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APPENDIX B: REPORT ON FINITE ELEMENT ANALYSIS

Finite Element Model For the Whole Bridge

Tables 6 through 8 detail the properties of the various materials used to model the composite bridge deck.

Table 6. Material properties (composite).

Laminate Unit Value Unit Values for Horizontal Walls Thickness = 0.20" Values for Inclined Walls Thickness = 0.24" Values for graphite (thickness for each layer = 0.172in)
Elastic modulus of 0 degree, Ex psi 3.89 E+6 3.43 E+6 3.13 E+6
Elastic modulus of 90 degree, Ey psi 1.77 E+6 2.73 E+6 2.03 E+6
Shear modulus, Gxy psi 0.86 E+6 0.75 E+6 1.32 E+6
Ultimate tensile strength of 0 degree psi 39,960 33,000 50,960
Ultimate tensile strength of 90 degree psi 19,890 10,340 44,340
Ultimate compressive strength of 0 degree psi 70,000 54,120 35,710
Ultimate compressive strength of 90 degree psi 33,430 37,060 35,710
Ultimate shear strength psi 14,580 14,770 9,090
Poisson's ratio 0.223 0.231modeling 0.184

Table 7. Material properties (concrete).

Properties Unit Value
Compressive strength psi 1.32E+4
Tensile strength psi 2.35E+3
Elastic modulus psi 2.16E+6

Table 8. Material properties (steel).

Properties Unit Value
Elastic modulus psi 2.90E+7
Poisson's ratio   0.3

Result

Using AASHTO Load and Resistance Factor Design (LRFD) Bridge Design specifications:

  • Load Factor for Lane Load = 1.75.
  • Load Factor for Truck Load = 1.75*(1+0.33) = 2.3275.

Tables 9 through 11 show the response of the deck under service load, as obtained from finite element analysis. The finite element model used property values that were primarily derived from the physical testing of as-fabricated composite specimens.

Table 9. Service load deflection and failure index with concrete, small footprint (6 by 7 in2), with lane load.

Loading Maximum Deflection (in.) (Service Load) Square root of Tsai-Hill Index (R)
(√ITH)
(LRFD)
HL-93 0.284 0.413

Maximum local deflection between two girders = 0.02 inches.

Table 10. Service load deflection and failure index with graphite, small footprint (6 by 7 in2), no lane load.

Loading Maximum Deflection (in.) (Service Load) Square root of Tsai-Hill Index (R)
(√ITH)
(LRFD)
HL-93 0.357 1.38

Maximum local deflection between two girders = 0.17 inches.

Table 11. Service load deflection and failure index with graphite, large footprint (10 by 20 in2), no lane load.

Loading Maximum Deflection (in.) (Service Load) Square root of Tsai-Hill Index (R)
(√ITH)
(LRFD)
HL-93 0.279 0.853

Maximum local deflection between two girders = 0.088 inches.

The most critical element (the element with the highest Tsai Hill index under LRFD loading) is located under the area of applying the truck load (on the top flange). The stress states for these elements are presented in tables 12 through 15.

Table 12. State of stress in the critical composite element (SL loading), small footprint, no lane load.

Element No. S11 (psi) % of Ultimate S22 (psi) % of Ultimate S12 (psi) % of Ultimate
Under truck load
 (vertical wall)
-19342 27 -28021 84 13 0.09

Table 13. State of stress in the critical composite element (LRFD loading), small footprint, no lane load.

Element No. S11 (psi) % of Ultimate S22 (psi) % of Ultimate S12 (psi) % of Ultimate
Under truck load
 (vertical wall)
-45019 64 -65219 195 30 0.2

Table 14. State of stress in the critical composite element (SL loading), large footprint, no lane load.

Element No. S11 (psi) % of Ultimate S22 (psi) % of Ultimate S12 (psi) % of Ultimate
Under truck load
 (vertical wall)
-2391 7 -8197 23 168 2

Table 15. State of stress in the critical composite element (LRFD loading), large footprint, no lane load.

Element No. S11 (psi) % of Ultimate S22 (psi) % of Ultimate S12 (psi) % of Ultimate
Under truck load
 (vertical wall)
-5565 16 -19079 53 390 4

Figures 33 through 41 graphically illustrate the finite element model made for the proof-of-concept bridge.

Figure 33. Diagram. 3D view.
Figure 33. Diagram. 3D view.

Figure 34. Diagram. Half of FRP deck (7 panels with 11 cells and 1 panel with 8 cells).
Figure 34. Diagram. Half of FRP deck (7 panels with 11 cells and 1 panel with 8 cells).

Figure 35. Diagram. Cross-section of a part of the FRP deck.
Figure 35. Diagram. Cross-section of a part of the FRP deck.

Figure 36. Diagram. Girders.
Figure 36. Diagram. Girders.

Figure 37. Diagram. Cross-section of the girders.
Figure 37. Diagram. Cross-section of the girders.


Figure 38. Diagram. Loading and boundary conditions.
Figure 38. Diagram. Loading and boundary conditions.

Figure 39. Diagram. Deflection (service load), small footprint.
Figure 39. Diagram. Deflection (service load), small footprint.

Figure 40. Diagram. Mesh
Figure 40. Diagram. Mesh.

Figure 41. Diagram. Tsai-Hill Index (LRFD), small footprint.
Figure 41. Diagram. Tsai-Hill Index (LRFD), small footprint.

Page last modified on May 18, 2012.
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