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 s = F s A o Tensile stress, : original area.

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)