DOS Steel Bridge-2

8/7/2019 DOS Steel Bridge-2

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Part 1: BRIDGE STRUCTURES

Lecture-2

DESIGN OF STRUCTURES

STEEL DESIGN


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DESIGN OF CONCRETE DECK SLAB

Minimum Slab Thickness

Absolute Minimum Thickness =

175 mm (9.7.1.1)

Traditionally, the minimum

thickness was specified in

AASHTO Standard Specification

for the purpose of deflectioncontrol.

However, AASHTO LRFD

removes all the requirements for

maximum deflection and leaves itto the judgment of the designer.

Therefore, the thickness of slab

for deflection control is now

optional. (2.5.2.6.3)

S = slab span (mm)

L = span length (mm)


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Slab span (S) is determined from

1-Face-to-Face distance for slab monolithic with beam (i.e. cast into one piece)

2-For composite slab on steel or concrete girder, the distance between the face of the

webs


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Minimum clear cover for reinforcing

steel and pre-stressing steel (5.12.3)

Adjustments for Water-Cement Ratio:

a. For W/C < 0.4, the concrete tends to be

dense; therefore can use only 80% of the

value in the table (i.e. multiply by 0.8)

b. For W/C > 0.5, the concrete tends to be

porous; the value in the table must be

increase by 20% (i.e. multiply by 1.2)

If there is no initial overlay of wearing

surface, should add another 10 mm to the

clear cover on the top surface to allows

for some wear and tear

Minimum Cover of Reinforcement


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Types of Slab Reinforcement

The deck slab may be designed as One-Way Slab with main reinforcement perpendicular

or parallel to the traffic direction

1-Main reinforcement perpendicular to traffic

Found in girder bridges

Girder Spacing must not be too large

2-Main reinforcement parallel to traffic Slab on floor beams (Truss Bridges)


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1-Conventional reinforced concrete decks

supported on girders

2-Slab superstructures, cast-in-place,

longitudinally reinforced

3-Stay-in-place formwork decks

Types of Deck


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ANALYSIS AND DESIGN METHODS OF CONCRETE DECK SLAB

Methods for designing slab are

1. Empirical Method (9.7.2)

2. Approximate Method (Strip Method) (4.6.2.1)

3. Refined Method including

a. Classical force and displacement methods

b. Yield Line Method

c. Finite Element Analysis


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1-Empirical method

Empirical method is based on the test data (this is why it is called empirical) that the

primary mechanism of the bridge deck under wheel load is not flexure but rather

complex arch-action and punching shear.

Empirical method of design can be only used forconcrete isotropic decks (having two

identical layers of reinforcement, perpendicular to and in touch with each other)

supported on longitudinal components.


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1-Empirical method

Conditions that must be satisfied in order to use the Empirical Method

1. cross-frames or diaphragms are used throughout the cross-section at lines of

support

2. the supporting components (girders) are made of steel and/or concrete3. the deck is fully cast-in-place (no precast!) and water cured

4. the deck has uniform depth except any local thickening.

5. core depth of the slab is not less than 100 mm.

6. the effective length (or slab span S) 4.1 m

7. the ratio of effective length (S) to design depth is between 6 and 18

8. the minimum depth of the slab is 175 mm, excluding the wearing surface

9. the specified 28-day fc

of the deck concrete is > 28 MPa


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1-Empirical method

Conditions that must be satisfied in order to use the Empirical Method (Continued)

10. There should be an overhang beyond the centerline of the exterior girder equal to a

minimum of 5 times the depth of slab or 3 times depth of slab with vertical barrier.

11. A minimum of two shear connectors shall be placed at a spacing of 600 mm C/Cbetween the steel girders and the deck slab. For concrete girders, stirrups extending

into the slab satisfy this requirement.

Isotropic bottom layer steel should have a minimum area of 0.570 mm2/mm width of slab.

Isotropic top layer steel should have a minimum area of 0.380 mm2/mm width of slab.

