The observed failure modes can be generally grouped into the following categories: diagonal crushing without yielding **shear** reinforcement, yielding of **shear** reinforcement in combination with localized diagonal crushing, yielding and rupture of **shear** reinforcement, distributed diagonal crushing, **shear** failure at the web / bulb interface, and failures precipitated by strand slip. The modes of failure for all of the test **girders** are described in Figures 5.1a through 5.1t. Each of these figures consists of two text boxes and selected photographs. The left text box presents material strengths, reinforcement details, and the applied load at failure or ultimate. In the right text box, the condition of the structure just prior to failure and the mode of failure are described. This includes the ratio of the support reaction force at first **shear** cracking to the support reaction force at failure/ultimate ( R(first crack)/R(failure)), the equivalent reaction ratio for first stirrup yield (R(first stirrup yield)/R(failure)), the average stirrup strain at peak loading, and whether or not slip had occurred of strands or along **shear** cracks. In addition, a brief description of the type of failure is presented. At the bottom of each summary, several images are used to describe the condition of the structure immediately before and/or just after failure. Table 5.2 provides a summary of the condition of each girder just prior to failure or at a level of sustained maximum load for girder ends that did not fail; the summary information includes the support reaction force, the condition of the web **concrete** above the support, the maximum recorded stirrup strain, prestressing strand slip, and information on the web **shear** cracks. Much of the information presented in Table 5.2 was also presented in Figure 5.1 but it is presented again in a more concise manner for the convenience of the reader.

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In order to develop and test a tool that can accurately predict the **shear** **capacity** of pre- stressed **concrete** beams, a numerical model that is constructed based on reliable and precise experimental parameters was required. In this chapter, the development and validation of a FEA model to predict the **shear** **capacity** of **prestressed** **concrete** bridge **girders** are presented. Validation of the FEA model was achieved by comparing numerical results to the experimental results presented in Chapter 2, as well as a collection of independent beam tests documented in the technical literature. In this study, VecTor2 (Wong et al., 2013) FEA code was considered for modeling and computing the **shear** **capacity** of **prestressed** **concrete** **girders** presented in Chapter 2. This FEA code has been developed at the University of Toronto by researchers studying reinforced **concrete** behavior and applications of the finite element method. VecTor2 is a program based on the Modified Compression Field Theory (MCFT) (Vecchio and Collins, 1986) and the Disturbed Stress Field Model (DSFM) (Vecchio, 2000) for nonlinear finite element analysis of two-dimensional reinforced **concrete** membrane structures. Using VecTor2, finite element models with fine mesh can be constructed. The cracked **concrete** behavior can be modeled by VecTor2 as an orthotropic material with smeared rotating cracks. This methodology is applicable for reinforced and **prestressed** **concrete** structures that require a relatively fine mesh to model reinforcement details and local crack patterns.

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The available reliability methods are presented in several books [17, 18]. Reliability analysis can be performed using iterative procedures, by Monte Carlo Simulations or using special sampling techniques. Limit States are the boundaries between safety and failure. There are three types of limit states. Ultimate Limit States (ULS) are mostly related to the bending **capacity**, **shear** **capacity** and stability. Serviceability Limit States (SLS) are related to gradual deterioration users comfort or maintenance costs. The third type of limit state is fatigue. This paper is focused on the ultimate limit state of the moment carrying **capacity** [13].

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Over-height vehicles impacting **prestressed** **concrete** (PS) and reinforced **concrete** (RC) bridge **girders** is a frequent problem experienced by the majority of transportation departments all over the world. The most common practice used to restore a damaged bridge is to cut out the damaged girder and replace it with a new one. More recently, alternative methods have been examined to help decrease the costs of replacing damaged **girders** and minimizing closure time. The research reported in this thesis considered three scenarios to examine the effectiveness of using Carbon Fiber Reinforced Polymers (CFRP) to restore impact-damaged PS **girders** to their original **capacity**. The first scenario investigated the effectiveness of CFRP sheets to repair a 54 ft (16.4 m) long girder with one ruptured prestressing strand caused by an over-height vehicle impact. The second scenario investigated the effectiveness of CFRP sheets to repair two 54 ft (16.4 m) long **girders** with various numbers of prestressing strands ruptured artificially at midspan. The final scenario examined the effectiveness of CFRP sheets to repair a **shear**-critical specimen with four prestressing strands artificially ruptured near the support.

