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Concrete Properties: Stress, Strain, and Reinforcement
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MODULE 1 PROPERTIES OF CONCRETE AS A CONSTRUCTION MATERIAL INSTRUCTOR: JOHN LORENZ S. TUALA MODULE DETAILS Module Description This module discusses the types of structures concrete is typically used, the stress-strain characteristics of concrete, its mechanical properties, the properties of its reinforcement, and the reference code of practice. Learning Outcomes CO 1. Understand the in-depth stress-strain characteristics of concrete for all stages of loading. Upon successful completion of this chapter, the student should be able to understand the following: Structural uses of concrete Concrete stress-strain characteristics Concrete mechanical properties Properties of concrete reinforcement Use of reference code of practice OUTLINE Concrete in Structures Stress-Strain Characteristics Mechanical Properties Properties of Reinforcement Codes of Practice CONCRETE IN STRUCTURES WIND TURBINE FOUNDATION ROAD PAVEMENTS CONCRETE IN STRUCTURES BRIGES Dome Structures CONCRETE IN STRUCTURES NUCLEAR COOLING TOWERS DAMS [Khun Dan Prakan Chon Dam] CONCRETE IN STRUCTURES MULTI-STORY BUILDINGS STRESS-STRAIN CHARACTERISTICS BEHAVIOR OF CONCRETE UNDER SIMPLE COMPRESSION • Concrete is mainly used against compressive stresses. Thus, it is necessary to study its behavior under these stresses. • Components of concrete are elastic, and brittle. However, the behavior of the hardened mixture is nonlinear & ductile. • This behavior is due to the gradual formation of microcracks within the specimen. • 30% to 40% of Compressive Strength. Bond cracks in the paste-aggregate interface, however, the behavior is linear. • Discontinuity Limit. Beyond 50% or 60%, this marks the formation of the mortar cracks between bond cracks. • Critical Stress. At 75% to 80%, the behavior becomes more nonlinear, and this marks the onset. STRESS-STRAIN CHARACTERISTICS STRESS-STRAIN CHARACTERISTICS STRESS-STRAIN CHARACTERISTICS MECHANICAL PROPERTIES OF CONCRETE COMPRESSIVE STRENGTH • • • • • ASTM C31: Standard Practice for Making and Curing Concrete Test Specimens in the Field ASTM C39: Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens The testing method involves cylindrical concrete specimens 6in in diameter and 12in in height. 4in by 8in cylinders are now accepted as stated in ACI Section 26.12.1.1. The standard compressive strength also refers to the strength of concrete at 28 days. STATISTICAL VARIATIONS IN CONCRETE STRENGTH • For a compressive strength test with a sample size of 176: โช Average strength is 3940psi โช Lowest strength is 2020psi โช Highest strength is 6090psi • Variations in the actual results from the target strength maybe caused by variations in material proportioning, transporting, placing, compacting of the specimens. MECHANICAL PROPERTIES OF CONCRETE STATISTICAL VARIATIONS IN CONCRETE STRENGTH ๐๐ก๐๐๐๐๐๐ ๐ท๐๐ฃ๐๐๐ก๐๐๐, ๐ = ๐ฅ๐ − ๐ฅาง 2 ๐−1 ๐๐ก๐๐๐๐๐๐ ๐ท๐๐ฃ๐๐๐ก๐๐๐, ๐ = 615๐๐ ๐ ๐ ๐ถ๐๐๐๐. ๐๐ ๐๐๐๐๐๐ก๐๐๐, ๐ = ๐ฅาง ๐ถ๐๐๐๐. ๐๐ ๐๐๐๐๐๐ก๐๐๐, ๐ = 0.156 = 15.6% • 15.6% of the data will have values less than ๐ฅาง − ๐ . COMPRESSIVE STRENGTH MECHANICAL PROPERTIES OF CONCRETE APPLICATIONS OF STATISTICAL FINDINGS • If V is to be no more than 10%, 15% or 20%, and ๐ฅาง − ๐ is 3000psi, the distribution of the results of the compressive tests and their mean values ๐๐๐ is shown in the figure. • • • • ๐ถ. ๐. ๐, ๐ is used as a measure of control for concrete strength, ๐′๐ . For ACI Committee 214: โช Poor control ๐ > 20% โช Average Control ๐ = 15% โช Excellent Control ๐ < 10% For Nowak & Szerszen (2001): โช Poor control ๐ > 14.0% โช Average Control ๐ = 10.5% โช Excellent Control ๐ < 7.0% Nowak & Szerszen (2001) is more representative of modern ready-mix concrete COMPRESSIVE STRENGTH MECHANICAL PROPERTIES OF CONCRETE COMPRESSIVE STRENGTH ACI 318-14 SECTION 26.12 CONCRETE EVALUATION & ACCEPTANCE CRITERIA Section 26.12.2.1a Frequency of Sampling Section 26.12.3.1b Acceptable Strength Level • At least once a day. • At least once for each 110m3 of concrete. • At least once for each 460m2 of surface area for slabs or walls • Every arithmetic average of any three consecutive strength tests equals or exceeds f’c. • No strength test falls below f’c by more than 3.5MPa if f’c is 35MPa or less; or by more than 0.10f’c if