bridge design loads

OutlineLoads on Bridges Typical LoadsDead Load Live LoadLive Load of Vehicle Pedestrian Load Dynamic Load Allowance

Design Lane AASHTO HL93 LoadsTruck Tandem Uniform Load

LL Combinations LL PlacementInfluence Line Design Equation Design Charts

EGCE 406 Bridge Design Loads on Bridge

Other Loads Oh L dFatigue Wind W d Earthquake Mahidol University First Semester, 2009

Multiple Presence Distribution to Girders

Praveen Chompreda

Load and Resistance Factor Design D i

Loads on BridgeDD = downdrag (wind) DC = dead Load of d dL d f structural and nonstructural components DW = dead load of wearing surface EH = earth pressure (horizontal) EL = secondary forces such as from posttensioning ES = earth surcharge load (vertical) EV = earth pressure (vertical) BR = breaking force of vehicle CE = centrifugal force of vehicle (at curves) CR = creep of concrete CT = vehicle collision force (on bridge or at piers) CV = vessel collision force (bridge piers over river) EQ = earthquake FR = friction IC = ice IM = d dynamic load of vehicles i l d f hi l LL = live load of vehicle (static) LS = live load surcharge PL = pedestrian load SE = settlement SH = shrinkage of concrete g TG = load due to temperature differences TU = load due to uniform temperature WA = water load/ stream pressure WL = wind on vehicles on bridge WS = wind load on structure

Typical Loads T i lL dDead Loads: DC/DW Live Loads of Vehicles: LL Pedestrian Load: PL Dynamic (Impact) Loads: IM

Dead Load: DCDead load includes the self weight of: structural components such as girder, slabs, cross beams, etc nonstructural components such as medians, railings, signs, etc But does not i l d the weight of wearing surface (asphalt) B d include h i h f i f ( h l) We can estimate dead load from the materials densityMaterial Concrete (Normal Weight.) Concrete (Lightweight) Steel Aluminum Alloy Wood y Stone Masonry Density (kg/m3) 2400 1775-1925 7850 2800 800-960 2725

Dead Load of Wearing Surface: DWIt is the weight of the wearing surface (usually asphalt) and utilities ( i ( ll h lt) d tiliti (pipes, lighting, etc) Different category is needed due to large variability of the weight compared with those of structural components (DC)Asphalt surface may be thicker than designed and may get laid on top of old layer over and over

Density of asphalt paving material = 2250 kg/m3 Average Thickness of asphalt on bridge = 9 cm

Tributary Area for Dead Loads yDead loads are distributed to girder through Tributary AreawDC or wDW

DC, DWSection for maximum moment is not the same as the section for maximum shear For simply-supported beamsMaximum M occurs at midspan Maximum V occurs over the supportAs we shall see in the designs of girders, the Critical Section for shear is about d from the support.(where d is the effective depth of section, approximately 0.8h) At this point, shear is slightly lower than at the support. If we use shear at the support for the design of stirrups, we are conservative.

M=wL2/8

V=wL/2 V= L/2

Live Loads of Vehicles: LL

Live Loads of Vehicles: LLLive load is the force due to vehicles moving on the bridge There are several types of yp vehiclesCar Van V Buses Trucks Semi-Trailer Special vehicles Military vehicles

The effect of live load on the bridge structures depends on many parameters including:span length weight of vehicle axle l d (load per wheel) l loads (l d h l) axle configuration position of the vehicle on the bridge (transverse and longitudinal) number of vehicles on the bridge b f hi l h b id (multiple presence) g girder spacing p g stiffness of structural members (slab and girders)

Live Loads of Vehicles: LL

Bridge LL vs. Building LLBRIDGE LL is very heavy (several tons per wheel) ) LL can be series of point loads (wheel loads of trucks) or uniform loads (loads of smaller vehicles) Need to consider the placement within a span to get the maximum effect p g Loads occur in one direction within lanes Need t N d to consider also the placement of id l th l t f loads in multiple spans (for continuous span bridges) Dynamic effects of live load cannot be ignored BUILDING LL is not very heavy, typical 300-500 kg/m2 g LL is assumed to be uniformly distributed within a span Do not generally consider placement of load within a span Loads are transferred in to 2 directions Need to consider various placements of loads for the entire floor Do not generally consider dynamic/impact effect of live loads

