Bridge Design Loads

Outline

Loads on Bridges Typical Loads

Mahidol University First Semester, 2009

Praveen Chompreda

Live Load of Vehicle Pedestrian Load Dynamic Load Allowance

Fatigue W d Wind Earthquake …

Design Lane AASHTO HL93 Loads Truck Tandem Uniform Load

LL Combinations LL Placement Influence Line Design Equation Design Charts

O h LLoads Other d

Loads on Bridge

Dead Load Live Load

EGCE 406 Bridge Design

Multiple Presence Distribution to Girders

Load and Resistance Factor D i Design

Loads on Bridge

DD = downdrag (wind) DC = dead d d Load L d off 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 i load l d off vehicles hi l LL = live load of vehicle (static) LS = live load surcharge PL = pedestrian load SE = settlement SH = shrinkage g of concrete 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

T i l LLoads Typical d Dead Loads: DC/DW Live Loads of Vehicles: LL Pedestrian Load: PL Dynamic (Impact) Loads: IM

Dead Load: DC

Dead Load of Wearing Surface: DW

Dead load includes the self weight of: structural components such as girder, slabs, cross beams, etc… nonstructural components such as medians, railings, signs, etc… B d But does not include i l d the h weight i h off wearing i surface f (asphalt) ( h l) We can estimate dead load from the material’s density Material

Density (kg/m3)

Concrete (Normal Weight.)

It is the weight of the wearing surface ( (usually ll asphalt) h lt) and d utilities tiliti ((pipes, i lighting, etc…) Different category is needed due to large variability of the weight compared with those of structural components (DC)

2400

Concrete (Lightweight)

1775-1925

Steel

7850

Aluminum Alloy

2800

Wood

800-960

Stone Masonryy

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

2725

Tributaryy Area for Dead Loads

Dead loads are distributed to girder through Tributary Area wDC or wDW

DC, DW

Section for maximum moment is not the same as the section for maximum shear For simply-supported beams

Maximum M occurs at midspan Maximum V occurs over the support

M=wL2/8

V= L/2 V=wL/2

As 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.

Live Loads of Vehicles: LL


Live load is the force due to vehicles moving on the bridge There are several types yp of vehicles

Car V Van 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 lloads d (load (l d per wheel) h l) axle configuration position of the vehicle on the bridge (transverse and longitudinal) number b off vehicles hi l on the h bridge b id (multiple presence) ggirder spacing p g stiffness of structural members (slab and girders)

Bridge LL vs. Building LL

BRIDGE

BUILDING

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 p to get g the maximum effect Loads occur in one direction within lanes N d to Need t consider id also l the th placement l t off loads in multiple spans (for continuous span bridges) Dynamic effects of live load cannot be ignored

LL is not very heavy, typical 300-500 kg/m g 2 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 Lane

Need to know how many lanes there is on the bridge Design Lane ≠ Actual Traffic Lane 3.0 m

Place them to get maximum effects on span

Various V i Live Loads

Consider dynamic effects

Distribute Load to each girder

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

3.3 m to 4.6 m (3.6 m recommended)

Number of Design Lanes

= Roadway width/ 3.6 36m ≥ No. of Actual Traffic Lane Number of Lane must be an integer g (1,2,3,…) ( , , , ) – there is no fraction of lane (no 2.5 lanes, for example) For roadway width from 6 m to 7.2 m, there should be 2 design lanes, each equal ½ of the roadway width

Design Truck Design Tandem roadway width

Uniform Lane Load


For design purpose, we are interested the kind of vehicle that produce the worstt effect ff t AASHTO has 3 basic types of LL called the HL-93 loading (stands for Highway Loading, Loading year 1993)

Design truck Design tandem Uniform loads

1. Design Truck

HS-20

The 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 d maximum i effect ff Need to multiply this load by dynamic allowance factor (IM)

2. Design Tandem

3. Uniform Lane Loading

110 kN per axle

110 kN per axle

PROFILE

55 kN Loading L Lane

Two axle vehicle with 110 kN on eachh axle 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 3 1 kN/m2) 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

