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45 Chapter 4 PCSSS Numerical Studies: Practical Span Ranges, Applicability of Design Recommendations, and Other Issues 4.0 Introduction and Organization A combined numerical and experimental approach was used to investigate issues associated with the development of design recommendations for the precast composite slab span system. In a few cases, where appropriate, design recommendations for the PCSSS were based on information obtained from the literature or previous studies conducted by the researchers (Smith et al. 2008, Eriksson 2008). Issues of interest included: ⢠Determination of range of applicability for PCSSS bridges (Section 4.1) ⢠Control of reflective cracking across the longitudinal joint between precast flanges o Effect of transverse reinforcement spacing (Section 4.2) ⢠Applicability of slab-span design recommendations to PCSSS bridges o Live load distribution factors (Section 4.3) o Skew effects (Section 4.4) ⢠Composite action between the precast and CIP ⢠Effect of restraint moment due to time-dependent and thermal gradient effects ⢠End zone stresses in precast inverted tee sections (Section 4.5) ⢠Support conditions (Section 4.6) ⢠Determination of appropriate magnitude of patch load to be applied to laboratory specimens to represent range of possible span lengths (Section 4.7) This chapter primarily focuses on the numerical investigations associated with these issues. Regarding the range of applicability for the PCSSS, it was expected to be most efficient for relatively short to moderate span bridges. A parametric study was conducted over a range of span lengths for both simply-supported and continuous PCSSS models to provide greater insight into the range of spans that could be efficiently bridged using the PCSSS. Because of the shallow member depths associated with this type of superstructure, the service behavior and effective moment capacity of the section was largely dependent on the amount of prestress force, due to the fact that the moment arm is relatively short in comparison to traditional girder-type bridges. For this reason, one of the primary limiting components of the precast inverted-T design was the level of prestress that could be achieved, while the appropriate stress limits in the specification were satisfied. The parametric study therefore was utilized to identify the appropriate span lengths that could be efficiently achieved, and the corresponding prestress force and member depths that would be required, which is summarized in Section 4.1. A primary issue of importance for the NCHRP 10-71 study was the development of durable connection concepts. In the case of PCSSS bridges, the control of the development of potential reflective cracking is key to the achievement of a durable system. There is the potential for the development of reflective cracks in the CIP from stress raisers associated with the precast portion of the section (i.e., above the joint between the precast flanges and near sharp corners of the precast section). With regard to the issue of reflective crack control, numerical studies summarized in this chapter were used to investigate the effect of the transverse reinforcement spacing on reflective crack control, as well as on transverse load transfer. These studies are described in Section 4.2. Reflective crack control was also investigated extensively through the laboratory studies described in Chapters 5 and 6 which detail the results of the laboratory bridge and subassemblage tests, respectively.
46 PCSSS bridges are very similar to slab-span systems, with two exceptions. First, the adjacent flanges of the precast inverted-Ts used to create the PCSSS bridges cause discontinuities in the system along the interface of the adjacent flanges; and second, the composite nature of the PCSSS requires additional design considerations. To investigate the applicability of slab-span design recommendations to PCSSS bridges which feature the discontinuity along the adjacent flanges, numerical studies were conducted as described in Sections 4.3 and 4.4 regarding live load distribution and skew effects. Numerical models of the PCSSS featured discontinuities along the adjacent flanges which were compared to the results of models of monolithic systems. In some cases, additional models were developed to investigate the influence of potential reflective cracking on the performance of the systems. The PCSSS was expected to provide live load distribution in a similar manner to that of traditional monolithic slab-span superstructures, a conclusion that was supported by the numerical modeling. Furthermore, the effects of skew were expected to increase the magnitude of longitudinal shear stress in the region between the tips of the precast flanges, especially in the exterior joints between the members. Several FEM models were utilized to provide insight into the behavior of the system and the potential increases in stress at various locations of the system due to skew, and to determine the applicability of the current specifications to the PCSSS. The composite nature of the PCSSS required an investigation of the detailing requirements across the interface between the precast and CIP. In addition, the composite nature of the system required investigation of the potential for the development of restraint moments due to the time-dependent effects of creep and shrinkage. The required detailing across the interface between the precast and CIP to ensure composite action was investigated through a review of the literature, as well as through laboratory studies of the PCSSS Concept 1 and 2 bridges which were subjected to ultimate load tests as described in Chapter 5. The effect of restraint moments in the PCSSS were investigated numerically and experimentally in a previous study by the researchers, the results of which can be found in Smith et al. (2008) and Eriksson (2008). These results summarized in Section 3.3 provided the basis for the associated design recommendations in this study. The precast inverted-T sections of the PCSSS also required review of associated design recommendations for the precast prestressed elements particularly for the development of detailing requirements associated with end zone stresses because current requirements were found to be developed considering I-sections rather than panel systems. This aspect was investigated numerically and experimentally as described in Section 4.5. The connection between the precast elements and the substructure was investigated primarily by means of examination of structural plans for existing PCSSS structures. This review is summarized in Section 4.6. Numerical analyses were also used to determine the patch load to be used for the laboratory investigations conducted on the Concept 1 and 2 PCSSS bridges discussed in Chapter 5. These analyses are summarized in Section 4.7. 4.1. Parametric Study to Investigate Practical Span Ranges and Associated Precast Sections The weight associated with the precast composite slab span system, like most slab bridges, was expected to limit the range of applicable spans to what may be considered short to moderate spans. The PCSSS was expected to be a practical system for bridges with spans up to approximately 60 ft. In an effort to clearly identify and document the range of spans and associated section dimensions and design details for the PCSSS, a parametric study was completed. The study aimed to identify efficient span
47 lengths, as well as the required prestress forces and to ensure that the compression and tension stress limits were satisfied in the inverted-T sections. Span lengths of 20, 30, 50, and 65 ft. were identified as practical and efficient for the precast slab span system. The 20 ft. span length was chosen to represent the shortest practicable span length; the span range between 30 and 50 ft. was selected because of the large applicability of this system, while the 65 ft. span was chosen as a maximum feasible span length for the PCSSS. In addition, with the recommendation from K. Molnau (Mn/DOT), more representative configurations were considered, which included 20-30-20 ft., 30-50-30 ft., and 50-50-50 ft. three-span continuous systems. Because it was expected that a two-span 50-50 ft. would not differ significantly from the behavior of the 30-50-30 ft. three span bridge, a sole 65-65 ft. configuration was selected to investigate two-span systems. Moment envelope curves were developed for the configurations listed above, and were considered for two dynamic load situations as specified by the AASHTO (2010) LRFD specifications, HL-93 and Tandem vehicles, in addition to a static uniformly distributed lane load of 640 lb/ft.2 patterned along the length of the system. A dynamic allowance factor equal to 0.33 was selected for the moving load cases. Live load distribution factors were calculated according to a modified version of the AASHTO (2010) specifications (Article 4.6.2.3), Equivalent Strip Widths for Slab-Type Bridges, as shown in Eqn. (4.1.1). The effective lane width was considered with two or more lanes loaded, and the limiting lane width factor of 12.0W/NL was not considered. (4.1.1) where E is the equivalent lane width when two or more lanes are loaded (in.), L1 is the modified span length taken equal to the lesser of the span length or 60.0 (ft.), and W1 is the modified edge-to-edge width of the bridge taken to be equal to the lesser of the width or 60.0 (ft.). Initially positive and negative restraint moments were assumed to be zero during this portion of the study, which corresponded with the assumption that the CIP concrete was placed after the precast members were at a relatively old age. When the casting of the bridge deck is completed much later than the casting of the precast elements (i.e., 90 days as specified by the specification) the time-dependent drivers of positive restraint moments can be neglected (however the effects of thermal gradients should be considered). Later consideration included the calculation of the restraint moments for two configurations, the 50-50- 50 ft. and 65-65 ft. systems. In both cases, the age of the precast members was taken to be 14 days when continuity was established. The moments were calculated using the PCA method (Freyermuth, 1969). Depending on the age of the precast at which continuity is made and the amount of time since continuity, the PCA method is considered to predict accurate magnitudes for the maximum positive moments but generally overestimates the negative restraint moments. The method is based on both structural mechanics concepts and creep/shrinkage experimental data. In this study, the positive restraint moments were more thoroughly considered because they were expected to influence the design of the system more significantly than the negative restraint moments. The positive restraint moments increase the magnitude of the positive moment at midspan at service, and are difficult to resist because of the limited locations available to include continuous reinforcement near the bottom of the section at the piers (i.e., in the troughs between the precast webs). The material properties utilized in each model were identical. The concrete compressive strength of the CIP and precast concrete was taken to be 4 and 6 ksi, at 28-days, respectively. The precast concrete strength was assumed to be 5 ksi at transfer. A 6 in. thick composite CIP deck was identical in each model. The strands were assumed to be 0.5 in. diameter Grade 270 low relaxation strands pulled to a
