Thermal Gradient

At the time of bond, the concrete in the girder is assumed to have zero stress. A thermal gradient can form if the temperature does not change uniformly through the depth of the section. The thermal gradient can cause mechanical stresses in the section required to achieve compatibility, additional curvature and, therefore, camber. Figure 6.34 and Figure 6.35 show how the temperature varied through the depth of Girders 1 and 2, respectively, at midspan changed between the times of bond and release, which was approximately 24 hours after casting for full-scale girder Test 4. Data points missing through at particular depths were associated with faulty gages. The temperature gradient at the time of release is a function of the temperature profile at the time of bond. It can be seen that there is a large temperature range that falls within the assumption that bond occurred between 6 and 10 hours after casting. In either case, the girder appears to cool more quickly at the top of the section, so the change in curvature due to the thermal gradient would cause the girder to deflect downward.

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Figure 6.34: Temperature through Girder 1 section at midspan at various time steps during Test 4 fabrication

Figure 6.35: Temperature through Girder 2 section at midspan at various time steps during Test 4 fabrication

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To determine the effects of the thermal gradient on camber, temperature changes through the girder sections from bond to release were analyzed to determine the curvature induced by the thermal gradient, as given by Equation (6-19) derived by Barr et al.

(2005). In the equation, positive curvature is defined in the same sense as is positive moment. That is, positive curvature corresponds to downward deflection.

(6-19)

where:

Ai Cross-sectional area of material i

Ei Modulus of elasticity of material i

Ii Moment of inertia of material i about the composite centroid

y Vertical coordinate measured downward from composite centroid αi Coefficient of thermal expansion of material i

ΔT(y) Change in temperature at height y relative to temperature at the time of bond ϕ0 Curvature induced by thermal gradient

For each full-scale test, the girder cross section was divided into sections based on the locations of thermocouples through the height. The temperature in each section at a given point in time was assumed to be uniform. For each division of the girder area, the concrete and steel were considered separately and the net sectional properties of each material about the composite centroid of the entire girder section were determined.

The deflection induced by the thermal gradient was determined by integrating the curvatures along the length of the simply-supported girder. Because the temperature through the depth of the section was only monitored at midspan, the curvature was assumed to be constant along the length of the girder. Equation (6-20) gives the deflection based on those assumptions:

(6-20)

where:

Lg Length of girder from end to end

δ Midspan deflection due to thermal gradient

The assumed time of bond significantly affects the potential effects of thermal gradient on deflection just after release. Figure 6.36 shows the estimated deflections due

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to the difference in temperature between bond and release for each full-scale girder test assuming times of bond ranging from 6 to 12 hours after casting to account for the later time at which it was believed the strand in Test 2 bonded (approximately 11 hours after casting). Test 1 was omitted due to lack of data through the depth of the girder sections. The direction of the deflections in the figure correspond to the convention used when describing girder camber (i.e., positive upward).

Figure 6.36: Estimated deflections due to thermal gradient between bond and release for full-scale tests

It is clear that the estimated deflection depends greatly on the assumed time of bond (i.e., when the concrete is assumed to have hardened and have zero stress).

However, within the assumed time of bond range, the estimated deflections indicate that much of the difference in estimated and measured camber at release for each full-scale test could be accounted for by considering the effects of the thermal gradient. It should be noted that the estimated deflections due to thermal gradients in the figure were

determined with many underlying assumptions that were made due to lack of data. The calculations were based on no more than seven thermocouples through the section and the curvature due to the thermal gradient was assumed constant along the girder length.

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6.7.2.5 Summary

Multiple factors that could account for differences between estimated and measured release cambers were discussed in the previous subsections, including

variations in concrete MOE at release, losses in strand force due to abutment movement and dead end slip, variations in strand force along the length of the bed as the concrete hardens, friction between the girders and the precasting bed, and thermal gradient through the depth of the girder. The factors that are believed to be the most significant are the reduction in camber due to the non-recoverable loss of prestress force and the thermal gradient effect. The other factors are believed to be unlikely to have a large effect on camber.

To demonstrate the potential effects of the thermal gradient on release camber, the estimated deflections due to thermal gradient shown in Figure 6.36 were superimposed with the estimated release cambers shown in Figure 6.32 and compared with the measured release cambers for the full-scale tests. Table 6.12 shows the maximum, minimum, and expected downward deflections due to thermal gradient. Note that negative values represent downward deflections. The expected downward deflection is based on the assumption that bond occurred when the concrete temperature at midspan on Strand 1 reached 100°F. Figure 6.37 shows the estimated release cambers without

considering the deflection due to thermal gradient (i.e., the values from Figure 6.32) compared with the TEA estimated camber considering the maximum and expected downward deflections due to thermal gradient.

Table 6.12: Maximum, minimum, and expected downward deflection due to thermal gradient

Test No. 1 2 3 4

Max. Downward Deflection [in] NA -0.94 -0.73 -0.28 Min. Downward Deflection [in] NA -0.06 0.12 0.06 Expected Downward Deflection* [in] NA -0.94 -0.11 -0.19 *Assuming bond occurred when concrete temperature at midspan on Strand 1 reached 100°F

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Figure 6.37: Estimated cambers considering deflection due to thermal gradient The estimated camber considering the expected downward deflection due to thermal gradient was very close to the measured release camber for Tests 2 and 4. The expected deflection due to thermal gradient was not close for Test 3, but the maximum downward deflection was reasonable. It should be noted that the estimated deflections due to thermal gradient were based on multiple assumptions and are not expected to be accurate. However, the estimations were expected to provide the potential magnitudes of the effects of thermal gradient. Based on the information in Figure 6.37, it is reasonable to believe that the effects of thermal gradient could significantly affect girder camber at release and account for differences between estimated and measured cambers.