f’c exceeds 35MPa. Section 26.12.3.1c Steps to increase subsequent test results MECHANICAL PROPERTIES OF CONCRETE STRENGTH UNDER TENSILE & MULTIAXIAL LOADS ASTM C78: Standard Test Method for Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading) • Determines the flexural tensile strength or modulus of rupture, ๐๐ , of a standard concrete beam. • 6๐ ๐๐ = 2 ๐โ โช M is the moment โช b is the width of specimen โช h is the overall depth of specimen MECHANICAL PROPERTIES OF CONCRETE STRENGTH UNDER TENSILE & MULTIAXIAL LOADS ASTM C496: Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens • Determines the splitting tensile strength of concrete, ๐๐๐ก • 2๐ ๐๐๐ก = ๐๐๐ โช P is the maximum applied load โช l is the length of the specimen โช d is the diameter of the specimen MECHANICAL PROPERTIES OF CONCRETE STRENGTH UNDER TENSILE & MULTIAXIAL LOADS Relationship between Compressive and Tensile Strengths of Concrete โ โ Modulus of Rupture โช ๐๐ = 0.62λ ๐′๐ Splitting Tensile Strength โช ๐๐๐ก = 0.56λ ๐′๐ Strength under Biaxial and Triaxial Loadings MECHANICAL PROPERTIES OF CONCRETE Biaxial Loading of Uncracked, Unreinforced Concrete โ B-D-B’ and Zone 1 โช โช Concrete is under biaxial tension, Strength is close to uniaxial tension like in Fig. (b). โ A-B and A’-B’ and Zone 2 โช โช โช Concrete is under tension in one axis and compression in another. Concrete cracks at a lower tensile strength than in Zone 1 and under uniaxial tension. The lower tensile strength is the result of limiting tensile strain than strength. โ A and A’ and Zone 3 โช โช Concrete is under uniaxial compression, Failure is governed by tensile cracks parallel to the compressive stresses, โ A-C-A’ and Zone 4 โช โช โช โช Concrete is under biaxial compression. Tensile cracks form parallel to the unloaded side. This loading delays cracking and results to a more ductile concrete. It also results to greater compressive strength. MECHANICAL PROPERTIES OF CONCRETE Biaxial Loading of Uncracked, Unreinforced Concrete โ B-D-B’ and Zone 1 โช Failure occurs when concrete cracks. โ A-B and A’-B’ and Zone 2 โช โช Failure occurs when concrete cracks. This happens to concrete in the web of beams. โ A and A’ and Zone 3 โช โช Concrete is under uniaxial compression, This happens to concrete under split-cylinder test. โ A-C-A’ and Zone 4 โช โช โช Concrete is under biaxial compression. Failure occurs when concrete is crushed. For a well-reinforced concrete, failure occurs through crushing because the reinforcement prevents failure through cracking. MECHANICAL PROPERTIES OF CONCRETE Compressive Strength of Cracked Reinforced Concrete ๐2๐๐๐ฅ 1 = ′ ๐๐ 0.8 + 170๐1 ๐2 ๐2 ๐2 = ๐2๐๐๐ฅ 2 − ๐0 ๐0 2 Assuming a parabolic curve for Fig. (b): Importance: • Tensile strains in concrete should be limited to avoid failure. • The first two equations represent smeared properties which was a breakthrough in the finite element analysis of concrete. ๐2 = ๐′๐ ๐2 1− ๐′๐ MECHANICAL PROPERTIES OF CONCRETE Triaxial Loadings ๐1 = ๐′๐ + 4.1๐3 โ Normal concrete ๐1 = ๐′๐ + 2.0๐3 โ Lightweight concrete โ High-strength concrete MECHANICAL PROPERTIES OF CONCRETE Tangent and Secant Moduli of Elasticity โ Initial Tangent Modulus of Elasticity โช The slope of the stress-strain curve at the origin โ Tangent Modulus of Elasticity โช The slope of a line that is tangent to a point on the stress-strain curve. โ Secant Modulus of Elasticity โช The slope of a line from the origin and through the point on the curve. โช Typically, the point on the curve represents a stress of 0.4๐′๐ which is the stress at service level. MECHANICAL PROPERTIES OF CONCRETE Stress-Strain Curve for NormalWeight Concrete in Compression Establishing the Mathematical Model for the Stress-Strain Curve of Concrete in Compression 1. Initial Tangent Modulus of Elasticity increases with increasing compressive strength. 2. The rising portion of the stress-strain curve resembles a parabola with its vertex at the maximum stress. 3. The strain at maximum stress increases as the concrete strength increases. 4. The slope of the descending branch for concrete strength up to 6000psi is flatter than the ascending branch; and increases with increasing strength. 