is required to control cracking as the concrete strength is increased.

Transverse reinforcement, which usually consists of stirrups, is required in all regions wherethere is a significant chance of diagonal cracking. Transverse reinforcement may consist of:• stirrups making an angle not less than 45° with the longitudinal tension reinforcement,• welded wire fabric, with wires located perpendicular to the axis of the member, provided

that the transverse wires are certified to undergo a minimum elongation of 4.0%,measured over a gage length of at least 100 mm including at least one cross wire, or

• anchored prestressed tendons, detailed and constructed to minimize seating and time-dependent losses, which make an angle not less than 45° with the longitudinal tensionreinforcement.

y

vcv

f

Sbf083.0A ′=



Torsional reinforcement shall consist of both transverse and longitudinal reinforcement.Transverse reinforcement shall consist of closed stirrups perpendicular to the longitudinalaxis of the member.

Maximum Spacing of Transverse Reinforcement: The spacing of the transversereinforcement shall not exceed the following:

if Vu < 0.1 f'c bv dv, then: s ≤ 0.8 dv ≤ 600 mm (12.35)

if Vu ≥ 0.1 f'c bv dv then: s ≤ 0.4 dv ≤ 300 mm (12.36)

where: bv = effective web width taken as the minimum web width within the depth dv,modified for the presence of ducts where applicable

dv = effective shear depth taken as the distance, measured perpendicular to theneutral axis, between the resultants of the tensile and compressive forces dueto flexure, but it need not be taken less than the greater of 0.9d, or 0.72h (mm)

s = spacing of transverse reinforcement (mm)

In determining bv at a particular level, the diameters of ungrouted ducts or one-half thediameters of grouted ducts, at that level, shall be subtracted from the web width.

Design and Detailing Requirements: Transverse reinforcement shall be anchored at bothends. For composite flexural members, extension of beam shear reinforcement into the deckslab shall be considered when determining if the development and anchorage provisions aresatisfied.

The design yield strength of non-prestressed transverse reinforcement shall not exceed 400MPa.

Components of inclined flexural compression and/or flexural tension in variable depthmembers shall be considered when calculating shear resistance.

Sections near Supports: Regions of members where the plane sections assumption of flexuraltheory is not valid shall be designed for shear and torsion using for example the strut-and-tiemodel. Where the reaction force, in the direction of the applied shear, introducescompression into the end region of a member, the location of the critical section for shearshall be taken as the larger of 0.5 dv cot θ or dv from the internal face of the support.

The nominal torsional resistance Tn, in Nmm, shall be taken as:

(12.37)

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°.

S

CotfAA2T

yton

θ=



Deformations – 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 andcamber, the elastic behavior shall apply.

In the absence of a more comprehensive analysis, instantaneous deflections shall becomputed using the modulus of elasticity for concrete and taking the moment of inertia aseither the gross moment of inertia, Ig, or an effective moment of inertia, Ie, given by Equation12.38:

(12.38)

for which:

Mcr = fr Ig / yt (12.39)

where: Mcr = cracking moment (N-mm)fr = modulus of rupture of concreteyt = distance from the neutral axis to the extreme tension fiber (mm)Ma = maximum moment in a component at the stage for which deformation is

computed (N-mm)

For prismatic members, effective moment of inertia shall be taken as the value obtained fromEquation 12.38 at mid-span for simple or continuous spans, and at support for cantilevers.For continuous non-prismatic members, the effective moment of inertia shall be taken as theaverage of the values obtained from Equation 12.38 for the critical positive and negativemoment sections.

Unless a more exact determination is made, the long-time deflection shall be taken as theinstantaneous deflection multiplied by the following factor:

• If the instantaneous deflection is based on Ig, the factor: 4• If the instantaneous deflection is based on Ie, the factor: 3.0 - 1.2 (A′s/As) > 1.6

where: A′s = area of compression reinforcement (mm2)As = area of non-prestressed tension reinforcement (mm2)

The contract documents shall require that deflections of segmentally constructed bridgesshall be calculated prior to casting of segments based on the anticipated casting and erectionschedules and that they shall be used as a guide against which actual deflectionmeasurements are checked.

gcr

3cr

g

3

a

cre II

Ma

M1I

M

MI ≤

��

�

��

��

�

�−+��

�

�=



For structures such as segmentally constructed bridges, camber calculations should be basedon the modulus of elasticity and the maturity of the concrete when each increment of load isadded or removed, as specified in section 9.1: Concrete: Shrinkage and Creep.

Axial Deformation: Instantaneous shortening or expansion due to loads shall be determinedusing the modulus of elasticity of the materials at the time of loading.

Instantaneous shortening or expansion due to temperature shall be determined with theCoefficient of Thermal Expansion given in accordance with section 3.21: TemperatureRanges, Setting Temperature, and Seasonal Temperature.

Seismic Lateral Load Distribution:

These provisions shall apply to diaphragms, cross-frames and lateral bracing, which are partof the seismic lateral force resisting system in common slab on-girder bridges in SeismicZone 4. The provisions of section 3.19: Earthquake Effects: Calculation of Design Forces,Seismic Zones 1-3 shall apply to Seismic Zones 1-3.

The designer shall demonstrate that a clear, straightforward load path to the substructureexists and that all components and connections are capable of resisting the imposed loadeffects consistent with the chosen load path. The flow of forces in the assumed load pathmust be accommodated through all affected components and details including, but notlimited to flanges and webs of main beams or girders, cross-frames, connections, slab-to-girder interfaces and all components of the bearing assembly from top flange interfacethrough the confinement of anchor bolts or similar devices in the substructure.

The analysis and design of end diaphragms and cross-frames shall consider horizontalsupports at an appropriate number of bearings. Slenderness and connection requirements ofbracing members that are part of the lateral force resisting system, shall comply withapplicable provisions specified for main member design.

SLABS (RIBBED, PLAIN)

A recommended design checklist/schedule for RC simple span solid slab bridge is given inForm 12-6. A worked example of a slab bridge design is given in the appendix.



Form 12-6: Checklist for Single Span RC Slab Design

1. Specify the quality of construction materials used and their strengths

2. Calculate material properties( maximum steel ratio, modulus of rupture, etc...)

3. Assume preliminary dimensions for the different parts of the superstructure

4. Calculate the preliminary thickness of Slab

5. Draw a sketch of the cross section (of the superstructure) with the above preliminary

dimensions

6. Calculate the dead load moment at some fraction intervals of the span length

7. Calculate the dead load shear force per unit width of slab at support

8. Calculate the lateral live load distribution width

9. Calculate the impact factor

10. Tabulate the standard truck & Military loading live load moments at the above-

specified intervals and take the maximum of the two at every point for strategic bridges.

11. Calculate the pedestrian live load (if any)

12. Calculate the live load shear force per unit width of slab at support

13. Prepare envelop for the maximum factored moment at the specified points

14. Prepare the maximum factored shear force at support

15. Calculate the reinforcement required at mid-span and some other bar cutoff points

16. Check the steel ratio of the reinforcement provided at mid-span

17. Calculate the transversal distribution reinforcement required as some percentage of

the reinforcement required at mid-span.

