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1、 1 Appendix 9:Assessment of Likelihood of Damage Progression Determining the likelihood of progression of any type of damage within the FRP deck will require judgment based on damage metrics found within the FRP composites industry. Clearly, any level of damage is not desired, but the specific issue
2、 following the discovery of damage is if the severity is significant enough to cause immediate lane closure and repair, or if action can be taken at a later time so long as public safety and the integrity of the overall deck is not impacted. As discussed in previous sections the main load-carrying m
3、ember of a sandwich panel is the top facesheet which is continually subject to material stresses from direct traffic and impact loads. The top facesheet is the first structural element which will require scrutiny from any deterioration or signs of damage on the wear surface. Probably the two most si
4、gnificant damage conditions for the facesheet are: 1) the separation of layers within in the facesheet, defined as a delamination, and; 2) the more severe case of full detachment a facesheet section from the underlying core, referred to as a debonded facesheet. These damage conditions may not be dir
5、ectly detectible and identified during routine inspections unless their size is significant enough to produce a visible bulge on the top surface, or in the case of a delamination, tap testing reveals its presence. The presence of noncritical damage to surrounding structural elements, such as reflect
6、ive cracking in the wear surface and local damage to joints, may signal the initiation of delamination, so closer examination of the underlying facesheet would be necessary. If no visible signs of physical change are apparent in the facesheet, then further examination is not needed. If a physical ch
7、ange or anomaly is discovered, the inspector has to determine if the conditions indicate the presence of a delamination or debond. A methodology is proposed to measurably determine if a detected delamination will likely become worse if unattended. The procedure is based on a simplified approach take
8、n from the damage inspection of honeycomb sandwich panels in the aircraft industry. The methodology is not intended to be a rigorous examination of failure, but is an approximate approach to determine if further degradation is likely based on measurable size of delaminations. 7.4.1 DETERMINATION OF
9、DELAMINATION SIZE THRESHOLD For sandwich panels or any construction with laminated sheeting, a report by the DOT/FAA1 discusses a delamination criteria proposed by Kassapoglou that establishes a delamination threshold size at which the progressive failure of the facesheet due to local delamination b
10、uckling is likely. This threshold is the maximum delamination or debond size that can be tolerated before affecting the global behavior of the panel under local compressive forces. While this procedure was developed for continuous core type 1 “Damage Tolerance of Composite Sandwich Structures,” DOT/
11、FAA/AR-99/91 Publication, Office of Aviation Research, Washington, D.C. 20591 2 honeycomb panels under compression loading, the principal can be applied to FRP deck panels subject to bending from wheel loads that impart compression forces in the facesheet. The main laminate stresses come from wheel
12、loads. In a delaminated or debonded section, compression stresses around its boundaries may initiate damage. The delaminated area acts like a separate plate section which may buckle if the total compression stresses applied to its boundaries are large enough. Figure 7.4-1 illustrates a typical delam
13、ination within a panel span. The buckling stress is dependent on size of the area and the threshold stress for buckling decreases for larger areas. Thus if the working stress resulting from wheel load, P, or any other source reaches or exceeds the buckling stress, the delamination may occur and can
14、continue to grow progressively under repeated loads. Figure 7.4-1. Schematic of a Local Delamination. The delamination shown is analogous to a free-standing clamped plate buckling under compression forces generated by wheel loads, thus the limit buckling stress can be derived from classic plate theo
15、ry. From Young2, the buckling formula for a clamped rectangular plate of dimension a x b (see Figure 7.1-4) subject to in-plane loads is expressed as 2 Young, Warren C., “Formulas for Stress and Strain,” McGraw-Hill, 6th edition, 1989 b a Top Facesheet thickness, Tf Deck core Bottom facesheet thickn
16、ess, Tf Delamination of effective size axb Proximity wheel load Lateral facesheet stress, Span between girders, D P Effective width, W=20” B B a Section B-B Sandwich deck TD Delamination 3 2 2 1 )x( = b T E KK f 7.4-1a where: = buckling stress in units of force/area 73. 5 6 . 3 x )x( 6 . 0 += e KK(e
