Composite Bridge Decking, Final Project Report

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	0.231 modeling	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.