Strength Limit State · 2020. 3. 11. · Strength Limit State Sect. 3.4.1 Strength I - basic condition w/ live load (no wind) Strength II - special, or permit, loads Strength III

Strength Limit State Sect. 3.4.1

Strength I - basic condition w/ live load (no wind)

Strength II - special, or permit, loads

Strength III - high wind w/o live load

Strength IV - high dead/live load ratio (primarily long span bridges)

Strength V - wind w/ live load.

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Assit. Pr. Dr. Yousif A. MansoorAdvance bridge concrete . Lecture 2

• The limit state refers to providing a sufficient strength orresistance to satisfy the inequality :

ΦRn ≥ η Σ γi Qi

• This limit state include the evaluation of resistance to bending, shear, torsion, and axial load.

• The statically determined resistance factor Φ will be less than 1.0 and will have values for different materials and strength limit

states.

STRENGTH LIMIT STATE

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Assit. Pr. Dr. Yousif A. Mansoor

3

Section 3: Loads and Load Factors

LOADS AND LOAD FACTORS

4



5



LOAD COMBINATION TABLE (AASHTO TABLE 3.4.1-1)

Load

Combination

Limit State

DC

DD

DW

EH

EV

ES

LCE

BR

PL

LS

WA WS WL FR

TU

CR

SH

TG SE

Use one of these at a time

EQ IC CT CV

STRENGTH – I γp 1.75 1.00 - - 1.00 0.50/1.20 γTG γSE - - - -

STRENGTH - II γp 1.35 1.00 - - 1.00 0.50/1.20 γTG γSE - - - -

STRENGTH - III γp - 1.00 1.40 - 1.00 0.50/1.20 γTG γSE - - - -

STRENGTH – IV

EH, EV, ES, DW, DC

ONLY

γp

1.5

- 1.00 - - 1.00 0.50/1.20 - - - - - -

STRENGTH – V γp 1.35 1.00 0.40 0.40 1.00 0.50/1.20 γTG γSE - - - -

EXTREME EVENT –

Iγp γEQ 1.00 - - 1.00 - - - 1.00 - - -

EXTREME EVENT –

IIγp 0.50 1.00 - - 1.00 - - - - 1.00 1.00 1.00

SERVICE - I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γTG γSE - - - -

SERVICE – II 1.00 1.30 1.00 - - 1.00 1.00/1.20 - - - - - -

SERVICE - III 1.00 0.80 1.00 - - 1.00 1.00/1.20 γTG γSE - - - -

FATIGUE – LL, IM,

AND CE ONLY- 0.75 - - - - - - - - - - -

Back

Type of LoadUse One of These at a Time

Maximum Minimum

DC: Component and Attachments 1.25 0.90

DD: Downdrag 1.80 0.45

DW: Wearing Surfaces and Utilities 1.50 0.65

EH: Horizontal Earth Pressure

Active

At-Rest

1.50

1.35

0.90

0.90

EV: Vertical Earth Pressure

Overall Stability

Retaining Structure

Rigid Buried Structure

Rigid Frames

Flexible Buried Structures other than

Metal Box Culverts

Flexible Metal Box Culverts

1.35

1.35

1.30

1.35

1.95

1.50

N/A

1.00

0.90

0.90

0.90

0.90

ES: Earth Surcharge 1.50 0.75

LOAD FACTORS FOR PERMANENT LOADS,

(AASHTO table 3.4.1-2)

Service Limit States

Intended to ensure the bridge performs acceptably during it’s design

life.

This relates to stress, deformation, and cracking under service loads.

University of Anbar

Dr. Yousif A. Mansoor

This limit state refers to restrictions on stresses, deflections and crack widths of bridge components that occur under regular service conditions.[A1.3.2.2]

• For the limit state the resistance factors Φ = 1.0 and nearly all the load factors γi are equal to 1.0.

• There are three service limit conditions given in the table to

cover different design situations.

SERVICE LIMIT STATE

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Assit. Pr.Dr. Yousif A. Mansoor

Service Limit States

Sect. 3.4.1

Service I - normal operational loads w/ wind, also control of cracking of RC members

Service II - overload for steel structures, control yielding of steel structures and slip of connections

Service III - tension (crack control) in prestressed concrete super structures

Service IV – tension (crack control) in prestressed concrete substructures

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Asssit. Pr.Dr. Yousif A. Mansoor

Fatigue and Fracture

Intended to limit crack growth under repetitive loads and fracture

during the design life.

Involves the live load (single truck) and dynamic response.

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• The restrictions depend upon the stress range excursions expected to

occur during the design life of the bridge.[A1.3.2.3].

• This limit state is used to limit crack growth under repetitive loads and

to prevent fracture due to cumulative stress effects in steel elements,

components, and connections.

• For the fatigue and fracture limit state, Φ = 1.0

• Since, the only load that causes a large number of repetitive cycles is

the vehicular live load, it is the only load effect that has a non-zero

load factor

FATIGUE AND FRACTURE LIMIT STATE

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Fatigue and Fracture

Two Limit States for Fatigue: Intended to limit crack growth under

repetitive loads and fracture during the design life.

