Preface
The book is largely based on research literature and the author's experience in working with structural engineers. The first part (chapter 1) presents the design methods used for earthquake-resistant design of reinforced concrete buildings.
Acknowledgments
CHAPTER 1
Seismic Design and Performance Verification
Earthquake Resistance in Concrete Buildings
Together, these chapters provide a strong foundation for conceiving, designing and verifying reinforced concrete buildings for seismic resistance. Structural systems that use precast or prestressed concrete or that use specialized "self-centering" systems are not weighted.
Early Developments
However, a thorough understanding of the topics covered in this book will serve as an effective basis for designing such systems. By 1976, the Uniform Building Code (UBC, 1976) had implemented many of the recommendations of Blume et al.
Current Practices
- Building Codes
- Conceptual Design
- Prescriptive Design Approach
- Performance-Based Design Approach
- Construction Inspection
These are usually determined by strength, serviceability, durability and other building code requirements. The owner or other responsible entity wants building efficiency that exceeds the minimum building code efficiency targets.
Building Performance
- Anticipated Response of Buildings to Earthquake Ground Shaking
- Performance Concepts
- Use, Occupancy, and Risk Classifications
- Building Performance Expectations
An early concept was to relate performance levels to the physical condition of the building as it was subjected to increasing lateral deformation (SEAOC, 1995). In effect, building performance is defined as being equal to the worst performance of any of the building's components.
Performance Verification
- Limit State Design
- Serviceability Limit State
- Ultimate Limit State (Load and Resistance Factor Design) 3
Such failures should have a small probability of occurring during the service life of the building. MacGregor (1983) describes the development of the LRFD factors and associated safety levels for reinforced concrete design.
Factored Load Combinations
- Capacity Design
- Displacement-Based Design
- Performance Evaluation under Earthquake Ground Shaking
- The Purpose and Organization of This Book
Use the capacity model to determine the required shear force in sections 1 and 2 of the beam of Example 1.1. Using the load combination shown in Figure 1.15, the moments can be summed around the left end to obtain the shear value at the right end.
CHAPTER 2
Steel Reinforcement
Preview
Steel Reinforcement Used in Buildings
- Standard Steel Reinforcement
- Reinforcement Grades and Availability
- Permitted Reinforcement
Eleven different sizes of deformed rebar are manufactured in the United States, with nominal diameters ranging from 3/8 in (10 mm) to 2.257 in (57 mm). In the United States, a green epoxy coating indicates that the epoxy was applied prior to the fabrication (cutting, bending) of the reinforcement. In the United States, ASTM A970 classifies headed bars as Class A (develops a minimum specified tensile strength of the rebar) or Class B (develops a minimum specified tensile strength and minimum specified elongation of the rebar).
The type and location of welded splices and other required welding of reinforcing bars shall be specified in the construction documents.
Steel Reinforcement under Monotonic Loading
- General Characteristics of the Stress–Strain Relation
- Tensile Properties of Steel Reinforcement
- Compressive Properties of Steel Reinforcing Bars
- Strain Rate Effect
The stress-strain relationship of steel reinforcement is measured in a standardized tension test of a full-size bar. At the peak of the stress-strain relationship, necking occurs, causing localized reduction in cross-sectional area and leading to failure in the necked region. The monotonic stress-strain behavior of A615 and A706 bars in the strain hardening region can be approximated by (Mander et al., 1984).
Instead, it is more common to assume that the tensile stress-strain relationship represents both tension and compression behavior.
Reinforcing Bars under Cyclic Loading
- Stress–Strain Response
- Low-Cycle Fatigue
Based on the data in Figure 2.7b, at these latter stages, the measured strength can be assumed to be the same as the static strength, which is suitable for dead loads and most live loads. Earthquake loading involves cyclic histories that are more complex than the constant-amplitude case in Figure 2.11a. Note the rebar strain history in Figure 2.16a and the corresponding stress-strain history in Figure 2.16b.
To use the analogy, first rotate the strain history so that it appears as a series of sloping surfaces (or pagoda roofs) and imagine rain flowing down each of them (Figure 2.16c).
