The tested composite girder was a 4,572 mm long I-shaped section having the cross-sectional dimensions shown in Figure 1(a). The web was reinforced with a total of six layers: these are two layers of E-glass rovings and three layers of randomly oriented E-glass Continuous Strand Mat (CSM) not 6. The top and bottom flanges were reinforced with eleven E-glass/carbon hybrid rovings combined with E-glass CSM layers for each; four layers of carbon roving, a layer of E-glass roving and six layers of E-glass CSM. The reinforcing scheme for the web and flanges are shown in Figure 1(b).

The weight fractions of the composite constituents of the web were examined following the technique described in Ye et al.[12], which was based on ASTM D 2584 [13]. Regarding the weight fractions of the constituents of the flanges, the technique described in ASTM D 3171 [14] was used. Since the carbon fibers are oxidized during a burn-out process, the technique outlined in Ye et al.[12] could not be utilized for the flange elements. Thus, digestion in nitric acid 70% solution was performed. After digestion for 168 h (1 week), the carbon and glass fibers were rinsed with acetone and water. The average weight and computed volume fractions of all constituents of the web and the flange elements are listed in Table 1.

Figure 2 shows both the member’s global coordinate system (X, Y, Z) and the member elements’ local coordinate system (x, y and z). The tensile, compressive and shear properties of the web materials of the pultruded composite I-shaped section specimen were determined according to ASTM D 3039 [15], ASTM D 3410 [16] and ASTM D 5379 [17], respectively.

The mechanical properties of the flange material of the specimen were also determined. Since the flanges do not have symmetric lay-ups, a flexural coupon test [18,19] was also carried out to obtain the extensional properties of the flange. For this flexural coupon test, twenty samples were cut from the top and bottom flanges in the x-direction. The obtained mechanical properties of the flange material are tabulated in Table 2.

E x b, σ x u b and ε x u b in the table are flexural modulus, flexural ultimate strength and strain of the flange in the x-direction, respectively. The test results from the flexural tests can be divided into two groups (Group I and Group II) according to the lay-up sequence shown in Table 2.

The material properties of the web material are summarized in Table 3. E x t, σ x u b, ε x u b and ν x y t in the table are extensional modulus, ultimate strength, ultimate strain and Poison’s ratio of the web in the x-direction, respectively. E x t, σ x u b, ε x u b and ν x y t in the table are extensional modulus, ultimate strength, ultimate strain and Poison’s ratio of the web in the y-direction, respectively. The superscript “t” indicates tensile loading direction. The compressive modulus, compressive ultimate strength, compressive ultimate strain and Poison’s ratio of the web are also listed in Table 3. The superscript “c” indicates compressive loading direction. Shear modulus (G_xy), strength ( τ x y u) and strain ( γ x y u) are also shown in Table 3.

Figure 3 shows a sketch of the test component subjected to four point asymmetric loading. Due to the asymmetric loading pattern, there is the maximum vertical shear force applied at the center of the specimen. Bending moment should be theoretically zero at the center of the beam. At the support and load application points, transverse stiffeners on both sides of the web were provided. A total of eight E-glass/vinylester tubular sections having nominal dimensions of 101.6 mm × 101.6 mm × 9.53 mm were used as transverse stiffeners. The girder was restrained against lateral movement by means of a total of eight steel plates having dimensions of 76.2 mm × 381 mm × 12.7 mm and the transverse stiffeners at the support and load application points. A spreader beam was placed between the load actuator and two bearing plates to apply the asymmetric loading to the specimen. By this loading mechanism, the applied load P was divided into 0.73 P and 0.27 P at the shown bearing contacts. A photograph of the test setup is shown in Figure 4.

The instrumentation in the girder consisted of strain rosettes manufactured by Vishay (CEA-125-UR-350) and displacement sensors that were Celesco PT1A string potentiometers with up to 254 mm measurement capacity and accuracy of 0.15% of full stroke range. Twenty strain rosette sensors were used to measure −45°, +45° and 0° directional strains as shown in Figure 5. Seventeen strain rosettes were attached on one side of the web and the other three strain rosettes were located on the other side of the web. The identifications of the strain rosettes are shown in Figure 6. Three locations (A-4, B-2 and C-1) were selected for back-to-back strain rosette applications to accurately determine the strains near buckling. Out-of-plane bending could also be observed by the measurement of the strains from the back-to-back rosettes at these points. Seven strain rosettes were aligned vertically on the center line A-A. Five strain rosettes were located on line B-B 165.1 mm from A-A. Five strain rosettes are also located on line C-C 330.2 mm from A-A. A photograph of the rosettes installed on the web surface is shown in Figure 7.