Analysis Strategy for LL

Design LaneNeed to know how many lanes there is on the bridge Design Lane Actual Traffic Lane3.0 m 3.3 m to 4.6 m (3.6 m recommended)

Number of Design LanesVarious V i Live Loads Design Truck Design Tandem Uniform Lane Load Place them to get maximum effects on span Moment/ Shear from Live Load to be used in the design of girders

Consider dynamic effects

Distribute Load to each girder

= Roadway width/ 3 6 m 3.6 No. of Actual Traffic Lane Number of Lane must be an integer (1,2,3,) there is no fraction of lane g ( , , , ) (no 2.5 lanes, for example) For roadway width from 6 m to 7.2 m, there should be 2 design lanes, each equal of the roadway width

roadway width

Live Loads of Vehicles: LLFor design purpose, we are interested the kind of vehicle that produce the worst effect t ff t AASHTO has 3 basic types of LL called the HL-93 loading (stands for Highway Loading year 1993) Loading,Design truck Design tandem Uniform loads

1. Design TruckHS-20The design truck is called HS-20 (stands for Highway Semi-Trailer with 20-kips weight on first two axles) Weight shown are for each one axle = 2 wheels Total Wt = 325 kN ~ 33 t t. Distance between second and third axles may be varied to produce maximum effect d i ff Need to multiply this load by dynamic allowance factor (IM)

2. Design Tandem110 kN per axle 110 kN per axle PROFILE

3. Uniform Lane LoadingTwo axle vehicle with 110 kN on each axle h l Need to multiply this load by dynamic allowance factor (IM) Lead to larger moment than the HS20 truck for simple-support p pp spans less than about 13.4 m Uniform load of 9.3 kN/m acting over a tributary width of 3 m. (i.e. the load is 3 1 kN/m2) 3.1 May be apply continuously or discontinuously over the length of the bridge to produce maximum effect No dynamic allowance factor (IM) for this load

55 kN Loading Lane L

55 kN

Traffic Directions 1.8 18m 55 kN 1.2 m 55 kN TOP VIEW


Live Load Combinations3 ways to add the design truck, design tandem, and uniform load togetherCombination 1 one HS20 truck on top of a uniform lane load per design lane C b 1: k f f l l d d l Combination 2: one Design Tandem on top of a uniform lane load per design lane Combination 3: (for negative moments at interior supports of continuous beams) place two HS20 design truck, one on each adjacent span but not less than th 15 m apart (measure from front axle of one truck to the rear axle of t( f f t l f t k t th l f another truck), with uniform lane load. Use 90% of their effects as the design moment/ shear

Various V i Live Loads

Place them to get maximum effects on span



Moment/ Shear from Live Load to be used in the design of girders

Load Combinations Transverse Placement Longitudinal Placement L i di l Pl

The loads in each case must be positioned such that they produce maximum effects (max M or max V) The Th maximum effect of these 3 cases is used for the design ff f h df h d

Live Load PlacementNeed to consider two dimensionsTransversely (for designs of slabs and overhangs)roadway width

Live Load Placement - TransverseThe design truck or tandem shall be positioned transversely such that the center of any wheel l d i not closer than: t f h l load is t l th30 cm from the face of the curb or railing for the design of the deck overhang 60 cm from the edge of the design lane for the design of all other components

min. 2'

Minimum distance from curb = 60 cm

Longitudinally (for design of main girder)

Note that the id N t th t if th sidewalk i not separated b a crashworthy t ffi b i lk is t t d by h th traffic barrier, must consider the case that vehicles can be on the sidewalk

Live Load Placement - LongitudinalNeed to place the LL along the span such that it produces the maximum effect ff t For simple 1-point loading, the maximum moment occurs when the load is placed at the midspanP

Live Load Placement - LongitudinalMethods of finding maximum moment and shear in spanInfluence Line (IL) Simple and Continuous spans Design Equation Simple span only Design Chart Simple span only

