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

How are the rigid-bar deflections v A and v B that are shown on the sketch related to the
member deformations δ 1 and δ 2 ? By definition, deformation is the difference between the
initial and final lengths of an axial member. Using the sketch of the deflected rigid bar, we
can define the deformation in member (1) in terms of its initial and final lengths:
δ
= L − L = ( L + v ) − L = v ∴ v = δ = 9.00 mm
1 final initial 1 A 1 A A 1
Similarly, for member (2),
δ
= L − L = ( L − v ) − L = −v ∴ v =− δ =−− ( 7.00 mm) = 7.00 mm
2 final initial 2 B 2 B B 2
With these results, the magnitude of the rigid-bar deflection at C can now be computed:
v = 0.75( v + v ) + v = 0.75(9.00 mm + 7.00 mm) + 7.00 mm = 19.00 mm
C A B B
The direction of the deflection is shown on the deformation diagram; that is, joint C
deflects 19.00 mm downward.
Deflection of D
The downward deflection of joint D is the sum of the rigid-bar deflection at C and the
elongation in member (3):
vD = vC + δ 3 = 19.00 mm + 10.00 mm = 29.0 mm
Ans.
mecmovies
ExAmpLE
m5.4 An assembly consists of three rods attached to rigid
bar AB. Rod (1) is steel, and rods (2) and (3) are aluminum.
The area and elastic modulus of each rod is noted on the
sketch. A force of 80 kN is applied at D. Determine the vertical
deflections of points A, B, C, and D.
The preceding examples considered structures consisting of parallel axial bars,
making the geometry of deformation for the structure relatively straightforward to analyze.
Suppose, however, that one is interested in a structure in which the axial members are not
parallel. The structure shown in Figure 5.9 consists of three axial members (AB, BC, and
BD) connected to a common joint at B. In the figure, the solid lines represent the unstrained
(i.e., unloaded) configuration of the system and the dashed lines represent the
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