A novel hybrid FRPaluminum truss system has been employed in a tworut modular bridge superstructure composed of twin inverted triangular trusses. The actual flexural behavior of a onerut truss has been previously investigated under the onaxis loading test; however, the structural performance of the onerut truss subjected to an offaxis load is still not fully understood. In this paper, a geometrical linear finite element model is introduced and validated by the onaxis loading test; the structural performance of the onerut truss subjected to offaxis load was numerically obtained; the dissimilarities of the structural performance between the two different loading cases are investigated in detail. The results indicated that (1) the structural behavior of the offaxis load differs from that of the onaxis load, and the offaxis load is the critical loading condition controlling the structural performance of the triangular truss; (2) under the offaxis load, the FRP trussed members and connectors bear certain outofplane bending moments and are subjected to a complicated stress state; and (3) the stress state of these members does not match that of the initial design, and optimization for the redesign of these members is needed, especially for the pretightened teeth connectors.
Truss is an efficient structural form. According to the type of cross section and the number of chord members, trusses can be classified as plane trusses, triangular trusses, rectangular trusses, and other polygon trusses. Among these various cross section trusses, the triangular truss shows remarkable structural advantages over the conventional plane and rectangular trusses, such as the evident weight and material savings compared to the rectangular truss [
In civil infrastructures, the triangular truss has been employed on a limited basis for a number of structures such as roof truss girders, transmission towers, highway overhead sign structures, crane booms, portal frames, and offshore oil rig platform legs [
However, in bridge engineering, especially for heavy traffic loading, the instances in which a bridge truss of this nature has been designed and constructed are fewer than those in civil infrastructures and aerospace engineering. Actually, the first triangulartruss bridge was completed in 1930, and it was a throughtype truss supporting two railway lines and constructed of latticebox girders with diagonal bracing forming a triangular pattern [
For the abovementioned triangulartruss bridges, except for their dead weight, the loads directly subjected to the trusses are mainly the vehicle traffic load normal to the chord members. The chord members mainly bear compression and tension loads or are simultaneously combined with the bending moment. For the twolane or multilane bridges, besides onaxis traffic load, these triangular trusses may also bear offaxis bending load, which has been recognized as the most critical load case and will lead to a certain torsional moment in the structure. In response to this problem, the literature [
In comparison with the paper that already published, the main attention in this work is to investigate the structural performance of the onerut triangular truss subjected to offaxis load. In this paper, a simple description of the modular hybrid truss is presented. A geometrical linear finite element model is introduced and validated by the previous onaxis loading test. The structural performance of the onerut triangular truss subjected to offaxis load was numerically obtained using the finite element model. The dissimilarities of the structural performance between the two different loading cases were then studied in detail.
A hybrid FRPaluminum space truss system was applied to a tworut bridge superstructure, which enables a modular structural form to be erected and dismantled manually with individual structural units. It has a span length of 12 m and a total width of 3.2 m. The tworut bridge is composed of twin triangular trusses, which are linked by transverse braces. Each truss was designed as an inverted triangular cross section with a 1.2 m width and 0.85 m depth (see Figure
3D view of the onerut triangulartruss system.
In the proposed triangulartruss system, pultruded FRP profiles and aluminum profiles for structural applications were selected for the trussed members (see Figure
For the FRP trussed members, it is worth noting that all of these members were designed initially as pure tensioncompression members and were only subjected to the axial direct forces in the preliminary design phase, in which the triangular truss was simplified as a plane truss model. In this analytical model, the triangular truss was simplified as a plane truss. The vertical and upper chord members were substituted for the two aluminum vertical web members and bridge deck, respectively. Then, the axial direct forces in the trussed members were calculated according to structural mechanics.
A novel joint system named the pretightened teeth connection (PTTC) is employed in the proposed modular triangular truss. Compared to the low connection efficiency attained using conventional compositematerial connection techniques for FRP tubes, the pretightened teeth connection (PTTC) has higher connection efficiency [
3D view of the composite tubular connection for (a) HFRP trussed members and (b) GFRP trussed members [
It is worth stressing that this pretightened teeth connector was preliminarily designed as a pure tensioncompression member; it was only subjected to the axial direct forces, and the bending moment was not considered or included. More information regarding the pretightened teeth connection, including its loadtransfer mechanism, can be found in [
Until now, four structural units of the prototype triangulartruss system have been fabricated by the factory. To understand the actual flexural behavior of the structure, these four prefabricated structural units were mounted as a simply supported structure and subjected to the onaxis fourpoint bending loading test, as shown in Figure
Singlespan simply supported triangular truss and its onaxis fourpoint bending loading test setup.
However, because one of the connectors of the specimen was damaged at a large loading level over the service load in the onaxis loading condition, the relevant experimental study was not conducted under an offaxis load in [
In order to understand the structural performance of the specimen subjected to offaxis load, a geometrical linear finite element model was used. The finite element model (FEM) of the modular composite triangular truss was established using the general purpose finite element analysis software ANSYS 10.0. The finite element model is simply introduced as follows.
To accurately simulate the proposed triangulartruss system, two types of elements (SHELL and BEAM elements) were employed to model the various structural members. The SHELL63 element was selected for the modeling of aluminum thin plate of the bridge deck, while the BEAM188 element was employed to simulate the crisscrossing “I” beams and trussed members, respectively. However, because it is difficult to precisely simulate the regions of the connectors located at both sides of the structural units, the connector and its conterminous chord members were all modeled using beam elements other than the solid elements. In the finite element model, the connectors were simplified as a segment of the corresponding chord members.
The coordinate system was defined with the
Finite element model of the onerut triangulartruss structure.
In this linear anisotropic material model, the buckling issue of the compressive members was not considered. The elasticity modulus and Poisson’s ratio used in the finite element model were provided by the manufacturer and are summarized in Table
Mechanical properties of all materials used in the finite element model.
Materials & members  Modulus of elasticity (GPa)  Poisson’s ratio 