Point of Max Moment

L/2

L/2

However, truck load is a group of concentrated loads. It is not clear where to place the group of loads to get the maximum moment REMEMBER: MAXIMUM MOMENT DOES NOT ALWAYS OCCURS AT MIDSPAN !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Live Load Placement Influence LineInfluence line is a graphical method for finding the variation of the structural t t l response at a point as a concentrated live load moves across t i t t t d li l d the structureStructural response can be support reaction, moment, shear, or displacement

Live Load Placement Influence Line



Live Load Placement Influence LineInfluence line is a powerful visualization tool for the effects of live load placements to th structural response l t t the t t l110 kN 110 kN

Live Load Placement Influence Line1.0 0.75 0 75 0.5 0.25 IL (RL)

For Point Load, the response is equal to the value of point load multiplied by the ordinate (y value) of (y-value) the influence line

1.0 0.751.0 0.75 0.5 0.25 IL (RL)

0.5 05 0.25 IL (RL)

For Uniform Load, the response is equal to the value of the uniform load multiplied by the area under the influence line within th i fl li ithi the uniform load

1.0 0.75 0.5 05 0.25 IL (RL)

1.0 0.75 0.5 0.25 IL (RL)


Live Load Placement Influence LineMller-Breslau Principle: If a function at a point on a beam, such as reaction, or shear, or moment, is allowed t act without restraint, the ti h t i ll d to t ith t t i t th deflected shape of the beam, to some scale, represent the influence line of the function.



Live Load Placement Influence LineNotesInfluence line tells you how to place the LL such that the maximum moment at a point occurs; i.e. you pick a point then you try to find what is the maximum moment at that point when loads are moved around It does not tell you where the absolute maximum moment in the span occurs; i.e. the maximum moment on the point you picked is not always the absolute maximum moment that can occur in the span (which ill ( hi h will occur at a different point and under a diff diff i d d different arrangement of loads)

Live Load Placement Influence LineFor series of concentrated load (such as the design truck), the placement of l d f maximum moment, shear, or reaction may not be apparent. f load for i t h ti tb t The maximum always occur under one of the concentrated loads but which one? Two methods Trial and Errors: Move the series of concentrated loads along the span by letting each load on the peak of IL Use when you have only 2-3 concentrated loads Can be tedious when you have a lot of concentrated loads


Live Load Placement Influence LineIncrease/ Decrease Method This method determine whether the response (moment, shear, or reaction) increases or decreases as the series of concentrated loads move into the span As the series of loads move into the span, the response increases. When it starts to decrease, youll know that the last position was y p the one that produce the maximum effect.

Train Loading (AREA: American Railroad Engineers Association)

Live Load Placement Influence LineIncrease/ Decrease Method For shear Sloping Line V = Ps(x2-x1) For moment Sloping Line M = Ps(x2-x1) IL for moment has no jumps! Jump V = P (y2-y1)

Live Load Placement Influence LineExample

Note: not all loads may be in the span at the same time. Loads that have just moved in or moved out may travel on the slope at a distance less than distance moved between 2 concentrated loads loads.


Live Load Placement Influence LineFor Statically Indeterminate Structures, the Mller-Breslau Principle also holds h ld If a function at a point on a beam, such as reaction, or shear, or moment, is allowed to act without restraint the deflected shape of the beam to restraint, beam, some scale, represent the influence line of the function For indeterminate structures, the influence line is not straight lines! g



Live Load Placement Design EquationAnother Method: Using Barres Theorem for simply supported spansThe absolute maximum moment in the span occurs under the load closet to the resultant f l h l force and placed i such a way that the d l d in h h h centerline of the span bisects the distance between that load and the resultant

Live Load Placement Design EquationResultant 145 kN 145 kN 0.73 m

35 kN

L/2 HS20 Resultant 145 kN 145 kN 0.73 m

L/2 Point of Max Moment

35 kN

M max = 81.25l +

172.1 387 kN-m l

M max = 55l +

19.8 66 kN-m l

L/2 HS20

L/2 Point of Max Moment

Mmax occurs at a section under middle axle located a distance 0.73 m from midspan

Mmax occurs at a section under one of the axle located a distance 0.30 m from midspan

