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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.
21
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
24
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
26
Section 4: Structural Analysis and Evaluation
4.6.2 - Approximate Methods of Analysis – Distribution Factors
27
Section 4: Structural Analysis and Evaluation
4.6.2 - Approximate Methods of Analysis – Distribution Factors
28
Section 4: Structural Analysis and Evaluation
4.6.2 - Approximate Methods of Analysis – Distribution Factors
29
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.
30
Section 4: Structural Analysis and Evaluation
4.6.2 - Approximate Methods of Analysis – Distribution Factors
31
Section 4: Structural Analysis and Evaluation
4.6.2 - Approximate Methods of Analysis – Distribution Factors
32
Section 4: Structural Analysis and Evaluation
4.6.2 - Approximate Methods of Analysis – Distribution Factors
33
Section 4: Structural Analysis and Evaluation
4.6.2 - Approximate Methods of Analysis – Distribution Factors
4.6.2.2.3c Skewed Bridges
34
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.
35
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
36
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:
38
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
39
Section 4: Structural Analysis and Evaluation
Special Analysis for Distribution Factors for Bending Moments and Shears in Exterior Girders
40
Section 4: Structural Analysis and Evaluation
Special Analysis for Distribution Factors for Bending Moments and Shears in Exterior Girders
41
To remember :-
The following design vehicular live load cases described in AASHTO-LRFD are considered:
42
To remember
The following design vehicular live load cases described in AASHTO-LRFD are considered:
43
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
.
44
EXAMPLE TO EXPLAIN THE LIVE LOAD (DFs ) AND LEVER RULE :-
45
EXAMPLE TO EXPLAIN THE LIVE LOAD (DFs ) AND LEVER RULE :-
EXTERIOR LANE LOADED :-
46
EXAMPLE TO EXPLAIN THE LIVE LOAD (DFs ) AND LEVER RULE :-
INTERIOR LANE LOADED (LANE 2) :-
47
REVIEW FOR LIVE LOAD :-
EXAMPLE TO EXPLAIN THE LIVE LOAD (DFs ) AND LEVER RULE :-
INTERIOR LANE LOADED (LANE 3) :-