Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

tube has an outside diameter of 1.50 in., a wall thickness of 0.1875 in.,
and a length L = 9.0 in. Rigid washers, each with a thickness t =
0.125 in., cap the ends of the copper tube. The bolt has 20 threads
per inch. That is, each time the nut is turned one complete revolution,
the nut advances 0.05 in. (i.e., 1/20 in.). The nut is hand tightened
on the bolt until the bolt, nut, washers, and tube are just snug,
meaning that all slack has been removed from the assembly but no
stress has yet been induced. What stresses are produced in the bolt
and in the tube if the nut is tightened an additional quarter turn past
the snug-tight condition?
Rigid washer
t
FIGURE p5.38
Tube (2)
Bolt (1)
L
Rigid washer
t
5.6 Thermal Effects on Axial Deformation
As discussed in Section 2.4, a temperature change DT creates normal strains
εT
= αD T
(5.10)
in a solid material. Over the length L of an axial member, the deformation resulting from
a temperature change is
δT = εTL = αD TL
(5.11)
If an axial member is allowed to elongate or contract freely, temperature change creates no
stress in a material. However, substantial stresses can result in an axial member if elongation
or contraction is inhibited.
Force–Temperature–Deformation Relationship
The relationship between internal force and axial deformation developed in Equation (5.2)
can be enhanced to include the effects of temperature change:
FL
δ = + αD TL
(5.12)
AE
The deformation of a statically determinate axial member can be computed from Equation
(5.12) since the member is free to elongate or contract in response to a change in temperature.
In a statically indeterminate axial structure, however, the deformation due to
temperature changes may be constrained by supports or other components in the structure.
Restrictions of this sort inhibit the elongation or contraction of a member, causing normal
stresses to develop. These stresses are often referred to as thermal stresses, even though
temperature change by itself causes no stress.
mecmovies
ExAmpLES
m5.11 A 20 mm diameter steel [E = 200 GPa; α = 12.0 ×
10 −6 /°C] rod is held snugly between rigid walls, as shown. Calculate
the temperature drop DT at which the shear stress in the 15 mm
diameter bolt becomes 70 MPa.
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