18. Check the adequacy of the slab thickness for shear at support. If the section is not

sufficient, either increase the slab thickness or provide shear reinforcement.

19. Design the edge beam (or the curb, if any)

20. Prepare sketch of the final dimensions of the superstructure with the reinforcement

21. Calculate all the vertical, longitudinal & transversal loads for substructure design andbearing design


..........................................................................................................................................................................



Cast-in-place longitudinally reinforced slabs shall be either conventionally reinforced orprestressed and shall be used as slab-type bridges and culvert tops. The concrete slab, whichshall be solid, voided (with hollow spares), or ribbed (i.e. Texspan), is supported directly onthe substructures.

The distribution of live load shall be determined by a two-dimensional analysis as per thesubchapter above or by the approximate method as specified in Chapter 13: ApproximateMethods of Analysis below. Slabs and slab bridges designed for moment in conformancewith the above-mentioned subchapter, shall be considered satisfactory for shear, otherwisealso the shear should be checked.

If a refined method (Chapter 3: Load Requirements, Section 3.10: Load Fatigue) is used theaspect ratio of finite elements and grid panels should not exceed 5.0. Abrupt changes in sizeand/or shape of finite elements and grid panels should be avoided.

Nodal loads shall be statically equivalent to the actual loads being applied.

Edge beams shall be provided, unless otherwise specified at lines of discontinuity. The edgeof the deck shall either be strengthened or be supported by a beam or other line component,which shall be either composite with, or integrated in, the deck. The edge beams shall bedesigned as beams whose width shall be taken as the effective width of the deck. If the edgeof a deck is composite with a structurally continuous barrier, no additional edge beam isrequired.

Equivalent strip widths: The equivalent width of longitudinal strips per lane for both shearand moment with one lane, i.e., two lines of wheels, loaded shall be determined as:

(12.40)

(the strip width has been divided by 1.20 to account for the multiple presence effect).

The equivalent width of longitudinal strips per lane for both shear and moment with morethan one lane loaded shall be determined as:

(12.41)

Where: E = equivalent width (mm)L1 = modified span length taken equal to the lesser of the actual span or 18 000

(mm)W1 = modified edge-to-edge width of bridge taken equal to the lesser of the actual

width or 18 000 mm for multi-lane loading, or 9000 mm for single laneloading (mm)

W = physical edge-to-edge width of bridge (mm)NL = number of design lanes as specified in section 3.8: Gravity Loads: Vehicular

Live Load.

11WL42.0250E +=

L11

N

WWL12.02100E ≤+=



For skewed bridges, the longitudinal force effects shall be reduced by the factor r:

r = 1.05 – 0.25 tan θ ≤ 1.00 (12.42)Where: θ = skew angle (DEG)

Transverse distribution reinforcement shall be placed in the bottoms of all slabs, exceptculvert tops or bridge slabs, where the depth of fill over the slab exceeds 600 mm, (seesection 5.6: Culverts: Design.) The amount of the bottom transverse reinforcement shall bedetermined either by two-dimensional analysis, or the amount of distribution reinforcementshall be taken as the percentage of the main reinforcement required for positive momenttaken as:

• for longitudinal reinforced concrete construction:

• for longitudinal prestressed construction:

where: L = span length (mm)fpe = effective stress in the prestressing steel after losses (MPa)

Transverse shrinkage and temperature reinforcement in the tops of slabs shall be providednear surfaces of concrete exposed to daily temperature changes and in structural massconcrete. Temperature and shrinkage reinforcement shall be added, so that the totalreinforcement on exposed surfaces is not less than that specified herein.

Reinforcement for shrinkage and temperature shall be in the form of bars, welded wire fabricor prestressing tendons. For bars or welded wire fabric, the area of reinforcement As in eachdirection shall not be less than:

As ≥ 0.75 Ag/fy (12.43)

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.

The provisions are based on the performance of relatively small-span structures constructedto-date. Any significant deviation from successful past practice for larger units, which shallbecome both structurally and economically feasible under these Specifications should bereviewed carefully.

GIRDERS (SIMPLE SPAN, CONTINUOUS, BOX)

Simple Span RC Deck Girder Design

Simple span RC Deck Girder Bridges are relatively easy to calculate, but will generally give

%50L/1750 ≤

( ) ( ) %50410*L/f1750 pe ≤



a more expensive superstructure than a continuous one. A recommended designchecklist/schedule for RC single span RC Deck girder bridge is given in Form 12-7. Aworked example of a girder bridge design is given in the appendix.

Some recommended dimensions for cast-in-place girders, box and T-beams are:The thickness of top flanges serving as deck slab:• same as for bridge decks• not less than 5% of the clear span between fillets, haunches, or webs, unless transverse

ribs at a spacing equal to the clear span are used.

And for the bottom flange thickness not less than either:• 140 mm,• 1/16 of the distance between fillets or webs of non prestressed girders and beams, or• 1/30th of the clear span between fillets, haunches or webs for prestressed girders, unless

transverse ribs at a spacing equal to the clear span are used.

The thickness of webs shall be determined by requirements for shear, torsion, concrete coverand placement of concrete. For adequate field placement and consolidation of concrete,usually a minimum web thickness of 200 mm is needed for webs without prestressing ducts.For girders over about 2.4 m in depth, the above dimensions should be increased tocompensate for the increased difficulty of concrete placement. Changes in girder webthickness shall be tapered for a minimum distance of 12.0 times the difference in webthickness.

Reinforcement for Cast-in-place Girder, Box and T-beams

The reinforcement in the deck slab of cast-in-place T-beams and box girders shall bedetermined by either the traditional or by empirical design methods. Where the deck slabdoes not extend beyond the exterior web, at least one-third of the bottom layer of thetransverse reinforcement in the deck slab shall be extended into the exterior face of theoutside web and anchored by a standard 90° hook. If the slab extends beyond the exteriorweb, at least one-third of the bottom layer of the transverse reinforcement shall be extendedinto the slab overhang and shall have an anchorage beyond the exterior face of the web notless in resistance than that provided by a standard hook.

Interior Beams with Concrete Decks: The live load flexural moment for interior beams withconcrete decks shall be determined by applying the lane fraction specified in Chapter 13:Approximate Methods of Analysis. For preliminary design, the terms Kg/(L*ts

3) and I/J shallbe taken as 1.0.

For the concrete beams, other than box beams, used in multi-beam decks with shear keys:• Deep, rigid end diaphragms shall be provided to ensure proper load distribution.• If the stem spacing of stemmed beams is less than 1.2 m or more than 3.0 m, a refined

analysis shall be used.



Bridge deck overhangs shall be designed for the following design cases consideredseparately:• Design Case 1: the transverse and longitudinal forces specified in Table 3-1 - extreme

event limit state.• Design Case 2: the vertical forces specified in Table 3-1-extreme event limit state.• Design Case 3: the loads, specified in section 3.8: Gravity Loads, which occupy the

overhang - strength limit state.