48 stress of 202.5 ksi (75 percent of fpu). The flange thickness was kept constant at 3 in., and the standard width inverted-T sections of 6 ft. were used. The increased stiffness associated with the deck reinforcement was ignored during this study, which was consistent with similar calculations used by Mn/DOT during the design of bridge systems, and was conservative. Losses were calculated using the Zia method (1979). The primary metrics utilized to determine the appropriate design parameters for each configuration were the stress limits specified by AASHTO (2010). Two limit states were investigated, transfer and service. The compression and tension stress limits for each are shown in Table 4.1.1. Table 4.1.11 : Concrete stress limits utilized during parametric study PC Concrete Limit Value Transfer Compression -0.6âfci -3 ksi Tension 0.24ââfci 0.537 ksi Service Compression -0.45âfâc -2.7 ksi Tension 0.19ââfâc 0.465 ksi 1All units in Table 4.1.1 are in units of ksi, i.e., f`c is entered into the equations in units of ksi (regardless of whether there is a square root function or not) and the results of each stress limit are in ksi The design process was found to be governed by the stress limits at transfer at the ends of the beams, and the stress limits at service at midspan. In most cases, the tension limit for the bottom fiber at midspan at the service state was found to control. Table 4.1.2 presents a summary of selected optimized sections for the individual span lengths. For each of the optimized sections, the table summarizes the total precast section depth; the assumed flange thickness, which was taken as 3 in. (76 mm) except in the case of one of the spans which was designed to replicate the short spans in the Center City field implementation of the bridge; cross-sectional area; required number of strands to meet the service stress limits; required concrete compressive strengths at transfer and service to meet the required stress limits; total prestress force assumed immediately after transfer; span configuration in which the section was assumed; and the limiting stress ratios in the design of the sections. In cases where the design stresses were exceeded, recommended changes were provided to alleviate the limit exceedance. In cases where the compressive stress limits were exceeded, the design concrete compressive strengths at release were increased; in cases where the tensile stress limits were exceeded, the required mild reinforcement to carry the full tensile force is listed. As mentioned above, the bottom fiber tension stress limits controlled at service in most of the cases. Satisfying the bottom fiber tensile stress limits at service required increasing the number of tendons (total prestressing force) or increasing the depth of the section. An increase in the value of the maximum positive moment at midspan (longer spans), required a larger number of tendons to satisfy the stress limits and, when this was not feasible, the depth of the section was increased. When considering the effect of the positive restraint moments, the total positive moment acting at midspan was increased and so it was necessary to increase the amount of prestress for the same section. In considering the feasibility of the systems according to the different configurations described above, important issues were identified associated with the weight of the precast section that might be
49 controlled by truck load capacities in transport or crane capacities at erection. For the truck load limits, the sections should be limited to 80 kips (350 kN) without requiring a special permit. Typical crane capacities can readily handle the 80 kip (350 kN) capacity (this value could be as high as 130 kips (580 kN) in some cases). As an example, in the case of the 65 ft. (19.8 m) span section, an initial minimum depth of 20 in. (500 mm) was considered for the precast section, but it required three rows of tendons. The amount of prestress caused problems with the tensile and compressive stress limits at the ends at release and compressive stress limits at midspan at service. Increasing the depth of the precast section to 22 or 24 in. alleviated these issues to an extent. Using a 22 in. deep precast section with 54 tendons, required a concrete compressive strength at transfer of 6 ksi rather than the nominal value of 5 ksi. Using a 24 in. deep precast section with 46 prestressing tendons alternatively solved the problem but with this depth the weight of the precast section exceeded 80 kips, which could be an issue with transport. Table 4.1.2: Precast section dimensions and results of parametric study 1Represents the precast sections used in the Center City Bridge and Concept 1 and Concept 2 large scale laboratory specimens 2Bolded span lengths indicate the span utilized for the sectional design parameters in that column In summary, the range of span lengths considered during this study was found to provide a reasonable bound for applicable span lengths for the PCSSS. The 65 ft. simply supported system would require 54 Span Length [ft.] 20 30 221 221 45 50 62 65 Depth of Precast [in.] 8 10 12 12 14 16 20 22 Flange Thickness [in.] 3 3 5.25 3 3 3 3 3 Cross-Sectional Area [in.2] 460 560 710 650 750 840 1000 1100 Number of Strands 10 16 16 16 36 38 46 54 Concrete Strength at Transfer [ksi] 5 5 4.5 4.5 5.5 5.4 5.6 6 Concrete Strength at Service (ksi) 6 6 6 6 6 6 6 6 Prestress Force [kip] 306 500 500 500 1100 1200 1400 1700 Span Combination [ft.] 202- 30-20 20-30- 20 22-22 22-22 45-62-45 50-50-50 45-62-45 65-65 Limiting Ratios in Design of Sections End stresses at transfer including mild reinforcement and fci modifications required to satisfy end stresses ft /(0.24âfci ksi) <1 <1 <1 <1 1.51 1.73 2.04 2.11 Solution, As [in. 2] -- -- -- -- 6-#5 9-#5 10-#6 12-#6 fc /(0.6fci ksi) <1 <1 <1 <1 1.08 1.08 1.12 1.20 Solution, fci [ksi] -- -- -- -- fci'=5.4 fci'=5.4 fci'=5.6 fci'=6 Midspan stresses at service Section depth and number of strands were chosen to satisfy end stresses
50 0.5 in. diameter strands. Because the prestressed strand is concentrated within the 4 ft. web width of the inverted-T section, it would take more than two layers of strands at 2 in. centers to accommodate 54 tendons. This would not be the most efficient use of the system because the short member depths require that the longitudinal reinforcement is grouped as low in the member as possible to increase the eccentricity and moment arm. Also, at the lower bound, the 20 and 30 ft. spans provide a relatively economical design with the moderate member depth and number of tendons. 4.2. Parametric Study to Investigate Effect of Transverse Hook Spacing on Reflective Cracking Finite element parametric modeling was used to investigate the influence of the spacing between transverse hooked reinforcement on the transverse load transfer and reflective crack controlling capabilities of the PCSSS. The geometry of the bridge specimen was similar to that used in the large- scale Concept 1 laboratory bridge, consisting of a two-span continuous bridge, however each span utilized in the model was 30 ft. Each span consisted of two adjacent 6 ft. wide precast panels. Several models were developed to investigate the range of transverse hooked bar spacing between 6 and 18 in. Each model was constructed using 20 node quadratic continuum elements with reduced integration. The boundary conditions were roller supports at the ends of the bridge and a perfectly frictionless pin at the continuous pier. Loading was applied to correspond with the magnitude and patch size utilized in the laboratory study, which was 35 kip and 10 by 20 in., respectively. The load was oriented such that the long direction of the patch was perpendicular to the direction of the longitudinal precast joint. Two load cases were considered, the first was with loading centered at midspan directly over the precast joint and the second was at midspan with the edge of the load aligned with the edge of the vertical precast web, as illustrated in Figure 4.2.1. A summary of the FEM test cases is given in Table 4.2.1. Figure 4.2.1: Location and orientation of loading in the loaded span of the two-span bridge model Except for the transverse hooked bars crossing the longitudinal joint, rebar and prestressing strands were approximated as plates with negligible stiffness in all directions except axially in the orientation of the rebar. The transverse hooked bars were modeled as beam members with a 3/4 in. diameter circular
51 cross section. The transverse hooked bars were debonded for 1-1/2 in. on either side of the longitudinal joint for a total debonded length of 3 in., which was selected as an approximation of the bond condition between the rebar and concrete in the joint area. Four materials were used throughout the model. All CIP concrete was assumed to have an elastic modulus of 3,600 ksi, which was determined using AASHTO LRFD Article C5.4.2.4-1, assuming normal weight concrete with a compressive strength of 4,000 psi and Poissonâs ratio of 0.2. All precast concrete was modeled assuming an elastic modulus of 4,600 ksi, which was calculated using the above equation and normal weight concrete with strength of 6.5 ksi and Poissonâs ratio of 0.2. The plates used for modeling the rebar were assumed at have a modulus of elasticity of 1 psi and Poissonâs ratio of 0.2; the low elastic modulus of the plates was selected to ensure that they did not contribute to the section stiffness globally. All rebar layers embedded within the plates (including mild steel and prestressing strands) were modeled with a modulus of elasticity of 29,000 ksi and Poissonâs ratio of 0.3. In model Runs 1, 2, and 3 the cast-in-place was bonded only to the sides and top of the precast panel webs. The precast flanges were assumed to be unbonded from the CIP concrete. The unbonded flanges were selected to simulate the separation of the flanges from the CIP above the longitudinal joints. These runs assumed reflective cracking to approximately the depth of the elastic neutral axis in transverse bending for the 12 in. hooked bar spacing. The crack was assumed to extend vertically a distance of 9 in. from the bottom of the section. The fourth run depicted a fully bonded slab, where the CIP was completely bonded to the precast panels and the joint between the tips of the precast panels was eliminated through the use of tied elements between the adjacent members. This fourth run simulated a monolithic slab span.
