# 6505-9 - Stress-Strain Behavior of Concrete(1 At stress...

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1 Stress-Strain Behavior of Concrete Typical Stress-Strain Plot of Concrete (1) At stress below 30% of ultimate strength, the transition zone cracks remain stable. The stress-strain plot remains linear. (2) At stress between 30% and 50% of ultimate strength, the transition zone microcracks begin to increase in length, width and numbers. The stress-strain plot becomes non-linear. (3) At 50 to 60% of the ultimate stress, cracks begin to form in the matrix. With further increase to about 75% of the ultimate stress, the cracks in the transition become unstable, and crack propagation in the matrix will increase. The stress-strain curve bends towards the horizontal. (4) At 75 to 80% of the ultimate stress, the stress reaches a critical stress level for spontaneous crack growth under a sustained stress. Cracks propagate rapidly in both the matrix and the transition zone. Failure occurs when the cracks join together and become continuous.

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2 Elastic Moduli of Concrete Static Modulus of Elasticity - The slope of the stress-strain curve for concrete under uniaxial tension or compression loading. Secant Modulus - The slope of a line drawn from the origin to the point on the stress-strain curve corresponding to 40% of the failure stress. Tangent Modulus - The slope of a line drawn tangent to the stress-strain curve at any point on the curve. Chord Modulus - The slope of a line drawn between two points on the stress-strain curve. Dynamic Modulus - The modulus of elasticity corresponding to a small instantaneous strain. It can be approximated by the tangent modulus drawn at the origin. It is generally 20, 30 and 40% higher than the secant modulus for high-, medium- and low-strength concretes, respectively. Secant Modulus : Slope of SO (Note: S is at 40% failure stress.) Chord Modulus : Slope of SC Tangent Modulus : Slope of TT’ Dynamic Modulus : Slope of OD Test for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression (ASTM C 469) • The test uses a 6” X 12” cylindrical specimen, which is loaded in compression. A compressometer is used to measure the longitudinal strains, and an extensometer is used to measure the transverse strains on the specimen. •T h e chord modulus (E) is calculated as: E = (S 2 -S 1 ) / ( ε 2 - 0.00005) where S 2 = stress corresponding to 40% of ultimate strength S 1 = stress corresponding to a strain of 50 X 10 -6 ε 2 = longitudinal strain produced by stress S 2 •T h e Poisson’s ratio ( μ ) is calculated as: μ = ( ε t2 - ε t1 ) / ( ε 2 - 0.00005) where ε t2 , ε t1 = transverse strains produced by S
3 Estimation of Modulus of Elasticity of Concrete • ACI Building Code 318 E = w 1.5 X 33 f c ’0.5 where E = static modulus of elasticity in psi w = unit weight in lb/ft 3 f c = compressive strength in psi. • CEB - FIP Model Code

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6505-9 - Stress-Strain Behavior of Concrete(1 At stress...

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