The outermost layer of steel along the depth of the slab is to be placed in the direction of

the effective length.Spacing of steel must be 450 mm

4 layers of isotropic reinforcement (same in all directions) shall be provided

The minimum depth of the concrete slab to be used as a deck should not be less than 175

mm. (NHA suggests a minimum value of 220 mm). The wearing surface is separatelyprovided.

Reinforcement Requirement for Empirical Method


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2-Strip Method (Approximate Method)

Strip method is an approximate analysis method in which the deck is subdivided into

strips perpendicular to the supporting components (girder)

The slab strip is now a continuous beam and can be analyzed using classical beam theory

and designed as a one-way slab

Slab is modeled as beams and with girders as supports

Wheel loads are placed (transversely) on this slab to produced the maximum effect


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2-Strip Method

1. The deck is subdivided into strips perpendicular to the supporting components

(girder)

2. Determine the maximum moment (M+ and M-) based on classical beam theory(These moments are considered as representative and may be used for all panels.)

3. Determine the width of strip for each M+ and M- case

4. Divide the maximum moment by the width of strip to get the moment per 1 unit

width of slab

5. Design an RC slab for this moment the reinforcement required will be for 1 unit

width of slab (this is for the primary direction)

6. The reinforcement in the secondary direction may be taken as a percentage of those

in the primary direction


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2-Strip Method

Equivalent Strip Widths for Various

Parts of the Deck

S = spacing of supporting components

X = distance from load to point of support

+M = positive moment

-M = negative moment


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2-Strip Method

The previous procedure is quite complex for routine designs (need to consider transverse

placements of live loads to get the maximum effect). Therefore, AASHTO offers a

simplified procedure to determine maximum M+ and M- directly!!!

1. Slab is modeled as beams and with girders as supports

2. Determine the maximum M+ and M- from table (Table A4-1) based on the slab

span this is the LL+IM moment per mm.

3. M+ and M- from DL/DW are relatively small and may be approximated as

M=wl2/c where c ~ 10-12

4. Design an RC slab for this moment the reinforcement required will be for 1 mmof slab (this is for the primary direction)

5. The reinforcement in the secondary direction may be taken as a percentage of

those in the primary direction


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2-Strip Method)

The design section fornegative

moments and shear is taken as

the face of the beam for

monolithic construction and

concrete box beams and onequarter the flange width from

the center line of the support for

steel beams


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2-Strip Method

Distribution Steel

Reinforcement in the secondary direction may be determined as a percentage of

that in theprimary direction.


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2-Strip Method

Load Combination

In the case of deck design only one of five strength load combinations needs to be

investigated:

STRENGTH I

This limit state is the basic load combination relating to normal vehicular use of the

bridge (without wind).

U = [1.25 DC + 1.75 (LL + IM)]

Resistance factors for strength limit state:

0.90 for flexure and tension of reinforced concrete

1.00 for flexure and tension of prestressed concrete


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DISTRIBUTION OF LIVE LOAD TO GIRDERS

A bridge usually have more than one girder so the question arise on how to distributethe lane load to the girders

The problem is three-dimensional and involves complex behavior of load transfer

from concrete slab to steel girder.

The AASHTO bridge specification suggests many methods to analyze bridges, i.e.,

finite element analysis, grillage analysis, and a load distribution factor (LDF) equation.

Finite element analysis (FEA) is considered to be an accurate method, but it requiresmuch effort in data preparation, bridge modeling and analysis, and interpretation of

results.

The LDF equation is introduced to facilitate in determination of maximum moment in

the girders.

With the LDF equation, the maximum moment in the girders is obtained by

multiplying a moment from a one-dimensional bridge analysis by the value obtained

from the LDF equation.


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The wheel load distribution factor from the S/D equation, the AASHTO standard

equation (AASHTO 1996), for concrete slab on steel girder bridges with two or more

design lanes loaded is:

LDF=S/D

where S is girder spacing in mm and D is the co-efficient depending on the type of

superstructure, D=1670 for a bridge constructed with a concrete deck on pre-stressed

concrete or steel girders carrying two or more lanes of traffic.

