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TWO-WAY SLABS: BEHAVIOR, ANALYSIS, AND DESIGN 632 13-1 Introduction 632
TWO-WAY SLABS: ELASTIC AND YIELD-LINE ANALYSES 785 14-1 Review of Elastic Analysis of Slabs 785
FOOTINGS 812 15-1 Introduction 812
SHEAR FRICTION, HORIZONTAL SHEAR TRANSFER,
DISCONTINUITY REGIONS AND STRUT-AND-TIE MODELS 879 17-1 Introduction 879
DESIGN FOR EARTHQUAKE RESISTANCE 1027 19-1 Introduction 1027
Changes to load factors and load combinations in the 2011 edition of the ACI Code are presented in Chapter 2. He received the Distinguished Alumnus Award from the Departments of Civil and Environmental Engineering at the University of Illinois (2008) and Michigan State University (2009).
1-1 REINFORCED CONCRETE STRUCTURES
1-2 MECHANICS OF REINFORCED CONCRETE
1-3 REINFORCED CONCRETE MEMBERS
At the perimeter of the building, the floor loads are supported either directly on the walls, as shown in fig. In addition, the tops of the columns are enlarged in the form of capitals or brackets.
1-4 FACTORS AFFECTING CHOICE OF REINFORCED CONCRETE FOR A STRUCTURE
Suitability of material for architectural and structural function. A rein- forced concrete system frequently allows the designer to combine the architectural and
Flat tile floors are widely used in apartments because the underside of the tile is flat and therefore can be used as the ceiling of the room below. These are (a) building the forms, (b) removing these forms, and (c) supporting or supporting the new concrete to support its weight until its strength is sufficient.
1-5 HISTORICAL DEVELOPMENT OF CONCRETE AND REINFORCED CONCRETE AS STRUCTURAL MATERIALS
In the period from 1875 to 1900, the science of reinforced concrete developed through a series of patents. The history of reinforced concrete building codes in the United States was reviewed in 1954 by Kerekes and Reid [1-7].
1-6 BUILDING CODES AND THE ACI CODE
1-4 Committee on Concrete and Reinforced Concrete, "Standard Building Regulations for the Use of Reinforced Concrete," Proceedings, National Association of Cement Users, Vol. 1-5 Special Committee on Concrete and Reinforced Concrete, "Progress Report of Special Committee on Concrete and Reinforced Concrete," Proceedings of the American Society of Civil Engineers, 1913, pp.
2-1 OBJECTIVES OF DESIGN
Structural adequacy. Structural adequacy involves two major aspects
Maintainability. A structure should be designed so as to require a minimum amount of simple maintenance procedures
2-2 THE DESIGN PROCESS
From approximate analyzes of moments, displacements and axial forces, preliminary element sizes are selected for each potential scheme. The overall goal in this phase of the structural design is to meet the design criteria that deal with expediency, economy and to some extent maintainability.
2-3 LIMIT STATES AND THE DESIGN OF REINFORCED CONCRETE Limit States
Special limit states. This class of limit states involves damage or failure due to abnormal conditions or abnormal loadings and includes
However, for a water tank, the limit state of excessive crack width is as important as any of the failure limit states if the structure is to remain watertight [2-3]. In such a construction, the crack width limit state design can be considered before the failure limit states are checked.
2-4 STRUCTURAL SAFETY
Consequences of failure. A number of subjective factors must be consid- ered in determining an acceptable level of safety for a particular class of structure
The cost to society in lost time, lost income, or indirect loss of life or property due to a failure - for example, the failure of a bridge may result in intangible costs due to traffic congestion that may approach replacement costs. In some structures, the yielding or failure of one member causes a redistribution of load to adjacent ones.
