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Ch 1. Stress and Strain Multimedia Engineering Mechanics

Normal

Stress

Shear and

Bearing Stress

Normal

Strain

Hooke's

Law

Thermal

Effects

Indeterminate

Structures

Mechanics Thermal Effects Case Intro Theory Case Solution Example

Chapter

1. Stress/Strain

2. Torsion

3. Beam Shr/Moment

4. Beam Stresses

5. Beam Deflections

6. Beam-Advanced

7. Stress Analysis

8. Strain Analysis

9. Columns

Appendix

Basic Math

Units

Basic Equations

Sections

Material Properties

Structural Shapes

Beam Equations

Mechanics Tools

SearcheBooks

Dynamics

Fluids

Math

Mechanics

Multimedia

Mems

Statics

Thermodynamics

Author(s):

Kurt Gramoll

Kurt Gramoll

MECHANICS - THEORY

Thermal Strain

MaterialUS

(10-6/

oF)

SI

(10-6/

oC)

Steel 6.5 12

Aluminum 13 23

PVC 30 55

Concrete 5.5 10

Coefficient of Thermal Expansion, ,

for Common Materials

(Expanded List in Appendix)

When physical materials are heated, they generallyexpand due to atomic-level changes. This expansion

is proportional to the change in temperature. In terms

of strain, this relationship is written as

T= (T)

where is the coefficient of thermal expansion. This

constant is different for all materials and is generally a

positive number. There are a few materials that

contract when heated, and then this constant would

be negative.

The coefficient of thermal expansion represents a

quantity (i.e. strain) per degree C or per degree F.

Thermal Expansion

Thermal Expansion where

T = T2

- T1

The total deflection of a member that undergoes a

temperature change, T = T2

- T1, can also be written

as

T= L (T)

The deflection is in the direction of the length L.

For a 3D homogenous object, thermal expansion will

occur in all three directions. The total deflection in any

given direction will be a function of the length, width or

depth of the object.

There is no shear strain or shear deflection due to

thermal expansion.

Combined Thermal and Mechanical

Strain or Deflection

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Rod Between Two Fixed Walls -

Example of Stresses induced by

Thermal Expansion

Click to view movie (141k)

Generally, thermal expansion is accompanied with

mechanical deflection caused by a physical load.

When both force and temperature changes are

present, special care is needed when solving the

problem. Both the thermal and mechanical deflections

need to be compatible.

For example, if a simple rod is placed between two

fixed walls and heated, the rod will try to expand.

However, the walls will prohibit the normal thermalexpansion and induce a compression force. This force

is real and causes the rod to decrease in length. The

final result is the thermal expansion is offset by the

mechanical compression deflection (see diagram and

animation at left).

When both mechanical and thermal conditions are

present, a compatibility relationship needs to be

introduced to solve the problem. Further discussion of

compatibility conditions can be found in the following

section on Indeterminate Axial Structures.

Other Material Properties

Stress-Cycle (-n) Curves

(also called s-n Curves)

Cyclic Loading (Fatigue)

As structural members experience multiple

loading/unloading, their failure stress level will

decrease. For example, car axles or even aircraft

wings will experience millions of loadings over their

service life. For aluminum, the failure stress can

reduce by 70% of the original failure stress level.

To assist designers, charts called s-n curves are

developed through experiments. The charts show thefailure stress changes as the object is subjected to

cycles. In some industries, such as aircraft, extensive

testing on full scale models are required to insure the

structure will not failure before a certain number of

load cycles.

Typical Creep Curve

Viscoelasticity (Creep)

Another interesting property of many materials,

especially plastics, is viscoelasticity or creep. This

property models a material's tendency to flow over

time when under stress. The most common effect ofthis is the deformation of an object over time when

under a very low load. Even glass will creep over

time. Plastics tend to exhibit higher creep

characteristics then metals or ceramics.

anics eBook: Thermal Effects http://www.ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=me&

11/29/2012