1. unified design and other new concepts

7/23/2019 1. Unified Design and Other New Concepts

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1.1

Introduction to LRFD

Loads and Load Distributionand Other New Concepts

1.2

1. Design methodology

2. Load & load distribution

3. Major changes to concrete design

Unified provisions for flexure & axial load

Crack control prov isions

Temperature and shr inkage reinf.

Girders made continuous for live load

Shear: MCFT & STM

Prestress losses

Empirical design of decks

Overview of Presentation

1.3

AASHTO LRFD

(Load and Resistance Factor Design)

1993 - Adopted by AASHTO

1994 - 1st Edition

1998 - 2nd Edition

2004 - 3rd Edition

2007 - 4th Edition



1.4

AASHTO LRFD

Comprehensive specifications:

» Eliminate gaps & inconsistencies in the

AASHTO Standard Specs» Incorporate the latest bridge research

» Achieve more uni form margins of s afety or

reliability across a wide variety of

structures

» Take variability of the behavior of structural

elements into account, but present the

results in a format readily usable by bridge

designers

1.5

Major Changes

A new ph ilosophy of safety

Identification of limit states

Load and resistance factors based on

calibration

Refined load distri bution

New load models

Chapter on structural analysis

Unified approach for concrete design

Isotropic reinforced concrete deck design

Parallel commentary

1.6

Evolution of Design Methodologies

1. Service Load Design

(Allowable/Working Stress)

» Assumes linear elast ic concrete stress-

strain with f c ≤ 0.40 f c’

» Assumes linear elast ic steel stress-

strain with f s ≤ 24 ksi (Grade 60)

» Either concrete or steel limit governs

design

» Al l loads (D, L, W, E, etc .) assumed of

equal importance



1.7


2. Load Factor Design

» Non-linear concrete stress-strain

(equivalent rectangular stress block)» Bi-linear steel stress-strain

» Recognize larger variability of live load

compared to dead load

» Arbi trary load fac tors

Primary gravity load combination

U = 1.3[D + (5/3)(L+I)]

1.8


3. Load and Resistance Factor Design

» Non-linear concrete stress-strain

(equivalent rectangular stress block)

» Bi-linear steel stress-strain

» Recognize variability of loads and of

resistances

» Calibrated load and resistance factors

» Consistent reliability index for SLS

Primary gravity load combination

U = 1.25D + 1.75(L+I)

1.9

LRFD Calibration

Qmean

Rmean

Qn

Rn

γQn φRn

f(R,Q)

R,Q



1.10

Statist ical Data

Variability in loads

» Traffic: cars, trucks (different number of

axles), etc.

Variability in resistances

» Concrete compressive strength

» Reinforcing steel y ield strength

» Cross-section geometry

» Location of reinforcement

1.11

LRFD Calibration

Qmean

Rmean

Qn Rn

γQn

φRn

f(R,Q)

R,Q

1.12

LRFD Calibration

Qmean

Rmean

Qn Rn

f(R,Q)

R,Q

γQn

φRn



1.13

LRFD Calibration

R-Q

(R-Q)mean

βσ

Graphical

definition

of

reliability

index β

1.14

LRFD Calibration

Reliability Indices

0

1

2

3

4

5

Span Length

LFD

LRFD

200120906030

, ft

1.15

LRFD Limit States

The LRFD Specifications require examination o fseveral load combinations cor responding to thefollowing limit states:

» STRENGTH LIMIT STATE

strength and stability

» SERVICE LIMIT STATE

stress, deformation, and cracking

» FATIGUE & FRACTURE LIMIT STATE

stress range

» EXTREME EVENT LIMIT STATE

earthquakes, ice load, and vehicle and vessel

collision



1.16

3.4.1 Load and Load DesignationSTRENGTH I : normal vehicular use without wind

STRENGTH II : owner design / permit vehicles without wind

STRENGTH III : bridge exposed to wind exceeding 55 mph

STRENGTH IV : very high dead-to-live load ratios

STRENGTH V : normal vehicular use with 55 mph wind

SERVICE I : normal operational use of the bridge with a 55 mphwind and nominal loads. Also control cracking ofreinforced concrete structures.

