ES035 – LESSON
DEFORMATION
3:
SIMPLE
STRAIN
AND
HOOKE’S LAW (Proportional Limit)
•Stress is proportional to strain
NORMAL/AXIAL STRAIN (ε)
•In general terms, strain is a geometric quantity that
measure the deformation of a body
•Ratio of the axial change in length caused by an applied
load, to the original length, L
•Also known as unit deformation (m/m; in/in)
Where: E = Modulus of Elasticity or young’s Modulus
In terms of deformation:
Assumptions:
•Constant cross-section
Limitations:
•Constant cross-section
•Uniform axial loading
•Uniform axial loading
•Material is homogeneous and isotropic
•Material is homogeneous and isotropic
•Stress must not exceed proportional limit
If one of the 1st three assumptions is not met,
SAMPLE PROBLEMS:
1. A 4 mm Ø steel wire, 3.2 m long, carries an axial
tensile load P. Find the maximum safe value of P
if the allowable normal stress is 280 MPa and the
elongation of the wire is limited to 4mm. Use
E=200GPa.
STRESS-STRAIN DIAGRAM
•PROPORTIONAL LIMIT–From the origin to this point,
the stress-strain curve is a straight line
•ELASTIC LIMIT–Point
deformation occurs
beyond
which,
permanent
•YIELDPOINT–Point beyond which, increase in strain
without increase in applied load
•ULTIMATE STRENGTH – Highest ordinate on the stressstrain curve
•RUPTURESTRENGTH–Stress at failure; considering
necking gives true rupture strength
2. The steel propeller shaft ABCD carries the axial
loads shown in figure. Determine the change in
the length of the shaft caused by these loads. Use
E = 29 x 106 psi for steel.
3. The rigid bar ABC is supported by a pin at A and
a steel rod at B. Determine the largest vertical
load P that can be applied at C is the stress in the
steel rod is limited to 35 ksi and the vertical
movement of end C must not exceed 0.12 in.
Neglect the weights of the members.