Live Load Placement Design EquationCase Load Configuration Moments (kips-ft) and shears (kips) Loading and limitations (x and l in feet)

Live Load Placement Design EquationIf we combine the truck/tandem load with uniform load, we can get the following f ll i equations f maximum moment i spans ti for i t in

32A

32

8

M ( x) = Px 4.51

x 42 l l

x

x 42 V ( x ) = P 4.51 l l

Truck loading g P = 16 kips MA MB for: l > 28 x l/3 x + 28 l VA > VB for any x

8B

32

32

x25 25C

x 21 7 M ( x) = Px 4.51 l l x x 21 V ( x) = P 4 4.5 l l x 2 M ( x) = 50 x1 l l x 2 V ( x) = 501 l l

Truck loading P = 16 kips MB MA for: l > 28 x > l/3 14 x l/2

Tandem loading is more severe than truck loading for l 37 ft

x0.64 k/ftD

x

(l x) 2 l V ( x) = 0.64 x 2 M ( x) = 0.64 x

Lane loading


Live Load Placement Design ChartBending Moment in Simple Span for AASHTO HL-93 Loading for a fully loaded lane Moment in kips-ft IM is included 1 ft = 0.3048 m 1 kips = 4.448 kN 1 kips-ft = 1.356 kN-m

Live Load Placement Design ChartShear in Simple Span for AASHTO HL-93 Loading for a fully loaded lane Shear in kips IM is included 1 ft = 0.3048 m 1 kips = 4.448 kN

Live Load Placement Design ChartDesign chart is meant to be used for preliminary designs. We assume that maximum moment occurs at midspan this produces slightly lower maximum moment than the Design Equation method method. However, the error is usually small. Maximum shear occurs at support. However, the chart does not have x = 0 ft. The closest is 1 ft from support.In general, the bridge girder much higher than 1 ft. Therefore, shear at 1 ft is still higher than the shear at critical section for shear (at d) so we are still conservative here here.

Live Load Placement Design Chart




Other Loads Oh L dFatigue Wind W d Earthquake


Design Chart for Negative Moment due to Live Load Combination 3 at Interior Support of Continuous Beams with Equal Spans For one lane loading IM is included


Pedestrian Live Load: PLUse when has sidewalk wider than th 60 cm Considered simultaneously with truck LL Pedestrian only: 3.6 kN/m2 Pedestrian and/or Bicycle: 4.1 kN/m2 No IM factor (Neglect dynamic effect of pedestrians)




Consider dynamic effects Dynamic y Allowance Factor (IM)



Dynamic Load Allowance: IMSources of Dynamic EffectsHammering effect when wheels hit the discontinuities on the road surface H ff h h l h h d h d f such as joints, cracks, and potholes Dynamic response of the bridge due to vibrations induced by traffic y p g y

Dynamic Load Allowance: IM

Actual calculation of dynamic effects is very difficult and involves a lot of unknowns To make life simpler, we account for the dynamic effect of moving vehicles by multiplying the static effect with a factor Dynamic Load Allowance Factor IM

Effect due to Static Load

Effect due to Dynamic Load

This IM factor in the code was obtained from field measurements

Dynamic Load Allowance: IMAdd dynamic effect to the following loads:Design Truck D T k Design Tandem


But NOT to these loads:Pedestrian Load Design Lane Load g Table 3.6.2.1-1 (modified) ( )Component Deck Joint All li i states limit All other components above ground Fatigue/ Fracture Limit States All Other Limit States Foundation components below ground IM 75%






Multiple P M l i l Presence of LL f Distribution Factors

15% 33% 0%

* Reduce the above values by 50% for wood bridges

Multiple Presence of LL

Multiple Presence of LLWe take care of this by using Multiple Presence Factor 1.0 for two lanes and less for 3 or more lanes This is already included (indirectly) into the GDF Tables in AASHTO code so we do not need to multiply this again Use this only when GDF is determined f d i d from other analysis h l i (such as from the lever rule, computer model, or FEM) p )

Number of Loaded Lane 1 2 3Weve considered the effect of load placement in ONE lane But bridges has more than one lane Its almost impossible to have maximum load effect on ALL lanes at the same time The more lanes you have, the lesser chance that all will be loaded to maximum at the same time