SERVICE II : control yielding of steel structures and slip ofconnections

SERVICE III : control cracking of prestressed concretesuperstructures

SERVICE IV : control cracking of prestressed concretesubstructures

FATIGUE : repetitive vehicular live load and dynamic responsesunder a single truck

1.17

Basic LRFD Design Equation

ΣηiγiQi ≤ φRn = Rr Eq. (1.3.2.1-1)

where:

ηi = Load Modi fier = ηD ηR ηI

ηi ≥ 0.95 for maximumγ

’s

ηi = < 1.00 for minimumγ

’s

γi = Load factor

φ = Resistance factor

Qi = Nominal force effect

Rn = Nominal resistance

Rr = Factored resistance = φRn

IRD

1

η

1.18

Table 3.4.1-1 Load Combinations and Load FactorsUse One of These at a

Time

Load Combination

Limit State

DC

DD

DW

EHEV

ES

LL

IM

CE

BRPL

LS

WA WS WL FR TU

CR

SH

TG SE

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, DWDC 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-I γp γEQ 1.00 - - 1.00 - - - 1.00

- - -

EXTREME-II γp 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 & CEONLY - 0.75 - - - - - - - - - - -



1.19

3.3.2 Load and Load Designation

DD = d ow nd rag

DC = dead load of structuralcomponents andnonstructuralattachments

DW = dead load of wearingsurfaces and utilities

EH = horizontal earth pressure

EL = accumulated locked-inforce effects resultingfrom the constructionprocess, including thesecondary forces frompost-tensioning

ES = earth surcharge load

EV = earth fill vert ical pressure

BR = vehicular braking force

CE = vehicular centrifugalforce

CR = cr eep

CT = vehicular col lis ion force

CV = vessel coll ision force

EQ = ear thquake

FR = f ri cti on

IC = i ce l oadIM = vehicular dynamic load

allowance

LL = veh icular l ive load

LS = l ive load surcharge

PL = pedestrian l ive load

SE = set tlement

SH = s hr in kag e

TG = temperature gradient

TU = uniform temperature

WA= water load and st reampressure

WL= wind on l i ve load

WS= wind load on st ructure

1.203.6.2.1 Dynamic Load Allowance

(Impact - IM)

The LRFD Specifications simpl y require a

constant magnification of IM = 33% be applied to

the design truck or design tandem only. The

magnification is not applied to the design lane

load.

This simple approach is based on a study, which

revealed that the most i nfluential factor affecting

dynamic impact is roadway surface roughness.

Exceptions are as follow s:

Deck joints: IM = 75%

Fatigue limit state: IM = 15%

1.21

Design Tandem

Two 25.0 KIP axles spaced 4.0 FT apart

Design Lane Load

Uniformly distributed load of 0.64 KLF

3.6.1.2.1 Design Vehicular L ive LoadsDesign Truck



1.22

5.5.4.2 Resistance Factors

Std SpecsLRFD

5.5.4.2Flex – RC 0.90 0.90

Flex – PS 1.00 1.00

Shear – RC 0.85 0.90

Shear – PS 0.90 0.90

Compression 0.70 / 0.75 0.75

Bearing 0.70 0.70

1.23

Table 4.6.2.2.1-1 Common Superstructures

1.24

Type of Beams

ApplicableCross-Section

from Table

4.6.2.2.1-1 Distribution FactorsRange of

Applicability

One Design Lane Loaded:0.10.4 0.3

30.06 14 12.0

g

s

K S S

L Lt

⎛ ⎞⎛ ⎞ ⎛ ⎞

+ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

Two or More Design Lanes Loaded:0.10.6 0.2

30.075

9.5 12.0

g

s

K S S

L Lt

⎛ ⎞⎛ ⎞ ⎛ ⎞+ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

3.5 16.0

20 240

4.5 12.0

4

s

b

S

L

t

N

≤ ≤

≤ ≤

≤ ≤≥

10,000 ≤ K g ≤ 7,000,000

Concrete Deck, FilledGrid, Partially Filled

Grid, or Unfilled GridDeck Composite withReinforced Concrete Slabon Steel or ConcreteBeams; Concrete T-Beams, T- and Double T-Sections

a, e, k and alsoi, j

if sufficientlyconnected toact as a unit

use lesser of the values obtained from theequation above with N b = 3 or the lever rule

N b = 3

Table 4.6.2.2.2b-1 Distribution of Live Loads

Per Lane for Moment in Interior Beams

Notes: 1) Units are in LANES and not WHEELS!

2) Refer to specified limits of applicability.

3) No multiple presence factor applied (tabulated equations)

4) May be Different for Positive and Negative Flexure Locations!



