Lecture # 5 and 6 Objectives: 1): Relating Stress to Strain using experimental method. 2): Plotting...
-
Upload
dominic-willis -
Category
Documents
-
view
220 -
download
6
Transcript of Lecture # 5 and 6 Objectives: 1): Relating Stress to Strain using experimental method. 2): Plotting...
Lecture # 5 and 6Lecture # 5 and 6
Objectives:Objectives:
1): Relating Stress to Strain using experimental method.
2): Plotting Stress verses Strain (Stress – Strain diagram)
3): Extracting mechanical properties from – diagram.
The Tension and Compression Test
Typical steel specimen withattached strain gauge.
Electrical-resistanceStrain gauge.
The Stress – Strain Diagram
0
0
L
A
P
Conventional and true stress-strain diagramsfor ductile material (steel) (not to scale).
True Stress – Strain Diagram
Stress-Strain diagram for mild steel
Stress – Strain Behavior ofDuctile and Brittle Materials
Percent elongation = %1000
0
L
LL f
Percent reduction of area = %1000
0
A
AA f
Hooke’s Law
(mm/mm)
E
Typical Stress-Straincurve showingmodulus of resilience, MR.
Typical Stress-Straindiagram showing
modulus of toughness, MT.
Poission’s ratio.Poission’s ratio.
h
h
b
b
d
d
ensionlateraloriginal
ncontractiolateral
dim
1
(a) Lateral contraction for a bar in tension with
(b) Cross-sectional dimensions.
Deflection Due to Axial Loading
AE
PL (in.) or (mm.)
(a)Undeformed bar and
(b)Bar subject to axial force showing deformation.
Deflection Due to Axial Loading
(in.) or (mm.)ii
ii
iEA
LPN
1
Bar with intermediate axial loads.
Bar with changes in cross section and intermediate loads.
Deflection Due to Axial Loading
(in.) or (mm.)L
dxxExA
xP
0 )()(
)(
(a)Bar with variable cross sectional area and
(b)Bar subjected to loading that varies with x.
Elastic Strain verses Plastic Strain
Strain Hardening