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DETERMINATION OF EI FOR PULTRUDED GFRP SHEET PILE PANELSYixin Shao, Cynthia Giroux and Zeid BdeirMcGill UniversityMontreal, Quebec, CanadaAbstractThe flexural rigidity, EI, plays an especially important role in fiber reinforced polymercomposite sheet pile wall design. Determination of EI is usually affected by the presence of the sheareither due to the short testing span or to the low shear modulus of composites. To reduce or eliminate theeffect of shear on the determination of flexural rigidity of composite sheet pile panels, this paper is topropose a test method that is based on Bank’s multi-span approach and Timoshenko’s beam theory.Tests were performed using three-point and four-point bending set-ups, with single composite sheet pilepanel at six different spans, and with connected two panels at eleven spans. The results showed that sixEIs determined independently from different set-ups, at different deflection points along the beam andwith different cross sections gave values that differed from each other by less than 3%. The EI sodetermined was a constant independent from the test span, the test set-up, the location of the deflectionpoint on the beam, or the number of data points used in linear regression. Apparent EIs calculated fromsingle span tests were strongly span-dependent and approached asymptotically to the value determinedby multi-span approach. It was likely that the multi-span approach yielded the highest possible flexuralrigidity that could be measured. The shear effect was therefore eliminated.IntroductionThe pultruded fibreglass reinforced polyester composite sheet pile wall is a unique and one of itskind waterfront structure. The corrosion resistance and high strength-to-weight ratio of composites arethe primary characteristics supporting this choice of material. The use of composites also features lowmaintenance, reduced life-cycle costs, dimensional stability, and near-zero environmental toxicity.Composite sheet piling products have been currently used to a limited degree, or experimentallyfor light retaining structures along the waterfront and the coastline. Because of the lack of the fieldapplication history, the height of composite sheet piling is presently limited to 2 - 5 meters.Experimental projects included renovation of decayed timber walls as well as construction of newretaining walls. Standard procedure of installation is followed without any special equipment required.The important parameter in sheet pile wall design is the flexural rigidity, EI, especially for FRPcomposite sheet pile wall. The wooden plank sheet pilings are about 50 mm 300 mm solid in crosssection. For precast concrete sheet piles, the cross sections range from 500 to 800 mm wide and 150 to250 mm thick. Steel sheet piles in the United States and Canada, have thickness about 10-13 mm. Sheetpile sections may be Z, deep arch, low arch, or straight web sections. Compared to the traditionalpilings, the composite sheet panels exhibit relatively low flexural rigidity owing to their thin walledstructure (3-5mm thick) and low Young’s modulus of panel members (E 30-40 GPa). To help guidethe proper use of composite piling products, US Army Corps of Engineers had set a number ofspecifications to classify products of different duties (Lampo, et al. 1998). The target flexural rigidities,EI, for different grades were proposed in a demonstration project for pultruded composite sheet pilings:1

Light-duty: 5x103-1x104 to 1x104-5x104 kip-sq in/ftMedium-duty: 5x104-1x105 to 1x105-5x105 kip-sq in/ftHeavy-duty: 5x105-1x106 to 1x106-5.5x106 kip-sq in/ftTo check with the specifications for a given product, it is essential to properly characterize the EIof the product. Determination of EI is usually affected by the presence of the shear. To avoid sheareffect on the EI, ASTM D-790 recommended the span to depth ratio of the beam tests be at least 16:1.For the sheet pile walls made of traditional materials, the deflections due to shear might be negligible ifthe span is large enough. However, for composite materials, in addition to short span effect, the lowshear modulus (G) could also cause the shear deflection to be significant.This paper is to report an experimental study on determination of flexural rigidity of thepultruded composite sheet pile panels with reduced or eliminated shear effect. Bank’s approach wasadopted in three-point and four-point bending tests with various spans. Bank (1989) developed a methodto simultaneously determine the section Young’s modulus and the section shear modulus by usingTimoshenko’s deflection equation. The approach was modified in this paper to directly determine the EI,instead of E alone. Results from the three-point bending tests were compared with that from four-pointbending tests to check the consistency, so were the results from single panel tests compared withconnected double panel tests. The dependence of the flexural rigidity on the test conditions was alsodiscussed.Deflection EquationEquation (1) gives the general form of Timoshenko’s beam deflection theory. BecauseTimoshenko’s theory uses superposition of the bending and shear deflections, it is limited to the linearelastic range of the material.δ C1 PL3 C 2 PL ( EI ) (kAG )(1)Here, the deflection, δ, depends on the applied load, P, the span length, L, the flexural rigidity,EI, and the shear rigidity, kAG. The constants, C1 and C2, depend on the load case and on the particularlocation along the span length that the deflection is desired. Values for C1 and C 2 are given in Table 1for the cases of three-point bending and four-point bending at one-third span. Note that the flexuralrigidity is defined as the product of the section flexural modulus, Es, and the second moment of area, I,and the shear rigidity as the product of the factored area, kA, and the section shear modulus, Gs. Thefactor, k, is the shear coefficient for composite beams in flexure.Table 1: Constants used in Timoshenko’s equationCentre-point deflectionQuarter-point deflection(δx L/2)(δx L/4)C1C2C1C23-point bending1111148476884-point bending23129112966230482

