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Introduction to Bridge Engineering

CONCRETE BRIDGES

- Lecture 4 (II)

Presented By

CONCRETE BRIDGES

Presented To

PROF. DR. AKHTAR NAEEM KHAN CLASSMATES

- YASIR IRFAN BADRASHI
- QAISER HAYAT

Topics to be Presented

CONCRETE BRIDGES

- Example Problem on
- (i). Concrete Deck Design
- (ii). Solid Slab Bridge Design
- (iii). T-Beam Bridge Design

7.10.1

- CONCRETE DECK DESIGN

CONCRETE DECK DESIGN

Problem Statement

- Use the approximate method of analysis 4.6.2 to

design the deck of the reinforced concrete T-Beam

bridge section of Fig.E-7.1-1 for a HL-93 live

load and a PL-2 performance level concrete

barrier (Fig.7.45). - The T-Beams supporting the deck are 2440 mm on

the centers and have a stem width of 350 mm. The

deck overhangs the exterior T-Beam approximately

0.4 of the distance between T-Beams. Allow for

sacrificial wear of 15mm of concrete surface and

for a future wearing surface of 75mm thick

bituminous overlay. Use fc30 MPa, fy400Mpa,

and compare the selected reinforcement with that

obtained by the empirical method A9.7.2

A. DECK THICKNESS

- The minimum thickness for concrete deck slabs is

175 mm A9.7.1.1. - Traditional minimum depths of slabs are based on

the deck span length S to control deflection to

give Table A2.5.2.6.3-1

Use hs 190 mm for the structural thickness of

the deck. By adding the 15 mm allowance for the

sacrificial surface, the dead weight of the deck

slab is based on h 205mm. Because the portion

of the deck that overhangs the exterior girder

must be designed for a collision load on the

barrier, its thickness has been increased by 25mm

to ho230mm

B. WEIGHTS OF THE COMPONENTS TABLE A3.5.1-1

- For a 1mm width of a transverse strip.
- Barrier
- Pb 2400 x 10-9 Kg/mm3 x 9.81 N/Kg x 197325 mm2

- 4.65 N/mm
- Future Wearing Surface
- WDW 2250 x 10-9 x 9.81 x 75 1.66 x 10-3

N/mm - Slab 205mm thick
- Ws 2400 x 10-9 x 9.81 x 205 4.83 x 10-3

N/mm - Cantilever Overhanging
- Wo 2400 x 10-9 x 9.81 x 230 5.42 x 10-3

N/mm

C. BENDING MOMENT FORCE EFFECTS GENERAL

- An approximate analysis of strips perpendicular

to girders is considered acceptable A9.6.1. The

extreme positive moment in any deck panel between

girders shall be taken to apply to all positive

moment regions. Similarly, the extreme negative

moment over any girder shall be taken to apply to

all negative moment regions A4.6.2.1.1. The

strips shall be treated as continuous beams with

span lengths equal to the center-to-centre

distance between girders. The girders are

assumed to be rigid A4.6.2.1.6 - For ease in applying the load factors, the

bending moments will separately be determined for

the deck slab, overhang, barrier, future wearing

surface, and vehicle live load.

1. DECK SLAB

- h 205 mm,
- Ws 4.83 x 103 N/mm,
- S 2440 mm
- Placement of the deck slab dead load and results

of a moment distribution analysis for negative

and positive moments in a 1-mm wide strip is

given in figure E7.1-2 - A deck analysis design aid based on influence

lines is given in Table A.1 of Appendix A. For a

uniform load, the tabulated areas are multiplied

by S for Shears and S2 for moments.

Fig.E7.1-2 Moment distribution for deck slab

dead load.

1. DECK SLAB

- R200 Ws (Net area w/o cantilever) S
- 4.83 x 10-3 (0.3928) 2440 4.63 N/mm
- M204 Ws (Net area w/o cantilever) S2
- 4.83 x 10-3 (0.0772) 24402
- 2220 N mm/mm
- M300 Ws (Net area w/o cantilever) S2
- 4.83 x 10-3 (-0.1071) 24402
- - 3080 N mm/mm
- Comparing the results from the design aid with

those from moment distribution shows good

agreement. In determining the remainder of the

bending moment force effects, the design aid of

Table A.1 will be used.