Traffic Directions 18m 1.8 55 kN

TOP VIEW

55 kN 1.2 m


Live Load Combinations

3 ways to add the design truck, design tandem, and uniform load together




Load Combinations Transverse Placement L i di l Pl Longitudinal Placement



Combination C b 1 one HS20 truckk on top off a uniform 1: f lane l load l d per design d lane 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 th 15 m apartt (measure than ( from f front f t axle l off one truck t k to t the th rear axle l off another truck), with uniform lane load. Use 90% of their effects as the design moment/ shear

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

Live Load Placement

Live Load Placement - Transverse

Need to consider two dimensions

Transversely (for designs of slabs and overhangs)

The design truck or tandem shall be positioned transversely such that the center t off any wheel h l lload d iis nott closer l than: th

roadway width

30 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'

Longitudinally (for design of main girder)

Live Load Placement - Longitudinal

Need 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 midspan

Point of Max Moment

L/2

Minimum distance from curb = 60 cm

P

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 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Note N t th thatt if th the sidewalk id lk iis nott separated t d bby a crashworthy h th ttraffic ffi bbarrier, i must consider the case that vehicles can be on the sidewalk


Methods of finding maximum moment and shear in span

Influence Line (IL) – Simple and Continuous spans Design Equation – Simple span only Design Chart – Simple span only

Live Load Placement – Influence Line


Influence line is a graphical method for finding the variation of the “ t t l response”” att a point “structural i t as a concentrated t t d live li load l d moves across the structure

Structural response can be support reaction, moment, shear, or displacement




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


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

1.0 0 75 0.75

110 kN

0.5 0.25 IL (RL)

1.0 0.75

05 0.5 0.25

1.0 0.75

IL (RL)

0.5 0.25 IL (RL)

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

1.0 0.75

05 0.5 0.25 IL (RL)

1.0 0.75

0.5 0.25 IL (RL)



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





Notes

Influence 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 ( hi h will (which ill occur at a different diff point i and d under d a diff different arrangement of loads)

For series of concentrated load (such as the design truck), the placement off lload d ffor maximum i moment, t shear, h or reaction ti may nott be b apparent. 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



Increase/ 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, yyou’ll know that the last pposition was the one that produce the maximum effect.

Train Loading (AREA: American Railroad Engineers Association)


Increase/ Decrease Method For shear

Sloping Line

Jump

ΔV = Ps(x2-x1)

ΔV = P (y2-y1)

For moment Sloping Line

IL for moment has no jumps!

ΔM = Ps(x2-x1)


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

Example




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




Live Load Placement – Design Equation


Another Method: Using Barre’s Theorem for simply supported spans

0.73 m

Resultant 145 kN

The absolute maximum moment in the span occurs under the load closet l to the h resultant l fforce and d placed l d iin such h a way that h the h centerline of the span bisects the distance between that load and the resultant

145 kN

L/2

L/2 HS20

0.73 m

Resultant 145 kN

145 kN

L/2

35 kN

M max = 81.25l +

Point of Max Moment

Live Load Placement – Design Equation Case

Load Configuration

32

32

8

A

Moments (kips-ft) and shears (kips)

⎡ ⎛ M ( x) = Px ⎢4.5⎜1 − ⎣ ⎝

x ⎞ 42 ⎤ ⎟− l ⎠ l ⎥⎦

⎡ ⎛ x ⎞ 42 ⎤ V ( x ) = P ⎢4.5⎜1 − ⎟ − ⎥ l⎠ l ⎦ ⎣ ⎝

x

32

8 B

x 25 25 C

32

⎡ ⎛ x ⎞ 21 7 ⎤ M ( x) = Px ⎢4.5⎜1 − ⎟ − − ⎥ l⎠ l x⎦ ⎣ ⎝ x 21⎤ ⎡ V ( x) = P ⎢4 − 4.5 − ⎥ l l ⎦ ⎣ x 2⎞ ⎛ M ( x) = 50 x⎜1 − − ⎟ l l⎠ ⎝ ⎛ x 2⎞ V ( x) = 50⎜1 − − ⎟ l l⎠ ⎝

Loading and limitations (x and l in feet)

