1. CTC / MTC 222 Strength of Materials
Chapter 2
Design Properties of Materials

2. 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

3. 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

4. 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

5. 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

6. 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)]

7. 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