2. OVERHANG

- The parameters are
- ho 230 mm,
- Wo 5.42 x 10-3 N/mm2
- L 990 mm
- Placement of the overhang dead load is shown in

the figure E7.1-3. By using the design aid Table

A.1, the reaction on the exterior T-Beam and the

bending moments are

Fig.E7.1-3 Overhang dead load placement

2. OVERHANG

- R200 Wo (Net area cantilever) L
- 5.42 x 10-3 (1 0.635 x

990/2440) 990 6.75 N/mm - M200 Wo (Net area cantilever) L2
- 5.42 x 10-3 (-0.5000) 9902 -2656 N

mm/mm - M204 Wo (Net area cantilever) L2
- 5.42 x 10-3 (-0.2460) 9902 -1307 N

mm/mm - M300 Wo (Net area cantilever) L2
- 5.42 x 10-3 (0.1350) 9902 717 N

mm/mm

3. BARRIER

- The parameters are
- Pb 4.65 N/mm
- L 990 127 863 mm
- Placement of the center of gravity of the barrier

dead load is shown in figure E7.1-4. By using the

design aid Table A.1 for the concentrated barrier

load, the intensity of the load is multiplied by

the influence line ordinate for shears and

reactions. For bending moments, the influence

line ordinate is multiplied by the cantilever

length L.

Fig.E7.1-4 Barrier dead load placement

3. BARRIER

- R200 Pb (Influence line ordinate)
- 4.65(1.01.27 x 863/2440) 6.74 N/mm
- M200 Pb (Influence line ordinate) L
- 4.65(-1.0000) (863) -4013 N

mm/mm - M204 Pb (Influence line ordinate) L
- 4.65 (-0.4920) (863) -1974 N

mm/mm - M300 Pb (Influence line ordinate) L
- 4.65 (0.2700) (863) 1083 N

mm/mm

4. FUTURE WEARING SURFACE

- FWS WDW 1.66 x 10-3 N/mm2
- The 75mm bituminous overlay is placed curb to

curb as shown in figure E7.1-5. The length of the

loaded cantilever is reduced by the base width of

the barrier to give - L 990 380 610 mm.

Fig. E7.1-5 Future wearing surface dead load

placement

4. FUTURE WEARING SURFACE

- If we use the design aid Table A.1, we have
- R200 WDW (Net area cantilever) L (Net area

w/o cantilever) S - 1.66 x 10-3 (1.0 0.635 x 610/2440) x 610

(0.3928) x 2440) - 2.76 N/mm
- M200 WDW (Net area cantilever) L2
- 1.66 x 10-3 (-0.5000)(610)2 -309 N

mm/mm - M204 WDW (Net area cantilever) L2 (Net area

w/o cantilever) S2 - 1.66 x 10-3 (-0.2460)(610)2

(0.0772)24402 611 N mm/mm - M300 WDW (Net area cantilever) L2 (Net area

w/o cantilever) S2 - 1.66 x 10-3 (0.1350)(610)2

(-0.1071)24402 -975 N mm/mm

D. VEHICULAR LIVE LOAD

- Where decks are designed using the approximate

strip method A4.6.2.1, and the strips are

transverse, they shall be designed for the 145 KN

axle of the design truck A3.6.1.3.3. Wheel

loads on an axle are assumed to be equal and

spaced 1800 mm apart Fig.A3.6.1.2.2-1. The

design truck should be positioned transversely to

produce maximum force effects such that the

center of any wheel load is not closer than 300mm

from the face of the curb for the design of the

deck overhang and 600mm from the edge of the 3600

mm wide design lane for the design of all other

components A3.6.1.3.1

D. VEHICULAR LIVE LOAD

- The width of equivalent interior transverse

strips (mm) over which the wheel loads can be

considered distributed longitudinally in CIP

concrete decks is given as - Table A4.6.2.1.3-1
- Overhang, 11400.883 X
- Positive moment, 6600.55 S
- Negative moment, 12200.25 S
- Where X is the distance from the wheel load to

centerline of support and S is the spacing of the

T-Beams. Here X310 mm and S2440 mm - (Fig.E7.1-6)

D. VEHICULAR LIVE LOAD

Figure E 7.1-6 Distribution of Wheel load

on Overhang

D. VEHICULAR LIVE LOAD

- Tire contact area A3.6.1.2.5 shall be assumed

as a rectangle with width of 510 mm and length

given by

Where is the load factor, IM is the dynamic

load allowance and P is the Wheel load. Here

1.75, IM 33 , P 72.5 KN.

