Mohsen Shahawy, PHD, PE · 2018-03-09 · • Development of Live Load Distribution Factors for LU-girders with depths exceeding 65 in. ... the lever rule provide overly ... MOMENT

DEVELOPMENT OF U-BEAM PRESTRESSED CONCRETE

DESIGN STANDARDS

Engineering Consultants, Inc.

2018 LOUISIANA TRANSPORTATION CONFERENCESunday, February 25 - Wednesday, February 28, 2018

Mohsen Shahawy, PHD, PE

SDR Engineering Consultants, Inc.

SDREngineering.com

LOUISIANA U-GIRDER DEVELOPMENT

Task 1: General: Design, Detailing – LU Girders

Task 2: Distribution Factors for LU Girders Larger than 65 in.

Task 3: Design Aids – LU Girders

PHASE I:

Task 4: Design Aids – Bearing

PHASE II:

Task 5: Development Of Lu Girder Standards And Special Details

PHASE I: OBJECTIVE

• Evaluation of the current practice in other states to determine

the most appropriate shape for the LU-girders.

• Development of Live Load Distribution Factors for LU-girders

with depths exceeding 65 in.

WORK PLANPROPOSED LU-GIRDER SECTIONS

LU-72 LU-78

WORK PLANPROPOSED LU-GIRDER SECTIONS

LU-84

WORK PLANFRAMING PLANS

Three girder sections LU-72, LU-78 and LU-84

Bridge consists of three (3) LU-girders

SENSITIVITY STUDYMODELING TECHNIQUES

1- Grillage Model

(Transverse element for deck)

2- Planar Model

(Plate element for deck)

SENSITIVITY STUDYMODELING TECHNIQUES

3- Shell Model

(Plate element for deck and girders)

SENSITIVITY STUDY

Comparison of Modeling Techniques

Girder Feature Grillage Planar Shell

Exterior Moment (kip ft.) 5705 5632 5638

Interior Moment (kip ft.) 5592 5535 5575

SENSITIVITY STUDY

FindingsGrillage models yields results as accurate as the

sophisticated 3-D shell model.

Planar models yields results as accurate as the

sophisticated 3-D shell model.

Conclusion Planar models with ~2.5 ft. longitudinal elements will be

used in the parametric study.

Span Length (4 Variations)

• 100 ft., 110 ft., 120 ft. and 130 ft. for LU-72 girder



Girder Spacing (4 Variations)

• 12 ft., 14 ft., 16 ft. and 18 ft.

Overhang Width (2 Variations)

• 5 ft. and 7 ft.

Girder Stiffness (3 Variations)

• LU-72

• LU-78

• LU-84

WORK PLANPARAMETERS

Total No. of FE Models = 4 x 4 x 2 x3 = 96

WORK PLANCASES OF LOADING FOR EXTERIOR GIRDER

Case 1: One (1) Design Lane Loaded

Ext. Girder

Multi-Lane Presence Factor included

WORK PLANCASES OF LOADING FOR EXTERIOR GIRDER

Case 2: Two (2) Design Lanes Loaded

Ext. Girder

Multi-Lane Presence Factor included

WORK PLANCASES OF LOADING FOR INTERIOR GIRDER

Case 1: One (1) Design Lane Loaded Multi-Lane Presence Factor included

Int. Girder

WORK PLANCASES OF LOADING FOR INTERIOR GIRDER

Case 2: Three (3) Design Lanes Loaded Multi-Lane Presence Factor included

Int. Girder

WORK PLANMOMENT DISTRIBUTION FACTORS

LANES 1+2+3

Interior Girder

LANES 1+2

Exterior Girder

Service Live Load Moment from FE (MFE)


Lane Moment for LADV11 using Influence Line (MLANE)

32 k 32 k 8 k

Wlane = 0.64 kip/ft

• Impact factor included

• Magnification factor for LADV11 included


Moment Distribution Factors were determined as follows:

• 𝐷𝐹 (𝑜𝑛𝑒 𝑙𝑎𝑛𝑒 𝑙𝑜𝑎𝑑𝑒𝑑) =𝑀𝐹𝐸 (1 𝑙𝑎𝑛𝑒)

𝑀𝐿𝐴𝑁𝐸

• 𝐷𝐹 (𝑡𝑤𝑜 𝑜𝑟 𝑚𝑜𝑟𝑒 𝑙𝑎𝑛𝑒𝑠 𝑙𝑜𝑎𝑑𝑒𝑑) =𝑀𝐹𝐸 (2 𝑜𝑟 3 𝑙𝑎𝑛𝑒𝑠)


MOMENT DISTRIBUTION FACTORSEFFECT OF SPAN LENGTH

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

130 FT

120 FT

110 FT

100 FT

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

130 FT

120 FT

110 FT

100 FT

LU-72 Bridges

Interior Girder Exterior Girder

MOMENT DISTRIBUTION FACTORSEFFECT OF SPAN LENGTH

LU-78 Bridges


0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

135 FT

125 FT

115 FT

105 FT

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

135 FT

125 FT

115 FT

105 FT

MOMENT DISTRIBUTION FACTORS EFFECT OF SPAN LENGTH

LU-84 Bridges


0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

140 FT

130 FT

120 FT

110 FT

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

140 FT

130 FT

120 FT

110 FT

MOMENT DISTRIBUTION FACTORS EFFECT OF GIRDER SPACING

LU-72 Bridges


0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

100 105 110 115 120 125 130 135 140

Dis

trib

uti

on

Fac

tor

Span (ft.)

S 18 FT.

S 16 FT.

S 14 FT.

S 12 FT.

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

100 105 110 115 120 125 130 135 140

Dis

trib

uti

on

Fac

tor

Span (ft.)

S 18 FT.

S 16 FT.

S 14 FT.

S 12 FT.

SAME BEHAVIOR OBSERVED FOR LU-78 AND LU-84 BRIDGES

MOMENT DISTRIBUTION FACTORS EFFECT OF GIRDER STIFFNESS


0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

100 105 110 115 120 125 130 135 140

Dis

trib

uti

on

Fac

tor

Span (ft.)

72 IN. DEPTH

78 IN. DEPTH

84 IN. DEPTH

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

100 105 110 115 120 125 130 135 140

Dis

trib

uti

on

Fac

tor

Span (ft.)

72 IN. DEPTH

78 IN. DEPTH

84 IN. DEPTH

Girder spacing = 18 ft.

SAME BEHAVIOR OBSERVED FOR GIRDER SPACINGS 12, 14 AND 16 FT.

MOMENT DISTRIBUTION FACTORS EFFECT OF OVERHANG WIDTH


0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

OV 5 FT

OV 6 FT

OV 7 FT.

OV 8 FT.

OV 9 FT.

130 ft. Span

LU-72 Bridges

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

OV 5 FT

OV 6 FT

OV 7 FT.

OV 8 FT.

OV 9 FT.

130 ft. Span

MOMENT DISTRIBUTION FACTORS COMPARISON WITH AASHTO LRFD CURRENT PRACTICE


LU-72 Bridges

130 ft. Span

0.00

0.20

0.40

0.60

0.80

1.00

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

1 LANE LOADED

130 ft. Span

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

1 LANE LOADED

130 ft. Span

ONE LANE LOADED



LU-78 Bridges

0.00

0.20

0.40

0.60

0.80

1.00

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

1 LANE LOADED

135 ft. Span

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

1 LANE LOADED

135 ft. Span

ONE LANE LOADED



LU-84 Bridges

140 ft. Span

0.00

0.20

0.40

0.60

0.80

1.00

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

1 LANE LOADED

140 ft. Span

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO1 LANE LOADED

140 ft. Span

ONE LANE LOADED

Observations

MOMENT DISTRIBUTION FACTORSCOMPARISON WITH AASHTO LRFD CURRENT PRACTICE

For one design loaded lane, AASHTO formulas are

unconservative in their prediction for the moment distribution

factors for interior LU-girders with depths higher than 65 in.