Involves the live load (single truck) and dynamic response.

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Extreme Event Limit States

Intended to ensure survival under rare (unique) occurrences such as

earthquake, collision, avalanche.

Return intervals exceed the design life of the bridge.

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Extreme Event Limit States

Extreme Event I - earthquake.

Extreme Event II - ice, collision, hydraulic events w/ live load.

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Design Equation Issues

Force effects determined from an elastic structural analysis.

Resistance based on inelastic behavior (i.e., impending failure).

The above are inconsistent but are common practice for structural

design.

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17


AASHTO-LRFD Bridge Design Specification


Load: It is the effect of acceleration, including that due togravity.

Nominal Load: An arbitrary selected design load level.

Load Factor: A coefficient expressing the probability of variationsin the nominal load for the expected service life of the bridge.

Permanent Loads: Loads or forces which are, or assumed to be,constant upon completion of construction.

Force Effects: A deformation or a stress resultant, i.e.,thrust, shear, torque/or moment, caused by applied loads,imposed deformation or volumetric changes .

Some Basic Definitions:


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IMPORTANCE OF LOAD PREDICTION A structural engineer has to make a structure safe against failures.

The reasons for a structure being susceptible to failures are:

a) The loads that a structure will be called upon to sustain, cannot be predicted with certainty. قد يحمل المنشاء احمال الى حد قدرة اعضاءه والتياليمكن ان تكون مركزة في مكان

b) The strength of the various components cannot be assessed with full assertion. مقاومة معضم اعضاء الجسر اليمكن ان تقيم كوحدة واحدة

c) The condition of a structure may deteriorate with time causing it to loose strength.


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Load Classifications

Gravity load :

Permanent Loads (Sect. 3.5) p.p 75

loads of constant magnitude and/or location

known magnitude or estimated and checked

Transient Loads (Sect. 3.6 through 3.14) p.p76

loads of variable magnitude and/or location

established “design” value

Construction Loads (not included in LRFD specification

Lateral Loads:

Forces due to deformation :

Collision Loads:


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Permanent Loads

Dead Loads

self weight (150 pcf for concrete, 490 pcf for steel)

future wearing surface (2” of asphalt, ~25 psf)

stay-in-place forms (15 psf)

barrier rails, sidewalk, curb & gutter

utilities, signs

future widening

(see Table 3.5.1-1 for unit weights)


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Material Unit Weight (kcf)

Aluminum alloys 0.175

Bituminous wearing surfaces 0.140

Cast Iron 0.450

Cinder filling 0.060

Compacted sand silt or clay 0.012

Concrete:

Lightweight 0.110

Sand-lightweight 0.120

Normal weight with f’c < 5 ksi 0.145

Normal weight

with 5 ksi < f’c < 15 ksi

0.140 + 0.001 f’c

Loose sand silt or gravel 0.100

Soft clay 0.100

Rolled gravel, macadam, or ballast 0.140

Steel 0.490

Stone masonry 0.170

Wood:

Hard 0.060

Soft 0.050

Water:

Fresh 0.0624

Salt 0.0640

Transit rails, ties, and fastening per track 0.200 klf

Permanent gravity loads are the loads that remain on the bridge for an extendedperiod of time or for the whole service life.Such loads include:(A3.4.1-1 and A3.4.1-2 (From AASHTO LRFD Bridge DesignSpecifications)).p 70 &p71

1. Dead load of structural components and non structural attachments --------------------------------------- (DC)

dcقيمتيبيناختالفهناكاننالحظ , dwلقيمةاعلىانحيثdc is1.25لقيمةاعلىبينماdwهيالكتابمن102حاحصائياذلكتفسيرويمكنللطريقتبليططبقاتاضافةاحتمالبسببوذلك1.5

2. Dead load of wearing surfaces and utilities --- (DW)

3. Dead load of earth fill ---------------------------- (EV)العمقفيالموادكثافةمنالحملويحسبculvertمعالتعاملعند

4.Earth pressure load ------------------------------- (EH)5. Earth surface load --------------------------------- (ES)6. Downdrag ------------------------------------------ (DD)

pileالفيخاصة


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DEAD LOAD OF STRUCTURAL COMPONENTS AND NON-STRUCTURAL ATTACHMENTS (DC)

In bridges, structural components refer to the elements that are part

of load resistance system.

االحمالمقاومةمنظومةمنجزءاالجزاءوهي(اجزائه)الجسرمركباتجميعالىيشير

Nonstructural attachments refer to such items as curbs, parapets,

barriers, rails, signs , illuminators, etc. Weight of such items can be

estimated by using unit weight of materials and its geometry.

Load factors per table A3.4.1-1 and A3.4.1-2 apply here. (From

AASHTO LRFD 2014 Bridge Design Specifications).

والمحجالتاالسيجةمثللالحمالالمقاومةغيربهاويقصداالنشائيةغيرالعناصر

الهندسيةوتصميمهاكثافتهامعرفةمناالحمالمعرفةويمكنواالنارة


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DEAD LOAD OF WEARING SURFACES AND UTILITIES (DW)

This load is estimated by taking the unit weight times the thickness of the surface.