CHAPTER 3
Concrete
Preview
Composition and Structure of Concrete 1
Others can modify the setting and hardening characteristics of plastic concrete and can improve resistance to thermal cracking and freeze-thaw. Typically, the interfacial transition zone is the weakest of the three zones, and therefore its behavior controls the nonlinear properties and strength of concrete. Microcracks in the interfacial transition zone begin to extend at stress levels up to 40% of the compressive strength of concrete.
For high-strength concrete, the high strength of the mortar results in delayed cracking, so that the behavior is more nearly linear for higher stresses.
Concrete Strength
- Materials Characteristics and Proportions
- Curing Time and Conditions
- In-Place Concrete
- Test Specimen Parameters
- Expected Strength in Structures
Given the dependence of concrete strength on these variables, it should not be surprising that in-situ strength differs from that measured in a standardized test. The strength of the concrete at the top of the column is usually estimated as C = 0.85. ACI 318 specifies the frequency of sampling and testing of concrete and the strength required for acceptance.
Based on limited field testing, the California Department of Transportation (Caltrans) typically assumes a compressive strength of 1.5 for concrete in older construction.
Behavior in Uniaxial Monotonic Loading
- Compressive Stress–Strain Response
- Tensile Strength
- Strain Rate Effects
For high-strength concrete, increased strength of the cement paste and interfacial transition zone results in smaller microcracks, so that the stress-strain relationship is more linear than for lower-strength concrete. Although the stress-strain relationship for concrete is non-linear even at low stress levels, we commonly assume that it is linear for stresses up to about stress-strain point at (ASTM C469, 2010). The stress-strain relationship for concrete in tension is nearly linear with tensile strength, followed by a rapid reduction in tensile strength with increasing strain.
The tensile strength of concrete, which is usually measured in the split cylinder test, is much smaller than the compressive strength.
Behavior in Uniaxial Cyclic Loading
Cycles to the monotonic stress-strain relationship (Figure 3.10a): Each load cycle causes damage that is evident in the nonlinearity of the load branch. Cycles to constant loading (Figure 3.10b): The damage in each loading cycle results in a gradual accumulation of strain during cyclic loading. Cycles to constant load (Figure 3.10c): Under this load, the second cycle intersects the unloading branch of the first cycle at a point defined as the common point limit.
Karsan and Jirsa (1969) used the monotonic envelope, the common point limit curve, and the stability limit curve to define an analytical hysteresis model for concrete under cyclic loading.
Behavior in Multi-axial Stress States
- Plain Concrete in Biaxial Stress State
- Reinforced Concrete in Biaxial Loading
- Plain Concrete in Triaxial Stress State
As shown in Figure 3.12b, the volumetric strain (∆V⁄/V = ε1 + ε2 + ε3) increases beyond this point, which is a sign of more extensive microcracking just before failure. According to this model, the principal compressive strength f1 of the concrete is not only a function of the principal compressive strain ε1, but also of the principal tensile strain ε2 (Figure 3.13a). The relationship between the maximum principal compressive stress capacity fc1max and the principal tensile strain ε2 (negatively defined for tension) is shown in Figure 3.13b.
This results in a family of concrete compressive stress–strain relationships for different values of ε2, as shown in Figure 3.13d.
Fiber-Reinforced Concrete
An alternative to improving the tensile behavior of concrete is the addition of fibers, creating what is known as fiber-reinforced concrete. Steel strands are produced by cutting and crimping wire or sheet, or by machining or melt extrusion processes (Figure 3.16). Fiber-reinforced concretes that develop post-cracking hardening behavior are commonly referred to as high-performance fiber-reinforced concrete (HPFRC).
ACI considers steel fiber reinforced concrete acceptable for shear resistance if conditions (1), (2), and (3) are met: (1) The weight of deformed steel fibers is at least 100 lb/yd3 (582 N/m3) ; (2) the residual strength obtained in a bending test at a midspan deflection of 1/300 of the span is at least 90% of the measured first peak strength obtained in a bending test and 90% of the strength corresponding to fr; and (3) the residual strength obtained in a bending test at a midspan deformation of 1⁄150 of the span is at least 75% of the measured first peak strength obtained in a bending test and 75% of the strength corresponding to fr.