For one design loaded lane, the lever rule provide overly

conservative prediction for the moment distribution factor for the

exterior LU-girders with depths higher than 65 in.

New formulas are proposed to determine the moment distribution

factors for interior and exterior LU-girders

MOMENT DISTRIBUTION FACTORSPROPOSED FORMULAS

Interior Girder (One Loaded Lane)

AASHTO FORMULA PROPOSED FORMULA

𝑆

3.0

0.35𝑆𝑑

12 𝐿2

0.25𝑆

2.0

0.30𝑆𝑑

8.3 𝐿2

0.25

Exterior Girder (One Loaded Lane)

𝑺 ∶ Girder spacing

𝑳 ∶ Span length

𝒅 ∶ Girder depth

𝒅𝒆: Distance from the centerline of the exterior web of exteriorbeam at the deck level to the interior edge of the barrier


𝐿𝑒𝑣𝑒𝑟 𝑅𝑢𝑙𝑒 (1.28 + 𝑑𝑒/16.0)𝑆

2.0

0.30𝑆𝑑

8.3 𝐿2

0.25


Proposed Formula / FE Results (One Loaded Lane)


0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

PROPOSED

1 LANE LOADED

130 ft. Span

72 in. Depth

Interior Girder

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

PROPOSED

1 LANE LOADED

130 ft. Span

72 in. Depth

Interior Girder



LU-72 Bridges

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 OR MORE

LANES LOADED

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 LANES LOADED

130 ft. Span 130 ft. Span

TWO OR MORE LOADED LANES


Interior GirderExterior Girder

LU-78 Bridges

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 OR MORE LANES

LOADED

135 ft. Span

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 LANES LOADED

135 ft. Span




LU-84 Bridges

140 ft. Span

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 OR MORE LANES LOADED

140 ft. Span

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 LANES LOADED

140 ft. Span


Observations


For the case of two or more loaded lanes, AASHTO formulas are

unconservative in their prediction for the moment distribution

factors for interior and exterior LU-girders with depths higher than

65 in.

New formulas are proposed to determine the moment distribution

factors for interior and exterior LU-girders with depths higher than

65 in.



(0.97 + 𝑑𝑒/28.5)𝑆

6.3

0.60𝑆𝑑

12𝐿2

0.125

(0.92 + 𝑑𝑒/16.0)𝑆

3.6

0.35𝑆𝑑

12 𝐿2

0.10 1.2

Interior Girder (Two or More Loaded Lanes)


𝑆

6.3

0.60𝑆𝑑

12𝐿2

0.125𝑆

3.6

0.35𝑆𝑑

12 𝐿2

0.10

Exterior Girder (Two or More Loaded Lanes)







Proposed Formula / FE Results (Two or More Loaded Lanes)

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

PROPOSED

2 OR MORE LANES

LOADED

130 ft. Span

72 in. Depth

Interior Girder

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

PROPOSED

2 OR MORE LANES

LOADED

130 ft. Span

72 in. Depth

Interior Girder

SHEAR DISTRIBUTION FACTORS

• Service Live Load Shear was determined from FE (VFE)

• Lane Moment for LADV11 determined using Influence Line

(VLANE)

• 𝐷𝐹 (𝑜𝑛𝑒 𝑙𝑎𝑛𝑒 𝑙𝑜𝑎𝑑𝑒𝑑) =𝑉𝐹𝐸 (1 𝑙𝑜𝑎𝑑𝑒𝑑 𝑙𝑎𝑛𝑒)