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Various numerical and experimental studies over the past three decades have established that debonding is beneficial in reducing end stresses, and subsequently end cracking in bridge **girders**. Among these studies are early numerical work by Kannel, French, and Stolarski (1997), which mainly focused on release methodology of prestressing strands, but also reported that debonding strands for a short distance reduces end stresses through experimental programs. Later numerical studies by Okumus and Oliva (2013) also reported that debonding is effective in controlling end cracks and is more effective for some crack types than the use of draped strands. Furthermore, experimental research carried out by Ross et al. (2014) compared the use of debonded strands to other girder end region detailing (i.e., large diameter vertical reinforcement, vertical end-region post-tensioning, and end reinforcement with AASHTO LRFD specifications). A girder detailed in accordance with the AASHTO (2010) LRFD specifications was designated as the control specimen to evaluate the impact of these three other details on observed cracking. Ross et al. (2014) reported the use of debonding of 45 percent of total strands was more effective and observed smaller crack lengths and widths with debonding compared to the other end region detailing. Although these research studies establish and highlight the benefits of debonded strands in controlling end cracking, debonding can have negative impacts in other areas of design such as **shear** and flexural **capacity**.

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TxDOT currently uses Tx-series of PC **girders** for highway bridge construction. Tx-series **girders** have a web thickness of 178 mm and depths ranging from 711 to 1,829 mm. Typically Tx-series **girders** have a top slab with a thickness 203 mm and the minimum spacing between **girders** is 2,032 mm. In this research an internal Tx54 was considered with a top slab 2,032 mm wide. The resulting girder cross section was scaled down to 43 % to form the modiﬁed Tx28 girder, Fig. 1, which was used in seven of the tested **girders**. The other two **girders** had the same web thickness and effective depth, Fig. 2. Their bottom ﬂange had a higher depth by one inch to accommodate the additional longitu- dinal reinforcement required to increase the ﬂexure **capacity** and ensure having a **shear** failure at the ultimate load. Also, their top ﬂange had a reduced width equals to the width of the real top ﬂange scaled down by the same ratio to allow ﬂexure **shear** failure to happen at the ultimate load. These two modiﬁcations in the cross section should not have any effect on the **shear** cracking strength of the web.

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Reed and Peterman 9 conducted both flexural and **shear** tests on three full scale bridge **girders** that were replaced by the Kansas Department of Transportation. The three damaged **girders** were saw-cut in half longitudinally so that six single tee specimens were tested. Since an immediate bond-slip can be caused by an extended web **shear** crack into the transfer length, 10 Reed and Peterman 9 used two distinct setups for the **shear** test. They tested two **girders** with no overhang (NOH) and three **girders** with over- hang (OH). This test setup provided an understanding of the influ- ence of CFRP on the propagation of web **shear** cracks into the transfer length of the prestressing steel. 9 The **shear** **capacity** results for the tested specimens showed that the NOH specimens failed by a bond-slip that was induced by **shear** crack propagating into the transfer zone of the prestressing reinforcement. On the other hand, the OH specimens showed a higher **shear** **capacity** than the NOH specimens. The increase was likely due to the longitudinal CFRP wrap holding the web **shear** cracks closed and increasing the **shear** contribution due to aggregate interlock.

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to enhance the strength, ductility, and serviceability of the structural members, utilizing the prestressing force introduced to the **concrete**. Although many other steel– **concrete** composite girder systems have been devel- oped, as shown in Fig. 1, increasing demand continues for new horizontal composite members that can ensure reliable load-carrying performances and price competi- tiveness in the current construction market (Heo et al. 2007; Kim et al. 2011; Kim and Lee 2011). Therefore, in this study, the **prestressed** hybrid wide flange (PHWF) girder that can effectively resist external forces was devel- oped. Figure 2 shows the main concepts and the actual construction sequences of the proposed PHWF girder. The PHWF girder system was devised and designed to achieve superior deflection control performance and high flexural and **shear** capacities by introducing pre- stress into the **concrete** bottom flange. In addition, by utilizing the embedded steel member with trapezoidal- shaped multiple openings (Fig. 2), the horizontal **shear** strength and the composite performance between the cast-in-place (CIP) **concrete** and the PHWF girder can be significantly enhanced. In addition, the top steel flange of the embedded steel member was designed to achieve the sufficient **capacity** under positive flexural moments