من معرفة عدد طبقات التبليط وسمك كل طبقة

This value is combined with the DC loads per table A3.4.1-1 and A3.4.1-2 (From AASHTO LRFD Bridge Design Specifications).

The maximum and minimum load factors for the DC loads are 1.25 and 0.90 respectively and for DW loads are 1.5 and 0.65 respectively .

هنا لكي نالحظ الفرق وهو بسبب التفسيرات االحصائية


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DEAD LOAD OF EARTH FILL (EV)

This load must be considered for buried structures such as culverts.ويحسب على اساس عمق المواد وكثافتها فوق الجسر culvertخاص بالجسور من نوع

It is determined by multiplying the unit weight times the depth of the materials.

Load factors per table A3.4.1-1 and A3.4.1-2 apply here.

(From AASHTO LRFD Bridge Design Specifications).

EV has a maximum and minimum load factor of 1.35 and 0.9 respectively.


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EARTH SURFACE LOAD (ES)

The earth surcharge load (ES) is calculated like the EV loads with the only difference being in the load factors.

من الكتاب لتفسير االختالف p 102مع االنتباه الى اختالف المواد ويمكن الرجوع الى االحصائي وسببه

This difference is attributed to the variability.

Part or all of this load could be removed in the future or the surcharge material (loads) could be changed.

ES has a maximum and minimum load factor of 1.5 and 0.75 respectively. Assit. Pr. Dr. Yousif A. Mansoor

University of Anbar

DRAGDOWN (DD)

It is the force exerted on a pile or drilled shaft due to the soil movement around the element. Such a force is permanent and typically increases with time.

تزداد مع الوقت

Details regarding DD are outlined in AASHTO (LRFD) Section 10, Foundations.


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32



33



o An important note about γp: The purpose of γp is to account for the fact that sometimes certain loads work opposite to other loads.

• If the load being considered works in a direction to increase the critical response, the maximum γp is used.

• If the load being considered would decrease the maximum response, the minimum γp is used.

• The minimum value of γp is used when the permanent load would increase stability or load carrying capacity.

o Sometimes, a permanent load both contributes to and mitigates a critical load effect.

• For example, in the three span continuous bridge shown, DC in the first and third spans would mitigate the positive moment in the middle span.However, it would be incorrect to use a different γp for the two end spans. In

this case, γp would be 1.25 for DC for all three spans (Commentary C3.4.1 –paragraph 20).

34



As the name implies these loads change with time and may be applied from

several directions or locations.

والمواقعاالتجاهاتمختلففيوتطبقالوقتمعتتغيراحمال

Such loads are highly variable. متغيرةاحمالهي

Transient loads typically include gravity load due to the vehicular, rail or

pedestrian traffic as well as lateral loads such those due to wind, water, ice,

etc.

Engineer should be able to depict…

____ which of these loads is appropriate for the bridge under

consideration.

____ magnitude of the loads

____ how these loads are applied for the most critical load effect.

Transient Loads


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Transient Loads Live Loads (Sect. 3.6.1.1 to 3.6.1.3) pp 76 to p96

Fatigue (Sect. 3.6.1.4)

Vehicle dynamic load allowance (Sect 3.6.2)

Wind (Sect. 3.8)p99

and many others


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38



• Table 3.7: Load Combinations and Load Factors (AASHTO 2014, Table 3.4.1-1)

• Table 3.8: Load Factors for Permanent Loads, γp (AASHTO 2014, Table 3.4.1-2)

• Table 3.9: Load Factors for Permanent Loads due to Superimposed Deformations, γp (AASHTO 2012, Table 3.4.1-3)

39


Common Load Combinations for Steel Design

• Strength I: 1.25DC+ 1.50DW + 1.75(LL+IM)

• Service II: 1.00DC + 1.00DW + 1.30(LL+IM)

• Fatigue: 0.75(LL+IM)

40


Common Load Combinations for Prestressed Concrete


• Strength IV: 1.50DC + 1.50DW

• Service I: 1.00DC+ 1.00DW + 1.00(LL+IM)

• Service III: 1.00DC+ 1.00DW + 0.80(LL+IM)

• Service IV: 1.00DC+ 1.00DW + 1.00WA + 0.70WS + 1.00FR


Note: Fatigue rarely controls for prestressed concrete

41


Common Load Combinations for Reinforced Concrete


• Strength IV: 1.50DC+ 1.50DW


For transient load each code has described the following criterion:

Design lanes Vehicular Design loads Fatigue Loads Pedestrian Loads Deck and Railing Loads Multiple Presence Dynamic Effects Centrifugal Forces Braking forces other

Assist. Pr. Dr. Yousif A. Mansoor

University of Anbar

Number of lanes a bridge may accommodate must be established.

Two such terms are used in the lane design of a bridge:a) Traffic laneb) Design Lane.

Traffic Lane:The traffic lane is the number of lanes of traffic that the traffic engineer

plans to route across the bridge. A lane width is associated with a traffic lane and is typically 3.6 m.

