Axial Members
•
AXIAL MEMBERS, which support load only along their primary
axis, are the most basic of structural members.
•
Equilibrium requires that forces in Axial Members are always
Equal, Opposite, and Co

Linear.
•
In most cases, axial members have pinned ends.
•
Some examples of axial members include:
–
Bars;
–
Truss Members;
–
Ropes and Cables.
Axial Stress
•
If a cut is taken perpendicular to a bar's axis, exposing an
internal cross

section of area A, the
force per unit area
on the
face of this cut is termed
STRESS
.
•
The symbol used for normal or axial stress in most
engineering texts is
s
=
⡳楧浡(⸠
=
•
Stress in an axially loaded bar is:
–
s
= F/A
•
Stress is
positive
in
tension
(P>0) and
negative
in
compression
(P<0);
•
English units:
psi
(pounds per square inch), or
ksi
(kilopounds
per square inch);
Axial Stress
•
The axial stress of a member is determined by:
s
=
F / A
Where F = force applied along the longitudinal axis
of the member perpendicular to the cross
sectional area (A).
Axial Stress Example
•
A cylindrical steel bar has a diameter of ½”
•
The bar is attached at one end and a 5,000 lb
weight is hung from the steel bar
(axially
loaded)
•
What is the axial stress generated in the bar?
–
Area of a circle =
p
r
2
–
s =
F/A =5,000 lb/.20 in
2
=25,000 psi
Axial Strain
•
An axial bar of length L, and cross

sectional area A, subjected
to tensile force F, elongates by an amount, D.
•
The change in length divided by the initial length is termed
ENGINEERING STRAIN (or simply strain).
•
Strain is positive in tension and negative in compression
•
Strain is a non

dimensional length

a fraction.
•
Because strain is small, it is often given as a percentage by
multiplying by 100%: e.g., e = 0.003 = 0.3%.
Axial Strain
•
Axial strain is a measure of the
deformation to a member due to axial
stress.
e = d /
L
Where:
e
represents axial strain
d
r数e敳敮瑳
瑨攠捨慮c攠楮敮g瑨
=
=
䰠r数e敳敮瑳t瑨攠潲楧楮慬=汥湧瑨
=
Young's Modulus
•
Recall that all materials have a stiffness associated with them.
•
The stiffness of a material is defined through the relation:
s
= E
e
or E =
s / e
•
Where:
E is the YOUNG'S MODULUS or stiffness of the material.
e
is the axial strain
s
is the axial stress
•
Values of E for different materials are obtained experimentally from stress

strain curves.
Axial Strain Example
•
In the previous example, a cylindrical steel bar has a diameter
of ½” and a 5,000 lb weight is hung from the end (axially
loaded)
–
Young’s Modulus for steel is 29,000,000 psi
–
We found the axial stress to be 25,000 psi
•
What is the expected strain?
–
s
= E
e
or E =
s
/
e
or
e = s/
E
•
Where:
–
E is the YOUNG'S MODULUS or stiffness of the material.
–
e
is the axial strain
–
s
is the axial stress
•
e
= (25,000 psi)/(29,000,000 psi) = .00086 or .086%
Axial Strain Example (Cont.)
•
If the steel bar were 10 feet in length, what would the change
in length be when axially loaded?
•
e
=
d
=
⼠L
•
Where:
•
e
represents axial strain
•
d
represents the change in length (deformation)
•
L represents the original length
•
.00086 =
d /
10 feet
•
.0086 feet
Expected Deformation
d
=
•
Using Young’s Modulus, we can determine the expected
deformation of a member due to a constant force being
applied.
•
Where:
d =
Change in length
F = Force applied
L = Original length of member
A = Cross sectional area
E = Young’s Modulus
FL
AE
Expected Deformation
•
Using the Stress and Strain formulas, we found
the 10 foot steel rod is expected to change
length by .0086 feet when axially loaded with
5,000 pounds
•
Using the expected deformation formula, we
also find:
•
d
= FL/AE
•
=(5,000 lbs)(10 ft)/(.20 in
2
)(29,000,000 psi) = .0086 feet
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