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Mechanical Engineering Department
WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT
STRESS ANALYSIS ES-2502, C’2012
Lecture 04: Stress
19 January 2012
Mechanical Engineering Department
Instructor: Cosme Furlong HL-151
(508) 831-5126 [email protected]
http://www.wpi.edu/~cfurlong/es2502.html
General information
Teaching Assistants: Morteza Khaleghi HL-150
(508) 831-5125 [email protected]
Tatiana Popova
Mechanical Engineering Department
Stress: Definition: intensity of internal force: acting on a
specific plane passing through a point
Equivalent
force and
moment at
the section
FFR
oRoMM
O
Mechanical Engineering Department
Stress: Definition: intensity of internal force: acting on a
specific plane passing through a point
Finite force F acting on
a finite area A
Definition
Normal stress:
A
Fz
Az
0lim
Mechanical Engineering Department
Stress: Definition: intensity of internal force: acting on a
specific plane passing through a point
Finite force F acting
on a finite area A Definitions
Shear stresses:
A
Fx
Azx
0lim
A
Fy
Azy
0lim
A
Mechanical Engineering Department
Stress: Definition: intensity of internal force: acting on a
specific plane passing through a point
Finite force F acting on
a finite area A
Normal and shear
stresses on plane x
Mechanical Engineering Department
General state of stresses
Further sectioning leads
to a “stress cube”
State of stresses of
a finite size cube
Mechanical Engineering Department
State of stresses: normal stress equilibrium (1D)
Finite size cube:
stress cube
One-dimensional
normal stress
)(')( AA
;0F
Therefore,
'
Mechanical Engineering Department
State of stresses: shear stress equilibrium
Finite size cube:
stress cube
Forces:
)(')( yxyx zyzy
;0yF
Therefore, zyzy '
Moments:
yzxzyx yzzy )()(
;0xM
Therefore, yzzy
Mechanical Engineering Department
Average normal stress in an axially loaded bar
Tensile test
Necking
Typical results
Ductile
material
Brittle
material
Mechanical Engineering Department
Average normal stress in an axially loaded bar
Bar subjected to
axial load
Internal distribution
of forces
Mechanical Engineering Department
Average normal stress in an axially loaded bar
Internal distribution
of forces zRz FF
A
dAdF
AP
Average normal stress:
A
P
Mechanical Engineering Department
Average normal stress in an axially loaded bar
Tensile average
normal stress
Compressive
average normal
stress
Mechanical Engineering Department
Average direct shear stress
Bar subjected to
shear load
ABCD section
A
B
C
D
A
B
C
D
AV
AV
(Area under
shear)
(Internal
loading)
V
avgA
V
Mechanical Engineering Department
Average normal stress: example A
The casting shown is made of steel having a specific weight of st=490 lbf /ft3.
Determine the average compressive stress acting at points A and B.
Approach:
1) Define free-body
diagrams
2) Determine
internal loadings
3) Compute average
stresses
Mechanical Engineering Department
Average normal stress: example A
The casting shown is made of steel having a specific weight of st=490 lbf /ft3.
Determine the average compressive stress acting at points A and B.
Free-body diagram
(FBD)
Compute internal
loading
&
Average
compressive
stresses z
(Stress cube)
Mechanical Engineering Department
Average shear stress: example B
Wood joints 150 mm deep (perpendicular to the plane) are loaded as shown.
Determine the average shear stress developed along planes a-a and b-b.
Approach:
1) Define free-body
diagrams
2) Determine
internal loadings
3) Compute average
stresses
Mechanical Engineering Department
Average shear stress: example B
Wood joints 150 mm deep (perpendicular to the plane) are loaded as shown.
Determine the average shear stress developed along planes a-a and b-b.
Free-body diagram
(FBD)
Mechanical Engineering Department
Average shear stress: example B
Wood joints 150 mm deep (perpendicular to the plane) are loaded as shown.
Determine the average shear stress developed along planes a-a and b-b.
Compute internal
loading
&
Average shear
stresses (Stress
cube)
(Stress cube)
Mechanical Engineering Department
Reading assignment
• Chapter 1 of textbook
• Review notes and text: ES2001, ES2501