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1286 Solutions Manual
Using these results, the shear diagram may be drawn as follows.
We determine xusing similar triangles:
To construct the moment diagram, we use the shear diagram with the expression
xQ
Z
xP
„ƒ‚ …
area under V
vs. xplot
between xP
and xQ
Hence
MCD0; (15)
Statics 2e 1287
Using these results, the moment diagram may be drawn as follows.
To determine
MDM.x Dx/
, we take a cut at
x
and draw the FBD of the
bookshelf to the left of the cut.
Problem 8.77
Three beams are shown, along with four possible shear diagrams and four possible moment diagrams.
All forces and moments act in the directions shown. Without calculation, complete the table provided by
selecting the appropriate shear and moment diagrams that correspond to each beam. Your answers may
use a shear and/or moment diagram more than once. As an example, the answers for Beam 1 are provided
in the table.
Problem 8.78
Three beams are shown, along with four possible shear diagrams and four possible moment diagrams. The
distributed force acts in the direction shown. Without calculation, complete the table provided by selecting
the appropriate shear and moment diagrams that correspond to each beam. Your answers may use a shear
and/or moment diagram more than once.
Problem 8.79
A beam is supported by a roller at
A
and a device at
C
that allows vertical motion
of the beam while preventing horizontal motion and rotation. Use the equilibrium
approach to determine the shear and moment as functions of position, and draw the
shear and moment diagrams.
Problem 8.80
Members
ABC
and
CDE
are pinned to one another at
C
and have pin supports
at
A
and
E
. Determine the internal forces acting on: Cross sections
F
and
G
,
which are located immediately to the right of Aand the left of B, respectively.
Problem 8.81
Members
ABC
and
CDE
are pinned to one another at
C
and have pin supports
at
A
and
E
. Determine the internal forces acting on: Cross sections
H
and
I
,
which are located immediately to the right of
B
and the left of
C
, respectively.
(10)
Problem 8.82
To provide generous leg room, a quarter-circular member
AB
is used to support
a wall-mounted desk
CD
. Neglecting the weight of the members, determine
the internal forces acting on cross sections
E
,
F
, and
G
, which are located
immediately above point
A
, at the midpoint of member
AB
, and immediately
to the right of point B, respectively.
(14)
Summary:
NFD 1179 N; VFD0; MFD 69:04 Nm:(15)
We take a cut through cross section
G
and draw the FBD of member
AB
Problem 8.83
A historically important shipwreck is to be recovered, and a number of fragile wooden
beams must be lifted. Specify the dimension
d
(in terms of length
L
) where the two
lifting slings should be placed so that the maximum absolute value of the moment is as
small as possible. Assume the beams are straight with uniform weight distribution, and
the cables attached to the slings are vertical. Hint: The optimal value of
d
will give the
same absolute value of the moment at the slings as at the midpoint of the beam.
)d
LD
2.1/ (9)
D1
2:(10)
So, using
dDL=2
(both slings placed at the midpoint of the beam) will give
M1DM2
by virtue of these
moments being at the same location. While this is a correct solution in terms of satisfying the laws of physics,
Problem 8.84
Use the equilibrium approach to determine the shear and moment as functions of
position, and draw the shear and moment diagrams.
1300 Solutions Manual
We take a cut at an arbitrary position between points
B
and
C
and draw the FBD to the right of the cut to
determine the shear and moment as functions of position for 4mx8m.
Summary:
Problem 8.85
Use the equilibrium approach to determine the shear and moment as functions of
position, and draw the shear and moment diagrams.
6.L x/ D0; (15)
)MDw0L
6.L x/: (16)
Problem 8.86
Repeat Prob. 8.84 using the integration approach.
Problem 8.87
Repeat Prob. 8.85 using the integration approach.
