Chapter 03.03
Bisection Method of Solving a Nonlinear Equation-
More Examples
Mechanical Engineering
Example 1
A trunnion has to be cooled before it is shrink fitted into a steel hub.
Figure 1
Trunnion to be slid through the hub after contracting.
The equation that gives the temperature
to which the trunnion has to be cooled to obtain
the desired contraction is given by
f
T
0
10
88318
.
0
10
74363
.
0
10
38292
.
0
10
50598
.
0
)
(
2
4
2
7
3
10
T
T
T
T
f
f
f
f
f
f
T
Use the bisection method of finding roots of equations to find the temperature
to which
the trunnion has to be cooled. Conduct three iterations to estimate the root of the above
equation. Find the absolute relative approximate error at the end of each iteration and the
number of significant digits at least correct at the end of each iteration.
Solution
From the designer’s records for the previous bridge, the temperature to which the trunnion
was cooled was
. Hence assuming the temperature to be between
and
F
108
F
100
F
150
, we have
F
150
,
f
T
,
F
100
,
u
f
T
Check if the function changes sign between
and
.
,
f
T
u
f
T
,
03.03.1

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