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database show that ACI 318-11 provisions for **shear** transfer **capacity** of **concrete** are more un- conservative for lightweight **concrete** (LWC) beams than in NWC beams. A rational approach based on the upper-bound theorem of **concrete** plasticity has been developed to assess the reduced aggregate interlock along the crack interfaces and predict the **shear** transfer **capacity** of **concrete**. A simplified model for the modification factor is then proposed as a function of the compressive strength and dry density of **concrete** and maximum aggregate size on the basis of analytical parametric studies on the ratios of **shear** transfer **capacity** of LWC to that of the companion NWC. The proposed modification factor decreases with the decrease in the dry density of **concrete**, gives closer predictions to experimental results than that in the ACI 318-11 **shear** provision and, overall, improves the safety of **shear** **capacity** of LWC beams.

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CEN (2004)) was used for all cast-in-place elements of piers and **girders**. The initial prestressing was applied through 32 mm diameter Dywidag ST 85/105 threaded bars, with 1030 MPa nominal tensile strength and an initial jacking tension of 720 MPa. For each 59m-long cantilever, the longitudinal force above the pier was about 120 MN and was provided by a total of 266 cables. As mentioned in Section 1, after only a few years from the viaduct opening, monitoring field data started to exhibit a deflection drift that cannot be explained using classical creep models such as those found in most design codes, e.g. CEN (2004). In this respect, Figure 4 depicts the deflection trend recorded at cross section A of Figure 3(a). In stark contrast with the design prediction (CEN, 2004) of 160 mm in 1988, the actual deflection reached 230 mm with an apparent rate of 8 mm/year. A similar behavior was also observed for the other three box **girders**. These first observations prompted the owner to undertake, between 1988 and 1989, a radical intervention. Specifically, 10 cm of road pavement was removed from the cantilever arms and the suspended central beam, and replaced with a thinner layer of lightweight asphalt. The effect of this work is evident in Figure 4 through the immediate recovery of 70 mm in deflection and the disappearance of the deflection drift for a few years after the intervention. A second major maintenance activity was accomplished between 1998 and 1999, with the aim of repairing the **concrete** cover of the top slab, heavily deteriorated by the extensive use of salt during winter. The repair consisted of a scarification of the damaged **concrete**, replacement of corroded unprestressed bars, and restoration of the damaged **concrete** cover. In the following years, dumpy level measurements showed once more an increase in

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The deteriorated strength properties of the materials were calculated using these average temperatures. The **shear** **capacity** was then predicted using the simplified formulas of the Canadian Standards Association (CSA A23.3-04). The proposed method was validated using the experimental results by others and the predictions of the analytical method that utilizes MCFT. A set of simple design charts to determine the average temperature of **shear** reinforcement and **concrete** were also provided. Increasing cover thickness and cross section width were found to provide an effective way to inhibit temperature increase during exposure to fire. The proposed method for predicting the **shear** **capacity** of RC beams during fire exposure is simple and practical, and so can readily be used by structural engineers.

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Upon the completion of testing the ten half-scale AASHTO Type II **girders** under static loading and analyzing the results, the three top performing repair conﬁgurations from this set were duplicated and applied to the remaining three half-scale **girders** for dynamic loading tests (PS-11 to PS-13) to investigate fatigue properties of the repairs. The three best performing repairs from the initial ten half-scale **girders** that were chosen for fatigue testing were the two- layer and three-layer repairs with 20-in. (508 mm) spacing and the two layer with 36-in. (914.4 mm) spacing. These conﬁgurations were recreated exactly, maintaining the 8-in. (203-mm) wide longitudinal laminates which started at a length of 17 ft (5,181.6 mm) while reduced six in (150 mm) per each additional layer applied. Also, the 12-in. (304.8- mm) wide transverse U-wrappings extended to the top of the web of each girder. Loads, deﬂection, strains developed along the height of the girder, and strains developed along the span of the **girders**’ extreme bottom ﬁber were recorded for all **girders** during their testing. In addition, the modes of failure were also recorded.

