MODELS AND DESIGN PROCEDURES FOR BEHAVIOUR OF CONCRETE IN SHEAR 

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Chapter 3 INTERROGATION OF SHEAR TEST DATABASE

A database was compiled of previous experimental testing relating to the shear behaviour of concrete beams, to allow for a number of analyses to be conducted. The database consisted of almost 2000 RC beams and 500 PC beams from all accessible published research, locally and internationally, relating to the shear behaviour of concrete beams. This Chapter details the composition of the RC and PC databases, a variety of analyses conducted on the databases, and the conclusions resulting from the analyses.

Objectives

The main objective of the composition and analysis of the RC and PC databases mentioned above was to investigate the influence of various design parameters on the shear behaviour and ultimate shear capacity of concrete beams using available experimental data. By examining the trends in several failure criteria across a variety of parameters, it was possible to identify the parameters most influential in the shear performance of concrete beams over varying ranges of design parameters. Of most interest to the overall objective of the project, which was to assess the validity of absolute limits being placed on allowable shear stresses in high-strength concrete beams, were those parameters that were most influential on the total applied shear stress experienced by each tested beam.
A second objective of the analysis of previous experimental testing was to evaluate the ability of existing design standards to accurately predict the ultimate shear capacity of concrete beams. The accuracy of each of a number of international design standards was examined with varying input design parameters, allowing for identification of any ranges of the input parameters over which the design standard was either significantly conservative or significantly non-conservative. The use of experimental data in this analysis was particularly advantageous, as all current design standards rely, to varying degrees, on empirical data.
Finally, the composition of the RC and PC databases was used to inform the design of the experimental investigation detailed in Chapter 4.

Database composition

The database compiled for this investigation was divided into two sections: a RC database, and a PC database. This separation was instituted for a number of reasons. First, the procedure used in all major design standards to design a RC beam varies significantly from that for a PC beam. Also, inherent efficiencies in PC beams can result in considerable differences between RC beams and PC beams in section and span geometry. Finally, it is well established that the angle of inclination of compression struts, and resulting cracking, in PC beams is generally substantially lower than that found in RC beams. This dissimilarity of crack angles was considered important, as the inclination of shear cracks affects not only the concrete contribution to shear resistance, but also the contribution of any transverse reinforcement in the beam.
Together, the RC and PC databases contained details of all accessible experimental testing that was focused on determining the shear capacity of concrete beams, the earliest of which dated back to 1948. The databases were manually compiled by collating and documenting all accessible literature on previous experimental testing on shear behaviour, and eliminating all test units which did not exhibit shear failure or for which not all required parameters were available. Two large spreadsheets were used to collate the two databases, allowing for easy management and analysis of each database. A total of almost 2500 beams were included in the databases, with a large variety of concrete compressive strengths (between 6 MPa–128 MPa) and beam geometries.
In order for a beam to be added to the assembled database, the available information needed to include details of the geometry and reinforcement of each beam, as well as sufficient details to allow for both the calculation of applied flexural stresses and for calculation of predicted shear capacities based on the various design standards utilised in subsequent sections of this Chapter. Therefore, compilation of the RC and PC databases required the following information to be gathered for each beam:
General test information: name of researcher, date of research, and beam name Section geometry: section shape (rectangular, tee, or I-girder), beam height, effective depth, and web and flange thicknesses
Loading geometry: load span, support configuration (simply supported or continuous), load configuration (single point load, double point load or distributed loading), shear span-to-depth ratio (a/d)
Concrete material properties: compressive cylinder strength (or equivalent where cube tests or non-standard cylinders were used), maximum aggregate size
Longitudinal reinforcement properties: cross-sectional area, yield strength
Transverse reinforcement properties: cross-sectional area, yield strength, spacing
Prestressing properties (for PC database only): cross-sectional area, yield strength, ultimate strength, angle (if draped strands were used), effective prestress at time of testing (if not explicitly provided, this parameter was calculated based on NZS 3101 (Standards New Zealand 2006) provisions)
Failure details: maximum shear force at failure, observed crack angles (where provided).
Complete reproductions of both databases can be found in appendix A.