Continuous RC Deck Girder Design

In the design of continuous Bridge Girders it is essential that the settlement at one support isnot considerably greater than the others − called uneven settlement.Moment Redistribution: In lieu of more refined analysis, where bonded reinforcement isprovided at the internal supports of continuous reinforced concrete beams and where the c/de

ratio does not exceed 0.28, negative moments determined by elastic theory at strength limitstates shall be increased or decreased by not more than the following percentage:

+/- % ≤ 20 (1 – 2.36*c/de ) (12.44)

With c = The distance from the extreme compression fiber to the neutral axis (mm)de = The effective depth from extreme compression fiber to the neutral axis (mm)

Positive moments shall be adjusted to account for the changes in negative moments tomaintain equilibrium of loads and force effects.

Unless otherwise specified, diaphragms (secondary beams) shall be provided at abutments,piers and hinge joints to resist lateral forces and transmit loads to points of support.Intermediate diaphragms shall be used between beams in curved systems or where necessaryto provide torsional resistance and to support the deck at points of discontinuity or at anglepoints in girders. For curved box girders, having an inside radius less than 240 m, and forspread box beams, intermediate diaphragms shall be used.

In certain types of construction, end diaphragms shall be replaced by an edge beam or astrengthened strip of slab, made to act as a vertical frame with the beam-ends. Such typesare low I-beams and double T-beams. These frames should be designed for wheel loads. Thediaphragms should be essentially solid, except for access openings and utility holes, whererequired. It should however be remembered that the diaphragms at abutments and piersusually are used as jacking support for the exchanging of bearings.



FORM 12-7: CHECKLIST FOR SINGLE SPAN RC DECK GIRDER DESIGN

1. Specify the quality of construction materials used and their strengths

2. Calculate material properties( maximum steel ratio, modulus of rupture, etc...)

3. Assume preliminary dimensions for the different parts of the superstructure

3.1 Assume No of girders, depth, spacings, etc…

3.2 Thickness of Slab (between girders and cantilever overhang part)

3.3 Prepare sketch of the cross section of the superstructure with the above preliminary

dimensions

3.4 Specify the number of diaphragms (in the longitudinal sections)

3.5 Prepare sketch of the longitudinal cross section of the superstructure with the above

preliminary dimensions

4. Design of slab in between girders

4.1 Compute the dead load and live load moment and shear forces (with impact)

4.2 Multiply the above values with the specified coefficients

4.3 Calculate the main slab reinforcement

4.4 Calculate the distribution reinforcement

4.5 Check the slab thickness used above for adequency in shear

5. Design of overhang / cantilever slab

5.1 Compute the dead load moment and shear force

5.2 Compute the live loads moments from railing load and truck wheel load and take themaximum of the two

5.3 Multiply the above values with the specified coefficients

5.4 Design the section for flexure with the above factored moment

5.5 Check the slab thickness used above for adequency in shear

6. Design of Edge beam or Curb (if any)

7. Design of girders

7.1 Exterior Girder load analysis

7.2 Compute the dead loads at some fraction interval of the span length and at themaximum moment location

7.3 Compute the impact factor for the girder



7.4 Compute the truck live loads moment and shear forces at the above specified points

7.5 Ditto, but lane load

7.6 Multiply the maximum of the truck and lane moments and shear values with thespecified coefficients

7.7 Ditto the above five steps, but for Interior girder (if more than two girders)

7.8 Tabulate the summary of girder factored shear force and moment values at differentpoints for design

7.9 Check if the Exterior girder shear and moment are equal to or greater than the Interiorgirder

7.10 Prepare envelop for the maximum moment at every specified points

7.11 Compute the effective flange width of slab for exterior (and interior) girders

7.12 Compute the amount of reinforcement required at midspan

7.13 Compute the deflection at midspan and compare with the allowable. If thepreliminary depth of girder is not sufficient, increase the depth and revise starting fromstep 7.1

7.14 Compute the length of reinforcement at bar cut off points

7.15 Check the Serviceability requirements at midspan and bar cutoff points

7.16 Compute the extension length required at bar cutoff points

7.17 Prepare shear force diagrams for stirrup spacing

7.18 Compute the stirrup spacing at support and some other points

7.19 Check the maximum stirrup spacing

7.20 Compute the skin reinforcement required

8. Compute the reactions (maximum and minimum at supports)

8.1 Compute the reaction forces for bearing design

8.2 Compute the reaction forces for abutment and pier design

..........................................................................................................................................................................




RC Box Girder (and Hollow Pier Column) Design

Box girder bridges are different from ordinary girder bridges in the way the torsion andbuckling of webs have to be considered.

In the absence of more exact analysis, one quarter of the wind force on a box section shall beapplied to the bottom flange of the exterior box beam. The section assumed to resist the windforce shall consist of the bottom flange and a part of the web. The other ¾ of the wind forceon a box section, plus the wind force on vehicles, barriers, and appurtenances, shall beassumed to be transmitted to the supports by diaphragm action of the deck.

Lateral bracing in the box shall be provided if the section assumed to resist the wind force isnot adequate.

The wall slenderness ratio of a hollow rectangular cross-section shall be taken as (same asEquation 7-17):

(12.45)

where: Xu = the clear length of the constant thickness portion of a wall, according to theFigure 7-3 (mm)

t = thickness of wall (mm)λw = wall slenderness ratio for hollow columns

See section 7.5: Girders for other parameters.

Spacing of Reinforcement

The center-to-center lateral spacing of longitudinal reinforcing bars shall be no greater thanthe lesser of 1.5 times the wall thickness or 300 mm. The center-to-center longitudinalspacing of lateral reinforcing bars shall be no greater than the lesser of 1.25 times the wallthickness, or 300 mm.

Cross-ties shall be provided between layers of reinforcement in each wall. The cross-tiesshall include a standard 135° hook at one end, and a standard 90° hook at the other end.Cross-ties shall be located at bar grid intersections, and the hooks of all ties shall encloseboth lateral and longitudinal bars at the intersections. Each longitudinal reinforcing bar andeach lateral reinforcing bar shall be enclosed by the hook of a cross-tie at spacing no greaterthan 600 mm.

Splices

Lateral reinforcing bars shall be joined at the corners of the cross-section by overlapping 90°bends. Straight lap splices of lateral reinforcing bars shall not be permitted unless the

t

Xuw =λ



overlapping bars are enclosed over the length of the splice by the hooks of at least four cross-ties located at intersections of the lateral bars and longitudinal bars.

Hoops

Where details permit, the longitudinal reinforcing bars in the corners of the cross-sectionshall be enclosed by closed hoops. If closed hoops cannot be provided, then pairs of ”U”-shaped bars with legs at least twice as long as the wall thickness, and oriented 90° to oneanother, shall be used.

Bearings for single box sections shall be placed in pairs at supports where practical. Doublebearings shall be placed either inboard or outboard of the box section webs. Placing bearingsoutboard of the box reduces overturning loads on the bearings and may eliminate uplift.

