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Unformatted text preview: 09Ch09.qxd 9/27/08 1:37 PM Page 793 793 SECTION 9.11 Temperature Effects MAXIMUM DEFLECTION
Set n (x) 0 and solve for x a T0 2
2h 0 a dmax L2
13 a T0 c a dmax
(b) (T2 9 13 h
a T0 L3 T1) v¿ L3
6h L2 L
13 Downward ; v ¿ (x) a T0 x 3
4 a T0 3
3h Set n (x)
0 a T0 3
12 a T0 c a dmax C1 x L4
12 h a T0 L4
48 h L3 1) n(0) 0 C2 B.C. n(L) 0 C1 L
Downward a T0 x 4
+ C 1 x + C2
12 0 and solve for x dmax a T0 x 2
h dx 2 L3 x)
a T0 (x 4
12 h MAXIMUM DEFLECTION T0 x2 d2
– x (x) 0
a T0 L3
12 h Problem 9.11-5 Beam AB, with elastic support kR at A and pin support at B, of length
L and height h (see figure) is heated in such a manner that the temperature difference
T2 T1 between the bottom and top of the beam is proportional to the distance from
support A; that is, assume the temperature difference varies linearly along the beam:
T2 T1 T0x
in which T0 is a constant having units of temperature (degrees) per unit distance.
Assume the spring at A is unaffected by the temperature change.
(a) Determine the maximum deflection dmax of the beam.
(b) Repeat for quadratic temperature variation along the beam, T2
(c) What is dmax for (a) and (b) above if kR goes to infinity? T1 T0 x2. y
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11