RC beam database

The RC beam database contained a total of 2009 beams that were deemed relevant for inclusion. Only beams that could be confirmed to have failed in shear were included, as this investigation focused on shear performance and shear capacity.
Contained within the RC database were beams with a large variety of material properties, section sizes and reinforcement details – 1493 (74%) were fabricated with concrete compressive strengths of 40 MPa or lower; 226 (11%) were fabricated with concrete strengths between 40 and 60 MPa, and the remaining 290 (14%) were fabricated with concrete strengths greater than 60 MPa. The low number of experimental tests conducted on high-strength concrete beams can be seen in Figure 3-1 (a).
Figure 3-1 (b) shows that the vast majority (93%) of previous testing on RC beams has been on rectangular beams. Meanwhile, Figure 3-2 and Figure 3-3 show the over-representation in the database of test beams with effective depths below 400 mm. This over-representation is of particular significance for the shear capacity of beams with no transverse reinforcement, as previous research has shown that such beams exhibit markedly different shear capacities with varying section sizes. This size effect, however, is not considered significant for bridge beams as most, if not all, bridge beams contain at least minimum levels of transverse reinforcement, and it has been shown (Bazant and Kazemi 1991, Bazant and Kim 1984, So and Karihaloo 1993) that for such designs there is no significant size effect. Also, to achieve the large applied shear stresses that were of interest for this project, it was found that much higher levels of transverse reinforcement were provided than the minimum quantity specified in NZS 3101 (Standards New Zealand 2006), further diminishing the importance of the size effect for this research.
As mentioned in the previous section, the shear span-to-depth ratio (a/d) of the loading configuration of a test beam can greatly impact the observed shear performance of the beam. A total of 718 beams in the RC database were tested with a/d ratios lower than 2.5. The majority of the beams (1086) were tested with an a/d ratio between 2.5 and 5, and only 10% of tested beams had an a/d ratio greater than 5

PC beam database

The PC beam database contained a total of 485 beams that were deemed relevant for inclusion. It was important to omit any beams that could not be confirmed to have failed in shear, as this investigation focused on shear performance and capacity. The PC database was of particular relevance for bridge design, as the majority of concrete bridge superstructure construction in the past five decades has been of Prestressed Concrete rather than Reinforced Concrete.
Contained within the PC database were beams with a large variety of material properties, section sizes and reinforcement details. Concrete compressive strengths ranged from 12 MPa to 123 MPa, with over 60% of beams having concrete compressive strengths of less than 40 MPa, and only 10% greater than 60 MPa. This concrete compressive strength distribution can be seen in Figure 3-5 (a). The low number of experimental tests that have been conducted on high-strength concrete beams provides some explanation for the absolute 8 MPa limit imposed in NZS 3101:2006 on allowable shear capacity – a large proportion of shear design provisions are based on empirical data, and without the data to confirm the adequate shear performance of high-strength concrete beams it is more prudent for the authors of the design standard to limit the allowable shear stresses to known achievable levels.
Figure 3-5 (b) shows that the majority of previous testing has been performed on I-beams. Meanwhile, Figure 3-6 and Figure 3-7 show the vast under-representation of large test beams (d > 400 mm) in the database. This disparity in the size of experimental beams can be explained by the increase in both beam and test rig construction costs inherent in testing large beams to failure.
Of the 485 beams in the PC database, 321 beams contained no transverse reinforcement, with the remaining 164 beams containing at least the minimum transverse reinforcement required by NZS 3101 (Standards New Zealand 2006). It is well documented that beams tested with a loading configuration resulting in shear span-to-depth ratios (a/d) below 2.5 exhibit increased shear capacity due to deep beam effects(Collins et al. 1996, Hsu 1994, Smith and Vantsiotis 1982, Tan et al. 1995, Yang and Ashour 2008). This phenomenon explains the tendency of researchers to avoid such low a/d ratios, with only 12 beams tested having an a/d ratio below 2.5, 423 between 2.5 and 5, and the remaining 50 above 5. The vast majority of tests were conducted with a/d ratios below 5 because higher a/d ratios would result in greater applied bending moments, relative to the shear capacity of the beam, and would increase the likelihood of flexural failure.
Over 90% of the beams in the PC database failed at an applied shear stress below 8 MPa, and almost two-thirds of those beams failed at a shear stress of less than 4 MPa. This tendency towards lower levels of shear stress capacities, most likely due to the cost implications of increased cement quantities required for higher strength concrete, coupled with the under-representation of high-strength concrete beams in the database, can be seen in Figure 3-8. The main observation to be made from this figure is the presence of few beams that were suitable for addressing the primary objective of this project, which was to investigate the maximum applied shear stresses that can be relied upon in high-strength concrete beams.

