AASHTO-LRFD Bridge Design specification Section 4

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Section 4: Structural Analysis and Evaluation

AASHTO-LRFD Bridge Design specification

Section 4: Structural Analysis and Evaluation

• Lecture 5

• University Of Anbar

• Dr.Yousif A. Mansoor

Transverse Load

Distribution (see Barker & Puckett Chapter 11)

Transverse Load Distribution

For Slab-Girder bridges

Live Loads distributed transversely to longitudinal girders as a function of the deck stiffness and the relative stiffness of the girders

To a lesser extent cross frames, diaphragms, and bearings affect transverse load distribution

“Stiff” deck = more uniform distribution

“Stiff” girders = less uniform distribution

Transverse Section of Slab-Girder Bridge

Experimental Procedures

Deflectometers

TLD in Bridge

Transverse Load Distribution

AASHTO LRFD Options for TLD

Lever Rule (Sect. C4.6.2.2.1)

Refined Methods of Analysis

AASHTO Distribution Factors

Lever Method

Gives upper bound on load in a girder

Assume deck is hinged at girders and that load is only distributed to

girders directly next to point of load application

Deck overhang is treated as a canti-lever

One Lane -- Exterior

One Lane -- Interior Girder

Two Lanes -- Interior Girder

AASHTO LRFD Options for TLD

Lever Rule

Refined Methods of Analysis (Sect. 4.6.3.3)

AASHTO Distribution Factors

Refined Methods of Analysis

More rigorous and accurate analysis

Grillage Method (grid of elements modeling beams and deck)

Finite Element Method

Finite Difference Method

AASHTO LRFD Options for TLD

Lever Rule

Refined Methods of Analysis

AASHTO Distribution Factors

AASHTO SS 17th Edition Formula

S

AASHTO Design Truck

One truck on bridge

AASHTO 17th Edition Formula

Multiple truckson bridge

S

AASHTO Design Truck

AASHTO Design Truck

AASHTO 17th Edition Formula

Background:

gS

D

=

Where:

D is a constant dependent on bridge type (D = 5.5 for RC deck on steel or P/S girders)

S is the deck span, ft.

AASHTO LRFD DF Assumptions

(Sect. 4.6.2.2.1)

Width of deck is constant

Unless otherwise specified, the number of beams is not less than 4

Special provisions for unusual case of bridge with 3 beams (use lever rule for Nb = 3)

Beams are parallel and have approximately the same stiffness

Unless otherwise specified, the roadway part of the overhang, de, does not exceed 3 ft.

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

o The distribution of live load, specified in Articles 4.6.2.2.2 and 4.6.2.2.3, may be used for girders, beams,

and stringers, other than multiple steel box beams with concrete decks that meet the following

conditions and any other conditions identified in tables of distribution factors as specified herein:

1. Width of deck is constant;

2. Unless otherwise specified, the number of beams is not less than four;

3. Beams are parallel and have approximately the same stiffness;

4. Unless otherwise specified, the roadway part of the overhang, de, does not exceed 910 mm;

5. Curvature in plan is less than the limit specified in Article 4.6.1.2.4, or where distribution factors are

required in order to implement an acceptable approximate or refined analysis method satisfying the

requirements of Article 4.4 for bridges of any degree of curvature in plan; and

6. Cross-section is consistent with one of the cross-sections shown in Table 1.

de

16 kips

12”

de

AASHTO LRFD DF Assumptions Cont.

(Sect. 4.6.2.2.1)

Curvature in plan is less than the limit specified in Sect.

4.6.1.2

Cross section is consistent with one of the cross

sections shown in Table 4.6.2.2.1-1

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

• Design live load bending moment or shear force is the product of a lane load on a beam model and the

appropriate distribution factor.

MU,LL = (DF)(MBeam Line)

• The following Distribution Factors are applicable to Reinforced Concrete Decks on Steel Girders, CIP

Concrete Girders, and Precast Concrete I or Bulb-Tee sections.