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

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

x 0.64 k/ft D

x

Point of Max Moment

172.1 − 387 kN-m l

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

L/2 HS20

35 kN

(l − x) 2 ⎛l ⎞ V ( x) = 0.64⎜ − x ⎟ ⎝2 ⎠ M ( x) = 0.64 x

Lane loading

M max = 55l +

19.8 − 66 kN-m l

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


If we combine the truck/tandem load with uniform load, we can get the f ll i equations following ti ffor maximum i momentt iin spans


Live Load Placement – Design Chart


Bending 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 Chart Shear in Simple Span for AASHTO HL-93 Loading for a fully loaded lane


Design 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.

Shear in kips IM is included 1 ft = 0.3048 m 1 kips = 4.448 kN

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


Outline


For one lane loading





O h LLoads Other d

Design Chart for Negative Moment due to Live Load Combination 3 at Interior Support of Continuous Beams with Equal Spans

Dead Load Live Load



IM is included

Pedestrian Live Load: PL


Use when has sidewalk wider th 60 cm than 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: IM

Sources of Dynamic Effects Hammering effect H ff when h wheels h l hit h the h discontinuities d on the h road d surface f such as joints, cracks, and potholes Dynamic y response p of the bridge g due to vibrations induced byy traffic

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

Effect due to Static Load


IM

Effect due to Dynamic Load

This IM factor in the code was obtained from field measurements


Add dynamic effect to the following loads:


Design Truck D T k Design Tandem

But NOT to these loads:

Pedestrian Load Design g Lane Load


Table 3.6.2.1-1 ((modified)) Component Deck Joint All limit li i states All other components above ground Fatigue/ Fracture Limit States All Other Limit States Foundation components below ground

* Reduce the above values by 50% for wood bridges

IM 75%

15% 33% 0%





M l i l Presence Multiple P off LL Distribution Factors

Multiple Presence of LL

Multiple Presence of LL

Multiple p Presence Factor “m”

1

1.20

2

1.00

3

0.85

>3

0.65

We’ve considered the effect of load placement in ONE lane But bridges has more than one lane It’s 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

Distribution of LL to Girders

Number of Loaded Lane

A bridge usually have more than one girder so the question arise on how t distribute to di t ib t the th llane lload d tto the th girders id

AASHTO Girder Distribution Factor

DFs are different for different kinds of superstructure system DFs are different for interior and exterior beam

Two main methods Using AASHTO’s table: for typical design, get an approximate (conservative) value

roadway width

No need to consider multiple presence factor Exterior

Distribution Factor DF Lane Moment Girder Moment L Lane Sh Shear

Gi d Shear Girder Sh

Interior

Refined analysis by using finite element method

We 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 d determined i d ffrom other h analysis l i (such as from the lever rule, computer p model, or FEM))

Need to consider multiple p ppresence factor

Exterior

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

AASHTO Girder Distribution Factor

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

DF

Types (Continued)

DF

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

DFM

Distribution factor for moment in Interior Beams

DFM

Distribution factor for moment in Interior Beams (continued)

DFV

Distribution factor for shear in Interior Beams

DFM

Distribution factor for moment in Exterior Beams

DFV

Distribution factor for shear in Exterior Beams

GDF – Finite Element Analysis

GDF – Finite Element Analysis

Bridge Model

( ) (a)

(b) 3

(c) 1

Boundary (Support) Conditions

Load distribution in model

Moment and Shear in Typical Girder

Outline

At any section, if not using AASHTO’s GDF

MLL+IM, Girder = DFM×(Mtruck/tadem,Lane×IM + Muniform,Lane )×m VLL+IM, Girder = DFV×(Vtruck/tadem,Lane×IM + Vuniform,Lane )×m


At any section, if using AASHTO’s GDF

2

MLL+IM, Girder = DFM×(Mtruck/tadem,Lane×IM + Muniform,Lane ) VLL+IM, Girder = DFV×(Vtruck/tadem,Lane×IM + Vuniform,Lane )

Live L d Loads (Truck, Tandem and Lane Loads)

