Finite Element Modeling

To predict the performance of timber bridges, three finite element models of bridges subjected to static load testing were developed. Three models were chosen so that each location of static load testing would be represented and so that each of the models could be compared and contrasted for accuracy of analysis. The three models developed were of North Carolina bridge no. 560510, Montana bridge no. L25003009+09001, and Colorado bridge no. P-19-AS.

The objective was to create a model that nearly replicated the field results obtained from static live load testing. If this could be achieved, then hypothetically the model could be

subjected to various load cases and the results could be obtained without actually performing a full-scale test. One can clearly see the advantages of creating this model. Essentially, an infinite number of load tests could be performed through the use of the model and deterioration and other conditions could be simulated.

The North Carolina Bridge is a single span, two-lane timber solid sawn girder bridge with a bituminous wearing surface located in Madison County, North Carolina. Figure 8 shows a picture of the North Carolina Bridge.

Figure 8. North Carolina Bridge used for Finite Element Modeling

This bridge was subjected to static live load testing during the summer of 2006. From the load test, deflection results were obtained from which a finite element model could be calibrated.

Shown below in Figure 9 is the finite element model developed. This model consists of solid elements with anisotropic capabilities representing the girders, deck boards, and rails.

Figure 9. Finite Element Model of North Carolina Bridge

Unlike steel or concrete where the modulus of elasticity is well known, the timber modulus of elasticity varies considerably due to a number of factors including, but not limited to, species, grade, and moisture content. Consequently, a typical range for the modulus was

determined and a value was arbitrarily selected to first model the bridge. To calibrate the model it was decided that the midspan deflections should have nearly the same shape and magnitude of the load test midspan deflection results, thereby demonstrating that the load distribution and the flexural rigidity of the model was similar to that of the actual bridge. Loads replicating those of the test vehicle were applied to the model and midspan deflection results were obtained. If necessary, the effective modulus of elasticity was adjusted to better match the field results.

Figure 10 through Figure 12 shows the calibration results from when the field and finite element results were nearly equal when subjected to the same loading.

-0.100 0.000 0.100 0.200 0.300 0.400 0.500 0.600

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 10. North Carolina Finite Element Calibration Results Load Path 1

-0.100 0.000 0.100 0.200 0.300 0.400 0.500

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 11. North Carolina Finite Element Calibration Results Load Path 2

-0.100 0.000 0.100 0.200 0.300 0.400 0.500

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 12. North Carolina Finite Element Calibration Results for Load Path

The Montana Bridge is a single span, two-lane, solid sawn timber girder bridge with a bituminous wearing surface located near Wolf Creek, Montana. Figure 13 shows a picture of the Montana Bridge.

Figure 13. Montana Bridge used for Finite Element Modeling

This bridge was subjected to static live load testing during the summer of 2006. From the load test, deflection results were obtained from which a finite element model could be calibrated.

Shown below in Figure 14 is the finite element model developed and much like the previous model, this model consists of solid elements with anisotropic capabilities representing the girders, deck boards, and rails

Figure 14. Finite Element Model of Montana Bridge

Similar to the North Carolina Bridge, a typical range for the modulus of elasticity was determined and a value was arbitrarily selected to first model the bridge. To calibrate the model it was decided that the midspan deflections should have nearly the same shape and magnitude of the load test midspan deflection results, thereby demonstrating that the load distribution and the flexural rigidity of the model was similar to that of the actual bridge. Loads replicating those of the test vehicle were applied to the model and midspan deflection results were obtained. If necessary, the effective modulus of elasticity was adjusted to better match the field results.

Figure 15 through Figure 17 shows the calibration results from when the field and finite element results were nearly equal when subjected to the same loading.

-0.050 0.000 0.050 0.100 0.150 0.200 0.250

1 2 3 4 5 6 7 8 9 10 11 12

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 15. Montana Bridge Finite Element Calibration Results for Load Path 1

-0.050 0.000 0.050 0.100 0.150 0.200

1 2 3 4 5 6 7 8 9 10 11 12

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 16. Montana Bridge Finite Element Calibration Results for Load Path 2

-0.050 0.000 0.050 0.100 0.150 0.200 0.250

1 2 3 4 5 6 7 8 9 10 11 12

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 17. Montana Bridge Finite Element Calibration Results for Load Path 3

The Colorado Bridge is a single span, two-lane, solid sawn timber girder bridge with a bituminous wearing surface located near Trinidad, Colorado. Figure 18 shows a picture of the Colorado Bridge.

Figure 18. Colorado Bridge used for Finite Element Modeling

This bridge was subjected to static live load testing during the summer of 2006. From the load test, deflection results were obtained from which a finite element model could be calibrated.

Shown below in Figure 19 is the finite element model developed and much like the previous two models, this model consists of solid elements with anisotropic capabilities representing the girders and deck boards. One difference between the Colorado model and the previous two models is the absence of a railing. After running identical load cases with and without the railing in the North Carolina and Montana models it was observed that very little, if any, difference occurred in the maximum midspan deflection results. Consequently, the inclusion of a railing in the model was neglected.

Figure 19. Finite Element Model of Colorado Bridge

Much like the previous two models, a typical range for the modulus of elasticity was determined and a value was arbitrarily selected to first model the bridge. Again, to calibrate the model it was decided that the midspan deflections should have nearly the same shape and magnitude of the load test midspan deflection results, thereby demonstrating that the load distribution and the flexural rigidity of the model was similar to that of the actual bridge. Loads replicating those of the test vehicle were applied to the model and midspan deflection results were obtained. If necessary, the effective modulus of elasticity was adjusted to better match the field results. Figure 20 through Figure 22 shows the calibration results where the field results and finite element results were nearly equal when subjected to the same loading.

-0.050 0.000 0.050 0.100 0.150 0.200 0.250

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 20. Colorado Finite Element Calibration Results for Load Path 1

-0.050 0.000 0.050 0.100 0.150 0.200

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 21. Colorado Finite Element Calibration Results for Load Path 2

-0.050 0.000 0.050 0.100 0.150 0.200 0.250

G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12

Girders

Deflection (in) ANSYS

Field 1 Field 2

Figure 22. Colorado Finite Element Calibration Results for Load Path 3