52 Table 4.2.1: Summary of FEM runs to investigate effects of transverse hooked bar spacing Description Run Number 1 2 3 4 Run configuration PCSSS w/crack (6in. hook spacing, hooks lapped w/1in. stagger) PCSSS w/crack (12in. hook spacing, hooks lapped w/1in. stagger) PCSSS w/crack (18in. hook spacing, hooks lapped w/1in. stagger) Solid slab, no crack (12in. hook spacing, hooks lapped w/1in. stagger) Geometry Spans: 2 2 2 2 #Panels wide 2 (no outside flange) - 10ft wide Same Same Same Length 30ft-30ft Same Same Same Depth of precast section 3in.flange; 12in. web Same Same Same Depth of deck above precast web 6in. CIP Same Same Same Supports Pin at center support, rollers on ends Same Same Same Crack Simulated âcrackâ using contact elements. Bottom of section to 9in. from bottom (half depth). Same Same No Crack Material strength CIP Concrete 4ksi Same Same Same Precast Concrete 6.5ksi Same Same Same Reinforcement 60ksi Same Same Same Reinforcement Deck steel #8-#7-#7 @ 4in. oc Same Same Same Run along entire span length Transverse hooks in each direction (offset transversely by 1in.) #6@6in. (1" offset over joint) #6@12in. (1â offset over joint) #6@18in. (1â offset over joint) #6@12in. (1â offset over joint) Vertical location of transverse reinforcement 4-5/8â center of #6 from bottom of form Same Same Same Prestressing strands 16 in each PCSSS Same Same Same Transverse cage None None None None In each model run, it was enforced that at least one solid element along the length of the bridge was unfilled with transverse hooked bars (i.e., in the case of the 18 in. spacing, two elements were often unfilled per transverse hooked bar). This causes the plots to appear âspikyâ, as elements without rebar were free to open more than the reinforced elements. Figure 4.2.2 shows a comparison of the crack opening of runs where all elements were reinforced versus runs where at least every other element was unreinforced. The crack opening was measured directly above the precast joint, in the tension fiber of the CIP concrete. The case with all elements reinforced tended to fall between the bounds defined by the spikes in the plot for the case where not all elements had reinforcement. It was assumed that the case where not every element was reinforced better approximated the variations in the joint opening
53 for a physical bridge, so the method of leaving every other element void of rebar was used throughout the analyses. Figure 4.2.2: Crack opening in loaded span for 6 in. hooked bar spacing with or without one rebar per solid element The measured bar stress and maximum crack opening in the loaded span for load case 1 (i.e., load at midspan with the edge of the load aligned with the edge of the vertical precast web) is plotted as a function of the transverse hooked bar spacing in Figure 4.2.3. A strong linear relationship was observed between the stress in the bar and the measured crack opening at the precast flange-CIP interface and the spacing between the transverse reinforcement, with a correlation coefficient between the three data points of 0.999 and 0.993, respectively. The linear relationship between the bar spacing and both the stress in the reinforcement and maximum opening suggests that the effectiveness of the reinforcement is not degraded as more reinforcement is added. The proportional constant between the amount of reinforcement and the crack size/bar stress remained constant for the range of reinforcement spacing values considered during this study.
54 Figure 4.2.3: Maximum crack opening and transverse bar stress versus transverse hooked bar spacing in loaded span for load case 1 The effect of the spacing of the transverse hooked bars on transverse and longitudinal load distribution was also investigated during the parametric study. The transverse and longitudinal stress fields created by loading due to both load cases provided insight into the ability for each model to distribute the load throughout the structure. The transverse and longitudinal stress fields observed during the FEM runs for both load cases are shown in Figures 4.2.4-4.2.7. For the 6 and 12 in. spacing cases, the centerline of the patch load was centered over a pair of transverse hooks, while in the 18 in. spacing case the patch load straddles the hooks such that the edge of the patch load was relatively near the adjacent hooks. The center pier is illustrated in each model with the thick white line at the middle of each contour plot. Contour scales, which represent stress in units of psi, are also provided for each plot. For all cracked analyses (i.e., Runs 1 through 3), there was little variation in the overall distribution of the stresses, suggesting that the spacing of the transverse reinforcement had little effect on the ability for the PCSSS to distribute localized loading between adjacent panels and spans, which might be attributed to the proximity of the load to the reinforcement in all cases. As expected, noticeable variation in the transverse stress fields was observed between the cracked and uncracked model.
55 (a) 6 in. spacing (run 1) (b) 12 in. spacing (run 2) (c) 18 in. spacing (run3) (d) Uncracked (run 4) Figure 4.2.4: Transverse stress distribution in the compression (i.e., top) concrete fiber for load case 1 (units of stress are in psi) Center Pier
56 (a) 6 in. spacing (run 1) (b) 12 in. spacing (run 2) (c) 18 in. spacing (run 3) (d) Uncracked (run 4) Figure 4.2.5: Longitudinal stress distribution in the compression (i.e., top) concrete fiber for load case 1 (units of stress are in psi)
57 (a) 6 in. spacing (run 1) (b) 12 in. spacing (run 2) (c) 18 in. spacing (run 3) (d) Uncracked (run 4) Figure 4.2.6: Transverse stress distribution in the compression (i.e., top) concrete fiber for load case 2 (units of stress are in psi)
58 (a) 6 in. spacing (run 1) (b) 12 in. spacing (run 2) (c) 18 in. spacing (run 3) (d) Uncracked (run 4) Figure 4.2.7: Longitudinal stress distribution in the compression (i.e., top) concrete fiber for load case 2 (units of stress are in psi)
59 4.3. Parametric Study to Investigate Live-Load Distribution Factors for PCSSS The Interim 2010 AASHTO LRFD Design Specification provided design equations to determine the appropriate longitudinal moment demand for a given slab bridge system based on an effective lane width. The designer is then responsible for determining the proper amount and location of the longitudinal reinforcement and section geometry to satisfy the load demands. The specification provides further guidance in the design of the transverse reinforcement for slab bridges as a simple proportion of the total longitudinal tension reinforcement based on the span length of the structure, however the validity of this relationship when applied to the PCSSS was unknown. A total of nine finite element models were constructed to investigate the effects of the longitudinal discontinuity between precast members on the longitudinal and transverse distribution of load. The models were constructed using the same material and modeling assumptions as stated in Section 4.2, however symmetry was utilized in this case to minimize computation time. Four unique specimen geometries were investigated, including two three-span bridges with equal spans of 30 and 50 ft., as well as two simply-supported bridges also with spans of 30 and 50 ft. Each of the specimens had ten 6 ft. precast panels across the width to accommodate four 12 ft. lanes and two 6 ft. shoulders. Several variations in the state of the specimen near the precast discontinuity were considered, including both a bonded and unbonded interface between the precast flange and CIP concrete, as well as a monolithic slab with no precast discontinuity present. The parameters of each of the nine models are given in Table 4.3.1. A tandem load was utilized for all models, with a total load of 12.5 kip distributed over a 10 by 20 in. patch, as shown in Figure 4.3.1. The 12.5 kip load represents the tire load from the AASHTO tandem load of 25 kip axles spaced 4 ft. apart, with the transverse spacing taken to be 6 ft., as specified in Article 3.6.1.2.3 (AASHTO 2010), and assuming that the axle load is equally distributed to each tire. No dynamic load allowance (per AASHTO 2010 Article 3.6.2) was used to magnify the loading, which was consistent with the assumed loading for the design moments that were used for comparison. The center spans were loaded in the continuous models. The joint and panel numbering is shown in Figure 4.3.2, which represents the center span of the continuous models as well as the simple span. Five variations in the applied tandem loading were considered for each run, as described below: ⢠Tandem 1 â tandem loading centered over webs of panels 5 and 6 ⢠Tandem 2 â tandem loading centered over precast joints 4 and 5 ⢠Tandem 3 â double tandem loading centered over webs of panels 4,5,6,7 ⢠Tandem 4 â double tandem loading centered over precast joints 3,4,5,6 ⢠Tandem 5 â double tandem loading with 12.5 kip patch loads over joints 4 and 6 and a double patch load (i.e., 25 kips) over joint 5
