STRENGTH OF MATERIALS
TRAN MINH TU - University of Civil Engineering,
Giai Phong Str. 55, Hai Ba Trung Dist. Hanoi, Vietnam
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5
CHAPTER
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Geometric Properties of an Area
Contents
5.1. Introduction
5.2. First moment of area
5.3. Moment of inertia for an area
5.4. Moment of inertia for some simple areas
5.5. Parallel - axis theorem
5.6. Examples
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5.1. Introduction
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Dimension, shape?
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5.2. First Moment of Area
5.2.1. Definition
()
x
A
S ydA
()
y
A
S xdA
•Centroidal axes: are axes, which first moment of a plane A about them
is zero
•The first moment of a plane A about
the x- and y-axes are defined as
•Value: positive, negative or zero
•Dimension: [L3]; Unit: m3,cm3,...
5.2.2. The centroid of an area
•The centroid C of the area is defined as the point in the xy-plane that
has the coordinates