Transcript Introduction to Bridge Engineering

Introduction to
Bridge Engineering
CONCRETE BRIDGES
Lecture 4 (II)
CONCRETE BRIDGES
Presented To:
PROF. DR. AKHTAR NAEEM KHAN
&
CLASSMATES
Presented By:
YASIR IRFAN BADRASHI
&
QAISER HAYAT
2
CONCRETE BRIDGES
Topics to be Presented:

Example Problem on:
(i).
(ii).
(iii).
Concrete Deck Design
Solid Slab Bridge Design
T-Beam Bridge Design
3
7.10.1
CONCRETE DECK DESIGN
4
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 TBeam 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 fc’=30
MPa, fy=400Mpa, and compare the
selected reinforcement with that
obtained by the empirical method
[A9.7.2]
5
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]
S  3000 2440  3000
h min 

 181mm 175 mm
30
30
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 ho=230mm
6
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
7
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.
8
1. DECK SLAB

h = 205 mm,
Ws = 4.83 x 10–3 N/mm,
S = 2440 mm
WsS 2
(4.83103 )(2440) 2
FEM  

 2396Nm m/ m m
12
12


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.
9
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.
10
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
11
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
12
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
13
3. BARRIER




R200 = Pb (Influence line ordinate)
= 4.65(1.0+1.27 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
14
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
15
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
16
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]
17
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, 1140+0.883 X
Positive moment, 660+0.55 S
Negative moment, 1220+0.25 S
Where X is the distance from the wheel load to
centerline of support and S is the spacing of the TBeams. Here X=310 mm and S=2440 mm
(Fig.E7.1-6)
18
D. VEHICULAR LIVE LOAD
Figure E 7.1-6 : Distribution of Wheel load
on Overhang
19
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
IM 

l  2.28 1 
P
100

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.
20
D. VEHICULAR LIVE LOAD
 Thus
the tire contact area is
510 x 385mm
with the 510mm in
transverse
direction
shown in Figure.E7.1-6
the
as
21
D. VEHICULAR LIVE LOAD
22
D. VEHICULAR LIVE LOAD
Figure E 7.1-6 : Distribution of Wheel load
on Overhang
Back
23
D. VEHICULAR LIVE LOAD
3
24
D. VEHICULAR LIVE LOAD
m
mm
25
D. VEHICULAR LIVE LOAD
Fig.E7.1-7: Live load placement for maximum positive moment
(a) One loaded lane, m = 1.2
(b) Two loaded lanes, m = 1.0
26
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 (m=1.2)
are
200
204
27
D. VEHICULAR LIVE LOAD
For two loaded lanes
(m=1.0)
Thus, the one loaded lane case governs.
28
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 (m=1.2) as shown in Fig.E7.1-8.


The equivalent transverse strip width is
1220+0.25S = 1220+0.25(2440) = 1830 mm
Using Table A-1, the bending moment at location 300 is
29
D. VEHICULAR LIVE LOAD
4.
MAXIMUM LIVE LOAD REACTION ON EXTERIOR GIRDER
30
E. STRENGTH LIMIT STATE

The gravity load combination can be stated
as [Table A.3.4.1-1]
P
P
31
E. STRENGTH LIMIT STATE
32
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
33
E. STRENGTH LIMIT STATE
The values of the loads in Fig E7.1-10 are for a 1mathematical model strip. The concentrated wheel
load is for one loaded lane, that is,
W = 1.2(72500)1400 = 62.14 N/mm

Deck Slab:
1.
s
34
E. STRENGTH LIMIT STATE
2. Overhang
o
3. Barrier
200
35
E. STRENGTH LIMIT STATE
4. Future Wearing Surface
5. Live Load
36
E. STRENGTH LIMIT STATE
6. Strength-I Limit State
37
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.
38
F. Selection Of Reinforcement
u
39
F. Selection Of Reinforcement
40
F. Selection Of Reinforcement

Maximum reinforcement keeping in view the
ductility requirements is limited by [A5.7.3.3.1]
a  0.35d

Minimum reinforcement [5.7.3.3.2] for
components containing no prestressing steel is
satisfied if
As
fc '