60 Figure 4.3.1: Tandem loading located 2 ft. from midspan utilized for FEM live-load distribution study
61 Figure 4.3.2: Panel and joint numbering used in the placement of tandem loading for the center span of the continuous models and the simple-span models
62 Table 4.3.1: Summary of FEM runs to investigate longitudinal and transverse live-load distribution factors Description Run Number 1 2 3 4 5 6 7 8 9 Run configuration PCSSS w/ 3" crack PCSSS w/ 3" crack PCSSS w/ 3" crack PCSSS w/o crack PCSSS w/ 3" crack PCSSS w/ 3" crack PCSSS w/ 3" crack PCSSS w/o crack PCSSS w/ 15" crack Geometry Spans: 3 Single Single Single 3 Single Single Single Single #Panels wide 10â4lane bridge (12 ft. lanes + 6 ft. shoulders)\60ft.wide Same Same Same Same Same Same Same Same Length 30ft-30ft-30ft 30ft 30ft 30ft 50ft-50ft- 50ft 50ft 50ft 50ft 30ft Depth of precast section 3in.flange; 12in. web 3in.flange; 12in. web 3in.flange; 12in. web 3in.flange; 12in. web 3in.flange; 16in. web 3in.flange; 16in. web 3in.flange; 16in. web 3in.flange; 16in. web 3in.flange; 12in. web Depth of deck above precast web 6in. CIP Same Same Same Same Same Same Same Same CIP to precast interface above flange Unbonded Unbonded Bonded Monolithic Unbonded Unbonded Bonded Monolithic Unbonded Supports Rollers Same Same Same Same Same Same Same Same Crack Simulated âcrackâ using contact elements. Bottom of section to 3in. from bottom (precast joint). Bottom of section to 3in. from bottom (precast joint). Bottom of section to 3in. from bottom (precast joint). No crack, monolithic Bottom of section to 3in. from bottom (precast joint). Bottom of section to 3in. from bottom (precast joint). Bottom of section to 3in. from bottom (precast joint). No crack, monolithic Bottom of section to 15in. from bottom. Matâl strength CIP Concrete 4ksi Same Same Same Same Same Same Same Same Precast Concrete 6.5ksi Same Same Same Same Same Same Same Same Reinforcement 60ksi Same Same Same Same Same Same Same Same Reinforcement Deck steel #8-#7-#7 @ 4in. oc Same Same Same Same Same Same Same Same Run along entire span length Transverse hooks in each direction (offset transversely by 1in.) #6@12in. Same Same Same Same Same Same Same Same Model as a continuous bar across the section rather than as lapped steel Location of transverse reinforcement 4-5/8â center of #6 from bottom of form Same Same Same Same Same Same Same Same Prestressing strands 16 in each PCSSS 16 in each PCSSS 16 in each PCSSS 16 in each PCSSS 38 in each PCSSS 38 in each PCSSS 38 in each PCSSS 38 in each PCSSS 16 in each PCSSS Transverse cage None None None None None None None None None
63 In Runs 1, 2, 5, and 6 the CIP was bonded only to the sides and top of the panel webs while in Runs 3 and 7 the CIP was also bonded to the top of the precast flanges. In Runs 4 and 8 the system was assumed to be a monolithic slab with the discontinuity from the joint between the precast panels absent. Finally, Run 9 was similar to Run 2, except the crack was extended up to approximately the elastic neutral axis in transverse bending. In Run 9, the rebar crossing the cracked plane was debonded from the concrete a distance of 3 in. to either side of the cracked face. The longitudinal design moments for slab bridges are calculated by applying the design load over an effective lane width, which is dependent on whether loading is applied to a single lane or multiple lanes, per AASHTO (2010) Article 4.6.2.3. The two variations of effective lane widths account for multiple presence factors in that the effective strip width for single lane loading has been divided by a factor of 1.20. The factors do not represent a physical change in loading, but instead account for the likelihood of multiple vehicles traveling together; they are statistical factors to promote conservative design (in the case of single lane loading). The multiple presence factors were ignored in the modeled scenarios. The longitudinal design moments and associated curvatures are shown in Table 4.3.2 for both single and multiple lane loadings for the various runs. Table 4.3.2: AASHTO (2010) longitudinal design moments and curvatures Moment (kip-ft./ft. span) Curvature (με/in.) Run Single1 Multiple 2 Single Multiple 1 16.1 17.7 7.37 8.13 2 24.4 26.9 11.17 12.32 3 24.4 26.9 11.17 12.32 4 24.4 26.9 11.17 12.32 5 22.9 28.6 5.64 7.05 6 33.9 42.4 8.34 10.43 7 33.9 42.4 8.34 10.43 8 33.9 42.4 8.34 10.43 9 24.4 26.9 11.17 12.32 1âSingleâ is associated with all loading applied to a single lane 2âMultipleâ is associated with loading applied to two or more lanes The maximum longitudinal curvatures obtained from the FEM model with the Tandem 2 loading (patch load applied over joints 4 and 5) and Tandem 5 loading (patch load applied over joints 4 and 6 and double patch load applied over joint 5) are compared with the design curvatures in Table 4.3.3. The Tandem 5 loading was considered to be a worst case loading scenario with respect to expected lane loading because the tandems were spaced much closer than would be physically possible. In comparing the results of the FEM to design ratios, the PCSSS resulted in slightly higher values in comparison to those of the monolithic systems (e.g., for the Tandem 2 Load Case: 0.43 [Run 2] for PCSSS vs. 0.39 [Run 4] for the monolithic 30 ft. span sections, and 0.41 [Run 6] for the PCSSS vs. 0.39 [Run 8] for the monolithic 50 ft. span); however the results were still conservative. The ratio of the maximum longitudinal curvature to the design curvature among the nine runs loaded with the Tandem 5 load case ranged from 0.57 to 0.84 for run 8 and 9 respectively. This suggests that, even when reflective cracking
64 was assumed to have progressed vertically to within 3 in. of the extreme compression fiber, as in run 9, the design effective lane widths provided by AASHTO (2010) Article 4.6.2.3 prove to be conservative, and should therefore be utilized for the design of precast composite slab span bridge systems. Table 4.3.3: FEM and design longitudinal curvatures under Tandem 2 and Tandem 5 load cases Tandem 2 Load Case Curvature (με/in) Tandem 5 Load Case Curvature (με/in) Run Max FEM Design FEM/Design Max FEM Design FEM/DESIGN 1 3.72 7.37 0.50 6.76 8.13 0.83 2 4.76 11.17 0.43 8.81 12.32 0.72 3 4.41 11.17 0.39 8.25 12.32 0.67 4 4.35 11.17 0.39 8.14 12.32 0.66 5 2.68 5.64 0.48 NM1 7.05 NM 6 3.4 8.34 0.41 NM 10.43 NM 7 3.26 8.34 0.39 6.03 10.43 0.58 8 3.23 8.34 0.39 5.97 10.43 0.57 9 5.18 11.17 0.46 10.38 12.32 0.84 1Not measured Shaded rows indicate monolithic models 4.4. Parametric Study to Investigate Skew Effects Several additional challenges are present in the design of bridges with skewed supports, such that the primary axis of the substructure is not aligned perpendicularly to the longitudinal axis of the superstructure. The primary effects of skewed bridge construction are geometric, with some effect on moments, shears, and live-load distribution. A plan view of the pier details for a skewed PCSSS bridge is shown in Figure 4.4.1. According to the PCI Bridge Manual (2001), in solid slab-span bridge systems with skewed supports, the load tends to take a âshort cutâ between the obtuse corners of the span, while the load in skewed bridges supported by longitudinal I-girders tends to flow along the length of the supporting members (PCI 2001). The PCSSS was expected to be bounded by these behaviors, and would subsequently tend to exhibit the characteristics of longitudinal stringer bridges as the precast joint is degraded due to reflective cracking. Another primary concern regarding skewed PCSSS bridges was the effect of the skew angle on the maximum horizontal shear induced above the precast joint. Several FEM models were developed to investigate the relationship between the skew angle and the resulting magnitude of this stress. A total of eight FEM models were constructed for this portion of the study, with skew angles ranging from 0 to 45 degrees. For each of the skew angles selected, two corresponding FEM models were created, one with the presence of the 3 in. discontinuity between the precast joints and an unbonded surface between the top of the precast flanges and the CIP concrete and a second with a monolithic thickness and the absence of the precast joint. Each model was constructed as a single 30 ft. simple- span bridge structure. The material and other modeling parameters were identical to the previous runs, described in Section 4.2. The parameters of each of the eight FEM models are given in Table 4.4.1.