Equation (1) can be rearranged into Equation (2) which is in the form of a straight line withδPLas the dependent variable and L2 as the independent variable. Knowing the slope of the load-deflectionPcurve,, and the span, L , of each beam tested, this straight line can be plotted. The slope andδintercept of the line are inversely proportional to the flexural rigidity, EI , and the shear rigidity, kAG ,respectively. Theoretically, Equation 2 can be used to simultaneously determine the EI and kAG. Thispaper will only discuss the possibility of obtaining EI with reduced or eliminated shear effect byconducting multi-span tests with minimum number of tests.δPL C1 2 C 2L EIkAG(2)Experimental ProgramSingle Panel TestsThe composite sheet piles used in this study was designed and manufactured by PultronexCorporation (Nisku, Alberta). The corrugated profile of a single panel has a symmetric double Z crosssection. The panels are approximately 12.7cm deep, 42.5cm wide, and have a thickness varying from0.32cm to 0.47cm. The panels interlock with each other through the pin and eye connections on bothends to form a continuous wall (Figures 1 and 2). The pultruded profile consists of layers of E-glassrovings and mats in a polyester matrix.Tests were performed first with single panel in three and four-point bending tests (Figure 1) onspans of length 0.91, 1.52, 2.13, 3.05, 4.57, and 6.10 meters, (3, 5, 7, 10, 15, and 20 ft) within the linearproportional limit of the material. Tests on each span were repeated a minimum of three times. Thebeams were loaded using an MTS testing machine with an average loading rate of 0.03mm/s. Thedeflections at midpoint as well as at one quarter point along the span were measured using two linearvariable differential transducers (LVDTs) with ranges of 10cm. The data were recorded using aMeasurements Group System 5000 data acquisition system using the Strain Smart software. For fourpoint bending tests, the load points were equally spaced at one-third span. Rigid steel frames of squaretubes (25 mm x 25 mm x 2 mm thick) were constructed and positioned at the supporting and at theloading points of the beam in order to distribute the applied load and provide lateral confinement on theopen section of the sheet pile (Figure 1).Connected Double Panel TestsTo examine if the connected panels had different flexural rigidity, tests of connected doublepanels were also performed using the four point bending setup at equal space with eleven spans, 1.5, 1.8,2.1, 2.4, 3.1, 3.7, 4.3, 4.9, 5.5, 6.1, and 6.7 meters (5, 6, 7, 8, 10, 12, 14, 16, 18, 20, and 21.8 ft), andwithin the linear proportional limit. Each span test was repeated a minimum of three times. A pin and aneye were inserted at both ends of the connected double panels to simulate the connected wall as shownin Figure 2. Steel straps of size 2.5 cm (1 inch) wide and 1 mm thick were used to tie around the crosssection, in order to confine the panels and to limit the lateral displacement. The use of flexible steelstrapping at a uniform spacing of 61 cm (2 feet) was to provide a uniform restrain and prevent the panelsfrom being stiffened by rigid heavy steel frame.3

PLVDTs(a) Three-point bending set-up for single panel testsPLVDTs(b) Four-point bending set-up for both single and double panel testsFigure 1: Flexural test set-upsSteel StrappingStrain Gauge 2Strain Gauge 1LVDT 2LVDT 1Figure 2: Cross section of connected double panels4

