Chapter 4 Results of the Test Program

Statistical Analysis Method

A median based statistical approach termed the multi-response permutation procedure (MRPP) was used for statistical analysis of the withdrawal and slip test results.  The MRPP was developed by Pellicane et al, (Pellicane et al 1993).  It uses a permutation procedure as a statistical tool, which has been demonstrated by Pellicane et al (Pellicane et al 1984) to be useful for wood related applications.   It is a non-parametric method based on permutations and Euclidean distance functions.   The MRPP does not require assumptions to be made related to the fundamental underlying data distribution

Withdrawal Test Results

Withdrawal test results were used for three purposes: 1) to determine if less expensive threaded rod could be used in withdrawal tests instead of the Hilti dowel, 2) to select an adhesive for use in constructing the slip and layered beam specimens, and 3) as a quality control check on the setting of the adhesive.

Comparison of the Hilti Dowel and the Threaded Rod

Connector resistance under tensile load was examined at a common embedment depth into the wood layer.  Results for the Hi - 2.5 and Hi - 2.5a specimens (see Table 3.1) were compared.  Comparative tests were done for each connector. All specimens had an embedment depth of 2.5 inches. The adhesive used was the Hilti (HIT HY 150) product.  The mean, standard deviation, and the coefficient of variation for the failure loads and the displacements at failure were calculated for two groups of 10 replications.  Tables 4.1 and 4.2 summarize the results.

Table 4.1 - Failure loads for Hilti dowel and threaded rod specimens

Table 4.2 - Connector displacements at failure for Hilti dowel and threaded rod specimens

The mean failure load for the Hilti dowels and threaded rods were 1,150 pounds and 1,170 pounds, respectively.  The corresponding coefficients of variation for the failure loads were 20.2 percent and 15.7 percent, respectively. Ranges and mean values of failure loads were similar for each connector.  The corresponding ranges and mean values of displacement at failure varied greatly. The mean values for the Hilti dowel and threaded rod were 0.409 in. and 0.242 in., respectively.  For both connector types, the coefficient of variation for the failure displacements was more than twice that of the failure loads.

It was decided the less expensive, readily available threaded rod would be used in place of the Hilti dowel for subsequent withdrawal tests.

Comparison of Adhesive Test Results

The objective of the subsequent withdrawal tests was to compare the load capacities of the two adhesives under tensile loads. The intent was to determine which, if any, of two adhesives available in the U.S. would be used in the beam and deck tests.  Observed failure load results and the failure displacements are tabulated in Table 4.3 and Table 4.4, respectively.

Table 4.3 - Withdrawal test results, failure loads

Table 4.4 - Withdrawal test results, connector displacements at failure

At equivalent connector depths, the Borden adhesive specimens had considerably higher failure loads compared to the Hilti adhesive specimens.  At a depth of 2.0 inches the Borden product had a mean failure load 3,350 pounds compared to 1,200 pounds for the Hilti adhesive.  At a depth of 2.5 inches, the values were 4,220 pounds and 1,170 pounds, respectively.  The coefficient of variation values for the six groups ranged from 15.7 percent to 29.3 percent for the Hilti adhesive compared to a range of 10.0 percent to 11.4 percent for the Borden adhesive.  It is evident the Borden adhesive had more than twice the capacity of the Hilti adhesive and much less variability.

For the Borden adhesive specimens there was increased total load capacity with an increase in depth.  Table 4.3 indicates that the failure loads for the Borden specimens increase significantly with an increase in embedment depth.  Specimen group Re-1.5 had a mean failure load of 2,420 pounds compared to 4,220 pounds for the Re-2.5 specimens.  It also is observed that the displacement at failure decreased as the connector depths and failure loads increased.  The mean failure displacement was 0.210 inches for Re-1.5 group versus 0.150 inches for the Re-2.5 specimen group.

The Hilti adhesive specimens did not exhibit significant increased total load capacity for deeper embedment length.  In Table 4.3, a slight increase in connector total capacity is evident when going from the Hi-2.5 to the Hi-3.0 group.  However, a decrease in total capacity is evident when going from group Hi-2.0 to Hi-2.5.  In all six groups the coefficient of variationis extremely high for the displacements at failure, the extreme being 75.3 percent for the Borden adhesive at a depth of 2.5 inches.