65 Three load cases were considered for this portion of the study, outlined below. Each load case included a 35 kip load applied over a 12 by 12 in. patch. An illustration of the model and applied load cases is shown in Figure 4.4.2. ⢠Load Case 1 â loading applied at quarter span at center of outside panel near acute angle support ⢠Load Case 2 â loading applied at midspan at center of outside panel ⢠Load Case 3 â loading applied at quarter span at center of outside panel near obtuse angle support Figure 4.4.1: Placement of precast slab span panels at a skewed support
66 Table 4.4.1: Summary of FEM runs to investigate performance of skewed PCSSS Description Run Number 1 2 3 4 5 6 7 8 Run configuration PCSSS w/ 3" crack - 0 skew PCSSS w/ 3" crack - 15 skew PCSSS w/ 3" crack - 30 skew PCSSS w/ 3" crack - 45 skew PCSSS w/o crack - 0 skew PCSSS w/o crack - 15 skew PCSSS w/o crack - 30 skew PCSSS w/o crack - 45 skew Geometry Spans: Single Single Single Single Single Single Single Single #Panels wide 3 panels /18ft.wide Same Same Same Same Same Same Same Length 30ft Same Same Same Same Same Same Same Skew Angle 0 deg 15 deg 30 deg 45 deg 0 deg 15 deg 30 deg 45 deg Depth of precast section 3in.flange; 12in. web Same Same Same Same Same Same Same Depth of deck above precast web 6in. CIP Same Same Same Same Same Same Same CIP to precast interface above flange Unbonded Unbonded Unbonded Unbonded Monolithic Monolithic Monolithic Monolithic Supports Rollers Same Same Same Same Same Same Same Crack Simulated âcrackâ using contact elements. Bottom of section to 3in. from bottom (precast joint). Bottom of section to 3in. from bottom (precast joint). Bottom of section to 3in. from bottom (precast joint). Bottom of section to 3in. from bottom (precast joint). No crack, monolithic No crack, monolithic No crack, monolithic No crack, monolithic Matâl strength CIP Concrete 4ksi Same Same Same Same Same Same Same Precast Concrete 6.5ksi Same Same Same Same Same Same Same Reinforcement 60ksi Same Same Same Same Same Same Same Reinforcement Deck steel #8-#7-#7 @ 4in. oc Same Same Same Same Same Same Same Run along entire span length Transverse hooks in each direction (offset transversely by 1in.) #6@12in. Same Same Same Same Same Same Same Model as a continuous bar across the section rather than as lapped steel Location of transverse reinforcement 4-5/8â center of #6 from bottom of form Same Same Same Same Same Same Same Prestressing strands 16 in each PCSSS Same Same Same Same Same Same Same Transverse cage None None None None None None None None
67 Figure 4.4.2: Simply supported, three panel wide bridge and location of loading used for FEM models For all cases, the horizontal shear stress in the cast-in-place concrete was measured along the entire length and depth of the structure in the plane of the precast joint adjacent to the loading. The maximum horizontal shear stress in this plane was investigated for a range of skew angles for each of the load cases. The maximum horizontal shear stress measured in the models with a 3 in. deep precast joint and the associated monolithic models are shown in Figure 4.4.3 (a) and (b), respectively. (a) 3 in. precast joint (b) Monolithic Figure 4.4.3: Maximum horizontal shear stress measured in the cast-in-place concrete above the precast joint measured under the acute, midspan, and obtuse load cases
68 The horizontal shear stress in the models considered with load case 1, which had load applied near the acute pier connection, was observed to be reduced with increasing skew angles for both the section with the 3 in. flange joint as well as the monolithic model. The horizontal shear stress caused by load case 3, representing loading near the obtuse pier connection, for both the jointed and monolithic models remained relatively constant through the range of skew angles considered. For both model types, the midspan load case produced the most significant increase in horizontal shear stress, with an approximately 1/3 increase in the stress observed in both the jointed and monolithic models. The maximum shear stress from these three load cases defined stress envelopes for the jointed and monolithic models that varied with skew angle, shown in Figure 4.4.4. This maximum horizontal shear stress envelope remained relatively constant through the range of skew angles considered for both jointed and monolithic models. With increasing skew angle, the shear stress envelope increased by approximately 15% for the monolithic models and by less than 10% for the jointed models. The small variation and consistency between the models considering a 3 in. precast joint and a monolithic structure suggested that the effect of the precast joint in precast composite slab span construction was not expected to significantly affect the performance of the system in skewed applications. Figure 4.4.4: Maximum horizontal shear stress envelope above longitudinal precast joint considering all load cases for precast joint models and monolithic slab models. 4.5. End Zone Stresses in Precast Inverted Tee Sections Horizontal cracking frequently forms in the end region of prestressed concrete members when the prestressing strand is released and the prestress force is transferred to the concrete section. These cracks, which result from the vertical tension created by the transfer of prestress force, are defined as âspallingâ cracks, though often incorrectly labeled as âburstingâ or âsplittingâ cracks (Gergely et al., 1963). If unrestrained, these cracks can extend into the precast member and may negatively impact both the flexural and shear strength and durability of the section. Previous studies have suggested that these cracks cannot be eliminated, however vertically oriented reinforcing steel can limit crack width and propagation (Fountain, 1963). The first design parameters related to end zone stresses in prestressed members were introduced in the 1961 AASHTO Design Specification (AASHTO, 1961), that specified a minimum vertical reinforcement requirement for
69 pretensioned member end regions. This specification remained virtually unchanged since its introduction until the 2008 interim AASHTO LRFD specification incorporated changes to the specification, which included a change in the terminology of the end zone stresses from âburstingâ to âsplittingâ resistance of the pretensioned anchorage zones. The placement of large amounts of vertical reinforcement in the end regions of shallow inverted-T precast members caused congestion and difficulty in the placement of prestressing strand and concrete when 4 percent of the total prestressing force was used (i.e., AASHTO LRFD 2010). A historical study of the development of reinforcement designs for vertical end zone stresses indicated that the original design parameters were likely developed from a Marshall and Mattock (1962) study on horizontal end zone cracking in pretensioned I-girders, suggesting that design parameters provided in the specification may not be applicable to precast inverted-T sections. Also included in the modifications to the 2008 interim AASHTO LRFD specification was specific language for solid and voided slabs, as well as pretensioned box and tub girders. Variations in the spalling reinforcement details were investigated experimentally with the Concept 1 and 2 laboratory bridge specimens by varying the vertical end region reinforcement in the ends of the precast panels used in the laboratory bridges, which are discussed under the unnumbered heading âexperimental study,â included in this section. Because of the complicated state of stress near the end regions of prestressed members, two similar but unique modes of cracking may be observed. To limit the ambiguity regarding these stresses, the vertical tensile stresses which occur along the line of the prestressing forces were labeled as bursting stresses, while the vertical tensile stresses located away from the line of the prestressing force were labeled as spalling stresses, as illustrated in Figure 4.5.1. Figure 4.5.1: Spalling and bursting stresses near the end zone of prestressed members 1 2 3 1 - Spalling Stress 2 - Bursting Stress 3 - Prestress Force Beam Depth