Multiple p Presence Factor m 1.20 1.00 0.85 0.65

>3

Distribution of LL to GirdersA bridge usually have more than one girder so the question arise on how to di t ib t th lane l d t the girders t distribute the l load to th i d Two main methods Using AASHTOs table: for typical design, get an approximate (conservative) valueNo need to consider multiple presence factor

AASHTO Girder Distribution FactorDFs are different for different kinds of superstructure system DFs are different for interior and exterior beamroadway width

Exterior

Distribution Factor DF Lane Moment Girder MomentLane Sh L Shear Girder Sh Gi d Shear

Interior

Exterior

Refined analysis by using finite element methodNeed to consider multiple p p presence factor

DFs are available for one design lane and two or more design lanes (the larger one controls) Must make sure that the bridge is within the range of applicability of the g g pp y equation

AASHTO Girder Distribution FactorFactors affecting the distribution factor includes: Span Length (L) Girder Spacing (S) Modulus f l i i M d l of elasticity of b f beam and d k d deck Moment of inertia and Torsional inertia of the section Slab Thi k Sl b Thickness (ts) Width (b), Depth (d), and Area of beam (A) Number of design lanes (NL) Number of girders (Nb) Width of bridge (W)

DFFor AASHTO method first we must identify the type of superstructure (support beam & deck ( b d k types)

DFTypes (Continued)

DFMDistribution factor for moment in Interior Beams

DFMDistribution factor for moment in Interior Beams (continued)

DFMDistribution factor for moment in Exterior Beams

DFVDistribution factor for shear in Interior Beams

DFVDistribution factor for shear in Exterior Beams

GDF Finite Element AnalysisBridge Model

GDF Finite Element Analysis

( ) (a)

(b)3

(c) Boundary (Support) Conditions1 2

Load distribution in model

Moment and Shear in Typical GirderAt any section, if not using AASHTOs GDFMLL+IM, Girder = DFM(Mtruck/tadem,LaneIM + Muniform,Lane )m VLL+IM, Girder = DFV(Vtruck/tadem,LaneIM + Vuniform,Lane )m



At any section, if using AASHTOs GDFMLL+IM, Girder = DFM(Mtruck/tadem,LaneIM + Muniform,Lane ) VLL+IM, Girder = DFV(Vtruck/tadem,LaneIM + Vuniform,Lane )Placed such that we have maximum effects Live Loads L d (Truck, Tandem and Lane Loads) Place them to get maximum static effects Increase the static load by IM to account for dynamic effects Moment/ Shear from Live Load to be used in the design f i d d i of girders




Multiply y by DF


Fatigue Load gRepeated loading/unloading of live loads can cause fatigue in bridge components Fatigue load depends on two factorsMagnitude of LoadUse HS-20 design truck with 9m between 145 kN axles for determination of maximum effects of load f i ff fl d

Other Loads Oh L dFatigue Wind Earthquake Vehicle/ Vessel Collision

Frequency of Occurrence:Use U ADTTSL = average d il t k t ffi i a single l daily truck traffic in i l lane

Fatigue LoadADT Average Daily Traffic (All Vehicles/ 1 Direction) From Survey (and extrapolate to future) Max ~ 20,000 vehicles/day % of Truck in Traffic ADTT g y Average Daily Truck Traffic (Truck Only/ 1 Direction) Fraction of Truck Traffic in a Single Lane (p) ADTTSL Average Daily Truck Traffic (Truck Only/ 1 Lane) Table C3.6.1.4.2-1 Class of Hwy y Rural Interstate Urban Interstate Other Rural Other Urban Table 3.6.1.1.2-1 Number of Lanes Available to Trucks 1 2 3 or more p 1.00 0.85 0.80 % of Truck 0.20 0.15 0.15 0.10

Wind LoadHorizontal loads There are two types of wind loads on the structure WS = wind load on structure Wind pressure on the structure itself WL = wind on vehicles on bridge Wind Wi d pressure on the h vehicles on the bridge, which the load is transferred to the bridge superstructure Wind loads are applied as static horizontal load For small and low bridges, wind load typically do t l d t i ll d not control th t l the design For longer span bridge over river/sea, wind load on the structure is very important Need to consider the aerodynamic effect of the wind on the structure (turbulence) wind tunnel tests Need to consider the dynamic effect of flexible long-span b id under the l bridge d h wind dynamic analysis