12.9 FRAME BRIDGES

12.9.1 GENERAL

There are two common types of frame bridges − open frame and closed or cyclic frame. Theopen frame is designed as a continuous bridge with some simple frame computer program(see section 5.11: Software for Bridge Design). For multi span frame bridges with differentspan lengths and different heights of support, the calculations will be complicated and use ofa computer program is highly recommended.

It is common to make the deck with 45° chamfers if small span or 1:3 if larger than 8 mspan. If the height of the front-walls exceeds some 5 m it is usually advantageous to batterthe rear side. The moments and shear forces should be computed for every 1/10 of thetheoretical height and the same for the bridge slab.

12.9.2 DESIGN

Advantages:• Horizontal forces are resisted by framed hinges, which provide a more slender structure.• Moments from vertical loads are distributed to corners as well as to span which results in

less maximum moments than a simply supported slab.• Footings will be less than conventional abutment with the same height because some of

the earth pressure on the front-walls is resisted through friction under the footing.• Bearings and expansion joints are not necessary, which make it easier to maintain.Disadvantages:• Larger spans give a thick and heavy structure with large concrete and steel quantities,

which may give more expensive foundations, than a lighter structure.• Voids (0.5 meters 45°-type or 1:3 for larger spans than 12 m) shall be placed at the ends

of the slab, to minimize the quantity of concrete (self weight), which however thenincreases the difficulties of reinforcing and casting.

• The structural system is indefinite, which gives an increased sensitivity to settlements.



There are two different ways of tackling the design. The latest method is to consider thestiffness of the soil by means of springs under the foundation when calculating the staticalsystem. This however makes the calculation difficult such that computer programs usuallyare needed.

Earlier it was common to assume the moment between the foundation and the soil to beequal to zero, since it then may easily be calculated by hand. In the system calculation it ismost economically favorable to assume that the frame is one single monolithic structure –including the footings. This will give less stiffness, the moment between the footing and theframe will be less, and a smaller footing and less reinforcement will be required.

Footings on rock shall be provided with a so-called “reinforced joint” between the footingand the frame. It should however be checked if the soil is sulfuric (corrosion of thereinforcement) or if the contractor is familiar with the construction of this type of joint. Thedesign shall be made in the following order:

At cyclic frames the design begins with an estimate of the dimensions and calculation of thestiffnesses of each member/node. If appropriate the stiffness or spring coefficients of theground should be calculated and inserted in the frame program. The thickness of the fill ontop of the slab is very important for placing of the load (shear) as well as the magnitude ofthe load (moments).

Sharply skewed frame bridges (see Figure 5-8) should be avoided since the earth-pressuremight cause the bridge to “rotate” horizontally due to sliding and the sharp corners mighthave resulting uplift forces. Then the bridge and especially the deck should be designed withsome refined method such as FEM-analysis or finite strip method. The requirements are: a >0.3 b as indicated in Figure 5-8.

FORM 12-8: CHECKLIST FOR FRAME BRIDGE DESIGN

1. Assume preliminary dimensions2. Determine the Moment of Inertia and gross Area for the non-cracked sections.3. Load from lateral support displacement (usually 10 mm) should be considered for anopen frame bridge. In earthquake zone 4, a larger displacement shall be needed.4. Calculate the statical system as an elastic frame analysis.5. Check moment and shear capacity both in the Service- and Strength limit state.6. Check Service limit state: cracking, crack widths, deflection7. Check the Fatigue limit state of some points (corners and mid span)8. Calculate the moment in at least two directions.9. Calculate the reinforcement in at least 5 points of the frame deck.10. Direction of main moment shall be assumed as parallel to the support line usually.For alignment skewed < 45o or wider bridge the direction of moment varies from point topoint.11. Draw the envelope of maximum moments and develop the reinforcement12. Calculate the footings and check for shear.



12.10 PRECAST CONCRETE BRIDGES

12.10.1 GENERAL

Precast concrete bridges are designed in the same way as cast in-situ bridges. But since thetransport and hauling weight is limited to a maximum of some 200 kN (20 tons) for eachpanel, several joints need to be made in this bridge type. For example a 10-m slab for abridge has to be spliced at every 1,6 m width not to exceed 20 tons. As many as five truckshave to transport it to the site, which could be quite costly. Safe dimensions of panels shouldbe considered by the designer for each particular site.

These joints are the weak point of the structure. If possible they should be filled withconcrete, and reinforced to interact with and achieve the same strength as the adjacentstructure. The panels could also be kept in position by post tensioned tendons inserted inducts through the panels. For minor structures (culverts) the joints are often designed to takeshear forces only.

12.10.2 DESIGN

In the design of precast concrete components, all loading, restraint and instability conditionsfrom initial fabrication to completion of the structure, including, but not limited to, formremoval, storage, transportation and erection shall be considered. For transportation anderection, the component should be designed for not less than 1.5 times its self-weight. Fieldsplices shall be used where precast members exceed transportable lengths.

The minimum thickness of any part of precast concrete beams shall be as follows:• top flange: 50 mm (bulb-Tee and double-Tee types)• web, non post-tensioned: 125 mm (only with high quality performance)• web, post-tensioned: 165 mm (only with high quality performance)• bottom flange: 125 mm (bottom flange thickness of box-type sections)

Anchorages for lifting devices should not be cast into the face of a member that will beexposed to view or to corrosive materials in the completed structure.

The Detail Design and preparation of working drawings are usually made by the Contractor.All details of reinforcement, connections, bearing seats, inserts or anchors for diaphragms,concrete cover, openings, and fabrication and erection tolerances shall be shown in thecontract documents.

12.11 ARCH BRIDGES (MASONRY AND CONCRETE)

12.11.1 MASONRY ARCH BRIDGES

The design of a masonry arch bridge shall follow the checklist given in Form 12-9. A workedexample of a masonry arch bridge design is given in the appendix.



The first step of the design is to choose the most optimal shape of the arch and estimate thethickness of the arch barrel from Table 12-3 below. At spans less than 25 m the arch shouldpreferably be a multiple circular curve as in Figure 12-6 below. The quality of stones that canbe obtained at the bridge site must be determined using the compressive strength given inTable 5-2.

Figure 12-6 Recommended Arch ShapeNote: for ϕv see Equation 5.19

Span opening ( length ) m 8 9 10 12 15 20Thickness at crown (top) (d ) mThickness at abutment (d1) m

0.550.80

0.600.90

0.701.00

0.751.10

0.861.20

0.901.35

Table 12-3 Normal Thickness of Arch Barrel (Arch Ring)

Skewed arch bridges are very complicated both to construct and design (with Finite ElementModeling, FEM-analysis) and should therefore be avoided.

The stones can be placed either with or without mortar. If with mortar the joints should be assmall as possible, preferably not exceeding 25 mm. The 0.3 - 0.5-m thick stones in the archbarrel should be placed in some kind of bond. The length of the stones may vary between 0.4- 0.8 m. The falsework should not be removed until the joints are fully hardened. In order tocompensate for the settlement when falsework is removed, a certain ”camber” should beapplied at the top curve of the falsework.