D. VEHICULAR LIVE LOAD

- Thus the tire contact area is
- 510 x 385mm
- with the 510mm in the transverse direction as

shown in Figure.E7.1-6

D. VEHICULAR LIVE LOAD

D. VEHICULAR LIVE LOAD

Back

Figure E 7.1-6 Distribution of Wheel load

on Overhang

D. VEHICULAR LIVE LOAD

3

D. VEHICULAR LIVE LOAD

m

mm

D. VEHICULAR LIVE LOAD

- Fig.E7.1-7 Live load placement for maximum

positive moment - One loaded lane, m 1.2
- (b) Two loaded lanes, m 1.0

D. VEHICULAR LIVE LOAD

- If we use the influence line ordinates from Table

A-1, the exterior girder reaction and positive

bending moment with one loaded lane (m1.2) are

200

204

D. VEHICULAR LIVE LOAD

- For two loaded lanes (m1.0)

Thus, the one loaded lane case governs.

D. VEHICULAR LIVE LOAD

- 3. MAXIMUM INTERIOR NEGATIVE LIVE LOAD MOMENT.
- the critical placement of live load for maximum

negative moment is at the first interior deck

support with one loaded lane (m1.2) as shown in

Fig.E7.1-8. - The equivalent transverse strip width is
- 12200.25S 12200.25(2440) 1830 mm
- Using Table A-1, the bending moment at location

300 is

D. VEHICULAR LIVE LOAD

- 4. MAXIMUM LIVE LOAD REACTION ON EXTERIOR GIRDER

E. STRENGTH LIMIT STATE

- The gravity load combination can be stated as

Table A.3.4.1-1

P

P

E. STRENGTH LIMIT STATE

E. STRENGTH LIMIT STATE

- The T-Beam stem width is 350mm, so the design

sections will be 175mm on either side of the

support centerline used in the analysis. The

critical negative moment section is at the

interior face of the exterior support as shown in

the free body diagram - Fig. E7.1-10

Back

E. STRENGTH LIMIT STATE

- The values of the loads in Fig E7.1-10 are for a

1-mathematical model strip. The concentrated

wheel load is for one loaded lane, that is, - W 1.2(72500)1400 62.14 N/mm
- Deck Slab

s

E. STRENGTH LIMIT STATE

- 2. Overhang
- 3. Barrier

o

200

E. STRENGTH LIMIT STATE

- 4. Future Wearing Surface
- 5. Live Load

E. STRENGTH LIMIT STATE

- 6. Strength-I Limit State

F. Selection Of Reinforcement

- The effective concrete depths for positive and

negative bending will be different because of the

different cover requirements as indicated in this

Fig shown.

F. Selection Of Reinforcement

u

F. Selection Of Reinforcement

F. Selection Of Reinforcement

- Maximum reinforcement keeping in view the

ductility requirements is limited by A5.7.3.3.1 - Minimum reinforcement 5.7.3.3.2 for components

containing no prestressing steel is satisfied if

F. Selection Of Reinforcement

F. Selection Of Reinforcement

- POSITIVE MOMENT REINFORCEMENT

F. Selection Of Reinforcement

- Check Ductility
- Check Moment Strength

F. Selection Of Reinforcement

- 2. Negative Moment Reinforcement

Back

F. Selection Of Reinforcement

- Check Moment Strength
- For transverse top bars,
- Use No. 15 _at_225 mm.