Place them to get maximum static effects

Multiply byy DF

Moment/ Shear from Live Load to be used in the d i off girders design id






O h LLoads Other d

Increase the static load by IM to account for dynamic effects

Dead Load Live Load

Placed such that we have maximum effects


Fatigue g Load

O h LLoads Other d

Repeated loading/unloading of live loads can cause fatigue in bridge components Fatigue load depends on two factors

Magnitude of Load

Use HS-20 design truck with 9m between 145 kN axles for determination off maximum i effects ff off load l d

Fatigue Wind Earthquake Vehicle/ Vessel Collision

Frequency of Occurrence:

U ADTTSL = average d Use daily il ttruckk ttraffic ffi iin a single i l llane

Fatigue Load

Wind Load

ADT Average Daily Traffic (All Vehicles/ 1 Direction) From Survey (and extrapolate to future) Max ~ 20,000 vehicles/day

% of Truck in Traffic ADTT g Daily y Truck Traffic Average (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

% of Truck

Rural Interstate

0.20

Urban Interstate

0.15

Other Rural

0.15

Other Urban

0.10

Table 3.6.1.1.2-1 Number of Lanes Available to Trucks

p

1

1.00

2

0.85

3 or more

0.80

Horizontal 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 Wi d pressure on the Wind 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 l d ttypically load i ll d do nott control t l th 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) Æ wind tunnel tests Need to consider the dynamic effect of flexible l long-span b id under bridge d the h wind Æ dynamic analysis

Wind Load

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

WS (on Substructure)

T Tacoma Narrows N Bridge B id (Tacoma, (T Washington, W hi USA)

Earthquake Load: EQ

The bridge collapsed in 1940 shortly after completion under wind speed lower than the design g wind speed p but at a frequency q y near the natural frequency q y of the bridge The “resonance” effect was not considered at the time

Earthquake Load: EQ

Horizontal load

The magnitude of earthquake is characterized by return period Large return period (e.g. (e g 500 years) Æ strong earthquake Small return period Æ (e.g. 50 years) Æ minor earthquake

For large earthquakes (rarely occur), the bridge structure is allowed to suffer significant structural damage but must not collapse F smallll earthquakes For th k ((more lik likely l tto occur), ) the th bbridge id should h ld still till bbe iin 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

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

Earthquake Load: EQ

Water Loads: WA

Vehicular Collision Force: CT

Bridge structures are very vulnerable to vehicle hi l collisions lli i We must consider the force due to vehicle collision and designed for it

Typically 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


Typically 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 A an equivalent i l static i fforce off 1800 kN acting i hhorizontally i ll at 1.2 12 m above ground


Vessel Collision: CV No protection to the bridge piers

Bridge piers are protected No protection to the bridge structure

Better protection (still not sufficient)

Outline







O h LLoads Other d

Dead Load Live Load


AASHTO LRFD Designs D i Introduction Design Criteria Load Multiplier Load Factor and Load Combinations R i Resistance FFactors

Historical Development of AASHTO Code The first US standard for bridges in was published in 1931 (AASHO) Working stress design (WSD), based on allowable stresses

Now call “Standard Specifications”

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 Thailand’s ’ Department off Highway (DOH) ( O ) still refers f to Standard S Specification but will eventually switch to LRFD Specifications

Changes of LRFD from Standard Specifications

Design Criteria

Introduction of a new philosophy of safety Id tifi ti off ffour lilimit Identification it states t t (strength, (t th service, i fatigue, f ti extreme t event) 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 g method for plain, p reinforced and prestressed p concrete 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 side-by-side by side with the standard

Design Criteria

General design criteria in AASHTO LRFD Code:

Factored Load ≤ Factored Resistance

∑ ηγiQi ≤ ΦRn

LOAD Mean

Nominal N i l Nominal Load Resistance

Load Multiplier

η = ηI ηD ηR

Load Factor Nominal Load Effect

Mean Resistance

Load

Nominal Resistance R Resistance FFactor

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

Factored FAILURE Load

Factored Resistance

RESISTANCE

Load Multiplier

L dM Load Multiplier l i li

η = ηI ηD ηR

ηI = 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 states

For all other limit states

Load Multiplier

ηD = 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 states

1.05 for nonductile components p & connection which mayy fail in a brittle manner 1.00 for conventional designs 0 95 for 0.95 f components with i h enhanced h d ductility d ili e.g. has h additional ddi i l stirrups i for f shear reinforcements