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As an alternative to **shear** design based on beam theory, the truss analogy (strut-and-tie) method is also permitted in BS8110 and BS5400. This method emphasizes a different physical explanation of load carrying **capacity**, based on an assumed compressive stress trajectory in the **concrete**, reacted by tension in the main reinforcement, as indicated in Figure 1. Both codes imply that the tension force is taken mainly by reinforcement above the pile head - BS8110 suggests reinforcement in a strip of width three times the pile diameter centred on each pile is effective (analogous to the width of **shear** enhancement), while in BS5400, all reinforcement can be taken into account provided 80% of it is placed in strips anchored directly over the piles. KK

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Page ULTIMATE 61 3 CHAPTER STRENGTH PRESTRESSED OF REINFORCED AND CONCRETE BEAMS WITH REINFORCEMENT SUBJECTED TRANSVERSE TO PURE TORSION Summary 61 3.1 Introduction 62 3.2 Under 3.3 Fact[r]

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For safety reasons, an adequate resisting **capacity** of the **girders** against principal tensile stresses under ultimate loads is essential. Thus, many codes including the Canadian code, specify that the ultimate load calculated with maximum possible loss of prestressing force is to be the only require ment for the principal tensile stress criterion in design. Thus, the requirement is to check whether the magnitude of the maximum principal tensile stress in the girder exceeds the allowable value. If it does, the **concrete** is assumed to be cracked and will not follow the elasticity equation any more. However, if the maximum principal tensile stress does not exceed the allowable **concrete** tensile strength, then the **concrete** is assumed to remain uncracked and this would require only nominal amount of reinforcement against

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failed **shear** span was the only output of the NNs developed. Table 1 gives the ranges of input data in training, validation and test subsets used to develop the NNs. In the database, beam width of deep and slender beams ranged from 20 to 300 mm and from 100 to 457 mm, respectively, effective section depth is between 80 and 1,559 mm for deep beams and between 110 and 1,090 mm for slender beams, and longitudinal reinforcement ratio ranged between 0.0011 and 0.066 for deep beams and between 0.0028 and 0.066 for slender beams. The maximum ver- tical web reinforcement indices for deep and slender beams were 0.964 and 0.14, respectively, and the maximum horizontal web reinforcement index for deep beams was 1.847. The test speci- mens were made of **concrete** having a very low compressive strength of 11.2 MPa and 14.7 MPa for deep and slender beams, respectively, and a high compressive strength of 120 MPa and 125 MPa for deep and slender beams, respectively. Training, vali- dation and test subsets had 50%, 25%, and 25% of all specimens in the database, respectively. The input data in each subset were selected at equally spaced points throughout the database so that the range of input in training subset would cover the entire distri- bution of database and input in validation subset would stand for all points in training subset as shown in Table 1.

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present of vertical reinforcements. ea Eccentricity of loading along the side width a. eb Eccentricity of loading along the size width b. fa Aggregate interlocking [r]

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bers with no **shear** reinforcement should be reduced by half (Palmer and Schultz 2010, 2011), and as afore- mentioned, it is very difficult to provide **shear** reinforce- ment in the PHCS members produced by the extrusion method. According to the recent research conducted by Lee et al. (2014), Im et al. (2014), and Palmer and Schultz (Palmer and Schultz 2010, 2011), however, the strict restriction on the web-**shear** **capacity** of the thick PHCS members without the minimum **shear** reinforcement can be excessively conservative. Because the provisions on the web-**shear** strength of the PHCS members have a huge impact on precast industry, further experimen- tal investigations on thick PHCS members and detailed reviews on this issue are still required. As an example, Fig. 3 shows a typical underground precast parking struc- ture of a multiplex building constructed with the PHCS units. Due to heavy weight of soil, the top roof floors of the basement are commonly designed with thick PHCS members having a thickness of 300 mm or greater, and the required **shear** force to the web-**shear** **capacity** ratio ( V u /φV cw ) of the PHCS units at the critical section of the

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To assess the precision of the 3D-DIC setup for the pre- sented experiments, a number (N ¼ 50) of reference images were taken prior to each test under a zero-loading condition. The subset size was taken equal to 27 px whereas the stepsize was chosen equal to 3 px. Given the experimental setup, the physical dimension of 1 pixel approximated 1 mm. The subset was allowed to undergo an afﬁne transformation thus taking into account translation, rotation, **shear** and normal straining. As the displacements from one frame to another may be smaller than one pixel, the subset in the image of the deformed state is not likely to ﬁt on the pixel grid and an interpolation method between the pixels is needed. Therefore, a bicubic interpolation scheme has been adopted in the MatchID software during the analyses. Additionally, Gaussian preﬁltering (5 5 px kernel size) of the subset information was adopted as a low pass-ﬁlter to attenuate high- frequency signals and allow for proper interpolation. Based on the measured displacements u i (with i ¼ x; y; z), Green-

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