2. Geometric properties of sections
Axes of symmetry; centre of gravity of different sections (e.g., built-up plane figures,
standard steel sections); moment of inertia; radius of gyration)
3. Geometric properties of sections
Axis of symmetry is a line that divides an object into two equal halves, thereby
creating a mirror-like reflection of either side of the object.
4. Geometric properties of sections
Centroid and centre of gravity
• Centroid is a point where the whole area of the body is assumed to be concentrated
• Centre of gravity is point where resultant of parallel forces of attraction, formed by
weight of body passes.
• When the thickness of the body is not considered, then the center of gravity and
Centroid of a body is same and passes through the same point.
• C.G. or Centroid of figures can be found out by a) geometrical considerations, e.g. c.g.
of rectangle is at the point of intersection of diagonals b) by the methods of the
moments
6. Moment of inertia, radius of gyration
• Inertia is a property of body by virtue of which it tends to remain in its own state. A
force is required to change its state and the magnitude of forces depends upon the
masses
• Mass of the body is the measure of its inertia
• The moment of inertia is a physical quantity which describes how easily a body can
be rotated about a given axis.
• For a rotating body about an axis, inertia depends on the distribution of mass from its
axis of rotations along with mass, such property of rotating body is called as
rotational inertia of moment of inertia
• M.O.I is also called as second moment of area where as section modulus is called 1st
moment of area. Units of M.O.I are cm4.
7. Moment of inertia, radius of gyration
• Theorem of parallel axis IAA(about any axis) = IG(about centroidal axis)+ Ah2
• Theorem of perpendicular axis Izz= Ixx+Iyy
• Radius of gyration- it is the distance from the axis of reference where whole mass of
body is assumed to be concentrated so that moment of inertia of the body about
that axis is not altered
• Radius of gyration is the square root of the ratio of its moment of inertia to its area
• Section modulus is the quantity obtained by dividing the M.O.I of the cross-section of
a structure about its centroidal axis by the distance of extreme fibre from the
centroidal axis.
9. Practice Questions
1. The point through which the whole weight of the body acts is called
a) Inertial point b) Center of gravity c) Centroid d) Central point
2. The point at which the total area of a plane figure is assumed to be concentrated is
called
a) Centroid b) Centre of gravity c) Central point d) Inertial point
3. Where will be the centre of gravity of a uniform rod lies?
a) At its end b) At its middle point
c) At its centre of its cross sectional area
d) Depends upon its material
4. Where will be the center of gravity of the following section will lie in coordinates?
a) (6,3) b) (6,6) c) (6,1.5) d) (1.5,3)
10. Practice Questions
1. What is the moment of inertia of a circular section?
a) πD4/64 b) πD3/32 c) πD3/64 d) πD4/32
2. What is the moment of inertia of a rectangular section about a horizontal axis
through C.G?
a) bd3/6 b) bd2/12 c) b2d2/12 d) bd3/12
3. What is the moment of inertia of a rectangular section about a horizontal axis
passing through base?
a) bd3/12 b) bd3/6 c) bd3/3 d) bd2/3