5. The maximum strain reached decreases with increasing concrete strength. MECHANICAL PROPERTIES OF CONCRETE Equations for Compressive Stress-Strain Diagrams: Modified Hognestad โช Represents the stress-strain curve of concrete having strengths up to 6000psi. โช Consists of a second-degree parabola o Apex stress ๐′′๐ = 0.9๐′๐ 1.8๐′′๐ o Apex strain ๐0 = ๐ธ๐ o Terminating stress ๐๐ข = 0.85๐′๐ o Limiting strain ๐๐๐ข = 0.0038 โช The reduced strength ๐′′๐ = 0.9๐′๐ accounts for the differences between cylinder strength and member strength (e.g., concrete in beams). MECHANICAL PROPERTIES OF CONCRETE Stress-Strain Curve under Cyclic Loading MECHANICAL PROPERTIES OF CONCRETE Modulus of Elasticity Poisson’s Ratio MECHANICAL PROPERTIES OF CONCRETE Stress-Strain Curve for Normal-Weight Concrete in Tension PROPERTIES OF REINFORCEMENT TWO MOST COMMON REINFORCEMENT: HOT-ROLLED DEFORMED BARS WELDED WIRE REINFORCEMENT PROPERTIES OF REINFORCEMENT HOT-ROLLED DEFORMED BARS STANDARDS: ASTM A615 • Standard Specification for Deformed and Plain Carbon-Steel bars for Concrete Reinforcement • This standard is used for the most used reinforcing bars. ASTM A706 • Standard Specification for Low-Alloy Steel Deformed and Plain Bars for • This standard is used for bars with special applications where weldability, bendability, or ductility is important. • This standard requires bars to have longer elongation at failure and shorter bend test results (higher bendability). ASTM A996 • Standard Specification for Rail-Steel and Axle-Steel Deformed Bars • This standard is used for bars produced from discarded railroad rails or train car axles. • It is less ductile and less bendable than A615 steel and not widely available PROPERTIES OF REINFORCEMENT HOT-ROLLED DEFORMED BARS PROPERTIES OF REINFORCEMENT 300MPa HOT-ROLLED DEFORMED BARS 420MPa 520MPa HOT-ROLLED DEFORMED BARS PROPERTIES OF REINFORCEMENT PROPERTIES OF REINFORCEMENT HOT-ROLLED DEFORMED BARS MECHANICAL PROPERTIES: Less pronounced Yield Strength Yield Strength Tangent Modulus of Elasticity, ๐ธ๐ = 29000๐๐ ๐ PROPERTIES OF REINFORCEMENT HOT-ROLLED DEFORMED BARS MECHANICAL PROPERTIES: YIELD STRENGTH Histogram of Mill-Test Yield Strengths for Grade 60 Reinforcement 9.3% Coeff. of Variation • These mill tests are performed at a high rate of loading. • The static yield strength is determined for test at slower rates, which is 4ksi less than the mill-test yield strength. PROPERTIES OF REINFORCEMENT HOT-ROLLED DEFORMED BARS MECHANICAL PROPERTIES: FATIGUE STRENGTH o Structural fatigue is caused by cyclic loads such as those on bridge decks. o Cyclic loads cause repeated cycles of tension and compression stresses. o Failure occurs when extremes stresses are tensile. o Lower than 20,000 cycles, fatigue is not an issue for deformed bars. o Fatigue strength is independent of yield strength. o Fatigue failure may occur in the vicinity of welds or bends when the stress range exceeds 10ksi. o Fatigue strength decreases when: • Stress range increases • The lower stress in a cycle is reduced. Stress Range (Max Stress – Min Stress) vs. Cycles Endurance Limit PROPERTIES OF REINFORCEMENT HOT-ROLLED DEFORMED BARS MECHANICAL PROPERTIES: STRENGTH AT HIGH TEMPERATURES PROPERTIES OF REINFORCEMENT WELDED-WIRE REINFORCEMENT STANDARDS: ASTM A82 • Standard Specification for Steel Wire, Plain. ASTM A185 • Standard Specification for Steel Welded Wire Reinforcement, Plain ASTM A496 • Standard Specification for Steel Wire, Deformed ASTM A497 • Standard Specification for Steel Welded Wire Reinforcement, Deformed • • • • This reinforcement depends on crosswires to provide mechanical anchorage with the concrete. For deformed-wire fabric, the deformations provide additional anchorage. The minimum yield and tensile strength for smooth wire are 65ksi and 75si. The minimum yield and tensile strength for deformed wire are 70ksi and 80ksi PROPERTIES OF REINFORCEMENT WELDED-WIRE REINFORCEMENT PROPERTIES OF REINFORCEMENT WELDED-WIRE REINFORCEMENT CODES OF PRACTICE ASSIGNMENT Give five (5) other mathematical models for the stress-strain curve of concrete in compression. Summarize each of their description. LABORATORY ACI E702 LABORATORY TOOLS Acceptance of Concrete Compressive Strength Test Results according to ACI 318-14 PTC MathCAD Express CSI Section Builder REFERENCES ACI 318-14. (2015). Building code requirements for structural concrete (ACI 31814). Farmington Hills, MI: American Concrete Institute. Wight, J., & MacGregor, J. G. (2009). Reinforced concrete. Mechanics and Design.(5a ed.) EEUU: Pearson.
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