F. Selection Of Reinforcement

- 3. DISTRIBUTION REINFORCEMENT
- Secondary reinforcement is placed in the bottom

of the slab to distribute the wheel loads in the

longitudinal direction of the bridge to the

primary reinforcement in the transverse

direction. The required area is a percentage of

the primary positive moment reinforcement. For

primary reinforcement perpendicular to traffic

A9.7.3.2 - Where Se is the effective span length

A9.7.2.3. Se is the distance face to face of

stems, that is, - Se2440-350 2090mm

F. Selection Of Reinforcement

- So
- Dist.As 0.67(Pos.As)0.67(0.889)
- 0.60 mm2/mm
- For longitudinal bottom bars,
- Use No.10 _at_ 150 mm,
- As 0.667 mm2/mm

F. Selection Of Reinforcement

- 4. SHRINKAGE AND TEMPRATURE REINFORCEMENT.
- The minimum amount of reinforcement in each

direction shall be A5.10.8.2 - Where Ag is the gross area of the section for

the full 205 mm thickness. - For members greater than 150 mm in thickness,

the shrinkage and temperature reinforcement is to

be distributed equally on both faces. - Use No.10 _at_ 450 mm, Provided As 0.222 mm2/mm

G. CONTROL OF CRACKING-GENERAL

- Cracking is controlled by limiting the tensile

stress in the reinforcement under service loads

fs to an allowable tensile stress fsa A5.7.3.4 - Where
- Z 23000 N/mm for severe exposure conditions.
- dc Depth of concrete from extreme tension

fiber to center of closest bar 50 mm - A Effective concrete tensile area per bar

having the same centroid as the reinforcement.

G. CONTROL OF CRACKING-GENERAL

M MDC MDW 1.33 MLL

c

G. CONTROL OF CRACKING-GENERAL

Where density of concrete 2400 Kg/m3. fc

30 MPa. So that Use n 7

G. CONTROL OF CRACKING-GENERAL

- 1. CHECK OF POSITIVE MOMENT REINFORCEMENT.
- The service I positive moment at Location 204 is
- The calculation of the transformed section

properties is based on a 1-mm wide doubly

reinforced section shown in the Figure E7.1-12

G. CONTROL OF CRACKING-GENERAL

- Sum of statical moments about the neutral axis

yields

G. CONTROL OF CRACKING-GENERAL

- The positive moment tensile reinforcement of

No.15 bars at 25mm on centers is located 33 mm

from the extreme tension fiber. Therefore,

c

y

sa

sa

y

s

G. CONTROL OF CRACKING-GENERAL

- 2. CHECK OF NEGATIVE REINFORCEMENT
- The service I negative moment at location 200.72

is - The cross section for the negative moment is

shown in Fig.E7.1-13.

G. CONTROL OF CRACKING-GENERAL

- Balancing the statical moments about the neutral

axis gives

G. CONTROL OF CRACKING-GENERAL

- The negative moment tensile reinforcement of

No.15 bars at 225 mm on centers is located 53 mm

from the tension face. Therefore dc is the

maximum value of 50mm, and

sa

sa

H. FATIGUE LIMIT STATE

- The investigation for fatigue is not required in

concrete decks for multigirder applications

A9.5.3

TRADITIONAL DESIGN FOR INTERIOR SPANS

- The design sketch in Fig.E7.1-14 summerizes the

arrangement of the transverse and longitudinal

reinforcement in four layers for the interior

spans of the deck. The exterior span and deck

overhang have special requirements that must be

dealt with separately.

J. EMPERICAL DESIGN OF CONCRETE DECK SLABS

- Research has shown that the primary structural

action of the concrete deck is not flexure, but

internal arching. The arching creates an internal

compression dome. Only a minimum amount of

isotropic reinforcement is required for local

flexural resistance.

J. EMPERICAL DESIGN OF CONCRETE DECK SLABS

- 1. DESIGN CONDITIONS A9.7.2.4
- Design depth excludes the loss due to wear,

h190mm. The following conditions must be

satisfied

J. EMPERICAL DESIGN OF CONCRETE DECK SLABS

- 2. REINFORCEMENT REQUIREMENTS A9.7.2.5

J. EMPERICAL DESIGN OF CONCRETE DECK SLABS

- 3. EMPERICAL DESIGN SUMMARY
- while using the empirical design approach there

is no need of using any analysis. When the design

conditions have been met, the minimum

reinforcement in all four layers is

predetermined. The design sketch in the

Fig.E7.1-15 summarizes the reinforcement

arrangement for the interior deck spans.

