sm11 11

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PROBLEM (11.11) Two equal round bars are supported in line with one another and are
separated by a small gap (Fig. P11.11). Determine the temperature rise necessary to cause them
to:
(a) Just touch.
(b) Buckle elastically.
Given: a = 12 x 10-6 /°C, L = 1 m, d = 25 mm, δ = 1.2 mm
SOLUTION
(a) () ,
22
LT T L
δ
δ
α
α
Δ= Δ=
Substituting the given data:
3
6
1.2 10 50
2(12 10 )1 o
TC
−
−
×
Δ= =
×
(b) 262
(0.025) 490.9 10
4
Am
π
−
==× 494 (0.025) 19.17 10
64
π
I
m
−
==×
We have
() 2
PL
LT AE
δ
α
Δ
−=
Thus,
2
2
24
I
TLAL
δπ
α
α
Δ= +
or
29
66
2
(19.17 10 )
50 4(490.9 10 )(12 10 )(1) T
π
−
−−
×
+×× 50 8 58oC=+=
Δ=
Justification of the formula used:
46.25rIAd m=== m 1000 6.25 160Lr
=
= O.K.
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