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PRESERVATION OF MISSOURI TRANSPORTATION INFRASTRUCTURES
VOL I: Bridge Design & Load Rating
VALIDATION OF FRP COMPOSITE TECHNOLOGY
THROUGH FIELD TESTING
Strengthening of Bridge Y-0298Pulaski County, MO
Prepared for: Missouri Department of Transportation
University of Missouri-Rolla (Project Code R03MO5-1)
February 19, 2004
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TABLE OF CONTENTS
A. INTRODUCTION..................................................................................................... 1 A.1 GENERAL DESCRIPTION ................................................................................................ 1 A.2 OBJECTIVES ...................................................................................................................... 2 A.3 ASSUMPTIONS .................................................................................................................. 3
B. STRUCTURAL ANALYSIS.................................................................................... 4 B.1 LOAD COMBINATIONS ................................................................................................... 4 B.2 DESIGN TRUCK AND LOAD LANES ............................................................................. 5 B.3 SLAB ANALYSIS ............................................................................................................... 6
B.3.1 Bridge Analysis ................................................................................................. 7 B.3.1.1 Dead Load Analysis ............................................................................................... 7 B.3.1.2 Live Load Analysis ................................................................................................. 7
B.3.1.2.1 Design Truck Load Analysis (HS20-44) ...................................................................................... 7 B.3.1.2.2 Load Lane Analysis...................................................................................................................... 8
B.3.2 Summary of Results .......................................................................................... 9
C. DESIGN ................................................................................................................... 10 C.1 ASSUMPTIONS ................................................................................................................ 10 C.2 SLAB DESIGN .................................................................................................................. 11
C.2.1 Assumptions .................................................................................................... 11 C.2.2 Positive Moment Strengthening ...................................................................... 11 C.2.3 Negative Moment Check................................................................................. 12 C.2.4 Shear Check..................................................................................................... 12
D. MF-FRP DESIGN................................................................................................... 13 D.1 ASSUMPTIONS ................................................................................................................ 13 D.2 STRENGTHENING DESIGN........................................................................................... 16
D.2.1 Load Analysis ................................................................................................. 16 D.2.2 Geometrical Assumptions ............................................................................... 18 D.2.3 Flexural Strengthening.................................................................................... 18
E. LOAD RATING ...................................................................................................... 21
REFERENCES................................................................................................................ 24
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LIST OF TABLES
Table 1 – Slab Bending Moments and Shear Forces per Unit Strip ................................... 9 Table 2 – Material Properties............................................................................................ 10 Table 3 – Slab Geometrical Properties and Internal Steel Reinforcement ....................... 11 Table 4 – Slab Positive Moment Capacity........................................................................ 11 Table 5 – Slab Shear Capacity .......................................................................................... 13 Table 6 – Material Properties............................................................................................ 14 Table 7 – Parameters of the Design Section for the MF-FRP Strengthening................... 18 Table 8 – Strengthening Summary ................................................................................... 19 Table 9 - Maximum Shear and Moment due to Live Load............................................... 22 Table 10 - Rating Factor for the Slab Strengthened with CFRP Laminates (Bending
Moment).................................................................................................................... 22 Table 11 - Rating Factor for the Slab Strengthened with MF-FRP (Bending Moment) .. 22 Table 12 - Rating Factor for the Slab (Shear)................................................................... 23
LIST OF FIGURES
Figure 1 – Bridge Y-0298................................................................................................... 1 Figure 2 – Superstructure of the Bridge.............................................................................. 1 Figure 3 – Plan View of the Bridge .................................................................................... 4 Figure 4 – Truck Load and Truck Lanes ............................................................................ 5 Figure 5 – Loading Conditions ........................................................................................... 6 Figure 6 – Loading Conditions for Slab Analysis .............................................................. 6 Figure 7 – Design Truck Load Analysis ............................................................................. 7 Figure 8 – Load Lane Analysis........................................................................................... 8 Figure 9 – Slab Internal Reinforcement............................................................................ 11 Figure 10 – Strengthening of the Slab Deck..................................................................... 12 Figure 11 – Evaluation of Moment at a Section where V is max ..................................... 13 Figure 12 – Details of the Connection Concrete-FRP ...................................................... 15 Figure 13 – Slab Load Condition...................................................................................... 17 Figure 14 – Slab Longitudinal Bending Moment Distribution for One Span of the Bridge
................................................................................................................................... 18 Figure 15 – MF-FRP Strengthening of the Deck.............................................................. 19 Figure 16 – Pattern of the Bolts ........................................................................................ 20
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A. INTRODUCTION
A.1 General Description In the following report, the analysis and design procedures used in the upgrade of the
load-posted Bridge Y-0298, located in Pulaski County, MO are summarized. Figure 1 shows a picture of the bridge. The total bridge length is 30 ft and the total width of the deck is 24.0 ft.
