Introduction to AASHTO Load and Resistance Factor Design ...

Introduction to AASHTOLoad and Resistance Factor Design

Structural Supports for Signs, Luminaires Traffic Signals

OverviewLoads

Calibration

Dr. Jay A. Puckett, PE, F.ASCEDirector of the Durham

School University of NebraskaEmeritus Professor at

University of WyomingPresident BridgeTech, Inc.

Dr. Michael G. Barker, PEProfessor

University of Wyoming

Calibration of Design Equations

Puckett 2007, 2009, 2010

What load factors and resistance factors lead to an acceptably safe

and consistent design?

-Given the characteristics of the loads and structural materials

γ ϕ

γ

ϕ

≤ =

=====

∑ i i n r

i

i

n

r

Q R R

load factorsQ load effects

resistance factorsR resistanceR factored resistance

Safety or Reliability Index β• Failure is defined as the Strength < Load (S < L)• Probability of failure is the Probability (S < L)• Reliability (Safety) Index β is a measure of the

Probability (Strength < Load)

• Intent of LRFD - β high enough for adequate safety and consistent over a range of design scenarios.

β = the number of standard deviations that the mean value of the limit state failure function is on the safe side of failure

Puckett 2007, 2009, 2010

Statistical Properties

(showing normally distributed variables)

Reliability Index


𝜎𝜎𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝑆𝑆𝐿𝐿𝑆𝑆𝐿𝐿𝑆𝑆 = 𝜎𝜎2𝑆𝑆𝐿𝐿𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐿𝐿𝑆 + 𝜎𝜎2𝐿𝐿𝐿𝐿𝑆𝑆𝐿𝐿

𝜇𝜇𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝑆𝑆𝐿𝐿𝑆𝑆𝐿𝐿𝑆𝑆 = 𝜇𝜇𝑆𝑆𝐿𝐿𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐿𝐿𝑆 − 𝜇𝜇𝐿𝐿𝐿𝐿𝑆𝑆𝐿𝐿

Reliability Index


𝜷𝜷 =𝜇𝜇𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝑆𝑆𝐿𝐿𝑆𝑆𝐿𝐿𝑆𝑆𝜎𝜎𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝑆𝑆𝐿𝐿𝑆𝑆𝐿𝐿𝑆𝑆

Calibration

• Determine the statistical properties of loads• Determine the statistical properties of strength

(for optimal design using assumed φ and γi)• Determine β• Vary φ and γi until acceptable safety and

consistency achieved (“calibrate” to current accepted practice – current ASD procedures)

Loads Considered

Significant Dead Load EffectMostly Wind Load

• Dead & Wind• Ratio of Dead to Wind• Importance (300/700/1700 year wind)• Combined Moment & Torsion

Wind Regions Considered

• Coastal regions• Central US and Western US• Southern Alaska• West Coast

700 Year Basic Wind Speed mph (m/s)

LRFD Reliability Index β

Optimized Design φRn = γD1MD + γWMMRI Year Wind

Load Qµln Qσln Q

Strength Rµln Rσln R

Probability Properties

Reliability Index (Lognormal Distributions)

Assume φ, γD1 , and γW

All Reliability Analyses Based On:MD + M700 = 1.0For EquivalentComparisons

ASD Reliability Index β

Optimized Design Mallowed = (4/3)0.66FySx = MD + I M50

Load Qµln Qσln Q

Strength Rµln Rσln R

Probability Properties

Reliability Index (Lognormal Distributions)