1.00

1.05 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 1.00 for all bridges

Load Multiplier

ηR = 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 failure-critical critical (nonredundant) For strength limit states

1.05 for nonredundant members e.g. g a simple p span p bridges g 1.00 for conventional level of redundancy 0.95 for exceptional level of redundancy e.g. multi-girder continuous beam b id bridge


1 00 1.00

Loads & Probabilities

LLoad d Factor F & L dC Load Combinations bi i

How do we apply all the loads for the structural analysis?

Add all the mean (average) value of loads together?

Add all the extreme value of loads together?

γi

Loads & Probabilities

Load factors are d t determined i d so that, th t for f each factored load, the pprobabilityy of beingg exceeded is about the same for all load components. t

No, because we must consider the chance that the load may be larger or smaller than calculated. calculated 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 i as the h maximum i value l off another h load l d is i very small. ll

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

Limit States There are 4 types of “limit states” Ultimate Ulti t lilimit it states t t – involving i l i th the strength t th and d stability t bilit off th the structure, t t both local and global Strength g I,, II,, III,, IV Extreme Event limit states - relates to the structural survival of a bridge during a major earthquake, flood, or collision Extreme E Event E I,I II 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 Loads

DC = dead load of structural components and nonstructural attachments DW = dead d d load l d off wearing i surface f and d utilities 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 Loads

LL = 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

Load Combinations

Load Factors for DC, DW

CR = creep SH = shrinkage FR = friction TG = temperature gradient di TU = uniform temperature WA = water t load l d and d stream t pressure IC = ice load WL = wind on live load WS = wind load on structure SE = settlement

Consider Maximum case for Gravity load designs

Load Combinations

Load Combinations

Why do we need to have minimum and maximum load factors for permanentt loads? l d ? Isn’t I ’t it safer f to t consider id the th maximum??? i ??? Because in some cases, large permanent load can help reduce the force in the structure. structure

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 ggravityy load is small, this may be in tension. If the pier is concrete, it will crack!!!

Under U d High Hi h Compression

May be in Tension or Light C Compression i

Load Combinations

STRENGTH I: Basic load combination relating to the normal use of bridge. M i Maximum combination bi ti iis used d when h LL produces d th the same effect ff t as DC 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 pprevented 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

EXTREME 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

Load Combinations

Example of combinations:

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

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 0.90DC 0 65DW + 0.5(LL+IM) 0 5(LL IM) + 1.0EQ 1 0EQ (Extreme (E I) 1.25DC + 1.50DW + 0.5(LL+IM) + 1.0 (CT or CV) (Extreme I) 0 90DC + 0.65DW 0.90DC 0 65DW + 0.5(LL+IM) 0 5(LL+IM) + 1.0 1 0 (CT or CV) (Extreme (E t I)

Load Combinations

Notes on Load Combinations

For 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 1.00DC 1 00DW + 0.80(LL+IM) 0 80(LL IM) (S (Service i III III, P Prestressed) d)

Note 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 moment Critical o e t for o shear s ea iss d away from o the t e support. suppo t. Wee can calculate shear at this location for both dead load and live g of the section load IF we know the height

We estimate the height from past experiences of similar projects If we don’t know, we calculate shear at the support. pp This is conservative but may not be economical.

Resistance and Probabilities

R i Resistance FFactors

Φ

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

Resistance Factors

Resistance Factors

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

Concrete Structures Types

Φ

Flexure and Tension in Reinforced Concrete in Prestressed Concrete

00.90 90 1.00

g Concrete Shear in Normal Weight

0.90

Axial Compression

0.75

Bearing on Concrete

0.70

S Steel lS Structures Types

Φ

Flexure

1.00

Shear

1.00

Axial Compression (steel or composite)

0.90

Block shear

0.80

Tension Yielding limit state Fracture limit state

0.95 0 80 0.80

Bridge Design Loads

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