The mean failure load for each specimen group was normalized (divided by the depth of embedment) to determine a connection unit capacity per inch of embedment depth.  Table 4.5 lists the results. The mean capacity per unit depth for the Borden adhesive was 1,660 lb/in adhesive compared to 520 lb/in for the Hilti adhesive.  For the Borden adhesive specimens the normalized unit capacity was essentially the same for the three embedment depths.  This was not the case for the Hilti adhesive specimens which had a normalized unit capacity approximately 27 percent larger at a depth of 2.5 inches compared to the connector depths of 2.5 and 3.0 inches.

Table 4.5 - Connection capacities per inch of connector depth

The MRPP statistical method was used to compare each of the adhesives at different depths, and both adhesives at equivalent depths. Failure load was the sole parameter.  Table 4.6, tabulates the outcome for each specimen grouping, namely the statistical probability that the specimens in an individual grouping came from the same population group. For each of the first two groupings shown in Table 4.6, the probability that all specimens in the grouping were drawn from the same population is essentially zero.  This indicates that the adhesive type had a clear influence on the connection capacities at depths of 2.0 and 2.5 inches.  For grouping three, the three embedment depths compared for the Borden adhesive, the calculated probability level indicates that the connector depth had a clear influence on the connection capacity. For the fourth grouping, Hilti adhesive specimens at three embedment depths, the results indicate a one-twelvth probability that the specimens all came from the same population group.

Table 4.6 - Statistical population groups and results

For the Borden adhesive, brittle behavior was evident in the load-displacement graphs.  For this adhesive, failures were almost exclusively crumbling of the adhesive between the wood and the steel dowel connector.  Typically the wood splintered upward where fractured resin material had gotten caught between the wood and the threads of the connector.  When the connector separated from the wood the remaining adhesive material fell away from the steel dowel, exhibiting no direct bond to the steel.  Some bonding to the wood was evident.

For the Hilti adhesive, failure occurred between the wood and the adhesive material. After initial failure, the dowel and the adhesive separated from the timber as one piece.  Both adhesives exhibited stiff behavior up to failure followed by a sudden and diminishing capacity.

A decision had to be made about which glue to adopt for the continuing work.  The failure loads were deemed more convincing than the displacement data.  The Borden adhesive had superior capacity over the Hilti adhesive. A dowel depth of 1.5 inches was used for the layered beams.  At that embedment depth the Borden adhesive had a mean capacity of 2,420 pounds.  The Hilti adhesive was not tested at a depth of 1.5 inches.  However, the mean capacity at an embedment depth of 2.0 inches was 1196 pounds.  This is far less than the Borden adhesive at a lesser embedment depth.  although it does appear that the connector type does affect the connector displacement, the evidence is not conclusive. Based on the predictable behavior of the Borden adhesive compared to the Hilti adhesive the slip test specimens and the layered beam specimens were constructed using the Borden adhesive.  The purpose of the additional withdrawal tests was to examine the increase of strength in the Hilti adhesive due to tapping the holes.  Ten specimens were prepared with a 2.5 inch depth connector into the wood tested seven days after being glued.  A comparison of results was made on the earlier tests on the Hilti adhesive and the Borden resorcinol adhesive, but without tapping the holes.  The failure load and relative displacements were the two variables for comparison.  The mean, standard deviation and the coefficient of variation for the failure loads and the failure displacements were calculated for the three specimen groups.  The results are presented in Table 4.7 and 4.8.

Table 4.7 - Withdrawal test results, failure loads

Table 4.8 - Withdrawal test results, connector displacements at failure

From Table 4.7, the mean failure loads for the Hilti glue without tapping and the Hilti adhesive with tapping were 1,171 pounds and 4,733 pounds, respectively.  The increase in failure load due to tapping the holes was about 400 percent.  The coefficient of variation values was 16 percent for the tapped specimens and 9 percent for the non-tapped specimens using the Hilti glue. At equivalent connector depth, the tapped specimens using the Hilti adhesive had a mean failure load 12 percent higher than the one obtained for the specimens glued with the Borden adhesive and the variability was similar for both groups.

