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

m5.12 A rigid bar ABC is pinned at A and supported by a
steel wire at B. Before weight W is attached to the rigid bar
at C, the rigid bar is horizontal. After weight W is attached
and the temperature of the assembly has been increased by
50°C, careful measurements reveal that the rigid bar has
deflected downward 2.52 mm at point C. Determine
(a) the normal strain in wire (1).
(b) the normal stress in wire (1).
(c) the magnitude of weight W.
Incorporating Temperature Effects in Statically
Indeterminate Structures
In Section 5.5, a five-step procedure for analyzing statically indeterminate axial structures
was outlined. Temperature effects can be easily incorporated into this procedure by using
Equation (5.12) to define the force–temperature–deformation relationships for the axial
members, instead of Equation (5.2). With the five-step procedure, analyzing indeterminate
structures involving temperature change is no more difficult conceptually than analyzing
those same structures without thermal effects. The addition of the αDTL term in Equation
(5.12) does increase the computational difficulty, but the overall procedure is the same. In
fact, it is the more challenging problems, such as those involving temperature change, in
which the advantages and potential of the five-step procedure are most evident.
It is essential that Equation (5.12) be consistent, meaning that a positive internal force
F (i.e., a tensile force) and a positive DT should produce a positive member deformation
(i.e., an elongation). The need for consistency explains the emphasis on assuming an internal
tensile force in all axial members, even if, intuitively, one might anticipate that an axial
member should act in compression.
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ExAmpLE
m5.13 An aluminum bar (1) is attached to a steel post (2) at rigid
flange B. Bar (1) and post (2) are initially stress free when they are
connected to the flange at a temperature of 20°C. The aluminum bar
(1) has a cross-sectional area A 1 = 200 mm 2 , a modulus of elasticity
E 1 = 70 GPa, and a coefficient of thermal expansion α 1 = 23.6 ×
10 −6 /°C. The steel post (2) has properties A 2 = 450 mm 2 , E 2 = 200 GPa,
and α 2 = 12.0 × 10 −6 /°C. Determine the normal stresses in members
(1) and (2) and the deflection at flange B after the temperature
increases to 75°C.
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