stress has units: n/m 2 or lb f /in 2 engineering stress shear stress, : area, a f t f t f s f f f...
TRANSCRIPT
Stress has units: N/m2 or lbf/in
2
Engineering Stress• Shear stress, :
Area, A
Ft
Ft
Fs
F
F
Fs
= FsAo
• Tensile stress, :
original area before loading
Area, A
Ft
Ft
=FtAo
2f
2m
Nor
in
lb=
• Simple tension: cable
Note: = M/AcR here.
Common States of Stress
Ao = cross sectional
area (when unloaded)
FF
o F
A
o
FsA
M
M Ao
2R
FsAc
• Torsion (a form of shear): drive shaft
(photo courtesy P.M. Anderson)Canyon Bridge, Los Alamos, NM
o F
A
• Simple compression:
Note: compressivestructure member( < 0 here).(photo courtesy P.M. Anderson)
OTHER COMMON STRESS STATES
Ao
Balanced Rock, Arches National Park
• Bi-axial tension: • Hydrostatic compression:
Pressurized tank
< 0h
(photo courtesyP.M. Anderson)
(photo courtesyP.M. Anderson)
OTHER COMMON STRESS STATES
Fish under water
z > 0
> 0
• Tensile strain: • Lateral strain:
• Shear strain:
Strain is alwaysdimensionless.
Engineering Strain
90º
90º - y
x = x/y = tan
L L
wo
/2
L/2
Lowo
o
o
oo L
LL
L
L
Le
f
o
L
L o
f
L
L
L
dLln
Linear Elastic Properties
• Hooke's Law:
= E
Linear- elastic
E
F
Fsimple tension test
(If there is a linear response)
Modulus of Elasticity
• Modulus of Elasticity, E: (also known as Young's modulus)
“Stiffness” of the material
Linear behavior typically seen in metals and ceramics
Other materials do not have linear response(Grey cast iron, concrete, most polymers)
Tangent modulus: slope of stress strain curve at some specified level of stress
Units: Pressure (psi)
Secant modulus: slope of a secant drawn form the origin to some point on the
stress strain curve
Atomic Behavior• Slope of stress strain plot (which is proportional to the
elastic modulus) depends on bond strength of metal
Effect of Temperature
E = f(T)