Strengths
Chapter 10 Strains
1

1 Intro
•
Structural materials deform under the action of forces
•
Three kinds of deformation
•
Increase in length called an elongation
•
A decrease in length called a contraction
•
Change in shape called an angular distortion
•
Deformation per unit length is called linear strain
10

2 Linear Strain
•
Axial forces applied to a member tend to elongate or
compress the member
•
Original length L of the member is elongated to a length l+ @
after the tensile load P is applied. The total deformation is @
Greek lowercase letter delta
•
Linear strain defined as deformation per unit of original length
of the unstressed member
•
Formula 10

1 page 357 and page 358
10

3 Hooke’s Law
•
Linear relationship exists between stress and strain
–
to a
point
–
stress is proportional to the strain
–
beyond this limit
stress will no longer be proportional to strain
–
limiting value
is called the proportional limit of the material
–
this
relationship is called
hooke’s
law formula 10

2a page 358
•
Modulus of elasticity expressed usually as psi or
ksi
or
GPa
or
Mpa
•
Modulus of elasticity indicates its stiffness or ability of
material to resist deformation
•
210gpa for steel and 70gpa for aluminum
–
aluminum will stretch
three times more than steel of the same length when subjected
to the same stress.
10

4 Axial Deformation
•
Axial loaded member elongates under a tensile load and
contracts under compressive load
–
can be computed as long
as it does not exceed proportional limit
•
Figure 10

2 and formulas 10

4 10

5 page 359
•
For structural materials the moduli of elasticity for tension and
for compression are the same, so they will work for
compression or tension
–
tension forces are positive
–
compression forces negative.
•
Example 10

1 page 360
•
Example 10

2 page 360
•
Example 10

3 page 362
10

5 Statically Indeterminate
problems
•
When unknown forces in structural members cannot be
determined by the equilibrium equations alone
–
structure is
said to be statically indeterminate
–
statically indeterminate
problems
–
involve axially loaded members to be analyzed by
introducing the conditions of axial deformations
•
Example 10

4 page 363
•
Example 10

5 page 364
•
Example 10

6 page 365
10

6 Thermal Stresses
•
Homogeneous materials deformation due to temperature
change can be calculated using formula page 367 10

6
•
Stresses produced by a temperature rise or drop are called
thermal stresses
•
Example 10

7 page 368
•
Example 10

8 page 368
•
Example 10

9 page 369
10

7
P
oisson’s ratio
•
When a bar is subjected to an axial tensile load, it is elongated
in the direction of the applied load at the same time its
transverse dimension decreases
•
Axial compressive load is applied to the bar the bar contracts
along the axial direction while its transverse dimension
increases
•
Formula 10

7 page 371
•
Examples 10

10 page 371
10

8 shear strain
•
A shear force causes shape distortion of a body
•
Total deformation occurs over a length
•
Shear strain is thus the change in radians in a right angle
between tow perpendicular lines.
•
Use of
hookes
law
•
Formula 10

10 page 373
•
G is a constant of proportionality called the shear modulus of
elasticity or the modulus of rigidity.
•
Example
10

11 page 373
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