### Load Stress Analysis - Faculty of Mechanical Engineering

```SME
4133
Failure
of Engineering
Components
and Structures
SKMM
4133
Failure
of Engineering
Components
and Structures
MODULE 2
M.N. Tamin, UTM
SME
4133
Failure
of Engineering
Components
and Structures
SKMM
4133
Failure
of Engineering
Components
and Structures
Equilibrium equations
Complex stresses
Stress transformation
Mohr’s circle
Stress-strain relations
Stress concentration
M.N. Tamin, UTM
SME
4133
Failure
of Engineering
Components
and Structures
SKMM
4133
Failure
of Engineering
Components
and Structures
Mechanics of Materials
 A branch of mechanics that studies the
applied to a deformable body and the
intensity of internal forces acting within the
body.
M.N. Tamin, UTM
SME
4133
Failure
of Engineering
Components
and Structures
SKMM
4133
Failure
of Engineering
Components
and Structures
Typical Engineering Structures
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4133
Failure
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4133
Failure
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SYMBOL
UNITS
(Metrics)
UNITS
(Engineering)
Direct Force
F, P
N
lbf
Shear Force
V, Q
N
lbf
Torsion
T
Nm
lbf-ft
Bending Moment
M
Nm
lbf-ft
Fluid Pressure
p
Nm-2
psi
T
oC
oF
Temperature
Difference
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4133
Failure
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Components
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SKMM
4133
Failure
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Components
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M.N. Tamin, UTM
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4133
Failure
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Components
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SKMM
4133
Failure
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Equilibrium of a Deformable Body
A body is said to be in
equilibrium when the resultant
of all forces and moments
acting on the body is zero.
F 0
 Mo  0
M.N. Tamin, UTM
SME
4133
Failure
of Engineering
Components
and Structures
SKMM
4133
Failure
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Components
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Stress – intensity of a force
acting at a material point
M.N. Tamin, UTM
SME
4133
Failure
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Components
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4133
Failure
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Simple Stresses
Tr

J
P

A
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Failure
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4133
Failure
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Complex Stresses
T
A•
P
 Shear stress
A

Normal stress
 What is the magnitude of stress and strain on
specific plane at A?
 Does the stress and strain represent critical /
maximum values at A?
 If not…
 what is the maximum & minimum
(principal) stresses and maximum shear
stresses?
 What is the corresponding strain values?
 On which planes do these stresses act?
M.N. Tamin, UTM
SME
4133
Failure
of Engineering
Components
and Structures
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4133
Failure
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Stress Transformation Equations
 x 
 x  y
 xy  
2

 x  y
2
 x  y
2
cos 2   xy sin 2
sin 2   xy cos2
M.N. Tamin, UTM
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4133
Failure
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Components
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4133
Failure
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Components
and Structures
Mohr’s Circle
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Failure
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Failure
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Fracture Planes
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Failure
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Failure
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Engineering Stress and Strain
P
Lo
L
Engineering stress,
s
P
Ao
Engineering strain,
e
L

Lo
L - Lo
Lo
P – applied force
Ao – original cross-sectional area
Lo – original gage length
L – instantaneous length
P
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4133
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Engineering Stress-strain Curve
s
Fractured
Tensile failure in ductile
material is associated with
large plastic deformation.
Necking
So
Fractured
eTotal  eel + epl
Elastic
Plastic
e
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Engineering Stress-strain Curve
800
SS316 steel
STRESS,  (MPa)
600
Non-linear /Power-law
 = K(p)n
400
200
200
 = E
0
0.0
0.1
0.2
0.3
STRAIN, 
0.4
STRESS,  (MPa)
150
Linear
100
0.5
0.6
 = E
50
0
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
STRAIN, 
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Mechanical Properties of Some Materials
MATERIALS
E
GPa (!06 psi)
So
MPa(ksi)
SU
MPa(ksi)
AISI 1040
steel
207
(30)
413
(60)
620
(90)
Stainless
Steel 314
193
(28)
205
(30)
515
(75)
7075
Al alloy
72
(10.5)
105
(15)
230
(33)
Gray cast
iron
-
-
152
(22)
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Stress Concentration
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Stress Concentration
Stress concentration factor
Kt 
 max
 avg
M.N. Tamin, UTM
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4133
Failure
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4133
Failure
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Stress Concentration
M.N. Tamin, UTM
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4133
Failure
of Engineering
Components
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SKMM
4133
Failure
of Engineering
Components
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Stress Concentration Factors