Figure 1 – Bridge Y-0298
The structure has two spans each of which consists of a solid reinforced concrete slab
7 in. thick as depicted in Figure 2. Each span is considered simply supported on rein-forced concrete vertical walls. Both spans are 15.0 ft long.
Figure 2 – Superstructure of the Bridge
An inspection of this bridge revealed major concrete deterioration on the underside of the slab which would prevent the application of any bonded strengthening system in some areas. Due to the high cost of repairing the concrete, a system consisting of me-chanically-fastened (MF) FRP laminates was used to strengthen these areas. The analysis and design of this system are presented in this report.
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A.2 Objectives The objective of this document is to provide an analysis of the structure and the de-sign calculations for its strengthening using externally bonded fiber-reinforced polymer (FRP) systems. The FRP systems consist of FRP laminates to be installed by manual lay-up and pre-cured FRP laminates which are mechanically fastened.
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A.3 Assumptions The following assumptions are made: a) Nominal material properties for steel and concrete. At the onset of the project, exist-
ing material properties were validated in the field by extracting two concrete cores and steel bar sample. The resulting values are: f`c=4,000 psi, and fy=40 ksi.
b) Load configurations and analysis are consistent with AASHTO1 Specifications; and c) Design of the strengthening system is in compliance with ACI 440.2R-022 where ap-
plicable. Contrary to all other bridges considered for this project, blue prints for this structure were not available from MoDOT.
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B. STRUCTURAL ANALYSIS
B.1 Load Combinations Figure 3 shows a sketch of the bridge.
15'-0" 15'-0"
10'-6
"10
'-6"L
L
Figure 3 – Plan View of the Bridge
Ultimate values of bending moment and shear force are obtained by multiplying their
nominal values by the dead and live load factors and by the impact factor according to AASHTO Specifications as shown in Eq. (1): [ ]1.3 1.67( )u d D L Iω β= + + (1) where D is the dead load, L is the live load, βd=1.0 as per AASHTO Table 3.22.1A, and I is the live load impact calculated as follows:
50 30%125
IL
= ≤+
(2)
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and L=10.5 ft represents the span length from center-to-center of support. The impact factor can be assumed equal to 1.30 for both spans. It is to be noted that because of the 45 degree skew of the bridge, the effective center-to-center length of the span can be ex-pressed as L·cosα=15(cos45˚)=10.5 ft.
B.2 Design Truck and Load Lanes The analysis of the bridge is carried out for an HS20-44 truck load (which represents the AASHTO design truck load) having geometrical characteristics and weight properties as shown in Figure 4. There is no need to consider the 3S2 truck load for this bridge, since it will never govern the design.
According to AASHTO Section 3.6.3, roadway widths between 20.0 and 24.0 ft shall have two design lanes, each equal to one-half of the roadway width. However, the num-ber of design lanes will not affect the design since the unit-strip method will be used.
Two loading conditions are therefore required to be checked as laid out in Figure 5. The HS20-44 design truck load (Figure 5a) has a front axle load of 8.0 kip, second axle load, located 14.0 ft behind the drive axle, of 32.0 kip, and rear axle load also of 32.0 kip. The rear axle load is positioned at a variable distance, ranging between 14.0 and 30.0 ft. Given the specific bridge geometry, the worst loading scenario is obtained for the minimum spacing of 14.0 ft between the two rear axles. The load lane condition consists of a load of 640 lb per linear foot, uniformly distrib-uted in the longitudinal direction with a single concentrated load so placed on the span as to produce maximum stress. The concentrated load and uniform load is considered to be uniformly distributed over a 10’-0” width on a line normal to the centerline of the lane. The intensity of the concentrated load is represented in Figure 5b) for both bending mo-ment and shear force calculations. This load shall be placed in such positions as to pro-duce the maximum stress in the member.