A hinge made of a 20 mm rolled lead plate with 5 % antimony (yield strength of 40 MPa)placed in the center of the crown (highest point) of the arch barrel has proved to reduce themoments to almost zero. The spandrel walls should not be built until the falsework has beenremoved, or it will crack due to the deflection from the shrinkage of the mortar. To avoid allcracks, vertical joints every 5-m should preferably be applied. To reduce the dead load of thefilling on top of the arch but under the roadway, lightweight volcanic stones shall be used aslong as they are strong enough to carry the traffic load. Water outlets near the abutments inthe arch barrel must not be forgotten.



Form 12-9: Checklist for masonry Arch Bridge Design

1. The shape of an arch shall be selected so as to minimize flexure under the effect ofcombined permanent and transient loads.2. Calculate the dead load.3. Place the live load on half of the arch and check the compression in point A, B and C.Usually the crown C is most critical for compression strength (Figure 12-6).4. The abutments A and B should be checked for the position of the compression line,which should be within the core. If not, the shape of the arch should be changed.5. The shear at the abutments at point A should be checked6. Finally the forces on the superstructure should be calculated.

12.11.2 CONCRETE ARCH DESIGN

Non-reinforced concrete masonry bridges are calculated in the same way as stone masonry,and the design schedule given above shall be used.

The in-plane stability of the arch rib(s) shall be investigated using a modulus of elasticityand moment of inertia appropriate for the combination of loads and moment in the rib(s). Inlieu of a rigorous analysis, the effective length for buckling shall be estimated as the productof the arch half-span length and the factor δb =5/2*K as specified in Table 12-4 below:

Rise to SpanRatio

3-hingedArch

2-hingedArch

Fixed Arch

0.1-0.20.2-0.30.3-0.4

1.161.131.16

1.041.101.16

0.700.700.72

Table 12-4 K-Values for Effective Length of Arch Ribs

Where δb = moment magnifier for braced mode deflection

For the analysis of arch ribs, the factored moments or stresses shall be increased to reflecteffects of deformations as follows:

Mc = δb M2b + δs M2s (12.46)

where: M2b = Moment on compression member due to factored gravity loads that results inno appreciable sidesway, calculated by conventional first order elastic frameanalysis, always positive (Nmm).

M2s = Moment on compression member due to factored lateral or gravity loads thatresults in no sidesway, ∆, greater than lu/500, calculated by conventional firstorder elastic frame analysis, always positive (Nmm).

fc = δb f2b + δs f2s (12.47)



where: f2b = stress corresponding to M2b (MPa)f2s = stress corresponding to M2s (MPa)ϕ = resistance factor for axial compression

δb = Cm / (1- (Pu / ϕ Pe)) ≥ 1.0 (12.48)

where: Cm = 1.0Pu = factored axial load (N)Pe = Euler buckling load (N)ϕ = resistance factor for axial compression

δs = 1 / (1- (ΣPu / ϕ ΣPe)) (12.49)

When using the approximate second order correction for moment above, an estimate of theshort-term secant modulus of elasticity shall be calculated, as specified in section 5.6:Superstructure for RC Bridges above, based on a strength of 0.40 f′c.

The lever rule shall be used for the distribution of gravity loads in arches when analyzed asplanar structures. If a space analysis is used, either the lever rule or direct loading throughthe deck or deck system shall be used.

Arch ribs shall be reinforced as compression members. The minimum reinforcing of 1.0% ofthe gross concrete area shall be evenly distributed about the section of the rib. Confinementreinforcement shall be provided as required for columns.

Stability under long-term loads with a reduced modulus of elasticity may govern thestability. In this condition, there would typically be little flexural moment in the rib and theappropriate modulus of elasticity would be the long-term tangent modulus and theappropriate moment of inertia would be the transformed section inertia. Under transient loadconditions, the appropriate modulus of elasticity would be the short-term tangent modulusand the appropriate moment of inertia would be the cracked section inertia, including theeffects of the factored axial load.

Unfilled spandrel walls greater than 7.5 m in height shall be braced by counter-forts ordiaphragms. Spandrel walls shall be provided with expansion joints, and temperaturereinforcing shall be provided corresponding to the joint spacing. The spandrel wall shall bejointed at the springline. The spandrel fill shall be provided with effective drainage. Filtersshall be provided to prevent clogging of drains with fine material.

Drainage of the spandrel fill is important for durability of the concrete in the rib and in thespandrel walls and to control the unit weight of the spandrel fill. Drainage details shouldkeep the drainage water from running down the ribs.



12.12 COMPOSITE STEEL/CONCRETE BRIDGES

Steel and Concrete Composite Bridges should be calculated according to Chapter 3: LoadRequirements (see also Ref. 1). They should be calculated as an ordinary girder bridge withthe following important exceptions.

The data for the assumed transformed section in which the concrete slab is interactingtogether with the steel girders should be calculated. Then the system calculation and theconcrete slab should be designed, first transversally and then longitudinally. If end-wallswith attached wingwalls are used, the punching effect from the end plate of the steel beamsmust be considered for the design of the end-walls. Before the end-wall is designed howeverthe wingwalls should be calculated in order to use the continuous moments in the end-walls.In order to distribute the compression forces in the concrete slab a minimum longitudinalreinforcement of 1% shall be inserted with a certain spacing.

The steel girders are sometimes made as a hybrid structure i.e. of different steel qualitieswith a high tensile steel in the bottom flange that is more strained, and with intermediatesteel in the web and in the top flange. The girders used are to be checked for fatigue, and ifcontinuous, also for construction loads, i.e. order of concreting the bays if the beams are usedas falsework.

Steel structures should be cambered during fabrication to compensate for dead loaddeflection of the whole superstructure and for vertical alignment. Selective changes tocomponent length, as appropriate, shall be used for truss, arch and cable-stayed systems to:

• adjust the dead load deflection to comply with the final geometric position,• reduce or eliminate rib shortening,• adjust the dead load moment diagram in indeterminate structures.

Structural steel, including bracing, cross-frames and all types of gusset plates, except forwebs of rolled shapes, closed ribs in orthotropic decks, fillers and in railings, shall be not lessthan 8 mm in thickness.

The web thickness of rolled beams or channels and of closed ribs in orthotropic decks shallnot be less than 7.0 mm.

Where the metal is expected to be exposed to severe corrosive influences, it shall bespecially protected against corrosion, or sacrificial metal thickness shall be specified.The need for diaphragms or cross-frames shall be investigated for all stages of assumedconstruction procedures and the final condition. This investigation should include, but not belimited to, the following:

• transfer of lateral wind loads from the bottom of the girder to the deck and from the deckto the bearings,

• stability of the bottom flange for all loads when it is in compression,



• stability of the top flange in compression prior to curing of the deck, and• distribution of vertical dead and live loads applied to the structure.