HFRP members 


GFRP members 


Al alloy members 


Differ from [
Two different loading configurations in the finite element model. (a) Side view and (b) top view (dimensions in mm).
During the loading process for each case, the corresponding uniformly distributed wheel load was transformed into point loads acting on each node in the loading area of the thin plate. The numerical simulations were performed with eight loading levels (2P = 10, 20, 32, 40, 52, 60, 70, and 75 kN). The dead weight was not considered in this finite element analysis.
The stress state in certain FRP trussed members and the displacement at the midspan of the lower chord member were abstracted, respectively. The numerical results of the onaxis loading model are presented in Section
In this section, based on the onaxis fourpoint loading test that was conducted in previous work [
For this hybrid triangulartruss system, the deflection is an important factor affecting the normal use of the structure, considering the requirement of the guidelines. In the validation, the vertical displacement was compared for the numerical values and the experimental results. Indeed, in the onaxis fourpoint bending loading test [
Figure
Comparison of the vertical displacement between the numerical values and the experimental results.
For the internal axial direct forces, only two representative FRP trussed members (N2 and N5) were compared between the numerical solutions and the experimental results (see Figure
Comparison of the internal axial forces in the trussed members between FEA and test. (a) N2 and (b) N5.
In general, the finite element model (FEM) can accurately predict mechanical behaviors such as the deflections and internal forces of the proposed hybrid triangulartruss system. The modeling techniques can be used to analyze the structural performance of the specimen under the two different loading conditions.
In this section, the numerical results under the two different loading conditions are presented and compared to obtain the dissimilarities of the structural performance, including the vertical and horizontal displacement at the midspan of the lower chord member, the deformation of the HFRP lower chord member, and the stress state of FRP trussed members and the connectors.
Figure
Comparison of the displacement at the midspan of the lower chord member between the onaxis load and the offaxis load. (a) Vertical displacement and (b) horizontal displacement.
However, for the horizontal displacement, it clearly shows that the values vary dramatically between the onaxis loading and the offaxis loading curves (Figure
Figure
Variation in the overall horizontal displacement of the HFRP lower chord member with increasing applied offaxis load P.
In this section, the stress states in the FRP trussed members and the connectors were compared between the onaxis loading and the offaxis loading, respectively. The stress states include the axial direct stress, bending stress, and superimposed stress in the
Figures
Figure
Comparison of the jointing nodes. (a) The actual triangular truss and (b) the ideal simplified plane truss.
Contours of the internal direct axial stress in the HFRP lower chord members. (a) Onaxis loading case and (b) offaxis loading case (units in MPa).
Contours of the
Contours of the
Contours of the
Contours of the
In regard to the comparison of the two different loading models, the distributions of the bending stresses in the
However, for the bending stress in the
In addition to the aforementioned individual axial direct stress and the bending stress contours, the superimposed stress contours were also extracted and analyzed. Figures
Indeed, the aforementioned superimposed stress is a sum of the axial direct stress and the bending stress. That is, the superimposed stress in the
Combining Figures
Comparison of the maximum superimposed stress with the corresponding individual stresses in the lower chord members at the maximum load level of 75 kN.
Comparison of the maximum superimposed stress in the lower chord members  In 
In  

Superimposed stress  Axial direct stress  Bending stress  Superimposed stress  Axial direct stress  Bending stress  
Onaxis load  
Value (MPa)  78.63  79.22  −0.59  79.22  79.22  0 
Ratio (%)  /  100.75  −0.75  /  100  0 
Offaxis load  
Value (MPa)  81.54  78.51  3.03  169.06  78.51  90.55 
Ratio (%)  /  96.28  3.72  /  46.44  53.56 
Offaxis value to onaxis value ratio  1.037  0.991  /  2.134  0.991  / 
However, for the bending stress in the
For the connectors joining the lower chord members, the value and proportion of the axial direct stress and the bending stress accounting for the maximum superimposed stress were also extracted. The results are summarized in Table
Comparison of the maximum superimposed stress in the connectors at the maximum load level of 75 kN.
Comparison of the maximum superimposed stress in the connectors  In 
In 