Design Lane:Design lane is the lane designation used by the bridge engineer for the

live load placement. The design lane width may or may not be the same as the traffic lane.

DESIGN LANE


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DESIGN LANESAccording to AASHTO specifications,

•AASHTO uses a 3m design lane and the vehicle is to be positioned within that lane for extreme effect.

بما ان عرض الحارة اكبر من عرض المركبة يجب دراسة جميع اوضاع العربة داخل الحارة

•The number of design lanes is defined by taking the integral part of the ratio of the clear roadway width divided by 3.6m.[A3.6.1.1.1]

3.6عرض الحارة هو الفضاء الصافي بين المحجرات او ارصفة مقسوما على

•The clear width is the distance between the curbs and/or barriers. P103 book

In cases where the traffic lanes are less than 12 ft (3600 mm) wide, the number of design lanesshall be equal to the number of traffic lanes, and the width of the design lane is taken as the widthof traffic lanes. For roadway widths from 20 to 24 ft (6000 to 7200 mm), two design lanes shouldbe used, and the design lane width should be one-half the roadway width.


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VEHICULAR DESIGN LOADS•A study by the transportation Research Board (TRB) was used as the basis

for the AASHTO loads TRB (1990).

•Loads that are above the legal weight and are /or length limits but are

regularly allowed to operate were cataloged. Those vehicles that were above

legal limits but were allowed to operate routinely due to grandfathering

provisions are referred to as ‘Exclusion Vehicles’. المركبة االستثنائية

•These exclusion trucks best represents the extremes involved in the present

truck traffic.

•For analysis, simpler model was developed which represents the same

extreme load effects as the exclusion vehicles.

This model consists of three different loads:

1.Design truck

2.Design tandem

3.Design LaneAssit. Pr.Dr. Yousif A. Mansoor

University of Anbar

VEHICULAR DESIGN LOADS

Design Truck:

According to AASHTO design specifications(1996), the design truck is a model that

resembles the semitrailor truck. as shown in the figure.[A3.6.1.2]. p81

Variable Spacing

The variable spacing provide a more

satisfactory loading for continuous

spans and the heavy axle loads may

be so placed on adjoining spans as to produce maximum –ve moments.

This design truck has the same configuration since 1944 and is commonly referred to as

HS20-44(denoting Highway Semitrailer 20 tons with year of publication 1944).

TruckHL - 93

H: highway

L: LRFD

93 -year adopted


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يالحظ ان المسافة متغيرة يعني على حيث المهندس ان يعطي الحالة االخطرة

DESIGN TANDEM

The second configuration is the design tandem and is illustrated in the figure.

It consists of two axles weighing 110kN each spaced at 1.2m.

TANDEM: A tandem can be defined as two closely spaced and mechanically

interconnected axles of equal weight.

Tandem

4’

25 k 25 k


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DESIGN LANE LOADThe third load is the design lane load that consists of a uniformaly distributed load of

9.3 N/mm and is assumed to occupy a region 3m transversly. This load is same as

uniform pressure of 64 lbs/ft² applied in a 10ft (3m) design lane.

The load of design truck and design tandem must each be superimposed with the load

effects of the design lane load. This combination of load and axle loads is a major

deviation from the requirements of the earlier AASHTO standard specifications where

the loads were considered separately.

Lane

0.64 k/ft 0.064 k/ft

10’L’


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Live Loads

Truck

Lane

14’ to 30’14’

8 k 32 k 32 k

0.64 k/ft

4’

25 k 25 k

Tandem


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As it is quite likely that an exclusion vehicle could be closely followed by another heavily

load truck, it was felt that a third live load combination was required to model this event.

This combination is specified in AASHTO[A3.6.1.3.1] as illustrated in the figure.

“ for negative moment over the interior supports 90 percent of the load effect of two design trucks spaced at minimum of15m between lead axle of one truck and rear

axle of the other truck and 4.3m between two 145kN axles, combined with 90 % of

the effect of the design lane load. Table 8-2 p 106book

Nowak (1993) compared survey vehicles with others in the same lane to

the AASHTO load model and the results are shown in the figure.


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In summary three design loads should be considered , the design truck,

design tandem and design lane. These loads are superimposed three ways

to yield the live load effects , which are combined with the other load

effects as shown in tables.

The above mentioned three cases are illustrated in the table where the

number in the table indicate the appropriate multiplier to be used prior to

superposition. Dr. Yousif A. Mansoor

University of Anbar

Why Three parts to the HL-93?

Long spans:

Design lane load is typically predominant load

السائد في الفضاء العالي

Medium spans:

Design truck load is typically predominant load

Short spans:

Design tandem load is typically predominant load


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Vehicle Live Load

Design truck or tandem

Design lane load

A NOTIONAL load (the loads are not designed to model any one vehicle or combination of vehicles, but the spectra of loads and their associated load effects.)

