Experiment 1
Failure Criteria
and stress concentration
Static failure criteria
1. Ductile material (  f  0.05)
Max. Shear theory
Distortion energy
Ductile Coulumb-Mohr
2. Brittle material (   0.05 )
Max. normal stress
Brittle Coulumb-Mohr and modification
f
Maximum shear theory
 A  Sy
Case 1
Case 2
Case 3
Distortion energy theory
Von Mises stress
In general form
Plain stress or
plain strain
Maximum normal stress theory
Coulumb-Mohr and modification
S value
External load

S
For bending:
Mc
I

, therefore, S 
I
c
For torsion:
Tc
J
 = , therefore, S 
J
c
For axial load:
F
 = , therefore, S  A
A
Various load
Fatigue Testing
D=5mm
or
10mm
Endurance
limit for cast
iron (Sn)
Correction of endurance limit
Sn
S’n
Sn
S’n
Stress concentration and stress
raisers
• Stress concentration factor
max. local stress
Kf 
nominal stress
Varying stress in machine element
S max  S min
Sa 
2
S  S min
S m  max
2
Solving problems in which the stress is a
combination of alternating stress and
constant stress
For compression
mean load, no
effect on
endurance limit
Solderberg Diagram
1 S m KS a


N Sy
Sn
Gerber line
2
 Sm 
KS a
1 
 
 Su / N  S n / N
For shear load
1 S ms KS as


N S ys
S ns
Designing for variable load and
finite life
How to raise the endurance
strength
1. Autofrettage
2. Shot peening and surface rolling
3. Heat treatment
4. Laser treatment
5. Electro polishing
6. Others
Design Procedures
Static Load design
1. Determine the external force, and configuration
of the structure.
2. Determine the material of the structure.
3. Find the equation(s) of the stress in the
structure.
4. Determine the criteria of failure to be used.
5. Find the S value of the structure.
6. According to the S value find the appropriate
shape of the cross section.
Design for the various load
1.
2.
3.
4.
5.
6.
7.
8.
9.
Determine the type of the external force, and configuration of the
structure.
Determine the material of the structure.
Use fully corrected endurance limit for bending, Sn.
Apply stress concentration factors to torsion, bending and axial
stress components.
1
Multiply any alternating axial stress component by the factor kc ,ax .
Enter the resultant stress in to a Mohr’s circle analysis and find
the principle stresses.
Find the Von mises alternating stress  a .
Find the Sa/N according the failure criteria used.
Compare Von mises stress with Sa/N to find the dimension of the
part.
Practices 1
1. Try to write an Excel program which can
calculate the principle static stress, principle
shear stress, Von Mises stress of a simply
support beam of circular cross section under
bending load, axial load and torsion load. (see
figure in next page)
2. Use Distortion energy theory to find the
dimension of the beam under the loads given
in the figure in next page.
Fb
Torque
450
1000
Fb=10kg
Fc=10kg
Torque=10 N-m
Material : ultimate strength = 400MPa
Yielding strength =250MPa
FC
Practices 2
1. Try to write an Excel program which can used
the Solderburg Criteria to calculate Sa under
different loading conditions and safety factor N.
2. Use Von mises stress to find the dimension of
the beam under the loads given in the figure of
practice 1. If all the load is varied as shown in
figure (c) of following page. The surface of the
beam is machined (please write a Excel
program to do this).
Sa  Sm
S N  150MPa