Strength Analysis and Research of Composite Material Bridge Deck

The strength of each layer of composite bridge deck under different load conditions is analyzed and studied by Tsai-Wu tensor theory. The results indicate that, the characteristic strength values calculated in the predetermined reinforcement fabric are significantly smaller than those in the E-glass fiber layer, and the damage will first occur in E-glass fiber layer. Under various operating conditions, the characteristic strength values in each layer of FRP bridge panel are smaller than 1, and have a certain safety factor. The weak positions of each layer are related to the configuration of bridge panel. Tsai-Wu tensor theory can accurately evaluate the status of each layer, and supervise the design work of GFRP bridge panel.


Summary
From the perspective of composite material mechanics, the top, bottom, and web plates of GFRP bridge panel are all laminated plates.The failure of laminated composite materials starts from the single layer that first reaches the combined failure stress, then the overall stiffness of the laminated panel changes, and the stresses in each layer are redistributed, similar to "yielding" at the macro level.Then, as the load continues to increase, the next layer of failure occurs, and each layer of failure occurs until the entire laminated plate fails.When laminated plates fail, there are two states: first layer failure and final failure.The strength of GFRP bridge panel is directly related to the safety of driving.Therefore, the first layer failure principle should be adopted in the analysis and judged according to the strength criterion of unidirectional composite materials [1].This article analyzes the distribution of internal forces in each layer of GFRP bridge panel, and studies the strength of GFRP bridge panel using Tsai-Wu tensor theory.

Strength Criterion
Most experimental measurements of material strength are based on unidirectional stress states, but actual structural problems often involve plane stress states or spatial stress states.The commonly used strength theories include: maximum stress theory, maximum strain theory, Hill-Tsai strength theory, Hoffman strength theory, and Tsai-Wu tensor theory.
In the equation: σ1 is the longitudinal stress, Xt and Xc are the longitudinal tensile and compressive strength; σ2 represents the transverse stress, Yt and Yc represent the transverse tensile and compressive strength, τ12 is the in-plane shear stress, and S is the in-plane shear strength.
2) Maximum strain theory 11 11 11 In the equation: ε11 represents longitudinal strain, E11 represents longitudinal elastic modulus, Xt and Xc are the longitudinal tensile and compressive strength; ε22 represents transverse strain, E22 represents transverse elastic modulus, Yt and Yc represent the transverse tensile and compressive strength; γ12 represents shear strain, G12 represents shear modulus, and S represents in-plane shear strength.
3)Hill-Tsai(S.W. Tsai) strength theory In the equation: σ1 represents longitudinal stress, X represents longitudinal strength; σ2 represents transverse stress, Y represents transverse strength; τ12 is the in-plane shear stress, and S is the in-plane shear strength.
4) Hoffman strength theory In the equation: σ1 is the longitudinal stress, Xt and Xc are the longitudinal tensile and compressive strength; σ2 represents the transverse stress, Yt and Yc represent the transverse tensile and compressive strength, τ12 is the in-plane shear stress, and S is the in-plane shear strength.
5) Tsai-Wu (E.M. Wu) tensor theory In the equation: σ1 is the longitudinal stress, σ2 represents transverse stress, σ6 is the in-plane shear stress, 1 1 1 The maximum stress criterion and maximum strain criterion both compare the stress or strain components of composite materials with the basic strength, without considering the influence of shear stress; The Hill-Tsai criterion considers the influence of shear effect, but does not consider the influence of different tensile and compressive strengths of materials; On the basis of the Hill-Tsai criterion, the Hoffman strength theory also considers the influence of different tensile and compressive strengths of materials.There is varying degree of inconsistency between the strength theories and experimental results.The method to improve the consistency between the two is to increase the coefficients in the theoretical equations, and to use the Tsai-Wu criterion to predict the strength of composite materials is relatively more accurate.
The Tsai-Wu criterion is used to analyze the strength and safety reserve of GFRP bridge panel.The left side of equation ( 5) is the corresponding strength characteristic value, which is defined in this article as ζ, and the distribution in different layers of panel is studied.When the value is less than 1, it indicates that the GFRP bridge panel is in normal working condition under the corresponding load; When it is equal to 1, it indicates that the GFRP bridge deck is in a critical working state.And the positions where ζ larger than 1 indicate the location where the damage occurred.

Layer Design of the GFRP Deck
The GFRP panel(Figure 1.) is made from E-glass fiber (1200Tex), fiber reinforced cloth(0°/-45°/45°/90°) and vinyl ester resins.Figure 2. Layer of GFRP profile The FRP profile has a width of 200mm, and a height of 218mm.Figure 2. shows the layer of the profile .The top plate is 17mm thick and the bottom plate is 15mm.The top and bottom plate are made from 6 layers of E-glass fiber and 7 layers(2.4mmeach) of fiber reinforced cloth(0.4mmeach).The web have a thickness of 7mm, and is made from 3 layers of E-glass fiber(1.8mmeach) and 4 layers of fiber reinforced cloth(0.4mmeach).The fiber volume fraction is 0.55 in the E-glass yarn layer and 0.4 in the fiber reinforced cloth layer.