These loads are meant to model exclusion loads (short haul vehicles (i.e, solid waste trucks and concrete mixers)) that many state DOT’s allow. These exclusion vehicles best represent the extremes in loading that are present in truck traffic.p103


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Dual Truck (train)

Two design trucks with lane loading (

Rear axle spacing at 14 ft

Positioned for critical effect with min separation of 50 ft

Factor by 90 percent

Negative Moment and Reactions

Use AASHTO Distribution Factors

AASHTO 3.6.1.3.1

Side by side trucks taken care of by multiple presence factor


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Schematic Representation

14’14’ 14’ 14’≥ 50’

0.9 X

Interior Pier Reaction

0.64 k/ft


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Live - Load Summary

0.064 kips/ft

32 kips 32 kips 8 kips

14 to 30 ft 14 ft

0.064 kips/ft

25 kips 25 kips

4 ft

32 kips 32 kips8 kips

14 ft 14 ft

0.064 kips/ft

8 kips32 kips

14 ft 14 ft

32 kips

Design Truck

Load Multiplier = 1.0

Design Tandem


Two Design Trucks or Tandems with 50 ft of Headway



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FATIGUE LOADS

• A bridge is vulnerable to repeated stressing or fatigue.

• When the load is cyclic the stress level is below the nominal yield strength.

This load depends upon:

1. Range of live load stress

2. Number of stress cycles under service load conditions.


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FATIGUE LOADS

1. Under service load conditions, majority of trucks do not exceed the legal weight

limit. So it would be unnecessary to use the full live load model. Instead it is

accommodated by using a single design truck with the variable axle spacing of 9m

and a load factor of 0.75 as prescribed in table.[A3.4.1.1].

2. The number of stress load cycles is based on traffic surveys. In lieu of survey data,

guidelines are provided in AASHTO [A3.6.1.4.2]. The average daily truck traffic

(ADTT) in a single lane may be estimated as

ADTTSL = p(ADTT)

Where p is the fraction of traffic assumed to be in one lane as defined in table8.3.


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Fatigue Load (Truck)

30’14’

8 k 32 k 32 k

No lane loading

Do not consider tandem

Place in single lane


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Transient Load Designation

BR Vehicular braking force

CE Vehicular centrifugal force

CR Creep

CT Vehicular collision force

CV Vessel collision force

EQ Earthquake

FR Friction

IC Ice load

IM Vehicular dynamic load allowance

LL Vehicular live load

LS Live load surcharge

PL Pedestrian live load

SE Settlement

SH Shrinkage

TG Temperature gradient

TU Uniform temperature

WA Water load and stream pressure

WL Wind on live load

WS Wind load on structure


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PEDESTRIAN LOADSq• The AASHTO pedestrian load is 3.6 x 10-3 MPa, which is applied to sidewalk that are integral with a roadway bridge. AASHTO A3.6.1.6/ P90

قدم او مساوي لعرض 2هذا في حالة كون الممشى مخصص للسابلة فقط على ان يكون العرض اكثر من

.design laneال

• If load is applied on bridge restricted to pedestrian or bicycle traffic , then a 4.1 x 10-3

MPa is used.

• The railing for pedestrian or bicycle must be designed for a load of 0.73 N/mm both

transversely and vertically on each longitudinal

element in the railing system.[A13.8 and A18.9].

P1546 حيث ينتقل الحمل باالتجاهين الطولي والعمودي.

• In addition as shown in the figure ,

the railing must be designed to sustain a single

concentrated load of 890 N applied to the top rail in

any direction and at any location. Dr. Yousif A. Mansoor

University of Anbar

DECK & RAILING LOAD

•The gravity load for design deck should be design AASHTO

A3.6.1.3.3 p 86

•The deck must be designed for the load effect due to design truck or

design tandem , whichever creates the most extreme effect.

يجب ان التاخذ المركبتين معا بل تاخذ الحالة االسوء او االخطر•

على العموم lane loadال ياخذ في التصميم اال في حالة الجسور السقفية •

The deck overhang, located outside the p108

facia girder and commonly referred to

as the cantilever is designed for the load

effect of a uniform line load of 14.6 N/mm

located 300mm from the face of the

curb or railing as shown in the figure.

MULTIPLE PRESENCETrucks will be present in adjacent lanes on roadways with multiple

design lanes but it is unlikely that three adjacent lanes will be loaded

simultaneously with the three heavy loads.

Therefore, some adjustment in the design load is necessary. To account

for this effect AASHTO [A3.6.1.1.2] provides an adjustment factor for

the multiple presence. A table for these factors is provided.

shall not be applied to the fatigue يجب على المهندس دراسة جميع احتماالت

وضعية العربة على الجسر من حيث الموقع والعدد تبعا لعدد الحارات المرور التصميمة وعند

التحميل يسمح الكود بتخفيض قيمة الحمولة بزيادة عدد حارات التحميل وذلك الخذ بالحسبان

حالة وجود عربات على كامل الحارات التصميمة

for which one design truck is used,

regardless of the number of design

lanes. Where the single-lane approximate

distribution factors in Articles 4.6.2.2

and 4.6.2.3 are used, other than the

lever rule and statical method,

the force effects shall be divided by 1.20

DYNAMIC EFFECTS

Dynamics : The variation of any function with respect to time.

