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**CTC / MTC 222 Strength of Materials**

Chapter 2 Design Properties of Materials

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Chapter Objectives Define yield point, ultimate strength, proportional limit, and elastic limit Define modulus of elasticity and describe how it relates strain to stress Define Hooke’s Law Define Poisson’s ratio Define ductility Define a ductile material Define a brittle material

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**Strength Properties of Metals**

Proportional Limit – value of stress at which stress-strain curve becomes non-linear Elastic Limit – greatest value of stress at which no permanent deformation occurs upon unloading Yield Point – value of stress at which there is a significant increase in strain with little or no increase in stress Ultimate strength – the maximum stress a material is capable of developing

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**Modulus of Elasticity, E**

A measure of the stiffness of a material A material with a higher value of E will deform less than one with a lower value of E The ratio of the normal stress on an element to the corresponding strain Modulus of elasticity = normal stress / normal strain, or E = σ / ε Can be determined by the slope of the straight line portion of the stress-strain curve When stress is below the elastic limit, there is a straight-line relationship between stress and strain Hooke’s Law applies: σ = E ε

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Poisson’s Ratio, μ An applied force causes a load-carrying member to deform in the direction of the force At the same time, there is also deformation in the direction perpendicular to the force For example, a tensile force will cause the member to elongate in the direction of the load (axial strain) At the same time, there is also deformation in the direction perpendicular to the force (lateral strain) Poisson’s Ratio is the ratio of the lateral strain to the axial strain Poisson’s Ratio = μ = Lateral strain/Axial strain = -εL/ εa Values of Poisson’s ratio range from 0.1 to 0.5 Values for metallic materials range from 0.25 to 0.35

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**Modulus of Elasticity in Shear, G**

The ratio of the shearing stress on an element to the corresponding strain G = shearing stress / shearing strain = / g Also called Modulus of Rigidity G is related to the tensile modulus by Poisson’s ratio G = E / [2 (1 + μ)]

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Ductility Ductility – the ability to undergo significant deformation prior to failure (rupture) Ductile material - >5% elongation before rupture Gradual failure Brittle material - <5% elongation before rupture Sudden failure Steel is a ductile material Elongation at failure approximately 15 – 20% This makes steel a desirable construction material

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