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

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AxIAL dEFORMATION
An equilibrium equation and the corresponding deformation equation must be compatible;
that is, when a tensile force is assumed for a member in a free-body diagram, a
tensile deformation must be indicated for the same member in the deformation diagram. In
the configurations shown here, internal tensile forces have been assumed for all the axial
members. For the structure shown in Figure 5.11d, the displacement of the rigid bar at C
(Figure 5.11e) causes a contraction in member (2). As shown in Equations (5.8), this condition
produces a negative sign for δ 2 , and as a result, the geometry-of-deformation equation
in Equation (5.9) is slightly different from the geometry-of-deformation equation found for
the structure with two tension members [Equation (5.7)].
Rigid-bar structures with opposing axial members are analyzed in MecMovies
Examples M5.8 and M5.9.
mecmovies
ExAmpLES
m5.8 A pin-connected structure is loaded and supported
as shown. Member ABCD is a rigid bar that is horizontal
before the load P is applied. Members (1) and (2) are aluminum
[E = 70 GPa], with cross-sectional areas A 1 = A 2 =
160 mm 2 . Member (1) is 900 mm in length, and member (2)
is 1,250 mm. A load P = 35 kN is applied to the structure
at D.
(a) Calculate the axial forces in members (1) and (2).
(b) Compute the normal stress in members (1) and (2).
(c) Compute the downward deflection of the rigid bar
at D.
m5.10 An aluminum bar (2) is to be connected to a brass post (1).
When the two axial members were installed, however, it was
discovered that there was a 1/16 in. gap between flange B and the
post. The brass post (1) has a cross-sectional area A 1 = 0.60 in. 2 and
an elastic modulus E 1 = 16,000 ksi. The aluminum bar (2) has properties
of A 2 = 0.20 in. 2 and E 2 = 10,000 ksi.
If bolts are inserted through the flange at B and tightened until
the gap is closed, how much stress will be induced in each of the
axial members?
m5.9 Rigid bar ABCD is pinned at C and supported by
bars (1) and (2) at A and D, respectively. Bar (1) is aluminum
and bar (2) is bronze. A concentrated load P = 80 kN
is applied to the rigid bar at B. Compute the normal stress
in each bar and the downward deflection at A of the rigid
bar.