Influence of design parameters

The influence of a variety of design parameters on the shear capacity measured during previous experimental testing of concrete beams is discussed in this section. Both the RC and PC databases were analysed for these influences by observing any discernible trends in the performance of beams as each parameter was varied.
After initial analyses of the two compiled databases, it became clear that more-stringent criteria needed to be applied to the selection of beams included in the comprehensive analysis of the databases. There were two main factors leading to this decision. First, the inclusion of both PC and reinforced beams with no transverse reinforcement introduced an additional level of unnecessary complexity. The shear behaviour of concrete beams with no transverse reinforcement can differ markedly from the behaviour of beams that incorporate transverse reinforcement, as the presence of transverse reinforcement in a concrete beam not only allows for better crack control but also increases the influence of dowel action on the shear performance of the beam. The shear performance of concrete beams with no transverse reinforcement has also been shown (Bazant and Kazemi 1991, Bazant and Kim 1984) to be significantly influenced by the beam effective depth, which is a phenomenon commonly referred to as the ‘size effect’. It has also been shown (Bazant and Kazemi 1991, Bazant and Kim 1984) that the size effect is not influential in the behaviour of beams containing some transverse reinforcement. Additionally, the shear performance of concrete beams with no transverse reinforcement was deemed to be a topic with little relevance to this project, and to concrete bridge beams in general, as the overwhelming majority of concrete bridge beams are designed to contain at least minimum levels of transverse reinforcement.
The second factor that led to the decision to refine the databases for the analysis procedure was the inclusion of beams tested with shear span-to-depth ratios (a/d) lower than 2.5. Beams with an a/d ratio lower than 2.5 are known (Yang and Ashour 2008, Tan et al. 1995, Smith and Vantsiotis 1982) to exhibit increased shear capacities that are deemed to be artificially enhanced, as such capacities are not replicable when the beam is subjected to different loading conditions. These artificially enhanced capacities would skew the databases. Therefore, the decision was taken to omit all beams that were tested with an a/d ratio below 2.5. This decision was validated by the awareness that bridge beams generally have a long span, and support moving loads, and therefore a reliance on restricting loading conditions to a/d ratios would be completely unrealistic.
Introduced in this section is the term ρvfvy, which refers to the transverse reinforcement ratio, ρv, multiplied by the yield stress of the transverse reinforcement, fvy. The term ρvfvy was used in the following analyses to normalise the quantity of transverse reinforcement when assessing the effect of varying levels of transverse reinforcement. Also included in this section is a line of best fit for each plot, which was generally chosen to be linear unless a different line type was observed to be more representative of the trend of the data.

RC database

The original RC database, detailed in section 3.2.1, was refined by eliminating all beams that either:
could not be confirmed to have failed in shear, or
exhibited signs of anchorage failure, or
were expected to have flanges significantly influence shear capacity, or
contained no transverse reinforcement, or
had an a/d ratio lower than 2.5 during testing.
The final RC database contained 160 beams, of which 38 had a concrete compressive strength lower than 40 MPa, 95 had a concrete compressive strength ranging between 40 and 80 MPa, and the remaining 27 had a concrete compressive strength exceeding exceeding 80 MPa. The majority of the 160 beams failed at relatively low applied shear stresses, with 129 beams failing at a shear stress below 4 MPa, 23 beams failing at a shear stress between 4 MPa and 8 MPa, and only 8 beams failing at a shear stress of greater than 8 MPa.

Concrete compressive strength

Figure 3-9 shows the ultimate shear capacity of RC test beams with varying concrete compressive strengths and varying transverse reinforcement quantities. For beams with low to moderate levels of transverse reinforcement (ρvfvy < 4 MPa), there is a relatively well-defined correlation between increasing concrete compressive strength and ultimate shear capacity. While the number of beams with high levels of transverse reinforcement was insufficient to reasonably detect any trends, it was notable that all such beams failed at a shear stress greater than 8 MPa.

Effective depth

In Figure 3-10, the ultimate shear capacity of beams in the refined RC database is plotted against the effective depth of the beams. For beams with very low levels of transverse reinforcement (ρvfvy < 1 MPa), there is evidence of a general decrease in ultimate shear capacity as the effective depth increases from 200 mm to 400 mm. This capacity decrease is an indication of some influence of size effects, and can be explained by the quantity of transverse reinforcement provided being close to the minimum quantity specified in design standards, above which size effects are considered to be negligible. As the transverse reinforcement in a beam decreases, some characteristics of the beam will tend towards the characteristics of a beam with no transverse reinforcement, and this phenomenon is demonstrated by the presence of a size effect for beams with lower quantities of transverse reinforcement. In Figure 3-10 there is no evidence of this size effect for beams with moderate and high levels of transverse reinforcement (ρvfvy > 1 MPa).