K. COMPARISON OF REINFORCEMENT QUANTITIES

- The weight of reinforcement for the traditional

and empirical design methods are compared in

Table.E7.1-1 for a 1-m wide transverse strip.

Significant saving, in this case 74 of the

traditionally designed reinforcement is required,

can be made by adopting the empirical design

method. - (Area 1m x 14.18m)

L. DECK OVERHANG DESIGN

- The traditional and the empirical methods does

not include the design of the deck overhang. - The design loads for the deck overhang are

applied to a free body diagram of a cantilever

that is independent of the deck spans. - The resulting overhang design can then be

incorporated into either the traditional or the

empirical design by anchoring the overhang

reinforcement into the first deck span.

L. DECK OVERHANG DESIGN

- Two limit states must be investigated.
- Strength I A13.6.1 and Extreme Event II

A13.6.2 - The strength limit state considers vertical

gravity forces and it seldom governs, unless the

cantilever span is very long.

L. DECK OVERHANG DESIGN

- The extreme event limit state considers

horizontal forces caused by the collision of a

vehicle with the barrier. - The extreme limit state usually governs the

design of the deck overhang.

L. DECK OVERHANG DESIGN

- 1. STRENGTH I LIMIT STATE
- The design negative moment is taken at the

exterior face of the support as shown in the

Fig.E7.1-6 for the loads given in Fig.E7.1-10. - Because the overhang has a single load path and

is, therefore, a nonredundant member, then

L. DECK OVERHANG DESIGN

L. DECK OVERHANG DESIGN

L. DECK OVERHANG DESIGN

- 2. EXTREME EVENT II LIMIT STATE
- the forces to be transmitted to the deck

overhand due to a vehicular collision with the

concrete barrier are determined from a strength

analysis of the barrier. - In this design problem, the barriers are to be

designed for a performance level PL-2, which is

suitable for - High-speed main line structures on freeways,

expressways, highways and areas with a mixture of

heavy vehicles and maximum tolerable speeds

L. DECK OVERHANG DESIGN

- The maximum edge thickness of the deck overhand

is 200mmA13.7.3.1.2 and the minimum height of

barrier for a PL-2 is 810mm. - The transverse and longitudinal forces are

distributed over a length of barrier of 1070mm.

This length represents the approximate diameter

of a truck tire, which is in contact with the

wall at the time of impact. - The design philosophy is that if any failures are

to occur they should be in the barrier, which can

readily be repaired, rather than in the deck

overhang. - The resistance factors are taken as 1.0 and

the vehicle collision load factor is 1.0

M. CONCRETE BARRIER STRENGTH

- All traffic railing systems shall be proven

satisfactory through crash testing for a desired

performance level A13.7.3.1. If a previously

tested system is used with only minor

modification that do not change its performance,

then additional crash testing is not required

A13.7.3.1.1 - The concrete barrier shown in the
- Fig.E7.1-17 (Next) is similar to the

profile and reinforcement arrangement to traffic

barrier type T5 analyzed by Hirsh(1978) and

tested by Buth et al (1990)

M. CONCRETE BARRIER STRENGTH

c

t

Fig. W7.1-17 (Concrete Barrier and connection to

deck overhang.)

M. CONCRETE BARRIER STRENGTH

..(E7.1-8)

M. CONCRETE BARRIER STRENGTH

t

t

M. CONCRETE BARRIER STRENGTH

- 1. MOMENT STRENGTH OF WALL ABOUT
- VERTICAL AXIS,MWH.
- The moment strength about the vertical axis is

based on the horizontal reinforcement in the

wall. The thickness of the barrier wall varies

and it is convenient to divide it for calculation

purposes into three segments as shown in Fig.

E7.1-18

M. CONCRETE BARRIER STRENGTH

M. CONCRETE BARRIER STRENGTH

- Neglecting the contribution of compressive

reinforcement, the positive and negative bending

strengths of segment I are approximately equal

and calculated as

nI

M. CONCRETE BARRIER STRENGTH

- For segment II, the moment strengths are slightly

different. Considering the moment positive if it

produces tension on the straight face, we have

n pos

n neg

n II

M. CONCRETE BARRIER STRENGTH

- For segment III, the positive and negative

bending strengths are equal and

nIII

nII

nI

nIII

M. CONCRETE BARRIER STRENGTH

- Now considering the wall to have uniform

thickness and same area as the actual wall and

comparing it with the value of MwH.

