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

calculation. Before proceeding, it may be helpful to consider various calculation skills that
are often used in typical beam and loading configurations.
Skill 1—Using the slope to calculate the deflection: The beam slope at location A
may be needed in order to calculate the beam deflection at location B.
Skill 2—Using both the deflection and slope values to calculate deflections:
Both the beam slope and the beam deflection at location A may be needed to
calculate the beam deflection at location B.
Skill 3—Using the elastic curve: Equations are given in beam tables for the beam
slope and deflection at key locations, such as the free end of a cantilever beam and
the midspan of a simply supported beam. There are many instances, however, when deflections
must be computed at other locations. In these instances, deflections can be calculated
from the elastic curve equation.
Skill 4—Using both cantilever and simply supported beam equations: For a
simply supported beam with an overhang, both cantilever and simply supported beam
equations are required to compute the deflection at the free end of the overhang.
Skill 5—Subtracting the load: For a beam with distributed loads on only a portion of
a span, it may be expedient to consider first the distributed load over the entire span.
Then, the load can be cancelled out on a portion of the span by adding the inverse of the
load (i.e., a load equal in magnitude, but opposite in direction). This skill may also be
useful for cases involving linearly distributed loadings (i.e., triangular loads).
Skill 6—Using known deflections at specific locations to compute unknown
forces or moments: This skill is particularly useful in analyzing statically indeterminate
beams.
Skill 7—Using known slopes at specific locations to compute unknown forces
or moments: This skill is also useful in analyzing statically indeterminate beams.
Skill 8—A beam and loading configuration may often be subdivided in more
than one manner: A given beam and loading may be subdivided and added in any
manner that yields the same boundary conditions (i.e., deflection and/or slope at the supports)
as those in the original beam configuration. Alternative approaches may require
fewer calculations to produce the same results.
The skills in the preceding list are presented with examples and interactive problems
in MecMovies M10.3 and M10.4 (8 Skills: Parts I and II) and in MecMovies
M10.5 (Superposition Warm-Up).
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dETERMININg dEFLECTIONS
by THE METHOd OF
SuPERPOSITION
MecMovies
ExAMPLES
M10.3 and 10.4 8 Skills: Parts I and II