# Conceptual Design of Composite Bridge Sandwich Structure
## 3 Results and Discussion
### Lay-up [45/\(-\)45]  
For parametric optimization, three different types of woods were used as the core material. Cross-ply laminate \([45/-45]\) is optimized for minimum mass and thickness on the same loading and boundary conditions. Starting from 1 mm thickness, the number of ply layers was varied to 48, and with the addition of each number, the thickness of 1 mm was increased for each ply angle to the total value. Seven different parameters were studied for the stability of the structure. Values of material constraints Tsai-Wu, Tsai-Hill, and MS should be greater than unity. The second is the deformation must be less than 32 mm according to the span limit relation span/500. All the results obtained from FEA are three are mentioned in Table 4 under ULS and SLS conditions. For the Bamboo wood core, there were two cases for the CFRP. For ULS, the MS criterion, Tsai-Wu (\(SF_{TW}\)) criterion, Tsai-Hill (\(SF_{TH}\)) criterion and the core factor were 4.84, 4.75, 4.36, and 53.8, respectively, and were greater than 1. The fiber plies for skins were \([45_{10}/-45_{10}]_{20}\), which showed that the total number of fiber laminates was 20 on either side with a core thickness of 400 mm. The deformation was in the safe limit, and the value was \(-0.032\) m equals to the maximum allowable value of \(-0.032\) m. This configuration has 43,280 kg of the total mass. The values of Equivalent stress and Maximum shear stress were 5.40 MPa, and 2.83 MPa, which were lower compared to the value of tensile strength. So, the bridge was safe in this configuration. For the ULS condition with GFRP skin, the above-stated criteria were 7.77, 7.21, 7.01, and 77.5, respectively, with the lay-up of \([45_{11}/-45_{11}]_{22}\), and the core of 440 mm. However, the thickness and mass drastically increased to 484 mm and 50,266 kg, respectively. The deformation, in this case, was 0.028 m.  
For the SLS conditions, the bamboo core and CFRP laminate skin, the MS criterion, Tsai-Wu (\(SF_{TW}\)) and Tsai-Hill (\(SF_{TH}\)) criteria and core factor were 11.26, 11.05, 10.14, and 56.59, respectively. The values of all the criteria mentioned above were greater than unity, and thus these values were suitable for our required configuration. We have also checked the values of equivalent, and maximum shear stresses, which in this case were 4.52 MPa and 2.34 MPa, respectively, and were lower than the yield strength of the core material. All seven parameters showed that the configuration \([45_{11}/-45_{11}]_{22}\), with the core of 440 mm, is safe for our model. The total deformation, in this case, was recorded as 0.024 m, with a total mass of 50,266 kg. When the skin was changed to GFRP, the values of these parameters were 14.99, 13.91, 13.49, and 72.69, respectively. However, the values of equivalent stress and maximum shear stress were increased to 4.46 MPa and 2.31 MPa, respectively. Deformation was increased to \(-0.028\) m, with the same weight of 50,266 kg. In the case of Paulownia with CFRP sheets under ULS conditions, the readings of MS, \(SF_{TW}\), \(SF_{TH}\), and CF are 2.95, 3.04, 2.95, and 23.43, respectively, for the thickness of \([45_{10}/-45_{10}]_{20}\). The values of equivalent stress and maximum shear stress were lower than Bamboo and equal to 3.75 MPa and 1.94 MPa, and it was less than tensile strength. The mass was reduced to 20,560 kg, for the same value of thickness as compared to the bamboo wood core. This showed that the Paulownia core is relatively better than the bamboo core. However, in this case, the value of deformation is \(-0.049\) m, which is greater than 0.032 m, so its thickness must be increased to satisfy the criteria. In the case of Paulownia core GFRP face skin, the above-mentioned factors were 6.099, 6.22, 5.18, and 40.39, respectively. The deformation was recorded at \(-0.032\) m. The thickness and overall mass were increased to 528 mm and 27,648 kg, respectively. The magnitudes of equivalent stress and maximum shear stress were increased to 2.66 MPa and 1.38 MPa, respectively.