24'-0"27'-2"
Clear Rodway Width
Parapet
1-ft
Cle
aran
ce
Parapet
Variable
HS20-44
14'-0"
8 K
14'-30'Spacing
32 K
6'-0
"
32 K
Figure 4 – Truck Load and Truck Lanes
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TRANSVERSELY DISTRIBUTED26.0 KIP FOR SHEAR18.0 KIP FOR MOMENT
0.64 KIP/FT OVER A 10 FT WIDTH
14'-0" TO 30'-0"
32.0 KIP8.0 KIP
14'-0"
32.0 KIP
a) Design Truck (HS20-44)
b) Load Lane Figure 5 – Loading Conditions
B.3 Slab Analysis The deck slab is considered to be a one-way slab system due to its large aspect ratio (panel length divided by the panel width). The effect of the skew will be neglected in this analysis.
The width of the slab strip to be used in the calculation is provided by AASHTO (Section 3.24.3.2) as follows (see Figure 6): 4 0.06 4 0.06(10.5 ) 4.6B L ft ft= + = + = (3) where L (ft) represents the length of the slab measured between supports’ centerline as previously defined in Section B.1.
6'-0"
4'-714" B
2'-358"
3'-0"
P=16 kipwheel load
Figure 6 – Loading Conditions for Slab Analysis
Figure 6 clearly demonstrates that there is no interference between two wheel loads. The bridge deck can therefore be analyzed as subjected to the concentrated load of the wheel only. This load will be placed in the most unfavorable position to maximize both moment and shear stresses.
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B.3.1 Bridge Analysis The bridge analysis is subdivided in: a) dead load analysis and b) live load analysis. It will be discussed in the next two sections. B.3.1.1 Dead Load Analysis The load due to both slab and asphalt layer self-weight can be expressed as follows: d s c a abh bhω γ γ= + (4) where b represents the slab unit strip (12 in.), hs and ha are the slab and asphalt layer thickness (7 and 8 in., respectively), and γc and γa represent the concrete and asphalt weight per cubic foot (150 and 108 pcf, respectively). From Eq. (4) one can get ωd=0.16 kip/ft. Maximum bending moment and shear force can be written as follows:
2 2(0.16)(10.5 ) 2.2 /8 8
(0.16)(10.5) 0.8 /2 2
dD
dD
LM k ft ft
LV kip ft
ω
ω
= = = −
= = = (5)
B.3.1.2 Live Load Analysis The live load analysis is subdivided in two sections; the first one is related to the de-sign truck load analysis (HS20-44), and the second one to the load lane analysis.
B.3.1.2.1 Design Truck Load Analysis (HS20-44) Figure 7 shows the bridge loading condition used to maximize moment (I) and shear (II), respectively.
II)
I)
d
P=16 kip
P=16 kipL
L-d
A
A
A
A
Section A-A
B
AsphaltLayerSlab
P
Figure 7 – Design Truck Load Analysis
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Moment and shear can be expressed as follows (per width “B”):
max
max
(16)(10.5) 424 4
10.5 7 /1216 15.110.5
PLM k ft
L dV P kipL
= = = −
− −= = =
(6)
Moment and shear to be used in the design can be found by dividing the previous val-
ues by the effective slab width, B, defined in Eq. (7) as follows:
max
max
42 9.1 /4.6
15.1 3.3 /4.6
L
L
MM k ft ftB
VV kip ftB
= = = −
= = = (7)
B.3.1.2.2 Load Lane Analysis Figure 8 shows the bridge loading condition used to maximize moment (I) and shear
(II), respectively. It is to be noted that both uniform and concentrated load have been di-vided by 10 ft which represents the transversal extension of the load lane. Moment and shear, already expressed per unit width, can therefore be written as follows:
2 2(0.064)(10.5) (1.8)(10.5) 5.6 /8 4 8 4
(0.064)(10.5) (10.5 7 /12)2.6 2.8 /2 2 10.5
ML
L V
P LqLM k ft ft
qL L dV P kip ftL
= + = + = −
− −= + = + =
(8)
II)
I)
d
P=18/10 kip/ft
P=26/10 kip/ftL/2
L-d
M
L/2
V
ωd
ωd
=0.64/10 kip/ft
=0.64/10 kip/ft
A
A
A
Section A-A
1'-0"
AsphaltLayerSlab
A
ft
Figure 8 – Load Lane Analysis
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B.3.2 Summary of Results Table 1 summarizes the results in terms of both unfactored and factored bending
moments and shear forces. Ultimate (factored) values are obtained by applying Eq. (1).