Dynamic Effects : The effects i.e., deformation or stress resultant due to

the dynamic loads.

• Due to the roughness of the road, the oscillation of the suspension

system of a vehicle creates axle forces. These forces are produced by

alternate compression and tension of the suspension system.

• This phenomenon which is also known as IMPACT is more precisely

referred to as dynamic loading.

• These axle forces exceed the static weight during the time the

acceleration is upward and is less than the static weight when the

acceleration is downward. Assit. Pr. Dr. Yousif A. Mansoor

University of Anbar

DYNAMIC EFFECTS

• As the dynamic effects are not consistent & is well portrayed by Bakht

& Pinjarker (1991 ) & Paultre (1992 ). It is most common to compare the

static & dynamic deflection.

• A comparison of static and dynamic deflections is illustrated in the

fig.8.12.

DYNAMIC EFFECTSFrom this figure dynamic effect is the amplification factor applied to the

static response.

This effect is also called dynamic load factor, dynamic load allowance or

impact factor and is given by,

IM = Ddyn

Dstat

Here Dstat is the maximum static deflection and Ddyn is the additional

defection due to the dynamic effects.

Dstat كيةوهذااالنتقال هو الموافق عند استخدام طرق التحليل االنشائي الكالسي)االنتقال الستاتيكي بدون االثر الديناميكي ) ا)

Ddynاالثر الديناميكي لحركة العربة ويساوي االنتقال الكلي مطروح منه االنتقال الستاتيكيهو.


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DYNAMIC EFFECTS

According to AASHTO specifications, DLA is illustrated in table

8.7[A3.6.2].


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DYNAMIC EFFECTS

Paultre(1992) outlines various factors used to increase the static loads to

account for dynamic load effect. The following illustration shows various

bridge design specifications from around the world.


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CENTRIFUGAL FORCES

For the purpose of computing the radial force or the overturning effect on wheel loads, the centrifugal effect on live load shall be taken as the product of the axle weights of the design truck or tandem and the factor p92 AASHTO

As a truck moves along a curvilinear path, the change in the direction of the velocity

causes a centrifugal acceleration in the radial direction. This acceleration is given by,

ar = V²

r

Where ‘ V ’ is the truck speed and ‘ r ’ is the radius of curvature of the truck movement.

Since F= ma , so substituting ar in the Newton’s second law of motion,

Fr = m V²

r

Where Fr is the force on the truck.

Since mass m = W

g

CENTRIFUGAL FORCESSo, we can substitute ‘ m ‘ in eq.above to obtain an expression similar to that given by

AASHTO,

Fr = V² W

rg

Fr = CW

Where C = 4 v²

3 Rg

Here v is the highway design speed(m/s), R is the radius of the curvature of traffic

lane(m), and F is applied at the assumed centre of mass at a distance 1800 mm above

the deck surface.[A3.6.3]

Because the combination of design truck with the design lane load gives a load

approximately four thirds of the effect of the design truck considered independently, a

four third factor is used to model the effect of a train of trucks.

Multiple presence factor may be applied to this force as it is unlikely that all the lanes

will be fully loaded simultaneously.

BRAKING FORCES

•Braking forces are significant in bridge loads consideration. This force is transmitted to

the deck and taken into the substructure by the bearings or supports. P113 book

•This force is assumed to act horizontally at 1800 mm above the roadway surface in

either longitudinal direction.

•Here , the multiple presence factor may be applied as it is unlikely that all the trucks in

all the lanes will be at the maximum design level.

•The braking force shall be

taken as 25% of the axle

weights of the design truck

or the design tandem placedin all lanes.

PERMIT VEHICLES AND MISCELLANEOUS CONSIDERATIONS

•Transportation agencies may include vehicle loads to model

characteristics of their particular jurisdiction.

For example the Department of Transportation in California (Caltrans)

uses a different load model for their structures as shown in the fig.8.19.


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LATERAL LOADS

Following forces are considered under lateral loads:

• Fluid forces

• Seismic Loads

• Ice Forces


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FLUID FORCES

• Fluid forces include

1.Water forces and

2.Wind forces.

• The force on a structural component due to a fluid flow (water or air) around a component is established by Bernoulli’s equation in combination with empirically established drag coefficients.


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WIND FORCES

• The velocity of the wind varies with the elevation above the ground and the upstream terrain roughness and that is why pressure on a structure is also a function of these parameters.

• If the terrain is smooth then the velocity increases more rapidly with elevation.

• The wind force should be considered from all directions and extreme values are used for design.

• Directional adjustments are outlined in AASHTO[A3.8.1.4].

• The wind must also be considered on the vehicle.This load is 1.46 N/mm applied at 1.8 m above the roadway surface.[A3.8.1.3].


