Strand Force Changes After Casting: Case B – Effects of

In typical prestressed concrete girder production, a number of strands are raised at the girder ends to reduce the strand eccentricity. This is referred to as “draping” the strands and its purpose is to reduce the tensile and compressive stresses in the top and bottom flange of the girder ends, respectively, due to strand eccentricity because stresses at the girder ends due to self-weight and external loads are zero in simply-supported members. Draping strands allows economic design of prestressed concrete girders

without exceeding tensile and compressive stress limits defined by bridge design codes in the girder ends.

To produce draped strands, mechanical anchors, called “hold-downs,” are fixed to the precasting bed at the “harp” points specified on the girder plans. The hold-downs contain rollers to minimize friction with the prestressing strands. During tensioning, the draped strands are pulled to a lower force than the straight strands. The remaining force is introduced when the draped strands are lifted to the correct height just outside the girder ends to achieve the proper eccentricity. To accomplish this, the draped strands are fed through a mechanical “horse” during fabrication that is lifted into proper position by a forklift. The assumptions in Case B consider the hold-downs as fixed points on the bed that prevent the girder from sliding and resist any force changes due to temperature.

The free strand, girder strand, and concrete forces between bond and release with the Case B assumptions were determined in a similar manner to the forces with the Case

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A assumptions. The only difference was in the free strand and girder lengths assumed in the calculations; consequently, the temperature profiles were different in Case B from Case A to reflect the average measured temperatures of the Case B assumed girder and free strand lengths. In Case A, the total length of the girders on the bed and the total length of free strand were considered. In Case B, only the free strand length from the abutment to the girder end and the girder length from the end to the nearest hold-down were considered. To reflect the Case B assumptions in estimating strand and concrete force changes, the equations in Section 3.3.3.1 were modified.

Equation (3-9), representing strain compatibility between the steel and concrete at the center of gravity of the strands (cgs), was unchanged with the exception of the

notation for the force changes in the girder strand and concrete, which were modified for Case B to reflect the consideration of the hold-downs, as shown in Equation (6-2). As in Equation (3-9), bending due to the eccentricity of the strands was ignored, and it was assumed that the change in length of the steel and concrete at the cgs are equal.

(6-2) where:

Anet Net cross-sectional area of concrete girder section

Aps Total area of prestressing strands

Ec Modulus of elasticity of concrete

Eps Modulus of elasticity of prestressing strand

αc Assumed coefficient of thermal expansion of concrete

αs Assumed coefficient of thermal expansion of steel

ΔPc,B-R,hold Resultant concrete force at center of gravity of strands with free strand

restraint between bond and just before release considering hold-downs ΔPs,B-R,hold Change in girder strand force with free strand restraint between bond and

just before release considering hold-downs

ΔTc,B-R Average change in temperature of concrete from bond to release between

the end of the bed and the first hold-down

Equation (3-10), showing that the force changes in the free strand and girder strand and the resultant concrete force must be in equilibrium, was also unchanged with the exception of the notation, as shown in Equation (6-3):

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(6-3) where:

ΔPfree,B-R,hold Change in free strand force between bond and release considering hold-

downs

Equation (3-11) showed that the change in length of the girder strand must be equal and opposite to the change in length of the free strand. The Case B assumptions state that the change in length of the free strand between the abutment and the girder end must be equal and opposite to the change in length of the girder strand from the girder end to the hold-down, as shown in Equation (6-4):

(6-4)

where:

Lfree Length of free strand between the abutment and the nearest girder end

xhold Distance from girder end to hold-down

ΔTfree,B-R Average change in temperature of free strand between the precasting bed

end and adjacent girder from bond to release

The three unknown force changes (ΔPs,B-R,hold, ΔPc,B-R,hold, and ΔPfree,B-R,hold) were solved using the previous three equations. The force change in the girder strand and the resultant force in the concrete considering the hold-downs are given by Equation (6-5) and (6-6), respectively. The free strand force change considering the hold-downs is given by Equation (6-7): (6-5) (6-6) (6-7) where:

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To determine the effects of the Case B assumptions, estimated free strand force changes were determined using measured temperature data from full-scale girder Test 4. Test 4 was examined due to the large amount of temperature measurements taken along the bed. Unique free strand force changes were found for the live (LE) and dead (DE) ends of the precasting bed by assuming different free strand lengths and temperature profiles in Equation (6-7). The free strand length was approximately 125 ft (38.1 m) between the LE abutment and the nearest girder end and 8 ft (2.4 m) between the DE abutment and the nearest girder end. The distance from the girder ends to the hold-downs was approximately 57 ft (17.4 m).

Figures 6.20, 6.21, and 6.22 show measured and estimated free strand force changes on Strand 1 during full-scale girder Test 4 for both Case A and Case B (DE and LE) assumptions assuming bond occurred at 3, 6, and 8 hours after casting, respectively. The three assumptions for the time of bond were chosen to bound the potential time of bond and appeared to best correlate the Case A strand force estimations with the measured values as shown in Figure 6.18.

Figure 6.20: Measured and estimated Strand 1 force changes after casting during Test 4 assuming bond occurred at 3 hours – Case B

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Figure 6.21: Measured and estimated Strand 1 force changes after casting during Test 4 assuming bond occurred at 6 hours – Case B

Figure 6.22: Measured and estimated Strand 1 force changes after casting during Test 4 assuming bond occurred at 8 hours – Case B

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It was expected that the estimated LE and DE free strand force changes under the Case B assumptions would reasonably match the LE and DE load cell readings,

respectively. From the figures, it can be seen that the estimations of the free strand force changes vary significantly between Case A and Case B. With the Case B assumptions, the LE free strand force changes were consistently underestimated and the DE free strand force changes were severely overestimated. The Case A assumptions more reasonably estimated the free strand force change for both the LE and DE for all assumed times of bond. These observations suggest that the hold-downs may not act as fixed points on the bed that resist all girder movement and forces. The slots through which the hold-downs are attached to the precasting bed are not cut to perfectly fit around the base of the hold- down, so some sliding is possible. However, the load cell readings showed differences in the free strand force changes at the LE and DE, which suggests that the girders are not free to slide along the bed, likely due to friction between the concrete and precasting bed. Because the Case A assumptions were found to better estimate the free strand force changes between bond and release, they were used in the thermal effects analysis for the remainder of this report.