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39 The negative moment caused by the dead load can be calcu- lated accurately since the weight of the specimen is known from the measured reactions. Referring to Figure 26 for direc- tions, a downward load of 50 kips was applied to the east span to keep the system stable. Then, an upward load of 80 kips was applied in the west span. The combination of the two loads reduced the west-end reaction to about 7 kips. The west end was jacked up, and the west support was removed. The jack was released. At this point a negative moment of 545 k-ft was being applied. The west cylinder load was then reduced in increments of 5 kips. Cracking occurred at a moment of 880 k-ft. This was less than the cracking moment of 930 k-ft calculated using the design concrete compressive strength for the deck slab, which was 4 ksi. Using the measured material properties, the expected cracking moment increased to 1,580 k-ft. The reduction in Figure 58. Slab cracking in full-size Specimen 2. strength was probably caused by the cracking that occurred in the deck slab during the positive moment testing. When the deck cracked, the cracks were always full depth (see NEGATIVE MOMENT CAPACITY Figure 62). As the negative moment increased, the deck continued to After the positive moment/continuity testing was com- crack and the cracks propagated down into the girders (see plete, the specimen was tested for negative moment capac- Figure 63). The joint began to open from the top (see Fig- ity. The deck was reinforced for negative load as required ure 64). Finally, the bottom of the girder crushed (see Fig- by the provision of the AASHTO LRFD Specifications (12). ure 65) at an applied moment of 2,250 k-ft, just 2% above Figure 61 shows the deck reinforcing. Using the design the failure moment capacity predicted using actual material concrete strength of 6,000 psi and assuming 60 ksi yield for strengths. The cracking that occurred during the positive the steel, the nominal moment capacity was calculated at moment testing did not affect the negative moment capacity, 1,630 k-ft. This capacity increased to 2,200 k-ft when recal- although it did reduce the negative cracking moment. culated using actual material properties of 11 ksi for the con- crete compressive strength and 80 ksi for yield of the steel. With the two-span configuration shown in Figure 26, the FINITE ELEMENT MODELING required applied load would have exceeded 200 kips/point. This would have required building a massive frame, and there To evaluate the behavior of positive moment connections, were concerns that this much load would cause local failures. a three-dimensional finite element model (FEM) was devel- The solution was to test the girder as a cantilever and to oped, which included nonlinear effects of cracking and crush- allow the dead load to apply some of the negative moment. ing of concrete as well as yielding of steel bars and strands. TABLE 3 Comparison of responses: cracked versus uncracked diaphragm Baseline, Baseline, Ratio Uncracked Cracked Highest/Lowest End Reaction East/Load East (lb) 14,500 16,000 1.10 End Reaction East/Load Both (lb) 11,000 14,500 1.32 End Reaction East/Load West (lb) 3,300 900 3.67 End Reaction West/Load East (lb) 2,500 2,200 1.14 End Reaction West/Load Both (lb) 10,200 12,900 1.26 End Reaction West/Load West (lb) 13,300 14,900 1.12 Strain East/Load East (microstrain) 62 71 1.15 Strain East/Load Both (microstrain) 51 66 1.29 Strain East/Load West (microstrain) 10 3 3.33 Strain West/Load East (microstrain) 10 9 1.11 Strain West/Load Both (microstrain) 46 53 1.15 Strain West/Load West (microstrain) 60 62 1.03

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40 18000 East Reaction Initial West Reaction Intial 16000 14000 Change in End Reactions (pounds) 12000 East Reaction Final 10000 8000 6000 West Reaction 4000 Final 2000 0 -2000 -4000 0 2 4 6 8 10 12 14 16 18 20 Time (min) Figure 59. Comparison of change in end reactions: initial and final loading. Among the available finite element programs, ANSYS was width cross section of the composite section required three- chosen owing to its efficient element library and material dimensional analysis. models for the analysis of reinforced and prestressed con- Concrete is modeled using eight-noded SOLID65 elements crete members (27). The choice of three-dimensional model- with three degrees of freedoms at each node. The element is ing was due to the fact that concrete element in ANSYS capable of simulating smeared cracking in three orthogonal is three-dimensional and accurate analysis of the variable directions, crushing, and plastic deformations. Steel reinforce- 80 East Beam Final West Beam Final Bottom Flange Strains (microstrain) 60 East Beam Initial 40 West Beam Initial 20 0 -20 0 2 4 6 8 10 12 14 16 18 20 Time (min) Figure 60. Comparison of change in bottom flange strains: initial and final loading.