ResultsSingle Panel TestsTypical curves within the linear proportional limit for the load versus midpoint displacement forthe six spans are given in Figure 3 for the four-point bending tests. Linear fits using the method of leastsquares were performed on the load-deflection curves in Figure 3. Four sets data of load versusdeflection were recorded in different set-ups (3-point and 4-point) and at different locations along thePbeam (midpoint and quarter point). The linear fit provided values for the slope, , for each span, L,which allowedδδPLand L2 to be calculated for use in the rearranged Timoshenko beam theory equation(Equation 2).For the deflection measured at the midpoint, the results of plotting this data withδas thePLdependent and L2 as the independent variables are plotted in Figure 4 for the four-point bending tests forall six span tests. For each span, at least three independent tests were performed and thus three sets ofδversus L2 were plotted in the same graph. As is seen, good repetition was achieved.PLSimilar data process was carried out for three-point bending tests.data on the63' spanLoad [kN]55' span47' span310' span15' span220' span100102030Midpoint Deflection [mm]Figure 3: Typical load-deflection curves at the midpointfor four-point bending linear tests (single panel, 1' 0.3048m)Linear fit was then carried out again using the least square method to determine the equation ofthe line in Figure 4. Based on Equation 2, the slope of the line was proportional to C1/EI and could beused to calculate the flexural rigidity for the case. Tests and data process were repeated for other threecases and results are presented in Table 2.5

61.0E-065.0E-070.0E 00y 8.85E-08x 1.91E-070102030240502L [m ]Fig. 4: Straight line used to determine the flexural rigidityfrom four-point bending based on the midpoint deflection (single panel)Connected Double Panel TestsSimilar procedure was followed for connected double panel tests. The typical load – deflectioncurves for eleven span tests are shown in Figure 5 for deflection measured from LVDT 1 at midpoint.Slope of each linear test was determined by averaging readings of LVDT1 and LVDT2 at midpoint.δ/PL versus L2 was then plotted in Figure 6 for eleven different spans. The linear fit of all data pointswas performed to find equation of the straight line. Based on equation 2, the slope could be used tocalculate the flexural rigidity of the connected panels. The same procedure was followed to obtain the EIfrom the quarter point load- deflection data. The final results were divided by two to obtain the rigidityfor single panel and also presented in Table 2 for comparison.91.5 m81.8 m72.1 mLoad (KN)62.4 m3.1 m3.7 m54.3 m44.9 m35.5 m216.1 m6.7 m00510152025Mid point deflection, LVDT1 (mm)Figure 5: Typical load – deflection curves at the midpointfor four-point bending linear tests (LVDT 1, connected double panels)6

2.50E-06y 4.425E-08x 1.351E-07R2 9.934E-012.00E-06-1δ/PL(N )1.50E-061.00E-065.00E-070.00E 000510152025230354045502L (m )Fig. 6: Straight line used to determine the flexural rigidityfrom four-point bending based on the midpoint deflection (connected double panels)The values obtained for the flexural rigidity agreed with each other for both three and four-pointbending tests, both midpoint and quarter-point data, and both single and double panels. The average wascalculated with a standard deviation of 2.9%. These self-checks are strongly supportive of the proposedexperimental method.Table 2: Flexural rigidity of single panel determined by multi-span test methodEI (single panel)3-point bending EI [kNm2]4-point bending EI [kNm2]EI (two connected panels)/24-point bending EI [kNm2]Average EI [kNm2]Midpointdeflection(δx L/2)Quarter-pointdeflection(δx %206 6Apparent Flexural RigidityThe apparent flexural rigidity, (EI)a, is defined as the resistance of a beam to deflection due toonly bending, neglecting shear deflections. The slopes of the load-deflection curves were used todetermine the apparent flexural rigidity based on the first term of Timoshenko’s equation. They arepresented in Figure 7 as (EI)a vs span to depth ratio. Obviously, the apparent flexural rigidity varied withthe span to depth ratio, indicating that shear did have effect on flexural rigidity obtained from singlespan tests. In both curves (mid and quarter points in Figure 7), the apparent flexural rigidity increased7

