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 (sigma).
• 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 r2
– 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 represents the change in length
L represents the original length
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 stressstrain 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/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
• Using Young’s Modulus, we can determine the expected
deformation of a member due to a constant force being
applied.
FL
d=
AE
• Where:
d = Change in length
F = Force applied
L = Original length of member
A = Cross sectional area
E = Young’s Modulus
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 in2)(29,000,000 psi) = .0086 feet