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41 Figure 61. Deck slab reinforcement. ment and prestressing strands are both modeled using the two- girder with equal stiffness and cracking moment. This method noded LINK-8 truss elements with three degrees of freedom was verified by comparing the behavior of a prestressed at each node. The element is capable of simulating plasticity, concrete girder modeled as an equivalent reinforced con- stress stiffening, and large deflections. The equilibrium equa- crete girder with the experiments of Elzanaty et al. (28) and tions are solved using the Adaptive Descent method; this fine element mesh (FEM) reported by Kotsovos and Pavlovic method switches to a stiffer matrix if convergence difficul- for the same experiment (29). ties are encountered and to the full tangent matrix as the solu- A FEM was created of the stub specimen (see Figure 66). tion converges. Due to the softening behavior of concrete, a Because of the large size of the model, only one-quarter of displacement control strategy is adopted. Information about the specimen was modeled. This model would simulate the the elements, convergence and solution methods can be found original experimental plan of lifting both ends simultaneously. in the cited reference. However, the actual experimental procedure was to fix one One of the challenges in modeling this type of bridge is the end and lift the other. It can be shown by simple structural construction sequence, in which the girders are first pre- analysis that this FEM will still provide accurate stresses, but stressed and then assembled together with the deck and dia- the deformation of the free end will be half that measured. phragm concrete. Several methods were tried, but the approach Therefore, when comparing FEM deflections with the exper- adopted was to model the continuous bridge system. Since iments, the FEM deflections are doubled. Three FEMs were the main concern is on the behavior of the diaphragm and created: no connection, bent strand, and bent bar. In all cases, since the stiffness of the prestressed girder is considerably the girder ends were not embedded in the diaphragm. higher than that of the diaphragm, it was decided to model Figure 67 shows the predicted load versus deflection graphs the prestressed girder as an equivalent reinforced concrete compared with all six stub specimens (although the models do not account for embedment or web bars). The experimental Slab Slab Top Flange Cracks Cracks Web Web Figure 62. Full-depth slab cracks negative moment capacity testing. Figure 63. Negative moment cracks in girder.

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42 Top Flange Top Flange Diaphragm Diaphragm Crack Crack Figure 66. Finite element mesh for the stub specimens. data shown are after 5,000 cycles. All of the specimen load vs. deflection lines are lower (less stiff) than the model, except Figure 64. Separation at top of joint under negative for Specimen 6 (bent bar, embedded, web bars). All of the moment. curves fall above the curve for no connection and below the curves for the bent bar and bent strand. The most probable reason for this is that the FEM did not account for the cold or construction joint at the beam-diaphragm interface. Such joints are much weaker than monolithic concrete. The experi- mental data end below the FEM data because failure in the Girder FEM is based on rupture of the steel in monotonic loading while the experimental specimens failed by pull-out or fatigue. The FEM was not capable of simulating these failure modes. Figure 68 shows the moment versus curvature relation- ship for the bent-strand model and the two bent-strand spec- imens, Specimens 1 and 3. The moment-curvature relation- ship obtained from the RESPONSE program (22), which was used to obtain the moment versus curvature response for the RESTRAINT program, is also shown. Note that a similar behavior to the load-deflection graphs is observed. Specimen 1 exhibits some odd behavior, but recall that this specimen may have sustained some damage because of thermal load before testing (see previous section). The Diaphragm moment-curvature relationship for the bent-bar Specimen 2 is shown in Figure 69 and confirms the behavior shown in Figures 67 and 68. The FEMs show promise in predicting the behavior of the connections, but some improvements are needed. First, the Crushing at joint between the girder and diaphragm should be modeled Bottom as a cold or construction joint. Second, the interface between the strands and the diaphragm concrete should be modeled appropriately to account for the slip observed in the experi- ments. Finally, the model must be able to account for pull- Figure 65. Crushing at bottom of joint under negative out and fatigue failures. Time and budget consideration pre- moment. vented further FEM studies.

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43 180 160 140 Bent Strand FE 120 Load (kips) 100 Bent Bar FE 80 o 60 40 No Positive Moment Connection FE 20 0 0 0.5 1 1.5 2 2.5 3 Deflection (inches) (a) 40 Bent Strand FE Bent Bar FE 35 6 3 4 5 1 30 2 25 Load (K) 20 15 10 No Positive Moment Conn ection FE 5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Deflection (in) (b) Figure 67. Stub specimen load versus deflection compared with FEM results.

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44 2500 Bent Strand Specimen 2000 Response Program Present FE Analysis Moment (kip-ft) 1500 400 Present FE Analysis 300 R esponse Program 200 Specimen 3 100 1000 M oment (kip-ft) 0 Specimen 1 -100 -200 500 -300 -400 -0.0001 0 0.0001 0.0002 0.0003 0.0004 C urvature 0 0 0 .0005 0 .001 0.0015 Curvature Figure 68. Stub specimen moment versus curvature compared with FEM results bent strand.

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45 750 Bent Bar Specimen Present FE Analysis 600 Moment (kip-ft) 450 450 Pres ent FE Analys is 300 Res ponse Program 150 300 M oment (kip-ft) Specimen 2 0 Wes t Side Response Program -150 150 -300 -450 -0.0002 -0.0001 0 0.0001 0.0002 C urvature 0 0 0.0002 0.0004 0.0006 0.0008 0.001 Curvature Figure 69. Stub specimen moment versus curvature compared with FEM results bent bar.