Wind Loads (WS, WL)WL WS (on Superstructure)

Wind Load

WS (on Substructure)

Tacoma Narrows Bridge (Tacoma, Washington, USA) T N B id (T W hiThe bridge collapsed in 1940 shortly after completion under wind speed lower than the design wind speed but at a frequency near the natural frequency of g p q y q y the bridge The resonance effect was not considered at the time

Earthquake Load: EQHorizontal load The magnitude of earthquake is characterized by return period Large return period (e g 500 years) (e.g. strong earthquake Small return period (e.g. 50 years) minor earthquake For large earthquakes (rarely occur), the bridge structure is allowed to suffer significant structural damage but must not collapse For F small earthquakes ( ll th k (more lik l t occur), the b id should still b i likely to ) th bridge h ld till be in the elastic range (no structural damage) Earthquake must be considered for structures in certain zones Analysis for earthquake forces is taught in Master level courses

Earthquake Load: EQThe January 17, 1995 Kobe earthquake h d its epicenter right th k had it i t i ht between the two towers of the Akashi-Kaikyo Bridge y g The earthquake has the magnitude of 7.2 on Richter scale The uncompleted bridge did not have any structural damages The i i l l Th original planned l d length was h 1990 meters for the main span, but the seismic event moved the towers apart by almost a meter!

Earthquake Load: EQ

Water Loads: WATypically considered in the design of substructures (foundation, piers, abutment) b t t) Water loads may be categorized into: Static Pressure (acting perpendicular to all surfaces) Buoyancy (vertical uplifting force) Stream pressure (acting in the direction of the stream) Loads depend on the shape and size of the substructure

Vehicular Collision Force: CTBridge structures are very vulnerable to vehicle collisions hi l lli i We must consider the force due to vehicle collision and designed for it

Vehicular Collision Force: CTTypically considered in the design of substructures (foundation, piers, abutment) b t t) The nature of the force is dynamic (impact), but for simplicity, AASHTO allows us to consider it as equivalent static load load. Need to consider if the structures (typically pier or abutment) are not protected by either: Embankment Crash-resistant barriers 1.37m height located within 3 m Any barriers of 1.07 m height located more than 3 m For piers and abutment located within 9 m from edge of roadway or 15 m from the centerline of railway track Assume an equivalent static f A i l i force of 1800 kN acting h i f i horizontally at 1 2 ll 1.2 m above ground

Vehicular Collision Force: CT

Vessel Collision: CVNo protection to the bridge piers

Bridge piers are protected No protection to the bridge structure Better protection (still not sufficient)



AASHTO LRFD D i DesignsIntroduction Design Criteria Load Multiplier Load Factor and Load Combinations Resistance F R i Factors





Historical Development of AASHTO CodeThe first US standard for bridges in was published in 1931 (AASHO) Working stress design (WSD), based on allowable stressesNow call Standard Specifications

Changes of LRFD from Standard SpecificationsIntroduction of a new philosophy of safety Identification f four li it states (strength, service, fatigue, extreme event) Id tifi ti of f limit t t ( t th i f ti t t) Development of new load models (including new live load) Development of new load and resistance factors Revised techniques for the analysis and load distribution New shear design method for plain, reinforced and prestressed concrete g p p Introduction of limit state-based provisions for foundation design Revised load provisions Hydraulics and scour Earthquake Ship collision Introduction of isotropic deck design process Commentary are now side-by-side with the standard side by side

Work on the new code bagan in 1988 93 1988-93 1st edition of AASHTO LRFD Specifications was published in 1994, the 2nd in 1998, 3rd in 2004 as an alternative document to the Standard , Specification By 2007, only AASHTO LRFD method is allowed for the design of bridges in the USA Now in 4th Edition Thailands Department of Highway (DOH) still refers to Standard f ( O ) f S Specification but will eventually switch to LRFD Specifications