This value is close to the one previously

calculated and is easier to find

M. CONCRETE BARRIER STRENGTH

- 2. MOMENT STRENGTH OF WALL ABOUT HORIZONTAL AXIS
- The moment strength about the horizontal axis is

determined from the vertical reinforcement in the

wall. - The yield lines that cross the vertical

reinforcement (Fig.E7.16-16) produce only tension

in the sloping wall, so that the only negative

bending strength need to be calculated. - Matching the spacing of the vertical bars in the

barrier with the spacing of the bottom bars in

the deck, the vertical bars become No.15 at 225mm - (As 0.889 mm2/mm) for the traditional design

(Fig.E7.1-14).

M. CONCRETE BARRIER STRENGTH

- For segment I, the average wall thickness is

175mm and the moment strength about the

horizontal axis becomes - At the bottom of the wall the vertical

reinforcement at the wider spread is not anchored

into the deck overhang. Only the hairpin dowel at

a narrower spread is anchored. the effective

depth of the hairpin dowel is Fig.E7.1-17 - d50161508 224 mm

M. CONCRETE BARRIER STRENGTH

IIIII

M. CONCRETE BARRIER STRENGTH

- 3. CRITICAL LENTH OF YIELD LINE PATTERN,LC
- Now with moment strengths and Lt1070mm known,

Eq.E7.1-9 yields

t

t

b

w

c

c

M. CONCRETE BARRIER STRENGTH

- 4. NOMINAL RESISTANCE TO TRANVERSE
- LOAD,RW
- From Eq.E7.1-8, We have

c

c

w

b

w

c

t

M. CONCRETE BARRIER STRENGTH

- 5. SHEAR TRANSFER BETWEEN BARRIER AND DECK
- The nominal resistance Rw must be transferred

acroass a cold joint by shear friction. Free body

diagrams of the forces transferred from the

barrier to the deck overhang are shown in the

Fig.E7.1-19

c

M. CONCRETE BARRIER STRENGTH

- The nominal shear resistance Vn of the interface

plane is given by A5.8.4.1

n

cv

vf

c

M. CONCRETE BARRIER STRENGTH

- The last two factors are for concrete placed

against hardened concrete clean and free of

laitance, but not intentionally roughened.

Therefore for a 1-mm wide design strip

n

cv

vf

fy

M. CONCRETE BARRIER STRENGTH

- The minimum cross-sectional area of dowels across

the shear plane is A5.8.4.1

v

vf

y

M. CONCRETE BARRIER STRENGTH

- The basic development length lhb for a hooked bar

with fy 400 MPa. Is given by A5.11.2.4.1 - and shall not be less than 8db or 150mm. For a

No.15 bar, db16mm and - which is greater than 8(16) 128mm and 150mm.

The modifications factors of 0.7 for adequate

cover and 1.2 for epoxy coated bars A5.11.2.4.2

apply, so that the development length lhb is

changed to - lhb0.7(1.2)lhb 0.74(292) 245mm

M. CONCRETE BARRIER STRENGTH

c

c

w

M. CONCRETE BARRIER STRENGTH

The standard 90o hook with an extension of

12db12(16)192mm at the free end of the bar is

adequate A5.10.2.1

M. CONCRETE BARRIER STRENGTH

- 6. TOP REINFORCEMENT IN DECK OVERHANG
- The top reinforcement must resist the negative

bending moment over the exterior beam due to the

collision and the dead load of the overhang.