 0.03
(bd )
fy
41
F. Selection Of Reinforcement
42
F. Selection Of Reinforcement
1. POSITIVE MOMENT REINFORCEMENT :
43
F. Selection Of Reinforcement

Check Ductility

Check Moment Strength
44
F. Selection Of Reinforcement
2. Negative Moment Reinforcement
Back
45
F. Selection Of Reinforcement


Check Moment Strength
For transverse top bars,
Use No. 15 @225 mm.
46
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]
3840
Percentage
 67%
Se
Where Se is the effective span length [A9.7.2.3]. Se is the distance
face to face of stems, that is,
Se=2440-350= 2090mm
3840
Percentage
 84%,Use67%
2090
47
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 @ 150 mm,
As = 0.667 mm2/mm
48
F. Selection Of Reinforcement
4. SHRINKAGE AND TEMPRATURE REINFORCEMENT.
The minimum amount of reinforcement in each direction shall be
[A5.10.8.2]
Tem p. As  0.75
Ag
fy
Where Ag is the gross area of the section for the full 205 mm thickness.
Temp . As  0.75
(205 1)
 0.38mm 2 / mm
200
For members greater than 150 mm in thickness, the shrinkage and
temperature reinforcement is to be distributed equally on both faces.
1
(Temp . As )  0.19 mm 2 / mm
2
Use No.10 @ 450 mm, Provided As = 0.222 mm2/mm
49
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]
Z
f s  f sa 
 0.6 f y
1/ 3
(d c A)
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.
50
G. CONTROL OF CRACKING-GENERAL
M = MDC + MDW + 1.33 MLL
c
51
G. CONTROL OF CRACKING-GENERAL
Where
 c = density of concrete = 2400 Kg/m3.
f’c
= 30 MPa.
So that
Ec  0.043(2400)
1.5
30  27700MPa.
200000
n
 7.2,
27700
Use n = 7
52
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
53
G. CONTROL OF CRACKING-GENERAL

Sum of statical moments about the neutral axis yields
54
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
55
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.
56
G. CONTROL OF CRACKING-GENERAL

Balancing the statical moments about the
neutral axis gives
57
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
58
H. FATIGUE LIMIT STATE

The investigation for fatigue is not
required in concrete decks for
multigirder applications [A9.5.3]
59
I.

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.
60
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.
61
J. EMPERICAL DESIGN OF CONCRETE DECK
SLABS
1. DESIGN CONDITIONS [A9.7.2.4]
Design depth excludes the loss due to wear,
h=190mm. The following conditions must be satisfied:
62
J. EMPERICAL DESIGN OF CONCRETE DECK
SLABS
2. REINFORCEMENT REQUIREMENTS [A9.7.2.5]
63
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.
64
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)
65
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.
66
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.
67
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.
68
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
R
 1.0 5
69
L. DECK OVERHANG DESIGN
70
L. DECK OVERHANG DESIGN
71
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”
72
L. DECK OVERHANG DESIGN




The maximum edge thickness of the deck overhand is
200mm[A13.7.3.1.2] 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
73
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 Slide) is similar to the
profile and reinforcement arrangement to
traffic barrier type T5 analyzed by
Hirsh(1978) and tested by Buth et al (1990)
74
M. CONCRETE BARRIER STRENGTH
c
t
Fig. W7.1-17 (Concrete Barrier and connection to deck
overhang.)
75
M. CONCRETE BARRIER STRENGTH
2

M c Lc 
2 
 …..(E7.1-8)
 8M b  8M w H 
Rw  

H 
 2 Lc  Lt 
76
M. CONCRETE BARRIER STRENGTH
t
t
77
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
78
M. CONCRETE BARRIER STRENGTH
79
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
80
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
81
M. CONCRETE BARRIER STRENGTH