70 Beam theory is not applicable in the end regions of prestressed concrete beams because the longitudinal strain is not linearly distributed through the depth of the cross section due to the introduction of the prestress force. Spalling stresses are a maximum at the end face of the member, typically near mid-height of the section and result in cracking at the end face which can propagate further into the member (Gergely et al., 1963). Bursting stresses occur along the line of the prestressing force, beginning a few inches into the beam and extending throughout the transfer length. Bursting stresses can result in strand slippage as cracking along the strand can eliminate bond between the strand and the concrete. Distribution of tensile stresses in the end region depends on the eccentricity of the prestressing force within the member. When the prestress acts at the centroid of the section, force is distributed symmetrically through the vertical member depth; in members with large eccentricity there is greater area above the prestressing force for stresses to distribute. This prestressing force is allowed to spread through a greater vertical distance which subsequently increases the spalling force near the end region. This is consistent with previous experimental work which related the maximum tensile stress location to eccentricity. Gergelyâs (1963) study on post-tensioned I-girders and rectangular sections found members with small eccentricities had maximum tensile stresses in the bursting zone and members with large eccentricities had maximum tensile stresses in the spalling zone. Hawkins (1960) corroborated Gergelyâs findings and also found that the eccentricity of the prestressing strand and the magnitude of maximum tensile stress in the spalling zone were positively related. Numerical Study FEM modeling was also performed to determine the magnitude and location of spalling and bursting stresses in the end region of precast inverted-T sections. Several simplifications were considered during the analysis to reduce the complexity and computational requirements of the model. The flanges were neglected to allow for the system to be modeled as a two-dimensional (2D) rectangular slab. Furthermore, the concrete was modeled as perfectly linearly elastic, which was appropriate up to the initiation of cracking. The transfer of the prestressing force was simulated by incrementing the force in the strand, from zero at the face of the section to the full magnitude at the transfer length (Lt), in 1/4 in. increments. Slip occurring between the strand and concrete was ignored. The transfer length was conservatively taken as 40 strand diameters (i.e., 20 in. for 1/2 in. strand), which was two-thirds of the transfer length specified by AASHTO (2010). The reduction in the transfer length from the AASHTO (2010) specification was selected to be conservative, as shorter transfer lengths are associated with higher vertical end zone stresses. Uniform and linear bond stress models were utilized, with the linear distribution decreasing with distance from the end face of the member. A total of 57 runs were completed during the numerical study, as documented in Table 4.5.1. Although the FEM model was not verified with experimental results from pretensioned beams, the models were compared to the results from Gergelyâs (1963) experimental study on a 6 by 12 in. post- tensioned rectangular beam. A 2D elastic model was created to simulate the physical experiment, with adequate correlation between the experimental and FEM model results, as shown in Figure 4.5.2, where the vertical axis represents the vertical tensile strains measured at midheight along the edge of the section and the horizontal axis corresponds to the distance from the end face of the specimen.
71 Figure 4.5.2: Validation of FEM model with experimental results from Gergely (1963) -1.0E-05 0.0E+00 1.0E-05 2.0E-05 3.0E-05 4.0E-05 5.0E-05 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from End Face (in.) S tr ai n (in ./i n. ) Experimental Results FEM Results
72 Table 4.5.1: Description of models run during parametric study Run # h (in.) Lt (in.) e (in.) e/h Bond Stress Distribution Run # h (in.) Lt (in.) e (in.) e/h Bond Stress Distribution 1 12 20 5 0.42 Uniform 30 6 20 2 0.33 Uniform 2 12 20 4 0.33 Uniform 31 18 20 6 0.33 Uniform 3 12 20 3.5 0.29 Uniform 32 24 20 8 0.33 Uniform 4 12 20 3 0.25 Uniform 33 30 20 10 0.33 Uniform 5 12 20 2.5 0.21 Uniform 34 36 20 12 0.33 Uniform 6 12 20 2 0.17 Uniform 35 42 20 14 0.33 Uniform 7 12 20 0 0.0 Uniform 36 6 20 2 0.33 Linear 8 12 20 5 0.42 Linear 37 18 20 6 0.33 Linear 9 12 20 4 0.33 Linear 38 24 20 8 0.33 Linear 10 12 20 3.5 0.29 Linear 39 30 20 10 0.33 Linear 11 12 20 3 0.25 Linear 40 36 20 12 0.33 Linear 12 12 20 2.5 0.21 Linear 41 42 20 14 0.33 Linear 13 12 20 2 0.17 Linear 42 8 20 1.6 0.20 Uniform 14 12 20 0 0.0 Linear 43 10 20 2.5 0.25 Uniform 15 12 6 4 0.33 Uniform 44 12 20 2.5 0.21 Uniform 16 12 10 4 0.33 Uniform 45 12 20 2.4 0.20 Uniform 17 12 12 4 0.33 Uniform 46 14 20 3.7 0.26 Uniform 18 12 16 4 0.33 Uniform 47 16 20 4.6 0.29 Uniform 19 12 20 4 0.33 Uniform 48 20 20 6.3 0.31 Uniform 20 12 24 4 0.33 Uniform 49 22 20 6.8 0.31 Uniform 21 12 28 4 0.33 Uniform 50 8 20 1.6 0.20 Linear 22 12 0 4 0.33 End1 51 10 20 2.5 0.25 Linear 23 12 6 4 0.33 Linear 52 12 20 2.5 0.21 Linear 24 12 10 4 0.33 Linear 53 12 20 2.4 0.20 Linear 25 12 12 4 0.33 Linear 54 14 20 3.7 0.26 Linear 26 12 16 4 0.33 Linear 55 16 20 4.6 0.29 Linear 27 12 20 4 0.33 Linear 56 20 20 6.3 0.31 Linear 28 12 24 4 0.33 Linear 57 22 20 6.8 0.31 Linear 29 12 28 4 0.33 Linear 1All force assumed to be applied at the end face to simulate post-tensioned case The spalling force magnitude and stress distribution into the beam was found to depend on many factors. The assumption of linear bond distribution (where bond stress decreases linearly into the section) creates larger spalling stresses which extend a shorter distance into the member than uniform bond distribution. As the ratio of eccentricity (e) and height (h) increases, the magnitude of the spalling stresses increase and extend further into the member. A shorter transfer length distributes the prestress over a shorter distance resulting in larger spalling stresses extending over a shorter distance into the member. As height increases, the spalling force increases and the distribution of the stress extends further into the member because of the greater vertical area over which to distribute the prestress. Bursting force magnitude and location is affected by eccentricity, transfer length, and height. Bursting forces increase with smaller e/h ratios and start further into the member. Shorter transfer lengths distribute forces over a shorter distance which results in larger bursting stresses and a smaller length
73 over which bursting stresses act. As member height increases, the magnitude of the bursting forces increase and the length over which the bursting stress acts is increased slightly. The length which bursting stresses extend is mostly based on transfer length but larger heights and smaller e/h values also increase the ratio of the length over which bursting stresses act to height. For smaller e/h values, bursting force is significantly larger than the spalling force. However, although the total force generated from the bursting stresses is larger than the total force generated from the spalling stresses, the bursting force acts over a much larger area. This provides a greater amount of concrete to resist the tensile forces. Figure 4.5.3 compares the bursting and spalling stresses for a member 12 in. in height with 2.4 in. eccentricity and a 20 in. transfer length. The maximum stress is larger for spalling than for bursting. Also, the maximum spalling stress occurs on the end face which is only restrained on one side making it more likely for a crack to form there. In the majority of historical studies on end zone cracking, detrimental cracking initiates on the end face of members. If cracks are found along the line of load, they are likely caused by a combination of bursting and radial stresses, as expressed in Uijlâs (1983) hollow core slab study. Figure 4.5.3: Comparison of Bursting and Spalling Stresses for Member e/h=0.20 The ratio of the predicted spalling force to the prestress force of slabs with a constant depth of 12 in. is shown in Figure 4.5.4. Table 4.5.2 shows the ratio of predicted spalling force to strand force as found through FE modeling of slabs with the same e/h ratio as the feasible precast inverted tee sections in Table 4.1.2. The spalling force ranged from 0.3 to 8.5 percent of the prestressing force. -0.0020 -0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0 0.5 1.0 1.5 2.0 2.5 x/h V er tic al S tr es s/ S tr an d S tr es s Bursting Stress Spalling Stress