A total of eight displacement sensors were used to measure the vertical and lateral deflections of the web. Seven locations, including two supporting points, were selected to measure vertical deflections using the potentiometers. They were V₁, V₂, V₃, V₄, V₅, V₆ and V₇ as shown in Figure 6. The vertical deflections at the supporting points (V₁ and V₅) were obviously zero. The locations of the potentiometers are also shown in Figure 7.

Figure 8 shows the locations of three additional displacement sensors used to measure the lateral deflections (L₁, L₂ and L₃) of the web at the center of the I-shaped section.The load was applied to the top of the load spreader as shown in Figures 4 and 5. The applied load was continuously increased to the failure point at which the web-flange junction fractured. An MTS 894 kN capacity load generator was used. The girder then was unloaded. The loading and unloading rates were 1.27 mm/s. The data were recorded electronically at a rate of 0.5 Hz.

Load-vertical deflection curves at five locations along the bottom of the lower flange are shown in Figure 9. The vertical deflections were measured using displacement sensors.

Figure 10 shows the lateral web displacements measured by potentiometers at three locations of the center of the girder.

Figures 11–13 show the shear strains in the x-y plane γ_xy, the difference in the shear strain values obtained from the back-to-back gages (γ_xy)₁ and (γ_xy)₂, and the average value of the shear strain γ_xy at locations A-4, B-2 and C-1, respectively. All Figures show clearly that prior to buckling the load-strain behavior were close to linear. The values of γ_xy were determined along with the axial strains from Equation (1) and the strain values recorded from the strain rosettes: (1) ε i = ε x cos 2 θ i + ε y sin 2 θ i + γ x y cos θ i sin θ i ( i = 1 , 2 , 3 )where ε_i’s are direct strain sensor readings from three sensors in a rosette, and θ_i’s are the orientation of the three strain gages.

The experimental buckling load was estimated from the load-lateral displacement curves obtained from the displacement sensors (Figure 10) and from the load-strain relation curves determined by the data points of strain rosettes (Figures 11–13). It was determined by taking the intersection point of the tangent drawn to a curve before and after buckling as outlined by Hoff, et al.[20]. This method is a well-known method called Bifurcation method. It is based on the phenomenon that the web surface should be sharply deformed at the moment of buckling. The critical load was determined by applying projection of the intersection onto the load-displacement and load-strain curves. Any analytical equation was not used to determine a shear buckling load in this study.

The evaluation results for the experimental buckling load by the data curves in Figures 10–13 were very consistent. Table 4 lists the evaluated shear buckling loads from the four data sets. Since the values were close enough, arithmetic means were calculated and listed. The determined shear buckling load was 295 kN.

The shear buckling load was also obtained using finite element computer program ABAQUS. The specimen was modeled three dimensionally using S8R5 element (8-node doubly curved thick shell, reduced integration). Figure 14 shows the finite element model of the I-shaped section. The specimen was modeled using a total of 1,800 elements and 6,345 nodes, which resulted in relatively fine mesh of which element aspect ratios were 1.08 for the web and 1.07 for the flange.

The orthotropic material properties determined using the coupon test results (Section 2.2) were used and the out-of-plane shear moduli (G_zx and G_yz) were assumed to be the same as in-plane shear modulus (G_xy). The loading and support points were identical to the experimental conditions. The bottom supports were modeled by restraining out-of-plane displacements and vertical movements. The node in the center of the bottom flange at a supported region was restrained against longitudinal translation to prevent a rigid body motion. The lateral (out-of-plane) displacements on the loading line were inhibited by the lateral supports and the loading areas on the top flange were also restrained in out-of-plane direction. The laterally supported areas on the web were also restrained in rotations and the displacement in the out-of-plane direction.

The total load P was divided into two forces P₁ and P₂ that had magnitudes of 0.73 P and 0.27 P, respectively to simulate the actual experimental loading conditions. The loads P₁ and P₂ were applied to the top flange as pressures on the area of 152 mm × 191 mm. This area was identical to that of the bearing plates placed on the top flange for the test. The stiffeners shown in Figure 4 were not included in the FEM modeling. Simplified displacement constraint conditions were applied instead: The lateral displacements of the web were assumed to be zero on the contact surfaces. The rotations about the longitudinal axis at the contacts were also fixed. Since the pure shear spot theoretically existed at the center of the test-section, the effect to the shear buckling load due to the usage of the stiffeners was not considered significant.

The shear buckling load was determined by taking the lowest positive eigen-value (first mode of buckling). The critical buckling load obtained from the finite element analysis was 292 kN. Figure 14 shows the buckled shape of the I-shaped section. The displacement magnification factor in the figure is 7.0. Additional post-processing figures with static and buckling analyses are also available [21].