For segment III, the positive and negative
bending strengths are equal and
nIII
nI
nII
nIII
82
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
83
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
84
(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]
d=50+16+150+8 = 224 mm
85
M. CONCRETE BARRIER STRENGTH
II+III
86
M. CONCRETE BARRIER STRENGTH
3. CRITICAL LENTH OF YIELD LINE PATTERN,LC
Now with moment strengths and Lt=1070mm known,
Eq.E7.1-9 yields
t
c
t
b
w
c
87
M. CONCRETE BARRIER STRENGTH
4. NOMINAL RESISTANCE TO TRANVERSE
LOAD,RW
From Eq.E7.1-8, We have
w
c
t
b
w
c c
88
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
89
M. CONCRETE BARRIER STRENGTH

The nominal shear resistance Vn of the interface
plane is given by [A5.8.4.1]
n
cv
vf
c
90
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
91
M. CONCRETE BARRIER STRENGTH

The minimum cross-sectional area of dowels
across the shear plane is [A5.8.4.1]
vf
v
y
92
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]
100db
lhb 
fc'
and shall not be less than 8db or 150mm. For a No.15
bar, db=16mm and
lhb 
100(16)
 292m m
30
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
lhb=0.7(1.2)lhb = 0.74(292) = 245mm
93
M. CONCRETE BARRIER STRENGTH
c
c
w
94
M. CONCRETE BARRIER STRENGTH
The standard 90o hook with an extension of 12db=12(16)=192mm at
the free end of the bar is adequate [A5.10.2.1]
95
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 (Lc+2H) is
96
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
97
M. CONCRETE BARRIER STRENGTH

Bundling a No.10 bar with No.15 bar at 225mm
on centers, the negative moment strength
becomes
s
n
98
M. CONCRETE BARRIER STRENGTH

this moment strength will be reduced because
of the axial tension force
T = Rw/(Lc+2H)
By assuming the moment interaction curve
between moment and axial tension as a straight
line (Fig.E7.1-20]
99
M. CONCRETE BARRIER STRENGTH
u
st
100
M. CONCRETE BARRIER STRENGTH
101
M. CONCRETE BARRIER STRENGTH
102
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 ldh=16+150+8=174mm>155mm
103
M. CONCRETE BARRIER STRENGTH
104
M. CONCRETE BARRIER STRENGTH
105
M. CONCRETE BARRIER STRENGTH
106
M. CONCRETE BARRIER STRENGTH
db
107
M. CONCRETE BARRIER STRENGTH
108
7.10.2
SOLID SLAB BRIDGE DESIGN
109
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
fc’=30MPa and fy=400 MPa. Follow the slab
bridge outline in Appendix A5.4 and the
beam and girder bridge outline in section 5Appendix A5.3 of the AASHTO (1994) LRFD
bridge specifications.
110
7.10.2: SOLID SLAB BRIDGE DESIGN
111
A. CHECK MINIMUM RECOMMENDED
DEPTH [TABLE A2.5.2.6.3-1]
112
B. DETERMINE LIVE LOAD STRIP
WIDTH [A4.6.2.3]
1. One-Lane loaded:
Multiple presence factor included [C4.6.2.3}
1 1
113
B. DETERMINE LIVE LOAD STRIP
WIDTH [A4.6.2.3]
114
C. APPLICABILITY OF LIVE LOADS FOR DECKS
AND DECK SYSTEMS
1. MAXIMUM SHEAR FORCE – AXLE LOADS [FIG.E7.2-2]
115
C. APPLICABILITY OF LIVE LOADS FOR DECKS
AND DECK SYSTEMS
116
C. APPLICABILITY OF LIVE LOADS FOR DECKS
AND DECK SYSTEMS
1. MAXIMUM BENDING MOMENT AT MIDSPANAXLE LOADS [FIG.E7.2-3]
117
D. SELECTION OF RESISTANCE
FACTORS (Table 7.10 [A5.5.4.2.1]
118
E. Select load modifiers [A1.3.2.1]
119
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
120
G. CALCULATE LIVE LOAD FORCE
EFFECTS
1. INTERIOR STRIP.
121
G. CALCULATE LIVE LOAD FORCE
EFFECTS
2. EDGE STRIP [A4.6.2.1.4]
122
G. CALCULATE LIVE LOAD FORCE
EFFECTS
123
H. CALCULATE FORCE EFFECTS FROM
OTHER loads
1. INTERIOR STRIP, 1-mm WIDE
124
H. CALCULATE FORCE EFFECTS FROM
OTHER loads
2. EDGE STRIP, 1-MM WIDE
125
I. INVESTIGATE SERVICE LIMIT STATE
1. DURIBILITY
126
I. INVESTIGATE SERVICE LIMIT STATE
a. MOMENT- INTERIOR STRIP
s
y
127
I. INVESTIGATE SERVICE LIMIT STATE
b. MOMENT-EDGE STRIP
128
I. INVESTIGATE SERVICE LIMIT STATE
2. CONTROL OF CRACKING
s
a.
sa
INTERIOR STRIP
r
c
r
s
c
129
I. INVESTIGATE SERVICE LIMIT STATE
Location of neutral axis
cr
130
I. INVESTIGATE SERVICE LIMIT STATE

