462
AppendixA . Area Moments of Inertia
A/57 Determine the polar moment of inertia of the circular area without and with the central square hole.
Ans.I, - | 57lRa without hole
with hole
1. L40,1R4.
PROBLEMS
tntroductory Probtems
A/55 Determine the percent reduction n in the polar moment of inertia of the rectangular plate due to the
introduction of the rectangular hole. The l-y axes
are centeredon the plate
Ans.n - 6.2'qo
l+
h
b
7a
ProblemA/55
A/56 Determine the moment of inertia about the r-axis of
the squarearea withoul. and with the central circu.I t
lar hole.
ProblemA/17
A/58 Calculate the polar radius of grration of the shaded
area about the center O ofthe larger circle.
v
2R
2R
Problem A/18
Iitttd
A A(.
'tr5ti 4-
ProblemA/55
Article A/5
A/!9 The cross-sectional
area of a wide-flangel-beamhas
the dimensionsshown.Obtain a closeapproximation
to the handbook value of 1, = 657 ln.a by treating
the sectionasbeingcomposedofthree rectangles.
Ans I' = 649 int
Problems 465
A/42'Calculate the moment of inertia of the crosssection
of the beamaboutits centroidalr.-axis.
-1
l
150mm
_J
Problem
A/42
Representqtiv e Problems
0.628"
problem A/J9
\ A/4l lDetermine the moments of inertia of the Z-section
-/ about its centroidal *6- andye-axes.
Ans.i, - 22.6r Lo6tmmo
A,/40 Determine the moment ofinertia ofthe shaded area
about the r-axis in two ways. The wall thickness is
I
20 mm on all four sides ofthe rectangle.
i-
;
^^.,.^A.
ta = tt,atlr-tu-,mm_
-:
ProblemA/43
Problem A/40
A/41 Calculate the moment of inertia of the shaded area
abour the r-axis.
Ans. 1, :4.53(106) mm4
80 mm
ProblemA/41