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OCR for page 59
59 APPENDIX B Stresses In Overlays Reference: Choi, D., D.W. Fowler, and D.L. Wheat, "Thermal Stresses in Polymer Concrete Overlays," Properties and Uses of Polymers in Concrete, ACI Special Publication No. 166, 1996, pp. 93122. This reference provides a method for analytically predicting the stresses in TPOs because of temperature changes. The method is facilitated by the graphs that are shown in chapter two, Figures 12, 13, and 14, respectively, for shear, normal and axial stresses. It should be noted that the stresses in these graphs are for one-way or beam elements; for overlays that are two- way elements, the stresses must be multiplied by 1/(1- o), where o is the coefficient of thermal expansion of the overlay. EXAMPLE: TPO with moderate thickness and low-modulus epoxy resin The following properties are assumed: Overlay thickness, to = 0.40 in. Overlay modulus, Eo = 100,000 psi Substrate thickness, ts = 8.0 in. Substrate modulus, Es = 4,000,000 psi Overlay thermal coefficient, o = 15 10 -6 in./in./F Substrate thermal coefficient, s = 6 10 -6 in./in./F Overlay Poisson's ratio, o = 0.25 Temperature drop, T = 35F Differential strain between overlay and substrate, T = (o - s) T T = (15 6) 10 -6 in./in./F 35F = 315 in./in. Because the stresses shown in chapter two, Figures 12, 13, and 14 are based on T = 500 in./in., the stresses from the graphs must be multiplied by the ratio of 315/500 = 0.63. Because the graphs were developed for beam elements and the overlay is a two-way system, the stresses must be multiplied by 1/(1 - o) = 1/(1 - 0.25) = 1.33. From chapter two, Figures 11, 12, and 13, for to /ts = 0.05 and Eo /Es = 0.025, find stresses and multiply by modification factors: Shear stress = 27 psi 0.63 1.33 = 23 psi, Normal stress = 20 psi 0.63 1.33 = 17 psi, Axial stress = 76 psi 0.63 1.33 = 64 psi. EXAMPLE: TPO with greater thickness and high-modulus epoxy resin The following properties are assumed: Overlay thickness, to = 1.0 in. Overlay modulus, Eo = 2,000,000 psi Substrate thickness, ts = 8.0 in. Substrate modulus, Es = 4,000,000 psi Overlay thermal coefficient, o = 12.5 10 -6 in./in./F

OCR for page 59
60 Substrate thermal coefficient, c = 5.5 10-6 in./in./F Overlay Poisson's ratio, o = 0.22 Temperature drop, T = 35F Differential strain between overlay and substrate, T = (o - s) T T = (12.5 5.5) 10-6 in./in./F 35F = 245 in./in. Because the stresses shown in chapter two, Figures 12, 13, and 14 are based on T = 500 in./in., the stresses from the graphs must be multiplied by the ratio of 245/500 = 0.49. Because the graphs were developed for beam elements and the over- lay is a two-way system, the stresses must be multiplied by 1/(1 - o) = 1/(1 - 0.22) = 1.28. From chapter two, Figures 12, 13, and 14, for to /ts = 0.05 and Eo /Es = 0.5, find stresses and multiply by modification factors: Shear stress = 309 psi 0.49 1.28 = 194 psi, Normal stress = 154 psi 0.49 1.28 = 97 psi, Axial stress = 1070 psi 0.49 1.28 = 672 psi. Discussion The two examples illustrate the very significant effect that using high-modulus, thick overlays has on the stresses produced compared with using thinner, low-modulus overlays. These stresses should be compared with the bond strength, shear strength, and the tensile strengths for the overlay as determined by lab tests. The strengths should be divided by an appropri- ate factor of safety.