2-5 PROBABILISTIC CALCULATION OF SAFETY FACTORS
The resistance and load factors in the ACI codes from 1971 through 1995 were based on a statistical model that assumed that if there was a 1/1000 chance of 'overload' and a 1/100 chance of 'understrength' , the chance that an “overload” and an “understrength” would occur simultaneously. The factors for ductile beams were originally derived so that a magnitude of the loading effects would exceed 99 times out of 100. The factors for coupled columns that fail in a brittle manner were divided by 1.1 a second time to reflect the effects of the mode of failure.
2-6 DESIGN PROCEDURES SPECIFIED IN THE ACI BUILDING CODE Strength Design
Prior to 2002, Appendix A of the ACI Code allowed the design of concrete structures by either strength design or working stress design. Similarly, the strut-and-tie models presented in Chapter 17 (ACI Appendix A) provide estimates of the lower limit capacity of concrete structures if. a) the strut-and-lie model of the structure represents a statically acceptable distribution of forces.
2-7 LOAD FACTORS AND LOAD
COMBINATIONS IN THE 2011 ACI CODE
In previous editions of the ACI code, Two was combined with dead load, D, in ACI Eq. This book will use only the load factors and strength reduction factors specified in Chapter 9 of the ACI Code.
2-8 LOADINGS AND ACTIONS
External pressure coefficient, When wind blows past a structure, it exerts a positive pressure on the windward wall and a negative pressure (suction) on the leeward
These loads produce internal forces and moments that are in balance with the external loads. If the beam undergoes creep, the magnitude of the internal forces and moments decreases, as experimentally shown by Ghali, Dilger and Neville [2-17].
2-9 DESIGN FOR ECONOMY
2-10 SUSTAINABILITY
The American Concrete Institute's Building Code Requirements for Structural Concrete[2-10] is the recognized standard for the design of concrete structures and is adopted by reference to the International Building Code. ACI has recently established a durability committee (ACI Committee 130) tasked with working with other ACI technical committees, including the building code committee, to incorporate durability issues into design requirements for concrete structures .
2-11 CUSTOMARY DIMENSIONS AND CONSTRUCTION TOLERANCES
Sustainability considerations are typically not incorporated into national building codes such as the widely used International Building Code [2-14]. Many ACI documents and standards refer to material standards developed by the American Society for Testing and Materials (ASTM), and ASTM has also developed a sustainability committee to work with its technical committees to include sustainability considerations in the development and revision of ASTM standards.
2-12 INSPECTION
The cement industry is actively working to reduce CO2 emissions in all three areas through the use of alternative fuels to fire kilns, plant modifications to improve energy efficiency, carbon capture and storage systems, and more fuel-efficient cement handling and distribution systems. As previously mentioned, the carbon footprint per cubic yards of concrete are also reduced by using supplemental cementitious materials, such as fly ash, slag cement, and silica fume, to replace some of the cement in a typical mix design.
2-13 ACCURACY OF CALCULATIONS
2-14 HANDBOOKS AND DESIGN AIDS
2-19 Komiteti ACI 347, “Udhëzues për Formwork për Betonin (ACI 347-04),”ACI Manual of Concrete Practice, American Concrete Institute, Farmington Hills, MI, 32 f. 2-24 ACI Committee 301, “Specifications for Structural Betoni (ACI 301-05),”ACI Manual of Concrete Practice, American Concrete Institute, Farmington Hills, MI, 49 pp.
433-1CONCRETE
3-2 BEHAVIOR OF CONCRETE FAILING IN COMPRESSION
These cracks have little effect on the concrete at low loads, and the stress-strain curve remains linear up to 30 percent of the concrete's compressive strength, as shown by the solid line in Fig.3-1. As a result, the stage of stable crack propagation extends almost to the ultimate strength of the concrete.
3-3 COMPRESSIVE STRENGTH OF CONCRETE
- Maturity of concrete. Young concrete gains strength as long as the concrete remains about a threshold temperature of to or to Maturity is the
- Obtain and test the cores. Use standard methods to obtain and test the cores as given in ASTM C4 Carefully record the location in the structure of each core, the
- Convert the core strengths, to equivalent in-place strengths, As an approximation for use in design, this is done by using
- Compute the equivalent specified strength from the in-place strengths
- Obtain and test the cores. The cores were tested in an air-dried condition
- Compute the equivalent specified strength
Unwashed marine aggregates also lead to a breakdown of the concrete structure over time. The development of compressive strength of concrete is strongly influenced by moisture conditions during curing.
