ENGR 211 Lecture 16
Fall 2007
Civil Engineering
Moment of Inertia
Moment of Inertia
part 2
part 2
Compression
Tension
Force Couple
I
Civil Engineering
Definitions
Definitions
2
2
x
x
I
y dA
k
A
=
=
∫
2
2
y
y
I
x dA
k A
=
=
∫
•Where
I
is Moment of Intertia
•And
k
is the radius of gyration
Remember how we solved for the centroid of an Area
much the same way.

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ENGR 211 Lecture 16
Fall 2007
Civil Engineering
Moments of Inertia
Moments of Inertia –
•
They are inversely proportional to
the stresses in beams that cause
failure.
•
They are proportional to the
stiffness of beams.
•
They are second moments of area.
Civil Engineering

ENGR 211 Lecture 16
Fall 2007
Civil Engineering
Strength of Materials
Strength of Materials
Real Materials fail when too much
stress is applied
•
Axial Stress
– Tension
– Compression
•
Shear Stress
•
Bending Stress
Civil Engineering
Axial Stress
Axial Stress
Tension (or Compression)
Cross-sectional area
T
σ
axial
=

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