Finite Element Model of GFRP Bridge Panel
The strength of the GFRP bridge deck model was analyzed using a finite element program.Figure .3 shows the FEA model.The layer of the GFRP panel is simulated by orthotropic materials with the material parameters listed in Table .1 [2][3].The rule of mixture model is used [4][5][6], and the material parameters for each layer are calculated as shown in Table 2.The static response of GFRP bridge deck under load conditions 1 and 2 are analyzed and the strength of each layer is studied.According to the FRP material design manual [7][8], the basic strength indicators for single layer are determined, as shown in Table 3.In finite element analysis, factors such as material layering, component cross-sectional form, and component size are considered, the influence of adhesive layers between GFRP profiles is ignored.The load with a value of 100kN is applied at mid span of the panel within a 0.2*0.6marea, as shown in Figure 4.The stress distribution at different positions in the GFRP bridge deck model under two working conditions are calculated and the strength of the GFRP bridge deck is evaluated according to the Tsai-Wu strength criterion.    .4 shows that under load condition 1, the maximum ζ in point a ~ f is 0.4195, which is the layer 12 of measure point c.Thus, under load condition 1, when the load level is 100kN, the ζ in each layer of the panel is less than 1, mean the panel is in a safe stress state.The ζ in each layer of measure point a which is at top of the web is small; and the ζ in measure point d ~ f, which is at the variable cross-section of the bottom plate, are greater than 0.2; Although measuring point c is located directly below the loading area, the ζ in layer 2 at measuring point e are bigger than that of measuring point c, this means when symmetrically loaded, the weak parts of each layer are related to the shape of the bridge panel.3873 which is at the connection of bottom plate and the web, and is bigger than the ζ at position of the connection of top plate and the web (maximum value is 0.2863).When compare measurement point j and k, although measurement point j is located directly below the loading zone, due to the change in section stiffness, the ζ of measure point k(maximum value is 0.3873) is bigger than that of measure point j(maximum value is 0.3391).Under load condition 2, the weakest position of the section is the connection of the web and the bottom plate below the loading area, The maximum ζ is 0.3901, which is in layer 12 at measure point l , is smaller than 1, thus the panel is in a safe stress state .The 1/3/5/7/9/11/13 layers are fiber reinforced cloth, while 2/4/6/8/10/12 layers are E-glass fiber layer.The transverse tensile strength of the fiber reinforced cloth is 30 times the transverse strength of E-glass fiber layer, and the transverse compressive strength is 8 times the compressive strength of the E-glass fiber layer.Therefore, the calculation ζ in the fiber reinforced cloth is significantly smaller than that in the E-glass fiber layer.As the load level increases, failure will first occur in the E-glass fiber layer.

Conclusion
This article analysed the advantages and disadvantages of the maximum stress criterion, maximum strain criterion, Hill-Tsai criterion, Hoffman criterion, and Tsai-Wu criterion, and uses Tsai-Wu criterion to analyse the safety of GFRP bridge panel.The following conclusions are obtained: 1. the calculation ζ in the fiber reinforced cloth is significantly smaller than that in the E-glass fiber layer.As the load level increases, failure will first occur in the E-glass fiber layer.
2. The calculation ζ of the GFRP panel under load condition 1 and 2 are smaller than 1 : At load condition 1 , the ζ in layer 12 at top plate under loading area is 0.4195, with a safety factor of 2.38 times.Under load condition 2, the ζ in layer 12 at the connection of top plate and web under loading area is 0.3901, with a safety factor of 2.56 times.
3. The Tsai-Wu criterion can accurately evaluate the status of each layer, and the evaluation results can guide the design of GFRP bridge panel.

Figure 1 .
Figure 1.Cross section of GFRP bridge panel.Figure2.Layer of GFRP profile The FRP profile has a width of 200mm, and a height of 218mm.Figure2.shows the layer of the profile .The top plate is 17mm thick and the bottom plate is 15mm.The top and bottom plate are made from 6 layers of E-glass fiber and 7 layers(2.4mmeach) of fiber reinforced cloth(0.4mmeach).The web have a thickness of 7mm, and is made from 3 layers of E-glass fiber(1.8mmeach) and 4 layers of fiber reinforced cloth(0.4mmeach).The fiber volume fraction is 0.55 in the E-glass yarn layer and 0.4 in the fiber reinforced cloth layer.The parameters of each layer of the profile from the outside to the inside are as follows: the 1st /7th/13th layer consists of two layers of 450g/m 2 fiber reinforced cloth(0/90-1/1), the 3rd/5th/9th /11th layer consists of two layers of 450g/m 2 fiber reinforced cloth(-45/45-1/1), and the 2nd/4th/6th/7th/10th /12th layer consists of 1200Tex E-glass fiber.

Figure 4 .
Figure 4. Diagram of the load conditions.The load with a value of 100kN is applied at mid span of the panel within a 0.2*0.6marea, as shown in Figure 4.The stress distribution at different positions in the GFRP bridge deck model under two working conditions are calculated and the strength of the GFRP bridge deck is evaluated according to the Tsai-Wu strength criterion.

Figure 5 .Figure 5 .
Figure 5. Distribution of ζ under load condition 1 in the panel

Figure 6 .
Figure 6.Measure points in the cross-section.

Figure. 7 Figure 7 .
Figure 7. Distribution of ζ under load condition 2 in the panel Figure.7 shows that the maximum area of ζ in the panel is the connection area of web and bottom plate under loading area, and other larger areas are the connection of top/bottom plate and the web which is near the loading area.Measure point s in the cross-section of the panel, with the number of g ~l, shown in Fig.8 are determined by the distribution of ζ .Table.5 shows the ζ at measure point s in each layer under load condition 2.

Figure 8 .
Figure 8. Measure points in the cross-section.Table 5. ζ of each layer under load condition 2.

Table 1 .
Material parameters of fiber and resin.

Table 2 .
Material parameters of single layer of FRP profile.

Table 3 .
Basic strength indicators of layer.

Table 4 .
ζ of each layer under load condition 1.

Table 5 .
ζ of each layer under load condition 2.