17、xponential curve fit of data presented in Reference 3). E = effective Youngs modulus of the face sheet v = Poissons ratio Tf = facesheet thickness b = width of the delamination a = length of the delamination x = rectangular aspect ratio, a/b, of the delamination The Youngs modulus and Poissons ratio
18、 of the facesheet are values that can be obtained from the engineering specifications of the deck. The direct application of this equation, however, is limited by the measurements an inspector must make. In practice the exact size and shape of the delamination will not be readily obvious, and in thi
19、s form the equation has little practical application to inspection. For inspection, we are interested in establishing a conservative threshold stress that can be compared with arbitrary delamination shapes, therefore it is more practical to recast this equation into a usable formula based on a measu
20、rable size. It is difficult enough for inspectors to find facesheet delaminations or debonds, but once found, determining the dimensions of the defect would be very approximate. In order to simplify the inspection task, it is reasonable to suggest a widest width measurement be measured for the entir
21、e delamination. This would assume that the affected area is a square, so therefore, a = b in equation 7.4-1a. Accordingly, x =1.0 and, KK(x) = 7.7 Therefore, 2 2 2 2 1 7 . 7 1 )( = d tE b tE xKK 7.4-1b 4 where d = maximum measurable diameter of the delamination. Figure 7.4-2. Schematic of a Local De
22、lamination with an Arbitrary Shape. Note that this is a simplified formula to determine delamination threshold sizes for purpose of inspection and is not a rigorous prediction of catastrophic failure; it is intentionally conservative so as to provide a safe lower bound estimate for inspection. Addit
23、ional assumptions for use of this formula are: The facesheet has nearly equal stiffness in the longitudinal and transverse directions. If the facesheets are known to be orthotropic, the effective modulus can be approximated by E = TL EE EL=Longitudinal modulus ET=Transverse modulus Compression stres
24、s at the mid-span drives failure Application to general delamination sizes A plot of the buckling stress versus delamination size is shown in Figure 7.4-3. Top Facesheet thickness, Tf Deck core Bottom facesheet thickness, Tf Lateral facesheet stress, Span between girders, D Sandwich deck TD d Maximu
25、m measured dimension 5 Figure 7.4-3. Facesheet Critical Stress versus Delamination Size. Note the unit of d is in feet. Figure 7.4-3 essentially shows the drop in buckling stress capacity of the facesheet versus measured size of a delamination, for the range of thicknesses of the top facesheet in FR
26、P panels. The cut-off stress is the material failure stress of the laminate itself. Typically, the compression strength of a facesheet made with quasi-isotropic lay-up (equal stiffness in the longitudinal and transverse directions) range between 27,000 to 34,000 psi. The 27,000 psi level is shown he
27、re which denotes the stress level at which material failure, as opposed to panel buckling, will occur. As shown in Figure 7.4-3 a delamination may extend to over a foot in width before theoretically failing. Accordingly, the panel will still be able to sustain repeated traffic loads as long the impa
28、rted stresses remain below the indicated buckling stresses. Establishing Residual Load Capacity How does one use the above relationship to determine residual load capacity of the FRP deck before repairs are made? Conservatively, using simple beam theory to determine the relationship between a wheel
29、load and the fiber stresses due to simple bending of a strip of deck, a critical load, P, to critical stress, , to, delamination size, a, can be established. Facesheet Buckling Stress versus Delamination Width - 10,000 20,000 30,000 40,000 50,000 60,000 0.02.04.06.08.0 Delamination width, d (ft) Del
30、amination Buckling Stress (psi) Tf = .125“ Tf = .25“ Tf = .50“ Tf = .75“ Typical fiberglass compression stress, 27,000 psi 6 Assuming a worst case moment condition based on simply supported beam equilibrium, shown in Figure 7.4-4, the normal facesheet stress is: Moment, M, and facesheet force, F M P
31、 D 4 := * F M TD := 7.4-2 where: P = Wheel load at center span M = bending moment due to center load, P D = Span between girders Td = Sandwich deck thickness F = Force resultant on facesheets W = Effective compression load width, assume to be 20” (about 2 x tire foot print) Tf = Facesheet thickness
32、The working stress in the facesheet, therefore, due to P is: w F W Tf := 7.4-3 Back substituting the above equation 7.4-3 into the moment equation 7.4-2 gives: P4 wTfTDW D := 7.4-4 Figure 7.4-4. Free Body Diagram for Simple Sandwich Beam. While not entirely correct, the free body diagram ignores con
33、centrated vertical core stiffness that may exist in webs. Tf 7 The relationship in equation 7.4-4 can now be used to determine critical load capacity of the deck to existing delamination size in conjunction with equation 7.4-1. Note that the wheel load is now a function of deck geometry and girder s