3-4 STRENGTH UNDER TENSILE AND MULTIAXIAL LOADS Tensile Strength of Concrete
Thus, the tensile strength is approximately proportional to the square root of the compressive strength. Failure occurs when the highest stress in the member approaches the uniaxial compressive strength of the concrete.
3-5 STRESS–STRAIN CURVES FOR CONCRETE
The rising part of the stress-strain curve looks like a parabola with its apex at the maximum stress. The envelope of this curve is very close to the stress-strain curve of a monotonic test.
3-6 TIME-DEPENDENT VOLUME CHANGES
- Compute expected shrinkage strain in slab
- Compute expected shrinkage strains in the wall
- Relative shrinkage strain and expected crack width
- Compute creep coefficient for time since loading
- Compute the total stress-dependent strain
- Compute the expected shortening of the pedestal related to stress-dependent strains
- Compute the transformed area at the instant of loading, (Transformed sections are discussed in Section 9-2.)
- Compute the age-adjusted effective modulus, and the age- adjusted modular ratio,
-36) is used to calculate the age of concrete when the load is applied to the element. Concrete properties and exposure are the same as in Examples 3-2 and 3-3.
3-7 HIGH-STRENGTH CONCRETE
As a result, the shrinkage of high-strength concrete is about the same as that of ordinary concrete. Test data suggest that the creep coefficient of high-strength concrete is considerably less than that of normal concrete [3-8].
3-8 LIGHTWEIGHT CONCRETE
Concrete shrinkage is roughly proportional to the percentage of water by volume in the concrete. Shrinkage and creep of lightweight concrete are similar to or slightly greater than normal concrete.
3-9 FIBER REINFORCED CONCRETE
Ideally, the tensile behavior of fiber reinforced concrete should be evaluated by direct tension tests. For structural applications, it is desirable that fiber reinforced concrete exhibits at least some deflection hardening behavior.
3-10 DURABILITY OF CONCRETE
Breakdown of the structure of the concrete due to freezing and thawing
ACI Code Section 4.3 establishes maximum water/cement material ratios of 0.45 and minimum concrete strengths of 4500 psi for concrete, depending on the severity of the exposure. Again, drainage must be provided so that water does not collect on the surface of the concrete.
3-11 BEHAVIOR OF CONCRETE EXPOSED TO HIGH AND LOW TEMPERATURES
When concrete freezes, pressure builds up in the water in the pores, which leads to the breakdown of the concrete's structure. The split cylinder tensile strength of the same concrete increased from 600 psi at to 1350 psi at -75°F.
3-12 SHOTCRETE
3-13 HIGH-ALUMINA CEMENT
3-14 REINFORCEMENT
To review the resistance of existing buildings, the yield strength of the bars must be known. When the tempering temperature exceeds about 850°F, both yield and ultimate strength drop significantly.
3-15 FIBER-REINFORCED POLYMER (FRP) REINFORCEMENT
By the time the bar temperature reaches 480°F, the tensile strength has dropped to about 20 percent of the strength at room temperature. In the ACI beam design philosophy, the value of the strength reduction factor ranges from 0.65 for members where the strain in the extreme tensile steel is zero or compression to 0.90 for beams in which the bar strain is at its extreme. exceeds 0.005 strain in tension.
3-16 PRESTRESSING STEEL
What is the meaning of “critical stress”. a) relating to the structure of the concrete. Use the maturity concept to estimate its strength as a fraction of the strength after 28 days of standard curing.
PROBLEMS
3-9 ACI Committee 214, "Evaluation of Strength Test Results of Concrete (ACI 214R-02)," ACI Manual for Concrete Practice, American Concrete Institute, Farmington Hills, MI, 20 pp. MacGregor, “Statistical Analysis of the Compressive Strength of Concrete in Structure,” ACI Materials Journal, Vol.
