LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
MODULE 2
LOAD AND STRESS ANALYSIS
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS
Load
Equilibrium equations
Complex stresses
Stress transformation
Mohr’s circle
Stress-strain relations
Stress concentration
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
A branch of mechanics that studies the relationships between external loads applied to a deformable body and the intensity of internal forces acting within the body.
Mechanics of Materials
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Applications involving combined loading
Typical Engineering Structures
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Types of Loading on Structures
LOAD 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
Temperature Difference
T oC oF
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Types of Loading on Structures
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
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.
0
0
oM
F
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Stress Under General Loading Conditions
Stress – intensity of a force acting at a material point
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Simple Stresses
J
Tr
A
P
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Complex Stresses
T
P•A
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?
A
Shear stress
Normal stress
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Stress Transformation Equations
2sin2cos22 xy
yxyxx
2cos2sin2 xy
yxyx
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Mohr’s Circle
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Fracture Planes
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Engineering Stress and Strain
P – applied force
Ao – original cross-sectional area
Lo – original gage length
L – instantaneous length
s =
P
Ao
e =
DL
Lo
= L - Lo
Lo
Engineering stress,
Engineering strain,
P
P
LLo
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Engineering Stress-strain Curve
e
So
PlasticElastic
s
Necking
Fractured
Fractured
Tensile failure in ductile material is associated with large plastic deformation.
eTotal = eel + epl
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
STRAIN,
0.0 0.1 0.2 0.3 0.4 0.5 0.6
ST
RE
SS
, (
MP
a)
0
200
400
600
800
STRAIN,
0.0000 0.0002 0.0004 0.0006 0.0008 0.0010
ST
RE
SS
, (
MP
a)
0
50
100
150
200
= E
Linear
Non-linear /Power-law
= E
= K(p)n
SS316 steel
Engineering Stress-strain Curve
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Mechanical Properties of Some Materials
MATERIALS E GPa (!06 psi)
So
MPa(ksi)
SU
MPa(ksi)
AISI 1040steel
207(30)
413(60)
620(90)
Stainless Steel 314
193(28)
205(30)
515(75)
7075Al alloy
72(10.5)
105(15)
230(33)
Gray cast iron
- - 152(22)
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Stress Concentration
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Stress Concentration
Stress concentration factor
avgtK
max
SKMM 4133 Failure of Engineering Components and Structures
LOAD AND STRESS ANALYSIS M.N. Tamin, UTM
SME 4133 Failure of Engineering Components and Structures
Stress Concentration
SKMM 4133 Failure of Engineering Components and Structures
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