Table 1 – Slab Bending Moments and Shear Forces per Unit Strip
Load Analysis Mu
(k-ft/ft) Vu
(kip/ft)
Dead - 2.2 0.8 HS20-44 9.1 3.3 Live Lane Load 5.6 2.8 HS20-44 28.5 10.4 Total
Factored Lane Load 18.7 8.9
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C. DESIGN
Section C of this report details the design of the standard CFRP strengthening. The design of the mechanically fastened FRP is detailed later in Section D.
C.1 Assumptions Strengthening design is carried out according to the principles of ACI 440.2R-02
(ACI 440 in the following). The properties of concrete, steel, and FRP laminates used in the design are summarized in Table 2 including other FRP systems that may not be rele-vant to this bridge. The reported FRP properties are guaranteed values. The FRP sys-tems used in the design of this bridge are highlighted in Table 2, The φ factors used to convert nominal values to design capacities are obtained as specified in AASHTO for the as-built and from ACI 440 for the strengthened members.
Table 2 – Material Properties
FRP Type System Properties Concrete f`c (psi)
Steel fy (ksi) NSM
System Manual Lay-up
Pre-cured Laminate
Tensile Strengthf*
fu (ksi)
Modulus Ef (ksi) FRP
Size or Thickness tf (in)
Type-1a - - 300 19,000 0.079x0.63 Type-1b - - 300 19,000 4/8 bar size - Type-2 - 550 33,000 0.0065 4,000 40
- - Type-3 360 30,000 0.055 Material properties of the composite reinforcement reported by manufacturers, such as the ultimate tensile strength, typically do not consider long-term exposure to environ-mental conditions, and should be considered as initial properties. Composite properties to be used in all design equations are given as follows (ACI 440):
*
*
fu E fu
fu E fu
f C f
Cε ε
=
= (9)
where ffu and εfu are the FRP design tensile strength and ultimate strain considering the environmental reduction factor (CE) as given in Table 8.1 (ACI 440), and f*
fu and ε*fu rep-
resent the FRP guaranteed tensile strength and ultimate strain as reported by the manufac-turer (see Table 2). The FRP design modulus of elasticity is the average value as re-ported by the manufacturer. FRP properties in the case of NSM system relate to the gross section whereas in the case of manual lay-up relate to net fiber area.
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C.2 Slab Design
C.2.1 Assumptions Slab geometrical properties and the assumed internal steel flexural reinforcement are summarized in Table 3 and Figure 9.
Table 3 – Slab Geometrical Properties and Internal Steel Reinforcement
Span Slab Thickness hs (in)
Slab Width b (in)
Tensile Steel Area As (in2/ft)
Effective Depth d (in)
Compression Steel Area A’s (in2/ft)
Effective Depth d’ (in)
Both Spans 7 12 #8@6”=1.58 5.75 #6@6”=0.88 1.75
A =#8@6"=1.58 in /fts2
A =#6@6"=0.88 in /fts2'
134"d'
dh 534" 7"
Figure 9 – Slab Internal Reinforcement
C.2.2 Positive Moment Strengthening The strengthening recommendations summarized in Table 4 are suggested for the case of mid-span location (maximum positive moment) for both spans.
Table 4 – Slab Positive Moment Capacity
FRP Type Span Strengthening Scheme φMn
(k-ft/ft) Mu (k-ft/ft)
No FRP 23.5 Type-2 All 2 Plies 8” wide @12” ocs 28.9 28.5
Figure 10 shows the strengthening scheme for the deck of the bridge. The portions of
the figure which show no Type-2 FRP will be strengthened with Type-6 FRP. The de-sign of this system is addressed in Section D.
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8'-0"
@12" ocs8" wide2 Plies
Figure 10 – Strengthening of the Slab Deck
C.2.3 Negative Moment Check The slab has been assumed to be simply supported. No negative moment exists.
C.2.4 Shear Check The concrete contribution to the shear capacity has been assumed to be based on Eq. (11-5) of ACI 318-993 as follows:
' '1.9 2500 3.5uc c w w c w
u
V dV f b d f b dM
ρ⎛ ⎞
= + ≤⎜ ⎟⎝ ⎠
(10)
where ρw=As/bwd, Vu and Mu represent ultimate bending moment and shear force acting at the same cross-section, respectively, and bw and d are width and effective depth of the girder.