If permanent cross-frames or diaphragms are included in the structural model used todetermine force effects, they shall be designed for all applicable limit states for the calculatedforce effects. As a minimum, diaphragms and cross-frames shall be designed to transfer windloads, and shall meet the following slenderness requirements:

l/r ≤ 140 for Tension members subject to stress reversals;l/r ≤ 240 for Bracing members subject to stress reversals;

K* l/r ≤ 120 for Compression main members;K* l/r ≤ 140 for Compression bracing members;

where: l = unbraced length (mm)r = minimum radius of gyration (mm)K = effective length factor. Physical bracing lengths shall be multiplied by aneffective length factor, K, to compensate for rotational and translational boundaryconditions other than pinned ends. For bolted or welded end connections at bothends: K = 0.750. For pinned connections at both ends: K = 0.875

Connection plates for diaphragms and cross-frames shall be welded or bolted to bothcompression and tensioned flanges of the cross-section.

At the end of the bridge and intermediate points where the continuity of the slab is broken,the edges of the slab shall be supported by diaphragms or other suitable means.

Connections and splices for main members shall be designed at the strength limit state fornot less than the larger of:

• the average of the flexural moment, shear or axial force due to the factored loadings at thepoint of splice or connection and the factored flexural, shear or axial resistance of themember at the same point, or

• 75% of the factored flexural, shear or axial resistance of the member.

End connections for diaphragms, cross-frames, lateral bracing or floorbeams for straightflexural members shall be designed for the factored member loads.

An example of a composite bridge design is presented in the appendix CB.

12.13 TIMBER BRIDGES

12.13.1 GENERAL

Sawn lumber shall comply with the requirements of EBCS-5 (Ref. 10) and the TechnicalSpecifications.



When solid sawn beams and stringers are used as continuous or cantilevered beams, thegrading provisions applicable to the middle third of the length shall be applied to at least themiddle two-thirds of the length of pieces to be used as two-span continuous beams and to theentire length of pieces to be used over three or more spans or as cantilevered beams.

12.13.2 DIMENSIONS

Structural calculations shall be based on the actual net dimensions for the anticipated useconditions. Dimensions stated for dressed lumber shall be the nominal dimensions. Netdimensions for dressed lumber shall be taken as 12 mm less than nominal, except that the netwidth of dimension lumber exceeding 150 mm shall be taken as 20 mm less than nominal.

For rough-sawn, full-sawn, or special sizes, the actual dimensions and moisture content usedin design shall be indicated in the contract documents.

These net dimensions depend on the type of surfacing, whether dressed, rough-sawn, or full-sawn.

The designer should specify surface requirements on the plans. Rough-sawn lumber istypically 3 mm larger than standard dry dressed sizes. It is impractical to use rough-sawn orfull-sawn lumber in a structure that requires close dimensional tolerances.

For more accurate dimensions, surfacing can be specified on one side (S1S), two sides(S2S), one edge (S1E), two edge (S2E), combinations of sides and edges (S1S1E, S2S1E,S1S2E) or all sides (S4S).

12.13.3 MOISTURE CONTENT

The moisture content of lumber 100 mm or less in nominal thickness shall not be greaterthan 19 %.

12.13.4 BASE RESISTANCE AND MODULUS OF ELASTICITY

Base resistance and modulus of elasticity for sawn lumber shall be as specified in Tables 11-1 to 11-3.

Allowable stresses are provided for ten-year load duration and dry use. Factors listed in thisChapter transform allowable stress to the lower 5th percentile of the ultimate stress for two-month load duration and wet use.

12.13.5 REQUIREMENT FOR PRESERVATIVE TREATMENT

All wood used for permanent applications shall be either of the special quality and kindgiven in section 11.3 Requirements for Timber, or pressure impregnated with woodpreservative in accordance with the requirements of the Technical Specifications.



Insofar as is practicable, all wood components should be designed and detailed to be cut,drilled, and otherwise fabricated prior to pressure treatment with wood preservatives. Whencutting, boring, or other fabrication is necessary after preservative treatment, exposed,untreated wood shall be specified to be treated in accordance with the requirements of theTechnical Specifications.

Unless otherwise approved, all structural components that are not subject to direct pedestriancontact shall be treated with oil-borne preservatives. Pedestrian railings and nonstructuralcomponents that are subject to direct pedestrian contact shall be treated with water-bornepreservatives or oil-borne preservatives in light petroleum solvent.

The oil-borne preservative treatments have proven to provide adequate protection againstwood attacking organisms. In addition, the oil provides a water-repellant coating that reducessurface effects caused by cyclic moisture conditions. Water-borne preservative treatments donot provide the water repellency of the oil-borne treatment, and components frequently splitand check, leading to poor field performance and reduced service life.

Direct pedestrian contact is considered to be contact that can be made while the pedestrian issituated anywhere in the access route provided for pedestrian traffic.

Preservative treated wood shall be tested and inspected in accordance with the requirementsof the Technical Specifications. Fire retardant treatments shall not be applied unless it isdemonstrated that they are compatible with the preservative treatment used as recommendedby the product manufacturer and applicator. Use of fire retardant treatments is generally notrecommended.

An example of a timber bridge design is given in the appendix TB.

12.14 OTHER TYPES OF BRIDGES

12.14.1 PRESTRESSED CONCRETE BRIDGES

To calculate prestressed concrete bridges without software is a tedious job, especially forcontinuous bridges. Post tensioned simply supported single span beams may however becalculated by hand. They should be calculated according to Chapter 3: Load Requirements(see also Ref. 1).

Prestressed Superstructure design:



FORM 12-10: CHECKLIST FOR PRESTRESSED SUPERSTRUCTURE DESIGN

1. Interaction between deck and girder shall be assumed2. Calculate the Moment of Inertia with the Modulus of Elasticity3. Calculation of system for the following cases:

Construction stageMounting of beams, if precast beamsCasting of deck in different construction stagesPavement loadsTraffic loads

4. Calculation of the cross-sections with cracked section5. Joints perpendicular to the strands shall be reinforced with at least 0.5% in every part(deck, web, etc.)

For prestressed bridges or parts thereof the following shall apply:• Tensioning Schedule shall be made by the designer for post-tensioned beams, etc.• Construction Schedule if necessary (complicated structures)• Quality Control Schedule shall be made for concreting, welding, piling etc., by the

Designer. It shall consist of a general part and documentation, reporting requirements,

and a technical part for sensitive and essential parts of the bridge construction.

12.14.2 STEEL TRUSS BRIDGES

In half-through-trusses the compressed top chord of a simple span truss shall be designed toresist a lateral force of not less than 4.0 kN/m length, considered as a permanent load for theStrength I Load Combination and factored accordingly (note: Rectangular hollow pipes areespecially well suited as compressed members in this case).

The lever rule shall be used for the distribution of gravity loads in trusses when analyzed asplanar structures. If a space analysis is used, either the lever rule or direct loading throughthe deck or deck system shall be used.

Where loads, other than the self-weight of the members and wind loads thereon, aretransmitted to the truss at the panel points, the truss shall be analyzed as a pin-connectedassembly.