STEEL STRESS
s
s
y
c
y
sa
131
I. INVESTIGATE SERVICE LIMIT STATE
b. EDGE STRIP
½(103)(x2) = (35 x 103)(510-x)
cr
132
I. INVESTIGATE SERVICE LIMIT STATE

STEEL STRESS
s
133
I. INVESTIGATE SERVICE LIMIT STATE
3. DEFORMATIONS [A5.7.3.6]
e
c e
cr
cr
a
a
e
cr
134
I. INVESTIGATE SERVICE LIMIT STATE
g
cr
t
e
135
I. INVESTIGATE SERVICE LIMIT STATE
By using Ig: [A5.7.3.6.2]
136
I. INVESTIGATE SERVICE LIMIT STATE
b. LIVE LOAD DEFLECTION: (OPTIONAL)[A2.5.2.6.2]
allow
LL  IM
137
I. INVESTIGATE SERVICE LIMIT STATE
4607mm
138
I. INVESTIGATE SERVICE LIMIT STATE
Back
139
I. INVESTIGATE SERVICE LIMIT STATE
140
I. INVESTIGATE SERVICE LIMIT STATE

DESIGN LANE LOAD
Lane
141
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.
142
I. INVESTIGATE SERVICE LIMIT STATE
5. Concrete stresses [A5.9.4.3].
As there is no prestressing therefore
concrete stresses does not apply.
143
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 (m=1). From
Fig.E7.2-8
144
I. INVESTIGATE SERVICE LIMIT STATE
145
I. INVESTIGATE SERVICE LIMIT STATE
a. TENSILE LIVE LOAD STRESSES:
One loaded lane, E=4370mm
s
146
I. INVESTIGATE SERVICE LIMIT STATE
b. REINFORCING BARS:[A5.5.3.2]
min
147
J. INVESTIGATE STRENGTH LIMIT STATE
1. FLEXURE [A5.7.3.2]
RECTANGULAR STRESS DISTRIBUTION [A5.7.2.2]
(2/7)
a. INTERIOR STRIP:
148
J. INVESTIGATE STRENGTH LIMIT STATE
149
J. INVESTIGATE STRENGTH LIMIT STATE
150
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  TG = 0
151
J. INVESTIGATE STRENGTH LIMIT STATE
So the strength limit state governs.
Use No.30 @ 150 mm for interior strip.
152
J. INVESTIGATE STRENGTH LIMIT STATE
b. EDGE STRIP
153
J. INVESTIGATE STRENGTH LIMIT STATE
STRENGTH I:
Use No. 30 @ 140mm for edge strip.
154
J. INVESTIGATE STRENGTH LIMIT STATE
2. SHEAR
Slab bridges designed for moment in
conformance with AASHTO[A4.6.2.3]
maybe considered satisfactory for
shear.
155
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.
156
K. DISTRIBUTION REINFORCEMENT
[A5.14.4.1]
a. INTERIOR SPAN:
157
K. DISTRIBUTION REINFORCEMENT
[A5.14.4.1]
b. EDGE STRIP:
158
L. SHRINKAGE AND TEMPRATURE REINFORCEMENT

Transverse reinforcement in the top of the slab
[A5.10.8]
159
M. DESIGN SKETCH
160
TABLE A-1
BACK
161
BACK
162
163