Shear strengthening of slab-deck systems is not a viable solution. The as-built shear capacity is summarized in Table 5. No shear strengthening will be provided on the slab since the values of the as-built shear capacity is acceptable.
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Table 5 – Slab Shear Capacity
Span φVn (kip/ft)
Vu (kip/ft)
All 10.4 10.4
The ultimate moment acting at the same cross-section where the shear is checked has been calculated as follows (see Figure 11):
max@
(15.1)(7 /12) 1.9 /4.6VM k ft ft= = − (11)
M@ Vmax
d=7" Section ofMaximum Shear
dL-d
=1.9 k-ft/ft
P=16 kip
Figure 11 – Evaluation of Moment at a Section where V is max
D. MF-FRP DESIGN Section D of this document pertains to the design of mechanically fastened FRP
strips. The analysis and design procedures which follow differ from what has been shown in the earlier portions of this document.
D.1 Assumptions Mechanically-Fastened FRP laminate design is carried out according to the principles
of ACI 440.2R-02 (ACI 440 in the following). The properties of concrete, steel and FRP laminates used in the design are summarized in Table 6. The φ factors used to convert nominal values to design capacities are obtained as specified in AASHTO (2002) for the as-built and from ACI 440 for the strengthened members.
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Table 6 – Material Properties
Concrete Steel FRP - SAFSTRIP Compressive
Strength '
cf [ ]psi
Yield Strength
yf [ ]ksi
Modulus of Elasticity
sE [ ]ksi
Tensile Strength
*fuf
[ ]ksi
Modulus of Elasticity
fE [ ]ksi
Thickness ft
[ ]in
Width fw
[ ]in 4000 40 29000 85.4 8800 0.125 4.00
The maximum strength that the MF-FRP strengthening can develop depends on the
capacity of the bolt-strip connection and, therefore, on the number of fasteners used. In order to mechanically fasten the FRP laminate to the concrete, the optimal solution
in terms of mechanical behavior of the connection was found as a result of an experimen-tal program conducted at UMR. The chosen fastening system consists of:
Bolt with ribs under the head (diameter 3/8 in. and total length 2.75 in. - Figure 12). The shear capacity Tc of the bolt embedded in the concrete depends upon the embedment depth hb and the strength of the concrete f’c. The shear strength of the bolt, Tb, becomes equal to 5.0 kip when f’c = 4000 psi and hb = 2.5 in;
Steel washer (inner diameter 7/16 in., outer diameter 1 in. and thickness 1/16 in. - Figure 12);
Epoxy between the washer and the FRP and throughout the hole on the FRP; Epoxy at the interface FRP-concrete.
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116"1"
Steel Washer
Wedge-Bolt
Surfaces Soaked by Epoxy
Concrete Surface
34" 3
4"
38"
212"
716"
Steel Washer
Wedge-Bolt
Epoxy
Figure 12 – Details of the Connection Concrete-FRP
Bond tests on the connection FRP-fastener showed that at the ultimate conditions, the
applied load is uniformly distributed between all the fasteners. In addition, it was ob-served that for concrete having an f’c = 4000 psi, the failure mode of the connection is due to the bearing of the FRP. The experimental ultimate load supported by this connec-tion was found to be 4.5 kip. For design purposes, a safety factor equal to 1.8 was as-sumed and therefore the design capacity of the connection is Rb=2.5 kip.
The presence of the epoxy at the FRP-concrete interface was not taken into account while computing the ultimate capacity of the bolt-FRP connection. In fact, it was as-sumed that at the ultimate conditions, when the bonding is lost, the entire load is sup-ported by the bolts. This provides a very conservative approach.
Under these assumptions, the minimum number of fasteners nb,min to anchor each FRP strip so that failure of the FRP controls, is given by:
,minFRP
bb
FnR
= (12)
where FFRP is the maximum load that the FRP strip experiences at ultimate conditions. Assuming CE = 0.85 (i.e., carbon plate exposed in exterior non aggressive ambient) and
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taking into account the net area of the strip (i.e., subtraction of the area lost to insert the bolt), from Eq. (12) the minimum number of bolts to reach the ultimate capacity of the FRP strip is 26. If fewer bolts are used, the failure would occur at the connection (i.e. bearing of the FRP strip).
