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Lesson 2. Strength of materials Sections 1.4 – 1.6. Today’s lesson will cover:. The Stress/Strain diagram aka curve Elasticity, Plasticity and Creep (what may happen to a specimen of material under a constant load, not some scary guy you just passed in the hallway on the way to class…)

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Lesson 2

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Lesson 2

Strength of materials

Sections 1.4 – 1.6

Today’s lesson will cover:

The Stress/Strain diagram aka curve

Elasticity, Plasticity and Creep (what may happen to a specimen of material under a constant load, not some scary guy you just passed in the hallway on the way to class…)

Linear elasticity, Hooke’s Law, and Poisson’s Ratio

Stress and Strain Example

To the document reader!

tensile strength testing

Good video to watch on tensile test


Watch this on your own (it is on the wiki space home page)

Take out your twizzlers!

Unwrap them but don’t eat them (yet)

measuring stress and strain

Standard size specimens, e.g., L = 2” and d = 0.505”

Load is applied and gradually increased

Elongation is measured

Since dimensions of specimen are known, we can calculate stress and strain from the load and elongation, respectively:

Then, we can plot stress vs. strain and determine various mechanical properties and types of behavior of the material.

“Nominal” vs. “true” stress and strain

The Stress-Strain Curve (structural steel in tension)

Now, drawn to scale…Structural steel is “ductile”

Necking occurs in the plastic region



after the yield stress is passed, strain will keep increasing but stress will remain the same



Elasticity & plasticity

In the top chart, the stress (load) never exceeds the proportional limit

The material “snaps” back once load removed. It behaves elastically.

In the bottom chart, the stress exceeds A. When load is removed, it doesn’t “snap” all the way back. There is a residual strain.

“E” is called the elastic limit. Below that stress, completely elastic. Above, only partially elastic.

The “plasticity” of a material describes how much of its deformation remains after a load is removed.


A type of strain that is time-dependent.

Sometimes (usually at high temperatures), materials will continue to elongate—develop more strain—with the passage of time.

Example—a wire sagging

Example—turbine blades in jet engines “Creeping”

Linear elasticity, Hooke’s Law, and Poisson’s Ratio

This version of Hooke’s Law applies only to longitudinal stresses and strains developed in simple tension or compression

Note: material must be homogeneous and isotropic. Also, Poisson’s Ratio is constant only in the linearly elastic region. Ordinary materials will have a positive Poisson’s Ratio

Hooke’s Law describes the linearly elastic region of the stress-strain curve:

E is the “Modulus of Elasticity” or “Young’s Modulus”, and is a physical property of the material (not of its shape).

When a specimen is elongated, it contracts in the dimension normal to the load. This is called lateral contraction. The ratio of the change in lateral strain to normal strain is Poisson’s Ratio:

Poisson’s ratio is another physical property of a material

Young’s modulus is another name for the modulus of elasticity



poisson’s ratio relates lateral strain with axial strain




Problem 1.4-7 on HW#1

You’re given a table of loads and elongations as well as dimensions of specimen. Need to plot the stress-strain curve, and determine:

Proportional limit

Modulus of Elasticity

Yield stress at 0.1% offset (see page 42)

Ultimate stress

Percent elongation in 2.00 inches

Percent reduction in cross-sectional area

(see page 43 for last two)

What I want to see:

Key terms, symbols, constants, etc.

Linear region: occurs between zero load and the proportional limit. Stress vs. strain is proportional here.

Proportional limit: stress at which the relationship between stress and strain is no longer proportional. Strain increases faster than stress.

Yield Stress: Stress at which the plastic region of the stress-strain curve begins.

Ultimate stress: stress at which specimen begins to “neck”. The highest load applied to the specimen during the test occurs at the ultimate stress.

Key terms, symbols, constants, etc.

Plastic region: part of curve where specimen deforms without an increase in applied load

Strain Hardening: area of curve where material undergoes changes to its crystalline structure. Increased loading is required to increase deformation.

Necking: the narrowing of the test specimen after the ultimate stress that culminates in fracture.

E = Modulus of Elasticity: stress over strain; the slope of the curve in the linear region.

ν = Poisson’s Ratio (Greek lowercase “Nu”); negative 1 times lateral strain over axial strain

take aways

HW#1 due Monday (check your answers against those in back of the book after solving each problem)

Quiz on Monday—review lesson slides!

Join wiki space

Register you clickers for this class

Have a good weekend!


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