Use LTS – 6 Allowable Stress Design

All Reliability Analyses Based On:MD + M700 = 1.0For EquivalentComparisons

700-Year MRI

Minimum of the 4 regions

Average over the 4 regions

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

00.20.40.60.811.2

Beta

M Wind/M Total

Minimum Beta - 700 Year

LRFD

ASD

700 Year MRICorresponds toASD I = 1.00

φ 0.90

γD 1.10 1.25

γW 1.00 0.00

700-Year MRI

Minimum of the 4 regions

Average over the 4 regions

ASD Range of β LRFD Range of β

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

00.20.40.60.811.2

Beta

M Wind/M Total


LRFD

ASD


φ 0.90

γD 1.10 1.25

γW 1.00 0.00

1700-Year MRI

φ 0.90

γD 1.10 1.25

γW 1.00 0.00

0.000.501.001.502.002.503.003.504.00

00.20.40.60.811.2

Beta

M Wind/M Total

Average Beta - 1700 Year

LRFD

ASD

0.000.501.001.502.002.503.003.504.00

00.20.40.60.811.2

Beta

M Wind/M Total


LRFD

ASD


300-Year MRI

φ 0.90

γD 1.10 1.25

γW 1.00 0.00

0.000.501.001.502.002.503.003.504.00

00.20.40.60.811.2

Beta

M Wind/M Total

Average Beta - 300 Year

LRFD

ASD

0.000.501.001.502.002.503.003.504.00

00.20.40.60.811.2

Beta

M Wind/M Total


LRFD

ASD


Reliability Index with MRI

Midwest & West Reliability Index

(Midwest and West)Load Ratio [WL/(DL+WL) = 0.5]Risk Category

Traffic Volume Typical High LowADT<100 3.03 3.89 3.03100<ADT<=1000 3.60 3.89 3.031000<ADT<= 10000 3.60 3.89 3.03ADT>10000 3.89 3.89 3.03Typical: Failure could cross travelwayHigh: Support failure could stop a life-line travelwayLow: Support failure could not cross travelwayRoadway sign supports: use 10 years (Low) (Midwest and West)Load Ratio [WL/(DL+WL) = 1.0]

ImportanceTraffic Volume Typical High LowADT<100 2.77 3.62 2.77100<ADT<=1000 3.35 3.62 2.771000<ADT<= 10000 3.35 3.62 2.77ADT>10000 3.62 3.62 2.77Typical: Failure could cross travelwayHigh: Support failure could stop a life-line travelwayLow: Support failure could not cross travelwayRoadway sign supports: use 10 years (Low)

Risk CategoryTraffic Volume Typical High LowADT<100 300 1700 300100<ADT≤1000 700 1700 3001000<ADT≤10000 700 1700 300ADT>10000 1700 1700 300Typical: Failure could cross travelwayHigh: Support failure could stop a life-line travelwayLow: Support failure could not cross travelwayRoadside sign supports: Use 10 years

ASD with I=1: β = 3.74

ASD with I=1: β = 2.69

Impact – Importance of MRI

0.60

0.70

0.80

0.90

1.00

1.10

1.20

00.20.40.60.811.2

Ratio

M Wind/M Total

LRFD Required Resistance Ratios (RnT/Rn700)

Rn300/Rn700

Rn1700/Rn700

Impact – LRFD vs ASD

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

00.20.40.60.811.2

Ratio

M Wind/M Total

Required Resistance Ratios (LRFD/ASD)

LRFD/ASD

WIND has HIGHER Variability

Makes Sense

Calibration Summary

• LRFD Calibrated to Current ASD• MRI 300 ~ I=0.87, • MRI 700 ~ I=1.00, • MRI 1700 ~ I=1.15

• LRFD Provides Adequate Safety as Calibrated to Current ASD (β high enough)

• LRFD Provides More Consistent Safety over the Range of Design than ASD (β more uniform)

Calibration Summary

• LRFD & ASD Result in Same Strength Design for Wind Moment/Total Moment ~ 0.60

• High Mast Pole LRFD Strength ~ 10-15% Higher

• Mast Arm LRFD Strength ~5-8% Lower

Calibration Summary

• Risk Category has Significant Impact– High Mast Poles

• +10% or more for High Risk• -10% or more for Low Risk

– Mast Arm Poles• +5% or more for High Risk• -5% or more for Low Risk

Introduction to AASHTO Load and Resistance Factor Design ...

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