Design CriteriaGeneral design criteria in AASHTO LRFD Code:

Design Criteria

Factored Load Factored Resistance

iQi RnLoad Multiplier

LOAD MeanLoad

Mean Resistance Nominal N i l Nominal Load Resistance

RESISTANCE

= I D R

Load Factor Nominal Load Effect

Nominal Resistance Resistance F R Factor

Load and resistance factors serve as partial safety factors They are determined using the code calibration procedure

Factored FAILURE Load

Factored Resistance

Load MultiplierI = Importance factor The owner may declare a bridge or any structural component and connection to be of operational importance. For strength and extreme event limit states1.05 for bridge considered of operational importance e.g. the only bridge crossing the river 1.00 for typical bridges 0.95 for bridge considered nonimportant

Load Multiplier L d M l i li

= I D R

For all other limit states1.00 for all bridges

Load MultiplierD = Ductility factor (Brittle v.s. Ductile failure) The structural system shall be proportioned and detailed to ensure the development of significant and visible inelastic deformations at the strength and extreme event limit states before failure failure. For strength limit states1.05 for nonductile components & connection which may fail in a brittle p y manner 1.00 for conventional designs 0.95 for 0 95 f components with enhanced ductility e.g. has additional stirrups for ih h d d ili h ddi i l i f shear reinforcements

Load MultiplierR = Redundant factor Multiple load path and continuous structures should be used. Main elements whose failure is expected to cause the collapse of the bridge shall be designated as failure-critical (nonredundant) failure critical For strength limit states1.05 for nonredundant members e.g. a simple span bridges g p p g 1.00 for conventional level of redundancy 0.95 for exceptional level of redundancy e.g. multi-girder continuous beam bridge b id

For all other limit states1.00

For all other limit states1.00 1 00

Loads & Probabilities

Load F L d Factor & Load Combinations L d C bi i

How do we apply all the loads for the structural analysis?Add all the mean (average) value of loads together?No, because we must consider the chance that the load may be larger or smaller than calculated calculated.

Add all the extreme value of loads together?No, because then the bridge must have to resist an enormous load and that would make it really expensive! The chance that the maximum value of one load occurring at the same time as the maximum value of another load is very small. i h i l f h l di ll

i

We need to consider several cases where each case we have one load at its maximum value expected while other loads are around their mean values

Loads & ProbabilitiesLoad factors are determined so that, for d t i d th t f each factored load, the p probability of being y g exceeded is about the same for all load components. t

Limit StatesThere are 4 types of limit states Ultimate limit t t Ulti t li it states i l i th strength and stability of th structure, involving the t th d t bilit f the t t both local and global Strength I, II, III, IV g , , , Extreme Event limit states - relates to the structural survival of a bridge during a major earthquake, flood, or collision Extreme Event I, II E E I Serviceability limit states involving the usability of the structure including stress, deformation, and crack widths Service I, II, III Fatigue limit state - relates to restrictions on stress range to prevent crack growth as a result of repetitive loads during the design life of the bridge Fatigue All limit states are equally important (AASHTO LRFD 1 3 2 1) 1.3.2.1)

Permanent LoadsDC = dead load of structural components and nonstructural attachments DW = dead load of wearing surface and utilities d dl d f i f d tiliti EL = accumulated locked-in force effects resulting from the construction process p DD = downdrag EH = horizontal earth pressure load ES = earth surcharge load EV = vertical pressure from dead load of earth fill

Transient LoadsLL = vehicular live load IM = vehicular dynamic load allowance PL = pedestrian live load LS = live load surcharge BR = vehicular braking force CE = vehicular centrifugal force CT = vehicular collision force CV = vessel collision force EQ = earthquake CR = creep SH = shrinkage FR = friction TG = temperature gradient di TU = uniform temperature WA = water load and stream t l d d t pressure IC = ice load WL = wind on live load WS = wind load on structure SE = settlement

Load Combinations

Load Factors for DC, DW

Consider Maximum case for Gravity load designs

Load CombinationsWhy do we need to have minimum and maximum load factors for permanent loads? Isnt it safer to consider the maximum??? t l d ? I t f t id th i ??? Because in some cases, large permanent load can help reduce the force in the structure structure.

