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

at B. The right-hand side represents the internal work performed by the virtual internal
forces f as the members they act on move through the real internal deformations that occur
in them in response to the real external loads P 1 and P 2 .
From the tabulated results,
2
(282.408 kN ⋅m)(1,000 N/kN)(1, 000 mm/m)
(1 kN) ⋅D B =
2 2
(525 mm )(70,000 N/mm )
D = 7.68 mm
B
Ans.
Since the virtual load was applied in a downward direction at B, the positive value of
the result confirms that joint B does become displaced downward.
ExAmpLE 17.11
For the truss shown, members BF, CF, CG, and DG each
have cross-sectional areas of 750 mm 2 . All other members
have cross-sectional areas of 1,050 mm 2 . The elastic
modulus of all members is 70 GPa. Compute
(a) the horizontal deflection at joint G.
(b) the vertical deflection at joint G.
Plan the Solution
Calculate the length of each truss member. Determine the
real internal forces F j in all of the truss members, using
an appropriate method, such as the method of joints or
the method of sections. To compute the horizontal deflection
at G, remove all loads from the truss, apply a unit load horizontally at joint G, and
perform a second truss analysis to determine the member forces f j created by the horizontal
unit load. Construct a table of results from the two truss analyses, and then apply
Equation (17.30) to determine the horizontal deflection D of joint G. To compute the
vertical deflection at G, remove all loads from the truss, apply a unit load vertically at
joint G, and perform a third truss analysis to determine the member forces f j created by
the vertical unit load. Construct a table of results from the two truss analyses, and then
apply Equation (17.30) to calculate the vertical deflection D of joint G.
SolutioN
4.0 m
(a) Horizontal Deflection of Joint G: Compute the member lengths and record them in
a column. Note the member cross-sectional areas and record them in a second column.
With the real external loads acting on the truss, perform a truss analysis to determine
the real internal forces in each of the truss members. Record these real internal forces
in a third column.
Remove the real loads from the truss. Since the horizontal deflection of the truss at
joint G is to be determined, apply a horizontal virtual load of 1 kN at that joint. For this
analysis, the virtual load will be directed to the right. Perform a second analysis of the
truss in which the only load acting on the truss is the horizontal virtual load. This second
analysis yields the virtual member forces f. Record these forces in a column.
A
F
B
C
G
D
75 kN 50 kN
3.0 m 3.0 m 3.0 m 3.0 m
E
25 kN
759