• Also applies to Precast Concrete Tee and Double Tee Sections when sufficient connectivity is present.

Bridge Superstructure Design Course 25

Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

o 4.6.2.2.2e Skewed Bridges

• When the line supports are skewed and the difference between skew angles of two adjacent lines of supports

does not exceed 10°, the bending moment in the beams may be reduced in accordance with Table 1.

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

4.6.2.2.3c Skewed Bridges

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

• The longitudinal stiffness parameter, Kg, shall be taken as:

The parameters A and I in Eq. 1 shall be

taken as those of the noncomposite beam.

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

4.6.2.2.2d Moment Distribution - Exterior Beams

o Lever Rule:

• Assume a hinge develops over each interior girder and solve for the reaction in the exterior girder as a fraction of

the truck load.

• 6’ = 180 mm

• 2’ = 600 mm

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

4.6.2.2.2d Moment Distribution - Exterior Beams

o Lever Rule:

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Section 4: Structural Analysis and Evaluation

4.6.2 - Approximate Methods of Analysis – Distribution Factors

4.6.2.2.2d Moment Distribution - Exterior Beams

o Lever Rule:

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Section 4: Structural Analysis and Evaluation

Special Analysis for Distribution Factors for Bending Moments and Shears in Exterior Girders

• This additional investigation is required because the distribution factor for girders in a multi girder

cross-section, Types “a,” “e,” and “k” in Table 4.6.2.2.1-1, was determined without consideration of

diaphragm or cross-frames. The recommended procedure is an interim provision until research

provides a better solution.

• The procedure outlined in this Section is the same as the conventional approximation for loads on

piles.

• where:

• R = reaction on exterior beam in terms of lanes

• NL = number of loaded lanes under consideration

• e = eccentricity of a design truck or a design lane load from the center of gravity of the pattern of girders (mm)

• x = horizontal distance from the center of gravity of the pattern of girders to each girder (mm)

• Xext = horizontal distance from the center of gravity of the pattern of girders to the exterior girder (mm)

• Nb = number of beams or girders

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Section 4: Structural Analysis and Evaluation

Special Analysis for Distribution Factors for Bending Moments and Shears in Exterior Girders

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Section 4: Structural Analysis and Evaluation

Special Analysis for Distribution Factors for Bending Moments and Shears in Exterior Girders

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To remember :-

The following design vehicular live load cases described in AASHTO-LRFD are considered:

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To remember

The following design vehicular live load cases described in AASHTO-LRFD are considered:

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To remember :-

o SUMMARY:-

UPDATED LOAD CASES ( LL+IM)

IM:- DYNAMIC LOAD ALLOWENCE ( COMMONLY KNOWN AS IMPACT FACTOR )

STRENGTH & SERVICE LIMIT STATES :-

• 100% ( 1.33 TRUCK+LANE ) ………………………………. ALL REGIONS

• 100% ( 1.33 TANDEM+LANE ) ………………. ……………ALL REGIONS

• 90% ( 1.33 DOUBLE TRUCK+LANE ) ……………………. NBR ONLY

• 100% ( 1.33 DOUBLE TANDEM+LANE ) ………………. ... NBR ONLY

FATIGUE LIMIT STATE :-

• 1.15 FATIGUE TRUCK

LIVE LOAD DEFLECTION :-

• 1.33 TRUCK

• 25% ( 1.33 TRUCK ) + LANE

.

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EXAMPLE TO EXPLAIN THE LIVE LOAD (DFs ) AND LEVER RULE :-

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EXAMPLE TO EXPLAIN THE LIVE LOAD (DFs ) AND LEVER RULE :-

EXTERIOR LANE LOADED :-

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EXAMPLE TO EXPLAIN THE LIVE LOAD (DFs ) AND LEVER RULE :-

INTERIOR LANE LOADED (LANE 2) :-

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REVIEW FOR LIVE LOAD :-

EXAMPLE TO EXPLAIN THE LIVE LOAD (DFs ) AND LEVER RULE :-

INTERIOR LANE LOADED (LANE 3) :-