Shear span-to-depth (a/d) ratio

As all beams with a shear span-to-depth (a/d) ratio lower than 2.5 were omitted from the refined RC database used for this analysis, it was anticipated that the parameter a/d would not have a discernible influence on the shear capacity of the test beams. Figure 3-11 shows the shear capacity of RC test beams versus their a/d ratios, and despite the presence of significant scatter, the data confirms the hypothesis that changes in the a/d ratio for values greater than 2.5 does not significantly influence the shear capacity of RC beams. It was noted that the only beams to exhibit shear capacities greater than 8 MPa were those with a large amount of transverse reinforcement (ρvfvy > 4 MPa), and that to achieve those high shear stresses the test beams needed to have an a/d ratio close to 2.5. This observation was valuable in informing the researcher for the design of the experimental investigation, detailed in Chapter 4, as this observation provided some warning of possible difficulties associated with achieving shear failure at high loads while avoiding flexural failure.

CONTENTS
ANALYSIS AND DESIGN OF HIGH-STRENGTH CONCRETE BRIDGE GIRDERS AND SEISMICALLY ISOLATED
BRIDGES 
ABSTRACT 
ACKNOWLEDGEMENTS 
LIST OF FIGURES 
INTRODUCTION 
1.1 WEB SHEAR IN NEW ZEALAND CONCRETE BRIDGE BEAMS
1.2 ANALYSIS AND DESIGN OF SEISMICALLY ISOLATED BRIDGES
1.3 OUTLINE OF THE THESIS
MODELS AND DESIGN PROCEDURES FOR BEHAVIOUR OF CONCRETE IN SHEAR 
2.1 SHEAR TRANSFER MECHANISMS
2.2 PARAMETERS INFLUENCING SHEAR BEHAVIOUR
2.3 MODELS FOR CONCRETE SHEAR BEHAVIOUR
2.4 DESIGN PROCEDURES
2.5 CONCLUSIONS
INTERROGATION OF SHEAR TEST DATABASE 
3.1 OBJECTIVES
3.2 DATABASE COMPOSITION
3.3 INFLUENCE OF DESIGN PARAMETERS
3.4 EVALUATION OF SHEAR DESIGN STANDARDS
3.5 CONCLUSIONS
EXPERIMENTAL INVESTIGATION OF WEB SHEAR STRENGTH 
4.1 OBJECTIVES AND SCOPE
4.2 TEST RIG
4.3 DESIGN OF TEST BEAMS & SETUP
4.4 CONSTRUCTION OF TEST BEAMS
4.5 TESTING
4.6 TEST RESULTS
4.7 CONCLUSIONS
ANALYSIS OF EXPERIMENTAL RESULTS 
5.1 CAPACITY ANALYSIS
5.2 DESIGN CODE BASED ANALYSIS
5.3 ALTERNATIVE LIMITS FOR NZS 3101
5.4 CONCLUSIONS
ANALYSIS OF CONCRETE AND REINFORCING STEEL STRAIN BEHAVIOUR IN CONCRETE WEBS 
6.1 OBJECTIVES
6.2 STRAIN ANALYSIS
6.3 FINITE ELEMENT MODELLING AND ANALYSIS
6.4 CONCLUSIONS
PARAMETRIC ANALYSIS OF THE PERFORMANCE OF SEISMICALLY ISOLATED BRIDGES 
A BI-MODAL METHOD FOR ANALYSIS OF SEISMICALLY ISOLATED BRIDGES WITH HEAVY
SUBSTRUCTURES
CONCLUSIONS AND RECOMMENDATIONS 
9.1 CONCLUSIONS FOR SHEAR PERFORMANCE OF HIGH-STRENGTH CONCRETE BRIDGE BEAMS
9.2 CONCLUSIONS FOR ANALYSIS AND DESIGN OF SEISMICALLY ISOLATED BRIDGES
GET THE COMPLETE PROJECT
ANALYSIS AND DESIGN OF HIGH-STRENGTH CONCRETE BRIDGE GIRDERS AND SEISMICALLY ISOLATED BRIDGES