.The S/D equation, first introduced in 1930s, involves only one parameter. Although

the S/D equation is simple to use, it is considered to be unsafe for some bridges and too

conservative for others.

The effects of various parameters such as skew, continuity, and deck stiffness were

ignored in this expression and it was found to be accurate for a few selected bridge

geometries and was inaccurate once the geometry was changed.

AASHTO GIRDER DISTRIBUTION FACTORS


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Development of a formula for a broad range of beam and slab bridges, includingprestressed concrete and steel girder bridges was needed.

Much research was carried out using finite element analysis, grillage analysis, and field

tests to arrive at more accurate expressions for DFs.

The maximum moment at a critical location is determined with an analytical or

numerical method and is denoted as Mrefined. Next, the same load is applied to a single

girder and a 1D beam analysis is performed. The resulting maximum moment/shear is

denoted as Mbeam. The distribution factor (g) is defined as:

DFs are different for different kinds of superstructure system

DFs are different for interior and exterior beam

DFs are available for one design lane and two or more design lanes (the larger one

controls)

Must make sure that the bridge is within the range of applicability of the equation.

AASHTO GIRDER DISTRIBUTION FACTOR


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Factors affecting the AASHTO LRFD distribution factor includes:

Span Length (L)

Girder Spacing (S)

Modulus of elasticity of beam and deck

Moment of inertia and Torsional inertia of the section

Slab Thickness (ts)

Width (b), Depth (d), and Area of beam (A)

Number of design lanes (NL)

Number of girders (Nb)

Width of bridge (W)



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Condition for Applicability of DFs for concrete deck on steel or concrete beams.

1. Spacing of beams, S, should be between 1.1 and 4.9 m.

2. Thickness of deck slab, ts, should be between 110 and 300 mm.

3. Length of beam should be between 6.0 and 73.0 m.4. Number of longitudinal beams in the cross-section, Nb, should be greater than or

equal to 4.

5. The width of deck should be constant.

6. Multiple presence factor is not to be applied when the using the given expressions.

However, it is always to be considered if the lever rule is used to the find the force

effects.

7. If beam spacing exceeds 4.9 m, the live load on each beam shall be the reaction of

the loaded lanes based on the lever rule.

8. Beams should be parallel and should have approximately the same stiffness.9. The curvature in plan is less than the specified AASHTO limit.

10. The roadway part of the overhang, de, does not exceed 910 mm.


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Notation Used

g = distribution factor

S = spacing of beams or webs (mm)

L = span of beam (mm)

Nb

= number of beams, stringers or girders

ts = depth of concrete slab (mm)

n = modular ratio between beam and deck materials

I= moment of inertia of beam (mm4)

eg= distance between the centers of the basic beam and deck (mm), considered zero for

non-composite beamsA = area of stringer, beam or girder

Kg =n(I+Aeg2), longitudinal stiffness parameter (moment of inertia of one beam modified

to equivalent concrete section and transferred to a point at the center of the slab)

Kg/Lts3

= a parameter proportional to the ratio of beam stiffness to total slab stiffness intransverse direction at the level of the slab centerline

de = distance between the center of exterior beam and the interior edge of curb or traffic

barrier mm). It shall be taken positive if the exterior web is within the roadway inside the

curb and negative when it is outside the roadway.


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The lever rule is a method of analysis which involves a statical distribution of load

based on the assumption that each deck panel is simply supported over the girder,

except at the exterior girder that is continuous with the cantilever. Because the load

distribution to any girder other than one directly next to the point of load application isneglected, the lever rule is a conservative method of analysis.

LEVER RULE

Multiple presence factor is not to be applied when the using the

given expressions by the

specifications (already included in

the equations). However, it is

always to be considered if the lever

rule is used to the find the force

effects.

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DOS Steel Bridge-2