Urban and Civil

Nov 29, 2013 (4 years and 5 months ago)

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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
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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

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
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11 page 373