Chapter Review
Guide to Evaluation of Strength Test Results of Concrete,” ACI Manual of Concrete Practice, American Concrete Institute, Farmington Hills, MI, 16 s. Guide for Obtaining Cores and Interpreting Compressive Strength Results,” ACI Manual of Concrete Practice, American Concrete Institute, Farmington Hills, MI, 17 s. Nondestructive Test Methods for Evaluation of Concrete in Structures” (gengodkendt 2004), ACI Manual of Concrete Practice, American Concrete Institute, Farmington Hills, MI, 62 pp.
A Guide to Curing Concrete” (Reapproved 2008), ACI Manual of Concrete Practice, American Concrete Institute, Farmington Hills, MI, 31 p.
CHAPTER 4
Confined Concrete
Preview
Behavior of Confined Concrete Sections
As shown, the plain concrete specimen P reaches peak load at longitudinal strain 0.003, which corresponds to the strain at peak stress in companion test cylinders, followed by rapid loss of strength as the plain concrete shears over an inclined plane. Cover concrete begins to spall at longitudinal strain around 0.004, evident by vertical splitting of the cover concrete and a reduction in load resistance. Columns A and B regain some of the lost strength as strain is further increased, while column C continues to shed load with increasing strain.
Failure occurs when the hoops break, accompanied by longitudinal bending of the reinforcement and partial direction of the hooks 90° at the B-column junctions.
Mechanism of Concrete Confinement
- Passive Confinement of Concrete
- Columns with Spiral and Circular Hoop Reinforcement
- Columns with Rectilinear Hoop Reinforcement
- Loading Rate Effect
- Aggregate Density Effect
- Compressive Strength Effect
- Cyclic Loading Effect
- Reinforcement Details
As a column core is axially loaded, the expansion of the core concrete presses outward against the enclosing reinforcement. So far we have expressed the confinement stress in terms of the stress fs in the transverse reinforcement. A closing effectiveness coefficient is determined according to the configuration and longitudinal spacing of the hoops (Figure 4.11).
The strength of the limited core. 4.14), we can use the strength ratio given in Figure 4.6 to determine the limited concrete strength.
Analytical Modeling of Confined Concrete
- Strain at Peak Stress
- Maximum Strain Capacity for Confined Concrete
- Stress–Strain Relation
Scott et al. 1982) proposed that strain capacity was proportional to confining pressure; Kaar et al. 1978) suggested that it was proportional to the square of the confining pressure; 2001) proposed that it was proportional to the square root of the limiting stress. Each of the models cited has been shown to provide good correlation with measured laboratory test results. 1In the reinforced concrete literature, D is sometimes defined as the core diameter measured from the centerline or inside of the spiral or circular ring reinforcement.
3 Confinement of cylindrical cores and buckling restraint for compressed longitudinal bars is derived from the curvature of the circular hoop or spiral.
CHAPTER 5
Axially Loaded Members
- Preview
- Some Observations on the Behavior of Compression Members
- Analysis Assumptions for Compression Members
- Service Load Behavior of Compression Members
- Linear Elastic Response
- Effects of Drying Shrinkage and Creep
- Inelastic Behavior of Compression Members
- Cover and Core Concrete
- Longitudinal Reinforcement
- Load–Displacement Response
- Transverse Reinforcement Required for Ductility
Based on the known stress-strain relations, we then establish the stress in each of the materials at each point in the cross-section (figure 5.3c). Equilibrium of this free body establishes the internal forces P and M. FIGURE 5.3 Concrete compression member under concentric axial compression. In contrast, longitudinal bars not supported at a corner by a tie (eg, bar b in Figure 5.8a) must rely on the bending stiffness of the brace for support, i.e.
For circular or spiral hoops, the lateral restraint is provided by the radial component of hoop tension (Figure 5.8c).
