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

and the deformation of member (2) is
FL 2 2
( −12,776.3 N)(400 mm)
δ2
= + α 2 D TL 2 =
2 2
AE
(620 mm )(70,000 N/mm )
2 2
−6
+ (22.5 × 10 /C)(20 ° ° C)(400 mm)
=− 0.1178 mm + 0.1800 mm = 0.0622 mm
Contrary to our initial assumption in the deformation diagram, member (1) actually contracts
and member (2) elongates. This outcome is explained by the elongation caused by the
temperature increase. The rigid plate actually rotates counterclockwise about C.
mecmovies
ExAmpLE
m5.15 A brass link and a steel
rod have the dimensions shown at
a temperature of 20°C. The steel
rod is cooled until it fits freely into
the link. The temperature of the
entire link-and-rod assembly is
then warmed to 40°C. Determine
(a) the final normal stress in the
steel rod.
(b) the deformation of the steel
rod.
ExERcISES
m5.13 A composite axial structure consists of two rods joined at
flange B. Rods (1) and (2) are attached to rigid supports at A and C,
respectively. A concentrated load P is applied to flange B in the direction
shown. Determine the internal forces and normal stresses in
each rod after the temperature changes by the indicated DT. Also,
determine the deflection of flange B in the x direction.
(a) the internal force in rod (1).
(b) the normal stress in rod (2).
(c) the normal strain in rod (1).
(d) the downward deflection of the rigid bar at B.
FIGURE m5.13
m5.14 A rigid horizontal bar ABC is supported by three vertical
rods as shown. The system is stress free before the load is applied.
After the load P is applied, the temperature of all three rods is
raised by the indicated DT. Determine
126
FIGURE m5.14