EGR 236 Properties and Mechanics of Materials
Lecture 09: Stress Concentrations
Spring 2014
Today:
-- Homework questions:
-- New Topics:
-- Stress Concentrations
-- Homework: Read Section 4.7
Work Problems from Chap 4: 93, 95, 100
Following today's class you should be able to:
-- Understand what types of features and discontinuities cause stress level
to increase.
-- Calculate expected values of stress in the vicinity of discontinuous
features.
Stress Concentrations:
The axial deformation equation that we have worked with so far is effective
for determining stress in members with uniform shape and composition at
locations in the body that are located sufficiently far enough away the point of
load application.
Directly around the point of load application, the stresses and strains can be
considerably higher than the stress predicted by that of the axial load equation.
The higher stresses at the point of an applied load are called stress
concentration points.
Stress concentrations also arise at locations along the axial member where
the geometry undergoes a change in the cross sectional area or material
composition. This is especially true if the change occurs very suddenly
and abruptly.
We have looked at the
stress set up in one
such example during
the FEA lab 1.
In lab one a model of a
flat plate with a hole in
the middle was
subjected to an axial
load. The maximum
stress levels found to
be near the hole.
Examples of common stress concentration patterns:
When designing a part we will be interested in determining the largest stress.
This max stress will limit the maximum load that can be carried.
The FEA tools are extremely useful to predict stresses that occur with
changing geometry. The FEA tool offers a way to predict the maximum stress
for whatever geometry of part is shown.
Another method used to
determine the maximum
stress of some common
geometry changes can be
found using readily available
graphical stress concentration
tables.
While limited to simple
cases, the tables can be useful
to predict the stress
concentration factor in the
vicinity of holes and internal
fillets on flat plates subjected
to axial loading.
The stress concentration
factor, K, may is defined as
 max  K ave
This value depends very
heavily on the sharpness of
the hole or corner. Very
sharp corners amplify the
stress. One of the most
important general design rules
you should always keep in
mind when designing a part
subjected to loads, is to avoid
sharp internal corners.
Example 1:
-----------------------------------------------------------------------------------------------
Example 1:
----------------------------------------------------------------------------------------------Find Stress Concentration factor:
D = 60 mm
d = 40 mm
t = 10 mm
r = 8 mm
Find: D/d and r/d
D 60

 1.5
d
40
and
r
8

 0.2
d 40
Reading the K value from
the table for internal
fillets: K ≈ 1.85
Find Average Stress:
F
P
 ave 

A td
combining this with the stress concentration equation:
KP
 max  K ave 
td
allows us to solve for the largest force P that can be held.
 td (165MPa)(10mm)(40mm N / mm2
P 

)
 35675 N
K
1.85
MPa
Example 2:
The resulting stress distribution along the section AB for the bar is shown
in the figure.
a) From this distribution, determine the approximate resultant axial force
P applied to the bar.
b) What is the stress-concentration factor of this geometry.
-----------------------------------------------------------------------------------------------
a) Approximate axial force, P
P    dA  [Area Under Stress-Cross Section Diagram]
By inspection:
25  28  33
 29 ksi
3
A  (0.75in)(6  0.4in)  1.8in2
 ave 
Therefore:
P   ave A  (29ksi )(1.8in2 )  52.2 kip
b) Stress Concentration:
K 
 max
 ave
where
 ave 
25  28  33
 29 ksi and
3
so
K 
36ksi
 1.24
29ksi
 max  36 ksi