74 Figure 4.5.4: Ratio of spalling force to prestress force as a function of ratio of eccentricity to precast member depth for linear and uniform bond stress distributions, with h= 12 in and Lt = 20 in. Table 4.5.2: Ratio of Spalling Forces to Prestress Forces as Predicted by FE Models for Slabs with Equivalent e/h as Feasible Precast Inverted Tee Sections, using both Uniform and Linear Bond Stress Distributions, varying h and e/h and constant Lt Depth of Precast (in.) =20 in. 8 10 121 122 14 16 20 22 e/h (in.) 0.20 0.25 0.20 0.21 0.26 0.29 0.31 0.31 Spalling Force assuming uniform bond stress distribution/ Total Strand Force 0.003 0.011 0.004 0.005 0.019 0.033 0.065 0.067 Spalling Force assuming linear bond stress distribution/ Total Strand Force 0.006 0.021 0.009 0.011 0.030 0.052 0.085 0.085 1Laboratory Bridge Specimen with 5.25 in. flange height 2Laboratory Bridge Specimen with 3.0 in. flange height Experimental Study Four different variations in the vertical steel configurations were considered during the laboratory study, with each configuration repeated twice. The reinforcement details for each configuration are shown in 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 e/h S pa lli ng F or ce / P re st re ss F or ce Linear Bond Stress Distribution Uniform Bond Stress Distribution
75 Table 4.5.3. The vertical reinforcement in configurations 1 and 2 provided less than half of the 1.0 in.2 required by the AASHTO (2010) specification. The area of vertical reinforcement provided in configuration 4 was sufficient according to the specification; however it did not meet the placement requirements because the reinforcement extended farther into the section than the larger of 3 in. or one quarter of the total member depth (i.e., the reinforcement was not adequately grouped near the end of the beam). The vertical reinforcement in configuration 3 met all requirements of the specification, and consisted of No. 5 four legged stirrups spaced at 2 in. An additional No. 5 four legged stirrup was also placed a distance of 4 in. from the face in configuration 3. Table 4.5.3: Vertical reinforcement in configurations 1-4 of the precast members utilized in experimental study Configuration Description of Vertical End Zone Reinforcement Cross Section View of Stirrup Elevation View of Reinforcement Spacing 1 #3 stirrup at 2 and 4 in. total area = 0.44 in2 2 #4 stirrup at 2 in. total area = 0.40 in.2 3 #5 four legged stirrup at 2 and 4 in. total area = 2.5 in.2 4 #5 stirrup at 2 and 4 in. total area = 1.2 in.2 The end regions of the panels used in the Concept 1 laboratory bridge were well instrumented to investigate the state of stress immediately after release. On the side face of each section, rosettes were placed at midheight, 2 in. from the end face. A single strain gage was attached to each vertical stirrup with vertical placement ranging from 5.5 in. to 7.5 in. from the bottom of the precast section. The concrete and steel gages were monitored before, during, and after transfer. Readings were taken every minute, starting at 56 minutes before release and until 88 minutes after release. The average of the strain readings taken in the fifteen minutes before release was used to zero the remaining measurements. The measured strains in each end section of the precast members used for the Concept 1 laboratory bridge are recorded in Table 4.5.4. The magnitudes of the strains observed in the end sections of the inverted-T sections were negligible, and no signs of cracking were detected, visually or via the instrumentation. The results from the experimental study suggested that the precast concrete at the
76 time of transfer, which was measured to have a compressive strength of 7410 psi at an age of 1 day (Smith et al., 2008), was sufficient to resist vertical tensile stresses in the end zones regardless of the reinforcement details. Table 4.5.4: Maximum of the measured strain values in end regions of precast members used for Concept 1 laboratory bridge in the 88 minutes after transfer of prestress force Span 1 Span 2 Stirrup Location from End Face 2 in. 4 in. 2 in. 4 in. Northwest Vertical Stirrup Size #3 #3 #3 #3 Steel Gages (με) 3.5 -3.6 19 -4.8 Concrete Gages (Vertical Leg of Rosette) (με) -21 n/a 7.2 n/a Northeast Vertical Stirrup Size #4 n/a #4 n/a Steel Gages (με) -1.1 n/a 16 n/a Concrete Gages (Vertical Leg of Rosette) (με) 3.0 n/a 35 n/a Southwest Vertical Stirrup Size 2 - #5 2 - #5 2 - #5 2 - #5 Inner1 Outer 2 Inner Outer Inner Outer Inner Outer Steel Gages (με) -3.7 16 -4.2 0.8 -8.7 6.2 -7.2 -1.9 Concrete Gages (Vertical Leg of Rosette) (με) 0.4 n/a 17 n/a Southeast Vertical Stirrup Size #5 #5 #5 #5 Steel Gages (με) -1.1 -7.1 -20 -8.6 Concrete Gages (Vertical Leg of Rosette) (με) 1.4 n/a 24 n/a 1 Inner â inner stirrup of four-legged stirrup 2 Outer â outer stirrup of four-legged stirrup Summary and Application to Design Results from the finite element study revealed that the relationship between e2/(h*db) to the ratio of tensile spalling force to prestress force is reasonably approximated by a straight line as shown in Figure 4.5.5. Because the true bond stress distribution is somewhere between uniform and linear bond stress,
77 an average between these two assumptions was developed, as shown in Figure 4.5.5. The equation for this straight line approximation is , (4.5.1) where T is the spalling force and P is the strand force. Figure 4.5.5: Ratio of Spalling Force to Prestress Force for varying e2/(h*db ) Vertical steel reinforcement does not carry the vertical tensile stress until the concrete cracks. If the spalling stresses are small enough in a member for the concrete tensile strength to prevent cracking, vertical tensile steel is not necessary for the member. To calculate the concrete area to be considered in providing tensile resistance, the area over which spalling forces act must be determined. Based on the slab span sections studied, the shortest distance into the member the spalling stress extends is h/12. This becomes a conservative estimate as the section increases in height and e/h. The area of concrete to resist this tensile strength is conservatively estimated as the product between h/12 and the distance between the outermost prestress strands (bs) and can be written as , (4.5.2) where Tc is the tensile force that can be resisted by the concrete, fc is the concrete compressive strength at 28 days, h is the height of the member, and bs is the distance between the outermost pretension strands. If the design tensile force is smaller than the tensile force resisted by concrete (T < Tc), it is reasonable to assume cracking will not occur and vertical tensile steel is not needed in the end region to resist the spalling force. Otherwise, steel must be placed within the end region of the member to resist 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 e 2 /(h*d b ) S pa lli ng F or ce / S tr an d Fo rc e Uniform Bond Stress Distribution Linear Bond Stress Distribution Design Recommendation
78 the tensile force found in Eqn. (4.5.1). The area of steel needed to resist the predicted spalling force is given by , (4.5.3) where As is the area of steel and fs is the allowable working stress of vertical reinforcement. Application of these recommendations to the designs resulting from the parametric study described in Section 4.1 result in the end zone reinforcement identified in Table 4.5.5. The last line of the table includes the AASHTO 2010 requirements for comparison, which are incorrectly referred to as splitting resistance rather than spalling resistance requirements in AASHTO. Table 4.5.5: Spalling reinforcement for Precast Inverted-T Sections Height (in.) 8 10 12 12 14 16 20 22 Number of Strands 12 16 16 16 36 38 46 54 Strand Diameter (in.) 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 Total Prestress Force at Jacking (k) 370 500 500 500 1100 1200 1400 1700 Concrete Compressive Strength at Transfer (ksi) 5.0 5.0 4.5 4.5 5.5 5.5 5.6 6.0 e (in.) 1.6 2.5 2.4 2.5 3.7 4.6 6.3 6.8 T (k) (Eqn. 4.5.1) 1.0 7.5 4.6 5.4 32 51 97 126 Tc (k) (Eqn. 4.5.2) 17 21 24 24 32 36 45 51 Vertical Steel Needed? No No No No No Yes Yes Yes As (in. 2) (Eqn. 4.5.3) -- -- -- -- -- 2.6 4.9 6.3 h/4 -- -- -- -- -- 4.0 5.0 5.5 Stirrup Bar Size -- -- -- -- -- #6 #6 #6 As (in 2) per AASTHO Article 5.10.10.1 0.74 1.0 1.0 1.0 2.2 2.4 2.8 3.4 4.6. Connection Details between Superstructure and Substructure The bearing and connection details between the bridge superstructure and the supporting substructure were investigated by a review of existing PCSSS bridges constructed by the Minnesota Department of Transportation. Because no problems have been encountered in the existing field bridges, the same details may be deemed appropriate in future applications of PCSSS bridges. Some modifications are recommended to reduce the potential for restrained shrinkage in the transverse direction. Figure 4.6.1 shows an elevation view of the bearing detail at one of the two continuous supports for the Center City Bridge, one of the original field implementations of the PCSSS. The pile caps in this particular