• 𝐷𝐹 (𝑡𝑤𝑜 𝑜𝑟 𝑚𝑜𝑟𝑒 𝑙𝑎𝑛𝑒𝑠 𝑙𝑜𝑎𝑑𝑒𝑑) =𝑉𝐹𝐸 (2 𝑜𝑟 𝑚𝑜𝑟𝑒 𝑙𝑎𝑛𝑒𝑠)


SHEAR DISTRIBUTION FACTORS COMPARISON WITH AASHTO LRFD CURRENT PRACTICE


LU-72 Bridges

130 ft. Span

ONE LANE LOADED

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

1 LANE

LOADED

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

1 LANE

LEVER RULE


Observations

SHEAR DISTRIBUTION FACTORSCOMPARISON WITH AASHTO LRFD CURRENT PRACTICE

For one loaded lane, AASHTO formulas are very conservative in

their prediction for the shear distribution factors for interior and

exterior LU-girders with depths higher than 65 in.

New formulas are proposed to accurately predict the shear

distribution factors for U-girders.

SHEAR DISTRIBUTION FACTORSPROPOSED FORMULAS

Interior Girder (One Loaded Lane)


𝑆

10

0.6𝑑

12 𝐿

0.1

No Change

Exterior Girder (One Loaded Lane)






Lever Rule (1.09 + 𝑑𝑒/16)𝑆

10

0.6𝑑

12 𝐿

0.1 0.80


Proposed Formula / FE Results (One Lane Loaded)


0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

PROPOSED

1 LANE LOADED

130 ft. span

72 in. depth

Exterior girder

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

RPOPOSED

1 LANE LOADED

130 ft. span

72 in. depth

Interior girder



LU-72 Bridges

130 ft. Span

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 OR MORE

LANES

LOADED

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18D

istr

ibu

tio

n F

acto

rSpacing (ft.)

FE ANALYSIS

AASHTO

2 LANES

LOADED

130 ft. Span


130 ft. Span



LU-78 Bridges

135 ft. Span

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 OR MORE

LANES

LOADED

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 LANES

LOADED





LU-84 Bridges

140 ft. Span

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

AASHTO

2 OR MORE

LANES

LOADED

0.60

0.80

1.00

1.20

1.40

1.60

12 14 16 18D

istr

ibu

tio

n F

acto

rSpacing (ft.)

FE ANALYSIS

AASHTO

2 LANES

LOADED



Observations


For two or more loaded lanes, AASHTO formulas are very

conservative in their prediction for the shear distribution factors

for interior and exterior LU-girders with depths higher than 65 in.

New formulas are proposed to accurately predict the shear

distribution factors for U-girders.



(0.80 + 𝑑𝑒/10)𝑆

7.4

0.8𝑑

12 𝐿

0.10

(0.90 + 𝑑𝑒/14)𝑆

7.1

0.65𝑑

12 𝐿

0.125 0.80

Interior Girder (Two or More Loaded Lanes)


𝑆

7.4

0.8𝑑

12 𝐿

0.10𝑆

7.1

0.65𝑑

12 𝐿

0.125

Exterior Girder (Two or More Loaded Lanes)






Proposed Formula / FE Results (Two or More Lanes Loaded)


0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

PROPOSED

2 OR MORE LANES

LOADED

130 ft. span

72 in. depth

Interior girder

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

12 14 16 18

Dis

trib

uti

on

Fac

tor

Spacing (ft.)

FE ANALYSIS

PROPOSED

2 OR MORE LANES

LOADED

130 ft. span

72 in. depth

Exterior girder

CONCLUSIONSSUMMARY OF OBSERVATIONS

AASHTO formulas were found to be unconservative or very

conservative in their prediction for the moment and shear

distribution factors for interior and exterior LU-girders with

depths higher than 65 in.

New formulas are proposed to accurately predict the moment

and shear distribution factors for interior and exterior LU-

girders.

Documents

Mohsen Shahawy, PHD, PE · 2018-03-09 · • Development of Live Load Distribution Factors for LU-girders with depths exceeding 65 in. ... the lever rule provide overly ... MOMENT