The properties of the plane region are J ¯ C ^ = 1000 in . 4 , I x = 7000 in . 4 , and I y = 4000 in . 4 . Calculate A , I ¯ x , and I ¯ y for the region.
The properties of the plane region are J ¯ C ^ = 1000 in . 4 , I x = 7000 in . 4 , and I y = 4000 in . 4 . Calculate A , I ¯ x , and I ¯ y for the region.
Solution Summary: The author explains how the polar moment of inertia about the point O can be calculated.
The properties of the plane region are
J
¯
C
^
=
1000
in
.
4
,
I
x
=
7000
in
.
4
,
and
I
y
=
4000
in
.
4
.
Calculate
A
,
I
¯
x
,
and
I
¯
y
for the region.
An AISI 1018 steel ball with 1.100-in diameter is used as a roller between a flat plate
made from 2024 T3 aluminum and a flat table surface made from ASTM No. 30 gray
cast iron. Determine the maximum amount of weight that can be stacked on the
aluminum plate without exceeding a maximum shear stress of 19.00 kpsi in any of the
three pieces. Assume the figure given below, which is based on a typical Poisson's
ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress
occurs for these materials.
1.0
0.8
Ratio of stress to Pmax
0.4
90
0.6
στ
Tmax
0.2
0.5a
a
1.5a
2a
2.5a
За
Distance from contact surface
The maximum amount of weight that can be stacked on the aluminum plate is
lbf.
A carbon steel ball with 27.00-mm diameter is pressed together with an aluminum ball
with a 36.00-mm diameter by a force of 11.00 N. Determine the maximum shear
stress and the depth at which it will occur for the aluminum ball. Assume the figure
given below, which is based on a typical Poisson's ratio of 0.3, is applicable to estimate
the depth at which the maximum shear stress occurs for these materials.
1.0
0.8
Ratio of stress to Pma
9 0.6
στ
24
0.4
Tmax
0.2
0
0.5a
a
1.5a
Z
2a
2.5a
За
Distance from contact surface
The maximum shear stress is determined to be
MPa.
The depth in the aluminum ball at which the maximum shear stress will occur is
determined to be [
mm.
Chapter 9 Solutions
International Edition---engineering Mechanics: Statics 4th Edition
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