D.2 Strengthening Design
D.2.1 Load Analysis The continuity of the deck over the girders was conservatively neglected. This led to
model the deck as a slab simply supported between two supports. Figure 13 shows the worst loading condition for the slab side to be strengthened by
MF-FRP. The design value was determined from the truck design condition when the rear axle of the truck is in the middle of the span. The load of the wheel was spread over a surface 20 '' 10 ''× as prescribed in the AASHTO (2002) Section 4.3.30. A commercial Fi-nite Elements Program (SAP 2000) was used to analyze the structure. The ultimate mo-ment found from this analysis was (See Figure 14):
12.45 ukip ftM
ft⋅
= .
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15'-0" 15'-0"
10'-6
"L 10
'-6"L
4'-0"
TRUCK 1HS20-44
TRUCK 2HS20-44
8 kip4 kip
Figure 13 – Slab Load Condition
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Figure 14 – Slab Longitudinal Bending Moment Distribution for One Span of the Bridge
D.2.2 Geometrical Assumptions The geometrical properties and the internal steel flexural reinforcement of the design
cross section are summarized in Table 7. Due to the corrosion phenomena of the bars at both sides of the bridge, for the computation of the flexural reinforcement the area of steel was assumed being half of the existing.
Table 7 – Parameters of the Design Section for the MF-FRP Strengthening
Slab Thickness
Slab Width Slab Longitudinal Tensile Steel Area
Effective Depth
H
[ ]in
B
[ ]in , .s slab longA
[ ]2in
.slab longd
[ ]in
7.0 12 0.555 345
D.2.3 Flexural Strengthening Table 8 summarizes the strengthening recommendations for the damaged sides of the
superstructure of the bridge. Figure 15 details the longitudinal flexural strengthening. It
kip ftft
⎡ ⎤⋅⎢ ⎥⎣ ⎦
( ) HS20-441 22.58 wheel LP I P kipγβ= + =
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can be observed that the strips were placed parallel to the guardrail. This solution was adopted for two reasons:
1. The FEM analysis showed that the stresses are higher in that direction. Therefore putting the reinforcement in the direction were the stresses are maximum would have optimized the amount of strengthening.
2. This solution allows for a better anchorage of the strip. The pattern of the bolts for longitudinal and transversal reinforcement is showed in
Figure 16.
Table 8 – Strengthening Summary
Design Capacity nMφ
[ ]ftkip ⋅
Moment Demand
uM [ ]ftkip ⋅
Section Strengthening Scheme
Un-strengthened Strengthened
Longitudinal Direction
Side A: 2 Plates for Each Span Side B: 4 Plates for Each Span
7.36 12.53 12.45
a) Value corresponding to a 12" wide stripe of the deck
SIDE BSIDE A
Bonded FRP2 FRP Plates @ 6''4'' wide11' 0'' longFastened with 12 Bolts
2 FRP Plates @ 6''4'' wide11' 0'' longFastened with 12 Bolts
Guardrail
Guardrail
Abutment 1
Abutment 2
Abutment 3
Figure 15 – MF-FRP Strengthening of the Deck
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2" 10"
2"
5'-6"
CLDeckAbutment
FRP Design Strip(12 Bolts)
1'-10"
1' 6"1'1' 1'
Figure 16 – Pattern of the Bolts
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E. LOAD RATING
Bridge load rating calculations provide a basis for determining the safe load carrying capacity of a bridge. According to MoDOT, anytime a bridge is built, rehabilitated, or reevaluated for any reason, inventory and operating ratings are required using the Load Factor rating. All bridges should be rated at two load levels, the maximum load level called the Operating Rating and a lower load level called the Inventory Rating. The Op-erating Rating is the maximum permissible load that should be allowed on the bridge. Exceeding this level could damage the bridge. The Inventory Rating is the load level the bridge can carry on a daily basis without damaging the bridge.
In Missouri, for the Load Factor Method the Operating Rating is based on the appro-priate ultimate capacity using current AASHTO specifications (AASHTO, 1996). The Inventory Rating is taken as 86% of the Operating Rating.
The vehicle used for the live load calculations in the Load Factor Method is the HS20 truck. If the stress levels produced by this vehicle configuration are exceeded, load post-ing may be required.