The mean failure loads for each group were normalized to determine a connection capacity per inch of embedment depth.  The results are contained in Table 4.9.

Table 4.9 - Connection capacities per inch of connector depth

The results produced a mean capacity per unit depth of 468 lb/in for the Hilti specimens with no tapping, 1,688 lb/in for the Borden adhesive specimens and 1,893 lb/in for the Hilti with tapping specimens.

The MRPP statistical method was applied to compare the Hilti adhesive with a tapped hole with each of the other adhesive conditions.  Failure load was the only parameter.  Results are shown in Table 4.10.   For the first two comparisons shown in Table 4.10, the probability that all specimens were drawn from the same population is essentially zero.  This indicates that the way of bonding the steel rod influenced the connection capacities.  The result is not as conclusive when the Hilti adhesive with tapping and the Borden adhesive without are compared.  That result indicates a 1/51 probability that the specimens all come from the same population group (i.e. that the different conditions had no influence).

Table 4.10 - MRPP statistical method result

The Borden adhesive exhibited brittle behavior, which was evident by the sudden failures observed on the load-displacement graphs. For both adhesives, the load-displacements curves up to failure were almost straight lines, and no ductility of the connections was observed. This is exemplified in Figures 4.1 and 4.2. For the Hilti glue specimens with tapping, the connection showed a less stiff behavior up to failure as exemplified in Figure 4.3.

The Hilti glue used when tapping the holes had a superior capacity over the Borden adhesive and the Hilti adhesive without tapping the predrilled holes. The variation of the displacement data was also reduced. Thus, the layered deck specimens were constructed using the Hilti adhesive with tapped holes.

Slip Test Results

The primary purpose of the slip tests was to observe the interlayer force-slip deformation behavior and failure modes of the shear key/anchor connection. Another purpose was to quantify the slip behavior of various notch dimensions for future use in analytical modeling. In such modeling the concept of a slip modulus (as described in Section 2.2) is used. Figures 4.4 (a) and 4.4 (b) show the load-slip behavior for two layered slip specimens made with notch B. Results were similar to those observed by Thompson (Thompson 1974). After some irregularities at low loads, the specimens showed predominantly linear load - slip behavior until initial failure. Failure was followed with a drop off in load occurring either suddenly or gradually. The reserve resistance is attributed to the connector subsequently being subjected to interlayer shear.

Determination of the Slip Modulus

Because of the unique behavior observed for the wood-concrete specimens, an alternate method for obtaining the slip modulus had to be established. A slip modulus for each specimen was determined by fitting a linear curve to the data representing the steepest portion of the load-slip curve. Typically, this included data lying between the point when linear behavior began (after slippage at the beginning of the test had ceased) to a point where incidental nonlinear behavior ensued (normally just before failure).

Mean slip modulus values for the various notch sizes tested are presented in Table 4.11. Evidence that the slip modulus increased as the notch dimensions increased was seen in the 2x4 and 4x4 specimens when going from Notch A to Notch B. Specifically, 32 percent and 21 percent increases were observed for the 2x4 and 4x4 specimens, respectively. The trend was not as evident when going from Notch B to Notch C. For the 2x4 specimens, the mean slip modulus increased by less than 1 percent and for the 4x4 specimens a decrease of 12 percent was observed between notch B and notch C.

Table 4.11 - Slip modulus results for notch comparison

The slip modulus results combined for all notch sizes are presented in Table 4.12 for 2x4 and 4x4 specimens. The mean value of the slip modulus for the 2x4 specimens (145,600 lb/in) was 16 percent higher than that of the 4x4 specimens (125,500 lb/in). The coefficients of variation were similar for both groups (23.0 percent and 27.0 percent, respectively).