1.25

Lever Rule

1.26

Unified Design Provisions

1.27

Bridge Specifications

AASHTO Standard

» Section 8 – Reinforced Concrete

» Section 9 – Prestressed Concrete

AASHTO LRFD

» Section 5 – Concrete Structures

– Reinforced concrete

– Prestressed concrete

– Partially prestressed concrete (New in LRFD)

– Parallel commentary & References



1.28

AASHTO Standard

Maximum reinforcement

Reinf. Conc. ρ

max = 0.75 ρ

bal (8.16.3.1.)Prest . Con c. (p*f *su) ≤ 0.36 1 (9.18.1)

1.29

Unified Design Provisions for Reinforced and

Prestressed Concrete Flexural and Compression

Members

Beams Ductile behavior

Columns Non-ductile behavior

φ Factors selected based on behavior

1.30

Unified Provisions - Background

AASHTO LRFD (’06)

Mast, Robert F., “Unified Design Provisions fo r

Reinforced and Prestressed Concrete Flexural &

Compression Members,” ACI Structural Jrnl., Mar- Apr il 1992, pp. 185-199.



1.31

Unified Provisions Applicability

Flexural & compression members

R/C, P/S, and combinations

Steel at various depths

Sections of any shape

Composite sections

Tension-controlled c olumns

1.32Walt Disney World Monorail - 1971

1.33

Unified Design Provisions –

Key Concept

Strength reduction factor, φ,

depends on

maximum net tensile strain, t ,

at nominal resistance, Mn



1.34

5.2 - Definitions

Net Tensile Strain - The tensile strain at

nominal resistance exclusive of strains

due to effective prestress, creep,shrinkage, and temperature.

1.35

5.2 - Definitions

Extreme Tension Steel — The

reinforcement (prestressed or

nonprestressed) that is farthest from

the extreme compression f iber.

1.36

5.2 - Definitions

t = Net tensile st rain

dt = Depth to extreme tension steel

dt

t

0.003

ColumnStrainBeam



1.37

5.2 - Definitions

t Extreme tension steel strain

at nominal resistance, due to applied loads

t

c a = 1c C

T

Pn

Mn

0.003

1.38

5.2 - Definitions

Compression-Controlled Strain Limit —

The net tensile strain ( t ) at balancedstrain condi tions. See Article 5.7.2.1.

1.39

5.7.2.1 – Balanced Strain Condit ion

f y /Es (or 0.002)

0.003



1.40

5.2 - Definitions

Compression-Controlled Section — A

cross section in wh ich the net tensile

strain ( t ) in the extreme tension steelat nominal resistance is less than or

equal to the compression-controlled

strain limit.

[Usually 0.002]

1.41

5.2 - Definitions

Tension-Controlled Section — A cross

section in which the net tensile strain

( t ) in the extreme tension steel atnominal resistance is greater than or

equal to 0.005.

1.42

5.5.4.2 Resistance Factors φ

P/S

Transi tion Tension -

Controlled

Compression-

Controlled

1.00

R.C.

φ

t = 0.002 t = 0.005

0.90

0.75

Net Tensile Strain

⎟

⎠

⎞

⎜

⎝

⎛

1c

d15.065.0 t

φ

⎟

⎠

⎞

⎜

⎝

⎛

1c

d25.0583.0 t

φ



1.43

Effect of Variation in φ

Design flexural members as tension-controlled

sections. Adding reinforcement beyond thislimit reduces

φ

, because of reduced ductil ity,

resulting in no gain in design strength

It is better to add sufficient compression

reinforcement to raise the neutral axis and

make the section tension-controlled

1.44

Effect of Variation in φ

ρ = As/bd

φMn

bd2

1.45

10.3.3-4 – Strain Conditions

td

c

Compression-

Controlled

Tension-

Controlled Transition

c 0.003= 0.003

t 0.002≤ t0.002 0.005< t 0.005≥

0.003

c c

c ≤ 0.375 d t 0.375 d t < c < 0.6 d t c ≥ 0.6 d t



1.46

Ductility Comparison

Standard vs . LRFD Specs.

1.47Example – R.C. Beam

Given: f’c = 4 ksi; f y = 60 ksi

Assume s teel yiel ds

T = Asf y = 3(0.79)60 = 142.2 kips

a = T/(0.85 f’cb) = 3.49 in. c = a/ 1 = 4.1 in.