The tables below show the Rating Factor and Load Rating for this bridge. The method for determining the rating factor is that outlined by AASHTO in the Manual for Condition Evaluation of Bridges (AASHTO, 1994). Equation (13) was used:
( )
1
2 1C A DRF
A L I−
=+
(13)
where: RF is the Rating Factor, C is the capacity of the member, D is the dead load effect on the member, L is the live load effect on the member, I is the impact factor to be used with the live load effect, A1 is the factor for dead loads, and A2 is the factor for live loads. Since the load factor method is being used, A1 is taken as 1.3 and A2 varies depending on the desired rating level. For Inventory rating, A2 = 2.17, and for Operating Rating, A2 = 1.3.
To determine the rating (RT) of the bridge Equation (14) was used: ( )RT RF W= (14)
In the above equation, W is the weight of the nominal truck used to determine the live load effect.
For Bridge Y-0298, the Load Rating was calculated for a number of different trucks, HS20, H20, 3S2, and MO5. The different ratings are used for different purposes by the bridge owner. For each of the different loading conditions, the maximum shear and maximum moment were calculated. An impact factor is also taken into account for load rating. This value is 30% for Bridge Y-0298. The shear and moment values for the deck are shown in below in Table 9.
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Table 9 - Maximum Shear and Moment due to Live Load
Truck Maximum Shear (kip)
Maximum Moment
(k-ft)
Maximum Shear with
Impact (kip)
Maximum Moment
with Impact (k-ft)
HS20 3.4 8.7 4.5 11.3 MO5 3.4 8.8 4.4 11.4 H20 2.6 6.0 3.4 7.8 3S2 2.8 6.0 3.6 7.8
Table 10 and Table 11 give the results of the Load Rating pertaining to bending moments for the deck reinforced with CFRP laminates and MF-FRP laminates respectively, while Table 12 shows the results for shear.
Table 10 - Rating Factor for the Slab Strengthened with CFRP Laminates (Bending Mo-ment)
Truck Rating Factor (RF)
Rating (RT) (Tons)
Rating Type
HS20 1.780 64.1 Operating HS20 1.066 38.4 Inventory MO5 1.759 63.3 Operating H20 2.198 44.0 Posting 3S2 2.198 80.5 Posting
* All Units Expressed in English System
Table 11 - Rating Factor for the Slab Strengthened with MF-FRP (Bending Moment)
Truck Rating Factor (RF)
Rating (RT) (Tons)
Rating Type
HS20 1.683 60.6 Operating HS20 1.008 36.3 Inventory MO5 3.365 121.1 Operating H20 2.894 57.9 Posting 3S2 2.894 106.0 Posting
* All Units Expressed in English System
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Table 12 - Rating Factor for the Slab (Shear)
Truck Rating Factor (RF)
Rating (RT) (Tons)
Rating Type
HS20 1.618 58.3 Operating HS20 0.969 34.9 Inventory MO5 1.655 60.7 Operating H20 1.841 36.8 Posting 3S2 1.721 63.1 Posting
* All Units Expressed in English System Since the factors RF with which posting is determined are greater than 1 the bridge does not need to be load posted. In addition, from Table 12 the maximum operating and inven-tory load can be found as 58.3 T and 34.9 T respectively.
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REFERENCES 1 AASHTO, 2002: “Standard Specifications for Highway Bridges”, 17th Edition, Pub-
lished by the American Association of State Highway and Transportation Officials, Washington D.C.
2ACI 440.2R-02, 2002: “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures,” Published by the American Concrete Institute, Farmington Hills, MI.
3 ACI 318-99, 1999: “Building Code Requirements for Structural Concrete and Commen-tary (318R-99),” Published by the American Concrete Institute, Farmington Hills, MI.
4 AASHTO (1996): “LRFD Bridge Design Specifications”, Second Edition, Published by the American Association of State Highway and Transportation Officials, Washing-ton D.C.
5 Bank, L. C., Lamanna A. J., Ray, J. C., and Velásquez G. I. (2002): “Rapid Strengthen-ing of Reinforced Concrete Beams with Mechanically Fastened, Fiber-reinforced Polymeric Composite Materials”, US Army Corps of Engineers, Washington D.C.
6 Bank, L. C., Borowicz D. T., Lamanna A. J., Ray J. C., and Velásquez G. I. (2002): “Rapid Strengthening of Full-sized Concrete Beams with Powder-actuated Fasten-ing Systems and Fiber-Reinforced Polymer (FRP) Composite Materials”, US Army Corps of Engineers, Washington D.C.