Table 4.12 - Slip modulus results for wood comparison

From Table 4.11, the slip modulus values ranged from 79,300 lb/in to 219,300 lb/in for the 2x4 specimens and from 65,700 lb/in to 174,900 lb/in for the 4x4 specimens. The slip modulus tended to be higher for the 2x4 specimens compared to the 4x4 specimens. This is expected since the bearing area of the notch connection also is larger. One would expect that the ratio of areas would be similar to the ratio of the resulting slip modulus, with all other factors being the same. The ratio of bearing area of the 4x4 relative to the 2x4 specimens is about 0.80. The ratio of mean slip moduli is 0.96 for type 4x4-A relative to type 2x4-A, 0.88 for 4x4-B/2x4-B, and 0.77 for 4x4-C/2x4-C. The average of the three ratios is 0.84, which is slightly larger than the ratio of areas, which was 0.80.

Failure Loads

The range of maximum load values observed for the various sets of slip specimens for each notch detail are listed in Tables 4.13 and 4.14. No obvious pattern is evident in the range of values shown in Table 4.12, except the coefficient of variation increased when going from notch A to notch B to notch C. However, in Table 4.14 the maximum loads are to be higher for the 2x4 specimens compared to the 4x4 specimens.

Table 4.13 - Slip test failure loads for notch comparison

Table 4.14 - Slip test failure loads for wood comparison

Two specimens, one from each wood group (2x4 and 4x4), had unusually low failure loads and likewise the same two specimens had lower slip modulus values. In a few of the 4x4 specimens, some low-level residual resistance was evident when the concrete seemed to rely on the shear resistance of the dowel after initial material failure. In general however, the specimens had minimal load carrying capacity after initial failure.

MRRP statistical analyses was performed using slip modulus and failure load as separate parameters. Table 4.15 indicates the three sample groups studied. The first two groups were used to compare the three different notch sizes for the two lumber configurations. It was hypothesized that the notch dimensions would effect the slip modulus and failure load values. The third group served to compare the two lumber configurations, namely 2x4s vs. 4x4s. It was hypothesized that the lumber configuration would influence the slip modulus and failure load values. although all specimens are included in the calculations, differences in notch size is not taken into account.

Table 4.15 - Statistical population groups and results for slip tests

The MRRP statistical analysis indicates a 1/200 probability that the 2x4 specimens, including the three notch sizes, constitute one population. This result implies that the notch dimensions influence the slip modulus and failure loads for the 2x4 specimens. For the 4x4 specimens there is a 1/2.5 probability that the 4x4 specimens all came from the same population. So notch dimension evidently was not a factor. The third result implies a 1/25 probability that all specimens (2x4 and 4x4) came from the same population.

Description of Failures

Failure characteristics evident in the slip specimen tests were divided into seven types. The characteristic types are listed below.

Often, more than one characteristic occurred simultaneously in an individual specimen. For example, if a specimen had a shear failure in the concrete across the top of the notch (Type 2) it also had generalized concrete failure in the vicinity of the notch (Type 3). In contrast, when a failure was noted by wood shear (Type 1) this was normally the only visual failure characteristics apparent. For this reason the failure types were grouped to form four failure "modes." The resulting failure modes defined by their associated failure types are given in Table 4.16.

Table 4.16 - Slip test failure modes

Fifty-three of the 60 specimens were easily classified in one of the four failure modes. For the remaining seven specimens, failure modes appeared somewhat unique and therefore were not easily classified into a failure mode. The results are given in Table 4.17.

Table 4.17 - Slip test failure mode occurrences categorized with specimen designation

Incidences of Failure Mode I was most prevalent in the 2x4 specimens existing in all three notches A, B, and C and nearly absent in the 4x4 specimens. Incidences of Failure Mode II was evident in all specimens. Incidences of Failure Modes III and IV were for the most part absent in the 2x4 specimens.
Layered Beam Test Results

Layered Beam Test Results

Load-Displacement Behavior

For each specimen a plot was made of the average point load (average of the two point loads) versus the measured mid span deflection. Typically, the beams exhibited essentially linear load-deflection behavior up to an initial sudden failure. Figures 4.5 and 4.6 are representative results for a 2x4 and 4x4 beam specimen, respectively. Erratic behavior was detected at the initiation of loading for nearly all the beam specimens. This is attributed to attempts to equate the two point loads, which were controlled separately. Typically, the irregular behavior subsided at load levels of approximately 2,000 pounds.