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Wind load

• The equation for velocity profile used by AASHTO [A3.8.1.1] is

where VDZ is the design wind speed at design elevation Z (mph) [same as V(Z ) in Eq. 8.13], VB is the base wind

velocity of 100mph (160 km/h) yielding design pressures, V0 is the “friction velocity,” a meteorological wind

characteristic taken as specified in Table 8.8 for upwind surface characteristics (mph), and Z 0 is the “friction

length” of the upstream fetch, a meteorological wind characteristic taken as specified in Table 8.8 (ft).

Wind (Sect. 3.8.1)

Can act on the structure and the live load.

100 mph uniformly distributed on the exposed area.

Vary direction to determine extreme effect.

Wind on the live load is transmitted to the structure via the tires.

High wind and live load a somewhat unlikely occurrence.


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THE WIND PRESSURE ON THE STRUCTURE OR COMPONENT IS ESTABLISHED BY SCALING A BASIC WIND

PRESSURE FOR VB = 100 MPH (160 KM/H). THIS PROCEDURE IS

Wind load

From AASHTO pp101

Except where specified herein, where the wind is not taken as normal to the structure, the base wind pressures, PB,

for various angles of wind direction may be taken as specified in Table 3.8.1.2.2-1 and shall be applied to the

centroid of a single plane of exposed area. The skew angle shall be taken as measured from a perpendicular to the

longitudinal axis. The wind direction for design shall be that which produces the extreme force effect on the

component under investigation. The transverse and longitudinal pressures shall be applied simultaneously

WATER FORCES

• Water flowing against and around the substructure creates a lateral force directly on the structure as well as debris that might accumulate under the bridge.

• If the substructure is oriented at an angle to the stream flow, then adjustments must be made. These adjustments are outlined in the AASHTO [A3.7.3.2].

• Scour of the stream bed around the foundation should also be considered as it can result in the structural failure. AASHTO [A2.6.4.4.1] outlines an extreme limit state for design.


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SEISMIC LOADS

• Depending on the location of the bridge site, the anticipated earthquake/seismic effects can govern the design of the lateral load resistance system.

• In many cases the seismic loads are not critical and other lateral loads such as wind govern the design.


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PROVISIONS FOR SEISMIC LOADS

• The provision of the AASHTO specifications for seismic design are based on the following principles[C3.10.1]:

1. Small to moderate earthquakes should be resisted within the elastic range of the structural components without significant damage.

2. Realistic seismic ground motion intensities and forces are used in the design procedures.

3. Exposure to shaking from large earthquakes should not cause collapse of all or part of the bridge. Where possible damage should be readily detectable and accessible for inspection and repair.

ICE FORCES• Forces produced by ice must be considered when a

structural component of a bridge, such as a pier, is located in water and the climate is cold enough to cause the water to freeze.

• Due to the freeze up and break up of ice in different seasons ice forces are produced.

• These are generally static which can be horizontal when caused by thermal expansion and contraction or vertical if the body of water is subject to changes in water level.

• Relevant provisions are given in AASHTO section 3.9.

FORCES DUE TO DEFORMATIONIn bridge we have to consider the following forces due to deformation:

1. Temperature

2. Creep and Shrinkage

3. Settlement


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TEMPERATURETwo types of temperature changes must be included in the analysis of the

superstructure.

i. Uniform temperature change

ii. Gradient or non-uniform temperature change

Uniform temperature change:

In this type of temperature change, the entire superstructure changestemperature by a constant amount. This type of change lengthens orshortens the bridge or if the supports are constrained it will induce reactionsat the bearings and forces in the structure. This type of deformation isillustrated in the figure.

Gradient or Non-uniform temperature change:

In this type the temperature change is gradient or non-uniform heating or

cooling of the superstructure across its depth. Subjected to sunshine,

bridge deck heats more than the girder below. This non-uniform heating

causes the temperature to increase more in the top portion of the system

than in the bottom and the girder attempts to bow upward as shown in

the figure.

TEMPERATURE


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The temperature change is considered as a function of climate. AASHTO

defines two climatic conditions, moderate and cold.

Moderate climate is when the number of freezing days per year is

less than 14. A freezing day is when the average temperature is less than

0C.

Table 4.21 gives the temperature ranges. The temperature range is used

to establish the change in temperature used in the analysis.

TEMPERATURE

CREEP & SHRINKAGE

The effects of creep and shrinkage can have an effect on the structural

strength, fatigue and serviceability.

Creep is considered in concrete where its effects can lead unanticipated

serviceability problems that might lead to secondary strength.

Creep and shrinkage are highly dependent on material and the system

involved.


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SETTLEMENT

•Settlements occur usually due to elastic and inelastic deformation of the

foundation.

•Elastic deformation include movements that affect the response of the

bridge to other loads but do not lock in permanent actions.

•This type of settlement is not a load but rather a support characteristic

that should be included in the structural design.

•Inelastic deformations are movements that tend to be permanent and

create locked in permanent actions.

Assit. Pr Dr. Yousif A. Mansoor

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SETTLEMENT

•Such movements may include settlement due to consolidation,

instabilities, or foundation failures. Some such movements are the results

are the loads applied to the bridge and these load effects may be included

in the bridge design.

•Other movements are attributed to the behavior of the foundation

independent of the loads applied to the bridge.