Mn = T [d t-(a/2)] = 1672 in.-k = 139.3 ft-k

c/d t = 4.1/13.5 = 0.304 < 0.375 or

t = 0.003 [(d t-c)/c] = 0.0069 in./in. Tension-con tro lledMr = φMn = 0.90 (139.3) = 125.4 ft-k

a = 1c C

T

t

c

0.003 12”

3#8

d t = 13.5” 16”

1.48

Other Recently Adopted Provisions

Crack control provi sions (’05) Temperature and shrink age reinf. (’06)

Girders made continuous for live load (’07)



1.49

5.4.2.6 Modulus of Rupture

Appl ication f r

5.7.3.4 Crack control

5.7.3.6.2 Deflecti ons

5.7.3.3.2 Minimum flexural

reinforcement (’05)

5.8.3.4.3 To compute Vci

(4th AASHTO LRFD Edit ion,

2007)

psif 5.7

KSIf 24.0'

c

'

c

psif 3.6

KSIf 20.0

'

c

'

c

ps if 7.11

KSIf 37.0

'

c

'

c

1.50

5.7.3.4 Control of Cracking by Distribut ion

of Reinforcement (’05)

where

γe = exposure factor

= 1.00 for Class 1 exposure (cracks can be tolerated,

reduced concern about appearance and/or corrosion)

= 0.75 for Class 2 exposure (concern about appearance

and/or corrosion)

)14.3.7.5(d2f

700s c

ss

e

γ

)dh(7.0

d1

c

cs

1.51

5.7.3.4 Control of Cracking by Distribut ion

of Reinforcement (Cont’d)

where

d c = thickness of concrete cover measured from extreme

tension fiber to center of f lexural reinforcement located

closest thereto (in.) f s = tensile stress in reinforcement at service limit state

h = overall thickness or depth of component (in.)



1.52Concrete Drying

Data represents:

• 6 x 12 in. cylinders

• moist-cured 7 days, then drying at 73 deg. F and 50% RH

1.53

Shrinkage Stresses

1.54

5.10.8 Shrinkage and Temperature Reinf.

0.11 ≤ As ≤ 0.60

where

As = area of reinforcement in each direction and each

face (in.2 /ft)

b = least width of component section

h = least thickness of component section (in.2 )

f y = specified yield strength of bars ≤ 75 ksi

)18.10.5(f )hb(2

bh30.1 A

y

s



1.55

5.10.8 Shrinkage and Temperature Reinf.

Provide near surfaces of concrete exposed to daily

temperatures changes

Provide in structural mass concrete

May consist of bars or welded wire reinforcement

If h ≤ 6 in., use one layer

Maximum bar or wire spacing = 3h or 18 in.

If h > 36 in., maximum spacing ≤ 12 in.

1.565.14.1.4 Bridges Composed of Simple

Span Precast Girders Made Continuous

Art ic le revised and expand ed based on NCHRP

Project 12-53. Revisions to appear in 4th AASHTO

LRFD Edition (2007)

Reference

Miller, R.A., Castrodale, R., Mirmiran, A and

Hastak, M., Connection of Simple-Span Precast

Concrete Girders for Continuit y, National

Cooperative Highway Research Program Report

519, Transportation Research Board, National

Research Council, Washington, D.C., 2004.

1.57 Analysis of Precast Prestressed

Concrete Girders Made ContinuousNon-composite structure - simple span

• Prestress

• Girder self-weight

• Deck and other n on-composite loads

Composite structure - continuous span• Superimposed dead loads

• Future wearing s urface

• Live load

• Time-dependent effects

- Shrinkage

- Creep

- Temperature



1.58

Typical Continuity Connection

1.59

Components of Differential Shrinkage

1.60

Shrinkage Effect



1.61

Creep Effect

1.62

5.14.1.4.2 Restraint Moments

The bridge shall be designed for

restraint moments that may develop

because of time-dependent or other

deformations, except as allowed in

Article 5.14.1.4.4.

Restraint moments shall not be

included in any combination when the

effect of the restraint moment is to

reduce the total moment.

1.635.14.1.4.4 Age of Girder when

Continuity is Established

Minimum age of precast girder when

continuity i s established to be specified in

contract documents

Restraint moments to be computed based

on age of precast girder when continuity isestablished

Al ternat ive simpli fied procedure:

minimum girder age at least 90 days

when continuity is established



1.645.14.1.4.4 Simpli fied Procedure for

Precast Girders Made Continuous

Positive restraint moments = 0

Provide positive moment connection with

a factored resistance φMn ≥ 1.2Mcr

» Mild reinforcement embedded in the precast

girders and developed into the continui ty

diaphragm

» Pretensioning strands extended beyond the

end of the girder and anchored into th e

continuity diaphragm

1.65

What LRFD is NOT?

New unifi ed provisions for fl exure andaxial load

New unified provis ions for shear designusing modif ied compression-field theory

Strut-and-tie model for concrete

New limit states

New, more complex live-load dis tributionfactors

Many other state-of-the-art additions

Concluding Remarks

1.66

Concluding Remarks

Improvement over ASD and LFD

Uniform reliability index

Provides a framework for f uture

improvements Incorporates state-of-the-art design

procedures

1. unified design and other new concepts

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