with the increase of span length. This suggested that a lager deflection contribution from the shear waspresent with shorter spans compared to longer ones. The apparent flexural rigidity asymptoticallyapproached to 400KNm2, the EI determined by two-term Timoshenko’s Equation. It was likely that EIdefined by Equation 2 was the largest possible rigidity that could be experimentally measured. SinceEquation 2 separates the bending and shear contributions to the total deflection, the effect of shear on theEI is actually eliminated. ASTM D 790 suggests a span to depth ratio of 16/1 or higher be used in beamtests to avoid shear effect. At this suggested ratio, the apparent flexural rigidity of the sheet pile panelcounted to only 44% of the maximum possible value.450000400000MidpointQuarter point3500002EI (N m Span to Depth RatioFig. 7: Apparent flexural rigidities versus span-to-depth ratio (connected panels)Sensitivity of EI to Data ProcessIt was noticed during data processing that flexural rigidity (EI) was insensitive to the span andthe number of data points used in the linear fit. The flexural rigidity of connected double panels is theresult of tests of 11 spans, from 1.5 m to 6.7 m, the last two data points shown in Figure 8 with all spans.Effort was made to examine if only a few small span tests would be enough to generate the comparableEI. The results are shown in Figure 8, in which EI is plotted versus the largest span included in linear fit.For instance, the first set of EI (from both midpoint and quarter points) was computed by linearly fittingtest data of three smallest spans: 1.5, 1.8, and 2.1 meters. The largest span included in the linear fit was2.1 m. Thus, EI was plotted against 2.1m. Subsequently, the rest used test data of four spans with thelargest 2.4m, of five spans with the largest 2.7m, and so on until the last set of all spans with the largest6.7m. It was interesting to notice that variation of EI with test span and numbers of data in linear fit wasnot significant. In the other words, by using multi-span test method, EI could be determined consistentlyeven with only three small-span tests.8

500000EI (Nm2)400000Threesmallestspans300000All spans200000100000Midpoint EIQuarter point EI0012345678Largest Span Included in Linear Fit (m)Figure 8: Sensitivity of EI on largest span included in linear fit (connected panels)Discussion and ConclusionsThe flexural rigidities were determined for the fiberglass composite sheet pile panels using amodified Bank’s multi-span approach. Values were found by performing both three and four-pointbending tests, by taking deflection measurements at the midpoint and at the quarter-points of the span, aswell as by using single panel and connected double panels. Six flexural rigidity results fromindependent tests agreed well with a standard deviation of 2.9%. The frames used for confinement didnot affect the results. It seemed proper to group EI together as section parameter for composite sheet pilewall design. The flexural rigidity determined by the proposed multi-span method was quite differentfrom that measured by the traditional single span method unless the span to depth ratio was over 60. Themulti-span method gave the largest possible EI value with eliminated shear effect. EI so determined wasa section constant independent from span length and numbers of tests, as long as minimum of three testsof different spans were performed. The average EI of the single panel was about 206 kNm2. In UScustomary units, it was corresponding to 5.47 x 104 kip-sq in/ft and the product was graded in the lowend of medium duty according to specifications set by US Army Corps of Engineers. The same producthowever could be classified as light duty if only single span tests were performed. Therefore,standardization of the test method for composite sheet pile panels is necessary to make fair comparisonfor different products. The multi-span test method is strongly recommended in this regard.9

AcknowledgmentFinancial supports from Natural Science and Engineering Research Council (NSERC) of Canadaand from Pultronex Corporation of Alberta are gratefully acknowledged.References1. Bank, L. C. (1989). “Flexural and Shear Moduli of Full-Section Fiber Reinforced Plastic (FRP)Pultruded Beams”. Journal of Testing and Evaluation, 17(1), pp. 40-45.2. Lampo, R., et al. (1998). “Development and Demonstration of FRP Composite Fender,Loadbearing, and Sheet Piling Systems”. US Army Corps of Engineers Construction EngineeringResearch Laboratory Technical Report 98/123. September 1998.3. Timoshenko, S. (1955). Strength of Materials. New York: Litton Educational Publishing, Inc. pp.170-175.10

the span is large enough. However, for composite materials, in addition to short span effect, the low shear modulus (G) could also cause the shear deflection to be significant. This paper is to report an experimental study on determination of flexural rigidity of the pultruded composite sheet pile