Based on the strength of the 90o hooks, the

collision moment MCT (Fig.E7.1-19) distributed

over a wall length of (Lc2H) is

M. CONCRETE BARRIER STRENGTH

- The dead load moments were calculated previously

for strength I so that for the Extreme Event II

limit state, we have

u

M. CONCRETE BARRIER STRENGTH

- Bundling a No.10 bar with No.15 bar at 225mm on

centers, the negative moment strength becomes

s

n

M. CONCRETE BARRIER STRENGTH

- this moment strength will be reduced because of

the axial tension force - T Rw/(Lc2H)
- By assuming the moment interaction curve between

moment and axial tension as a straight line

(Fig.E7.1-20

M. CONCRETE BARRIER STRENGTH

u

st

M. CONCRETE BARRIER STRENGTH

M. CONCRETE BARRIER STRENGTH

M. CONCRETE BARRIER STRENGTH

The development length available for the hook in

the overhang before reaching the vertical leg of

the hairpin dowel is available

ldh161508174mmgt155mm

M. CONCRETE BARRIER STRENGTH

M. CONCRETE BARRIER STRENGTH

M. CONCRETE BARRIER STRENGTH

M. CONCRETE BARRIER STRENGTH

db

M. CONCRETE BARRIER STRENGTH

7.10.2

- SOLID SLAB BRIDGE DESIGN

7.10.2 SOLID SLAB BRIDGE DESIGN

- PROBLEM STATEMENT
- Design the simply supported solid slab bridge of

Fig.7.2-1 with a span length of 10670mm center to

center of bearing for a HL-93 live load. The

roadway width is 13400mm curb to curb. Allow for

a future wearing surface of 75mm thick bituminous

overlay. Use fc30MPa and fy400 MPa. Follow the

slab bridge outline in Appendix A5.4 and the beam

and girder bridge outline in section 5-Appendix

A5.3 of the AASHTO (1994) LRFD bridge

specifications.

7.10.2 SOLID SLAB BRIDGE DESIGN

CHECK MINIMUM RECOMMENDED DEPTH TABLE

A2.5.2.6.3-1

B. DETERMINE LIVE LOAD STRIP WIDTH A4.6.2.3

- One-Lane loaded
- Multiple presence factor included C4.6.2.3

1

1

B. DETERMINE LIVE LOAD STRIP WIDTH A4.6.2.3

C. APPLICABILITY OF LIVE LOADS FOR DECKS AND

DECK SYSTEMS

1. MAXIMUM SHEAR FORCE AXLE LOADS FIG.E7.2-2

C. APPLICABILITY OF LIVE LOADS FOR DECKS AND

DECK SYSTEMS

C. APPLICABILITY OF LIVE LOADS FOR DECKS AND

DECK SYSTEMS

- 1. MAXIMUM BENDING MOMENT AT MIDSPAN-
- AXLE LOADS FIG.E7.2-3

D. SELECTION OF RESISTANCE FACTORS (Table

7.10 A5.5.4.2.1

E. Select load modifiers A1.3.2.1

F. SELECT APPLICABLE LOAD COMBINATION (TABLE

3.1 TABLE A3.4.1-1)

- 1. STRENGTH I LIMIT STATE
- 2. SERVICE I LIMIT STATE
- 3. FATIGUE LIMIT STATE

G. CALCULATE LIVE LOAD FORCE EFFECTS

- 1. INTERIOR STRIP.

G. CALCULATE LIVE LOAD FORCE EFFECTS

- 2. EDGE STRIP A4.6.2.1.4

G. CALCULATE LIVE LOAD FORCE EFFECTS

H. CALCULATE FORCE EFFECTS FROM OTHER loads

- 1. INTERIOR STRIP, 1-mm WIDE

H. CALCULATE FORCE EFFECTS FROM OTHER loads

- 2. EDGE STRIP, 1-MM WIDE

I. INVESTIGATE SERVICE LIMIT STATE

- 1. DURIBILITY

I. INVESTIGATE SERVICE LIMIT STATE

- a. MOMENT- INTERIOR STRIP

s

y

I. INVESTIGATE SERVICE LIMIT STATE

- b. MOMENT-EDGE STRIP

I. INVESTIGATE SERVICE LIMIT STATE

- 2. CONTROL OF CRACKING
- INTERIOR STRIP

s

sa

r

c

r

s

c

I. INVESTIGATE SERVICE LIMIT STATE

Location of neutral axis

cr

I. INVESTIGATE SERVICE LIMIT STATE

- STEEL STRESS

s

s

y

c

y

sa

I. INVESTIGATE SERVICE LIMIT STATE

- b. EDGE STRIP

½(103)(x2) (35 x 103)(510-x)

