Mechanical Engineering Department WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT STRESS ANALYSIS ES-2502, C’2012 Lecture 04: Stress 19 January 2012
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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
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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
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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
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General state of stresses
Further sectioning leads
to a “stress cube”
State of stresses of
a finite size cube
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State of stresses: normal stress equilibrium (1D)
Finite size cube:
stress cube
One-dimensional
normal stress
)(')( AA
;0F
Therefore,
'
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State of stresses: shear stress equilibrium
Finite size cube:
stress cube
Forces:
)(')( yxyx zyzy
;0yF
Therefore, zyzy '
Moments:
yzxzyx yzzy )()(
;0xM
Therefore, yzzy
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P
P
Average normal stress in an axially loaded bar
Tensile test
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Average normal stress in an axially loaded bar
Tensile test
Necking
Typical results
Ductile
material
Brittle
material
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Average normal stress in an axially loaded bar
Bar subjected to
axial load
Internal distribution
of forces
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Average normal stress in an axially loaded bar
Internal distribution
of forces zRz FF
A
dAdF
AP
Average normal stress:
A
P
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Average normal stress in an axially loaded bar
Tensile average
normal stress
Compressive
average normal
stress
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Average normal stress in an axially loaded bar
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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
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Homework assignment
• As indicated on webpage of our course
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