79 bridge were precast, and the elevation view is shown through one of the sections featuring a vent hole through the pile cap into which dowels were placed prior to casting the CIP concrete. As shown in the figure, the main bearing support was provided by a 6 in. wide by 1/2 in. thick neoprene bearing pad, with the center of bearing located 12 in. from the edge of the pier. Polystyrene was utilized in the 9 in. between the edge of the pier and the neoprene, as well as the 4 in. between the neoprene and the end of the beam; the polystyrene was selected because it would prevent the egress of concrete during the closure pour and was crushable and would therefore not significantly affect the bearing geometry of the system. Figure 4.6.1: Bearing detail at continuous pier in Mn/DOT Bridge No. 13004 in Center City, Minnesota The neoprene and polystyrene were not located in the transverse joint between the precast sections nor in the regions beneath the flange cutouts. This enabled the CIP concrete to fill those regions to facilitate the negative moment resistance of the bridge by enabling the transfer of compressive forces low in the section across the pier. Vertical dowels were provided in the Center City Bridge to ensure that a mechanical connection was present between the substructure and superstructure. The vertical reinforcement was epoxied into holes drilled between the ends of the adjacent precast members at the continuous piers, and were subsequently embedded in the CIP closure pour. The vertical dowels consisted of No. 5 bars at 12 in. The placement of the vertical reinforcement in these locations was found to be difficult in some of the subsequent applications of PCSSS bridges, because the 4 in. gap between the ends of the precast panels does not always provide sufficient tolerance for the precast panel span lengths. For this reason, the placement of the vertical dowels in the 10 in. flange cutout region may be preferred; however eccentricity of the vertical dowels from the centerline between precast panels will allow for the introduction of a moment between the superstructure and substructure in plan, and should therefore be avoided. It is recommended that the vertical dowels be oriented along a single line bisecting the area
80 between adjacent precast panels at continuous piers. Because the reinforcement is not provided to prevent cracking, and is simply to provide dowel action in the case of differential displacement between the superstructure and substructure, it may be acceptable to place the reinforcement as a group in the 24 in. space between precast webs, however still along the line bisecting the specimens. A method considered by the Minnesota Department of Transportation to reduce the potential for the restraint of transverse shrinkage was to encase the vertical dowels in foam. The foam will likely only be beneficial if the CIP is debonded from the pier via a bond breaker. Consequently, in future applications of PCSSS bridges, it is recommended that a debonding material, such as a sheet of plastic be used, to prevent the CIP concrete from bonding to the substructure. 4.7. Numerical Determination of Laboratory Loading Mechanical loading was utilized in the laboratory to simulate traffic loading on the laboratory specimens (i.e., Concept 1 and Concept 2), described in Chapter 5. The Concept 1 specimen was developed based on the Center City Bridge, with some parameter variations (e.g., investigation of different flange thicknesses: 3 in. flange thickness in one span versus the 5-¼ in. flange thickness in the other span which emulated the Center City Bridge). The laboratory bridge specimens were fabricated with 12 in. thick precast panels and 6 in. cast-in-place topping. The approximately 22 ft. span lengths represented the outer spans of the Center City Bridge, which were a lower practical bound of PCSSS bridge spans. The same 18 in. deep section was used in all three spans (22-27-22 ft.) of the Center City Bridge, and could be used in even longer spans as indicated by Table 4.1.2. The use of the 18 in. deep section led to relatively low service stresses particularly in the end spans. In an effort to improve the relevance of the laboratory tests to longer spans, the magnitude of the patch load was selected after a numerical analysis of longer PCSSS bridges. The 35 kip value was expected to induce the same levels of transverse tensile stress in the joint region of the 22 ft.-5 in. laboratory bridge span as would be expected in a 30 ft. three-span continuous system. The 30 ft. continuous bridge was selected because it represented a reasonable value for the design span of a slab span system with 12 in. deep precast panels (although as shown in Table 4.1.2, it might be possible to use something as shallow as a 10 in. deep precast section for a 30 ft. span). The 35 kip patch load was applicable to both the two- span Concept 1 and simply-supported Concept 2 laboratory bridges, coincidentally, because loading was applied at the quarter points of the simply-supported Concept 2 specimen, which featured different transverse reinforcement details in each half of the bridge span. The numerical model was developed assuming an unbonded constraint between the precast flanges and CIP concrete, as illustrated in Figure 4.7.1. This was done to ensure that convergence would be achieved at the interface immediately above the precast joint. Figure 4.7.2 illustrates a modified four point AASHTO tandem design load on the three span 30 ft. continuous bridge, which consists of four 25 kip patch loads spaced in a 4 by 6 ft. grid. This modified tandem load pattern was based on twice the design tandem load, as specified in Article 3.6.1.2.3 (AASHTO 2010). The design tandem was doubled to provide an expected worst case scenario near the joint region, which represented two truck wheel loads placed as closely as possible directly over a longitudinal joint. The image is shown from the end span looking in the direction of traffic. The 6 ft. wide patch loads are placed directly above the precast joints, which represented the worst load case for the system.
81 Figure 4.7.1: Separation of top of precast joint from CIP concrete in 30 ft. continuous and laboratory bridge models Figure 4.7.2: Three span 30-30-30 ft. continuous bridge with AASHTO tandem loading, increased by a magnitude of two to account for two trucks side by side with adjacent wheels applied over the joint, applied for the numerical calculation of a patch load demand in laboratory bridge. The numerical models utilized for the Concept 1 and Concept 2 laboratory specimens are shown under deformation in Figure 4.7.3a-b, respectively. The Concept 1 model was analyzed with the patch load centered at midspan of both spans, while the Concept 2 model was loaded at the quarter points. The same numerical model was utilized to analyze the effect of the patch load for both specimens. For the Concept 2 bridge, which was a simply-supported span, the same two-span model was used with an assumed modulus of elasticity of the CIP and precast concrete in the span with the 5-¼ in. thick flange Separation of precast flange and CIP concrete End Span Center Span 6 ft. section 4 sets of 25 kip patch loads
82 set to be 1/100 of the modulus of elasticity of the CIP used in the loaded span modeled with a 3 in. flange, effectively creating a simply-supported boundary condition at the end of the bridge connected to the adjacent span. a) Concept 1 laboratory specimen â patch loading at midspan b) Concept 2 laboratory specimen â patch loading at quarter points. Second span modeled with modulus of elasticity of CIP equal to 1/100 CIP modulus of elasticity of loaded span Figure 4.7.3: Deflected numerical models of (a) Concept 1 specimen and (b) Concept 2 specimen for determination of patch loading in laboratory specimens The analyses suggested that the load required to induce similar levels of transverse tensile stresses in the 30 ft. continuous bridge and the loading cases of the laboratory bridge varied by less than two kips, and therefore, with a patch load of 26.7 kips required to induce similar levels of transverse stress in the laboratory bridge as the 30 ft. continuous bridge. Furthermore, the dynamic loading effects were considered through the use of a 33 percent increase in the static load, as specified in Article 3.6.2.1 of the AASHTO specification (2010). Therefore, the calculated load to be applied to the laboratory bridge to simulate a tandem vehicle loading on a 30 ft. continuous bridge was determined to be 35 kips (26.7 kips * 1.33).