cr

I. INVESTIGATE SERVICE LIMIT STATE

- STEEL STRESS

s

I. INVESTIGATE SERVICE LIMIT STATE

- 3. DEFORMATIONS A5.7.3.6

e

c

e

cr

cr

e

cr

a

a

I. INVESTIGATE SERVICE LIMIT STATE

g

cr

t

e

I. INVESTIGATE SERVICE LIMIT STATE

By using Ig A5.7.3.6.2

I. INVESTIGATE SERVICE LIMIT STATE

- b. LIVE LOAD DEFLECTION (OPTIONAL)A2.5.2.6.2

I. INVESTIGATE SERVICE LIMIT STATE

4607mm

I. INVESTIGATE SERVICE LIMIT STATE

Back

I. INVESTIGATE SERVICE LIMIT STATE

I. INVESTIGATE SERVICE LIMIT STATE

- DESIGN LANE LOAD

Lane

I. INVESTIGATE SERVICE LIMIT STATE

- The live load deflection estimate of 17mm is

conservative because Ie was based on the maximum

moment at midspan rather than an average Ie over

the entire span. - Also, the additional stiffness provided by the

concrete barriers has been neglected, as well as

the compression reinforcement in the top of the

slab. - Bridges typically deflect less than the

calculations predict and as a result the

deflection check has been made optional.

I. INVESTIGATE SERVICE LIMIT STATE

- 5. Concrete stresses A5.9.4.3.
- As there is no prestressing therefore concrete

stresses does not apply.

I. INVESTIGATE SERVICE LIMIT STATE

- 5. FATIGUE A5.5.3
- Fatigue load should be one truck with 9000-mm

axle spacing A3.6.1.1.2. As the rear axle

spacing is large, therefore the maximum moment

results when the two front axles are on the

bridge. as shown in Fig.E7.2-8, the two axle

loads are placed on the bridge. - No multiple presence factor is applied (m1).

From Fig.E7.2-8

I. INVESTIGATE SERVICE LIMIT STATE

I. INVESTIGATE SERVICE LIMIT STATE

a. TENSILE LIVE LOAD STRESSES One loaded lane,

E4370mm

s

I. INVESTIGATE SERVICE LIMIT STATE

- b. REINFORCING BARSA5.5.3.2

min

J. INVESTIGATE STRENGTH LIMIT STATE

- 1. FLEXURE A5.7.3.2
- RECTANGULAR STRESS DISTRIBUTION A5.7.2.2
- a. INTERIOR STRIP

(2/7)

J. INVESTIGATE STRENGTH LIMIT STATE

J. INVESTIGATE STRENGTH LIMIT STATE

J. INVESTIGATE STRENGTH LIMIT STATE

For simple span bridges, temperature gradient

effect reduces gravity load effects. Because

temperature gradient may not always be there, so

assume 0

J. INVESTIGATE STRENGTH LIMIT STATE

So the strength limit state governs. Use No.30 _at_

150 mm for interior strip.

J. INVESTIGATE STRENGTH LIMIT STATE

- b. EDGE STRIP

J. INVESTIGATE STRENGTH LIMIT STATE

STRENGTH I

Use No. 30 _at_ 140mm for edge strip.

J. INVESTIGATE STRENGTH LIMIT STATE

- 2. SHEAR
- Slab bridges designed for moment in conformance

with AASHTOA4.6.2.3 maybe considered

satisfactory for shear.

K. DISTRIBUTION REINFORCEMENT A5.14.4.1

- The amount of bottom transverse reinforcement

maybe taken as a percentage of the main

reinforcement required for positive moment as.

K. DISTRIBUTION REINFORCEMENT A5.14.4.1

- a. INTERIOR SPAN

K. DISTRIBUTION REINFORCEMENT A5.14.4.1

- b. EDGE STRIP

L. SHRINKAGE AND TEMPRATURE REINFORCEMENT

- Transverse reinforcement in the top of the slab

A5.10.8

M. DESIGN SKETCH

TABLE A-1

BACK

BACK

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