•These movements are treated as loads and are called imposed support

deformations.

•Imposed support deformations are estimated based on the geotechnical

characteristics of the site and the system involved. Detailed suggestions

are given in AASHTO, section 10.


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COLLISION LOADS

Collision loads include:

1.Vessel Collision load

2.Rail Collision Load

3.Vehicle Collision LoadAssit. Pr. Dr. Yousif A. Mansoor

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COLLISION LOADS

Vessel Collision load:On bridge over navigable waterways the possibility of vessel

collision with the pier must be considered. Typically, this is of concern for structures that are classified as long span bridges. Vessel collision loads are classified in AASHTO [A3.14].

Rail Collision Load:If a bridge is located near a railway, the possibility of collision of

the bridge as a result of a railway derailment exists. As this possibility is remote, the bridge must be designed for collision forces using extreme limit states.

Vehicle Collision Load:

The collision force of a vehicle with the barrier, railing and parapet should be considered in bridge design.

101


3.6 - Live Loads

o 3.6.1.1.1: Lane Definitions

• # Design Lanes = INT(w/3600 mm)

w is the clear roadway width between barriers.

Roadway widths from 6000 to 7200 mm shall have two design lanes, each equal to one-half the roadway width.

• 3.6.1.3.1: Application of Design Vehicular Loads

• The governing force effect shall be taken as the larger of the following:

• The effect of the design tandem combined with the design lane load

• The effect of one design truck (HL-93) combined with the effect of the

• design lane load

• For negative moment between inflection points, 90% of the effect of two design trucks (HL-93 with 14 ft. axle spacing) spaced at a minimum of 50 ft. combined with 90% of the design lane load

102


3.6 - Live Loads

103


o 3.4.1: Load Factors and Load Combinations

• Table 3.4.1-1 “Load Combinations and Load Factors” gives two separate values for the load factor for TU (uniform temperature), CR (creep), and SH (shrinkage). The larger value is used for deformations. The smaller value is used for all other effects.

TG (temperature gradient), γTG should be determined on a project-specific basis. In lieu of project-specific information to the contrary, the following values may be used:

• 0.0 for strength and extreme event limit states,

• 1.0 for service limit state where live load is NOT considered,

• 0.5 for service limit state where live load is considered.

For SE (settlement), γSE should be based on project specific information. In lieu of project specific information, γSE may be taken as 1.0.

• Load combinations which include settlement shall also be applied without settlement.

• The load factor for live load in Extreme Event I, γEQ, shall be determined on a project specific basis.

104


o 3.4.1: Load Factors and Load Combinations

When prestressed components are used in conjunction with steel girders, the following effects shall be

considered as construction loads (EL):

• If a deck is prestressed BEFORE being made composite, the friction between the deck and the girders.

• If the deck is prestressed AFTER being made composite, the additional forces induced in the girders and shear connectors.

• Effects of differential creep and shrinkage.

• Poisson effect.

105


3.4.2: Load Factors for Construction Loads

At the Strength Limit State Under Construction Loads:

• For Strength Load Combinations I, III and V, the factors for DC and DW shall not be less than 1.25.

• For Strength Load Combination I, the load factor for construction loads and any associated dynamic effects shall not be less than 1.5.

• For Strength Load Combination III, the load factor for wind shall not be less than 1.25.

• 3.4.3: Load Factors for Jacking and Post-Tensioning Forces

• Jacking Forces

• The design forces for in-service jacking shall be not less than 1.3 times the permanent load reaction at the bearing adjacent to the point of jacking (unless otherwise specified by the Owner).

• The live load reaction must also consider maintenance of traffic if the bridge is not closed during the jacking operation.

• PT Anchorage Zones

• The design force for PT anchorage zones shall be 1.2 times the

• maximum jacking force.

106


3.4.3: Load Factors for Jacking and Post-Tensioning Forces

o Jacking Forces

• The design forces for in-service jacking shall be not less than 1.3 times the permanent load reaction at the bearing adjacent to the point of jacking (unless otherwise specified by the Owner).

• The live load reaction must also consider maintenance of traffic if the bridge is not closed during the jacking operation.

o PT Anchorage Zones

• The design force for PT anchorage zones shall be 1.2 times the maximum jacking force.

107


3.5.1 Dead Loads: DC, DW, and EV

o DC is the dead load of the structure and components present at construction. These have a lower load factor because they are known with more certainty.

• DW are future dead loads, such as future wearing surfaces. These have a higher load factor because they are known with less certainty.

• EV is the vertical component of earth fill.

• Table 3.5.1-1 gives unit weight of typical components which may be used to calculate DC, DW and EV.

o If a beam slab bridge meets the requirements of Article 4.6.2.2.1, then the permanent loads of and on

the deck may be distributed uniformly among the beams and/or stringers.

o Article 4.6.2.2.1 basically lays out the conditions under which approximate distribution factors for live load can be

used.

Documents

Strength Limit State · 2020. 3. 11. · Strength Limit State Sect. 3.4.1 Strength I - basic condition w/ live load (no wind) Strength II - special, or permit, loads Strength III