Load CombinationsSTRENGTH I: Basic load combination relating to the normal use of bridge. Maximum combination i used when LL produces th same effect as DC M i bi ti is d h d the ff t DC. Minimum combination is used when LL produces opposite effect to DC. STRENGTH II: load combination for special vehicles specified by owner STRENGTH III: load combination where the bridge is subjected to high wind (> 90 km/h) and traffic is p ( ) prevented STRENGTH IV: load combination for long span bridges (>67 m span) which has large ratio of DC to LL STRENGTH V: load combination where bridge and traffic on the bridge is subjected to wind velocity of 90 km/h

Gravity Load If the gravity load of the superstructure is large, it offsets the wind load and we will get small compression here If the gravity load g y is small, this may be in tension. If the pier is concrete, it will crack!!! May be in Tension or Light Compression C i

Under Hi h U d High Compression

Load CombinationsEXTREME EVENT I: load combination for structural survival under major earthquake EXTREME EVENT II: load combination for structural survival under combination of events such as flood and vessel collision SERVICE I: load combination for normal operation of the bridge and for checking compression in prestressed concrete SERVICE II: load combination for steel bridges to control yielding SERVICE III: load combination relating to tension in prestressed concrete during service FATIGUE: load combination for fatigue and fracture due to repetitive LL and IM

Load CombinationsExample of combinations:1.25DC + 1.50DW + 1.75(LL+IM) (Strength I) 1.25DC + 1.50DW + 1.4WS (Strength III) 0.90DC + 0.65DW + 1.4WS (Strength III) 1.50DC + 1.50DW (Strength IV) 1.25DC + 1.50DW + 1.35(LL+IM) + 0.4(WS+WL) (Strength V) 1.25DC + 1.50DW + 0.5(LL+IM) + 1.0EQ (Extreme I) 0.90DC 0.65DW 0.5(LL+IM) 1.0EQ (Extreme I) 0 90DC + 0 65DW + 0 5(LL IM) + 1 0EQ (E 1.25DC + 1.50DW + 0.5(LL+IM) + 1.0 (CT or CV) (Extreme I) 0.90DC 0.65DW 0.5(LL+IM) 1.0 0 90DC + 0 65DW + 0 5(LL+IM) + 1 0 (CT or CV) (Extreme I) (E t

Load CombinationsFor slabs and girders designs, we normally have only DC, DW, and (LL+IM)1.25DC + 1.50DW + 1.75(LL+IM) (Strength I) 1.50DC + 1.50DW (Strength IV) 1.00DC + 1.00DW + 1.00(LL+IM) (Service I) 1.00DC + 1.00DW + 1.30(LL+IM) (Service II, Steel) 1.00DC 1.00DW 0.80(LL+IM) (Service III, Prestressed) 1 00DC + 1 00DW + 0 80(LL IM) (S i III P d)

Notes on Load CombinationsNote that the sections for maximum moment of dead load and live load are not the same!!!Dead Load: midspan Live Load: some small distance away from midspan

If we add them together, we are conservative! C t ca o e t o s ea s Critical moment for shear is d away from the support. We o t e suppo t. e can calculate shear at this location for both dead load and live g load IF we know the height of the sectionWe estimate the height from past experiences of similar projects If we dont know, we calculate shear at the support. This is pp conservative but may not be economical.

Resistance and ProbabilitiesResistance factor is determined so that the d t i d th t th reliability index, , is close to the target g value, T (about 3.5)

Resistance F R i Factors

Resistance FactorsResistance factors are different for different types of action (moment or shear, f example) and f different t h for l ) d for diff t types of materials (steel or f t i l (t l concrete). They are specified under each section of materials.

Resistance FactorsSteel S S l Structures Types Flexure Shear Axial Compression (steel or composite) Block shear 0.90 0 90 1.00 0.90 0.75 0.70 Tension Yielding limit state Fracture limit state 1.00 1.00 0.90 0.80 0.95 0.80 0 80

Concrete Structures Types Flexure and Tension in Reinforced Concrete in Prestressed Concrete g Shear in Normal Weight Concrete Axial Compression Bearing on Concrete

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