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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
-
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