Effective Length Factor, K: Physical column lengths shall be multiplied by an effectivelength factor, K, to compensate for rotational and translational boundary conditions otherthan pinned ends. In the absence of a more refined analysis, where lateral stability isprovided by diagonal bracing or other suitable means, the effective length factor in thebraced plane, K, for the compression members in triangulated trusses, trusses and framesshall be taken as:

• for bolted or welded end connections at both ends: K = 0.750• for pinned connections at both ends: K = 0.875



Minimum Thickness of Steel: Structural steel, including bracing, cross-frames and all types ofgusset plates, except for fillers and in railings, shall be not less than 8 mm in thickness.

An example of a steel truss bridge is given in the appendix GB. This is a pedestrian bridge,and was chosen to give an example of a loading significantly different from that of a standardbridge.

12.14.3 LARGE SPAN BRIDGES (ABOVE 50M SPAN)

Large span bridges (≥ 50 m) should be calculated according to AASHTO LRFD BridgeDesign Specifications, 2nd edition (Ref. 1) or later, together with Chapter 3 LoadRequirements.

12.15 BEARING DESIGN

Regarding recommended bearing types, see section 8.3: Bridge Details: Bearings. Thesuitability of various types of bearings as depicted in Figures 8-1, 8-2 and 12-7 is indicated inTable 12-6.

The most common bearing design in Ethiopia is the "Steel Plate Bearing" with two steelplates on top of each other without a PTFE layer in between. A dowel is used as guide and toresist transversal loads. This bearing is economical and usually made out of local "MediumGrade Steel." Although it is likely that this type of bearing will loose some of its mobilityafter some decades of corrosion, it functions quite well. It is however, recommended to use aPTFE layer. An example of such a design is given in the appendix.

The design Flow Chart should be as follows;

FORM 12-11: CHECKLIST FOR BEARING DESIGN

1. Calculate all relevant vertical and horizontal loads on the bearing2. Select steel quality3. Check the steel plates according to section 8.3: Bridge Details: Bearings4. Check horizontal forces resisted by the friction steel – concrete (i.e. µ=0.5)5. Check the necessary dimension of dowels and anchor bolts to resist the remaininghorizontal force.6. Check the actual concrete pressure7. If PTFE is used, check the actual PTFE pressure



Movement Rotation aboutBridge Axis Indicated

Resistance to LoadsType of Bearing

Long. Trans. Long. Trans. Vert. Long. Trans. Vert.

Plain Elastomeric Pad S S S S L L L L

Fiberglass-Reinforced Pad S S S S L L L L

Steel-ReinforcedElastomeric Bearing (e.g.PFTE)

S S S S L L L S

Plain Sliding Bearing S S U U S R R S

Curved Sliding SphericalBearing

R R S S S R R S

Curved Sliding CylindricalBearing

R R U S U R R S

Disc Bearing R R S S L S R S

Double Cylindrical Bearing R R S S U R R S

Pot Bearing R R S S L S S S

Single Roller Bearing S U U S U U R S

Multiple Roller Bearing S U U U U U U S

Table 12-5 Suitability of Different Bearing TypesNote: S = suitable

U = unsuitableL = Limited suitabilityR = Rarely used

Since the Steel reinforced elastomeric bearing is economical compared to a steel rollerbearing it is recommended as a first choice for medium/larger bridges with moderate loadsand movements. The catalogue from an approved manufacturer usually gives the allowablevertical and transversal loads. It is however important to check if the bearing can resist thedeflection angle for the selected type of bearing. Otherwise, a thicker bearing with morelayers must be selected. If the transversal load exceeds the capacity of this type of bearing asteel roller bearing or another type (i.e. Pot bearing) needs to be selected, although they shallbe more expensive. Bearing types are shown in Figure 12-7 (see also Figures 8-1 and 8-2).

The behavior of bearings is quite variable, and there is very little experimental evidence toprecisely define ϕ for each limit state. ϕ is taken to be equal to 1.0 where a more refinedestimate is not warranted. The resistance factors are often based on judgment and experience,but they are generally thought to be conservative.

GEOMETRIC REQUIREMENTS

The dimensions of the bearing shall be chosen taking into account both the contact stresses



and the movement of the contact point due to rolling. Each individual curved contact surfaceshall have a constant radius. Bearings with more than one curved surface shall be symmetricabout a line joining the centers of their two curved surfaces.

Figure 12-7 Common Bearing Types

Bearings shall be designed to be stable. If the bearing has two separate cylindrical faces, eachof which rolls on a flat plate, stability shall be achieved by making the distance between thetwo contact lines no greater than the sum of the radii of the two cylindrical surfaces.

A cylindrical roller is in neutral equilibrium. The provisions for bearings with two curvedsurfaces achieves at least neutral, if not stable, equilibrium.

A worked example of a roller bearing design is also given in the appendix RB.

12.16 SOFTWARE FOR BRIDGE DESIGN

12.16.1 GENERAL

There are hundreds of different computer programs used by Design Engineers in differentcountries. It has proven most practical to use a simple 2D-frame program, which allows formovable loads and load groups, as long as it is easy to insert the input data. These are usedmore frequently than the more sophisticated FEM programs, which generally are moretedious to use, although they usually give a more exact result. There are also called"modified FEM-programs" adopted to the USA Codes: AASHTO LRFD Specifications,AISC, ACI, AITC, etc. Sometimes these are combined with a CAD-program such as Visio



Draw or Visio PRO, which can import and export .dxf-files.

STRUCTURAL DESIGN PROGRAMS

Strip Step II is a simple general program for 2-dimensional frames, which is inexpensive.Unfortunately it is not useful for movable loads, which means the designer has to place theloads in the most unfavorable position, before calculating the moments and forces in eachnode or for each member.

STRUCT.etc PLUS (USA) is a general "modified Matrix"-program using STAAD3-2Dfor two-dimensional multiple analysis of Concrete, Steel or Timber Structures in the samerun. It has a built-in AISC Steel beam Section Library and CAD facilities able to generatecorresponding STAAD3-2D input tables.

CONSPAN LRFD 1.0 (Leap software, USA) is used for simple and continuous prestressedconcrete bridge superstructures. It is a Windows 95/NT program available in metric unitsand it works with automatic Moving Load Analysis with predefined LRFD-loads as well asuser-defined loads. It optimizes for the least number of Strands and uses all common Strandtypes.

Curved & Straight Steel Bridge Design & Rating (MDX Software, USA) is mainly used forcomposite steel girder and box girder bridges with complex girder systems and/or complexgeometry. It generates an optimal girder design according to AASHTO LRFD, ASD or LFDCode, including shear connectors, transverse stiffeners, bearings, bracings, etc. in metricsystem.

Brigade (Sweden) is a program, with an English Manual, tailor-made for RC FrameBridges, which unfortunately is quite expensive.

