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

mecmovies
ExAmpLES
m10.8 Determine the maximum deflection of the cantilever
beam. Assume that EI is constant for the beam.
m10.9 Determine the deflection at point C on the beam
shown. Assume that EI is constant for the beam.
ExAmpLE 10.10
The simply supported beam shown consists of a W16 × 40
structural steel wide-flange shape [E = 29,000 ksi; I =
518 in. 4 ]. For the loading shown, determine the beam deflection
at point C.
v
20 kips 30 kips
Plan the Solution
One of the standard configurations found in the beam tables is A
B
a simply supported beam with a concentrated load acting at a
location other than the middle of the span. The elastic curve
equation from this standard beam configuration will be used to
compute the deflection for the beam considered here, which has two concentrated loads.
However, the elastic curve equation must be applied differently for each load because it
is applicable only for a portion of the total span.
SolutioN
The solution of this beam deflection problem will be subdivided into two cases. In case
1, the 30 kip load acting on the simply supported beam will be considered. Case 2 will
consider the 20 kip load. The elastic curve equation for a simply supported beam with
a single concentrated load acting at a location other than the middle of the span is given
in the beam table as
C
4 ft 6 ft 3 ft 7 ft
D
E
x
Pbx
v =− ( − − ≤ ≤
6LEI L b x ) for 0 x a
2 2 2
(a)
For this beam, the elastic modulus is E = 29,000 ksi and the moment of inertia is
I = 518 in. 4 . The term EI, which appears in all calculations, has the value
4 6 2
EI = (29,000 ksi)(518 in. ) = 15.022 × 10 kip⋅in.
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