Superimposed stress  Axial direct stress  Bending stress  Superimposed stress  Axial direct stress  Bending stress  
Onaxis load  
Value (MPa)  114.15  59.50  54.65  82.35  82.35  0 
Ratio (%)  /  52.12  47.88  /  100  0 
Offaxis load  
Value (MPa)  114.15  59.26  54.89  160.08  82.35  77.73 
Ratio (%)  /  51.91  48.09  /  51.44  48.56 
Offaxis value to onaxis value ratio  1.000  0.996  /  1.944  1.000  / 
In addition, in the
In summary, the offaxis loading case plays a critical role in controlling the bending stress and the superimposed stress out of the plane in the lower chord members and connectors, respectively. When subjected to an offaxis load, there are certain outofplane bending moments in the lower chord members and the connectors, which is mainly due to the torsional moment of the truss along with the specific node configuration. When subjected to both an offaxis load and an offaxis load, the lower chord members and connectors bear a certain inplane bending moment, which is mainly attributed to the specific node configuration of the truss. The stress state in these members does not match that of the initial design, in which the lower chord members and connectors are only subjected to the axial direct forces and were pure tensioncompression members. In addition, the superimposed stress under an offaxis load is much larger than that under an onaxis load. The triangular truss should be designed critically according to the offaxis loading condition other than the onaxis loading condition.
For the HFRP lower chord members, the offaxis load is the critical loading condition controlling the
Indeed, if the isotropic aluminum material is used for these lower chord members, the bending problem cannot be highlighted. However, it should be given significant consideration for anisotropic composite materials because the interlaminar shear stress of the extrusiontype unidirectional fiberreinforced composite materials is low. When subjected to certain bending and shear stresses, the HFRP lower chord members will bear a complicated and harmful stress state that may cause the cracks of the FRP composite tube. Thus, the HFRP lower chord members should be designed critically according to the structural properties of the proposed triangular truss subjected to an offaxis load.
For the connectors, the bending stress and the axial direct stress also account for a nearly equivalent portion of the maximum superimposed stress in both the
Diagram of the loading state in the pretightened teeth connector.
When subjected to a local bending moment, the connector will bear certain additional longitudinal stresses along the connector. Indeed, in the connector, there are also certain shear forces that will cause local shear stress at the local area (the change position) of the cross section (see Figure
A hybrid FRPaluminum modular truss system was introduced, which is composed of twin triangular trusses and is connected by male jugs and female jaws based on the pretightened teeth connection technique. The structural performance of its onerut triangular truss subjected to an offaxis load was obtained numerically using the finite element model, which has been validated by the onaxis loading test. The dissimilarities of the structural performance between the two different loading cases were studied in detail. The following conclusions were drawn.
The structural behavior of the offaxis load differs much from that of the onaxis load, and the offaxis loading case plays a critical role in controlling the structural performance of the triangular truss. The triangular truss should be designed critically according to the offaxis loading condition other than the onaxis loading condition.
For the vertical displacement, two loadingdisplacement curves are both linear and notably close to each other under two different loading cases, and the maximum difference between the two curves is less than 1.9%. However, for the horizontal displacement, the values vary dramatically between the onaxis loading and the offaxis loading curves. The large horizontal displacements are mainly caused by the torsional moment of the truss subjected to an offaxis load.
For the internal force in the FRP trussed members (or the pretightened teeth connector), the only dissimilarity between the two different loading cases is the outofplane bending stress. The offaxis loading condition plays a critical role in controlling the outofplane bending stress and the superimposed stress. In addition, under an offaxis load, the maximum outofplane bending stress and superimposed stress is much larger than the corresponding inplane stresses.
For the FRP trussed members, the inplane bending stress possesses a small part of the superimposed stress, and the axial direct stress accounts for almost the entire part in either the onaxis loading case or the offaxis loading case. However, due to the torsional moment along with specific node configuration, these members bear certain outofplane bending stresses under offaxial loads. The outofplane bending stresses and the axial direct stresses account for a nearly equivalent portion of the maximum superimposed stress. This stress state does not match that of the initial design, in which the lower chord member was designed as a pure tensioncompression member. Therefore, these HFRP lower chord members should be redesigned critically according to the structural properties under offaxis loads.
Due to the specific node configuration, the pretightened teeth connectors bear a certain inplane bending moment under both loading cases; in addition, due to the torsional moment along with specific node configuration, they also bear a certain outofplane bending moment under an offaxis load. These bending stress and axial direct stress account for a nearly equivalent proportion of the maximum superimposed stress. Namely, both axial direct forces and the local bending moment exist in the connectors and the connectors are subjected to a complicated stress state. The stress state does not match up to that of the initial design using a simplified plane truss model, in which they were only subjected to pure tensioncompression forces. Thus, these connectors should also be redesigned and optimized for this type of modular triangular truss.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The research work reported in this paper was supported by the Major State Basic Research Development Program of China (973 Program) under Grant no. 2012CB026202 and the National Science and Foundation Program of China under Grant no. 11372355.