4-1 INTRODUCTION
In this textbook, bending moment diagrams will be drawn on the compression side of the part. In the region of positive moment (Fig. 4-2a), the tension steel is near the end of the beam, while in the region of negative moment (Fig.
4-2 FLEXURE THEORY
The resultant compressive force C, which is equal to the volume of the compressive stress block in Figure 4. 4-9d, but does not affect the value of the tensile (and thus compressive) force.
4-3 SIMPLIFICATIONS IN FLEXURE THEORY FOR DESIGN
The use of the constant has essentially disappeared from the ACI Code buckling theory. The internal moment arm of the compressive force in concrete about the central axis of a rectangular column is where c is the depth to the neutral axis (axis of zero stress).
4-4 ANALYSIS OF NOMINAL MOMENT STRENGTH FOR SINGLY REINFORCED BEAM SECTIONS
- Check that the tension steel is yielding. The yield strain is
- Compute a (assuming the tension steel is yielding)
- Check whether the tension steel is yielding. The yield strain for the reinforcing steel is
- Initially, assume that the stress in the tension reinforcement equals the yield strength , and compute the tension force
- Compute
With the depth to the neutral axis known, the yield assumption of the tension steel can be checked. Calculate the area of the compressive stress block so that .This is done for the equivalent rectangular stress block shown in Fig.
4-5 DEFINITION OF BALANCED CONDITIONS
The only difference is that the forces are labeled as (ball) and T(ball) to distinguish them from the forces in the procedure for the analysis of. However, the gain ratio at balanced conditions is a parameter often used in design.
4-6 CODE DEFINITIONS OF TENSION-CONTROLLED AND COMPRESSION-CONTROLLED SECTIONS
Calculate the strength reduction factor, and the resulting value of .As before, it is equal to that calculated in step 1. A simple calculation is used to find the distance from the end of the beam to the center of the tension reinforcement,g , and then find the value of.
4-7 BEAMS WITH COMPRESSION REINFORCEMENT
Change of mode of failure from compression to tension. When a beam fails in a brittle manner through crushing of the compression zone before the steel
The stress in the compression reinforcement is not known and cannot be determined until the depth to the neutral axis is determined. These bars are usually not confined in ties if the compression in them is not included in the calculation of the nominal moment strength of the section.
Use the iterative procedure discussed in the prior paragraphs to establish section equilibrium and find the depth to the neutral axis, c
Ties are required throughout the portion of the beam where the compression steel is used in compression when determining the nominal moment strength of a beam section. If the compression steel will be subjected to stress changes, or if this steel is used to resist torsion, closed stirrups should be used to restrain these bars.
Calculate the nominal moment strength, (step 10)
4-8 ANALYSIS OF FLANGED SECTIONS
Determine for a beam T-section that is part of a continuous floor system
4 stirrup, it is reasonable to assume that the distance from the extreme stress edge of the section to the center of the bottom layer of steel is about 2.5 inches. Thus, the distance from the tension edge to the center of the total tension reinforcement approximately 3.5 inches.
4-9 UNSYMMETRICAL BEAM SECTIONS
Compute
Use strength reduction factors from ACI Code Sections 9.2 and 9.3. b) Taking ray 1 as a reference point, we discuss the effects of varying and d on (Note that each ray has the same properties as ray 1 except for the lying quantity). -7 Calculate the negative moment capacity and check the beam shown in Fig. a) Calculate the effective width of the flange at mid-span.
5-1 INTRODUCTION
5-2 ANALYSIS OF CONTINUOUS ONE-WAY FLOOR SYSTEMS
For a floor system with uniformly spaced floor joists, the width of the tributary area is equal to the center-to-center spacing between the floor joists. Using the Mueller-Breslau principle to calculate an influence line for moment at Cis, illustrated in Fig.