Types of Beam Failures Observed

The beam failures were almost exclusively characterized by an initial tensile failure of the wood layer. The tensile failure occurred in the region of the span between the two load points. In this region, bending moment is at a maximum and essentially is a constant magnitude over the length.

In two of the 2x4 layered beams the wood failed in shear between a notch and the end of the beam. Shear failure of the wood layer was not observed in any of the 4x4 specimens. Once the wood layer had failed, loads were resisted by the concrete layer and thus failure propagated to that layer. When failure was in the concrete (initially or after) the failure often included hairline cracks in the concrete that extended approximately along the plane of the inclined surface of the notch up through the concrete layer. Cracks most often occurred between a load point and the adjacent interior notch. This type of failure appeared similar to a typical shear failure in concrete. One of the 4x4 specimens had a failure best characterized as the concrete buckling upward and, thus, separating from the timber layer. The layer separation was above the south interior notch indicating that the dowel had pulled out of the adhesive connection to the wood.

Failure Loads

The average of the two point loads, at failure, was tabulated and a summary of the results is shown in Table 4.18.

Table 4.18 - Summary of failure loads for beam specimens

It is evident that the failure range and mean load results were similar for both the 2x4 and 4x4 specimens. The coefficient of variation was slightly larger for the 4x4 specimens compared to the 2x4 specimens.

Composite Action Observed

The degree of composite action developed in the beam specimens was determined using a definition given by Pault et al (Pault et al 1977, Pault 1977). The pertinent equations are as follows:

  Composite Action Available (C.A.A.) = (N- C)/N	(4.1)
  Efficiency (EFF) = (N-I)/(N-C)			(4.2)
  Composite Action Observed (C.A.O.) = (EFF)*(C.A.A.)	(4.3)

  where:
	C = theoretical (calculated) fully composite deflection,
	I = incomplete composite action (measured deflection), and
	N = theoretical (calculated) non-composite deflection.

The fully composite response was computed by ordinary beam analysis using a transformed section calculation, which assumes that the two layers were bonded throughout their entire length. For the fully non-composite response, the EI values of each layer were simply added together. The slope of the measured load-displacement data was determined by fitting a linear function to the data based on linear regression. Data between an average load of 2,000 pounds and the failure load were used for the curve fit.

Deflections were measured at mid-span and below both loading points, thus allowing for the efficiency calculation to be done for each deflection measurement location. A summary of the observed composite behavior for the specimens determined from mid-span response is given in Table 4.19.

Table 4.19 - Summary of efficiencies determined from midspan deflections

Both sets of specimens had the same mean efficiency (67.2 percent), and the median values were nearly equivalent. This is a significant improvement on the 10-20 percent efficiency observed by Chen, et al [Chen, et al 1992] in their tests of wood-concrete T-beams depending on interlayer shear transfer by mechanical connectors only.

Layered Decks Test Results

The primary objectives of the layered deck tests was to quantify the degree of composite action evident and to see how effectively the concrete slab distributed loads in the transverse direction. The transverse deflected shapes of the decks were compared before and after casting the concrete slab.

To facilitate interpretation of the results, the deflected shapes of the bare wood sections and the wood-concrete composite sections were superimposed on the same graphs for each cross-section (north, central and south) and for each position of the point loads.

Properties of Wood

The actual bending modulus of elasticity, E, of wood used in the deck was measured using an ultrasonic device (SYLVATEST ®) (Sandoz 1996). The measurement is based on the principle of the physical relationship between the speed of propagation of an ultrasonic wave in wood and the mechanical properties of the wood itself. Moisture content and temperature in the wood are also accounted for by the instrument. Parameters, such as the number of knots, the angle of the grain and the density of the wood, are wholly integrated into the ultrasonic process. Measurements were conducted prior to cutting the notches into wood. A summary of the results is given in Table 4.20 together with the bending modulus of elasticity value tabulated in the 1991 National Design Specification (Design Values for Wood Construction 1993).

Table 4.20 - Summary of modulus of elasticity results for wood deck specimens

The measured modulus of elasticity results are significantly higher than the NDS value. The listed NDS values are based on a visual grading and it is well known that the wood mechanical properties are underestimated by that method.