Otherwise most structural design calculations, without complicated iterations and loops, canquite easily be written in EXCEL and/or MathCAD. MathCAD is one of manymathematical programs, that makes it relatively easy to handle difficult mathematicalexpressions such as Differential Equations, Fourier series, etc. It is written in clear formulaexpression and may easily be imported by Excel and included in an Excel sheet. Someexamples of other simple but time saving and quality improving programs are:

• “RC beam moment and shear design”, “Properties of Cross section of RC Girder Deck”,“RC T-beam design”, “Design of RC End wall”, “RC Wingwall design”, “Bearingdesign”, “RC Punching design”, “RC Column design”, “RC Footing design”, “RCFootings for Masonry Abutments”, “Cantilever RC Retaining wall”, “Gravity Retainingwall design”, “Properties of Cross section of welded steel beam”, “Welded Steel Beamshear design”, “Prestressed (post tensioned) RC beam design”, etc.

It is very important that such programs are thoroughly checked before use by others than theprogrammer, otherwise it is almost impossible to find errors or “bugs” in the design.



A skilled EXCEL programmer can of course make even more complicated programs, whichshall be different combinations of the above mentioned small sheets, such as:• RC Slab superstructure design program• RC T- girder superstructure design program• RC Box girder superstructure design program• Piers with framed columns on either combined or isolated footings

12.16.2 FINITE ELEMENT MODELING (FEM) PROGRAMS

STAAD III is probably the most widespread (110 000 worldwide users) 3-dimensional FEMprogram for structural design. It is especially suited for certain curved and/or box girder largebridges. It is often sold together with Stardyne and Visual Draw in a packet calledSTAAD/Pro Core (at present 29 000 Br/each; "upgrade version" is available for 3 500 Br).

SAP 2000/NL PUSH is another similar widely used structural design analysis program. It isvery suitable for bridges since it includes movable loads. Its earlier versions Sap 80 and 90have been used by students at Addis Ababa University.

These large and universal programs shall be adapted to the specific design wanted. This willmake them faster and easier to use for the “common designer” who does not need all thefeatures in the general programs.



FORM 12-12: CHECKLIST FOR BASIC STEPS FOR THE DESIGN OF CONCRETE BRIDGES

This outline is intended to be a generic overview of the design process using the simplifiedmethods for illustration. It should not be regarded as fully complete, nor should it be used asa substitute for a working knowledge of the provisions of this section.

BEAM AND GIRDER SUPERSTRUCTURE DESIGNA. Develop General Section

Roadway Width (Highway Specified)Span ArrangementsSelect Bridge Type

B. Develop Typical SectionTop FlangeBottom FlangeWebsStructure DepthReinforcement

Minimum ReinforcementTemperature and Shrinkage Reinforcement

Effective Flange WidthsIdentify Strut and Tie Areas, if any

C. Design Conventionally Reinforced Concrete DeckDeck SlabsMinimum DepthEmpirical DesignTraditional Design

Strip MethodLive Load ApplicationDistribution ReinforcementOverhang Design

D. Select Resistance FactorsStrength Limit State (Conventional)

E. Select Load ModifiersDuctilityRedundancyOperational Importance

F. Select Applicable Load Combinations and Load FactorsG. Calculate Live Load Force Effects

Select Live Loads and Number of LanesMultiple PresenceDynamic Load AllowanceDistribution Factor for Moment

Interior Beams with Concrete DecksExterior Beams



Skewed BridgesDistribution Factor for Shear

Interior BeamsExterior BeamsSkewed Bridges

Reactions to SubstructureH. Calculate Force Effects from Other Loads identifiedI. Investigate Service Limit State

Evaluate P/S LossesStress Limitations for P/S TendonsStress Limitations for P/S Concrete

Before LossesAfter Losses

Investigate DurabilityCrack ControlInvestigate Fatigue, if applicableCalculate Deflection and Camber

J. Investigate Strength Limit StateFlexure

Stress in P/S Steel - Bonded TendonsStress in P/S Steel - Unbonded TendonsFactored Flexural ResistanceLimits for Reinforcement

Shear (Assuming no Torsional Moment)General RequirementsSectional Design Model

Nominal Shear ResistanceDetermination of β and θLongitudinal ReinforcementTransverse ReinforcementHorizontal Shear

K. Check DetailsCover RequirementsDevelopment Length - Reinforcing SteelDevelopment Length - Prestressing SteelSplicesAnchorage Zones

Post TensionedPre Tensioned

DuctsTendon Profile Limitation

Tendon ConfinementCurved TendonsSpacing Limits

Reinforcement Spacing Limits



Transverse ReinforcementBeam Ledges

SLAB BRIDGESGenerally, the design approach for slab bridges is similar to beam and girder bridgeswith some exceptions as noted below.A. Check Minimum Recommended DepthB. Determine Live Load Strip WidthC. Applicability of Live Load for Decks and Deck SystemsD. Design Edge BeamE. ShearF. Distribution ReinforcementG. If Not Solid

Check if Voided Slab or Cellular ConstructionCheck Minimum and Maximum DimensionsDesign DiaphragmsCheck Design Requirements

SUBSTRUCTURE DESIGNA. Establish Minimum Seat WidthB. Compile Force Effects Not Compiled for Superstructure

WaterEffect of ScourEarthquakeTemperatureSuperimposed DeformationVehicular CollisionBraking ForceCentrifugal ForceEarth Pressure

C. Analyze Structure and Compile Load CombinationsLoad CombinationsSpecial Earthquake Load Combinations

D. Compression MembersFactored Axial ResistanceBiaxial FlexureSlenderness EffectsTransverse ReinforcementShear (Usually Earthquake Induced)Reinforcement LimitsBearingDurabilityDetailing and Seismic

E. Foundations (Structural Considerations)ScourFootings



REFERENCES

1. AASHTO LRFD Bridge Design Specifications, SI Units, 2nd Edition, 1998.Washington: American Association of State Highway and Transportation Officials.

2. The Ethiopian Building Code Standard (EBCS), Vol. 8, “Design of Structures forEarthquake Resistance,” 1995.

3. Ethiopian Building Code Standard (ECBS), Vol. 7, “Foundations,” 1995.4. Mononobe, N. “Earthquake-proof Construction of Masonry Dams.” In Proc., World

Engineering Conference, Vol 9, 1929.5. Okabe, S. “General Theory of Earth Pressure.” Journal of the Japanese Society of Civil

Engineers, Vol 12, No. 1, 1926.6. Seed, H. B. and R. V. Whitman. “Design of Earth Retaining Structures for Dynamic

Loads.” In Proc., ASCE Specialty Conference on Lateral Stresses in the Ground andDesign of Earth Retaining Structures, American Society of Civil Engineers, New York,1970.

7. Richards. R. and D. G. Elms. “Seismic Behavior of Gravity Retaining Walls.” Journalof the Geotechnical Engineering Division, ASCE, Vol 105, No. GT4, 1979.

8. Ethiopian Building Code Standard (ECBS), Vol. 2, “Structural Use of Concrete,” 19959. Taylor, A. W., R. B. Rowell, and J. E. Breen. Design Behavior of Thin Walls in

Hollow Concrete Bridge Piers and Pylons. Research Report 1180-1F. Center forTransportation Research, University of Texas at Austin, 1990.

10. Ethiopian Building Code Standard (ECBS), Vol. 5, “Utilization of Timber,” 1995.