Page 15 - Mechanical Engineers Reference Book

1/4 Mechanical engineering principles

Table 1.1 Centres of gravity and moments of inertia or second moments of area for
two-dimensional figures
Shape G I
Triangular area j = hi3 IGG = bh3136
I,, = bh3112
x+*4x
Rectangular area

yb:
Circular sector x = -__ I,, = - (a - sin’.)
2r sin a
r4
1
4
3
a
= - (a + 2 sin's)
1
r4
I,, 4
gx
Slender rod
I,, = m(b2 + c2)112
I,, = m(c2 + a2)/12
Izz = m(a2 + b2)112

Circular cone I’ X = h14 I,, = 3m3110
3m2 mh’
+
I,, = -
~
20 10

Torsion equation: If a circular shaft is subject to a torque (T) 1.3 Dynamics of rigid bodies
then the following equation holds:
1.3.1 Basic definitions
TIJ = rlr = GOIL
1.3.1.1 Newton’s Laws of Motion
where J is the polar second moment of area, G the shear
modulus, L the length, 0 the angle of twist, T the shear stress First Law A particle remains at rest or continues to move in
and Y the radius of the shaft. a straight line with a constant velocity unless acted on by an
external force.