34、pacing. 7.5 CHARTS FOR ASSESSMENT RATINGS OF FRP DECKS This section contains working charts for two deck depths, 8 in. and 5 in. deep section for girder spacing from 2 ft to 10 ft. Instruction for using the charts is given in Figure 7.5-1. Figure 7.5-1 Diagram for using load capacity charts of FRP d
35、eck with delaminations Notes on use and limitations: delamination delamination size given wheel load How to Use the Charts Deck Specifications: Deck Depth Facesheet Thickness Facesheet Strength Facesheet Modulus Deck Depth Girder Spacing delamination size given wheel load Look for size on horizontal
36、 axis ? delamination size Want min capacity Residual wheel load capacity axis ? Want residual wheel load capacity given Want residual wheel load capacity given delamination sizecapacity Look for wheel capacity on vertical axis 8 1. Charts apply to fiberglass composite decks spanning between girders
37、in girder/stringer type bridge superstructure 2. Reference load capacity is AASHTO HS-20 and HS-25 3. Facesheet reference modulus of elasticity is 2.4x 106 psi which is a typical stiffness value for structural fiberglass laminates. For other values a correction factor to the wheel load capacity, P c
38、an be applied as follows: Correction for different modulus: )( )( *)( referenceE actualE chartPP = Figure 7.5-2 Deck parameters for delamination charts Consideration of Safety Factors in Residual Capacity Unlike bridge decks built with conventional materials, there is no standard safety factor appli
39、cable to FRP deck construction. Most past projects have specified independent safety factors of 3.0 or more of design loads. In view of this, the developers of this manual decided to present the assessment data with an assumed safety factor = 3.0. In determining the residual capacity of decks using
40、these charts, therefore, a safety factor can be applied by dividing the residual wheel capacity as determined from the charts and or formula by a preferred Safety Factor, Top Facesheet thickness, Tf Girder Spacing, S TD d P d Maximum delamination width (measured in any direction) Wheel load 9 orSafe
41、tyFact CapacityLoadWheel CapacityWorking= RESIDUAL CAPACITY FOR 8” FRP DECKS Mid-span Wheel Capacity versus Delamination Size 4-feet Girder Spacing 0 5,000 10,000 15,000 20,000 25,000 0.02.04.06.08.0 Delamination width, d (ft) Residual Wheel Load Capacity (lb) Tf = .125“ Tf = .25“ Tf = .50“ Tf = .75
42、“ HS-25 Load (20 kips) Deck specifications: -Fiberglass facesheet (see legend) -Facesheet modulus, E=2.4 msi -Factor of Safety = 3.0 Mid-span Wheel Capacity versus Delamination Size 6-feet Girder Spacing 0 5,000 10,000 15,000 20,000 25,000 0.02.04.06.08.0 Delamination width, d (ft) Residual Wheel Lo
43、ad Capacity (lb) Tf = .125“ Tf = .25“ Tf = .50“ Tf = .75“ HS-25 Load (20 kips) Deck specifications: -Fiberglass facesheet (see legend) -Facesheet modulus, E=2.4 msi -Factor of Safety = 3.0 10 Mid-span Wheel Capacity versus Delamination Size 8-feet Girder Spacing 0 5,000 10,000 15,000 20,000 25,000 0
44、.02.04.06.08.0 Delamination width, d (ft) Residual Wheel Load Capacity (lb) Tf = .125“ Tf = .25“ Tf = .50“ Tf = .75“ HS-25 Load (20 kips) Deck specifications: -Fiberglass facesheet (see legend) -Facesheet modulus, E=2.4 msi -Factor of Safety = 3.0 Mid-span Wheel Capacity versus Delamination Size 10-
45、feet Girder Spacing 0 5,000 10,000 15,000 20,000 25,000 0.02.04.06.08.0 Delamination width, d (ft) Residual Wheel Load Capacity (lb) Tf = .125“ Tf = .25“ Tf = .50“ Tf = .75“ HS-25 Load (20 kips) Deck specifications: -Fiberglass facesheet (see legend) -Facesheet modulus, E=2.4 msi -Factor of Safety =
46、 3.0 11 RESIDUAL CAPACITY FOR 5” FRP DECKS Mid-span Wheel Capacity versus Delamination Size 4-feet Girder Spacing 0 5,000 10,000 15,000 20,000 25,000 0.02.04.06.08.0 Delamination width, d (ft) Residual Wheel Load Capacity (lb) Tf = .125“ Tf = .25“ Tf = .50“ Tf = .75“ HS-25 Load (20 kips) Deck specif
47、ications: -Fiberglass facesheet (see legend) -Facesheet modulus, E=2.4 msi -Factor of Safety = 3.0 Mid-span Wheel Capacity versus Delamination Size 6-feet Girder Spacing 0 5,000 10,000 15,000 20,000 25,000 0.02.04.06.08.0 Delamination width, d (ft) Residual Wheel Load Capacity (lb) Tf = .125“ Tf = .
48、25“ Tf = .50“ Tf = .75“ HS-25 Load (20 kips) Deck specifications: -Fiberglass facesheet (see legend) -Facesheet modulus, E=2.4 msi -Factor of Safety = 3.0 12 Mid-span Wheel Capacity versus Delamination Size 8-feet Girder Spacing 0 5,000 10,000 15,000 20,000 25,000 0.02.04.06.08.0 Delamination width,
49、 d (ft) Residual Wheel Load Capacity (lb) Tf = .125“ Tf = .25“ Tf = .50“ Tf = .75“ HS-25 Load (20 kips) Deck specifications: -Fiberglass facesheet (see legend) -Facesheet modulus, E=2.4 msi -Factor of Safety = 3.0 Mid-span Wheel Capacity versus Delamination Size 10-feet Girder Spacing 0 5,000 10,000 15,000 20,000 25,000 0.02.04.06.08.0 Delamination width, d (ft) Residual Wheel Load Capacity (lb) Tf = .125“ Tf = .25“ Tf = .50“ Tf = .75“ HS-25 Load (20 kips) Deck specifications: -Fibergl