Properties of Concrete

Standard cylinders were cast from the ready made concrete and cured in accordance with the American Society for Testing and Materials (ASTM) procedures. ASTM Standard C192-90a (Annual Book of ASTM Standards 1995), "Standard Practice for Making and Curing Concrete Test Specimens in Laboratory" covers the preparation and curing of the concrete cylinders. Cylinders were of standard dimensions and were consolidated with a small hand held vibrator and then moist cured. ASTM C39-94 (Annual Book of ASTM Standards 1995), "Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens" recommends testing three or more cylinders at 14 and 28 days. In this study four cylinders were tested at 14 days and another four at 28 days for each concreting.

The measured compressive stresses for individual cylinders are given in Tables 4.21 and 4.22.

Table 4.21 - Individual cylinder compression test results, rectangular deck

Table 4.22 - Individual cylinder compression test results for the skewed deck

The American Concrete Institute Building Code Requirements for Structural Concrete, ACI318-95 section 8.5.1 (American Concrete Institute 1995), indicate the modulus of elasticity, E_c, is to be calculated using the following formula:

(4.4)

where:
    Wc  = unit weight of the hardened concrete,
    fc' = compressive strength of concrete at 28 days.

The average value of the strength results at 28 days was used for computation of the concrete modulus elasticity E_c. The results are given in Table 4.23.

Table 4.23 - Concrete moduli of elasticity calculation

Properties of Other Materials

Properties of the adhesive were provided by the withdrawal tests. The Hilti dowels have the following mechanical properties as available from the supplier:

    Modulus of elasticity E = 210,000 N/mm2 (30,500 ksi),
    Yield strength fy = 460 N/mm2 (65.3 ksi).

Rectangular Deck

A point load of 1,236 lb was applied to the bare wood deck and the composite wood-concrete deck to compare the displacements of the transverse sections. The superimposed, transverse displacements (north, central and south) for the four positions of the point loads are shown in Figures 4.7-4.10.

Figures 4.7 and 4.8 show that the transverse deformations of the wood deck alone are not completely uniform along the cross-section for the edge point loads I and II. Only the boards located near the load are deformed, transmitting loads from one to another by the shearing of the screws that are holding them together. For position #1 (position #2), the deformed boards, which participate in the transfer of the point load, represent only 30 percent (45 percent) of the total cross-section. Thus, 70 percent (55 percent) of the dimensional lumber was ineffective in contributing to the stiffness of the deck. In contrast, the corresponding displacements of the composite wood-concrete deck are almost linear (uniform) with only a slight concavity of the curve near the application point of the load. Essentially, the full width of the wood-concrete deck was effective in distributing the point load. Figures 4.9 and 4.10 show a similar result for load positions III and IV (located along on the longitudinal axis of the deck). A maximum displacement is achieved under the point load itself. Displacement diminishes rapidly and symmetrically away from the point load on either side of the load. Only about 60 percent of the boards contribute to load distribution In the case of the composite wood-concrete section, the displacements of the deck are almost uniform along the cross-section. Essentially, the entire width of the composite wood-concrete deck is effective in resisting load.

Skewed Deck

A point load of 577 lb was applied the bare wood deck and the composite wood-concrete decks to compare displacements of the transverse sections. The superimposed, transverse deformations (north, central and south) for the six positions of the point loads are shown in Figures 4.11-4.16.

Figures 4.11-4.13 show that the transverse deflected shapes of the bare wood deck are not uniform along its cross-section for the edge point loads I, II and III. Similar to the rectangular deck, only the boards located close to the application point of the loads are deformed. The deformed boards represent approximately 55 percent of the total cross-section. This percentage is larger than that observed for the rectangular wood deck because the bonding system of the planks was denser, increasing the shearing capacity to transfer loads from one board to another. But 45 percent of the dimension lumber was ineffective. The corresponding transverse displacements of the wood-concrete composite section are almost linear.

Figures 4.14-4.16 show the transverse deformations of the bare wood skewed deck have a "humped" shape for interior point load positions IV, V and VI as was observed for the rectangular deck. Due to the skewed angle of the deck, the curves are not symmetric and the maximum deflection is not achieved directly under the point load application. For these three positions, the entirety of the boards deflected, but the transverse distribution of the point loads was non-uniform. The deformation was concentrated in the region near the load. The corresponding transverse displacements of the composite wood-concrete deck are more uniformly distributed across the width. Essentially, all boards are effective in resisting the load.

Composite Action Observed

Pault, et al's method was chosen to assess the degree of composite behavior observed in the two layered deck specimens. The finite element method (FEM) was used to determine the theoretical deformations of the two composite decks under point loads (fully composite and fully non-composite responses). The software used, CASTEM 2000, was developed in Europe. This mechanical procedure consists in creating a domain with an infinite number of material points by using a framework of several basic domains each having its own infinite number of unknowns. The type of elements to be used in a finite element analysis depends specifically on the problem to be studied. For this study, a 3D model responded best to the problem. A single, iso-parametric cubic element with eight nodes was used to model the wood and concrete elements.

For the finite element analysis, three fundamental assumptions were used:

1. Wood is an orthotropic, linear, elastic material
2. Concrete is an isotropic, linear, elastic material
3. Wood layers composed of vertically-nailed planks act as a plate with orthotropic, elastic properties.

The modulus of elasticity of the concrete was determined for the two sets of concrete cylinders and was described earlier. The Poisson's ratio was assumed to be v = 0.25 (Merritt, et al 1996).

The average values of modulus of elasticity, measured along the longitudinal axis of the wood planks, which constitute the rectangular deck and the skewed deck, were determined using the Sylvatest®. The remaining orthotropic, elastic properties were determined using the tables established by Bodig and Goodman (Bodig, et al 1973). The moduli of elasticity measured along the transverse and radial axis, as well as the shear modulus differ between the rectangular deck and skewed deck, since these values are based on EL values which are different for each of the two decks. Poisson's ratio was assumed to remain constant. The elastic properties introduced in the model had the following values:

Since the values of RL and TL are very small for wood, they were not taken into account in the calculations.

For the fully non-composite response of the structures, the wood and concrete layers were simply added. No connection between the wood and the concrete plates was taken into account. The fully composite response was computed by blocking any slip between the two layers so that the surfaces of the two plates were completely bonded together.

Deflections of the decks for the two situations (fully composite and non-composite responses) were calculated with a point load placed in the center (positions II and IV for the rectangular deck and the skewed deck," respectively). The loads introduced correspond to point loads applied during laboratory testing. Two levels of loads were introduced for each deck. The rectangular deck was loaded with a point load at 1,236 lb and then at 3,500 lb. The skewed deck was loaded with a point load at 577 lb and then at 1,500 lb. Deflections were measured below loading points. A summary of the observed composite action is shown in Tables 4.24 and 4.25.

Table 4.24 - Composite behavior results, rectangular deck

.

Load[lb]	N[in]	I[in]	C[In]	C.A.A[%]	EFF[%]	C.A.O[%]
1,236	0.162	0.041	0.031	80.9	92.4	74.8
3,500	0.459	0.118	0.088	80.8	91.9	74.3

Table 4.25 - Composite behavior results, skewed deck

Load[lb]	N[in]	I[in]	C[in]	C.A.A[%]	EFF[%]	C.A.O[%]
577	0.104	0.038	0.022	78.8	80.5	63.4
1,500	0.265	0.095	0.057	78.5	81.7	64.1

Both specimens produced high efficiencies for both point loads. Mean efficiencies of 92.2 percent and 81.1 percent were reached for the rectangular deck and the skewed deck, respectively. These optimistic results have to be interpreted with caution. For the computation of the fully composite and fully non-composite deflections using the finite element method, the wood layers were assumed to act as plates with orthotropic linear elastic properties. If this assumption was true for the longitudinal axis of timber, the transverse elasticity of the decks was overestimated. By assuming this hypothesis, calculations of the structures were simplified, but the theoretical deflections were underestimated. A model of the wood layers that would take into account the nailing of the boards would give results closer to the reality and the efficiencies would be reduced. Further studies are in progress to refine the finite element modeling.